Reactions in the Solid State, Volume 22 (Comprehensive Chemical Kinetics)

COMPREHENSIVE CHEMICAL KINETICS

COMPREHENSIVE Section 1. THE PRACTICE AND THEORY OF KINETICS

Volume 1 Volume 2 Volume 3

The Practice of Kinetics The Theory of Kinetics The Formation and Decay of Excited Species Section 2. HOMOGENEOUS DECOMPOSITION AND ISOMERISATION REACTIONS

Volume 4 Volume 5

Decomposition of Inorganic and Organometallic Compounds Decomposition and Isomerisation of Organic Compounds Section 3. INORGANIC REACTIONS

Volume 6 Volume 7

Reactions of Non-metallic Inorganic Compounds Reactions of Metallic Salts and Complexes, and Organometallic Compounds Section 4. ORGANIC REACTIONS (6 volumes)

Volume 8 Volume 9 Volume 10 Volume 12 Volume 13

Proton Transfer Addition and Elimination Reactions of Aliphatic Compounds Ester Formation and Hydrolysis and Related Reactions Electrophilic Substitution at a Saturated Carbon Atom Reactions of Aromatic Compounds Section 5. POLYMERISATION REACTIONS (3 volumes)

Volume 14 Volume 14A Volume 15

Degradation of Polymers Free-radical Polymerisation Non-radical Polymerisation Section 6. OXIDATION AND COMBUSTION REACTIONS (2 volumes)

Volume 16 Volume 17

Liquid-phase Oxidation Gas-phase Combustion Section 7. SELECTED ELEMENTARY REACTIONS (1 volume)

Volume 18

Selected Elementary Reactions Section 8. HETEROGENEOUS REACTIONS (4 volumes)

Volume 19 Volume 20 Volume 21 Volume 22

Simple Processes at the Gas-Solid Interface Complex Catalytic Processes Reactions of Solids with Gases Reactions in the Solid State Additional Section KINETICS AND TECHNOLOGICAL PROCESSES

CHEMICAL KINETICS EDITED BY

C.H. BAMFORD M.A.,Ph.D., Sc.D. (Cantab.), F.R.I.C., F.R.S. Campbell-Brown Professor o f Industrial Chemistry, University o f Liverpool AND

C.F.H. TIPPER Ph.D.(Bristol), D S c . (Edinburgh) Senior Lecturer in Physical Chemistry, University of Liverpool

VOLUME 22

REACTIONS IN THE SOLID STATE

ELSEVIER SCIENTIFIC PUBLISHING COMPANY AMSTERDAM - OXFORD - NEW YORK 1980

ELSEVIER SCIENTIFIC PUBLISHING COMPANY

335 Jan van Galenstraat P.O. Box 211,1000 AE Amsterdam, The Netherlands Distributors f o r the United States and Canada ELSEVIER/NORTH-HOLLANDINC.

52, Vanderbilt Avenue New York, N.Y. 10017

Library of Congress Card Number: 68-29646 ISBN 0-444-41631-5 (Series) ISBN 0-444-41807-5 (Vol. 22) with 22 illustrations and 17 tables

@ Elsevier Scientific Publishing Company, 1980 All rights reserved. N o part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior written permission of the publisher, Elsevier Scientific Publishing Company, P.O. Box 330, 1000 AH Amsterdam, The Netherlands Printed in The Netherlands

COMPREHENSIVE CHEMICAL KINETICS

ADVISORY BOARD Professor S.W. BENSON Professor SIR FREDERICK DAINTON Professor G. GEE the late Professor P. GOLDFINGER Professor G.S. HAMMOND Professor W. JOST Professor G.B. KISTIAKOWSKY Professor V.N. KONDRATIEV Professor K.J. LAIDLER Professor M. MAGAT Professor SIR HARRY MELVILLE Professor G. NATTA the late Professor R.G.W. NORRISH Professor S. OKAMURA the late Professor SIR ERIC RIDEAL Professor N.N. SEMENOV Professor Z.G. SZABO Professor 0. WICHTERLE

Contributors to Volume 22 All chapters in this volume have been written by W.E. BROWN

Chemistry Department, Rhodes University, Grahamstown 6140, South Africa

D. DOLLIMORE

Department of Chemistry and Applied Chemistry, Salford University, Salford M 5 4WT, England

A.K. GALWEY

Chemistry Department, Queen's University, Belfast BT9 5AG, Northern Ireland

Section 8 deals with reactions which occur at gassolid and solidsolid interfaces, other than the degradation of solid polymers which has already been reviewed in Volume 14A. Reaction at the liquidsolid interface (and corrosion), involving electrochemical processes outside the coverage of this series, are not considered. With respect to chemical processes at gassolid interfaces, it has been necessary to discuss surface structure and adsorption as a lead-in t o the consideration of the kinetics and mechanism of catalytic reactions. The whole of Volume 22 is devoted to the kinetics and mechanisms of the decomposition and interaction of inorganic solids, extended to include metal carboxylates. After an introductory chapter on the characteristic features of reactions in the solid phase, experimental methods of investigation of solid reactions and the measurement of reaction rates are reviewed in Chapter 2 and the theory of solid state kinetics in Chapter 3. The reactions of single substances, loosely grouped on the basis of a common anion since it is this constituent which most frequently undergoes breakdown, are discussed in Chapter 4, the sequence being effectively that of increasing anion complexity. Chapter 5 covers reactions between solids, and includes catalytic processes where one solid component remains unchanged, double compound formation and rate processes involving the interactions of more than three crystalline phases. The final chapter summarises the general conclusions drawn in the text of Chapter 2-5. The editors are very grateful for much invaluable advice from their colleague, Professor D.A. King. C.H. Bamford C.F.H. Tipper

This Page Intentionally Left Blank

Contents

Preface

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vii

Chapter 1 Introduction

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1 Characteristic features of decomposition reactions of solids . . . . . . . . . . 2 The literature of solid phase reactions . . . . . . . . . . . . . . . . . . . . . . . . . 3 . Scope of the present review and arrangement of subject matter . . . . . . . . 4 . Classification of chemical reactions of solids . . . . . . . . . . . . . . . . . . . . 4.1 Decomposition of a single solid . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Reactions of types: solid + gas and solid + liquid . . . . . . . . . . . . . 4.3 Solidsolid reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

3 9 11 12 12 14 15

Chapter 2 Experimental

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1. Accumulatory pressure measurements of evolved gas . . . . . . . . . . . . . . . 2 . Mass loss measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 . Evolved gas analysis (EGA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Mass spectrometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Gas chromatography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Other methods of gas analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Non-isothermal methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Absorption or evolution of heat . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 . Computer coupling and data processing . . . . . . . . . . . . . . . . . . . . . . . 7 . Microscopic techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1 Optical microscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Electron microscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8. Diffraction methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 . Surface area measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 0 Spectroscopic methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.1 Infrared spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2 Mossbauer spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3 X-ray photoelectron spectroscopy (XPS or ESCA) . . . . . . . . . . . . 11 Magnetic measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Magnetic susceptibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Magnetic resonance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2. Electrical measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.1 Electrical conductivity measurements . . . . . . . . . . . . . . . . . . . . . 12.2 Other electrical measurements . . . . . . . . . . . . . . . . . . . . . . . . . . 12.3 Application of electric fields . . . . . . . . . . . . . . . . . . . . . . . . . . . 13. Sample preparation and pretreatment . . . . . . . . . . . . . . . . . . . . . . . . . 13.1 Sample preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.2 Dehydration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.3 Mechanical treatment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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17 19 19 21 21 22 23 23 24 24 24 24 25 27 28 29 29 30 30 31 31 31 32 32 32 33 33 34 34 34

13.4 Irradiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.5 Controlled addition of impurities . . . . . . . . . . . . . . . . . . . . . . . . 14. Influence of atmosphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 . Experimental methods for studying solid- olid interactions . . . . . . . . . .

35 35 36 37

Chapter 3 Theory of solid state reaction kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 1 . Laws of nucleation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 1.1 The nucleus formation process . . . . . . . . . . . . . . . . . . . . . . . . . 42 1.2 Laws of nucleation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 2 Laws of growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 3. Formal theories of isothermal solid state decompositions . . . . . . . . . . . . 49 3.1 Kinetic expressions derived for interface advance reactions . . . . . . . 49 3.1.1 Nucleation obeying a power law with constant rate of interface advance (normal growth) . . . . . . . . . . . . . . . . . . . . . 50 3.1.2 Random nucleation according to the exponential law followed by normal growth . . . . . . . . . . . . . . . . . . . . . . . . 50 3.1.3 Impingement and coalescence of developed nuclei and ingestion of undeveloped nucleation sites . . . . . . . . . . . . . . . . . 51 3.1.4 Rapid and dense nucleation, or initial rapid surface growth, followed by advance of interface from all, or certain specific. surfaces into the bulk of crystallites . . . . . . . . . . . . . . . . . 59 3.1.5 Other models for nucleation and growth of compact nuclei . 62 3.1.6 General comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 3.2 Kinetic expressions derived for “chain-type” reactions . . . . . . . . . . 65 3.3 Kinetic expressions derived for diffusion limited reactions . . . . . . . 68 3.4 Influence of particle size distribution on kinetic characteristics . . . . 72 3.5 Rate equations commonly used in kinetic analyses of isothermal 72 reactions of solids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. Tests of obedience of isothermal kinetic data to theoretical kinetic equa76 tions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 77 4.2 Identification of the rate equation . . . . . . . . . . . . . . . . . . . . . . . 4.3 Application of rate equations to particular regions of the a-time curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 4.3.1 The induction period . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 4.3.2 The acceleratory region . . . . . . . . . . . . . . . . . . . . . . . . . 80 4.3.3 The deceleratory region . . . . . . . . . . . . . . . . . . . . . . . . . 81 81 4.4 Statistical methods in kinetic analysis . . . . . . . . . . . . . . . . . . . . . 84 4.5 Interpretation of kinetic observations . . . . . . . . . . . . . . . . . . . . . 4.5.1 The zero-order reaction . . . . . . . . . . . . . . . . . . . . . . . . . 84 4.5.2 Avrami-Erofe’ev equation (n = 2) . . . . . . . . . . . . . . . . . . 85 5. Variation of reaction rate with temperature . . . . . . . . . . . . . . . . . . . . . 86 5.1 Application of the Arrhenius equation to solid state reactions . . . . . 87 5.2 Significance of the Arrhenius parameters . . . . . . . . . . . . . . . . . . . 88 92 5.3 Rates of interface reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 The compensation effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 6 Kinetic investigations using rising temperature techniques . . . . . . . . . . . 97 6.1 Kinetic analysis of non-isothermal rate measurements . . . . . . . . . . 99 6.2 Integral methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 101 6.2.1 Methods using tabulated values of the exponential integral 6.2.2 Methods using a simple approximation for the exponential integral . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

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Methods using a series expansion as an approximation for the exponential integral . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.4 Methods involving a reference temperature 6.2.5 Methods involving different heating rates . . . . . . . . . . . . . 6.3 Differential methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.1 Methods involving direct use of the basic equation . . . . . . . 6.3.2 Difference-differential methods . . . . . . . . . . . . . . . . . . . 6.3.3 Methods involving a reference temperature . . . . . . . . . . . . 6.3.4 Methods involving different heating rates . . . . . . . . . . . . . 7 . The reaction interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.3

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103 105 105 106 106 107 107 107 109

Chapter 4 Decomposition reactions of solids

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1. Dehydration of crystalline hydrates . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Structures of crystalline hydrates . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Kinetics of nucleation and growth during dehydrations . . . . . . . . . 1.2.1 Nucleation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.2 Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.3 Shapes of nuclei . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.4 Diffusion-controlled dehydrations . . . . . . . . . . . . . . . . . . 1.3 The Polanyi-Wigner equation . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 The S m i t h q o p l e y effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5 Kinetics of dehydration of representative crystalline hydrates . . . . . 1.5.1 Copper sulphate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5.2 Other sulphates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5.3 Other inorganic solids . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5.4 Metal carboxylates . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 . Decomposition reactions of binary compounds (also including hydroxides) 2.1 Hydroxides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.1 Magnesium hydroxide . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.2 Other inorganic hydroxides . . . . . . . . . . . . . . . . . . . . . . 2.1.3 Hydroxyhalides and related salts . . . . . . . . . . . . . . . . . . . 2.1.4 Clay minerals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Oxides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 Extended imperfections in oxides . . . . . . . . . . . . . . . . . . 2.2.2 Mechanisms and products of oxide decomposition . . . . . . . 2.2.3 Dissociation of oxides . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Hydrides, carbides, nitrides and related substances . . . . . . . . . . . . 2.3.1 Decompositions rate-limited by a surface or desorption step: comparable in some respects with heterogeneous catalytic processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.2 Reactions rate-limited by an interface process . . . . . . . . . . 2.3.3 Reactions rate-limited by a diffusion process . . . . . . . . . . . 2.3.4 Transition metal sulphides . . . . . . . . . . . . . . . . . . . . . . . 2.3.5 Related reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Azides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.1 Group I1 azides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.2 Group IA azides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.3 Other azides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Fulminates and cyanamides . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.1 Fulminates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.2 Cyanamides

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115

117 118 120 120 121 123 123 123 125 130 130 131 133 134 135 136 136 137 138 140 142 144 145 146 146 151 152 155 156 156 158 158 158 161 163 165 166 166

3 . Decomposition of metal salts of oxyacids . . . . . . . . . . . . . . . . . . . . . . 3.1 Metal carbonates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1 Calcium carbonate . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.2 Other Group IIA carbonates . . . . . . . . . . . . . . . . . . . . . . 3.1.3 Silver carbonate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.4 Lead carbonate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.5 Manganese(I1) carbonate . . . . . . . . . . . . . . . . . . . . . . . . 3.1.6 Carbonate decompositions . . . . . . . . . . . . . . . . . . . . . . . 3.2 Metal sulphates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Group IIA sulphates . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.2 Group IIIA sulphates . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.3 First period transition metal sulphates . . . . . . . . . . . . . . . 3.2.4 Other metal sulphates . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.5 Metal salts of other sulphuroxyacids . . . . . . . . . . . . . . . . 3.3 Metal nitrates and nitrites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Metal phosphates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.1 Group IA phosphates . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.2 Group IIA phosphates . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.3 Other metal phosphates . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Metal perhalates, halates and halites . . . . . . . . . . . . . . . . . . . . . . 3.5.1 Perhalates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5.2 Halates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5.3 Metal halites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5.4 General comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6 Metal permanganates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6.1 Potassium permanganate . . . . . . . . . . . . . . . . . . . . . . . . 3.6.2 Other Group IA metal permanganates . . . . . . . . . . . . . . . . 3.6.3 Barium permanganate . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6.4 Silver permanganate . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7 Metal chromates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 . Decompositions of ammonium salts . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Ammonium salts containing oxyanions of the non-metals . . . . . . . . 4.1.1 Ammonium perchlorate . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.2 Ammonium halates . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.3 Ammonium sulphate . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.4 Ammonium nitrate . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.5 Ammonium phosphates . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.6 Ammonium carbonate . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.7 Ammonium carboxylates . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Ammonium salts containing oxyanions of the metals . . . . . . . . . . . 4.2.1 Ammonium permanganate . . . . . . . . . . . . . . . . . . . . . . . 4.2.2 Ammonium perrhenates . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.3 Ammonium chromates . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.4 Ammonium molybdates and tungstates . . . . . . . . . . . . . . . 4.2.5 Ammonium vanadates . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.6 Ammonium uranates . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Other ammonium compounds . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.1 Ammonium azide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.2 Ammonium complex salts . . . . . . . . . . . . . . . . . . . . . . . 4.3.3 Ammonium zeolites . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.4 Ammonium thiocarbamate . . . . . . . . . . . . . . . . . . . . . . . 5 . Decompositions of metal carboxylates . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Metal alkanoates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.1 Metal formates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

166 167 169 171 172 173 173 174 174 175 178 178 180 180 182 184 184 185 185 185 186 188 190 190 191 191 193 193 194 194 195 196 196 199 200 201 201 202 203 203 203 204 205 206 206 207 207 207 208 208 208 208 210 210

5.1.2 Metal acetates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.3 Other metal alkanoates . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Metal alkandioates and realted compounds . . . . . . . . . . . . . . . . . 5.2.1 Metal oxalates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.2 Metal malonates and succinates . . . . . . . . . . . . . . . . . . . . 5.2.3 Metal tartrates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.4 Metal citrates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.5 Metal maleates and fumarates . . . . . . . . . . . . . . . . . . . . . 5.3 Metal salts of aromatic carboxylic acids . . . . . . . . . . . . . . . . . . . 5.4 General discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 . Decompositions of coordination compounds . . . . . . . . . . . . . . . . . . . . 6.1 Metal ammine compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1.1 Cobalt(II1) ammine azides . . . . . . . . . . . . . . . . . . . . . . . 6.1.2 Ammine cobalt thiocyanates . . . . . . . . . . . . . . . . . . . . . . 6.1.3 Ammine aquo cobalt salts . . . . . . . . . . . . . . . . . . . . . . . 6.1.4 Ammine nickel salts . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Metal pyridine compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3 Compounds containing polydentate ligands . . . . . . . . . . . . . . . . . 6.4 Other kinetic studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5 General comment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Decompositions of solid solutions and double salts . . . . . . . . . . . . . . . . 7.1 Decompositions of twocomponent solid solutions . . . . . . . . . . . . 7.1.1 Dolomite, (Ca,Mg)COs . . . . . . . . . . . . . . . . . . . . . . . . . 7.1.2 Mixed hydroxides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1.3 Mixed carboxylates . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1.4 Other solid solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Doping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

.

216 217 218 218 224 225 226 226 227 228 231 232 233 234 234 235 235 236 238 239 239 241 241 242 243 245 245 246

Chapter 5 Reactions between inorganic solids

..............................

1. Reactant mixtures and experimental methods . . . . . . . . . . . . . . . . . . . 2 . Mechanisms of reaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Surface o r gas-phase diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.1 Area of interparticulate contact between reactants . . . . . . . 2.1.2 Initial formation (nucleation) and growth of the product phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.3 Melting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.4 Reactant mobility and particle coarsening . . . . . . . . . . . . . 2.2 Interface reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Diffusion across a barrier layer . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Classification of solidsolid interactions . . . . . . . . . . . . . . . . . . . 3. Decomposition of a solid catalyzed by a solid . . . . . . . . . . . . . . . . . . . 3.1 Decomposition reactions catalyzed by the solid product . . . . . . . . 3.2 DecomDosition reactions catalvzed by a solid additive . . . . . . . . . . 3.2.1 Decomposition of NH4C104 . . . . . . . . . . . . . . . . . . . . . . 3.2.2 Decomposition of other salts of oxyhalogen acids . . . . . . . . 3.2.3 Decomposition of silver oxalate . . . . . . . . . . . . . . . . . . . . 3.2.4 Decomposition of silver carbonate . . . . . . . . . . . . . . . . . . 3.2.5 Decomposition of silver and other azides . . . . . . . . . . . . . . 4 Reactions between solids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Reactions of the type A(s) -+ AB(s) . . . . . . . . . . . . . . . . . . . . . . 4.1.1 Zinc ferrite formation . . . . . . . . . . . . . . . . . . . . . . . . . .

.

247 249 252 253 253 254 255 256 256 257 259 260 261 262 263 265 265 266 266 267 267 267

4.2

4.3 4.4

4.1.2 Other spinel formation reactions . . . . . . . . . . . . . . . . . . . 4.1.3 Calcium silicate formation and related reactions . . . . . . . . . 4.1.4 Tungstate and molybdate formation reactions . . . . . . . . . . 4.1.5 Double iodide formation . . . . . . . . . . . . . . . . . . . . . . . . 4.1.6 Other reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Reactions of the type A(s) + B(s) C(s) + D(g) . . . . . . . . . . . . . . 4.2.1 Reaction of lithium carbonate with ferric oxide . . . . . . . . . 4.2.2 Reactions of barium carbonate with various oxides . . . . . . . 4.2.3 Molybdate and tungstate formation reactions . . . . . . . . . . . 4.2.4 Oxidation of carbon . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.5 Other reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Reactions of the type AB(s) + CD(s) AD(s) + CB(s) . . . . . . . . . . More complicated reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . --f

--f

Chapter 6 Conclusions

.............................................. 1. Decompositions of solids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

.

.................................... Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Interactions of solids

Index

..................................................

268 270 270 271 272 272 273 273 275 277 278 279 282

283 283 286 288 289 323

1

Chapter 1

Introduction

Application of the term decomposition to a chemical process is, in general, intended to signify the breakdown of one or more constituents of the reactant into simpler atomic groupings. Thermal decomposition is intended t o imply that such reorganization is brought about by a temperature increase. (Th'e word pyrolysis has the same meaning.) In this review, we are concerned with the thermal decomposition of solids. This term may be regarded as encompassing all processes which involve the destruction of the stabilizing forces of the crystal lattice of a reactant solid, including both chemical reactions and physical reorganizations (e.g. melting, sublimation and recrystallization). In general usage, a more restricted meaning of the definition has become acceptable and is specifically applied to those processes in which bond redistribution yields a solid residue of different chemical identity from that of the reactant. The thermal decomposition of a solid is, therefore, represented by where A is the reactant, B and C are the product or products and (s) and (9) specify the solid and gaseous phases, respectively. Interactions between solids may, in general, be represented by A(s) + D(s) + Products where the products may be solid, liquid and/or gaseous. The thermal decomposition of a solid, which necessarily (on the above definition) incorporates a chemical step, is sometimes associated with the physical transformations to which passing reference was made above: melting, sublimation, and recrystallization. Aspects of the relationships between physical transitions and decomposition reacti,ons of solids are discussed in a book by Budnikov and Ginstling [ 11. Since, in general, phase changes exert significant influence upon concurrent or subsequent chemical processes, it is appropriate t o preface the main survey of the latter phenomena with a brief account of those features of melting, sublimation, and recrystallization which are relevant t o the consideration of thermal decomposition reactions. Melting. Loss of crystallinity of a solid reactant through melting, or eutectic formation, or dissolution in a product often results in an enhanced rate of decomposition as a consequence of the relaxation of the bonding forces responsible for lattice stabilization. The appearance of a

2

liquid phase during the decomposition of solid reactants (e.g. metal nitrates or oxychlorides and organic substances) is often accompanied by an increased rate of product evolution. The presentation and discussion of observations for thermal decomposition reactions of solids should normally include due consideration of the possible occurrence of melting and the role of any liquid phase formed. There is no generally acceptable comprehensive theory of melting. A feature of the fusion process, which is usually regarded as important in theoretical treatments of the subject, is the inability of a solid to superheat, and only a very small number of exceptions to this generalization are known [ 21. This almost universal onset of liquefaction immediately upon reaching the melting point is in sharp contrast with the reverse process since supercooling of the vast majority of liquids can be demonstrated under appropriate conditions. In a review of the subject, Ubbelohde [3] points out that there is only a relatively small amount of data available concerning the properties of solids and also of the (product) liquids in the immediate vicinity of the melting point. In an early theory of melting, Lindemann [4]considered that when the amplitude of the vibrational displacements of the atoms of a particular solid increased with temperature to the point of attainment of a particular fraction (possibly 10%) of the lattice spacing, their mutual influences resulted in a loss of stability. The Lennard-Jones-Devonshire [5] theory considers the energy requirement for interchange of lattice constituents between occupation of site and interstitial positions. Subsequent developments of both these models, and, indeed, the numerous contributions in the field, are discussed in Ubbelohde’s book [ 31. Christian [ 61 treats melting as a nucleation and growth process, and discusses the possibility that the surface may be its own nucleating agent and lattice defects or impurities retained in such regions may similarly facilitate the formation of the melt. The melting process is, therefore, always effectively a two-phase phenomenon and any theoretical explanation must be based on consideration of the interactions between phases which differ in the degree of ordering. Kuhlmann-Wilsdorf [ 71 provided a new theoretical approach in which melting was ascribed to the unrestricted proliferation of dislocations at the temperature for which the free energy of formation of glide dislocation cores becomes negative. Several physicists have shown interest in this model which has not so far been accorded similar attention in the chemical literature. The theory of melting continues to be the subject of recent publications, including consideration of vacancy concentrations near the melting point [ 8,9], lattice vibrations and expansions [ 8,lO-121. Meanwhile, the phenomenon also continues t o be the subject of experimental investigations; Coker et al. [ 131, from studies of the fusion of tetra-n-amyl ammonium thiocyanate, identify the greatest structural change as that which

3

occurred in the phase transition which preceeded melting. Solid and molten states of the salt are believed to possess similar structures, the significant difference being identified as the ability of the hydrocarbon chain to kink and unkink after fusion. The electrical conductivity of the solid increased as the melting point was approached. Allnatt and Sime [14] similarly found an anomalously large increase in the electrical conductivity of sodium chloride in the vicinity (i.e. within -4 K) of the melting point. Clark e t al. [ 151 considered premelting transitions in the context of a general theory of disorder in plastic crystals. As with other properties of solids, the increased relative significance of surface energy in very small (i.e. micrometre-sized) crystals influenced the melting points [ 2,16,17] and diffusion at this temperature. Quantitative studies of rates of melting of solids are impracticable since superheating is effectively forbidden and the rate of the endothermic phase change is determined by the rate of heat supply and the thermal conductivity of the solid. Sublimation. During sublimation, the lattice constituents of the solid are directly transferred t o the gas phase without the intervention of liquefaction, though there may be mobile intermediates a t the surface of the heated solid. Various features of the sublimation process have been reviewed by Somorjai [18] and by Rosenblatt [19] who included consideration of kinetic aspects. Rhead [ 201 has discussed diffusion processes at surfaces. Recrystallization. The recrystallization of a solid may result in the production of a higher temperature lattice modification, which permits increased freedom of motion of one or more lattice constituents, e.g. a non-spherical component may thereby be allowed to rotate. Such reorganizations are properly regarded as premelting phenomena and have been discussed by Ubbelohde [3]. The mechanisms of phase transitions have been reviewed by Nagel and O’Keeffe [21] (see also Hannay [22]). Recrystallization may also result in the elimination of regions of local lattice distortion, e.g. dislocations, grain boundaries etc., without change in chemical composition or, indeed, lattice configuration: such behaviour has been described by Christian [ 61. Where two phases are present, certain particles of the discontinuous phase may grow a t the expense of other (smaller or less perfect) crystallites so reducing the total interfacial energy [ 23,241. Reactions involving the precipitation of a new phase from supersaturated solution are of great commercial importance, e.g. carbide formation during the manufacture of ferrous alloys [ 251, and the crystallization of glasses [ 12461.

1. Characteristic features of decomposition reactions of solids The main distinguishing features of reactions involving solids are that (i) the chemical transformation occurs within a restricted zone of the solid,

4

characterized by locally enhanced reactivity (this zone is often referred to as the reaction interface); and (ii) where more than a single reactant is involved, solid products may constitute a barrier layer which tends to oppose further reaction. Both of these mechanistic representations have been widely applied in interpretations of observations on solid state reactions and there is ample experimental evidence for their existence in most, but not necessarily all, systems. The reactivity and chemical properties of solids are strongly influenced by the relative immobility of the constituent ions or molecules in the lattice of the reactant phase (and perhaps also including the product phase). Because nominally identical chemical groupings in a solid reactant may occopy different positions in the crystal structure, and because this structure may contain imperfections, it follows that the reactivity of such groups may vary with their position in the solid. In regions of local distortion, the forces of lattice stabilization may be relatively diminished, with consequent increase in the probability of reaction. This contrasts with the homogeneous behaviour of similar groups in the liquid or gaseous phase. Thus, during rate processes in solids, it is often observed that there are localized regions or sites of preferred onset of reaction. Such initiation usually occurs at a surface, leading to the development of a zone of preferred chemical transformation, which thereafter progressively advances into adjoining volumes of unreacted material. The occurrence of reaction is usually regarded as being exclusively restricted t o the reactantproduct interface at which local conditions markedly enhance the ease of the chemical transformation, as compared with the reactivity of ions or molecules elsewhere within the bulk of the crystal. The kinetic characteristics of the overall process are determined by the velocity of advance of this interface into the unchanged reactant and the variation in its effective area with time. The concentrations of reactants are of little significance in the theoretical treatment of the kinetics of solid phase reactions, since this parameter does not usually vary in a manner which is readily related to changes in the quantity of undecomposed reactant remaining. The inhomogeneity inherent in solid state rate processes makes it necessary to consider always both numbers and local spatial distributions of the participants in a chemical change, rather than the total numbers present in the volume of reactant studied. This is in sharp contrast with methods used to analyse rate data for homogeneous reactions in the liquid or gas phases. The reaction interface can be defined as the nominal boundary surface between reactant and the solid product. This simple representation has provided a basic model that has been most valuable in the development of the theory of kinetics of reactions involving solids. In practice, it must be accepted that the interface is a zone of finite thickness extending for a small number of lattice units on either side of the nominal contact sur-

5

TABLE 1 Types of imperfection which represent deviations from the ideal lattice in real crystals

1. Phonons (atomic vibrations about mean positions) 2. Excitons (energetic combination of electron and positive hole) 3. Electrons and positive holes 4. Point defects (Schottky, Frenkel, unoccupied lattice sites, misplaced units) 5. Non-stoichiometry (excess of one structural constituent) 6. Impurities (foreign constituents accepted into the structure). I. Dislocations (edge and screw: imperfections in lattice alignments) 8. Surfaces (and edges, corners, steps, etc.)

t

I i

Predominantly electronic imperfections Imperfections localized in the vicinity of a small number of lattice sites

Extended imperfections

Notes (i) These various types of imperfections may occur in combination and interact in various ways, e.g. to form colour centres e- + anion vacancy -+ F centre etc. (ii) Reaction mechanisms formulated to account for the decompositions of various solids have involved the participation of each of the above eight different types of imperfection.

face. The reaction interface may be regarded as a complex crystal imperfection, partially constituted of reactant, which is evidently in a state of enhanced reactivity since it is here that there is preferential, if not exclusive, product formation. So important are lattice imperfections in the reactions of solids that it is considered appropriate to list here the fundamental types which have been recognized (Table 1).More complex structures are capable of resolution into various combinations of these simpler types. More extensive accounts of crystal defects are to be found elsewhere [1,26,27].The point which is of greatest significance in the present context is that each and every one of these types of defect (Table 1)has been proposed as an important participant in the mechanism of a reaction of one or more solids. In addition, reactions may involve structures identified as combinations of these simplest types, e.g. colour centres. The mobility of lattice imperfections, which notably includes the advancing reaction interface, provides the means whereby ions or molecules, originally at sites remote from crystal imperfections and surfaces, may eventually react. Nucleation is the process by which the reaction interface is initially established, at perhaps a limited number of points in the reactant, usually at a surface and possibly at an imperfection [ 281. The initially generated germ nucleus, consisting of a few atoms only is generally regarded as unstable due to the high ratio of surface strain to volume. It may, however, develop into a growth nucleus, which increases in size through advance of the reactant-product interface into the bulk of the crystallite, so reducing

6

the relative importance of the surface strain term. There are extensive discussions of the nucleation process in solid state reactions [ 1,26,28-321. Since interface advance represents reactant consumed and product formed, the progress of this process is a measure of reaction rate and the controlling factors determine the kinetic characteristics of the chemical change under consideration. From this approach, the following five general kinetic tenets have been used as a widely accepted basis for the interpretation of kinetic behaviour in decompositions and interactions of inorganic solids. These are presented together here for ease of reference, and explanatory paragraphs follow. (i) The rate of reaction of a solid is proportional to the aggregate effective area of the reactant-product interface. (ii) The rate of interface advance through an isotropic reactant under isothermal conditions is constant. (iii) In the large majority of solid phase reactions, the temperature dependence of the rate coefficient obeys the Arrhenius equation. (iv) When one or more product phases constitute a barrier layer to direct contact between two solid reactants, the overall reaction rate may be controlled by the rate of diffusion of a species through the interposing phases. (v) The rate of reaction of a solid with a gas or liquid solute may include a dependence upon the prevailing concentration of the latter reactant. References to the experimental observations which provide the justification for these generalizations will .be made below (see also refs. 28-32). Examples of exceptional or apparently anomalous behaviour are also known. Tenets ( i ) and (ii). These are applicable only where the reactant undergoes no melting and no systematic change of composition (e.g. by the diffusive removal of a constituent) and any residual solid product phase offers no significant barrier to contact between reactants or the escape of volatile products [ 33,341. When all these conditions are obeyed, the shape of the fraction decomposed ( a ) against time ( t ) curve for an isothermal reaction can, in principle, be related to the geometry of formation and advance of the reaction interface. The general solution of this problem involves intractable mathematical difficulties but simplifications have been made for many specific applications [ 1,28-31,351. Tenet (iii). Rate coefficients ( h ) measured for many solid phase rate processes obey the relation h = A exp(--E/RT)

where T is the temperature (K), within the limits of experimental accuracy (though this is not a particularly sensitive test). By analogy with the application of the same equation to homogeneous reactions, the coefficients A and E are often referred t o as the reaction frequency factor and

7

the activation energy, respectively. More recently, however, doubts have been expressed concerning the significance of these terms in heterogeneous rate processes [36]. This topic is of such importance that discussion is deferred to a later section (Chap. 3.5). Tenet (iv). The influence of a barrier layer in opposition to the progress of reaction may be expected to rise as the quantity of product, and therefore the thickness of the interposed layer, is increased [35,37,38]. Thus, the characteristic kinetic behaviour of the overall process may be expected to include contributions from both geometric factors and the barrier effect, though in specific instances one or other of these may be dominant. Tenet (v). Experimental studies of the interaction of a solid with a gas, liquid or solute must ensure that there is uniform availability of the homogeneous participant at all surfaces within an assemblage of reactant crystallites if meaningful kinetic measurements relating t o the chemical step are to be obtained. If this is not achieved, then diffusion rates will control the overall rate of product formation. Such effects may be particularly significant in studies concerned with finely divided solids. In addition to the above tenets, which are primarily concerned with the kinetics of interface advance within the reactant, a number of other factors may exert an appreciable control over kinetic characteristics. Some of the more important are mentioned in the following paragraphs. ( i ) Definition of the fractional reaction (a). A necessary prerequisite of any kinetic study is the unambiguous definition of a in terms of some directly measurable parameter. This is not always as straightforward as it may seem. The pressure of gas evolved in a constant volume system may deviate from direct proportionality to a where, for example, (a) progressive changes in composition of the mixture of gases evolved results from secondary catalytic reactions proceeding on a residual phase (as in the decomposition of oxalates [ 391 ) or (b) an initial deceleratory (surface) process precedes the main decomposition reaction (as in the decomposition of nickel oxalate [40]).Again, mass loss does not measure a for any single reaction in the sequence of a multistep dehydration process where there is overlap between sucessive stages. In most of those reactions which have attracted greatest interest, it has been assumed (sometimes with the support of experimental measurements) that the parameter used to determine (Y is directly proportional to the extent of reaction and that parallel or consecutive contributions to product formation are absent. ( i i ) Particle size variation within the reactant. The shapes of a-t curves for reactions of solids have been shown to be significantly influenced by changes in the distributions of sizes and shapes of the crystals which comprise the reactant [ 41,421.This is clearly due to variations in the geometry of the surface production of nuclei and the subsequent interface advance in particles of different dimensions. Ideally, kinetic studies would be concerned with single crystals of simple and constant geometry but, in prac-

8

tice, it is often necessary to use assemblages of crystallites which usually contain a range of sizes. Delmon [30] has discussed this aspect of kinetic behaviour in some detail. (iii) Pretreatment of the reactant. The reactivity of a solid can often be markedly influenced by various types of pretreatment [ 30,43-451 including irradiation, cold-working and the conditions of dehydration. The controlled addition of impurities can also result in significant changes in kinetic characteristics [ 46,471. All these pretreatments change both the concentrations and distributions of lattice imperfections and, in consequence, different samples of the same salt may exhibit significantly different rates of reaction and shapes of a - t i m e curves. Crushing will, of course, change particle sizes and shapes [see (ii), above]. ( i u ) Reuersibility. Some solid state reactions are reversible and rate measurements for such processes must be made under conditions which ensure that the influence of the opposing reaction is eliminated, or due allowance for the effect must be incorporated into the kinetic analysis. The problems which arise will be discussed in detail during consideration of specific systems. ( u ) Melting. While the absence of bulk fusion during reaction is usually readily detected, it is not always possible to demonstrate convincingly that no melting whatsoever has occurred in the immediate vicinity of the reaction interface. Mobility of reactant constituents is enhanced at surfaces and such movements may be compared with the freedom of motion of ions or molecules in a liquid [ 48,491. There is no point of discontinuity between increasing freedom of motion on the surface and the appearance of a thin (“two-dimensional”) layer of liquid. The possible formation of low melting point eutectics between reactant and products must also be considered. (ui)Slow growth of germ nuclei. As an exception to tenet (ii) in the above list, the initial rate of growth of germ or small nuclei in certain substances is appreciably less than the constant rate of interface advance subsequently attained and maintained thereafter [ 29,50-541. (uii) Temperature inhomogeneities within the reactant mass. Reactions involving large enthalpy changes can cause significant variations between the actual temperatures prevailing locally within the reactant mass and the nominal value measured for the reaction vessel [55]. Such effects exert some control on the magnitude of a and da/dt and are relatively greater at higher temperatures (more rapid reaction and, therefore, larger rate of heat change) and in larger masses of reactant. For endothermic reactions, estimates of self-cooling were first made during the early (-1935) rate studies of water removal from crystalline hydrates and carbonate dissociations [ 281. Self-heating effects in exothermic reactions have been less frequently considered. Temperature inhomogeneities within the reactant mass can also exert an important influence on apparent kinetic behaviour and sophisticated treatments of this problem have been made with special

9

reference to non-isothermal rate measurements, e.g. DTA [ 56-58]. (viii) Other factors. A variety of other factors are known to influence the kinetic characteristics of certain decomposition reactions of solids. Amongst these may be mentioned recrystallization [ 591, sublimation [59] (an inert gas may influence transport rates) and the presence of a reactive gas [60,1247]. (ix)Reactions in which the interface does not advance. Reactions are known in which a mobile constituent of the reactant phase relatively rapidly diffuses t o existing crystallite boundaries and the chemical desorption step at this immobile surface is rate-limiting. This group of reactions has been the subject of relatively few detailed kinetic investigations and includes the decompositions of some hydrides, carbides and nitrides in which the interstitial atoms can migrate with comparative ease [ 611, and at least one hydrate [62]. Such reactions constitute important exceptions to much that has been said above [paragraphs (i)--(viii) and tenet (ii)]. The effective area of reaction interface does not change with a, and the rate of product evolution can, in principle, be controlled by either the rate of diffusion of the appropriate constituent to the active surface or the rate of a subsequent desorption step. Kinetic behaviour is, therefore, subject to some control by the effective ratio of the surface area to the volume of the reactant crystallites. 2. The literature of solid phase reactions

Although the literature contains a very large number of research articles concerned with the kinetics and mechanisms of reactions involving solids, there are comparatively few authoritative, critical and comprehensive reviews of the formidable quantity of information which is available. Probably the most important general account of the field is the book Chemistry of the Solid State, edited by Garner [63]. Chapters 7-9 are particularly relevant in the present context as they provide a systematic exposition of the kinetic equations applicable to the decomposition of single solids (Jacobs and Tompkins [ 281 ) and their application to endothermic [64] and exothermic [65] reactions. Principles of Solid State Chemistry by Budnikov and Ginstling [ l ] is largely concerned with interactions between solids, though there are also accounts of the reactions of single substances. A similar book by Schmalzried [66] provides a general survey of the many aspects of the field. Volume 4 of the series Treatise on Solid State Chemistry (edited by Hannay [67]) is devoted to reactivity of solids and is concerned with the kinetics and mechanisms of chemical change. Delmon [ 301 has provided a comprehensive exposition of the kinetic characteristics of decomposition reactions of single solids and gassolid interactions, including the consequences of diffusion. Tabulated data for many important interface-con-

10

trolled rate expressions are provided. Barret [31] gives a general account of the kinetics of heterogeneous reactions with particular emphasis on the role of defects in the barrier layer in controlling reaction rate. Young’s book, Decomposition of Solids [ 291 is largely concerned with a detailed mechanistic consideration of the reactions of a number of selected solids. Chemistry of Solids by Galwey [26] is an introductory text. Solid State Chemistry: Whence, Where and Whither? is a very personalized account of particular aspects of the field by the pioneer Hedvall [ 681. Among a number of articles on more restricted features of the kinetics of reactions of solids is that by Hamson [69], in an earlier volume of the present series, which gives an account of the rate characteristics of solid state decomposition reactions and also of the interactions of a solid with a gas, liquid or one or more other solid reactants. The treatment includes consideration of nucleation and growth phenomena and of heat and mass transfer. The role of lattice defects in reaction mechanisms is also discussed. There is also a chapter concerned with the evaluation of kinetic data from isothermal experiments in Keattch and Dollimore’s book A n Introduction t o Thermogravimetry [33] dealing with the problem of fitting a-t data to kinetic expressions, a facet of the subject which has been discussed by many other workers [70-741. Sharp [75] reviewed the use of DTA in the determination of reaction kinetics and a monograph by SestLk et al. [76] deals with the uses of thermal analysis in the study of heterogeneous processes with particular reference to reaction rates. Hulbert [ 771 has considered the kinetics of solid interactions in powder compacts. Vorontsov [ 781 discusses the role of the solid products in controlling kinetic characteristics during the occurrence of both autocatalytic and impedance phenomena. Galwey [ 321 has provided a general review of the literature (1967-1972) devoted to thermal decomposition reactions of solids. Dollimore [ 791 has been more particularly concerned with the dissociation of metal hydroxides and oxides. Investigations into the removal of water from crystalline hydrates have been critically surveyed by Dunning [ S O ] and by Lyakhov and Boldyrev [ S l ] ; the former author was particularly Concerned with the mechanism of nucleation in these reactions. Many authoritative accounts of both general and specific aspects of the reactions of solids and related topics appear as plenary lectures and research papers in the series of International Symposia on the Reactivity of Solids [ 82-86]. The material presented at these meetings reflects contemporary interests in a diverse and developing field, so that changes in emphasis are to be discerned in the content of the successive symposia held at four-yearly intervals. Reference can also be made here to the conference on Reaction Kinetics in Heterogeneous Chemical Systems in which useful review material is found [ 871.

11

3. Scope of the present review and arrangement of subject matter No unifying theoretical concepts have been recognized which can be used to provide satisfactory criteria for the comprehensive classification of the kinetics and mechanisms of reactions involving solids. Thus the scope and treatment of the subject cannot be entirely systematic. General problems encountered during any attempt to review the field include the following. (i) Many solids melt either before or during reaction with a consequent change in kinetic characteristics. Often, reports of rate studies involving solids omit any categorical statement as t o whether or not reaction was accompanied by melting, thereby reducing the intrinsic value of the work. (ii) The reactions of compounds containing common atomic groupings or ions do not necessarily exhibit comparable kinetic characteristics. (iii) The greatest research effort has been directed towards the investigation of the kinetics and mechanisms of those solid state decompositions which yield gaseous products, since these are most easily studied quantitatively. In general, the simplest reactions have (understandably) been preferred and the observations collected have enabled the theoretical basis of the subject to be developed. Relatively less is known concerning the rate characteristics of the more complex processes. (iv) Studies of reactions of solids have, in the past, often been concerned with a restricted range of compounds, each of which has been the subject of several distinct investigations. These include BaN6, KMn04, NH4C104, NiC204, CaC03 and CuS04 * 5 H z 0 . Each might almost be regarded as having achieved the status of a model substance and the results obtained have been responsible for the development of much of the theory of the subject. More recently, however, the range of solid reactants investigated has been extended. Some such work has been concerned with comparisons of activation energies for a series of solids containing a common constituent, e.g. the transition metal oxalates [ 88,891. An investigation of the effect of systematic variations of reactant composition on decomposition kinetics has been made [ 471. (v) The nature of the bonding in solids is not always known in detail and the lattice interactions involved are not always directly comparable with the more familiar linkages present in free molecules. Very few quantitative correlations between detailed crystal structure and solid phase reactivities have been made, although some such investigations have been attempted E90-951. A most valuable account of the structures of inorganic solids has been given by Wells [96]. In the present review of the kinetics and mechanisms of decomposition and chemical interactions of inorganic solids, emphasis is placed on reports appearing in the approximate period 1955-1976, though many references to earlier work have been included t o maintain a balance in the treatment. Some of the citations have been particularly selected to

12

provide access t o earlier articles. The term “inorganic” is here extended to include metal carboxylates since kinetic studies of the pyrolyses of these salts (especially the oxalates and formates) are closely comparable with those of the “true” inorganic solids and historically have been regarded as reactants important in the development of the field. Following a well-established practice of the subject, and a feature of its literature, our account discusses the behaviour of certain individual compounds at much greater length than is given to other related substances. Such extended treatment is devoted to those single solids for which the decomposition reactions are most completely understood and the conclusions obtained are useful in the consideration of more complicated systems. The reactions of single substances (Chap. 4) are loosely grouped on the basis of a common anion, since it is this constituent which most frequently undergoes breakdown and, although this criterion is not completely satisfactory, it does allow certain features of reaction mechanisms t o be considered together. The sequence of treatment approximately follows that of increasing anion complexity. The final chapter (Chap. 5) concerns interactions between solids, widely interpreted to include catalytic processes (where one solid reactant constituent is unchanged on completion of a decomposition) but also considers double compound formation and the more complicated field of rate processes involving the interactions of more than three crystalline phases. 4. Classification of chemical reactions of solids

A generalized scheme, which summarizes certain of the most frequently observed kinetic characteristics for the reactions of a solid alone or with a gas, a liquid (solute) or another solid, is given in Table 2. The following processes may control the rate of product formation. (i) A chemical reaction at an advancing interface (following a nucleation step). (ii) A chemical reaction at a static interface (following diffusion of appropriate species to that interface). (iii) Diffusion of reactants (in a homogeneous phase or across a barrier of product) t o the reaction interface at which the chemical step is fast. The significance of diffusion generally increases with reaction rate in the sequence of gas, liquid and solid reactants and (sometimes) with the extent of reaction (a),particle size, etc. The controlling factor (i.e. a chemical step or diffusion) may change during the course of reaction. It is a primary objective of most fundamental kinetic investigations to identify the rate-limiting process. 4.1 DECOMPOSITION OF A SINGLE SOLID

The term recrystallization in Table 2 can include sintering but may also occur during decomposition. Sintering processes are very often studied as

13 TABLE 2 Reactions of solids. Scheme of reaction pathways indicating relationships with kinetic characteristics -+ Sintering Recrystallization. --, + Melting + Sublimation On heatinga + Decomposition single solid \Isomerization (complex compounds) decomposition

/

2

1

Reaction Decomposition single solid

Mechanism Of

a

Kinetic characteristics

+ Growth Reaction at immobile surface

Interface phenomena { Geometric control Interface control or

{ Diffusion control

Reaction of a solid with a gas Interface phenomena Geometric control

Reaction of a solid with a liquid (or solute) Reaction of a solid with a solid}

Barrier layer formation

Diffusion across barrier control {(reaction deceleratory)

As with solid and gas

I

As with solid and gas

Diffusion in the liquid may be important, particularly where no barrier layer is formed Normally the immobility of reactants inhibits reaction and barrier layer fortion is more common

Notes (i) Diffusional effects generally increase from the top to the bottom of the table as the restrictions on reactant-reactant contact become more significant. (ii) A t low temperatures, the reaction of a solid may not proceed beyond the surface layer.

phenomena distinct from the decomposition reaction (e.g. dehydration) but the recorded observations are a direct result of the previous and distinct solid state decomposition [97]. Growth of particle sizes of reactant and/or product at the decomposition temperature may influence kinetic characteristics [98,99]. The shapes of a--t curves are sensitive to the relative ease of nucleation: where many product particles are formed rapidly at the onset of reaction, the rate process is deceleratory throughout, whereas the slow development of a restricted number of nuclei results in a sigmoid-shaped a--t relation. There have been few attempts to classify decomposition reactions of solids. Gamer [64] made only the broad distinction between endothermic processes (which are often reversible and include dissociation of crystalline hydrates and carbonates) and exothermic processes (which are usually

14 TABLE 3 Classification of solid state reactions according to Boldyrev [ 1001 Initial step

Reaction mechanism

'

11. Bond rupture involves electron transfer

IIa. Transfer occurs within anionic o r cationic sublattice IIb. Radical intermediate formed

Examples

I

Decompositions of alkali permanganates or perchlorates Various mechanisms involved, as in the decomposition of silver oxalate o r

irreversible, as in the decompositions of BaN,, KMn04 etc.). More recently, Boldyrev [ 100,101] has proposed the more detailed scheme shown in Table 3. Since then, he has emphasized [102,103] the importance of lattice imperfections and anisotropy in controlling the sites of occurrence of reaction and the relative significance of nucleation and growth processes. He concludes that identification of the factors which control autolocalization of reaction would markedly increase our understanding of the reactivity of solids. 4.2 REACTIONS OF TYPES: SOLID + GAS AND SOLID + LIQUID

Although neither of these classes falls within the scope of this review, it is nevertheless appropriate to indicate their relationships with the present subject. The kinetic characteristics of reactions of gases with solids are largely determined by whether or not the product represents a barrier to its continued formation. Where a coherent and adherent layer of product is generated, the reaction is characteristically deceleratory throughout and the rate is determined by diffusion through this layer of progressively increasing thickness. The theory of such reactions, in which lattice imperfections are identified as promoting the migratory process, has been developed in the important and widely studied field of metal oxidation [37, 381. Other examples of diffusion-controlled reactions are known, for example [lo41 the reaction CuC11.2s+ Clz. Where no barrier layer is produced, the patterns of kinetic behaviour resemble the behaviour of single

15

solids. Nucleation and growth processes occur in the reactions of nickel oxide with hydrogen (which has been the subject of detailed study [30, 1051) and of KBr + Clz [ 1061. The reaction interface probably does not advance during the (catalytic type) reaction of iron nitride with hydrogen [61] and no residual phase is formed on oxidation of carbon [ 1071. Since the “free energy’’ of a molecule in the liquid phase is not markedly different from that of the same species volatilized, the variation in the intrinsic reactivity associated with the controlling step in a solid-liquid process is not expected to be very different from that of the solid-gas reaction. Interpretation of kinetic data for solid-liquid reactions must, however, always consider the possibility that mass transfer in the homogeneous phase of reactants to or products from, the reaction interface is rate-limiting [ 108,1091. Kinetic aspects of solid-liquid reactions have been discussed by Taplin [ 1101. 4.3 SOLID-SOLID REACTIONS

Rate processes involving the interaction of two or more solids constitute Chap. 5 of this review. Dominant and recurrent features of the literature concerned with solidsolid reactions are the occurrence of barrier layers and the relative immobility of at least one reactant [lll].At the temperatures required to achieve a significant rate of diffusion of a mobile participant through the barrier phase, such entities undergo relatively rapid surface migrations. The nucleation process is, therefore, effectively completed by the production of a surface covering of product very soon after heating and the subsequent deceleratory process is diffusion-controlled. Fundamental kinetic studies have been concerned with a relatively restricted range of systems and, again, the simplest reactions, including those which involve gaseous products, are the most extensively studied. At the present time the following groups of rate processes can be used as a basis for classification. (i) Decomposition of a solid catalyzed by a solid. (ii) Double compound formation (A + B AB: one solid product). (iii) Double compound formation with gas evolution A + C -+ AD + E(g). (iv) Other reactions. Some studies of more complicated systems have been attempted but, as the number of variables increases, the complexities of interpretation and the difficulties in obtaining meaningful kinetic data become intractable. +

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Chapter 2

Experimental

Experimental measurements of reaction rates usually form part of a more comprehensive investigation undertaken to determine the mechanism of a chemical change. In general, the most reliable theoretical explanations of observed behaviour are based on data obtained from different, but complementary, investigative techniques. Accordingly, some reports of reactions of solids include mention of the use of several diverse experimental methods and this trend accounts for the relatively long list, given below, of the many principles exploited directly or indirectly in the measurement of kinetic characteristics. Approaches primarily concerned with rate determinations often provide evidence relating to other features of the reaction (e.g. variations in stoichiometry, or that the process proceeds to completion in more than a single step, etc.), while ancillary experimental techniques (microscopic observations, etc .) are required to supplement conventional kinetic data in the formulation of a reaction mechanism. Measurements of overall reaction rates (of product formation or of reactant consumption) d o not necessarily provide sufficient information to describe completely and unambiguously the kinetics of the constituent steps of a composite rate process. A nucleation and growth reaction, for example, is composed of the interlinked but distinct and different changes which lead to the initial generation and to the subsequent advance of the reaction interface. Quantitative kinetic analysis of yield-time data does not always lead t o a unique reaction model but, in favourable systems, the rate parameters, considered with reference t o quantitative microscopic measurements, can be identified with specific nucleation and growth steps. Microscopic examinations provide positive evidence for interpretation of shapes of fractional decomposition (cu)-time curves. In reactions of solids, it is often convenient to consider separately the geometry of interface development and the chemical changes which occur within that zone of locally enhanced reactivity. While the topochemistry of interface advance can be observed, the chemistry of reactions proceeding within that interface, localized inside the bulk of reactant particles, is less easily investigated. Intermediates cannot be isolated without destruction of the specialized environment in the strained region at the juxtaposition of two phases where these are generated. Identification of those species which are the necessary participants in a chemical transformation can be difficult since the total quantity

18

present may be low. Moreover, the use of spectral and/or resonance techniques for their detection is precluded in many systems of interest where the product is opaque, metallic and/or defective. It is difficult t o establish whether reactant groupings or local lattice defects are true participants and the existence of a molecular or ionic grouping does not prove that it is a significant or necessary stage in the chemical transformation. Intermediates also may be adsorbed on surfaces. Some of the problems which arise in the study of kinetics of heterogeneous reactions have been discussed elsewhere [36]. As a result of these inherent difficulties, kinetic and mechanistic characteristics of interface phenomena are often inferred from indirect evidence. Several techniques to which reference is made below describe imaginative experimental approaches which allow the collection of meaningful information concerning the changes occurring at, or within, the reactant boundaries. In principle, any parameter quantitatively related t o the extent of reaction (a) can be used for rate studies, though, in practice, product gas evolution, mass loss and enthalpy changes have found the most widespread application. Coupling such techniques with analytical measurements (mass spectrometry, gas chromatography, etc.) provides information on the stoichiometry of reaction. Concurrent or parallel microscopic observations are invaluable in establishing the interface geometry. More detailed characterizations of the phases present, including possible topotactic relationships, are afforded by X-ray diffraction measurements. Intermediates and reaction precursors can, in suitable systems, be identified (and sometimes be determined quantitatively to give a ) by electrical, magnetic or spectral measurements.,The textures of products can be determined from surface area measurements. The effects of reactant pretreatment, often a significant influence on kinetic behaviour, have also been studied. Examples of those diverse experimental techniques which have found profitable application in investigations of the reactions of solids are mentioned below. References to the advantages, problems and limitations of non-isothermal compared with isothermal measurements of a-time variations will be made in Chap. 3. This introduction would not be complete without reference to the importance of determining, in every system, whether or not the reaction truly occurs in the solid. I t is always appropriate to examine whether the experimental methods used include due consideration of the possibility of melting (perhaps locally), sublimation or phase transformation during reaction, and whether such an occurrence exerts a significant influence on the kinetic characteristics and mechanism. Techniques used in experimental measurements of reaction rates are reviewed in Vol. 1 of this series, including specific descriptions of methods used t o study homogeneous and heterogeneous rate processes by Batt [112] and by Shooter [113]. A number of experimental approaches t o the investigation of reactions of solids are described by Budnikov and Ginstling [ 11.

19

1. Accumulatory pressure measurements of evolved gas The kinetics of many decompositions are conveniently studied from measurements of the pressure of the gas evolved in a previously evacuated and sealed constant volume system. I t is usually assumed, and occasionally confirmed, that gas release is directly proportional t o a, so that the method is most suitable for reactants which yield a single volatile product by the irreversible breakdown of a substance that does not sublime on heating in vacuum. A cold trap is normally maintained between the heated reactant and the gauge t o condense non-volatile products (e.g. water vapour) and impurities. The method has found wide application, notably in studies of the decomposition of azides, permanganates, etc., and has been successfully developed as an undergraduate experiment [ 114-1161. Various methods of gas pressure measurement have been used, including manometer, McLeod gauge, glass spoon gauge [ 1171, Pirani gauge and mass filter pressure gauge [118]. Procedural methods have ranged from manual operation to the use of high speed and computer recording of responses from the electrical devices. A method of extending the lower end of the temperature range for studies of very slow rate processes, through the use of an automatic recording system, has been described by Hill e t al. [ 1171. The use of ultra-high vacuum systems [ 1191, with several gauges covering different pressure ranges, offers an alternative approach to measurements for the early stages of reaction. It is necessary, however, to make corrections for gauge pumping and adsorption on the walls of the system. Whenever a rate process involves or is preceded by the release of a condensable product, some error is inevitably introduced during the period of diffusion of this temporary gas from reactant t o cold trap. Accumulatory pressure measurements have been used to study the kinetics of more complicated reactions. In the low temperature decomposition of ammonium perchlorate, the rate measurements depend on the constancy of composition of the non-condensable components of the product mixture [ 1201. The kinetics of the high temperature decomposition [59] of this compound have been studied by accumulatory pressure measurements in the presence of an inert gas to suppress sublimation of the solid reactant. Reversible dissociations are not, however, appropriately studied in a closed system, where product readsorption and diffusion effects within the product layer may control, or exert perceptible influence on, the rate of gas release [ 1211. 2. Mass loss measurements

The development and ready availability of reliable and accurate electronic microbalances [ 33,122-1281 have led to their wide application in kinetic studies of the decomposition of solids. Certain of the disad-

20

vantages mentioned for pressure measurements are less important or are effectively eliminated, since reaction can proceed in a controlled environment ranging from high vacuum to a pressure of several atmospheres of gas of specified composition which can be altered at will. The main problems encountered in microbalance applications [ 1281 are thermomolecular flow effects at low pressures, accurate sample temperature calibration and, more specifically, the influence of volatile product on rates of reversible decomposition reactions [ 1291. Mass loss determinations refer to the total change resulting from reactant decomposition and usually include contributions from a mixture of product compounds, some of which would normally be condensed under conditions used for accumulatory pressure measurements. Such information concerned with the overall process is, however, often usefully supplemented by evolved gas analyses (EGA) using appropriate analytical methods. Sestak [130] has made a detailed investigation of the effects of size and shape of reactant container on decomposition kinetics and has recommended that the sample be spread as a thin layer on the surfaces of a multiple plate holder. The catalytic activity of platinum as a reactant support may modify [ 1311 the apparent kinetic behaviour. For isothermal measurements, it is advisable to use a furnace of low thermal capacity unless suitable arrangements can be made to transport the sample into a preheated zone. The Curie point method [132] of temperature calibration is ideally suited for microbalance studies with a small furnace. A unijunction transistor relaxation oscillator, with a thermistor as the resistive part with completion of the circuit through the balance suspension, has been suggested for temperature measurements within the limited range 298-433 K [ 1331. Constant rate thermogravimetry has been described [ 134-1371 for kinetic studies at low pressure. The furnace temperature, controlled by a sensor in the balance or a pressure gauge, is increased at such a rate as to maintain either a constant rate of mass loss or a constant low pressure of volatile products in the continuously evacuated reaction vessel. Such nonisothermal measurements have been used with success for decomposition processes the rates of which are sensitive to the prevailing pressure of products, e.g. of carbonates and hydrates. Searcy and co-workers [ 121,138-1401 have adapted the Langmuir method [ 1411 of vapour pressure measurement to the determination of kinetics of solid phase decompositions. The use of an appropriate design of holder for the single crystal of reactant enables the reversible carbonate dissociation reaction to be confined t o a single face, thus eliminating uncertainties arising from the changing geometry during interface advance. Since it was observed that the rate of the zero-order reaction in vacuum (a constant rate of interface advance) was independent of thickness of product layer, it is concluded that diffusion effects did not control the rate of carbon dioxide release. The measured flux of product gas, J , is compared

21

with the maximum possible flux, calculated from the standard free energy change, AGzec, for the decomposition using the Hertz-Knudsen-Langmuir equation

where Peg is the equilibrium pressure of the product at temperature T. For a simple vaporization process

--J - vaporization coefficient Jmax

Chemically similar substances have comparable vaporization coefficients, so that rates of vaporization, J, can be predicted from J,,,, determined using equilibrium data. Beruto and Searcy [ 1211 have suggested the similar use of the decomposition coefficient providing that due consideration is given to the occurrence of unstable intermediates. Flynn and Dickens [142] have translated the relaxation methods of fluid kinetics into terms applicable to solid phase thermogravimetry. The rate-determining variables such as temperature, pressure, gas flow rate, gas composition, radiant energy, electrical and magnetic fields are incremented in discrete steps or oscillated between extreme values and the effect on reaction rate determined.

3. Evolved gas analysis (EGA) As pointed out above, accumulatory pressure and weight loss measurements usually refer to the total reaction. When there are several volatile products, it is necessary to identify all components and investigate progressive changes in gas composition. Quantitative determinations of the amounts of each product (EGA) should, ideally, be combined with measurements of the total extent of reaction, although Garn [ 1431 has recommended caution in the interpretation of results from simultaneous measurements. Instrumentation for gas analysis has been reviewed by Lodding [ 1441 and is also discussed in the biannual reviews by Murphy [145]. The most widely applied techniques of EGA have been mass spectrometry and gas chromatography. 3.1 MASS SPECTROMETRY

Qualitative or quantitative mass spectrometric analysis can be made by one of two alternative configurations. Either the sample is decomposed in the high vacuum chamber of the mass spectrometer (MS) itself or reaction proceeds in an external system at higher pressure (e.g. a microbalance)

22

from which samples are withdrawn and admitted to the MS through a suitable inlet. Wiedemann [ 1461 has discussed the conditions which must be satisfied in order that accurate kinetic measurements may be obtained. Decomposition of the reactant within the MS, where the path length to the detector is short, reduces the probability of secondary gas-phase reactions and fractionation which may arise when sampling from higher pressure. Useful descriptions of MS techniques, applied to the study of desorption and gassolid reactions, have been given by Dollimore and co-workers [ 147,1481. Techniques of data storage and processing [ 149,1501 and automation [151] in EGA by MS methods have been described. Volatile products may include metal-containing species [ 1521. The quadrupole mass spectrometer has been found to be particularly suitable for EGA in thermal analysis. Published reports include descriptions of the various systems used [ 153-1551 and applications in studies of the pyrolysis of polymers [155], minerals [156] and many inorganic solids [ 157-1 591. The high sensitivity of the M S [ 1601 makes it a particularly appropriate tool for the investigation of nucleation and growth processes, since it is possible to measure rates during the early part of the reaction using small samples or individual crystals. The influence of residual gases [ 1601 on the initiation of reaction can also be determined. Short scan times enable very rapid reactions e.g. detonations, to be studied, and it is also possible to measure simultaneously the rate of evolution of several different product molecules. A novel application [ 1611 of EGA is in the study of crystal transformations by detection of the release of organic molecules occluded by the reactant solid during preparation. 3.2 GAS CHROMATOGRAPHY

The gas chromatograph (GC) resembles the MS in providing both qualitative and quantitative EGA but is significantly slower in operation. The interval between analyses is normally controlled by the retention time of the last component to be eluted from the column; such delay may permit the occurrence of secondary reactions between primary products [ 1621. Several systems and their applications have been described [ 144,1631671; sample withdrawal can be achieved [164] without the necessity for performing the reaction in an atmosphere of carrier gas. By suitable choice of separation column or combination of columns [162], it is possible to resolve species which are difficult to measure in a small low-resolution MS, e.g. HzO, NH3, CH4, Nz and CO. Wiedemann [168] has made a critical comparison of results obtained by MS and GC techniques and adjudged the quality of data as being about equal.

23

3.3 OTHER METHODS OF GAS ANALYSIS

Methods of EGA using selective sorption, condensation of effluent gases, infrared absorption and thermoparticulate analysis have been reviewed by Lodding [ 1441. The use of simple gas burette systems should not be forgotten and an Orsat gas analysis apparatus can provide useful measurements in studies of the decomposition of formates [ 1691. Problems have been encountered in the determination of water released: Kiss et al. [170-1721 have measured the formation of this compound from infrared analyses of the acetylene evolved following reaction of water with calcium carbide. Kinetic data may be obtained by wet methods: ammonia, determined by titration after absorption in an aqueous solution, has been used to measure a-time values for the decomposition of ammonium salts in a fluidized bed [ 1731. 4. Non-isothermal methods

The techniques referred to above (Sects. 1-3) may be operated for a samp!e heated in a constant temperature environment or under conditions of programmed temperature change. Very similar equipment can often be used; differences normally reside in the temperature control of the reactant cell. Non-isothermal measurements of mass loss are termed thermogravimetry (TG), absorption or evolution of heat is differential scanning calorimetry (DSC), and measurement of the temperature difference between the sample and an inert reference substance is termed differential thermal analysis (DTA). These techniques can be used singly [33,76,174] or in combination and may include provision for EGA. Applications of non-isothermal measurements have ranged from the rapid qualitative estimation of reaction temperature to the quantitative determination of kinetic parameters [ 175-1771. The evaluation of kinetic parameters from non-isothermal data is dealt with in detail in Chap. 3.6. Other parameters which have been used to provide a measure of a include physical dimensions (thermomechanical analysis, TMA) [ 1261, magnetic susceptibility [ 178,1791, light emission [ 180,1811, reflectance spectra (dynamic reflectance spectroscopy, DRS) [ 1821 and dielectric properties (dynamic scanning dielectrometry, DSD) [ 183,1841. For completeness, we may make passing reference here to the extreme instances of non-isothermal behaviour which occur during self-sustained burning (studied from responses [ 1851 of a thermocouple within the reactant) and detonation. Such behaviour is, however, beyond the scope of the present review.

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5 . Absorption or evolution of heat Although discussions concerning the interpretation and value of kinetic data obtained from non-isothermal measurements continue, the reservations expressed do not apply when DSC and DTA methods are used in the isothermal mode [186,1248]. The isothermal record in DSC is a plot of (dH/dt) against time and such a plot can provide both kinetic and thermodynamic information since the area under the response curve is proportional to the enthalpy change for the reaction concerned. Dorko et al. [ 176,187,1881 have given a comprehensive account of the kinetic analysis of isothermal DSC traces. The technique has been used in detailed studies of dehydration [ 1891 and polymerization [ 1901 reactions. Various applications of isothermal DTA have been discussed by Sharp [ 751. Ingraham and Marier [ 1911 have used the method to study the decompositions of CaC03, Ca(OH),, BaClz . HzO and NiS04. 6 . Computer coupling and data processing

The experimental systems considered above are capable of a considerable degree of automation with computer control of the reactant environment according to a preset programme or in response t o specific features of the reaction and data capture for high speed detection systems (e.g. the MS). Applications in this area [ 192-1991 are expanding rapidly with systems ranging in sophistication from the on-line use of programmable desk calculators to large computers. Some of the problems of interfacing have been reviewed [ 1961.

7. Microscopic techniques 7.1 OPTICAL MICROSCOPY

Direct microscopic observations of the sample in the decomposition apparatus [119] or on the hot stage of the microscope [200] can yield information concerning the crystallinity, surface texture and occurrence of melting, sintering, sublimation, etc. of both reactants and products as interaction proceeds. Direct observations of the distributions of nuclei (if any) and the changing geometry of reaction interface (where this can be identified) are of great importance in providing substantiation, and sometimes deciding between alternatives, in the kinetic interpretation of shapes of a - t i m e curves. In favourable systems, it is possible to make quantitative measurements of rates of nucleus formation and interface advance, thus separating contributory factors which appear as compound terms in overall yield-time determinations. A classic contribution in this field is

25

Wischin’s study [201] of nucleation and growth of the product barium during decomposition of BaN6.In other rate processes where the crystallites are small, opaque, of roughened surface, etc., reactant and product cannot be distinguished and microscopic observations yield no useful data. The various techniques which may be used to provide optimum conditions for the examination of specimens have been described [ 202-2051. If the sample is opaque, then microscopic investigation is limited to the surface. The depths of penetration for the study of transparent crystals are controlled by the limited depth of field of the optical microscope at high magnifications. This limitation can sometimes be overcome by cleavage of the crystal at an appropriate value of a and examination of the surfaces exposed [ 1201. References to the profitable exploitation of microscopic techniques in kinetic studies can be found in the work of Thomas and co-workers [91, 206-2101, Herley et al. [211] and of Flanagan and his collaborators [212,213]. The rates of advance of reaction interfaces have been measured from direct observations on single crystals and the kinetic parameters so obtained are compared with results for mass loss determinations. The effects of the introduction of crystal imperfections and the role of such species in mechanisms of reaction are also considered. Surface features can also be revealed by etching, which permits identification of points of intersection of line dislocations with the surface, and this is valuable in determining the role of these imperfections in chemical processes [ 45,2141 and, in particular, nucleus formation. Smaller topographical details can be rendered visible by the evaporation of a thin (<0.5 nm) film of gold onto the surface [215,216]. Heights and depths of surface features can be determined by interferometry [ 203-2051. Microcinematography has also been used [217] to record the progress of solid phase reactions. 7.2 ELECTRON MICROSCOPY

The principal advantage of electron microscopy is the attainment of higher magnifications than are possible by optical methods and the availability of complementary selected area examinations by diffraction methods for phase characterization and by electron probe microanalyses. The technique is, however, relatively demanding and cannot be directly applied to unstable materials since high vacuum is used and samples are heated by the electron beam. Early studies were limited t o the examination of very thin specimens or sectioned material. More recently, some of the limitations have been overcome in part through the use of replicas of the surface. This approach cannot, of course, yield information concerning changes within the bulk of the reactant crystallites. The development and the recent increase in availability of the scanning electron microscope with its considerable depth of field and reduced beam intensity has widened the range of samples which can be examined

26

directly. The main problems of microscopy, however, remain the instability of samples, especially hydrates, in the high vacuum system of the microscope and in the electron beam, though the effects may be reduced somewhat by the use of a cold stage. The possibility that the sample, or other materials present, may react with the residual gases in the microscope must also be considered [ 2181. The metal or carbon coating procedure required to reduce surface charging of insulating materials may introduce artefacts or possibly substantially alter significant properties of the surface. The thermal emission during coating may damage the specimen since temperatures up t o 570 K have been measured [ 2191. Replication avoids the problem of sample deterioration in the instrument, but it is destructive in that reaction of the material cannot be continued after the replica has been prepared. Transitory features cannot be detected unless a series of preparations are examined corresponding to increasing progress of the reaction considered. The textures of replicas have been shown [220] to be in satisfactory agreement with those of the original surface as viewed in the scanning electron microscope. The uses and interpretations of observations made through sample replication procedures are illustrated in the studies of decomposition of metal carboxylates by Brown and co-workers [ 97,221-2231. Both heated stages [ 2241 and ambient temperature gas environments [225,226] have been developed for use in electron microscopy and both are combined [ 227,2281 in the controlled atmosphere instrument. Pressures of up to 30 kPa and temperatures up to 1500 K have been used in studies of a wide variety of solid-as and catalytic reactions [ 2291. Robinson [ 2301 has developed a specimen chamber for use in the scanning electron microscope whereby the surface charging of insulators is reduced by a relatively high water vapour pressure (1kPa). Direct observations of the decompositions of a wide range of inorganic compounds [231-2461, which are unstable in the electron beam, particularly azides and silver halides, have provided information concerning the mechanisms of radiolysis: these are often closely related t o the processes which operate during thermal decomposition. Sample temperatures estimated [234] to occur at low beam intensity are up to -470 K while, at higher intensity, 670 K may be attained. Some limitations of optical microscopy were apparent in applying [ 247-2491 the technique to supplement kinetic investigations of the low temperature decomposition of ammonium perchlorate ( AP), a particularly extensively studied solid phase rate process [ 591. The porous residue is opaque. Scanning electron microscopy showed that decomposition was initiated at active sites scattered across surfaces and reaction resulted in the formation of square holes on m-faces and rhombic holes on c-faces. These sites of nucleation were identified [ 2111 as points of intersection of line dislocations with an external boundary face and the kinetic implications of the observed mode of nucleation and growth have been discussed [211].

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8. Diffraction methods X-Ray and electron diffraction measurements have been most usually used to characterize the phases present in any reactant mixture, and provide a means of identification of solid reactants, intermediates and products. In addition to such qualitative analyses, the method can also be used quantitatively, with suitable systems, t o determine the amounts of particular solids present [ 1111, changes in lattice parameters during reaction, topotactical relationships between reactants and products, the presence of finely divided or strained material, crystallographic transformations, etc. Where diffraction methods are used to supplement other studies, it may be sufficient to withdraw material for examination intermittently. When working with samples in an electron microscope, the phases present may be identified at intervals by using the instrument in the diffraction mode. It has been found advantageous in certain systems t o design equipment which allows more continuous monitoring of the structures of the crystals participating in the reaction, Gbrard and co-workers [ 250-2531 have developed an apparatus in which X-ray diffraction studies can be made during water removal from a hydrate in an atmosphere containing a controlled quantity of product, and the extent of reaction ( a ) is determined from the enthalpy change. This use of complementary measurements has been applied in investigations of the changes in structure and orientation relationships [ 2541 which occur during water removal from several hydrates (alkaline earth oxalates, cadmium hydroxide, copper sulphate and others). Direct kinetic measurements from the changes in diffracted beam intensities with time during heating of the reactant are illustrated in the work of Haber e t al. [255]. Garn [126] has reviewed the apparatus used to obtain X-ray diffraction measurements in thermal analysis. Wiedemann [ 2561 has designed equipment capable of giving simultaneous thermogravimetric and X-ray data under high vacuum. X-Ray diffraction studies enable the presence, or absence, of topotactic relationships between reactant and product to be detected [92,102,257-2601. Results are sometimes considered with reference t o the pseudomorphic shape of residual crystallites. The changes in structure during electron-induced decomposition, or during thermal decomposition on a heated stage in an electron microscope can be quantitatively interpreted through consideration of electron diffraction data [ 261-2641. Selected area electron diffraction combined with analyses using “real space crystallography” has been used [ 265,2661 to investigate the electron beam induced decomposition of SnS2.

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9.Surface area measurements Reactions of solids are sometimes accompanied by marked changes in specific surface area [ 47,48,98,99,267-274,1247,12491 and such changes are not always readily apparent unless specifically sought. The development of an internal pore structure, reactant disintegration, product sintering, recrystallization, etc. may provide important indications of the factors which control the decomposition mechanism, and thus reaction rates [ 47,48,98,99,275,1247,1249]. The early stages of many thermal decompositions are characterized by an increase in reactant area, due to the development of an internal porosity, but also as a result of stress-induced disintegration resulting from differences in densities, and thus volumes occupied, by reactant and product [ 48,98,273,275].This tendency to increase the surface area is in the opposite direction to the requirement for a solid to minimize the surface energy through destruction of the pore structure by recrystallization or, more commonly, sintering [ 48,991.Progressive changes in the measured surface area, perhaps supplemented with density determinations, represent the resultant of the opposing disintegration and sintering effects and may be directly related to the kinetics of decomposition [ 98,2751. Most surface area measurements are based on the interpretation of the low temperature equilibrium adsorption of nitrogen or of krypton on the solid using the BET theory [33,269,276-2781. There is an extensive literature devoted to area determinations from gas adsorption data. Estimates of surfaces may also be obtained from electron micrographs, X-ray diffraction line broadening [279]and changes in the catalytic activity of the solid phase [ 2801. The surface area of the product is also dependent upon the atmosphere prevailing during reaction, particularly the availability of water during dehydration processes [ 281-2831 which permits or which facilitates recrystallization. Decomposition of low surface area compounds can provide a route for the preparation of solids of high surface area and high catalytic activity [ 284,2851. It is important to distinguish clearly between the surface area of a decomposing solid [i.e. aggregate external boundaries of both reactant and product(s)] measured by adsorption methods and the effective area of the active reaction interface which, in most systems, is an internal structure. The area of the contact zone is of fundamental significance in kinetic studies since its determination would allow the Arrhenius pre-exponential term to be expressed in dimensions of area-' (as in catalysis). This parameter is, however, inaccessible to direct measurement. Estimates from microscopy cannot identify all those regions which participate in reaction or ascertain the effective roughness factor of observed interfaces. Preferential dissolution of either reactant or product in a suitable solvent prior to area measurement may result in sintering [ 2861.The problems of identify-

29

ing Arrhenius parameters with specific interface processes have been discussed [36]. 10. Spectroscopic methods 10.1 INFRARED SPECTROSCOPY

Infrared (IR) investigations can be made on a sample of reactant previously heated to a known extent of reaction ( a ) and studied in the form of a mull or in an alkali halide disc. An alternative approach is to incorporate the reactant substance in a compact alkali halide disc [ 2871 which is intermittently withdrawn from the reaction vessel for infrared measurements at appropriate intervals. Heated sample holders [ 288,2891 permit repetitive scanning of the spectrum or continuous monitoring of a peak of interest during decomposition. Hisatsune and co-workers [ 290-2991 have made extensive kinetic studies of the decomposition of various ions in alkali halide discs. Widths and frequencies of IR absorption bands are an indication of the extent to which a reactant ion forms a solid solution with the matrix halide. Sodium acetate was much less soluble in KBr than in KI but the activation energy for acetate breakdown in the latter matrix was the larger [ 2971. Shifts in frequency, indicating changes in symmetry, have been reported for oxalate [ 2941 and formate [ 3001 ions dispersed in KBr. The thermal decomposition reactions of KN3, TIN3, and AgN3 have been studied in the corresponding halide matrices [301]. The formation of NCO- from trapped COz was described and labelling with "N established that only a single end-N atom of the azide ion was involved in NCO- formation. The photodecomposition of PbN6 and the effects of dopants have been followed [302] by the changes produced in the near and the far infrared. Most gaseous products, including water [303], are not retained in the disc which, as a consequence of the disruption, may require repressing. Carbon monoxide shows some tendency to undergo disproportionation (to COz and C). Traces of CNO- are often found in heated discs [291]. Where a product is opaque, for example in those reactions which yield a metal, studies are only practicable in the initial stages of decomposition (e.g. to a 0.05 for AgZCO3[288]). Ion exchange [304] and hydration [305] reactions occurring during grinding and storage have also been discussed. The effects of matrix dehydration of BaClz 2 H 2 0 in DSC [ 3061, and reactions of KMn04 and KI04 with matrix material have also been investigated [ 307,3081. Infrared measurements have been complemented with emission (IR) spectra [309], ESR [297] and Raman spectra [310] (providing the material does not decompose in the laser beam [311]). IR measurements can be used in the qualitative characterization of inter-

-

-

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mediates formed during the stepwise dissociation of complex compounds [ 3121. 10.2 MOSSBAUER SPECTROSCOPY

The Mossbauer effect [ 313-3161, i.e. recoil-free nuclear gamma resonance, may be used to provide information (through isomer shift and quadrupole splitting) on changes in oxidation state, site occupancy and symmetry of suitable ions during the course of solid state reactions. Iron ions have been most extensively studied [317-3201, notably as the hexacyanoferrates [321,322]; tin ions have also been used and the method shown to apply to other systems [323]. Gallagher and Schrey [324] obtained the Mossbauer spectra of both europium and iron at stages during the thermal decompositions of EuFe(CN), * 5 H 2 0 and NH4EuFe(CN,) * 4 HzO. Alternatively, the suitable ions may be used as dopants and their behaviour during reactions of the matrix observed. Initial attempts to apply Mossbauer spectroscopy to the study of solid state decompositions, and the experimental techniques required, have been described [ 314-3161. Quenching from reaction temperature [ 3251 has been shown to result in changes in site occupancy, and even in the absence of such effects, the enhanced thermal vibrations at reaction temperatures means that the sites indicated at ambient temperatures can only represent approximations t o conditions of decomposition. Meaningful kinetic data can, however, be obtained if the changes which occur on quenching are reproducible [ 325,3261. Halsey and Pritchard [ 3271 emphasized the necessity for careful control of atmosphere if reliable results are to be obtained. Increased diffusiveness of the Mossbauer peaks is interpreted as indicating a “loosening” of the relevant ion in its site [ 3251. Mossbauer spectra may be complemented by magnetic susceptibility measurements [ 3281. Products of decomposition may be of such small particle size that superparamagnetism is exhibited [ 3291 (e.g. by Fe20, [ 324,3261 where the characteristic six-line spectrum of antiferromagnetic Fe203is replaced by a doublet with an isomeric shift corresponding to Fe3+). Mossbauer spectra may also be used to study radiolytic decompositions [ 3301. 10.3 X-RAY PHOTOELECTRON SPECTROSCOPY (XPS OR ESCA)

The information contained in ESCA (Electron Spectroscopy for Chemical Analysis) spectra [331] makes the method particularly suitable for determinations of surface compositions, chemical bonding of surface atoms and changes which occur at solid surfaces during reaction [ 3121. Applications of this technique to the study of reactions of and between solids are awaited with interest.

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11. Magnetic measurements 11.1 MAGNETIC SUSCEPTIBILITY

Electrobalances suitable for thermogravimetry are readily adapted for measurements of magnetic susceptibility [ 333-3361 by the Faraday method, with or without variable temperature [337] and data processing facilities [ 3381. This approach has been particularly valuable in determinations of the changes in oxidation states which occur during the decompositions of iron, cobalt and chromium oxides and hydroxides [339] and during the formation of ferrites [340]. The method requires higher concentrations of ions than those needed in Mossbauer spectroscopy, but the apparatus, techniques and interpretation of observations are often simpler. 11.2 MAGNETIC RESONANCE

Magnetic resonance techniques, EPR (ESR) and NMR, can be used [341,342] to obtain information about atomic, ionic, molecular and crystallographic states before, during and after solid state reactions. Only a very restricted use has been made of the NMR of solids [ 342-3451. The intensity of the EPR resonance absorption is a measure of the number of paramagnetic centres present [ 3461, while the type of line observed and the measured g factor are indications of the interactions of the paramagnetic particles and of their distribution within the matrix. Such spectra are much more sensitive to changes in crystal field and atomic orientations than X-ray diffraction and are not dependent upon crystallinity [347]. The nature of the paramagnetic particles may be discerned from the superfine structure of the spectrum. The high sensitivity and selectivity of the EPR response enables diamagnetic systems t o be doped with very low concentrations of paramagnetic ions, the fate of which can be followed during the progress of a reaction. The criteria [347] for the use of such tracer ions are that they should give a distinct EPR spectrum, occupy a single coordination site and have the same valency as, and a similar diffusion coefficient to, the host matrix ion. Kinetic data are usually obtained by comparison with standard materials. Particularly successful applications of the EPR technique have been made in studies of the decompositions of dithionates [346,348] and of azides [349,350]. It was shown that rupture of the S-S bond in the dithionate ion yielded ion radicals, * SO;. These species, trapped in a matrix of product sulphate, give strong EPR signals and are only destroyed on calcining t o 900-1000 K. Product prepared at lower temperature accelerates the decomposition of pure dithionate and induces other reactions involving free radicals. The kinetics of production and destruction of radical intermediates at various temperatures have been studied [ 3481. The formation of N; and N; during the radiolysis of azides has been investigated [349].

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12.Electrical measurements Kabanov [351] has provided an excellent review of the application of measurements of electrophysical effects in studies of the thermal decomposition of solids, including surveys of electrical conductivity, photoconductivity, dielectric measurements and interface (contact), Hall and thermal (Seebeck) potentials. Care must be exercised in applying the results obtained in such studies to the interpretation of data for thermal decomposition in the absence of an applied electric field since many examples have been given [ 3521 in which such a field markedly influences the course of decomposition. 12.1 ELECTRICAL CONDUCTIVITY MEASUREMENTS

There have been numerous studies concerned with the measurement of electrical conductivities of solids subject to thermal decomposition. Garner and Haycock [353], working with LiA1H4, provided one of the earliest clear correlations between changes in electrical conductivity and the kinetics of thermal decomposition. The charge carriers were identified as F’-centres and it was suggested that association of such F’-centres along line defects led t o the formation and growth of aluminium nuclei. Other solids which have been investigated in detail include, inter alia, several azides [ 354-3561, NH4C104[ 59,357-3621 and KMn04 [ 3631. Proposed reaction mechanisms have suggested that in many rate processes the nature of the conducting species may change during the course of decomposition. There is evidence [364] that, even in the absence of pyrolysis, the conducting entity may vary with the physical form of the reactant. The temperature dependence of electrical conductivity has been used [ 3651 t o distinguish between the possible structural modifications of the MnOz yielded by the thermal decomposition of KMn04. In studies involving additives, it is possible t o investigate solid-solution formation, since plots of electrical conductivity against concentration of additive have a characteristic V-shape [ 3661. 12.2 OTHER ELECTRICAL MEASUREMENTS

Measurements of photoconductivity and of the Hall potential [ 3671 are accurate and unambiguous methods of detecting electronic conduction in ionic solids. Kabanov [351] emphasizes, however, that the absence of such effects is not conclusive proof t o the contrary. From measurements of thermal potential [368], it is possible to detect solid-solution formation, to distinguish between electronic and positive hole conductivity in semi-conductors and between interstitial and vacancy conductivity in ionic conductors.

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Measurements [ 113,3681 of interfacial (contact) potentials or calculated values of the relative work functions of reactant and of solid decomposition product under conditions expected to apply during pyrolysis have been correlated with rates of reaction by Zakharov et al. [369]. There are reservations about this approach, however, since the magnitudes of work functions of substances have been shown to vary with structure and particle size: especially high values have been reported for amorphous compounds [ 370,3711. Kabanov [351] estimates that the electrical field in the interfacial zone of contact between reactant and decomposition product may be of the order of lo4 lo6 V cm-'. This is sufficient to bring about decomposition. The variations of dielectric constant and of the tangent of the dielectricloss angle with time provide information on the mobility and concentration of charge carriers, the dissociation of defect clusters, the occurrence of phase transitions and the formation of solid solutions. Techniques and the interpretation of results for sodium azide are described by Ellis and Hall [372].

-

12.3 APPLICATION OF ELECTRIC FIELDS

Kabanov and Zingel [ 3521 have recently published a comprehensive review of studies of the effect of application of continuous or periodic electric fields on the reactant during thermal decomposition of a solid. They comment on the superficiality of most of the work discussed. The application of an electric field is contrasted with the effect of selected additives as a means of obtaining information on the mechanism of a decomposition reaction. Both may alter the concentration of free electrons in the solid, but the effect of the field is more apparent in the vicinity of the surface. An example of an investigation of the effect of an electric field on a reaction is to be found in the work of the Panafieu et al. [373] on KN3.

13. Sample preparation and pretreatment The method of preparation of the solid reactant, and the pretreatment it receives prior t o reaction, may profoundly influence its reactivity. Nucleation is often controlled by the area and the perfection of available surfaces, and the sizes and shapes of the constituent particles of a powder exert an obvious control over the rates and geometry of interface development. Where reaction proceeds in a sequence of successive steps, the reactant of each later stage is the product of the preceding reaction and has probably undergone lattice reorganization, with changes in the size, shapes and perfection of the component crystallites. Such changes are of particular significance where dehydration (or loss of other ligand) precedes the

34

reaction of interest. In many instances, product crystallinity is markedly dependent on the prevailing availability of water vapour during dehydration [43,374]. Grinding and other forms of mechanical pretreatment [375], exposure to diverse forms of radiation and ageing of the reactant during storage may all influence the course of subsequent decomposition. Impurities in the reactant may participate in reactions and this can be turned to useful account through the investigation of the effect of specific additives introduced as solid solution (doping) [47] or the presence of separate particles of product [222] or catalyst [120] phase in close proximity to the reactant. Ruzek [376] has discussed problems which arise in the definition of the initial state of the reactant in solid state reactions. 13.1 SAMPLE PREPARATION

For most kinetic studies, sample preparation has been limited t o the crystallization of commercially available material or t o the use of relatively simple methods of synthesis and purification. Reactants used have often been in the form of either large single crystals grown from solution or an assemblage of small crystallites. Growth of crystals t o a suitable size has sometimes been a problem, but the silica gel technique [377,378] has been successfully used to obtain particles of an appropriate size from relatively insoluble precipitates. Alternatively, very small crystals of uniform size may be prepared [118,119] by evaporation of droplets of dilute solutions in vacuum and the collection of the residual crystals on a charged plate. Reactants have also been prepared by freeze drying [ 3793841, where an aqueous solution of the compound is introduced into a stirred, chilled (-193 K) hexane bath. The small frozen spheres of product in ice are screened and freeze dried by sublimation at low pressure. Chain-like aggregates, related to the ice structure formed during freezing, have been observed [ 3791 in the dried compound and any such artefactual structure would influence the kinetics of subsequent reaction. 1 3 . 2 DEHYDRATION

The kinetics and mechanisms of dehydration of crystalline hydrates are considered in Chaps. 4 and 5. It is, however, relevant to mention here that the conditions during dehydration can influence the reactivity of the anhydrous salt (or lower hydrate) formed. Thus, anhydrous solids produced under high vacuum are often amorphous, while those prepared in the presence of appreciable amounts of water vapour may be crystalline [281-283,3741. 13.3 MECHANICAL TREATMENT

Mechanical treatment of samples, ranging from comminution by grinding t o imposition of stresses along defined crystallographic directions in

35

single crystals [385], may increase the number or extent of structural imperfections and hence alter the reactivity. It is also possible that disintegration may destroy sites of greatest local stress (probable sites of preferred nucleation) which may be relieved during crack propagation. Mechanical treatment alone may be sufficient to induce significant decomposition: such processes are termed mechanochemical or tribochemical reactions and the topic has been reviewed [ 385,3861. In some brittle crystalline solids, for example sodium and lead azides [ 3871 , fracture can result in some chemical change of the substance. An extreme case of such behaviour is detonation by impact [232,388]. Fox [389] has provided evidence of a fracture initiation mechanism in the explosions of lead and thallium azide crystals, rather than the participation of a liquid or gas phase intermediate. The processes occurring in solids during the action of powerful shock waves have been reviewed by Dremin and Breusov [ 3901. Compression of powder samples into pellets can also influence the kinetics of decomposition [ 97,391-3931 , mainly through hindering the escape of reaction products. 13.4 IRRADIATION

The energy available in various forms of irradiation (ultraviolet, X-rays, y-rays) may be sufficient to produce in the reactant effects comparable with those which result from mechanical treatment. A continuous exposure of the crystal to radiation of appropriate intensity will result in radiolysis [394] (or photolysis [29]). Shorter exposures can influence the kinetics of subsequent thermal decomposition since the products of the initial reaction can act as nuclei in the pyrolysis process. Irradiation during heating (co-irradiation [ 395,3961) may exert an appreciable effect on rate behaviour. The consequences of pre-irradiation can often be reduced or eliminated by annealing [397]. If it is demonstrated that irradiation can produce or can destroy a particular defect structure (from EPR measurements [398], for example), and if decomposition of pre-irradiated material differs from the behaviour of untreated solid, then it is a reasonable supposition that the defect concerned participates in the normal decomposition mechanism. 13.5 CONTROLLED ADDITION OF IMPURITIES

Doping of solid reactant involves the introduction of a controlled amount of an impurity into solid solution in the host lattice. Such impurities can be selected to cause the generation or destruction of those electronic or structural defects which participate in the rate process of interest. Thus, the influence of the additive on kinetic behaviour can provide evidence concerning the mechanism of reaction [46,47]. Even if the

36

additive results in no change in the numbers of such defects, the diffusion characteristics of those already present may be altered by the presence of the impurities. In addition, the additive may introduce, enhance or reduce catalytic activity of the solid product and may also alter the response of the solid to radiation [ 3991. There have been many instances of examination of the effect of additive product on the initiation of nucleation and growth processes. In early work on the dehydration of crystalline hydrates, reaction was initiated on all surfaces by rubbing with the anhydrous material [ 4001. An interesting application of the opposite effect was used by Franklin and Flanagan [62] t o inhibit reaction at selected crystal faces of uranyl nitrate hexahydrate by coating with an impermeable material. In other reactions, the product does not so readily interact with reactant surfaces, e.g. nickel metal (having oxidized boundaries) does not detectably catalyze the decomposition of nickel formate [ 2221. 14. Influence of atmosphere Solid state reactions have been studied in atmospheres which extend from the residual gases present in high Torr) or ultra-high (
37

lower oxide [ 4081,the presence of oxygen will be particularly significant if the normal product and the oxidized product have a different reactivity for the interface process [ 39,94,409].A reducing atmosphere (hydrogen) accelerates the decomposition of nickel oxalate [ 2861 by removing product surface oxide and so enhancing the activity of the metal at the interface.

15.Experimental methods for studying solidsolid interactions The experimental methods used to investigate solidsolid interactions need not, in principle, be any different from those used to study the thermal decomposition of solids. Those methods, however, which rely on the measurement of parameters related to the loss of gaseous product cannot be applied to those solidsolid reactions where no gas is evolved. The characteristic feature of solidsolid reactions which controls, to some extent, the methods which can be applied t o the investigation of their kinetics, is that the continuation of product formation requires the transportation of one or both reactants to a zone of interaction, perhaps through a coherent barrier layer of the product phase or as a monomolecular layer across surfaces. Since diffusion at phase boundaries may occur at temperatures appreciably below those required for bulk diffusion, the initial step in product formation may be rapidly completed on the attainment of reaction temperature. In such systems, there is no initial delay during nucleation and the initial processes, perhaps involving monomolecular films, are not readily identified. The subsequent growth of the product phase, the main reaction, is thereafter controlled by the diffusion of one or more species through the barrier layer. Microscopic observation is of little value where the phases present cannot be unambiguously identified and X-ray diffraction techniques are more fruitful. More recently, the considerable potential of electron microprobe analyses has been developed and exploited. The properties of barrier layers, oxides in particular, and the kinetic characteristics of diffusioncontrolled reactions have been extensively investigated, notably in the field of metal oxidation [31,38].The concepts developed in these studies are undoubtedly capable of modification and application to kinetic studies of reactions between solids where the rate is determined by reactant diffusion across a barrier layer. Measurements of product gas evolution, mass loss or evolved gas analysis may all be used to study the kinetics of a solidsolid interaction provided that there is strict adherence to the condition that gas evolution occurs concurrently with the solid state process. Clearly this approach is only applicable if there is direct experimental support for a single step process. For example, carbon dioxide release is identified [410]as being

38

concurrent with double oxide formation in the reaction Li2C03 + Fe203= 2 LiFeO, + CO, Isothermal and non-isothermal measurements of enthalpy changes [ 761 (DTA, DSC) offer attractive experimental approaches to the investigation of rate processes which yield no gaseous product. The determination of kinetic data in non-isothermal work is, of course, subject to the reservations inherent in the method (see Chap. 3.6). If the phases present can be unambiguously identified, microscopy can be used to determine the geometry of interface initiation and advance, and to provide information about particle sizes of components of mixed reactants in a powder. Problems of interpretation arise where materials are poorly crystallized and where crystallites are small, opaque, porous or form solid solutions. With the hot-stage microscope, the progress of reactions can be followed in some instances and the occurrence of sintering and/or melting detected. Evidence concerning the identity of the mobile species can be obtained from observation [ 406,411-4131 of the dispositions of product phases and phase boundaries relative to inert and immobile markers implanted at the plane of original contact between reactant surfaces. Movement of the markers themselves is known as the Kirkendall effect [414]. Carter [415] has used pores in the material as markers. Product layer thickness has alternatively been determined by the decrease in intensity of the X-ray fluorescence from a suitable element which occurs in the underlying reactant but not in the intervening product layers [ 4161. Measurements of electrical conductivity permit the identification of the charge-carrying species in the solid phase and also the detection of ionic melts [111,417]. Bradley and Greene [418], for example, could determine the kinetics of reactions between AgI, KI and RbI because the product (K, Rb)Ag41s had a considerably higher conductivity than the reactants. The conductivity of the reactant mixture was proportional t o the thickness of the product layer. Product yields may also be determined by magnetic measurements, as in the formation of ferrites [340], where kinetic data were obtained at reaction temperature. Quantitative applications of Mossbauer spectroscopy have also been described [326]. In favourable systems, selective dissolution of components from reactant-product mixtures, that have been heated for appropriate time intervals, coupled with chemical analyses, have been used t o obtain kinetic data for solidsolid reactions [419]. Thus MgO is the only component which will dissolve in dilute HC1 and, therefore, can be specifically extracted from mixtures reacting as follows

MgO + Cr203= MgCr204

39

Similarly, during the reaction MgO + FezO, = MgFez04 unreacted MgO (again) can be extracted using NH4C1solution. Additional information concerning the mechanisms of solidsolid interactions has been obtained by many diverse experimental approaches, as the following examples testify: adsorptive and catalytic properties of the reactant mixture [ 1,1111, reflectance spectroscopy [420], NMR [421], EPR [ 3471, electromotive force determinations [ 4211, tracer experiments [422], and doping effects [423]. This list cannot be comprehensive. Electron probe microanalysis has also been used as an analytical (rather than a kinetic) tool [ 422,4241 for the determination of distributions of elements within the reactant mixture. Infrared analyses have been used [425] for the investigation of the solid state reactions between NH3 and SOz at low temperatures in the presence and in the absence of water. Infrared, X-ray diffraction, DTA, TG, electrical conductivity and solubility measurements have been used to investigate the mechanisms of tribochemical reactions between solids [ 385,3861. Scanning electron microscopy and replication techniques provide information concerning the outer surfaces of the sample only. Accurate electron microprobe analyses require smooth surfaces. To use these techniques profitably, it is therefore necessary to incorporate these requirements into the experimental design, since the interfaces of interest are often below the external particle boundary. To investigate the zones of interest, two general approaches to sample preparation have been used. (i) The reactant is prepared as two separate crystals, or powder compacts, which are held together at a common, and initially well-defined, interface. After a controlled reaction interval, changes can be measured by the techniques mentioned in samples prepared as polished surfaces cut normally to the initial interface contact plane. The original flat contact surface eliminates difficulties which arise from changing reaction interface geometry, but the contact zone thus generated may be atypical and contain unusually high concentrations of imperfections and impurities. (ii) After reactions in a loose powder, or adherent compact, the particles may be sectioned individually. Changes in sizes, textures, and surface compositions are readily determined. Difficulties are, however, encountered in locating the original boundaries, the relative positions of the exposed surfaces within sectioned particles and thus the geometry of interface advance. The reactivity of individual particles may vary somewhat so that examination of many crystallites may be required to obtain sufficient information to allow a kinetic analysis to be made. The analytical data are, however, also of value in the formulation of the detailed reaction mechanism, and provide information on the identity of intermediates (if any), migrating species, etc.

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41

Chapter 3

Theory of Solid State Reaction Kinetics

Two alternative methods have been used in kinetic investigations of thermal decomposition and, indeed, other reactions of solids: in one, yield-time measurements are made while the reactant is maintained at a constant (known) temperature [28] while, in the second, the sample is subjected to a controlled rising temperature [ 761. Measurements using both techniques have been widely and variously exploited in the determination of kinetic characteristics and parameters. In the more traditional approach, isothermal studies, the maintenance of a precisely constant temperature throughout the reaction period represents an ideal which cannot be achieved in practice, since a finite time is required to heat the material to reaction temperature. Consequently, the initial segment of the a (fractional decomposition)--time plot cannot refer to isothermal conditions, though the effect of such deviation can be minimized by careful design of equipment. The ratedetermining step in any solid phase reaction can be either (i) diffusion, i.e. the transportation of participants to, or from, a zone of preferred reaction, or (ii) a chemical reaction, i.e. one or more bond redistribution steps, generally occurring at a reaction interface. Intermediate behaviour, and transition regions from one type to the other, are also known. It is usually a preliminary part of any investigation to establish the range of conditions under which each alternative applies: in mechanistic studies,,measurements are frequently concerned with rate processes from which the effects of diffusion are specifically excluded. Preliminary work may also determine the influence, on kinetic characteristics, of such variables as the total mass of reactant, including particle sizes, distribution and disposition, the availability of other possible reactants, and the pressure and composition of all volatile substances, including products, in the immediate vicinity of the reactant. The stoichiometry of the overall change, if not already known, should also be established. Characteristic features of a - t i m e curves for reactions of solids are discussed with reference to Fig. 1, a generalized reduced-time plot in which time values have been scaled to to.*= 1.00 when a = 0.5. A is an initial reaction, sometimes associated with the decomposition of impurities or unstable superficial material. B is the induction period, usually regarded as being terminated by the development of stable nuclei (often completed at a low value of a). C is the acceleratory period of growth of such nuclei, perhaps accompanied by further nucleation, and which extends t o the

42

Fig. 1. Generalized a-time plot summarizing characteristic kinetic behaviour observed for isothermal decompositions of solids. There are wide variations in the relative significance of the various stages (distinguished by letter in the diagram). Some stages may be negligible or absent, many reactions of solids are deceleratory throughout. A, initial reaction (often deceleratory); B, induction period; C, acceleratory period; D, point of inflection at maximum rate (in some reactions there is an appreciable period of constant rate); E, deceleratory (or decay) period; and F, completion of reaction.

maximum rate of reaction at D. Thereafter, the continued expansion of nuclei is no longer possible, due to impingement and consumption of reactant and this leads to the deceleratory or decay period, E, which continues until completion of reaction, F. One or more of these features (except D) may be absent or negligible; variations in their relative importance results in the appearance of a wide variety of different types of kinetic behaviour [26,28] in which the maximum reaction rate, D, is achieved at different values of a . In the quantitative analysis of the shapes of a-time curves, it is usually assumed that the isothermal rate of reaction per unit area of interface is constant, so that progressive changes in rate provide a measure of the time-dependent variations in the effective areas of reactant-product contact. In quantitative kinetic analyses, it is sometimes convenient to use data from which the influences of any initial reaction, A, have been subtracted. Increases in reaction rate with temperature are often found t o obey the Arrhenius equation, from which the apparent values of the reaction frequency factor, A , and the activation energy, E, are calculated. The possibility that the kinetic obedience changes with temperature must also be considered. 1. Laws of nucleation 1.1 THE NUCLEUS FORMATION PROCESS

The nucleation process involves conversion of a small volume of reactant into a stable particle of product and continued reaction (growth)

43

occurs preferentially at the interfacial zone of contact between these two phases. Sites of initiation of reaction are widely regarded as occurring exclusively at reactant surfaces and are frequently identified as possessing locally enhanced reactivity. Nucleation necessarily results in destruction of the precursory feature responsible and by the time that a specific nucleus has developed sufficiently to be examined by electron microscopy or optically it has entered the growth phase. Thus discussions of the mechanisms and characteristics of nucleation are largely speculative. Jacobs and Tompkins [28] consider the nucleation process in the general reaction

The first-formed individual atoms (ions or molecules) of B cannot be regarded as a distinct and separate phase but initially, at least, are expected t o tend t o conform to the structure of, and retain their former positions with reference to, the reactant phase A. During the continued accumulation of atoms (ions or molecules) of B, the consequent increase in total deformation strain energy will lead to a transformation to the structure characteristic of the stable product, solid B. This is quantitatively expressed [ 281 as a change in free energy by

AGl = m A G , + uy Where the particle of B contains m molecules, AGB is the bulk free energy change per molecule, u is the shape factor (47rrz for a spherical interface) and y is the strain energy per unit area of interface. For a spherical nucleus, where um is the volume of product per “molecule”,

m = -4nr3 3um and from these two equations AG1 = a m z f 3- bm where a is directly proportional to the strain energy and -b is the bulk free energy change per molecule. Thus, if y is positive, AG1 must pass through a maximum [ 281 at a critical size

and the nucleus attains equilibrium with its surroundings at

When m < m,, product assemblages are unstable and thermodynamic considerations predict that the product (B) will tend t o revert to the reactant unless the local statistical fluctuations of energy are sufficient to achieve

44

the sequence of events required to attain the critical quantity of product in the nucleus and m -,m,. Particles of B which are larger than the critical size are stable and further growth through progression of the reaction interface is permissible. Small nuclei, less than the critical volume ( m < m c ) , are commonly termed germ nuclei, whereas those exceeding this minimum dimension ( m > m , ) have attained the status of growth nuclei. A theoretical treatment, similar t o that given above for spherical nuclei, may be provided for disc-shaped nuclei of only one or two “molecules” thickness ( S x ) on reactant surfaces. For these rr2Sx m=urn

u = 2rr2 + 27rrSx Neglecting the second term in

0,we

find that

AG1 = mAGB + 2murn(6x)-’y =am-bm The form of this expression differs from that for spherical nuclei [ 281 (see above). Here, the equilibrium condition

is at a / b = 1and growth is possible when 2umy

< -AG1

SX

There is, therefore, no critical size requirement for growth, which is solely determined by the a : b ratio. This treatment indicates that the role of critical size is also probably dependent on shape, though there are clearly problems in providing a meaningful representation of topography in assemblages which contain a small number of atoms. Nucleus production may continue after those first formed have advanced into the growth stage, though an established reaction interface is now identified as the zone of greatest reactivity for product generation. If the free energy of activation for the growth process ( A G & is less than that for nucleation ( A G ; ) , then the‘growth of existing product particles will predominate over the formation of new nuclei [ 2 0 1 , 4 2 6 , 4 2 7 ] .If, however, the magnitudes of these parameters are comparable ( A G g + AGfi), reaction will proceed through the production of larger numbers of relatively smaller nuclei. The first condition results in the appearance of atime curves with a strongly developed acceleratory period, whereas this feature is less pronounced when nuclei are more numerous. Since very small nuclei cannot be directly observed, information relating t o the kinetics of nucleation and early growth is normally determined from the detailed shape of the initial segment of the yield-time curve.

45 1.2 LAWS OF NUCLEATION

Several laws of nucleation have been developed [28--311 on the assumption that local fluctuations of energy of the crystal at preferred sites are sufficient t o overcome the barriers t o the production of a stable particle of product. The following kinetic representations have been discussed. (i) Instantaneous nucleation. (ii) Single-step nucleation, giving either (a) the exponential law, or (b) the linear law. (iii) Multi-step nucleation, giving the power law. In principle, there is also the possibility that concurrent reactions, with different kinetics, may proceed at more than one type of site or at different crystal faces. Single-step nucleation, (ii) above, requires the unsatisfactory assumption that the generation of a single molecule (atom, ion-pair, etc.) of product constitutes the establishment of a nucleus. (It would seem to be more realistic to regard this as the outcome of several distinct chemical steps.) The mathematical treatment expressing the probability of the occurrence of this unimolecular process is

k l = v exp(-AGa/RT) = U S l exp(-EJRT) where v is the frequency of lattice vibration and S1 is the term including the entropy of activation (= exp(ASa/R)). Thus the nucleation rate is

dN

-=

dt

k,(N, -N)

where N is the number of nuclei present at time t and No is the total number of potential nucleus forming sites. On integration N = No [l - exp(-kit)] and differentiation gives the Exponential Law o f Nucleation

dN -

dt

= k l N o exp(-klt)

When AGa is large, k is small. The exponential may be expanded, as far as the cubic term, viz.

dN

- = hlNo(l - k l t

dt

+ :kit2 - %k:t3...)

allowing a generalized treatment [74].If k l t << 1,then dN/dt + klNo or N = klNot, the Linear Law of Nucleation. If h l t >> 1, then No + N at small values of t, effectively Instantaneous Nucleation. It is difficult to envisage what is meant by the individual interactions which together constitute the “several steps” required in nucleation under

46

(iii), above. These steps could be either successive processes in the vicinity of a particular site, or the interactions of several mobile energetic participants (excitons, interstitial ions, etc.), while the product species are presumably immobilized. Bagdassarian [ 4 2 8 ] considered the kinetics of steps in which a germ nucleus accommodates p atoms (ions or molecules) of product and, on the attainment of this number, was converted t o a growth nucleus. I t was assumed that the rate coefficients for addition of individual atoms were equal below p

ko = kl = k2

=

... = k,-l

= kl

and above p were again equal, but greater in value, so that

k, = kp+l = kp+2=

... = k ,

and k,

> k1

This leads t o the Power Law of Nucleation

N = kFtP A more general development of this treatment was provided by Allnatt and Jacobs [ 4291. The differential equation which expresses the number of germ nuclei, N i , which have received i atoms is

2

_ _--k i - l N i - l ( t ) - k i N i ( t )

The limiting conditions which apply are

N i = 0 for i

< 0; Ni = 0 for i > 0 for time t = 0;

N i = N o YO] for i = 0 for time t = 0; Ni = 0 for i = 0 for time t =

00.

The above differential equation can be integrated through the use of the Laplace transformation, and, taking due consideration of the limits, this gives

N i ( t )= N o [ O ] k o k l k 2...

(5 z=o

exp(-kz t ) i

If k i t << 1,the simplifications which result are for one step:

N l ( t )= N o [ O ] k o t= K l t

for two steps: N z ( t )= N o [ O ] k o k l t = z KztZ for 0 steps:

N p ( t )= N o [ O ] k o... kptP= K p t pand cWp/dt = Ktp-’

These are Power Laws of Nucleation.

47

Barrett [ 311 has summarized the laws of nucleation as follows. (1)Nucleus formation in a single stage. (a) Random nucleation among N o pre-existing sites

N = No[l - exp(-k,t)] (b) Instantaneous nucleation: N = N o (c) Slow nucleation ( h , t << 1):N = h,No t (2) Multiple step nucleus formation. (a) k,t << 1:then Np = Nokptp (b) and (c) kpt 1or <<1:expressions are complicated (see Barrett [31]). Kinetic measurements for the nucleation process in, inter alia, the dehydration of alums and other sulphates and in the decompositions of azides have provided experimental evidence [ 28,64,65,201,400,426,427, 4301 for the operation of the above rate laws. More references are to be found in the systematic literature survey given below in Chap. 4. The production and distribution of nuclei may be influenced by surface damage [64], reactant irradiation [45], the presence of water vapour [431] (i.e., product), sublimation of a metallic product [97] and a variety of other factors which must be eliminated or controlled if meaningful kinetic data are to be obtained. From a microscopic study of the surface textural changes prior to, during and following the appearance of dehydration nuclei on certain alums, Galwey and Guarini [ 12501 conclude that surface stress deformation may be an important factor in the production and development of nuclei. On freshly cleaved and partially dehydrated surfaces of KA1(S04)z 12 HzO and KAlo~49Cr0~5,(S04)z * 1 2 HzO, such textural modifications in the vicinity of germ and growth nuclei were attributable to the development of strain, later followed by cracking. The significant result is that reactant distortion, preceding and later associated with nucleation in these alums, is visible microscopically. Such co-operative superficial movements, involving a crystal boundary thickness of perhaps 1pm, is on a scale which contrasts with the events involving a small number of ions that provides the basis for the theories of nucleation described above. Clearly, more observational data are required to investigate fully the role and significance of strain in nucleus generation.

+

2. Laws of growth

If, as is generally assumed, the rate of linear advance of the reactantproduct interface is constant, the radius, r, at time t , of a nucleus generated at time t,, is

r = k , ( t - t,) This behaviour has been identified from microscopic measurements for growth of nuclei during the dehydration of crystalline hydrates [ 4311, the

48

decomposition of BaN6 [ 2011 and diverse other solid phase reactions. I t is generally believed that for many systems there is a period of initial growth relatively slower than that ultimately achieved [ 28,51,430]. Appropriate allowance for this effect can be incorporated into rate equations by assuming [28,430] the initial linear growth rate, k : , is smaller than that measured later ( k : < k r ) . The assumption that the rate of radius increase is constant can be regarded as a satisfactory simplification for certain types of more complicated behaviour. The possibility that it is an approximation should, however, be remembered in estimating volumes of product where grwoth rates vary with crystallographic direction. In many reactions, the nuclei exhibit characteristic shapes, e.g. hexagonal [432] in the dehydration of KHC204* f HzO, “horn-shaped” in the dehydration [426] of CuS04 5 H 2 0 and others in the dehydrations of various alums [431]. Hemispherical nuclei, indicative of equal rates of growth in all directions, are found in the decomposition of barium azide [ 2011 and the dehydration of chrome alum [427]. An additional possibility is that growth proceeds preferentially across surfaces, followed by relatively slower penetration of the interface into the bulk of crystallites, as in the decomposition of nickel formate [375]. In this particular instance, the interface is apparently incoherent since the dense metallic product does not occupy the volume of reactant from which it was derived but remains as individual and separated particles [ 4331. For many compounds, direct observational data concerning nucleus development (sizes, shapes, etc.) are not available, since one (or two) dimensions of the thin disc or filamentous product particles are below the limits of identification, or there is irregular distribution of reaction sites due to crack propagation and breakdown of intergranular material. The kinetic analyses of these systems are made on the assumption that the controlling features of the behaviour are comparable with those reactions for which observational information is available. In general, it is assumed that dr/dt is constant (here r represents a linear dimension) and this may be supplemented by a term to allow for branching of nuclei, where such nuclei have the thickness of one, or a small number, of lattice units. A branching process can be regarded as an alternative mechanism of nucleation and may be incorporated in this term (i.e. dN/dt) in the development of rate equations. The account of the formal derivation of kinetic expressions for the reactions of solids given in Sect. 3 first discusses those types of behaviour which usually generate three-dimensional nuclei. Such product particles may often be directly observed. Quantitative measurements of rates of nucleation and growth may even be possible, thus providing valuable supplementary evidence for the analysis of kinetic data. Thereafter, attention is directed to expressions based on the existence of diffuse nuclei or involving diffusion control; such nuclei are not susceptible to quantitative

49

measurement by microscopic techniques. While this division is somewhat arbitrary, it does allow the argument to progress from systems possessing the most complete experimental basis for theoretical interpretation, to those which have been less comprehensively characterized. Following a common practice in the literature, significant rate expressions will be referred to by names which have become accepted through common usage: these may be descriptive (power law, etc.) or recall the names of workers who contributed towards their development (the Avrami-Erofe’ev equation, etc.). Examples of systems obeying each expression are restricted in the present section since the applications are exemplified more generally in the literature surveys which constitute Chaps. 4 and 5.

3. Formal theories of isothermal solid state decompositions The systematic treatment of interface advance reactions given by Jacobs and Tompkins [28] remains a valuable survey of the kinetics of solid phase decompositions. A later account was given by Young [29]. Greater mathematical emphasis is to be found in the books by Delmon [30] and by Barret [31]. 3.1 KINETIC EXPRESSIONS DERIVED FOR INTERFACE ADVANCE REACTIONS

Rate equations of the form f(a) = ht are derived through integrations of specific forms of the generalized expression [ 281 representing the summation of the growth of all nuclei, so that the volume of product at time t, V ( t ) ,is given by

This may (at least in principle) be integrated for any combination of a law of nucleation [the (cUV/dt) term] and a law of growth. A nucleus formed at time ti occupies a volume V(t,ti) at time t and

v(t,t j ) = o[r(t,t,)lA where X is the number of dimensions in which the nucleus grows (1, 2 or 3), u is a shape factor (e.g. 47r/3for a spherical nucleus) and t

r(t, ti) = J F(t) d t 9 where F(t) is the growth law. This is often a constant but may be different in the early stages (slow growth of germ nuclei). Those special cases of integration of eq. (l), which have found the most widespread application in the development of rate equations for reactions of solids, are discussed below.

50

3.1.1 Nucleation obeying a power law with constant rate of interface advance (normal growth) Nucleation and growth expressions for substitution in eq. (1)take the forms

n

Since V ( t )is directly proportional to a a = Ck$k&tfl+k= (kt)"

where C is a constant of proportionality and p + X = n. This is usually termed the power law. Many instances of the application of eq. (2) have been reported [434,435]; often, values of n are in the range 2-4 and the higher values (6-8) reported for the decomposition of barium azide [201, 4301 remain a matter for continued discussion (see Chap. 4). If the initial rate of growth of nuclei is slower than the constant value subsequently attained, the above expression remains applicable [ 281 provided that appropriate subtraction from the measured time is included, viz. a = k"(t-to)"

3.1.2 Random nucleation according to the exponential law followed by normal growth Here W / d t = kNNo eXp(-kNt) and V(t, t j ) = (T[kG(t- ti)]*and eq. (1) is integrated [ 281 to give, when X = 3 (3) On expanding the exponential term it is found [28], when kNt is s m d so that terms in ( k N t ) 5and above may be neglected, that

equivalent t o a form of the power law with n = 4, appropriate to the case

51

for p = 1 and = 3. Under the alternative approximation, where kNt is large, the cubic term is dominant, yielding the power law with n = 3. In such a reaction, nucleation is either rapidly completed or instantaneous (kN large), = 0 and h = 3 for three-dimensional growth. 3.1.3 Impingement and coalescence of developed nuclei and ingestion of undeveloped nucleation sites The power law, eqn. (2), is acceleratory for all values of n > 1 but clearly it is unrealistic to suppose that a nucleation and growth process, occurring in crystals of finite size, is capable of maintaining a continuous increase in reaction rate up to (Y = 1.00. Rate-time curves for chemical changes in many solids characteristically exhibit a maximum value (often attained between 0.3 < (Y < 0.8), after which the rate of product evolution diminishes and any kinetic expression applicable to the greater part of the overall process must include due consideration of the deceleratory (decay) period. Two factors are identified as exerting a restriction upon nucleus development, by acting in opposition to continued expansion, and thereby curtailing the acceleratory process: these are nucleus coalescence and ingestion. (i) Coalescence refers to the loss of interface which occurs when the active reaction zones of two or more growing nuclei meet. This is sometimes described as “overlap of nuclei”, by reference to their projected shape, in the absence of interference. The limits to growth of individual nuclei are set by their spacing. (ii) Ingestion refers to the elimination of a site, at which another nucleus could otherwise have developed, by the growth of an existing nucleus. Potential nucleation sites which never develop as independent nuclei are sometimes referred to as “phantom” nuclei, since their growth (imagined in the theoretical treatment) yields no real product. During reaction, the number of potential nuclei-forming sites present at time t, Nl(t), progressively diminishes from the initial value No, at t = 0, as N(t) of them form existing nuclei and N,(t) are eliminated by ingestion (i.e. converted t o phantom nuclei). Now No = N(t) + N,(t) + N,(t)

so that

-cw1 = cw + c w z Substituting cW=kNNl d t and d N 2 = [N1/(1-(~)]da and integrating, the nucleation law is [ 281

cw

-=

dt

kNNo exp(-k,t)

(1- ( Y )

(In a more general analysis, Allnatt and Jacobs [429] have removed the

52

restriction of the single-step nucleation in the Avrami treatment.) This can be substituted into the generalized rate equation, eqn. (l), but direct integration of the resulting expression is not possible for many cases of particular interest, including the growth of three-dimensional nuclei. Accordingly, the theoretical treatment then proceeds [ 281 by considering the extent of reaction which would have occurred if the two effects introduced under this heading (i.e. nucleus overlap and site ingestion) had caused no limitation to the quantity of product formed. The problem is then changed to the provision of a relationship between this so-called “extended” (i.e. notional) fractional decomposition, a E (including the growth of phantom nuclei and excluding losses from impingement) and the actual amount which occurs in the real reaction. A general but complicated solution to the resulting form of eqn. (1)is available [28] for the case in which growth involves the development of compact nuclei, but the formulae obtained are unwieldy. An important simplification can be made where there is three-dimensional growth of randomly distributed nuclei on large crystals: for this situation, Avrami [ 4361 has shown that do - 1 - a -dQE and

(4) where C is a constant. There is a close similarity between the form of this expression and eqn. (3). At low a, the effects of overlap and ingestion may be neglected and -ln(l - a) may be replaced by a , which is directly proportional t o V ( t ) in eqn. (3). When a (and t ) is large, the rate process becomes deceleratory and the expression applicable is -ln(l - a ) = k( kGt)3 which was also obtained by Erofe’ev [ 4371 by a different approach (incorporating contributions by Kholmogrov and Bel’kevich (see also refs. 438 and 439). It should be pointed out that Avrami’s contribution (unlike that of Erofe’ev) was particularly concerned with the nucleation process in phase transformations and few comments have been made concerning the applicability of the approach t o solid state decompositions [ 701. In contrast, Erofe’ev’s analysis is claimed to be applicable to both homogeneous and heterogeneous rate processes. Erofe’ev formulated a general expression from which both known and new rate equations may be developed without the requirement for setting up differential equations based on the law of mass action. The starting point in Erofe’ev’s [437] treatment is the degenerate q:,

53

which is the probability of an elementary event, such that the ith molecule of the component of the reaction does not react in the Kth time interval when 0 = to <

tl

< t z < ... t K - 1 < t K < ... < t n = t

Then, the probability of a complex event, Q i , that the ith molecule does not react in any of the above time intervals is K=n

If Pi is the probability that the ith molecule reacts by time t and p : is the probability that the ith molecule reacts in the Kth time interval, then

Pi=l-Qi

and

p:=l-qK

Taking logarithms and summing to the limit n = m

c ln(1 -P r ) -s Pi dt t

K=n

ln(1 - P i ) = lim

=

n-+m K = l

0

Summing over all possible values of i and normalizing (X N - ' ) for the N molecules of the component under consideration which are present at t = 0 gives N

li=N 1 -Cln(l-Pi)=----C sPidl N i=l 0 N i=l Since values of Pi for various molecules of the same component may differ by only infinitely small amounts for finite time intervals

-1c Pi) N i=l

-s( c t

i=N

1

=

i=N

N

i=l

Pi) d t

0

But i = N and

where P is the mean probability that an individual molecule will react by the time t ( P ) ,and

dt = p dt ( NL ii=sl p i ) is the mean probability that an individual molecule will react in the time

54

interval between t and t + dt(p dt). From these expressions it follows that t

P = 1- exp(-J

p dt) 0

When N is large, P may be identified as the fraction of reaction, a ;thus t

a = 1- exp(-J

p dt)

(5)

0

This is the generalized kinetic expression in which Erofe'ev has made no assumptions regarding special properties of the reacting system. The significance of this conclusion would appear t o have been insufficiently appreciated outside the U.S.S.R. The rate of reaction is given by -da = p e x p ( - J p dt t ) = p ( l dt 0

-a)

For an isothermal unimolecular reaction, p = K = constant, so that a = l-exp(Kt) For a bimolecular process between reactants A and B (initial concentrations a and b, respectively), the probability of reaction of an individual molecule of A is

K

p = -( b - a a )

V

Substituting this in eqn. (5), we find aA = 1- exp In

1

I

K a - bV If p = Ky( 1- a)-', where y is a constant representing, say, the quantity of an adsorbed species, then a - b exp -(b - a ) t

a = 1- exp ln(1- K y t ) = Kyt

In solid state reactions, the rate of nucleation may be given by either of the expressions m / d t = const. or W / d t = t' const. For both expressions, the probability (pdt) is proportional to the total volume of the spherical layers at the instant t at the peripheries of nuclei which originated at time T . The radii of the spheres at the inner and outer boundaries of these layers are

r =k,(t-~)

55

and r + dr = h,(t + dt--) Thus t

p dt = dt

J 4nk:(t

dlv

-T ) ~ dT

0

dt

Identifying p with a and substituting the two nucleation laws mentioned above, we obtain the expressions a = 1- exp(-Kt4)

(cW/dt = const.)

and cy =

1- e ~ p ( - K t ~ + ~ ) (dN/dt = t" const.)

Where reaction proceeds through the development of cylindrical nuclei, initiated at edges or surface cracks in the reactant solid, the expression is a = 1- exp(-Kt3)

and for flat nuclei a = 1- exp(-Kt2)

The Erofe'ev treatment, therefore, yields the rate equation -ln(l

-a ) =

Kt"

(6)

which is more general that the Avrami treatment with n = 3. In a further development of the probability treatment used by Erofe'ev, Kolar-Anid et al: [440,441] and Dorko et al. [442] have pointed out that the general function has the same form as the Weibull distribution [443, 4441

F(t) = l-exp[-(t--)/q]P where p = n and K = q-' and q, /3 and y are the scale, shape and location factors of the distribution, respectively. Three ranges of values of n were considered, >1,0.7-1.0 and <0.7. When n > 1 , and particularly when 3 < n < 4, the Weibull distribution readily reduces to a normal distribution if the Erofe'ev function is symmetrical about a = 0.5. [The Weibull distribution is symmetrical for n = 3.26, i.e. (1- In 2)-', and the inflection point varies only slowly with n.] Thus, under these conditions (3 < n < 4 and symmetry about a = 0.5), we may derive the parameters of the corresponding normal distribution (where p defines the half-life of the reaction and the dispersion parameter, u, is a measure of the lack of homogeneity of the surface centres), viz. p = (0.693/b)lln

56

u = (1.841/b)”” - p = (1.148/b)”“

b and n can then be determined from the plot of In[-ln(1 -- a ) ] against In t since

In[-ln(1 -a)] = n In t + In b

When n < 0.7, the In[-ln(1 -a)] against In t plots show curvature and linearity is improved if the latter parameter is replaced by t . This reduces the Weibull distribution to a log-normal distribution. Since both exponential and normal distributions are special cases of the more general gamma distribution, Kolar-Anid and Veljkovid [ 4411 compared the applicability of the Weibull and the gamma distributions. The shape parameter of the latter ( E ) was shown to depend exclusively on the shape parameter of the former (n). For 0.7 < n < 1, a normal distribution is obeyed indirectly, based on t’” via the gamma distribution with a shape parameter E = i. These various distributions reflect the variations in reactivity of the reacting sites. Johnson and Kotz [444] discuss in detail the Weibull and other distributions which find application when conditions of strict randomness of the exponential distribution are not satisfied. From an empirical point of view, the power transformation is a practical and convenient method of introducing a degree of flexibility into a model. Gittus [445] has discussed some situations in which the Weibull distribution may be expected t o find application, including nucleation and growth processes in alloy transformations. Dorko et al. [442] have used the Weibull distribution function for the consideration of reactions in which decomposition is accompanied by melting. Following a procedure described by Kao [446], they used a mixed Weibull function, written as a linear combination of separate functions, viz. with 0 < p < 1 F(t) = p F l ( t ) + (1-p)Fz(t) where p is a constant determined by experiment. Using this approach, it was found possible to determine the separate solid phase and liquid phase contributions to the overall decomposition. Taplin [1251], questioning the value of the approach developed by Kolar-Anid et al. [440,441], points out that no connection is established between the equations and the distribution of energy or of reactivity in the system. In consequence, their proposal must be regarded as a method of generating empirical rate equations and the demonstration of mere obedience t o such a relation adds little to our understanding of the processes concerned. Taplin concludes, therefore, that a more profitable method of interpreting kinetic results is t o obtain an improved description of the reaction geometry by independent measurements and t o give geometric parameters (including energy and reactivity) appropriate statistical distributions in space or time.

51

Yet another approach to the derivation of equations of the form of eqn. (6) has been given by Mampel [447]. The formation of nuclei which grow in two dimensions on a surface is regarded as comparable with random placement of circular discs, area rk&(t- t j ) * ,on a planar surface. The fraction of surface unoccupied by such discs is equated with (1- a). Discs which overlap represent nuclei which have impinged and coalesced during growth, while small discs entirely within the boundaries of a larger disc are phantom nuclei. The fraction of surface uncovered at time t is given by

(1- a ) = exp(-kNNok?,rt3/3) Mampel extended the treatment to include due allowance for three-dimensional growth of product into the particles by considering the latter to consist of a series of concentric thin spherical shells. The fractional reaction within each such shell was calculated and the total reaction found by integration to include all such shells. This analysis, which includes the effects of overlap, ingestion and also particle size of the reactant, is not amenable to general solution, but the following special cases are of interest. (i) When a is small, a = kt4 (a form of the power law). (ii) When the reactant particles are small, there is effectively a single nucleus generated on each crystallite and In(1-a) = C - k t where C and k are constants. (iii) When reactant particles are large, the form of the equation resembles the contracting volume relation (to be discussed below). The several distinct derivations of eqn. (6) originally provided [30] by Avrami [ 4361, by Erofe'ev [ 437,4481 and by Mampel [ 4471 and developed by others, is a consequence of the importance t o be attached t o this expression for the kinetic analysis of solid phase reactions. Written in general form

(6) it is often referred to as the Avrami-Erofe'ev (A-E) equation. This expression is found t o hold over the greater part (-0.05 < OL < 0.9) of many solid phase decompositions (examples are given in Chaps. 4 and 5 ) , phase transformations and recrystallizations of alloys [ 61 and, in modified form, may be applicable to reactions between solids [ 771. The exponent n = + h, where p is the number of steps involved in nucleus formation (frequently p = 1 or 0, the latter corresponding to instantaneous nucleation) and h is the number of dimensions in which the nuclei grow (A = 3 for spheres or hemispheres, 2 for discs or cylinders and 1 for linear development). Most frequently, it is found that 2 < n < 4. Since n is a compound term, the value determined does not necessarily provide a unique measurement of both 0 and h. Ambiguity may arise where, for example, n = 3 could be a consequence of (0 = 2, h = l),( p = 1, [-ln(l-a)]l'"

=k(t-t

0)

58

X = 2) or (0= 0, X = 3) and the distinction between these possibilities is most satisfactorily based upon independent evidence, such as microscopic observations. The growth of compact nuclei inevitably results in the consumption of surfaces and when these outer faces, the sites of nucleation, have been eliminated, 0 necessarily is zero: this may result in a diminution of n. The continued inward advance of the reaction interface at high a results in a situation comparable with the contracting volume reaction (discussed below): reference to this similarity was also made in consideration of the Mampel approach discussed above. Shapes of the deceleratory region of a-time curves for nucleation and growth reactions and the contracting volume rate process are closely similar [ 4091. Although it would appear that plots of In[-ln( 1- a ) ] against In(t - t o ) provide the most direct method for the determination of n from experimental a-time data, in practice this approach is notoriously insensitive and errors in to exert an important control over the apparent magnitude of n. An alternative possibility is to compare linearity of plots of [-In( 1- a ) ]'In against t : this has been successful in the kinetic analysis of the decomposition of ammonium perchlorate [ 2681. Another possibility is through the use of the differential form of eqn. (6)

which can be written in the approximate form

and with increasing values of n, the magnitudes of a and b increase and decrease in value, respectively [ 291. It is not possible to include the effect of particle size on kinetic behaviour in the general equation (1) without complicating the integration required. Some aspects of the influence of this variable are considered in the Mampel development of eqn. (6) and features of the effect of crystallite dimensions on rate behaviour emerge from the following very qualitative consideration of the consequences of a progressive particle size reduction for a reaction proceeding by a nucleation and growth process. Nucleus development in large crystals is an acceleratory process and the maximum slope of the a-time curve is expected t o increase as the reactant is subdivided, since a larger number of nuclei can be formed on the greater surface available per unit weight of solid. With further reduction in crystallite size, however, the volume of product which is formed as a consequence of each relatively difficult nucleation step is restricted to the volume of the particle nucleated. When crystallite dimensions are sufficiently small, the rate of reaction is controlled by nucleation in an assemblage of identical reactant fragments, and the first-order expression [eqn. (6) with n = 1, deceleratory] is obeyed: this model was mentioned above as a special case

59

of the Mampel treatment. For this system of random nucleation on a large number of small crystallites da _ - k(1-a) dt

and -ln(l-a)

=

kt

Such behaviour may occur in the final stages of solid phase decomposition reactions [ 449-4511. The Avrami-Erofe'ev equation, eqn. (6), has been successfully used in kinetic analyses of many solid phase decomposition reactions; examples are given in Chaps. 4 and 5. For no substance, however, has this expression been more comprehensively applied than in the decomposition of ammonium perchlorate. The value of n for the low temperature reaction of large crystals [268] is reduced at a 0.2 from 4 to 3, corresponding to the completion of nucleation. More recently, the same rate process has been the subject of a particularly detailed and rigorous re-analysis by Jacobs and Ng [ 4521 who used a computer to optimize curve fitting. The main reaction (0.01 < a < 1.0) was well described by the exact Avrami equation, eqn. (4), and kinetic interpretation also included an examination of the rates of development and of multiplication of nuclei during the induction period (a < 0.01). The complete kinetic expressions required to describe quantitatively the overall reaction required a total of ten parameters.

-

3.1.4 Rapid and dense nucleation, or initial rapid surface growth, followed by advance of interface from all, or certain specific, surfaces into the bulk o f crystallites When the initiation of reaction involves the development of a large number of closely spaced nuclei on all surfaces or, alternatively, on specific crystallographic surfaces, the kinetic characteristics of the overall rate process are determined by the geometry of advance of the reaction interface from these boundaries in the direction of the centres of the particles This type of behaviour can occur where concerned [28-31,453-4571. either (i) the free energy for nucleus formation is comparable with that of subsequent growth (AGE AG;) or, alternatively, (ii) the development of nuclei is anisotropic, whereby there is initial rapid and preferential advance of the reaction interface across the surfaces separating the points of independent initiation of reaction [ 4331 (abnormal surface growth). The induction period, if any, may be too short to permit detection, and the maximum reaction rate is attained at low a. Thereafter, the a-time curve is deceleratory. There is, however, no sharp distinction between such kinetic behaviour and the later stages of nucleation and growth pro-

+

60

cesses of the type discussed in the previous section. Indeed, in some early work by Garner and Tanner [400], the influence of a slow nucleation and an acceleratory period was removed by artificial initiation of reaction on all surfaces so that the kinetic analysis was simplified to the consideration of aprocess advancing at all faces of a crystal of known size and geometry.

( a ) Nucleation o n all faces If reaction occurs equally at all faces of a cube [ 28,291 of edge a , then, after time t , the volume of reactant remaining is a cube of edge ( a - 2kGt), thus ,3 - ( a - 2kGt)3 a= a3 and 1 - (1 - a)1/3 = k t (7) ( n = 3) This is often referred to as the contracting volume (cube or sphere) equation and is the simplest example of a more general family of expressions [ 28-31,432,453,458,4591, which includes consideration of different rates of interface advance in different crystallographic directions and of variations in crystallite dimensions and shapes. The approach is readily extended, by use of solid geometry, to allow for angles between planar surfaces. Some examples of characteristic behaviour are conveniently discussed with reference to the expression a = UbC - ( a - 2k,t)(b - 2kbt)(C- 2k,t)

abc which refers to reaction in a rectangular particle of edge dimensions a, b and c , into which the rates of interface advance are ha, k b and k,, respectively. Appropriate modification can be made where crystal face intersections are not right angles. When a b >> c and k, = k b = k,, the diminution in dimensions of the particle of unreacted solid is small in the a (>> h a t ) and b (>> k b t ) directions, so that the reaction is zero order, a (2k,/c)t. The rate process in the thin disc or plate-like particle is effectively constant, da/dt = k, since the rate of interface advance into the minimum dimension is constant and the influence of the contraction at the edges is small [460]. Similar consideration of a reaction readily initiated at all surfaces of a cylinder or column-shaped prism of reactant ( a >> b i c and k, = k b = h,) shows that

+

+

1-(1-a)”2=kt ( n = 2) (7) Rate equations expressing the a - t i m e variations resulting from the inward advance of a reaction interface from the existing surfaces of other reactant shapes follow directly by the application of simple geometric considerations. The approach can also include quantitative allowance for any

61

assumed particle size distribution using a summation technique. Approximate or limited kinetic relations can also be derived for more complex systems, e.g. development of cylindrical zones of product following reaction initiated at internal pore systems. In Mampel’s treatment [ 4471 of nucleation and growth reactions, eqn. ( 7 , n = 3) was found to be applicable t o intermediate ranges of a, sometimes preceded by power law obedience and followed by a period of firstorder behaviour. Transitions from obedience of one kinetic relation to another have been reported in the literature [ 409,458,4591. Equation (7, n = 3) is close to zero order in the early stages but becomes more strongly deceleratory when a > 0.5.

( b ) Nucleation restricted to specific crystallographic surfaces When reaction is absent from certain crystallographic surfaces, the formulation of rate equations based on geometric considerations proceeds exactly as outlined above, but includes only the advance of interfaces into the bulk of the reactant particle from those crystallographic surfaces upon which the coherent reactant/product contact is initially established. When reaction occurs only at the edges of a disc or plate-like particle

1 - (1 - LY)l’Z = ht

(7) ( n = 2) This is known as the contracting area (disc, cylinder or rectangle) equation and had found particular application in studies of the dehydrations of certain substances containing layer-type lattices. In these compounds, the water escapes from between the layers and the interface does not advance in directions perpendicular to these layers. Rate equations, which include due allowance for the angles between the active crystallographic faces, have been shown to describe measured a-time data satisfactorily [212, 2131. The kinetic changes which result from the prevention of water loss from selected crystal surfaces, by covering them with a water-impermeable resin, have been studied [62,213]. In one such investigation [213], the rate of dehydration of a treated crystal was very nearly constant when OL < 0.5, in accordance with expectation for onedimensional growth. The advancing interface reaction can be generally expressed as 1 - (1 - a ) l ’ n = ht

(7) where n is the number of dimensions in which the interface advances. In the contracting volume equation, n = 3; for the contracting area equation, n = 2; and, when there is linear advance of the interface in a single direction, n = 1 and zero-order kinetics are found. Zero-order kinetic behaviour, in an unusual dehydration reaction [ 621, has been shown to be due to the constant area of reaction interface and this interface has been identified as original surfaces of the reactant crystallites which do not advance. Water molecules are mobile within the

62

reactant structure and the desorption step at the immobile interface is rate-limi ting.

3.1.5 Other models f o r nucleation and growth of compact nuclei Models involving the growth of compact nuclei, following instantaneous, or during maintained, nucleation and including consideration of the effects of variations of crystallite shapes and sizes, have provided the theoretical foundation for that group of rate equations which have found the most widespread application in the kinetic analyses of solid-state decomposition. Alternative assumptions, on which the formulation of kinetic expressions may be based, include additional laws of nucleation (including autocatalytic behaviour), specified controls or restrictions on the spatial distribution of nuclei, the effects of particle size variations (which have already been mentioned) and the influences of particle sizes and shapes on reactions involving rapid but random nucleation but without subsequent abnormal surface growth. The kinetic expressions derived, assuming operation of specific features of these varied controls, cannot usually be represented simply by an equation of the form f(a) = k t , and this must be allowed for in analyses of rate measurements. Most decompositions yield smooth a-time curves and the theoretical equations proposed to account for such behaviour are obviously of generally similar form, so that the distinction between possible models rests upon detailed comparisons of shapes. Accurate experimental data are required to decide which of several curves provides the best description of a given set of a-time measurements, a problem which is discussed at greater length in Sect. 4. The introduction of one or more additional constants into any rate equation must, in general, increase the flexibility of the expression, i.e. its ability to fit different a-time curves, and consequently decrease the reliability of conclusions based on the kinetic obedience alone. A similar decrease in the reliability of kinetic testing and curve fitting occurs where a series of different expressions are shown to be applicable in a series of successive a ranges. If, however, the significant features of the assumed behaviour can be characterized and measured independently (e.g. by microscopy), then obedience to a particular rate equation (perhaps complicated but containing additional and independently determined rate parameters) is a valuable, indeed necessary, component of any kinetic investigation. Early observations of solid state decomposition reactions were often made with large crystals which yielded easily recognized nuclei, and the measurements made supported the model rate equations developed. Much subsequent work has been concerned with less readily observed changes and the kinetic analysis has frequently relied on the best fit to an expression containing but a single rate coefficient, f(a) = k t (though k may be a compound term, including k N and k G ) . The incorporation of additional or alternative assumptions into the for-

63

mulation of rate equations is illustrated here by reference to the following examples (which are discussed at greater length in ref. 28). These models are not intended to encompass all other imaginable possibilities.

( a ) Rapid and random nucleation without abnormal surface growth Topley and Hume [453], in a study of the dehydration of CaC03 * 6 H20,assumed the rapid initial formation of (on average) a single nucleus on the surface of each particle of reactant, represented as a sphere of radius a . In the absence of preferential surface development, the reaction interface penetrates the reactant at equal rates in all inward directions (kG = dr/dt) and the volume of material reacted at time t is that volume of a sphere, having its centre at the site of surface nucleation and of radius kGt, which falls within the reactant. The fractional reaction, the zone of interpenetrating spheres, at time t is

The sigmoid a-time curve passes through a maximum at a = 16/27 (= 0.593). The assumption that there is a single nucleus per crystallite may be unrealistic for the reaction of CaC03 6 H 2 0 since the expression was applicable only within a restricted range (0.3 < a < 0.7).

-

( b ) Continued nucleation, obeying the exponential law, followed by rapid surface growth Nucleation at N o potential sites is a continuing process expressed by the exponential law

dN

- = kNNoexp(-kNt)

dt

From the various possible geometric shapes of reactant crystallites, discussioy here will be restricted to a consideration of reaction proceeding in rectangular plates Bnd in spheres [ 281. A complication in the quantitative treatment of such rate processes is that reaction in those crystallites which were nucleated first may be completed before other particles have been nucleated. Due allowance for this termination of interface advance, resulting from the finite size of reactant fragments accompanied by slow nucleation, is incorporated into the geometric analysis below. (i) Rectangular plates. During reaction of rectangular plates nucleated on the larger surfaces only (dimensions a and b , and thickness, the smallest dimension, c ) , the volume of product at time t , following nucleation at time t j , is

V ( t , t i ) = 2 a b k G ( t- t i )

64

substituting these expressions into eqn. (1)and integrating [454] gives

This equation ceases to be applicable when tl > c/2kG since nuclei generated at t = 0 will then have penetrated the reactant particle. It is, therefore, necessary to make a subtraction from this equation to allow for interface removal resulting from the consumption of first-nucleated particles. At time t z ( > C / 2 k ~ (k’ ) =2k~/k~C [28] ) a = 1+ k’(1 - exp k’) exp(-kNt2)

or ln(1 - a) = -ln{k’(l

- exp

k’)} - kNt

Linear plots of ln(1 - a ) against t were obtained [454] for the removal of water from CaC03 - 6 HzO. The slope of the line gives the rate coefficient for the nucleation step. (ii) Spherical particles. A similar treatment may be provided for spheres of radius a and the growth term t o be included in eqn. (1)is in the form of a contracting volume expression V(t, tj) =

4n

-

3

[a3 - {a - k G ( t -

The formula obtained on integration is complicated [28] and again can only be applicable until t l = a/kG, at which time the first-formed nuclei will have removed the particles on which they were generated. Thereafter, as for rectangular particles described above, a plot of log(1 - a ) against time is linear and the slope gives the nucleation coefficient. When k N is very large, the expression simplifies, as expected from the assumptions, to the contracting volume equation [eqn. (7), n = 31. Although this particular analysis is of value in the systematic theoretical consideration of the consequences of nucleation and growth reactions, the complicated expressions which result have found few applications in recent work. In the original development [ 4541, ranges of application were shown to be of limited extent, involving initial and/or final deviations, and ambiguities of interpretation [28] reduced the precision, and therefore the value, of the mechanistic conclusions derived from this kinetic approach. 3.1.6 General comments

Substitution of appropriate functions for nucleation and growth rates into eqn. (1)and integration yields the f(a)-time relation corresponding to a particular geometry of interface advance. In real systems, the reactant

65

surface and zone of active decomposition may deviate appreciably from the idealized representations described above and it is useful to summarize here some effects which result in departure from strict obedience t o a proposed model. (i) There may be a period of initial relatively slow growth of nuclei. (ii) The rate of interface extension across a surface may be different from the rate of bulk penetration. (iii) Reactivity of surfaces and rates of interface advance may vary with crystallographic direction. (iv) Subsidiary interfaces may develop from the reactant/product contact resulting in a zone, rather than a surface, of reaction. (v) The volume of product will generally be different from that of the reactant from which it was derived, and thus the effective interface may not extend across the whole surface of the nucleus. (vi) In reversible reactions, a volatile product may be adsorbed on the surface of the residual phase and diffusive escape from the reaction interface hindered. (vii) Diffusion control may become significant in reversible reactions. (viii) The sizes and distribution of sizes of reactant particles may influence kinetic characteristics of rate processes. While, in principle, due allowance for these effects can be incorporated into any quantitative kinetic analysis, in practice the integration is made more complicated or the rate expressions become intractable. The incorporation of additional, and sometimes imperfectly defined, parameters does not always represent a meaningful refinement of the approach. 3.2 KINETIC EXPRESSIONS DERIVED FOR “CHAIN-TYPE” REACTIONS

The reference to “chain” reactions in this heading recalls the original development of these equations, based on the assumption that the reaction yielded intermediates of enhanced reactivity capable of activating a neighbouring lattice constituent. Parallels were drawn with the importance of highly reactive participants in gas phase chain reactions. While a variety of mechanisms can be imagined whereby the propagation process may proceed through a crystal, it is now possible to exclude definitely, for isothermal and relatively slow reactions, a model involving energy chains. Macdonald [461] has shown that it would be necessary to transfer the energy very rapidly (-lo-’’sec) from one activated participant t o the next to avoid dissipation of the energy as lattice vibrations. Thus energy chain processes would be expected to be rapid whereas it is found that for a variety of rate processes in solids, both slow and fast, the apparent magnitudes of activation energies are comparable. Furthermore, it has been shown experimentally [ 4621 that interruption of the decomposition of mercury fulminate (a rate process that obeys an equation based on the chain reaction model) and cooling the partially reacted salt t o ambient temperature did not reduce the absolute rate of the continued reaction

66

after the temperature had been restored to the value prior to interruption. Such temporary cooling would be expected to deactivate energy chains present and the absence of such an effect is accepted as evidence that the mechanism does not involve the direct transfer of locally retained energy. Following this demonstration of the inapplicability of the propagation of energy chains during reactions in solids, there have been attempts to provide alternative theoretical explanations of the group of rate expressions with which this section is concerned. The most generally acceptable alternative models envisage either (i) the development of needle or laminar nuclei (growth in one or two dimensions) which undergo branching (possibly at crystal imperfections [435])or (ii) the development of cracks in the reactant phase, resulting from strains in the vicinity of each established reactant/product contact, with reaction being initiated at the surfaces so exposed. Both models are consistent with the operation of a strongly acceleratory nucleation law (analogous t o chain branching) but there are important restrictions in their application. Although kinetic expressions based on the initiation and advance of one or two-dimensional nuclei are easily developed through incorporation of appropriate terms in eqn. (l), conclusions concerning the properties, disposition and interactions of nuclei are usually incapable of independent quantitative verification by observational (i.e. microscopic) methods. Similarly, for model (ii), crack propagation does not lend itself t o a quantitative mathematical representation or t o accurate measurement. Induced stresses, in reactions of both types, may result in the generation and multiplication of lattice imperfections, and, if these are significant participants in nucleation and/ or growth, they may contribute to the acceleratory character of reaction. Garner and Hailes [462] postulated a chain branching reaction in the decomposition of mercury fulminate, since the values of n(-10-20) were larger than could be considered consistent with power law equation [eqn. (2)] obedience. If the rate of nucleation is constant (0 = 1 for the generation of a new nuclei at a large number of sites, N o ) and there is a constant rate of branching of existing nuclei (k,), the nucleation law is dN/dt = k”o

+ kBN

Assuming linear propagation of nuclei, making appropriate substitutions into eqn. (1)and integrating, it may be shown that the total length of nuclei at time t, L ( t ) ,is given by

L ( t ) = (kNkJVo/kk) (exp(kBt) - kBt - 1) The terms (-k,t - 1) may be neglected when t proportional t o a =

k eXp(kBt)

> 5/kB and, since L ( t ) is (8)

sometimes called the exponential rate law (In a = k’t). The linear nucleation law, assumed in the above derivation, may be replaced by alternative

67

functions, but, if the chain branching step is important, an expression of the form of eqn. (8) will again be obtained, though the definition of k , in terms of k N ,k , and k G , will vary with the nucleation rate law used. Ageing of a reactant may influence kinetic characteristics through an increase in N o or a decrease in the area of the reactant, so that in older material the exponential law is often found to be inapplicable after a period of storage [ 434,463,4641. The strongly acceleratory character of the exponential law cannot be maintained indefinitely during any real reaction. Sooner or later the consumption of reactant must result in a diminution in reaction rate. (This behaviour is analogous to the change from power law to Avrami-Erofe'ev equation obedience as a consequence of overlap of compact nuclei.) To incorporate due allowance for this effect, the nucleation law may be expanded to include an initiation term ( k N N o ) ,a branching term ( k a ) and a termination term [ k T ( a ) ]in , which the designation is intended to emphasize that the rate of termination is a function of a, viz.

In two special cases, (i) k N large so that all available sites ( N o )are rapidly exhausted and (ii) k N very small so that { k , - k T ( a ) }>> kNNo,the same approximation is applicable

If it is assumed that the rate of reaction (daldt) is proportional to N , integration of this expression requires a knowledge of the relationship between k,, k T ( a ) and a . The treatment given here, due to Prout and Tompkins [465], considers the special case of symmetrically shaped sigmoid a-time curves, for which the point of inflection is at ai = i. The form of k T ( a ) may be inferred from the boundary conditions: at t = 0, a = 0 and I t T ( & ) = 0 ; at t = t i , a = ai = 0.5, da/dt attains a maximum value and k , = kT((Y)when kT((Y)= kB(Cr/CYi). Substituting in the nucleation equation dN/dt = k,(1 - a/ai)N,combining with da/dt = k'N and putting ai= 0.5, it follows that da - = kga( 1 - a) dt and on integration h [ a / ( l -a)] = kBt + C

(9)

This is known as the Prout-Tompkins equation and has found application to many systems, in addition to the thermal decomposition of potassium permanganate [465]with which it is often associated. The kinetic behaviour of silver permanganate was somewhat different and in a variation of

68

the above approach [ 4661, assuming that k B varied inversely with time, the equation lOg(Cr/(l -a)} = kB log t + C was derived which provided a much more satisfactory description of the yield-time data for this salt. Further modifications of the theory are required for consideration of cr-time curves which are sigmoid but not symmetrical. The use of kinetic expressions of the form of eqn. (9) predates the Prout and Tompkins treatment [465] and this relation is also referred to as the Austin-Rickett equation [467]. 3.3 KINETIC EXPRESSIONS DERIVED FOR DIFFUSION-LIMITED REACTIONS

In a diffusion-limited reaction, the overall rate is determined by the movement of one or more reactant species to, or a product from, a reaction interface; alternatively, heat transfer may be important. The kinetic characteristics of these reactions have been developed largely from studies of gassolid interactions (notably the oxidation of metals) and a short account of the relevant features of such behaviour is included here as a topic which is potentially important but hitherto not widely applied in kinetic studies of certain other chemical reactions of solids. Decompositions of solids are not usually controlled by transfer processes except for certain reversible reactions or where large heat changes are involved. The possibility that a diffusion limitation exists must, of course, be included in considering mechanistic interpretations of experimental data and possible contributions must be eliminated when using kinetic methods to identify factors controlling interface initiation and development. In contrast, a diffusion process is generally ratecontrolling for interactions between two solids, where reactants are originally retained in separate lattices. For many systems of interest (see Chap. 5) the product is generated at the zone of contact between two reactant particles and, if immobile, remains there. Therefore, if reaction is to continue, one or more species must be transported across an increasing barrier of product. The kinetic characteristics of many such processes are similar to those found for gassolid reactions [ 38,4681.Where rate control is dependent on transportation of a reactant across a barrier layer, the state (solid, liquid or gas) of a second reactant is of less significance provided it may rapidly reach all outer surfaces of the barrier. However, experimental difficulties in the accurate measurement of yield-time data for these solid + solid reactions often reduces the possibility of refinement of kinetic analyses. Since the interposition of a barrier layer diminishes the effective contact between reactants, the nucleation step in solid + solid reactions is usually completed very rapidly at temperatures conveniently used in studies of the bulk reaction and, accordingly, the rate processes are often deceleratory throughout. In addition to the progressive diminution in rate

69

as a consequence of the increase in barrier layer thickness, the kinetic characteristics are also significantly influenced by the shapes of reactant crystallites (as in other interfacial reactions). The simplest kinetic law obeyed, when the surface area is constant and the diminution of reaction rate is a consequence of increasing thickness of the barrier layer, is (10) This expression, the parabolic law [38,77,468],has been shown to be obeyed in the oxidation of metals, where the reactant is in the form of a thin sheet. Variations in behaviour are apparent when diffusion in the barrier layer is inhomogeneous as a consequence of cracking or due to the development of more than a single product layer. Alternative rate relations may be applicable, e.g. (Y

= (kct)”’

(Y

= k l log(kzt + k3)

OL =

kit + kz

(the logarithmic law) (the linear law)

The rate expression for reaction of a cylindrical particle (radius r ) is [ 4691 kl (1- a)ln(l -a) + a = t rz

and an extension by Valensi [470]includes consideration of reactions in which the volume of product is different from that of the reactant from which it was derived. A diffusion-limited reaction proceeding in spherical particles (radius r ) obeys a rate expression obtained by combining eqn. (10) with the contracting volume relation [eqn. (7),n = 31,viz.

usually called the Jander equation [ 4711. Modifications [472,473]take the form

If due allowance is made for the differences in reactant and product molar volumes (ratio, z - ’ ) then Carter [474]showed that

[I + (2 - 1)42/3+ ( z - i)(i- 4 2 / 3 = + 2(1 - z )

kt

(12)

which reduces t o the Ginstling-Brounshtein equation, eqn. (ll),when z = 1. Equation (12) was accurately obeyed in the oxidation of spherical particles of nickel having unusually homogeneous diameters. By careful attention to boundary conditions, it was shown that the fit extended

70

effectively up to (Y = 1.00; this was considered [474] to be an important feature of the kinetic analysis. The experimental approach and the interpretation of data represents a precision in the control of reaction variables that is not always achieved in kinetic studies. The above rate equations were originally largely developed from studies of gassolid reactions and assume that particles of the solid reactant are completely covered by a coherent layer of product. Various applications of these models to kinetic studies of solidsolid interactions have been given. Hulbert [ 771 discusses the consequences of the relatively large concentrations of lattice imperfections, including, perhaps, metastable phases and structural deformations, which may be present at the commencement of reaction but later diminish in concentration and importance. If it is assumed [ 4751 that the rate of defect removal is inversely proportional to time (the Tammann treatment) and this effect is incorporated in the Valensi [470]-Carter [474] approach it is found that eqn. (12) is modified by replacement of t by In t . This equation is obeyed [77] by many spinel formation reactions. Zuravlev et al. [ 4761 introduced the postulate that the rate of interface advance under diffusion control was also proportional to the amount of unreacted substance present and, assuming a contracting sphere (radius r ) model

The Dunwald-Wagner equation, based on the application of Ficks second law of diffusion into or out of a sphere (radius r ) [477], can be written

6 ln[a2(l-a)]

aZDt =

-7-

where D is the diffusion coefficient of the migrating species. Hulbert [77] points out that, in general, attempts to include an allowance for the influence of particle size variations in the reactant mixtures on kinetic analyses using the above equations have been unsatisfactory because some of the parameters are not readily defined. Kapur [42], working with powders of known crystal size distribution, indicated that the overall extent of reaction can be estimated by a summation of the individual contributions from each size fraction and thus the best kinetic fit determined. Komatsu [478] has put forward the hypothesis that reaction in many powder mixtures is initiated only at interparticle contact and that product formation occurs by diffusion through these contact zones. Here, one of the participating reactants is not covered with a coherent product layer. Quantitative consideration of this model leads t o a modified Jander equation.

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Reactions of the general type A + B -+ AB may proceed by a nucleation and diffusioncontrolled growth process. Welch [ 1111 discusses one possible mechanism whereby A is accepted as solid solution into crystalline B and reacts to precipitate AB product preferentially in the vicinity of the interface with A, since the concentration is expected to be greatest here. There may be an initial induction period during solid solution formation prior to the onset of product phase precipitation. Nuclei of AB are subsequently produced at surfaces of particles of B and growth may occur with or without maintained nucleation. Kinetic expressions for appropriate models of nucleation and diffusioncontrolled growth processes can be developed by the methods described in Sect. 3.1, with the necessary modification that, here, interface advance obeys the parabolic law [i.e. is proportional to ( D t ) ” * ] .(This contrasts with the linear rate of interface advance characteristic of decomposition reactions.) Such an analysis has been provided by Hulbert [ 771, who considers the possibilities that nucleation is (i) instantaneous (0= 0), (ii) constant (0= 1) and (iii) deceleratory (0 < /3 < l ) , for nuclei which grow in one, two or three dimensions (A = 1, 2 or 3, respectively). All expressions found are of the general form l o g ( 1- a ) = (ht)m where, for diffusioncontrolled reactions, m = 0 + X/2. This kinetic behaviour, therefore, closely resembles that characteristic of reactions proceedTABLE 4 Values of exponents in rate laws of the form - In(1 - a ) = ( k t ) ” as summarized by Hulbert [77] Model

Phase boundary control ( n )

Diffusion control (m)

4

3 3-4

2.5 1.5 1.5-2.5

Two-dimensional growth (Laminar particles of reactant) Nucleation rate ( 1 ) Constant ( 2 ) Zero ( 3 ) Deceleratory

3 2 2-3

2.0 1.0 1.0-2.0

One-dimensional growth (Lath-shaped particles of reactant) Nucleation rate ( 1 ) Constant ( 2 ) Zero ( 3 ) Deceleratory

2 1 1-2

1.5 0.5 0.5-1.5

Three-dimensional growth (Spherical particles of reactant) Nucleation rate ( 1 ) Constant (2) Zero (instantaneous) ( 3 ) Deceleratory

72

ing with constant rate of interface advance, eqn. (6), the only difference being in the significance of the exponent (n = p + A). A diffusion contribution reduces the relative importance of the acceleratory process since, for constant p and h, n must always be greater than m. Measurement of m does not always lead to the positive identification of a specific reaction mechanism since reasonable values can arise from alternative, but acceptable, combinations of and h, see Table 4. Moreover, the existence of diffusion control is not necessarily demonstrated by this kinetic approach since common values of m and n may result from diffusion- or interfacelimited reaction models. Independent evidence in support of any particular mechanism proposed must always be provided. If diffusion across a barrier layer is rapid compared with the rate of reaction at the advancing interface, then the overall rate is determined by the interface step (Sect. 3.1). Another reaction mechanism, which is conveniently mentioned under this heading, is due to Hill [ 4791 who suggested that ions (atoms or molecules) frorh the product may move through the dislocation network of the reactant and “activate” potential nuclei, particularly in the vicinity of the reaction interface. Thus a reaction zone, within which potential nucleusforming sites are activated, is developed in front of an advancing interface. With appropriate assumptions, this reaction model provides an alternative explanation of the exponential rate law, eqn. (8),which in Sect. 3.2 was discussed with reference to chain reactions. 3.4 INFLUENCE OF PARTICLE SIZE DISTRIBUTION ON KINETIC CHARACTERISTICS

Theoretical formulation of kinetic expressions from specified geometry and/or mechanisms of reaction have often assumed particles to be of a regular, perhaps defined, shape and of uniform size. Equations developed in this way have frequently been found to give a satisfactory representation of observed isothermal kinetic characteristics in many reactions of interest. Other authors have, however, introduced an allowance for particle size distribution [ 480-4821 into kinetic analyses. There is no doubt that variations in the average particle size and the particle size distribution of the reactant can produce appreciable effects in the kinetic characteristics of thermal decomposition reactions [ 1201. This is well illustrated by the behaviour of a-lead azide [389,449] where reaction of a single crystal obeys the contracting volume equation [eqn. (7), n = 31 and powder samples exhibit sigmoid a-time curves. Hutchinson et al. [483] have shown that this change is directly related to the particle size distribution of the sample. The decomposition of each individual particle is regarded as obeying the contracting volume equation, which can be written in the form

[

a p ( t ,r ) = 1 - 1 - ;ik;13

73

where p is the sample density, k / p the constant rate of interface advance and tb the time at which the particle of radius r commences reaction. It was found that tb = Cr1’3 where C is the induction period constant. The mass fraction, F(r) of particles of radius r is assumed to be a normal distribution

1 where the distribution parameters, s and R , were measured independently. The total fractional decomposition at time t is R’

a ( t )=

F(r)a,(t, r) dr 0 R2

R1

F(r) dr +

= 0

a p ( t ,r)F(r) dr R1

The first term allows for particles of radius less than or equal t o R1, which are completely decomposed at time t , and the second term includes particles which are only partially reacted at the same time. The expression for a ( t ) must be solved separately, by numerical integration, for each value of t. The parameters C and k / p were shown to be largely (
1- (1 -a)”” = k t

(7)

74

as demonstrated in various studies [ 41,212,456,4851. A particle size effect has been detected by Chou and Olson [486] in the isothermal decomposition of isothiocyanatopentammine cobalt(II1) perchlorate. Below a = 0.09, the larger crystals decompose relatively more rapidly than the smaller, whereas for a > 0.09, the reverse is true. This behaviour was attributed to enhanced nucleation in the larger particles due t o strain, but this favourable factor was later offset by the inhibiting influence of the product ammonia which accumulated in the larger crystals. 3.5RATE EQUATIONS COMMONLY USED IN KINETIC ANALYSES OF ISOTHERMAL REACTIONS OF SOLIDS

It is appropriate to terminate this section, concerned with the formal theories of solid state reactions, with a table summarizing those a-time TABLE 5 Rate equations which have found application in kinetic studies of solid phase reactions a Equation

Label

1 . Acceleratory rate equations

Power law al/n = kt Exponential law In 01 = k t

2. Sigmoid rate equations [-ln(1 = kt [-ln(1 - a)]"3= k t Avrami-Erofe'ev [ - l n ( l -a)]114 = k t Prout-JTompkins In[cx/(l- a)]= k t

( 6 , n = 2 ) A2 ( 6 , n = 3) A3 (6, n = 4 ) (9)

1

3. Deceleratory rate equations 3.1 Based on diffusion mechanisms One-dimensional diffusion a* = k t Two-dimensional diffusion ( 1 - LY) In( 1 -a) + ff = k t Three-dimensional diffusion [ 1- (1 l2 = kt [ 1- ( 2 ( ~ / 3 )] (1 =kt Ginstling-Brounshtein 3 . 2 Based on geometric models Contracting area 1- ( 1 -a)'" Contracting volume 1- ( 1 3.3 Based on order with respect to First order -In( 1- a)= k t Second order (1= kt Third order (1- a)-? = k t

=

kt

= kt

(10) (13) (14) (11)

D1 D2 D3 D4

( 7 , n = 2) ( 7 , n = 3)

R2 R3

(15) (16) (17)

F1

OL

a Rate coefficients, k , are different in each expression and times are assumed to have been corrected for any induction period, t o . In ref. 70. C Concentration is not usually a meaningful term in solid state reactions.

75

Fig. 2. Reduced time plots for the Avrami-Erofe’ev equation [eqn. (6)] with n = 2, 3 and 4 and tr = ( t / t o . p )the : Prout-Tompkins expression [eqn. (9)] is included as the broken line.

v v

d

02

04

06 00 10 1.2 Reduced time t, =(t/to,s)

Fig. 3. Reduced time plots, tr = ( t / t o . g ) , for the contracting area and contracting volume equations [eqn. (7), n = 2 and 31, diffusion-controlled reactions proceedings in one [eqn. (lo)], two [eqn. (13)] and three [eqn. (14)] dimensions, the GinstlingBrounshtein equation [eqn. ( l l ) ] and first-, second- and third-order reactions [eqns. (15)-(17)]. Diffusion control is shown as a full line, interface advance as a broken line and reaction orders are dotted. Rate processes become more strongly deceleratory as the number of dimensions in which interface advance occurs is increased. The numbers on the curves indicate the equation numbers.

76

relationships which have found greatest application in kinetic analyses. These are collected in Table 5, broadly classified on the shapes of the a-time relationship and further divided according t o the mechanism on which the derivation is based. The labelling scheme given by Sharp et al. [70] has also been included. Shapes of a-time curves for most of these relations are given in Figs. 2 and 3, and calculated numerical data are available in the literature [ 30,70,488]. 4.Tests of obedience of isothermal kinetic data to theoretical kinetic equations 4.1 INTRODUCTION

The purpose of many kinetic studies is t o obtain information conceming the reaction mechanism, through comparisons of a series of measured (a,time) values and the theoretical functions (e.g. those in Table 5 ) which have been derived from models based on the geometry of interface initiation and advance and/or diffusion processes occurring in the solid. The problem may be regarded as the identification of the functional relationship between a and time, f(a) = k t , where k is the conventional rate coefficient. Most methods of analysis proceed by determining which rate equation, of the type described in Sect. 3 provides the most accurate fit to the experimental data. Obedience to a particular relation is then consistent with, but not proof of, reaction through the model from which the relation was derived. Kinetic evidence alone cannot be regarded as a positive demonstration of the operation of a particular mechanism. Conclusions concerning the geometry of interface advance should be supported by independent evidence, e.g. microscopic observations [ 69,4871. If meaningful results are to be obtained from a kinetic analysis of a-time data, it is necessary to consider the possible contributions of errors arising from many sources. The following list is not comprehensive but indicates the sort of problems which are inherent in the approach. (i) a must be meaningfully defined and capable of accurate measurement. (ii) Onset of reaction may be preceded by an initial surface process. (iii) Error in measurement of the final yield may distort the shape of the a-time curve. [Both (ii) and (iii) can be regarded as factors in the definition of a, i.e. (i).] Accurate determination of final product yield is a major experimental difficulty in many systems. (iv) The composition of products may vary with a. (v) Enthalpy change during reaction may cause local and/or temporary deviations from the isothermal conditions. (The reaction vessel temperature must also be maintained at a constant value.) (vi) Rates of nucleation and/or growth may vary with crystallographic

surface and in different polymorphs of a single compound. (vii) Kinetic behaviour may change during the course of reaction (e.g. completion of nucleation, following crystallite disintegration, etc.). (viii) Rate characteristics are often varied by pretreatment (e.g. preirradiation, cold working, ageing, conditions of dehydration, etc.). (ix)The occurrence and significance of melting. (x) The influence of the distribution of particle sizes. We do not regard as being generally applicable the statement by Carter [474] that if a reaction model is to be regarded as valid, the kinetic obedience of data must be quantitatively consistent to 100%. The fit of many kinetic expressions is poor in the final stages and this has been attributed to a combination of effects which may include particle size, crystallite disintegration, sintering, chemisorption of product gases on a residual phase, poisoning, etc. Furthermore, some reaction models are applicable only within restricted ranges, such as the acceleratory or the decay period, or the algebraic form of the rate relation may be inapplicable to measured data at the limit, e.g. a = 1.00 can only be reached when t = m. There is also the possibility that the rate-controlling factor, or kinetic characteristics, can change during the progress of the reaction. The contracting volume relation, for example, is applicable only during the deceleratory phase of many rate processes [375,408] and it is common practice to incorporate a time correction factor term in the analysis to allow for the interval required for the establishment of a coherent interface on all reactant surfaces. 4 . 2 IDENTIFICATION OF THE RATE EQUATION

It is sometimes found that a given set of a-time observations are obeyed with equal accuracy by two different rate equations and the kinetic analysis resolves itself into a test of distinguishing the applicability .of the alternative functions of a . Four general approaches have been used in kinetic analyses. (i) Testing the linearity of a plot of f(a) against time; the slope is the rate coefficient for the overall reaction. (ii) Comparison of shapes of a-reduced time plots with lines calculated for various functions (for which tabulated data are available in the literature [30,33,70]). (iii) Comparison of measured (da/dt)--cll values with master curves [30] (very accurate values of a are required for the satisfactory application of this differential approach). (iv) Comparison of measured (da/dt)-reduced time values which can enhance the ease of discrimination between alternative kinetic obediences [ 12521. The reduced time method [in (ii), above] refers t o the scaling of time values to facilitate the comparison. It is often convenient t o use t, = 1.00

78

at a = 0.50 (Fig. 1).A particular value of this technique is that if isothermal measurements have been determined at several different temperatures, all data can be collected on a single plot, by the use of appropriate scaling factors, for comparison with the theoretical curves. Any systematic change in kinetic behaviour with temperature can be readily discerned. Various other common points for scaling (e.g. t, = 1.00 at a = 0.90) have been mentioned and sometimes recommended in the literature. Where the temperature coefficient of the induction period, or the acceleratory phase of reaction, differs from that obtaining later, it may be necessary to deduct (or add) an appropriate allowance from each time value before scaling or, alternatively, use two standard points (e.g. t, = 0.00 at a = 0.10 and t, = 1.00 at a = 0.90 [408]). An appropriate correction to a may also be required [60] where the main reaction is preceded by an initial rapid evolution of gas. A disadvantage inherent in the reduced time method of analysis, as discussed by Sharp et al. [70] Geiss [488] and others [30,33] is that it involves the comparison of curves. An alternative, and widely used, method of preliminary identification of the rate law providing the most satisfactory fit t o a set of data is through a plot of the form In {-ln(1 - a)} = n In t + const. Magnitudes of n have been empirically established for those kinetic expressions which have found most extensive application: e.g. values of n for diffusion-limited equations are usually between 0.53 and 0.58, for the contracting area and volume relations are 1.08 and 1.04, respectively and for the Avrami-Erofe’ev equation [eqn. (6)] are 2.00, 3.00 etc. The most significant problem in the use of this approach is in making an accurate allowance for any error in the measured induction period since variations in t [i.e. ( t + t o ) ] can introduce large influences upon the initial shape of the plot. Care is needed in estimating the time required for the sample to reach reaction temperature, particularly in deceleratory reactions, and in considering the influences of an induction period and/or an initial preliminary reaction. Jones et al. [73] have provided an alternative approach to the linearization of data using the tabulated reduced time values given by Sharp et al. [ 701. The experimental data are expressed in the form a, as a function of (t/t0.5)e, where the subscript e refers to the experimental data. Three broadly equivalent methods of plotting can be used. (i) The value a, at which (t/to.s)e has the same value as that in the master data ( t / t 0 . 5 ) mis plotted against the master value a,. Where the experimental data is in exact agreement with the master values, a, = a, and the plot of a, against a, will have slope unity and pass through the origin. (ii) Plots of (t/to.s)e against ( t / t 0 . 5 ) m for common values of a, and a, similarly should have slope unity and pass through the origin if the relation is obeyed.

79

(t/t&,,

[eqn.(6), n=2J

a,

[eqn.(6),n=2]

Fig. 4. Reduced time plots, t, = ( t / t o . s ) , for the isothermal decomposition of ammonium vanadyl oxalate using master data for the Avrami-Erofe'ev equation [eqn. (6), n = 21, by the application of a method of analysis [ 7 3 ] described in the text. The circles are experimental measurements and the lines correspond to exact agreement with the equation. (Reproduced, with permission, from Thermochimica Acta.)

(iii) Finally, where there is complete correlation, a plot of values of t, against (t/t0.5)mfor common values of a, and a m should be a straight line of slope (t0.5)ethrough the origin. Advantages [73] of the method include the direct determination of deviations through variations from linearity of the plot, also the analysis is sensitive and may be applied to any rate relation over the whole reaction 0 < a < 1. An example of the application of this technique is given in Fig. 4, where it can be seen that data for the isothermal decomposition of ammonium vanadyl oxalate give a linear plot through the origin of slope unity for master values from the AvramiErofe'ev equation [eqn. (6),n = 21. Manche and Carroll [1253] suggest that errors due to lag time at the onset of reaction can be avoided by using rates at fixed values of a in the determination of E values. Ng [74] has also considered the problem of deciding which of the rate expressions available provides the most satisfactory description of a given set of data. He provides a comprehensive table in which the most commonly used expressions are represented in terms of the general relationship

where 0 p < 1and 0 < q < 1.Sestbk and Berggren [ 4891 earlier provided a more general expression of the same form, viz. da - = k d ' ( 1 - a)" {-ln(1 - a)}' dt which is applicable to reactions proceeding during temperature increase.

80

4.3 APPLICATION OF RATE EQUATIONS TO PARTICULAR REGIONS OF THE a-TIME CURVE

Having identified the kinetic relation applicable to the data for a particular reaction by the general techniques outlined in the preceding paragraph, it is necessary to confirm linearity of the appropriate plot of the function f(a) against time. The special problems which relate to the induction period, the acceleratory and the deceleratory regions are conveniently considered separately. 4.3.1 The induction period The delay, to, preceding the onset of the main reaction may include contributions from (i) the time required for the sample to attain reaction temperature, th, (ii) additions t o th resulting from changes within the reaction sample, e.g. water removal (endothermic) from a hydrate, t d , phase transitions, etc. and (iii) slow processes preceeding establishment of the main reaction, which are to be regarded as the true induction period, ti. The effective values of t h , td and ti may show different temperature coefficients so that the magnitude of tO(=th + t d + ti) may vary with temperature in a complex manner, perhaps differently from that of the subsequent rate process. The magnitude of to can be measured from the intercept of a f(a)-time plot. The existence of the induction period can introduce uncertainty into a reduced time analysis if the temperature coefficient of to differs from that later applicable, and it is necessary to plot ( t - tO)/(tb - t o ) against a where tb is the time at which the selected common value of a is attained. The occurrence of a slow initial process can be reflected in deviations from linearity in the f(cy)-time plot, though in favourable systems the contribution may be subtracted before analysis [ 401. 4.3.2 The acceleratory region Kinetic analyses of solid phase reactions have, perhaps, found greatest application in the initial stages [ 291 since, in general, more precise measurements can be obtained and sometimes results may be considered with reference to microscopic observations. The power law [eqn. (2)] and exponential law [eqn. (S)] are often obeyed. Possible routes to the determination of the power law exponent are plots of a"" against time, or In a against In t , though an unambiguous result is not always apparent [375], particularly where there is an induction period ( t o ) or an initial evolution of gas ( a o )precedes the main reaction. Both methods of kinetic analysis were applied [490] t o a series of a - t i m e values calculated from a = a . + (ht,)" with a . = 0.02 and 0.04 and n = 2 or 3. Plots of a"" against t were found to be a most insensitive method for the determination of n, while

81

the values of n from plots of log a against log t were about 8% in error, deviation being greatest at low a. Kinetic analyses during the acceleratory stage of reaction, therefore, may necessitate corrections to both variables, (a - a o ) and/or ( t - to),and the plots used to identify the rate equation may be insensitive. Again, the importance of microscopic or other independent observations, is obvious. 4.3.3 The deceleratory region

It is particularly difficult t o correlate experimental data in this region with the requirements of a particular rate equation, though the problem is eased somewhat where the maximum rate is achieved at a low a and the deceleratory contribution correspondingly prolonged. This lack of sensitivity arises from the similarities of shapes of many a-time curves (Fig. 3), the possible influences of contributions from a. and to and errors in the determination of the final yield of products from the rate process of interest. In considering the significance of the last-mentioned factor, Brown and Galwey [ 4901, introduced errors into the final yield in a series of calculated data which otherwise exactly obeyed a particular rate equation and re-analyzed the distorted results. A final parameter (e.g. pressure, weight, etc.) error of 55% can have an appreciable effect (up to 20%) on the magnitude of the measured rate coefficient, k. Moreover, the shapes of a-time curves are changed sufficiently t o reduce the distinguishability of obedience t o alternative kinetic relations. We should also point out that the shapes of curves characteristic of the latter part of the AvramiErofe’ev equations [eqn. (6)] and the Prout-Tompkins relation [eqn. (9)] are comparable with those of the deceleratory equations, e.g. on completion of nucleation and initial growth, a layer of product may cover all reactant surfaces and behaviour thereafter is closely similar to the contracting volume model [ 4081. 4.4 STATISTICAL METHODS IN KINETIC ANALYSIS

Any experimentally measured set of (ai,ti) values for an isothermal reaction contains errors including (inter alia) inaccuracies in yield and time determinations and departure of temperature from the constant value temporarily and locally. In any quantitative kinetic analysis, several interdependent factors must be considered. (i) The most accurate identification of the measured a - t i m e curve with due regard for the scatter of data. (ii) Comparisons must be made between this plot and theoretical relations t o identify the most acceptable kinetic representation and reaction model. (This is more difficult where curves fit an equation only within restricted Q ranges.) (iii) The reaction rate coefficient, k, is calculated.

82

These steps may be completed separately or together, statistical methods can be employed and the computational labour reduced through the use of high speed computers. There have been few discussions of the specific problems inherent in the application of methods of curve matching to solid state reactions. I t is probable that a degree of subjectivity frequently enters many decisions concerning identification of a "best fit". It is not known, for example, (i) the accuracy with which data must be measured to enable a clear distinction to be made between obedience to alternative rate equations, (ii) the range of a within which results provide the most sensitive tests of possible equations, (iii) the form of test, i.e. f(a)-time, reduced time, etc. plots, which is most appropriate for confirmation of probable kinetic obediences and (iv) the minimum time intervals at which measurements must be made for use in kinetic analyses, the number of (a,t ) values required. It is also important t o know the influence of experimental errors in ag,to,particle size distributions, temperature variations, etc., on kinetic analyses and distinguishability. A critical survey of quantitative aspects of curve fitting, concerned particularly with the reactions of solids, has not yet been provided [490]. Green [491]has given a general account of the applications of statistical methods to kinetic analyses and, without mentioning specific examples, suggests the approach could be of value in rate studies of solid phase reactions. The steps in his treatment are given below [ 492,4931. (i) A test is made of reproducibility using several sets of isothermal (ai,ti) data, obtained under identical reaction conditions. of data from above is (ii) A single set (ai,ti), or the mean set (Gi, compared with corresponding values calculated for a particular model (a:, t:). This forms the null hypothesis, Ho. The comparison is quantified by an appropriate statistical parameter, e.g. the variance, ua. (iii) The same data are compared with calculated values for an alternative model (a:,t t ) , the alternative hypothesis, H', and the statistical parameter (say u:) is calculated. (iv) The parameters (a: and u:) are compared and a decision is made as to which if either, of the hypotheses (Ho or H') is acceptable within particular limits. (v) Kinetic parameters ( h , reaction order, etc.) for the selected rate expression are now calculated, together with their experimental uncertainties. These uncertainties are examined to determine whether they arise from experimental error in the measured data (ai,ti) or are t o be attributed t o a definite deviation from the selected hypothesis. (vi) Finally, data generated for the two hypotheses, Ho and H', may be compared. Statistical methods used in kinetic analyses have generally been based on a least-squares treatment. Reed and Theriault [ 4941 have considered the application of this approach to data which obeys the first-order

z),

83

expression [eqn. (15)]. Problems arise from the assumption that there is a normal distribution of errors in the observed quantities and this is inapplicable to the logarithmic terms of the linear plot of ln(1 - a) against time. They showed, moreover, that neglect of constant errors could result in the appearance of significant (- 25%) discrepancies in the calculated rate coefficients. Churchill [ 4951 points out that the statistical validity of the leastsquares treatment may not always be certain, since errors may not be random, but the method has the merit of being a standardized way of describing a correlation. Jacobs and Ng [ 4521 have made a particularly detailed kinetic analysis of the decomposition of ammonium perchlorate through a non-linear least-squares treatment based upon the Marquardt algorithm [ 4961. Dorko et al. [ 4421 used the Kolmogorov-Smirnov test [497] for excellence of fit, in applying the Weibull distribution (Sect. 3.1) to solid phase kinetic data. Available kinetic data are seldom of sufficiently high quality to warrant the application of high precision statistical treatment. This point is made forcefully by Churchill [ 4951 who states: “Our ability and inclination to postulate and construct models appear to exceed our ability and inclination to obtain good rate data. Improvement in rate correlations will come primarily from more and better measurements rather than from improvements in modelling or mathematical procedures.” De Tar and Day [ 4981 considered problems which arise in applying the first-order expression [eqn. (15)] to kinetic data of limited accuracy. If a is known to a high degree of accuracy (e.g. +0.1%), then small components (5--10%) of higher or lower order behaviour are detectable. When the accuracy of 01 is reduced to +1%, a second-order component of 25% could escape detection, and perhaps an even larger contribution might be missed within a limited a interval. Using exact values of a from known kinetic behaviour, the apparent rate coefficient, h , was found to depend on both the proportion of the non-first-order component and on the extent of reaction considered. Benson [499] and Livingstone [500] considered the influence of experimental accuracy on measured rate and temperature coefficients. To measure the rate coefficient to 0.196, the relative errors in each ai value must be <0.1% and the reaction interval should be at least 50%. Temperature control to achieve this level of precision must be 0.003% or *0.01 K at 300 K. For temperature control t o +1K, the minimum error in the rate coefficient is +5% and in the activation energy, measured over a 20 K interval, is +lo%. No allowance is included in these calculations for additional factors such as self-heating or cooling. Noms et al. [1254] discuss the application of several numerical methods to the determination of rate coefficients and of orders of solid state reactions of the contracting interface type.

84

4.5 INTERPRETATION OF KINETIC OBSERVATIONS

It has been pointed out at several places in the text above that the demonstration that a given set of (ai,ti) values obeys a particular kinetic expression does not constitute an absolute proof of the operation of the reaction mechanism from which that rate equation [f(a)-time] was derived. Geometric interpretations should always be supported by independent evidence; microscopic observations can be particularly valuable. (We may also note, in passing, that isothermal kinetic data, in general, give little information concerning the individual steps which contribute to the changes occurring a t the reaction interface: conditions in this zone are discussed in Sect. 7.) The following effects can reduce the accuracy of interpretation of kinetic data: (i) the reaction rate can be inhomogeneous within the reactant mass, (ii) the mechanism can change during reaction, (iii) the contribution from different processes (e.g. nucleation and growth) may vary with a, (iv) the presence of products may influence the changes occurring, (v) particle size effects, reactant pre-treatment, etc. However, even if data can be unambiguously identified with a single rate expression, it is possible that several alternative reaction models may lead to the same kinetic relation, as the following examples demonstrate. 4.5.1 The zero-order reaction A constant rate (zero-order kinetic behaviour) maintained during all, or the greater part of the process may be accounted for [ 4871 by the following reaction models, illustrated in Fig. 5. These alternatives may be distinguished by microscopic observations. (i) The ratecontrolling step is desorption at existing (immobile) crystal surfaces, as in the dehydration of U 0 2 ( N 0 3 ) z- 6 H 2 0 [ 621. (ii) Rapid formation of a small number of nuclei on lath-shaped reactant followed by growth in one dimension, as in the reaction of hexammine nickel perchlorate with water vapour [ 5011 [Fig. 5(a)]. (iii) Rapid and complete nucleation of all surfaces of reactant in the form of thin plates [Fig. 5(b)]. Contraction from the smaller edges is minimal and the rate is controlled by the advance of the larger, and effectively constant, area of surface, as in the decomposition of silver mellitate [ 4601. (iv) Rapid formation of product simultaneously over the curved surfaces and along the central axis of cylindrical reactant particles, as in the decomposition of cobalt oxalate [ 431 [Fig. 5(c)]. (v) Rapid and dense nucleation at equidistant planes perpendicular to longer axes of plate-like crystals, as in the decomposition of nickel malonate [ 5021 [Fig. 5(d)]. (vi) Interface advance in a single crystallographic direction, as in the

85

Fig. 5. Various dispositions of reaction interface which result in obedience to the zeroorder kinetic equation. Product is shown shaded: for explanation see text.

decomposition of thallium(1) azide [ 5031. (vii) Interface advance in a single direction has also been achieved artificially by coating appropriate crystal surfaces with a barrier to product release (only applicable in reversible reactions), as in the dehydration of copper(I1) fonnate tetrahydrate [ 2131.

4.5.2 Avrami-Erofe’ev equation (n = 2 ) Alternative models obeying this kinetic expression are given in Fig. 6. It is assumed that nucleation is rapid and complete. Thereafter, = 0 and growth is twodimensional ( A = 2, so that n = p + A = 2). If nuclei are generated on thin plates of reactant, shown confined to edges in Fig. 6, the nuclei developed are thin and semi-circular. If nuclei are developed at closely spaced points along linear features (perhaps dislocations) in the crystal bulk [Fig. 6(b)], or along surface lines, these rapidly overlap and growth proceeds as an increase in diameter of a cylindrical volume of product. The latter model is preferred for the decomposition of nickel oxalate [286].

86

Fig. 6. Two reaction models which result in obedience to the power law [eqn. (2), n = 21 at low a,o r the Avrami-Erofe’ev equation [eqn. (6),n = 2 1 over a more extensive range of a. In (a), there is growth of semi-circular nuclei in a thin plate of reactant; in (b), there is cylindrical growth of linear internal nuclei. In both examples, rapid nucleation (0 = 0 ) is followed by two-dimensional growth (A = 2).

5. Variation of reaction rate with temperature

Two alternative methods have been widely used t o investigate the influence of temperature on the kinetic characteristics of solid phase reactions. These are: (i) comparisons of isothermal data obtained for the same reaction occurring at various temperatures (discussed in the present section) and (ii) measurement of rate behaviour for the processes occurring during progressive variation in reactant temperature in a controlled manner (discussed in Sect. 6 and not further considered here). There is also the possibility of split-temperature runs, in which a reaction commenced isothermally at one temperature (TI), is completed (isothermally, again) at another (Tz)following a relatively rapid change from TI t o T2.The advantage of this method is that measurement of the rate may be made at the same a value and on the same sample. Reaction rates are related t o a and to temperature, T,by different and independent functions and a complete kinetic description of behaviour

87

requires characterization of both expressions da - a F(a)F'( T ) dt While it is generally true to state that reaction rates increase with temperature, such a qualitative statement is not specific enough to be useful and in some circumstances can be incorrect, e.g. at high a values when the deceleratory character of the reaction may be sufficiently great to offset the acceleratory effect of a slow temperature rise. The most accurate method of measuring the influence of temperature on reaction rate is t o separate the variables by first determining isothermal rate curves at a series of different temperatures and expressing each set of observations in the form f(a) = kt

The relationship between k and T has then usually been assumed to be of the form b log k = a - - or k = A exp(-E/RT) (18) T Innumerable experimental rate measurements of many kinds have been shown to obey the Arrhenius equation (18) or the modified form [ k = A'T" exp(-E/RT)] and, irrespective of any physical significance of the parameters A and E , the approach is an important, established method of reporting and comparing kinetic data. There are, however, grounds for a critical reconsideration for both the methods of application and the theoretical interpretations of observed obedience of experimental data for the reactions of solids to eqn. (18). 5.1 APPLICATION OF THE ARRHENIUS EQUATION TO SOLID STATE REACTIONS

Historically, the identification of a linear correlation between log k and T-' was empirical. First described by Hood [ 5041, the relationship was given some theoretical significance by van 't Hoff [505] who expressed the influence of temperature on equilibrium constants ( K , ) by an equation of similar form, viz.

AH

In K, = - -+ constant RT This equation is familiar from thermodynamics (but problems arise in its application to the properties of solids due to the difficulties inherent in defining reactant concentration). Arrhenius [ 5061 and Harcourt and Essen [ 5071 extended Hood's observations t o the form of eqn. (18) and a close examination of most textbook treatments suggests that this step was not

88

based on logical extension of theory but rather as a result of the intuitive comparison with the van 't Hoff equation. The Arrhenius relation has now achieved general acceptance and no alternative expression of comparable significance has been developed. Two interrelated aspects of the quantitative determination of the influence of temperature on reaction rates of solids merit comment: the insensitivity of eqn. (18)and alternative f(h)-T relationships [ 5081. ( i ) Insensitivity of eqn. (1 8). Plots of log k against T-' are notoriously insensitive and the influences of random and systematic errors on the fit of data to eqn. (18)and on the magnitudes of measured values of A and E are not always readily apparent (or fully appreciated). An alternative approach, more sensitive but, as yet, rarely used, is t o fit kinetic data t o a series expression. (This method has found application in the reporting of thermodynamic functions.) Plots of h against T are now rarely, if ever, given. ( i i ) Alternative f(k)-T relationships. The quantitative representation of measured data through mathematical relations embodies two distinct steps [ 36,5091 : (a) identification of a satisfactory function connecting the variables and (b) calculation of the best line through observations showing random scatter. The errors in the determined parameters should also be estimated. In much of the available published work concerning the influence of temperature on rate coefficients, it is implicity assumed that the Arrhenius equation provides the most satisfactory description of the dependence of k upon T . Then, only the second of the two objectives mentioned above is completed, i.e. the best line through the data is calculated by regression methods. Since the theoretical basis of eqn. (18)can be questioned (see below) and since there are (in the field of reactions of solids) remarkably few tests, or even discussions of alternative relationships, it is appropriate to point out here the possibility that the Arrhenius model is not necessarily the only or the best relation for all reactions. Many systems are found to give a good linear plot of log h against T-' but examples are also known where there are two straight lines [73] or the plot is curved [47]. The interpretation of such behaviour poses particular problems. 5 . 2 SIGNIFICANCE OF THE ARRHENIUS PARAMETERS

Arrhenius parameters determined for reactions of solids are frequently referred to by descriptive terms which arise through analogy with the representation of gas phase processes by the collision theory of reaction rates. E , the activation energy, is identified as the energy barrier which must be surmounted during transformation of reactants into products during the rate-limiting step. A , the frequency factor, is identified with the frequency of occurrence of the reaction configuration, first identified as a molecular encounter (a collision) and later as a specific vibration in

89

the reaction co-ordinate. Clearly, the requirement that reaction follows collision between two free-moving reactant species is untenable where a reactant is immobilized in the lattice of a solid or the transformation proceeds at a narrow interface between two crystalline phases. Therefore, if the Arrhenius equation is obeyed in heterogeneous rate processes [ 361, an alternative theoretical basis for it must be provided. The absolute reaction rate theory, in which the activated complex is regarded as a high energy atomic configuration, has been applied to many other aspects of the behaviour of solids, e.g. diffusion in crystals, and is discussed in Sect. 5.3. Before discussing such theories, it is appropriate t o refer t o features of the reaction rate coefficient, k. As pointed out in Sect. 3, this may be a compound term containing contributions from both nucleation and growth processes. Furthermore, alternative definitions may be possible, illustrated, for example, by reference to the power law a''" = k t or a = k't" so that k = A exp(-E/RT) or k' = n-"A" exp(-nE/RT). Measured magnitudes of A and E will depend, therefore, on the form of rate expression used to find k. However, provided k values are expressed in the same units, the magnitude of the measured value of E is relatively insensitive to the particular rate expression used t o determine those rate coefficients. In the integral forms of equations listed in Table 5, units are all (time)-'. Alternative definitions of the type da - = kf'(a) dt are listed by Heide et al. [ 5091 and these are given, with certain modifications, in Table 6 . The slope of the Arrhenius plot has units (temperature)-' but activation energies are usually expressed as an energy (kJ mol-'), since the measured slope is divided by the gas constant. There is a difficulty, however, in assigning a meaning t o the term "mole" in solid state reactions. In certain reversible reactions, the enthalpy (AH) + E, since E for the reverse reaction is small or approaching zero. Therefore, if an independently measured AH value is available (from DSC or DTA data), and is referred to a mole of reactant, an estimation of the "mole of activated complex" can be made. Garn [ 12551 believes that there is no discrete activated state in decompositions of solids; this is suggested by the observed wide variations in calculated activation energies. Since vibrational interactions transfer energy so rapidly within a crystalline solid, no substantial difference from the average is achievable. The most frequently occurring energy is the energy of the bulk crystal. Accordingly, the statistical distributions upon which the Arrhenius equation is based are not operative and this equation cannot be used unless it is independently verified for the particular system under consideration. Redfern [510] has suggested that the activation energy is the average

(D

0

TABLE 6 Differential, integral, and non-isothermal forms of kinetic expressions a Equation derived from equation number

Differential form

Iilcegral form

Exponents in

4d%t

kt =

-da-

k a m (1 -a)" dt x (-ln( 1 - a))P

m

10 8

n

p

0

0

A ln(da/dT) - X A h a A h a

A ln(da/dT) --- X +1 A h a A h a

ka-l

az 2

ha

In a

1

0

0

2a"Z

$

0

0

3a113 2

2 3

-0

0

A In(da/dT) =X A h a AIna

3"

4 1/4

i

o

o

Aln(da/dT) = -

a

0

0

0

2 (1 - (1 - a)ll2}

0

;

A ln(da/dT) = X A ln(da/dT) X +L A ln(1 - a ) - A ln(1 - a )

2, n = 2 2, n = 3

ka2I3

2, n = 4

ka3I4

2,n=11

7,n=1

7, n = 2

Rising temperature expression

k ( 1 -a)'"

-1

o

Aln(da/dT)--- X

A h a

A h a

1

+

A h a

X

A h a

+

+

7,n=3

15

k ( 1 - a)z1a

3{1 -(1 -a)113}

0

k ( l -a)

-In( 1- a)

0

1

0

1

;

3 {-ln(l-

0

1

;

4 {-In( 1 -

0

1

;

k ( 1 - a)(-ln(l -

2 {-1n(1-

6,n=3

k ( 1 - &)(-In( 1 -

6,n=4

k( 1-&)(-In(

(Y)}”’

a

k a ( l -a)

In 1- a

1

1

13

k(-In( 1 - a))-‘

(l-a)ln(l-a)+a

0

0

14

k ( 1 -(I

-a)ll3)-l(1 -

11

k ( (1-

- l)-’

a

( Y ) ~ / ~

0

0

6,n=2

9

0

2

(1-&)-I

1-

5

0

k ( 1 - a)’

16

2

A In( da/dT) X AIn(1-a) Aln(1-a)

A In( da/dT) AIn(1-a)

X +1 AIn(1-a)

A In(da/dT) +2 Ah(1-a) Aln(1-a) X A In( da/dT) - A In( -- 1- a) +I A In[-In( 1 - a ) ] A h[-ln( 1- a ) ] A In(da/dT) - A In( 1- a)X +z A In[-In( 1 - a ) ] A In[-h(l - a ) ] X A In(da/dT) - A In( 1 - a)+?

’

Aln[-ln(l

0 -1

+z

-a)]

A In(da/dT) -

A In(da/dT) X ~ ~ n [ - l n (-la ) l = T 1 n [ - l n ( l

53 (1 -( 1 - a)1/3}’

A In( da/dT) + A In( 1 - (1 A In( 1 - a)

7 (1 -$a-(1

A In(da/dT) + A In((1 -

-a)2/3}

AIn[-ln(l --a)]

X AIn[a(l-a)]-Aln[a(1-a)]

Based on a table given by Heide et al. [ 5091 with corrections and modifications indicated by G.R. Heal.

+1

-a)]

-1

x

+

A In( 1 - a) -

1) = X

92

excess energy that a reactant molecule must possess to react. Anderson [ 5111, however, prefers to regard both A and E as having empirical rather than theoretical significance. Both must be reported to define adequately the reaction rate. Bertrand et al. [ 12561 regard E as a composite function, comprised of contributions from numerous parameters, including the deviation from equilibrium and the thermal gradient. 5.3 RATES OF INTERFACE REACTIONS

An early attempt to apply an Arrhenius-type equation to a decomposition reaction was by Polyani and Wigner [ 5121 using the expression

dx

dt =

(g)

xo exp(-E/RT)

where the linear rate of interface advance, dx/dt, is expressed in terms of xo, the incremental advance from unit reaction, and v avibration frequency, the term %/RT arising because the critical energy required can be achieved through three degrees of vibrational freedom. The model was developed from the identification of dissociation of a particular bond, energy E , at the migrating decomposition interface with evaporation of surface-held species. This theory of reaction rates was discussed in some detail by Bradley [ 5131 and later applied by Topley [ 4551 to the loss of water from copper sulphate pentahydrate. The magnitude of v, a vibration frequency in the crystal lattice (interface or surface), is expected to be sec-’. If values of A calculated from experimental data, using eqn. (19), yield values of v within 10-10’ of this expected magnitude and the activation energy is close t o the enthalpy of dissociation, the rate process is regarded as obeying the Polanyi-Wigner relation and is said to be “normal”. Such rate processes include water evolution from hydrates (e.g. CuS04 5 HzO)and carbonate dissociation (e.g. CaC03). In other reactions, described as “abnormal”, both A and E values are unacceptably large. The relevant data (for 29 reactions) have been listed and discussed by Shannon [ 5141. The pre-exponential term was expressed as partition functions using the notation of absolute reaction rate theory so that

-

kT Q*

kr = 7* - exp(-E/RT)

Q

where Q* is the complete partition function for the activated complex excluding that for the reaction co-ordinate and Q is the partition function for the reactant: k, is a first-order rate coefficient, which should have units (time)-’ to be applicable in the absolute rate equation. For decompositions of the type

B(s) + C(g) Shannon assumes that atoms or molecules at the reaction interface have -+

93

vibrational, possibly also torsional and rotational, degrees of freedom with a Boltzmann distribution of energies. He also assumes that the rate of reaction is determined by the decomposition step and not by subsequent events. It is then possible to use published kinetic data to calculate the ratio (Q*/Q) in eqn. (20), and three patterns of behaviour were distinguished with (i) (Q*/Q) < 1, (ii) (Q*/Q) 1 and (iii) (Q*/Q) > 1. Ratios of Q* to Q can also be calculated from spectroscopic data and, from comparison between these values and those from experimental rate measurements, Shannon [ 5141 distinguishes the following two mechanisms of reaction. ( i ) Reaction proceeds through loss of gas f r o m the interface. Calculation of Q for CaCO, and MgC03, as examples, poses few problems but assignment of a value t o Q* requires a detailed specification of the structure of the activated complex, here regarded as being intermediate in character between the reactant anion and product. Shannon was able to demonstrate reasonable agreement between calculated and experimental (kinetic) values of (Q*/Q) for both solids. (ii) Reaction proceeds through formation of a mobile layer followed by desorption. In such reactions, the activated complex contains a larger number of degrees of freedom than the reactant. Where the process involves desorption of a mobile adsorbed water molecule, the spectroscopic data indicates (a) (Q*/Q) 4, assuming free rotation of the activated complex and (b) (Q*/Q) 5 X lo3 for free rotation and translational freedom of the activated complex in two dimensions. Since data obtained for dehydration reactions of alums give Q*/Q ratios of around unity and also of the order -lo3, it seems probable that both models may be applicable in specific systems. Cordes [515] has provided a more general treatment of reaction rates using similar concepts to those discussed by Shannon [514] (the latter model appears as one particular case). Two types of rate process are distinguished : bulk decomposition and surface reaction and three classes of bulk decomposition are identified, viz.

-

--

A + A* + products A+A

-+

A2* + products

unimolecular

1

bimolecular A + B + AB* products Cordes discusses the magnitudes of pre-exponential terms with reference to the partition function for the activated complex in which the following cases are recognized. Case 1: N o change in the degree of rotation or of excitation between reactants and the activated complex; two subdivisions are (1A) with completely free rotation and (1B)completely restricted rotation. Case 2: The activated complex is in a freer condition than reactants. Case 3: The activated complex is highly restricted in rotation. -+

94

TABLE 7 Numerical values of A / s Cordes [ 5151 Case

at 400 K for various reaction mechanisms according t o

A (s-l )

Unimolecular

Bimolecular

Bulk decomposition throughout the solid 1A 1015 Not applicable 1B 1015 1016 2 10’6 10’8 3 1012 1010 Surface decomposition on I0 p m particles 1A 1011 1B 10” 1012 2 10’2 1014 3 108 106 4 106

Case 4: Reactants are in equilibrium with a surface adsorbed layer (cf. Shannon’s second group [ 5141 ). The following assumptions are made: (i) the activated complexes are in equilibrium with the reactants, (ii) the energy of a molecule is not altered when an activated complex is substituted for a nearest neighbour, and (iii) the products do not affect the course of reaction, except t o define a boundary in surface processes. The various cases can be recognized from the magnitude of the pre-exponential term and calculated values [ 5151 are summarized in Table 7 . Low values of A indicate a “tight” surface complex whereas higher values are associated with a “looser” or mobile complex. Mechanistic conclusions based on measured and/or estimated magnitudes of v in eqn. (19) and the application of absolute reaction rate theory can be accepted only after critical consideration of the assumptions made and of the limitations inherent in the technique. Detailed and direct knowledge of conditions at any reaction interface is limited (Sect. 7 ) and identification of a specific bond rupture step as rate-controlling, involving species within a specialized and inaccessible zone, may require the adoption of an over-simplified model. Kinetic behaviour for rate processes at surfaces (interfaces) may be more complicated than is immediately apparent, since participating intermediates cannot be identified or measured and the significance of A and E values may be in doubt. Difficulties inherent in making meaningful rate measurements for heterogeneous catalytic reactions have been discussed elsewhere [ 361. It is also important that the experimentally determined Arrhenius

95

parameters (A and E ) should be demonstrated to be characteristic of the particular chemical step of interest. This is not always straightforward and problems encountered can be conveniently illustrated by reference to the (admittedly extreme) variability of data reported for the decomposition of CaC03. Zsak6 and Arz [516] list values of E of 110-1600 kJ mole-' and of A from lo2 t o lo6', determined by non-isothermal methods in a system for which kinetic characteristics are markedly sensitive to conditions prevailing in the immediate vicinity of the reactant. The isothermal data available for the same reaction were considered critically by Beruto and Searcy [121] who attribute the apparent agreement between E and the enthalpy of reaction, found in studies employing relatively large reactant masses, to (at least partial) diffusive control of gas escape across and equilibration processes within the product layer. Reliable rate studies for the forward reaction are, therefore, only obtained where the influence of the reverse step has been effectively eliminated. Kinetic parameters for the dehydration of nickel oxalate dihydrate [ 1291 have similarly been shown to be sensitive to prevailing conditions. Clearly, reliable kinetic data must be available before attempts are made t o provide a quantitative mechanistic explanation. 5.4 THE COMPENSATION EFFECT

The compensation effect occurs in a group of related reactions for which the influence of changes in A on reaction rate is offset to a greater or lesser extent by a sympathetic variation in E , often expressed as [ 361 logA = B + eE

(21) where B and e are constants. This effect has been observed in both heterogeneous and homogeneous [ 5171 rate processes. Several discussions of the significance of compensation behaviour have been given in the literature [ 516-5201, Garn [ 175,5181, considering various groups of solid state reactions, suggests that obedience of data to eqn. (21) may be a consequence of the operation of a common dominant rate-controlling factor (such as the rupture of an equivalent bond) in each member of the group of related reactions, which, therefore, occurs within the same temperature interval. This approach suggests the possibility that temperature coefficients of reaction rates in solids are not necessarily an acceptable basis for determining the energy requirement of the activation step. Such a conclusion might also be applicable t o homogeneous reactions. The problem (on which agreement has yet t o be reached) is to decide whether obedience of rate coefficients t o the Arrhenius equation (cf., the van 't Hoff relation) is sufficient evidence t o permit E to be positively identified with the energy requirement of an activation step. There are also the possibilities that diffusion and equilibrium [ 1211 in reversible reactions or heat transfer [520] processes may exert some control over

96

the magnitudes of apparent kinetic parameters. Zsako [519] accepts certain points in Garn's reappraisal of compensation behaviour but stresses that the existence of a linear relation between logA and E is a more general characteristic. Thus, while a physical interpretation for obedience to eqn. (21) cannot at present be provided, the relationship provides parameters which are useful in describing the reactivities of groups of related rate processes. There have been several reviews of literature reports of compensation behaviour [36,521,522]. The observations made are relevant in the present context since kinetic characteristics of surface processes may be applicable also to changes proceeding at a solidsolid interface (i.e., two surfaces). Some of the explanations proposed for compensation behaviour (discussed in greater detail, with citations, in ref. 36) are that (i) there is a characteristic temperature of onset of reactions; (ii) the catalyst surface is energetically heterogeneous; (iii) there is more than a single active surface; and (iv) an interrelationship exists between reaction entropy and enthalpy. The possibility that compensation effects arise as a result of surface heterogeneity has been extensively discussed in the literature. The kinetic consequences of temperature-dependent changes in the effective concentration of reactant have, however, been less extensively explored: both the collision theory of reaction rates and the Polanyi-Wigner model implicitly assume that there is a constant concentration of the precursors to product formation. However, the numbers per unit area and the mobilities of surface-held participants in an interface process may vary with temperature. If the effective concentration of such participants is [MI (possibly a composite term) the rate of product formation, dP/dt, per unit area is

A' and E' refer to the desorption, dissociation, decomposition or other surface reactions by which the reactant or reactants represented by M are converted into products. If [MI is constant within the temperature interval studied, then the values of A and E measured refer to this process. Alternatively, if the effective magnitude of [MI varies with temperature, the apparent Arrhenius parameters d o not specifically refer to the product evolution step. This is demonstrated quantitatively by the following example [36].When E' = 100 kJmole-' andA'[M] = 3.2 X lo3' moleculessec-', then rate coefficients at 400 and 500 K are 2.4 X 10'' and 1.0 X 10'' molecules sec-', respectively. If, however, E' is again 100 kJ mole-' and A'[M] varies between 3.2 X lo3' molecules sec-' at 500 K and z X 3.2 X lo3' molecules sec-' at 400 K, the measured values of A and E vary significantly, as shown in Fig. 7, when z ranges from to lo3. Thus, the measured value of E is not necessarily identifiable with the rate-limiting step if a concentration of a participant is temperature-dependent. This

97 Values of z

250r

w

100

I

I

I

30

40

50

Log (opparent A/rnolecules rn-'

5.')

Fig. 7 . Illustration of compensation behaviour, a linear relationship between log A and E , theoretically calculated on the assumption that the concentration of a participating surface intermediate varies with temperature [ 361. A more detailed explanation is given in the text.

may arise in solid phase reactions due to variations in surface equilibria or during complex reactions proceeding through a sequence of consecutive steps. Great care must, therefore, be exercised in attaching theoretical significance to experimentally determined values of A and E. The identification of an activation energy with a particular slow surface reaction requires perhaps greater knowledge of the specialized conditions prevailing at the interface than is often available or assumptions that cannot be demonstrated. 6. Kinetic investigations using rising temperature techniques

Since, in general, rates of reaction vary with both a and T,i.e. da - = Af'(a) exp(-E/RT) dt it is sometimes argued that it may be possible t o vary temperature in a systematic and controlled manner and so determine the complete kinetic behaviour [f(a)-time, A and El in a single experiment. Although close agreement between values of E determined by isothermal and by nonisothermal methods has been reported [272,523,524]for a number of decompositions, in other systems, including some reversible reactions, agreement has been less than satisfactory [516]. Clarke and Thomas [ 5251, in a compromise approach designed t o exploit the advantages of

98

both methods, suggest that the reliability of non-isothermal results can be improved if the isothermal f(a)-time relation is determined independently. Much space in the literature has been devoted to discussions [33,76, 176,12471 of the advantages, difficulties and limitations of the non-isothermal approach to kinetic studies. The present account is limited t o some general comments on the methods of kinetic analyses and detail is minimized. Application of eqn. (22) to rising temperature experiments requires obedience (i) of the rate process concerned to a single rate equation over the whole range of a and (ii) of the rate coefficient, k, t o the Arrhenius equation. Assuming these requirements to be met (and this is not acceptable in all systems), the kinetic analysis requires comparison of measured (a,T, t ) data with an appropriate form of eqn. (22). Integration of eqn. (22) is, however, not straightforward due t o the inclusion of the exponential term and an account of the various simplifications and approximations proposed to permit testing of obedience t o the various rate equations of interest occupies the greater part of the present section. Before this, however, it is appropriate t o refer t o experimental errors in rate measurements. It has already been pointed out that criteria for recognizing that isothermal rate measurements obey a particular kinetic expression in preference to all others are not generally available. The problems of curve fitting discussed in Sect. 4 are of even greater significance when temperature is an additional variable and the Arrhenius constants are not independently known. More comprehensive statistical treatments are required to achieve reliable kinetic analysis in the presence of the additional independent variable ( T ) and experimental inaccuracies may be of greater significance. Errors attributable to heat transfer during endothermic or exothermic rate processes, and/or concurrent removal of a volatile product in a reversible reaction, become of even greater importance in a change occurring during a progressive increase in reactant temperature, Sample heating, by definition, necessitates heat flow, so that material in direct contact with the heat source, perhaps the container, is at a higher temperature than that within the reactant mass and such differences are enhanced during an endothermic process (these are often also reversible dissociations). A temperature gradient is, therefore, developed within the reactant, for which allowance should be made. Although there are experimental and interpretative limitations [ 189, 5261 in the kinetic analysis of non-isothermal data, DTA or DSC observations are particularly useful in determining the temperature range of occurrence of one or perhaps a sequence of reactions and also of phase changes including melting. This experimental approach provides, in addition, a useful route to measurements of a in the study of reactions where there is no gas evolution or mass loss. The reliability of conclusions based on non-isothermal data can be increased by quantitatively determining the

99

influences of changes in reactant mass and heating rate on kinetic characteristics. Obviously, the analysis should use the maximum practicable number of (a,t, T) determinations. Microscopic examination of partially reacted salt, prepared under similar conditions of heating rate and atmosphere, can provide information which supports and facilitates the interpretation of kinetic measurements. 6.1 KINETIC ANALYSIS OF NON-ISOTHERMAL RATE MEASUREMENTS

Many non-isothermal kinetic studies use a linear rate of temperature increase from an initial value, To, so that the three equations involved can be written T = To + bT

k

=A

exp(-E/RT)

(18 )

da - = kf'(a) dt One possible approach (which has not found particular favour) is to put da - da dt - hf'(a) dT d t d T b where b = (dT/dt) = constant rate of heating, and hence

h=

(da/dT)b

f'(4

It would then be possible to verify obedience of data t o eqn. (18) from tabulated values of h and T. This has the advantage that plots of logh against T-' can be considered and these Arrhenius plots allow the calculation of A and E in exactly the same manner as data collected from a series of isothermal plots. The more usual analysis proceeds with retention of the Arrhenius equation to give the alternative expressions da dT

- = Ab-'f'(a)

exp(-E/RT)

da A f'(a) b

- = - exp(-E/RT)

In(%)

= In(+) - E

RT

A and E may be evaluated from the plot of log [(da/dT)/f'(a)] against T-' provided the form of f'(a) is known. Approximations for the f'(a)time function may sometimes be conveniently used. For example, when

100

the isothermal reaction is deceleratory, as in the dissociation of many carbonates, the first-order equation provides an acceptable alternative. When the a-time curve is sigmoid, it may not be necessary t o identify which of the several possibilities provides the best fit, it is sufficiently accurate t o select, from amongst those available, the form which leads t o the simplest algebraic treatment. Integration of the rising temperature rate expression can be represented as

Many relevant expressions for g(a) are listed in Table 6 and numerical magnitudes of f(a) have been tabulated by various authors [ 33,70,527]. For a number of systems, the first-order equation provides a satisfactory approximation, viz. 00

da

- -ln(l - a)

0

but higher orders ( n ) can only have limited application in heterogeneous systems. In general

Although approximate obedience to the first-order law may not have mechanistic significance and the exact kinetic relationship may not be established, the values of A and E found will be resonably accurate. The main difficulty in employing the integrated form of eqn. (23) is evaluation of Jexp(-E/RT)dT within the appropriate limits. Another problem is in the selection of an acceptable rate equation prior t o the comparison. There have been numerous reports in the literature of attempts to develop methods of elucidating kinetic data from non-isothermal measurements [ 76,528-5341 and it is appropriate, therefore, to attempt here a classification [ 534-536 J of these methods. A convenient, though not necessarily logical, division is under integral and differential methods, further sub-divided according to approximations used, the application of a reference temperature, or variation of heating rates. 6.2 INTEGRAL METHODS

In this approach, either CY-T data are used directly or the integral Jexp(-E/RT)dT is calculated.

101

6.2.1 Methods using tabulated values of the exponential integral

Putting U = E/RT, eqn. (23) becomes T

g(a) = Ab-'

j exp(-U)

1 exp(-U)U-2 UI

d T = -AEb-'R-'

TO

dU

UO

where Uo > U,in assigning limits and each represents a fixed value of U. This can be integrated by parts, giving &a) = AEb-'R-'[P(Ul) - P(Uo)]

with ma

P(Ul) =

exp(-U)U-* dU u1

where U1= U at the temperature of the sample. If Tois selected before initiation of reaction, then P( U,)is zero or negligible and g(a) = AEb-'R-'P(U1)

(24)

represents the equation for rising temperature data. Values of log P(U1) and U1,in appropriate ranges, have been tabulated and information in the literature includes data for a range of temperatures and activation energies [ 527,528,532,533,537-5411. Combination of eqn. (24) with the basic differential expression can be written A- (da/dt) eul _ B f'(a) from which it may be shown that

Tabulated values of log &( U,)have been given by Doyle [ 532,5331. Formally, this allows the determination of E from a single point on a thermogravimetric plot. By appropriate selection of temperature, accurate values of a 1 and (da/dT), can be found, allowing calculation of f'(al) and g(a,), hence Q ( U , ) . A t low values of a, suggested values are -0.05, many reactions can be regarded as being zero order, f'(a) + 1and g(a) + 0.05, which Doyle regards as an acceptable simplification in the calculation of E. Then

and tabulated values of log Q( V,)at low a gives U,and hence E. Zsak6 [ 5401 takes logarithms of eqn. (24) log (AEb-'R-') = log g(a) - log P(U1) = B'

102

where B' is characteristic of the reaction and independent of temperature. The validity of the rate functions f(a) can be tested by using data from rising temperature experiments to calculate g(a) at various temperatures. A trial and error method was used to find the value of E which corresponded to the most constant value of B'. Agreement was characterized by the standard deviation of individual values ( B i ) from the mean (B'). For r experimental points

The minimum value of y indicates the best value of E and the approach can also be used t o identify the most satisfactory rate equation. Satava and Skvara [ 5271 compared plots of -log P( U , ) against T with plots of log g(a) against temperature for the various functions mentioned above between 273 and 1273 K. Values of LY on the thermogravimetric curve were read off at 0.05 intervals together with the corresponding temperature, T,. Within the expected range, values of log g(a) for each rate expression were recorded on the same scale as that of the -log P( U , ) versus T plot. By superimposition of the temperature scales and lateral motion along the ordinate, the best comparison between the -log P( U,) and the log g(a) curves is identified, from which the value of E is found. The most probable rate expression can be identified and this allows calculation of A.

6.2.2 Methods using a simple approximation for the exponential integral Van Krevelen et al. [529,530] in rising temperature studies of coal pyrolysis, used the rate equation f(a) = k ( 1 -a)" so that

(1-a)-"da

= Ab-'

exp(-E/RT) d T

The exponential term was integrated by an approximate method. T, is the temperature at which the reaction rate (da/dT) is a maximum and we note that reaction proceeds within the temperature interval 0.9 T, to -1.1 Tm. Putting y = T,T' and using the above definition of U1,e x p ( 7 ) + y-' and exp(-U) = exp(-yU,) + (b-'y)-Um = (0.368 z - ' ) ~ , where Urn is the value of U at T,. Then bT dT g(a) = Ab-' Tm Integrating and taking logarithms

s(-)

In g(a) = ln[{Ab-'(U,

+ l)}(bT&l)um] + (Urn + 1)In T

103

From plots of In g(a) against In T with n = 0, 1 and 2, the plot which gives the best straight line identifies the value of n and from the slope Urn and hence E is calculated. (This approach can also be regarded as a "reference temperature method", see also Sect. 6.2.4). Alternative simple approaches t o approximations for the exponential integral exploit the linearity of the log P( U ) against U relation over short ranges [ 533,542,5431 logP(u)~--c-lU Doyle gives c = 2.315 and 1 = 0.4567 when 28 d U1 d 50 and c and 1 = 0.4667 when 18 < U1 d 35. Using the linear relationship log g(a) = log ( A E b - l R - ' ) - c - lER-'T-'

=

2.000 (25)

E may be found from a plot of log g(a) against T-' if 1 is given the appropriate value. The area under a thermogravimetric curve can also be used [ 535,5441, since P(@)

Area =

,f

g(a) dl

0

and, therefore, from eqn. (24) T

Area = AEb-lR-'

P( U ) dt

= AE*b-'R-'P(

U)

TO

However, from the work of Doyle [ 542,5451 cited above P(U) = C exp(1'U) where log C = -c and 1'/2.303 = 1. Then ln(area) = In (AE'Cb-'R-') - 1'ER-'T-' If the area at temperature T1 is F1and at Tz is F z , then

E = RTlTz(l')-1(T2 - T , ) In ( F z - F , ) from which E may be determined.

6.2.3 Methods using a series expansion as an approximation for the exponen tial integral Series expansions for P(U) have been extensively used, various limited ranges of terms being used by different investigators, but that most frequently employed is [ 532,5331 P(u) = U - 2 exp(-u)(1-

2! U-' + 3! U-'

... ( - l ) " ( n + I)! rn} .

104

for U > 16. Many alternative series have been proposed and discussed [ 534, 541, 543,546-5481. Data from these expansions can, of course, be tabulated and results used in numerical evaluation of the integral: there are numerous publications of this kind [ 76,527,528,532,534,537,538, 540,541,549-5541. Taking the first term only of the above-mentioned expansion gives [ 532,5331 P( v)

+ U-'

exp(-v)

then g(a)

exp(-U) + A E bR v2

-ARP --

bE

exp(-E/RT)

and ln{g(a)/P}

=

E constant - RT

However

which may be rearranged to give

from which the value of E may be calculated from a single temperature and the corresponding value of a or from the slope of a plot of In {g(a)/P} against T-'. The process of calculation becomes more complicated on adding further terms. Coats and Redfern [ 5551 effectively put (U-2)/Uequal t o a constant value and the relationship is equivalent t o that already given for In {g(a)/P} from the single term expansion. They assumed that f(a) = (1- a)" and determined n by testing values which have significance in solid state decomposition reactions (i.e. n = 0, 0.5, 0.67 and 1.00). Sharp [ 75,5561 has shown that the approach may be applied t o other functions of g(a). If it is assumed that the zero-order equation applied at low a,as a -+ 0, then g(a) + a. Summarizing E ln{g(a)/P) = ln(AEb-'R-') - RT =

ln{AEb-'R-'U-'(U-2)}

E - RT (for the single term expansion)

=

ln(AEb-'R-'(I - 2

y)) RT -

105

E

(for the second term expansion)

[

(

ln(a/P) = In AEb-'R-' 1- 2 -

--

RET

(for the zero-order relation, a < 0.4) and other expansions can be treated in a similar manner [ 557,5581. 6.2.4 Methods involving a reference temperature Mention of the approach given by van Krevelen et al. [529,530] has already been made. Other methods based on points of inflection have been described but in some treatments it would seem probable that the integration constant has been omitted [ 5591. Doyle's treatment [ 5331 avoids this error by using a characteristic temperature, 0 = T - T,, where T , is the temperature at which the reaction rate reaches a maximum. Doyle writes In g(a) = In g(a,)

- ER-'(T-'

- TIi' 1

and, with appropriate approximations, it may be shown that In g(a) + In g(a,) + EBR-'T;' However, Doyle has also given a relationship of this form using constants C and 1' (Sect. 6.2.2) and the single term expansion of Coats and Redfern [ 5551 gives In [ g ( a ) / P ]= In [g(a,)/P,]

+ lEBR-'T:'

Using appropriate rate equations in the above expressions, it is possible to determine the value of E . 6.2.5 Methods involving different heating rates

In this method, data are obtained for reaction proceeding at a series of different heating rates [ 539,560,5611. This reduces the advantage of the non-isothermal method and one might just as well perform a series of isothermal measurements for which the subsequent analysis will be both more accurate and much simpler. Use of the technique can be illustrated by reference to the work of Ozawa [561] which is quoted as typical. The Doyle equation [ eqn. (25)] above can be written log g(a) = log (AER-') -log b - c - 1ER-lT-l

A plot of log b against T:,f should then be linear, where ai is a specified value of a with a slope proportional t o E . This approach has been used to

106

study the decomposition of calcium oxalate [561] and some improvements in technique, designed to increase accuracy, are discussed. We terminate this section with reference to a method by Reich [ 5621 in which small and constant temperature steps, AT, were selected and the rate coefficient found by taking the exponent as a constant g(a)

=

Ab-' exp(-E/RT) AT

and

E ln{g(a)} = - __ + ln(Ab-' AT) RT For constant AT, E may be found from the graph of In {g(a)} against T-'. 6.3 DIFFERENTIAL METHODS

Direct application of the differential equation is perhaps the simplest method of obtaining kinetic parameters from non-isothermal observations. However, the Freeman+arroll difference--differential method [ 5311 has proved reasonably easy to apply and the treatment has been expanded to cover all functions f(a). The methods are discussed in a sequence similar to that used in Sect. 6.2.

6.3.1 Methods involving direct use of the basic equation The basic rate equation is

and a plot of In {(da/dT)/f'(a))against T-' gives both A and E if the form of f'(a) is known. The main source of error lies in the determination of (da/dT). Some workers advocate measuring this parameter from the fractional reaction occurring in a small time interval about a mean temperature. The procedure is simpler if the form of f(a) is known in advance [525,563-5671. A positive advantage of this method is that plots are reasonably linear if the correct kinetic expression has been selected but show an appreciable departure from this behaviour for other models [524]. The accuracy of (da/dT) measurements are increased if a number of observations, say 10, are taken on either side of the (a,T ) values of the point of interest and a polynomial expression fitted to this limited arc; the (da/dT) value is then determined numerically at the point required. This procedure is applied to each point in turn; the necessary calculations are facilitated by the use of a computer. In principle, values of n, E and A can be calculated for a kinetic expression of the form f(a) = k ( l -a)"

107

from three points on the a-T curve [568] and, if one of these corresponds to the temperature at which (da/dT) is a maximum, then only two points are required. The most satisfactory procedure is probably to take ( a , T ) values in groups of three along the a-T curve and obtain computer solutions for each triad in turn and, from these, critical comparisons permit the most probable value of n to be identified.

6 . 3 . 2 Difference-differential methods The treatment given here follows that of Freeman and Carroll [ 5311, which was also considered by others [ 534,5691. Again, the logarithmic form of the basic rate equation is used and the reaction order expressed in the form f(a) = k ( l -a)" so that, for incremental differences in (da/dT), (1- a) and 2'-', one can write Aln{b(da/dT)} = nAln(1 - a ) -EER-'AT-' Thus a plot of Aln{b(da/dT)}/Aln(l -a) against AT-'/Aln(l - a ) yields E from the slope and n from the intercept. The method is readily applied to other functions, f(a), and the appropriate formulae are given in Table 6 (pp. 90,91) from data by Heide et al. [ 5091.

6.3.3 Methods involving a reference temperature

A t the temperature, T,, for which (da/dT) is a maximum, ( d * a / d P )= 0 and [ 535,567,5701

---(-

d2a - A Ef(a) d{f(a)} ---)exp(-E/R dTz b RT' dT +

T)

Also

The appropriate rate expression may be substituted in these relations and comparison with observations allows E and n to be determined.

6.3.4 Methods involving different heating rates Two approaches are possible, those which do not and those which do use a reference temperature.

( a ) N o reference temperature Writing the rate equation in the logarithmic form for an nth order of reaction, we have E ln{(da/dT)(l - a ) " } = ln(Ab-') - RT

108

This can, of course, be tested directly for various values of n or written for any kinetic function, f(a), viz. E ln(da/dT) = ln(Ab-'f'(a)} - RT

A plot of (da/dT) against T-' for various values of a will give slope -ER-' and intercept ln(AB-'f'(a)}. The form of f(a) is not required [571]. (b) Use o f a reference temperature

The maximum rate of decomposition and associated values of a and T(=Tm) are noted. Early use of the method with first-order reactions [572] excited undue controversy since, in some cases, it was mistakenly concluded that the maximum reaction rate occurs at the peak temperature. For first-order reactions E = R pm(da/dT)m (1 - a)m but (da/dT), = Ab-'(l - a ) m exp(-E/RTm) Thus bER-'TA2 = A exp(-E/RTm) and ln(bT;')

=

ln(ARE-I) - E/RTm

so that E may be calculated from the slope of the linear plot of ln(bTA2) against T;' obtained from a series of a-T curves for different heating

TABLE 8 Relationship between reaction order, n, and the value of a corresponding t o maximum rate, h,during non-isothermal rate processes

(0 113 112 213 1 312

1.000) 0.808 0.750 0.702 0.632 0.556

2 3 4 5 10 ("

0.500 0.424 0.370 0.331 0.081 0.000)

109

rates [ 5731. If reaction kinetics are described by expressions of the form da- - h(1 - a)" dt

then Doyle [533] has shown that n is related to am. It can be shown [ 533,534,559,5731that nl/(l--n)A

(1 - a ) m

( n > 0 , n # 1)

which allows the order of reaction to be established from the value of a, (see Table 8).

7. The reaction interface A reaction interface is the zone immediately adjoining the surface of contact between reactant and product and within which bond redistributions occur. Prevailing conditions are different from those characteristic of the reactant bulk as demonstrated by the enhanced reactivity, usually attributed t o local strain, catalysis by products, etc. Considerable difficulties attend investigation of the mechanisms of interface reactions because this thin zone is interposed between two relatively much larger particles. Accordingly, many proposed reaction models are necessarily based on indirect evidence. Without wishing t o appear unnecessarily pessimistic, we consider it appropriate to mention here some of the problems inherent in the provision of detailed mechanisms for solid phase rate processes. These difficulties are not always apparent in interpretations and proposals appearing in the literature. (i) Identification of intermediates. At any instant during reaction, the total quantity of any intermediate temporarily existing within a layer a few molecules in thickness is small. Therefore, transitory unstable or reactive species residing within this specialized zone are unlikely to survive removal for identification. Characterization of the active participants is particularly difficult where (as is often the case) the phases present are finely divided, opaque (preventing spectral studies) and/or metallic (precluding the use of resonance detection methods). These difficulties are increased by the structurally disordered nature of interfaces, where there may be locally enhanced concentrations of defects, impurities and imperfections. (ii)Products. It is important that mechanistic studies should seek to identify the primary products of reaction rather than the equilibrium mixtures which follow subsequent reactions, perhaps occurring at catdytically active surfaces, e.g. metallic products. (iii) Effective area of the reaction interface. There is no completely reliable method of measuring the area of the reactant-product contact surface which is actively participating in a reaction. This zone is within the

110

mass of the solid and thus not amenable to measurement by gas adsorption (which will also include other surfaces). Estimations by microscopic methods may not detect irregularities on the molecular scale (cracking, etc.) and dissolution of one or other phase is expected to result in substantial modification of any fine structure of the residue remaining. Not all product particles necessarily maintain active contact with the reactant, particularly at high a , not all zones of contact are necessarily active in the reaction and the product does not necessarily occupy the volume of reactant from which it was derived [ 12471. In view of these several uncertainties, it follows that the preexponential factors for interfacial reactions cannot usually be expressed in units of [molecules reacting (area)-’ (time)-’]. Therefore, kinetic data for decomposition reactions of solids cannot be quantitatively compared with catalytic reactions believed to proceed by the same mechanisms (see decomposition of metal formates and of formic acid on the same metals [SS]). ( i u ) Kinetics o f interface reactions. In addition to reporting the stoichiometry of the overall reaction, it may be advantageous, in consideration of the interfacial mechanisms of such chemical changes, to employ the concepts of surface concentrations of active adsorbed intermediates and their reactivity during interactions of adsorbed species, which have found wide application in the field of heterogeneous catalysis [ 361. Species at a reaction interface may enjoy increased freedom, perhaps enhanced mobility, permitting bond reorganization and/or interaction with other participants in the chemical transformation. Many problems remain in the quantitative kinetic characterization of surface reactions, for which it is necessary to determine the quantities of intermediates participating (not all absorbed material is necessarily available for reaction) and their mobilities (which determines the possibility of interaction, the “collision number”). Consideration of reactions between two solids is, of course, more complicated than for rate processes proceeding on a single surface, since due allowance is required for other relevant contributory factors which may include the role of a second phase, effect of interactions between phases, space charge and charge transfer, creation and annihilation of imperfections (which are not necessarily localized at the interface), stresses, strains and cracking. Volatile product adsorption, perhaps on the residual phase or at or near the interface is of particular significance in influencing kinetic behaviour in reversible processes such as carbonate dissociation and water removal from crystalline hydrates. (u) Melting. One of the most difficult features in the determination of the mechanism of a reaction involving any crystalline material is the unambiguous demonstration that melting is completely absent. Local fusion can be very difficult t o detect experimentally and if progressively diminished towards monolayer quantities, the distinction between melting and mobile adsorbed species becomes a matter of definition. (Reactions often proceed relatively more rapidly in a melt where the stabilizing influence of the regular lattice is absent.)

111

The above short comments are intended to point out current problems in the accepted theories of interface reactions and the difficulties inherent in investigation of detailed reaction mechanisms. Despite these considerations, however, progress is being made in understanding the behaviour of solids and in identifying the factors which control reactivity; many specific systems are discussed in Chaps. 4 and 5. Boldyrev [lo31 has reviewed the factors concerned in autolocalization of reaction, i.e. interface development. A recent study which illustrates the necessity for the careful selection of reaction conditions in work intended to characterize interface phenomena is given by the accurate investigation by Beruto and Searcy of calcite dissociation [ 121,1391. Although many previous studies of this process had been published, these workers identified a new metastable, but localized, intermediate crystalline phase and give a critical discussion of the factors controlling product evolution during the reversible reaction. It is appropriate t o emphasize again that mechanisms formulated on the basis of kinetic observations should, whenever possible, be supported by independent evidence, including, for example, (where appropriate) X-ray diffraction data (to recognize phases present and any topotactic relationships [ 1257]), reactivity studies of any possible (or postulated) intermediates, conductivity measurements (to determine the nature and mobilities of surface species and defects which may participate in reaction), influence on reaction rate of gaseous additives including products which may be adsorbed on active surfaces, microscopic examination (directions of interface advance, particle cracking, etc.), surface area determinations and any other relevant measurements. In general, therefore, a full representation of the interface reaction should ideally include characterization of (i) all significant chemical changes at the reaction interface, described quantitatively with identities, concentrations and interactions (i.e. bond redistribution processes) of all participating intermediates, and (ii) phase reorganizations including recrystallization, topotactic relationships, cracking and sintering of all participating solids. We complete this section with a summary of the factors which may contribute to the facilitation of reaction at the interface [ 4871. (Some aspects of the mechanisms of solidsolid interactions, where rate is controlled by diffusion across a product barrier layer, are more appropriately discussed in Chap. 5 in the context of the reactions to which they apply.) Mechanisms of decomposition reactions at interfaces are conveniently considered with reference to the diagrammatic representations in Fig. 8 (R = reactant, 1,I’ = intermediates and P = product) and classified under the following headings. (i) Surface desorption. Preferred dissociation (reaction) at the reactant surface has been widely ascribed t o the unsymmetrical force fields operating here and the possibility of rapid escape of product. Desorption may

112

F

P

I

R

t

R

(a)

(b)

F1

Desorption from a surface

reactant

I

-

- - - !

- --- - - - -

product

strain (C)

product (cracking)

reactant (d )

Strain and cracking a t reaction interface

R

i'

/

';

reactant

1

product

P

(el Catalysis bysdid product

Fig. 8. Mechanisms of decomposition reactions occurring at interfaces. R = reactant; I, I' = intermediates; and P = product. A more detailed account of these phenomena is given in the text.

occur directly [Fig. 8(a)] or may follow surface interactions, some steps of which may be reversible [Fig. 8(b)] . No influence of the solid residue has been illustrated but any phase adhering to the reactant surface may chemisorb and/or hinder escape of the volatile product. (ii) Strain at the reaction interface. Mismatch of lattices at the interfacial contact phase [Fig. 8(c)] is believed to result in strain and accordingly the rate-limiting step (e.g. proton or electron transfer, bond rupture) may occur more readily than in unstrained material; hence there is preferred reaction at the interface. The mobilities of participants may also be

113

varied. If strain becomes insupportable, cracks [1250] may spread in advance of the interface exposing new surfaces at which nucleation then becomes possible [Fig. 8(d)]. (iii) Catalytic actiuity b y products. The product phase may promote a slow step in the decomposition sequence, and reaction may proceed as a catalytic process on this phase [Fig. 8(e)]. Various types of intermediate behaviour embodying features of more than one of these effects can be visualized. In addition to the considerations (i)-(iii) above, the interface may behave as a source or sink for the creation and/or annihilation of imperfections such as lattice defects and electrons, which can be important participants in the overall change (for clarity, such effects have not been included in Fig. 8). The decomposition characteristics of many solids are influenced by externally supplied energy such as irradiation, cold working, etc. Although crystal growth from solution has been frequently shown to proceed through preferential accumulation of material at a step edge on the surface, it does not appear t o have been suggested that the converse process, whereby decomposition results in growth of nuclei, proceeds by an analogous model, that is, erosion of a step edge. Spiral growth of nuclei is one explanation of preferential development of decomposition at dislocations observed, for example, in calcite dissociation [ 574,5751.

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Chapter 4

Decomposition Reactions of Solids

The literature relating t o the kinetics of solid phase decomposition reactions is considerable so that, t o provide a useful account within an acceptable length, it is necessary t o be selective. The present survey emphasizes those systems which have been most extensively investigated, since the most detailed information available, and the deductions drawn therefrom, may be expected to be of greatest value in advancing understanding of the factors that control the reactivity of solids. Coverage is intended to include representative examples of the various types of substance that decompose before melting. A main objective of most kinetic studies is the determination of the reaction mechanism. For solid state decompositions, this usually involves (i) characterization of the geometry of interface advance and (ii) investigation of any factors potentially capable of giving information concerning interface conditions and phenomena, the participating intermediates and their interactions. In selecting articles for inclusion in the reference list given below, emphasis has been placed on studies which provide kinetic evidence for proposed reaction mechanisms and which, at the same time, give access t o the earlier literature. Few comprehensive reviews exist. No single criterion has been recognized as constituting a satisfactory basis for the systematic classification of the kinetics of solid-phase reactions (Chapt. 1, Sect. 3). A classification based on the anion is preferred here since it is this constituent which undergoes breakdown in most reactions of interest and proposed reaction mechanisms for substances containing a common anion often include similar features. Kinetic characteristics of decomposition reactions of solids are not in general, directly related to the composition, structure or any other identifiable feature of the reaction or reactant. The shapes of a-time curves for substances containing common groups are frequently dissimilar, whereas comparable kinetic obediences may be found in the reactions of otherwise dissimilar materials [29]. The marked variations in the intensity with which different solids have been investigated also introduces difficulties into the presentation of a balanced survey of the field. Some compounds have been the subject of successive and detailed studies by several groups of workers (almost achieving the status of model reactants, e.g. inter alia, CuS04 * 5 H 2 0 , CaC03, BaN6, NH4C104and NiC204). Other and related substances have been largely or entirely ignored. However, now that the general features of the kinetic characteristics of reactions of solids have

116

been established, and various types of nucleation and growth phenomena recognized, greater interest is being directed towards determining the kinetic consequences of systematic changes of reactant cation and/or anion. (The occurrence of melting will of course, exclude a substance from consideration as a solid phase reaction, with the consequent appearance of gaps in surveys). The range of solid reactants studied has increased markedly in recent years, although interest has also been maintained in those which have already received considerable attention. Well-studied systems are often conveniently used in the development or refinement of experimental techniques. A convenient starting point in the present survey is the dehydration of crystalline hydrates since in many reactions, the residual product, after removal of lattice and/or co-ordinated water, is the reactant in a subsequent decomposition. This theme is conveniently continued through consideration of hydroxides and oxides, since oxides are the final residual products of many pyrolyses. The further binary compounds then discussed include hydrides, carbides and nitrides, which possess metallic character, followed by the contrasting behaviour of the ionic azides. Other compounds containing more complex constituent groups are considered. These include the metal salts of oxyacids and also ammonium salts (conveniently discussed as a group). Though not strictly entirely inorganic, the inclusion here of certain metal carboxylates is justified by the notable contributions made to the subject by studies of these solids. The final groups of co-ordination compounds are treated briefly since, with the notable exception of the hydrates, relatively less progress has been made in the kinetic characterization of the consecutive and/or concurrent reactions contributing to their overall decomposition. Reports of kinetic studies do not always include an explicit statement as to whether or not the reactant melted during reaction or, indeed, if this possibility was investigated or even considered (cf. p. 1).This aspect of behaviour is important in assessing the mechanistic implications of any data since reactions in a homogeneous melt, perhaps a eutectic, usually proceed more rapidly than in a crystalline solid. It is accepted that the detection of partial or localized melting can be experimentally difficult, but, in the absence of relevant information, it is frequently impossible to decide whether a reported reaction proceeds in the solid phase. Solid-state reactions have usually been studied either by isothermal or by non-isothermal methods, with few attempts to combine the advantages of these alternative and sometimes complementary approaches. For reasons stated in Chap. 3, the kinetic information obtained from isothermal studies appears to be more accurate and reliable, and these studies are emphasised in this review. Wherever appropriate, however, account is taken of non-isothermal studies as a valuable source of complementary information.

117

1. Dehydration of crystalline hydrates Although crystalline hydrates cannot be distinguished from other solid reactants on chemical or structural criteria, the considerable interest which has been directed towards investigation of the dehydrations of this group of substances makes it convenient t o discuss them as a single class. We adhere to this convention which has been well-established in the literature: dehydrations featured amongst the earliest studies of solid phase decompositions. It is appropriate t o point out that crystalline hydrates are correctly regarded as co-ordination compounds, and could, therefore, perhaps more appropriately be incorporated in Sect. 6 together with other compounds with which they are structurally related. Hydrates as a class, however, have been more intensively studied than any other group of co-ordination compounds. Dehydration reactions are typically both endothermic and reversible. Reported kinetic characteristics for water release show various a-time relationships and rate control has been ascribed t o either interface reactions or t o diffusion processes. Where water elimination occurs at an interface, this may be characterized by (i) rapid, and perhaps complete, initial nucleation on some or all surfaces [212,213], followed by advance of the coherent interface thus generated, (ii) nucleation at specific surface sites [ 2081, perhaps maintained during reaction [ 4261, followed by growth or (iii) (exceptionally) water elimination at existing crystal surfaces without growth [ 621. A most important feature of dehydration reactions is the influence of the product phase on the ease of water escape, since such residual material invariably tends, t o a greater or lesser extent, t o diminish the rate of diffusion of water from the reaction interface, an effect that is often referred to as impedance [64]. In these reversible reactions, the adsorption of evolved water by adjacent dehydrated solid may significantly influence the measured overall reaction rate. Thus, in the formulation of a reaction mechanism, it is necessary t o characterize all participating phases, particularly those in the immediate vicinity of the interface. This may be experimentally difficult since dehydrated salts are often amorphous, or pseudomorphous with the reactant, and certain anhydrous initial products undergo subsequent recrystallization. Moreover, water elimination from a number of reactants proceeds through the intermediate formation of one or more lower hydrates. Both stepwise dehydration and delayed recrystallization may be interrelated and vary with prevailing conditions, particAt low temperature and in ularly the water vapour pressure (PHZO). vacuum, CuSO, - 5 H 2 0 is dehydrated directly to the amorphous monohydrate, but in the presence of water vapour, a crystalline intermediate, CuSO, - 3 H 2 0 can be isolated [ 5761. Metastable intermediates can be formed when a hydrate is abruptly placed under conditions far from equilibrium [373]. In a number of systems, it is possible to demonstrate

118

the existence of a sequence of different intermediates: those identified during removal of water from MgS04 - 7 H 2 0 include MgS0, (6, 4, 2.5,2 and 1 H2O) [577]. Product phase recrystallization is facilitated by water vapour and is thus dependent on PHzowhich exerts an influence over structural reorganization, leading to development of cracks, channels and pores through which water may escape from the reaction interface. With the possibility that behaviour is sensitive t o PHZoand that intermediate phases of variable crystallite sizes may be formed, it is necessary t o exercise great care in propounding mechanisms from rate measurements for the overall change. Aspects of the analyses and interpretation of data for dehydrations are often discussed in the context of two generalizations, namely the Polanyi-Wigner equation [ 512-5141 [eqn. (19)] and the Smith-Topley (S-T) effect [578] as described in Sects. 1.3 and 1.4. 1.1 STRUCTURES OF CRYSTALLINE HYDRATES

Water [579] is present in the structure of true crystalline hydrates [580] either as ligands co-ordinated with the cation (e.g. [ C U ( O H ~ ) ~in] ~ ' CuSO, * 5 H20) or accommodated outside this co-ordination sphere within voids left in anion packing, further stabilized by hydrogen bonding (e.g. the remaining water molecule in CuSO, 5 H20). Every water molecule in a crystalline hydrate has, as its nearest neighbows [ 5791, two proton acceptors and at least one electron acceptor. Where only a single electron acceptor is present, co-ordination of the HzO molecule is approximately planar trigonal, and, when two are present, tetrahedral co-ordination is adopted. Large deviations from these configurations seldom occur. Classification [ 579-5821 of the water molecules in hydrates, on the basis of co-ordination of the lone pair orbitals, has been discussed further [579,581] and modified [580] (see Fig. 9 and Table 9). For example, the water in CuSO, * 5 H20 is located in three different environments: two H20molecules are in Class 1, type D; two are in Class l',type J, and the remaining one is in Class 2, type E. Makatun and Shchegrov [583] have considered the kinetics of water evolution in terms of retention of vibrational individuality of the H 2 0

-

Fig. 9. Environment of a water molecule in a crystalline hydrate: see also Table 9. (Redrawn from ref. 580, p. 3572: reproduced, with permission, from Acta Crystallographica.)

119 TABLE 9 Classification of water molecules in crystalline hydrates on the basis of co-ordination environment (Reproduced, with permission, from ref. 580: see also Fig. 9.) Type

C1

C2

C3

M+ M' M+ H H H

M+ M' H H M' H

Class 1 Co-ordination of oxygen with one cation, C1, positioned along bisector of the lone-pair orbitals. Class I '

(p

M+ M2+ H M"+

Is

M+ M2' H M"'

M

I

C1 along a lone-pair orbital.

Class 2 Co-ordination of oxygen with two cations, C2 and C3, along the lone-pair orbitals, giving an approximately tetrahedral arrangement around oxygen Class 3 Co-ordination of oxygen with three cations, C1, C2 and C3, to give an approximately trigonal bipyramidal arrangement about oxygen

Class 4 Co-ordination not specifically directed.

!I

A

'0 P

, Q R S T

M' H M' M+ H H

L

molecules, detected by infrared measurements. They suggest that hydrates may be classified according to whether the number of water molecules is greater than, equal t o or less than the cation co-ordination number. A shortcoming of this scheme is that no allowance is made for the influence of the anion. Moreover, when stepwise dehydration occurs, the number of steps does not always coincide with the number of water molecule environments in the original hydrate. Features of each stage of reaction could thus be predicted only on the basis of information on the state of the constituent water in each intermediate. It can be shown by spectroscopic measurements that many such intermediates are in stressed states, since anion symmetry is diminished. Proton mobility is markedly influenced by

120

the anion, particularly in lower hydrates, and it may be possible [ 5831 to characterize the state of the water by the displacement of hydrogen towards the anion (some hydrates can be regarded as complex acids). 1.2 KINETICS OF NUCLEATION AND GROWTH DURING DEHYDRATIONS

Early (ca. 1930) dehydration studies used gravimetric methods, often combined with photomicrography [ 641. Allowance for self-cooling of these endothermic reactions was usually made [ 5841 and the influence of water vapour pressure in controlling reaction rates was appreciated. These techniques have since been supplemented by X-ray diffraction, thermal analysis, infrared and NMR spectroscopy and measurements of proton conductivity. Results have been interpreted with due regard t o phase 2'). The problems which attend the determinastability diagrams (PHZO, tion of reliable kinetic information from non-isothermal measurements have been mentioned in Chap. 3, Sect. 6. Additional difficulties concern the effect of heating rate on the detection and characterization of intermediate hydrates [585], and the thermal consequences of melting and/or condensation of water followed by its subsequent evaporation.

1.2.1 Nucleation The formation of dehydration nuclei is markedly sensitive t o superficial imperfections of crystals, reaction often being preferentially initiated in damaged regions. Exceptional care is necessary in the preparation of surfaces which are acceptable for studies of nucleation kinetics. Even when such care has been exercised, unavoidable variations in defect structure from one crystal t o another may result in some irreproducibility of behaviour [ 12501. A t relatively low reaction temperatures and with crystals of exceptional perfection, the induction periods t o nucleus formation are sometimes very long (perhaps measured in days) and may vary from one crystal face to another. Studies in this field were particularly developed during the period 1930-1945 and the subject has been less intensively investigated since that period. Some early studies effectively eliminated the kinetic problems of interpretation which resulted from a long induction period followed by an acceleratory process by initiating reaction on all surfaces of a large crystal by rubbing with product particles. Following such treatment, reaction proceeded by advance of an interface of known geometry (a contacting volume process).

( a ) Instantaneous or initial very rapid nucleation The dehydration reactions of C U ( H C O ~- )4~H2O [213] and of Mn(CH02)2- 2 H20 [91,212] are characterized by the rapid initial production of a complete and coherent reactant-product interface at

121

preferred crystallographic surfaces. Kinetic studies of the nucleation steps involved are impracticable: the onset of reaction in the copper salt is very rapid [213] while the acceleratory phase (a < 0.15) in the manganese salt is too short-lived for kinetic analyses [212]. Nucleation sites in the dehydration of NiS04 - 6 H 2 0 were identified [208] as the points of intersection of line dislocations with the crystal surface, (001) face. The number of nuclei formed during the early stages of dehydration did not increase during subsequent reaction. UOz(N03)2 6 H 2 0 showed unusual behaviour [62] in that there was no induction period t o dehydration, the generation of specialized nuclei was apparently unnecessary since water evolution occurred by desorption at existing crystal surfaces and no migratory interface was developed. ( b ) Continued nucleation

The initiation of dehydration at the first-formed nuclei does not necessarily preclude the continued production of further nuclei elsewhere on unreacted surfaces. During dehydration of CuS04 - 5 HzO,the number of nuclei was shown [426] to increase linearly with time, whereas during water removal from NiS04 7 H 2 0 [50] the number of nuclei increased with the square of time, N t = k N ( t- t o ) z .(The latter behaviour contrasts with the instantaneous nucleation of NiS04 6 H 2 0 mentioned above.) Gamer and Jennings [431] studied nucleation during the dehydration of potassium and ammonium chromium alums. Detailed kinetic measurements were made for the relatively enhanced rate of nucleation which followed admission of water vapour to the solid after a period of vacuum nucleation. This catalytic effect of water vapour is ascribed to its participation in the reorganization of the lattice which had collapsed during previous treatment in vacuum.

1.2.2 Growth It is usually assumed in the derivation of isothermal rate equations based on geometric reaction models, that interface advance proceeds at constant rate (Chap. 3 Sects. 2 and 3). Much of the early experimental support for this important and widely accepted premise derives from measurements for dehydration reactions in which easily recognizable, large and well-defined nuclei permitted accurate measurement. This simple representation of constant rate of interface advance is, however, not universally applicable and may require modifications for use in the formulation of rate equations for quantitative kinetic analyses. Such modifications include due allowance for the following factors. (i) The rate of initial growth of small nuclei is often less than that ultimately achieved. (ii) Rates of interface advance may vary with crystallographic direction and reactant surface. (iii) The impedance t o water vapour escape offered by

122

the product layer may vary with PHZO. These effects may be temperaturedependent. Linear rates of reactant-product interface advance were observed during the dehydrations of Mn(HC0&.2 HzO [91,212] and of 4 HzO [ 2131. There was evidence for the manganese salt CU(HCOZ)~ [91] of a small initial rate increase during reactions at 335 K, though above 339K the rate of growth was constant throughout. It was concluded [213] for the copper salt that diffusion was not rate-limiting, even though escape of the evolved water necessitated transportation across interlaminar material. The rate of interface advance during dehydration of NiS04 * 6 HzO [208] was strictly linear above 313 K, while at lower temperatures it was initially somewhat lower but increased with nucleus diameter until a constant limiting value was reached. The rate of growth of nuclei in NiS04 * 7 HzO [50] was relatively slower during the induction period but became constant when nuclei were >0.01 mm. The rate of linear increase of diameters of dehydration nuclei in CuS04 * 5 HzO [ 5261 was also constant after completion of an initial slow stage; dehydration areas were star-shaped since the rate of growth varied with crystallographic direction. Anisotropic growth was even more pronounced in BaClz - 2 HzO [ 1891, where there was rapid initial, largely two-dimensional development of nuclei across the (010) faces. Two types of nuclei could be distinguished [51] in the dehydration of chrome alum. One type, often developed at low temperature and low reaction rate, was microcrystalline and believed to be relatively less stable than the other type in which the product assemblage gave the appearance of having undergone recrystallization since there was a star-shaped crack in the centre. Rates of isothermal growth of small nuclei were irreproducible but increased towards one or other of the two values which were characteristic of the two types o f , -lei. Dehydration rates varied from one individual reactant crystal t o aliother. Later work with chrome alum [586] showed that nuclei were hemispherical. The rate of interface advance into the crystal bulk was independent of thickness of the barrier layer and not, therefore, controlled by diffusive removal of the volatile product. The nuclei in mixed alums [586] ( Ail-Cr) were hexagonal or square and the initial relatively rapid rate of inert we in the linear dimension diminished by about half after a characteristic diameter had been reached. The growth of nuclei in mixed alums (scji? solutions) was apparently not a simple interface advance since reactio: was initiated beyond the established front. New zones were believed t o advance inwards towards the existing nucleus and also outwards, t o give each reaction zone the appearance of a number of concentric hemispheres. There is clearly scope for further study here [1250], as indeed there is for many of the expenmental approaches pioneered by Garner [64]. Furthermore, a number of theoretical concepts he proposed (e.g. the role of vacancies in the water lattice) are worth further detailed reconsideration.

123

1.2.3 Shapes o f nuclei A consequence of different rates of interface advance in different crystallographic directions is that the nuclei developed possess characteristic shapes. Examples include the half-ellipses on NiSO, * 7 HzO [50], square pyramids on NiS04 6 H 2 0 [208], stars on CuS04 5 H 2 0 [426] (though the shape varies with crystal face [587]), spherical or elliptical on MgS0, * 7 HzO [588] and other simple figures on alums [586]. At low temperature, ZnSO., 7 HzO [589] reacts with the formation of rectangular nuclei, while at higher temperatures and water vapour pressures, the nuclei tend to be rounded, with recrystallization resulting in cracking of the product assemblage. Garner and Jennings [431] conclude that nuclei of shapes other. than spherical occur most frequently during vacuum dehydrations, when the influence of the crystallographic structure of the reactant on the water elimination process is most significant. In the presence of water vapour, product phase reorganization is facilitated and nuclei tend to be hemispherical with irregular zones of reactant-product interfacial contact.

-

-

-

1.2.4 Diffusion-controlled dehydrations The reactions referred to in the above paragraphs all share the common feature that the rate is controlled by an interface process. This is not always operative and when there is diffusion control it may not be necessary to establish a sharp reactant-product contact. The dehydrations of the following solids have been identified as diffusion-controlled: CaSO, * 2 H 2 0 [590] (>383 K), P-CaSO, HzO [591], CaHP04 2 HzO [ 5921 and Na3NiP3OI0 1 2 H 2 0 [593]. Although kinetic measurements were not made for water release from hydrated barium acid oxalate [ 2531, it is suggested that water is loosely accommodated within channels of the lattice from which escape occurs with minor structural reorganization.

-

-

-

1.3 THE POLANYI-WIGNER EQUATION

This equation, eqn. (19), and aspects of its development and application have been discussed in Chap. 3, Sect. 5.3. Table 10 summarizes representative data for the dehydrations of crystalline hydrates, listing values of v, a s-l), and also the activation vibration frequency (expected t o be energy ( E ) and enthalpy of water removal (AH). In a number of instances, E and AH are of comparable magnitude. When available, the views of the authors concerned as t o the significance of the fit of their data t o eqn. (19) have been recorded. It should be remembered, however, that this does not always constitute an unbiased view of the theoretical significance of the relationship since there is a predisposition apparent in many reports towards accepting its general validity. Reactions where agreement

124 TABLE 10 Representative kinetic data for dehydrations of crystalline hydrates and some comparisons with predictions of the Polanyi-Wigner equation [eqn. (19)] Solid hydrate

E

Frequency factor

Dehydration enthalpies mole-' ) (kJ mole-' )

(vls-') ~~~

~~

~

C U S O ~. 5 HzO C U S O ~.3 HzO NiS04 .7HzO NH4 alum

~~~~~~~

10"

65

455 594 50 586

8.4

X

10"

K alum

2.2

X

10"

67

65

586

Chrome alum

1.2 3.6

X X

loz5

lo4

130 96

-42 54

51 584

4

X

' 0 1

125

X

- 10'

- 1033

High

+

46 -160 170 101 130

52 54

584

-

-75 47

Cu(HC02), .4 HzO

Fair agreement Fair agreement Fair agreement Not satisfactory

62 64,514 64,514 578 129 Not satisfactory 212 Normal u 91 AS small 213

52 58 57

Mn(HCOZ)? . 2Hz 0

Notes by authors

~

71 65 80 67

UOz(N03)z . 6HzO CaC03 .6HzO 2 KHCz04 . HzO MnC204 2 HzO NiC204 . 2 HzO

8

Ref.

(kJ

52

-

-

is satisfactory are described as "normal" (v l O I 3 s-' and E AH) whereas those with diverge are "abnormal". While the data included in Table 10 do not constitute an exhaustive survey, sufficient information is given to show that several important systems are not adequately described by the Polanyi-Wigner relation. It has been stressed above that experimental values of Arrhenius parameters for heterogeneous rate processes are not necessarily to be associated with a single rate-limiting step but may be composite terms arising through cooperative surface phenomena [ 361. Accordingly, we must express doubts about the value of applying eqn. (19),developed from a consideration of simple dissociation or evaporation steps, to possibly more complicated reactions. A further problem arises in those systems for which the magnitude of E is not readily determined. Significant uncertainties are found in the following dehydrations (ranges oL E, in kJ mole-', are shown bracketed): a-CaS04* HzO [590](32-82, 60-144); P-CaS04 * HzO [591] (25-200); CaHP04 - 2 HzO [592] (21-192); CaCZO4 HzO [282] (70-210); La2(C0& - 8 H 2 0 [595] (-500-700) and see also NiC204 2 HzO [129].The general application of eqn. (19)to solid phase dehydrations has yet to be demonstrated.

-

-

125 1.4 THE SMITH-TOPLEY EFFECT

The Smith-Topley (S-T) effect is the characteristic variation of isothermal dehydration rate (da /dt), with prevailing water vapour pressure (PHz0)shown in Fig. 10. (da/dt)D first decreases with increasing PH20,later rises to a maximum value and thereafter diminishes towards the zero rate of water loss that is achieved at the equilibrium dissociation pressure. For many hydrates, the reduction in (da/dt)Dfrom that characteristic of reaction in a good vacuum to that at PH2, 0.1 Torr is large (X -0.1) and the subsequent maximum may be more or less sharp. Since the reaction rate is, in general, represented by

-

the characterization of the individual functions, f A ( P H 2 0 ) and fB(a), requires the separate investigation of each variable while the other is held constant. Measurement of S-T behaviour, therefore, requires determinations of changes of (da/dt)D with PHZofrom either (i) values of rate at a selected value of a or (ii) rate coefficients from a rate expression which has been shown t o be obeyed over the range of PHZoinvestigated. Where nucleation is particularly slow, the initiation of reaction can be hastened by a strictly standardized preliminary preheating procedure to establish the reaction interface more rapidly [ 5961. The form of the (da/dt)D-PH20 curve and the position of the maximum may vary considerably with temperature and S-T behaviour may not be detected under certain conditions [ 5961. These effects [282,2911 may

3

(L

0

2 Water vopour pressure

4

26

/ Torr

Fig. 1 0 . Schematic representation of variations in rate of dehydration with prevailing water vapour pressure for certain crystalline hydrates. This is an example of SmithTopley behaviour. (Based on observations [ 6 4 ] for the dehydrations of CuSO4 . 5 HzO and MnC204 * 2 HzO.)

126

exert some influence over apparent values of A and E . The S-T effect has only been noted for dehydrations. The earliest report describing behaviour of the type shown in Fig. 1 0 was by Topley and Smith [578] from studies on MnC204- 2 HzO, also the subject of later work [597]. Many other hydrated salts show S-T behaviour, a representative list by Bertrand et al. [596] includes LiS04 - HzO, MgS04 4 HzO, CuS04 5 HzO, CuS04 3 H 2 0 , and Na2B405(0H)48 H 2 0 while other authors have shown the effect t o occur in (inter alia) CaCZO4* HzO [282] and P-CaSO, ;4 H 2 0 [591]. The reaction of ZnS04 * 7 HzO [81] is even more complicated since the (dcx/dt)D-PH20 curve includes two maxima and two minima. The S-T effect has not, however, been demonstrated in all dehydrations: it was either not detected or reported as absent for Mn(HC02)z* 2 H20 [212], C U ( H C O ~* )4~H20 [213] and UOz(N03)2- 6 HzO [62]. These conclusions must include the possibility that the effect could become detectable under hitherto untested conditions since the magnitude of S-T behaviour usually increases with reaction temperature. No single mechanistic explanation of the S-T effect has been accepted as possessing general validity: the salient features of the several alternative reaction models which remain under discussion are summarized below. There also exist the possibilities that there may be concurrent, consecutive or intermediate behaviour and that different mechanisms may operate for different solids.

(i) Properties of adsorbed water. In the earliest discussion of the effect, Topley and Smith [578] considered the influence on (dcI/dt)D of water adsorbed on the product solid which is in equilibrium both with water at the interface and water vapour in the surrounding atmosphere. The strength of adsorption of such water is expected t o vary with surface coverage, since surface bonding forces will probably be perturbed when adsorbed molecules occupy adjoining sites. From a qualitative consideration of this variation in ease of acceptance of a water molecule into the adsorbed layer with surface coverage, it was possible to explain [578] the observed pattern of kinetic behaviour. It was believed that the energy barriers to water movement were influenced by the configuration of water molecules but a quantitative treatment was not possible due to the absence of the necessary quantitative information concerning the sizes, spacings and dispositions of species at the interface. A variation of this approach has recently been provided by Lyakhov et al. [598] who, from measurements of water adsorption on CuS04 - 5 HzO, on MgS04 - 7 HzO, and on their respective dehydration products, discern a correlation between strengths of surface bonding and S-T behaviour. At low surface coverages, the mutual dipoledipole repulsions in the adsorbed layer inhibit water loss, in part by a blocking action on loss of water of crystallization and in part by polarization effects which provide a

127

barrier to water escape from the surface. At higher coverages, water with opposed orientation is retained by the anions (SO:-)and this results in changes of the effective polarization contributions and, in consequence, there is the increase in (da/dt)D t o the maximum of the S-T plot. It has also been shown [599] that a maximum on the (da/dt)D-PHZO plot can result from a catalytic effect by the product gas (water) on the desorption process. (ii) Product phase recrystallization. S-T behaviour has also been identified with progressive changes in product layer structure. The probable significance of the reorganization of the dehydrated material on kinetic characteristics was first pointed out by Volmer and Seydel [ 5971 and later described in detail by Garner [64]. During dehydration in high vacuum, the water molecules leave the interface without hindrance, passing easily through the product which may be unstable, amorphous or pseudowater may be adsorbed on the walls of narrow morphous. A t low PHZO, capillaries and the escape of further water, through these channels of molecular dimensions, is impeded. Some support for this model has been provided from adsorption measurements [64]. After the minimum in the (da/dt)D-PHZOcurve, the availability of water is sufficient to promote the formation of a crystalline product by a nucleation and growth process, schematically represented in Fig. 11. Recrystallization is accompanied by

Fig. 11. Schematic representation of dehydration followed by recrystallization of the product phase behind the advancing interface. This model provides an explanation of Smith-Topley behaviour (see text).

128

the development of channels, cracks and pores between particles through which water may readily pass, with a consequent rise in (da/dt)D. At higher values of PHZO, the increased rate of the reverse reaction results in a progressive diminution in the net rate of water loss, becoming zero at equilibrium. The central feature of this model, recrystallization, is often, but not invariably, associated with S-T behaviour. The absence of a change in structure is advanced as an explanation of the regular decrease of (da/dt)D with PHZo(i.e. the absence of a S-T effect) in the dehydrations of Mn(HC02)2 - 2 H2O [91,212] and Cu(HC02)2 * 4 H2O [213]. (iii) Heat and gas transfer a t the reaction interface. On this model, S-T behaviour is ascribed t o the development of local inhomogeneity at the reaction interface, resulting from departures from equilibrium due to control by rates of heat and mass transfer [ 5961. From kinetic studies of the dehydration reactions of LBO4 H20, MgS04 4 H20, CuS04 * 5 H20, CuS04 - 3 H2O and Na2B405(OH), 8 H20, over ranges of P H ~ O and temperature, it was shown that for each salt, S-T behaviour occurred within a welldefined temperature interval. The maxima and minima of S-T plots corresponded t o characteristic lines on the PH30-temperature stability diagrams involved, represented schematically in Fig. 12. The

-

-

Fig. 12. Schematic representation of variations in dehydration rates (k)with prevailing water vapour pressure (PH~O): These examples include Smith-Topley behaviour and indicate correlations with phase stability diagrams. (After Bertrand et al. [ 5961,reproduced with permission, from Journal of Inorganic and Nuclear Clemistry.)

129

diminution in reaction rate is attributed t o local departure from equilibrium conditions at the level of sub-grain boundaries within microdomains at the reaction interface. It has long been known that dehydrations of large crystals may be accompanied by self-cooling but less is known about local variations in heat and mass transfer during reaction, particularly in the vicinity of the reactant-product contact. Product recrystallization is not precluded. In a discussion of these results, Bertrand et al. [596,1258] point out that S-T behaviour is not a specific feature of any restricted group of hydrates and is not determined by the nature of the residual phase, since it occurs in dehydrations which yield products that are amorphous or crystalline and anhydrous or lower hydrates. Reactions may be controlled by interface or diffusion processes. The magnitudes of S-T effects observed in different systems are not markedly different, which indicates that the controlling factor is relatively insensitive to the chemical properties of the reactant. From these observations, it is concluded that S l ’ behaviour is determined by heat and gas diffusion at the microdomain level, the highly localized departures from equilibrium are not, however, readily investigated experimentally. (iv) Different rates of growth of different nuclei. In a kinetic study of the dehydration of CuS04 5 H20,Lyakhov et al. [1259] measured the rate of growth of the two classes of nuclei observed: star-shaped or round (CuS04 * HzO)and elliptical (CuS04 3 H20). It was shown that the rates of interface advance of these two distinct types varied differently with changes in PHZO. Elliptical nuclei (trihydrate) did not grow when < 0.1 Torr and the rate of growth of monohydrate decreased rapidly wlth increase in water vapour pressure in the region -1 Torr. Accordingly, product composition approached C u S 0 4 - H 2 0 in the region of the Smith-Topley minimum and tended towards CuS04 - 3 H20 near the maximum. The Smith-Topley effect was, therefore, ascribed to the existence of alternative reaction paths, the rates of which exhibited different PHzodependencies: CuS04 - 3 HzO was a metastable intermediate in the system discussed here.

(v) Discussion. Further work is undoubtedly required t o establish which (if any) of the above explanations can be generally or specifically accepted. Clearly it is desirable, since the effect is of wide occurrence, that the outstanding differences between the diverse theories should be resolved. At present recrystallization, (ii), probably commands the widest acceptance but the arguments supporting gas and heat transfer, (iii), deserve close attention and this model can be expected to be subject to further scrutiny in the near future. The above explanations, (i)-(iv), of S-T behaviour suggest that changes at the reaction interface may include the following factors which

130

exert some control over reaction rate: (i) participation of an adsorbed intermediate, (ii) phase reorganization, influencing product escape, (iii) local disequilibrium and (iv) alternative reactions. All these factors are also capable of exerting appreciable control over experimentally determined values of A and E . Moreover, the complexities of the phenomena described are in marked contrast with the simple dissociation step assumed in the development of the Polanyi-Wigner equation [eqn. (19)] so that this equation must be applied t o kinetic data for dehydrations with caution. 1.5 KINETICS OF DEHYDRATION OF REPRESENTATIVE CRYSTALLINE HYDRATES

The following survey of the kinetics of dehydration of crystalline hydrates includes examples of the various types of behaviour commonly observed and unusual systems which merit inclusion in a general review. In this section (and also those which follow), the content is inevitably the product of selection since every relevant article cannot be individually cited. 1.5.1 Copper sulphate

Smith and Topley [ 6001 reported rates of dehydration (mass loss area-' time-') for the dehydration of CuS04 - 5 H20 between 273 and 316 K and discussed problems encountered in the measurements of rates, which included trihydrate formation, impedance of water vapour escape by the product layer, and reactant self-cooling. Later, Topley [455] provided a statistical mechanical interpretation of the interface reaction, on the Polanyi-Wigner model, and concluded that it was just possible (within the estimated uncertainty limits) to account quantitatively for the measured rate of water evolution by a model assuming that dissociative desorption followed an activation step at the reaction interface. Bright and Garner [426], from microscopic observations, showed that the number of nuclei present on (110) faces of CuS04 5 H20 increased linearly with time and that the rate of increase of linear dimensions of the star-shaped nuclei was constant after completion of an initial period of slow growth. Later work [ 5871 extended measurements t o nine different crystal faces of the same solid and, from comparisons of shapes of nuclei developed on the different faces, it was concluded that water elimination proceeded preferentially in particular crystallographic directions, from which the (010) plane was identified as being the most important. Values of E reported for pentahydrate [600] and trihydrate [594] dehydrations are 76 and 6 5 kJ mole-', respectively. Lallemant et al. [601] measured rates of dehydration of both CuSO4 * 5 H2O and CuS04 - 3 H20and concurrently identified the phases present

131

by X-ray diffraction measurements. Both solids exhibit S-T behaviour [596] and, during the increasing segment of the curve of (daldt), against PHZO, water loss occurred appreciably in advance of the crystallographic transformation. When the reactant is placed under conditions far removed from equilibrium, the phase change occurs with the temporary intervention of a metastable intermediate [ 3731. From comparisons between positions of the maxima and minima on the S-T plot with the phase stability diagram, it was concluded [ 5961 that the effect is attributable t o an interaction between rates of bond disruption and rates of transportation of heat and gas within the microdomains at the reaction interface. The elliptical nuclei (trihydrate) formed during pentahydrate dehydration have been described and discussed [ 12601. Lyakhov et al. [598] have shown that the addition of monohydrate accelerates water loss from CuS04 5 H20 (see also ref. [Sl]) and, since the effect occurs even when direct contact between the two solids is prevented, it is concluded that the catalytic behaviour arises through an influence by the composition of the gases present (notably PHZO). These workers base their explanation of S-T behaviour in CuS04 5 H2O on adsorption phenomena (see Sect. 1.4). In a later study [1259] of the dehydration of CuS04 * 5 H 2 0 , it is shown that the dependency on PHZo of the rates of growth of elliptical nuclei (trihydrate product) is different from that characteristic of the development of star and round nuclei (monohydrate). This provides another explanation of S-T behaviour. Ng et al. [1261] report that dehydration of copper sulphate pentahydrate ( -'CuS04 * 3 H20) 320-336 K, obeys the Avrami-Erofe'ev equation [eqn. (6), n = 21 with E = 104 kJ mole-'. Dehydration of the trihydrate ( +CuS04 H20), 343.5-359 K, obeyed the same rate expression with E = 134 kJ mole-'. Activation energies are approximately equal to reaction enthalpies.

-

-

-

1.5.2 Other sulphates

Hydrated metal sulphates have long been used t o study water removal processes, and characteristic kinetic behaviour is conveniently illustrated by reference to these substances. Frost and co-workers [602,603] have investigated the structures, stabilities and adsorption properties of various intermediate amorphous phases, the immediate reaction products which can later undergo reorganization to yield crystalline phase. Measurements of the kinetics of the individual nucleation and growth steps in the reactions of several hydrated sulphates have been referred to in Sect. 1.2 though, perhaps surprisingly, these data were not combined in a kinetic analysis for the overall reaction in studies of the alums [51,431, 5861 or NiS04 7 H 2 0 [50]. Indeed, Lyakhov and Boldyrev [81], in one of the few reviews of the field, maintain that the satisfactory topochemical description of dehydrations is a problem which at present remains

-

132

largely unresolved. In certain studies, the influence of the acceleratory process was specifically removed by initial abrasion of the reactant with product. There are remarkably few convincing demonstrations that observed overall a-time relationships can be quantitatively related to individually measured kinetics of nucleation and of growth processes. Kinetic data and microscopic measurements were in agreement for the dehydration of MgS04 - 7 H20 [588]. The dehydration of NiS04 * 6 H 2 0 [208] obeyed the Avrami-Erofe’ev equation [eqn. (6), n = 21 between 0.001 < a < 0.96 and, since nucleation on the (001) faces was observed t o occur at points of emergence of dislocations, it was concluded that such sites must be randomly distributed. The dehydration of LiS04 HzO obeys the contracting volume equation [eqn. (7), n = 31 t o give [596] a crystalline anhydrous product, even when a vacuum is maintained throughout water removal. The rate of dehydration of MgS04 . 7 H,O varies with changes of crystal habit and depends on the relative areas of the (111) and (110) faces, since interface advance occurs more rapidly at the (111)surface. Water loss from this salt [373, 5771 proceeds to completion in steps, the reaction sequence being deterThe a-time curve for MgS0,- 4 HzO dehydration is mined by PHZO. sigmoid [596] and problems of kinetic interpretation arising from ineproducible nucleation rates were eliminated by preheating to a standard extent of reaction ( a = 0.29) after which the contracting volume equation [eqn. (7), n = 31 was obeyed. Studies of the dehydration of FeSO,. 7 H20have been largely concerned with the qualitative identification of residual products. While the anhydrous salt may be formed in the absence of oxygen, the presence of this reactant results in the production of basic iron(II1) salts and, ultimately, a-Fe203. The dehydration and interconversion reactions of the various forms of calcium sulphate [dihydrate, hemihydrate ( a and p pseudomorphs) and anhydrous salt (hexagonal and orthorhombic structures)] have been studied by Ball et al. [281,590,591] who compared their observations with the available rate and microscopic data. The important features of the complicated behaviour found are summarized in the scheme [ 2811 dihydrate

anhydrous salt + anhydrous salt (hexagonal) (orthorhombic) \ b P hemihydrate -+

More detailed consideration of the sensitivities of dehydration rates t o reaction conditions (PHz0,temperature) are given in the articles cited; reported values of E , at various PHZO, are summarized in Fig. 13. From kinetic observations, it was concluded that between 353 and 383 K, the dehydration of CaS04 2 HzO [ 5901 involved nucleation ( 0 in Fig. 13)and boundary control (0) but for 383-425 K, a diffusion mechanism (@) operated. The kinetics of dehydration of a-CaS04 - H 2 0 [590] (X,+)

133

*

X

o

*

I

0

x

*

@

20

+

+

I

I

10

*

30

I

I

40

I

50

PH*O /Torr

Fig. 13. Plot of variations of activation energy (E/kJmole-') with water vapour pressure @Hzo/TOrr) for dehydration o f calcium sulphate. Data from Ball et al. [281,590, 5911 who discuss the significance of these kinetic parameters. Dehydrations of CaS04 * 2 HzO, nucleation (a), boundary ( 0 ) and diffusion (@) control; a-CaS04 * HzO, diffusion control, below ( X ) and above (+) 415 K; O-CaSO4 . HzO, diffusion control (*).

were complicated between 341 and 384 K, behaviour depending on reaction conditions, with both phase boundary and diffusion processes exerting control: between 384 and 490 K, the latter was dominant. The dehydration of P-CaS04 - 1 H 2 0 [591](X) was diffusion-controlled, 388413 K. Taplin [110]has made a kinetic study of the rehydration of the hemihydrate. 1.5.3 Other inorganic solids

The vacuum decomposition of U O z ( N 0 3 ) z 6 . HzO at 213-243 K is mechanistically unusual in that neither interface reaction nor diffusion control is belived t o operate [ 621,the rate-limiting step being identified as desorption from the existing crystal surface. The reaction rate decreased systematically with PHZo(no S-T effect) and E was 46 kJ mole-'. The reaction in air, in the higher temperature interval, 313-333 K, obeyed [604]the contracting volume equation [eqn. (7),n = 31 and the apparent value of E was significantly greater (105kJ mole-'). Kinetic behaviour at >333 K was complicated by melting of the hexahydrate. The dehydration of CuH PO4 * 2 HzO [ 5921 is diffusion-controlled (409behav478 K) and E (190kJ mole-') is not changed by variations in PHZO: iour at >478 K is more complicated. The very large values of E for Laz(CO3)3 - 8 HzO [595]and their sensitivity t o PHZo(-700 kJ mole-' at 15 Tom water and -500 kJ mole-' at 10 Torr water) cannot be identified with a single step reaction, though at high temperatures, the value

134

(66 kJ mole-') is closer to those found for other systems. Dehydrations of various preparations of both BaC12 . 2 H 2 0 and BaC12 . H 2 0 [189] included an initial acceleratory process and obeyed the Avrami-Erofe'ev equation [eqn. (6), n = 2 and E = -75 kJ mole-'] except for large single crystals of the dihydrate, where the contracting area equation [eqn. (7), n = 21 was obeyed. From detailed comparisons between isothermal and non-isothermal rate measurements, it was concluded that great care is required t o obtain meaningful kinetic parameters from differential thermal analyses. Osterheld and Bloom [1262], after reviewing the available kinetic data for these dehydration reactions, report, from microscopic observations of the rate of interface advance, E values of 146 kJ mole-' (313-334 K ) for advance along each of the major crystallographic axes in BaC12 2 H 2 0 and BaC12 * H 2 0 . The entropy of activation values were also equal (238 JK-' mole-'). Between 334 and 346 K, these values along the (010) axes were reduced to 87 kJ mole-' and 56 JK-' mole-', respectively. It is suggested from some topotactic evidence that a possible mechanism of dehydration may involve minimum displacements of the heavy barium ions. The kinetics of decomposition of Ba(C103)2* H 2 0 [1263] are complicated and optical microscopy was used t o supplement thermal data. Arrhenius parameters showed a pronounced compensation effect. 1.5.4 Metal carbox y la tes

( a ) Formates

-

References have been made above to dehydrations of Mn(HC02)2 2 H 2 0 [91,212] and C U ( H C O ~* )4~H 2 0 [213]. The influence of the structure of dehydrated Ni(CH02)2 2 H 2 0 [ 118,6051 ( E dehydration, is 105 kJ mole-') on subsequent decomposition has been discussed [ 1181; removal of the last traces of water probably influences decomposition nucleation [ 3751.

-

( b ) Oxalates

Non-isothermal measurements of the temperatures of dehydrations and decompositions of some 25 oxalates in oxygen or in nitrogen atmospheres have been reported by Dollimore and Griffiths [ 391. Shkarin et al. [6061 conclude, from the similarities they found in the kinetics of dehydration of Ni, Mn, Co, Fe, Mg, Ca and Th hydrated oxalates (first-order reactions and all values of E 100 kJ mole-'), that the mechanisms of reactions of the seven salts are probably identical. We believe, however, that this conclusion is premature when considered with reference t o more recent observations for NiC204* 2 H20(see below [129]) where kinetic characteristics are shown to be sensitive t o prevailing conditions. The dehydration of MnC204 2 H 2 0 [607] has been found t o obey the contracting volume

-

135

equation [eqn. (7), n = 31 with E = 73 kJ mole-'. Nickel oxulute. The apparent value of E for NiC204* 2 H 2 0 dehydration is very sensitive t o the presence of small amounts of water vapour [129]. To determine the rates of dehydration in vacuum, it was found necessary to use the lowest practicable masses and t o extrapolate to zero mass of reactant. The value of E thus found (129 kJ mole-'), and the reaction rates, were appreciably larger than values previously reported. This careful experimental investigation focusses attention on the considerable difficulties which may attend the determination of a reliable value of E . The variations now apparent in available kinetic data [129] for NiC2042 H 2 0 dehydration make it desirable that further measurements, using this rigorous method, should be applied to establish the reliability of Arrhenius parameters for (other representative dehydration reactions, using conditions designed to minimize, as far as practicable, or to accurately define the influence of water vapour. Group I1 metal oxalates. The initial stages of water loss from CaC204* H 2 0 [282] obeyed the zero-order kinetic equation and values of E varied from -70 kJ mole-' in vacuum t o -205 kJ mole-' at PHZo 12 Torr. Mechanstic studies of the dehydrations of strontium and of barium hydrated oxalates have been reported by Watelle-Marion and her coworkers [ 253,6071 and conclusions are based predominantly on crystallographic changes and phase diagrams rather than kinetic evidence. In an unusual type of study, Gardner [1264] investigated the dehydration reaction

-

CaC204* 3 H 2 0 = CaC204* H2O + 2 H2O in aqueous solutions at various supersaturations, 298-313 K. This rate process was identified as occurring by a solid state mechanism with E 188 kJ mole-'. It is concluded that initial nucleation sites were probably located in the vicinity of the solidsolution interface since certain additives, notably phosphates, increased the induction period to the appearance of the monohydrate.

-

1.5.5 Conclusions Although rate studies of dehydration reactions have notably contributed towards the understanding of certain types of kinetic behaviour which are characteristic of rate processes occurring in solids, the observations at present available constitute neither a systematic nor a comprehensive investigation of this group of compounds. After the early interest and, in particular, Gamer's considerable contribution, there followed a period of comparative quiesence but a more recent re-examination of the unsolved problems has led to a resurgence of interest in dehydrations. The provision of a mechanistic explanation for Smith-Topley behaviour (first reported in 1935) and the determination of the significance of the magni-

136

tudes of apparent Arrhenius parameters remain topics under active discussion. Differences between explanations advanced by different workers remain unresolved. Recent reference [ S l ] has also been made to the problems which attend the provision of acceptable topochemical descriptions of these reactions. It has been shown (for at least one system [129]) that the determination of meaningful kinetic parameters requires greater control of experimental conditions than has sometimes been appreciated. Mechanistic explanations of dehydrations based on reaction rates, should, where possible, be considered in conjunction with available phase diagrams [ 253,6071 and structural information [ 6081. Mechanisms of nucleation and growth reactions in hydrates were discussed by Garner [64].Dunning [SO]has formulated a theory of nucleation based on the aggregation of site vacancies in the water lattice, the rate equations used being based on those applicable to homogeneous nucleation of droplets in a supersaturated vapour. This treatment was also extended to include the growth of existing nuclei. Niepce and Watelle-Marion [609] identify four distinct stages in the production of dehydration nuclei: (i) the individual loss of free water molecules, (ii) the elimination of water molecules from the crystal with surface vacancy formation, (iii) the aggregation of such vacancies with development of attractive forces, and (iv) the recrystallization of the new product phase t o yield a separate particle (see also ref. 1250). For many reactions in the subsequent sections, the product of dehydration constitutes the reactant in a decomposition. Account must be taken of the changes in structure and texture which accompany or follow withdrawal of water from the lattice (perhaps in several steps) in considering the kinetics of subsequent decompositions or interactions of the anhydrous solid.

2. Decomposition reactions of binary compounds (also including hydroxides) 2.1 HYDROXIDES

Although not strictly binary compounds, hydroxides are conveniently classified here between hydrated salts, since both release water on heating and incorporate certain common features of behaviour, and oxides, which are the usual residual product. A number of hydroxide decomposition studies have extended measurements to consider the relationship with subsequent higher temperature changes in the product oxide. Release of water from the crystalline hydroxides (dehydroxylation) differs from the dehydration of a crystalline hydrate (Sect. 1) in that product release must be preceded by chemical interaction between anions.

137

In general, this may be represented as proton transfer 2 OH-

-+

02-+ H 2 0

which often occurs at a reaction interface. Detailed information concerning the changes proceeding at the reactant-product contact have been inferred from results of diffraction measurements, since relatively perfect crystals of simple hydroxides, e.g. Mg(OH)2, are available and the structures of both reactant and product are comparatively simple. For several of those systems that have been investigated in greatest detail, it has been demonstrated that the oxide product bears a topotactic relationship to the hydroxide from which it was derived. On the principle of minimum displacement of lattice components, it has been found possible to deduce the probable ionic movements which occur during interface advance. Lattice strain and crystal cracking are important features of such reaction mechanisms. Rate parameters [(daldt),A , El measured for dehydroxylations are frequently sensitive to the availability of water vapour in the vicinity of the reactant and this accounts for the apparent variations in kinetic data sometimes found between different reports concerned with the same reaction. Water adsorbed on product adjoining the reaction interface could be expected to participate in the reversible proton transfer step, the precursor to water elimination. Despite this influence of PH2?on reaction rate, we are aware of no reported instance of S-T behaviour in dehydroxylations. The most intensively investigated dehydroxylation is probably the reaction of Mg(OH)2, though detailed results are also available for the hydroxides of certain other divalent cations. Several summaries of the mechanistic deductions obtained from such work, including literature sources, were presented at a conference at Dijon in 1974 [87]. The extensive literature concerned with the thermal analysis of hydroxides has been reviewed by Dollimore [79] who has also included the behaviour of oxides. Water elimination can be regarded as the first in a sequence of structurally related steps through which the hydroxide is converted into the thermally most stable oxide. Less detailed information is available concerning the rates of reactions of most hydroxy salts of inorganic acids; indeed, the qualitative changes occurring during stepwise or overall removal of water have not been established for many systems. The behaviour characteristics of a number of hydroxyhalides are mentioned below, as are the dehydroxylations of representative minerals. Some aspects of the relationships between the reactions of minerals and structurally similar metal hydroxides are critically discussed by Brett et al. [92]. 2.1.1 Magnesium hydroxide In a detailed mechanistic study of Mg(OH)z dehydroxylation, Gordon and Kingery [245] precede consideration of their kinetic data with an

138

account of microscopic and diffraction observations. There was evidence that dehydroxylation was a nucleation and growth process, accompanied by extensive cracking, since the molar volume of the residual product is much less (X0.65) than that of the reactant. From electron diffraction patterns, obtained before reaction and following partial dehydroxylation, it is concluded that growth of the product MgO is coherent since (111) planes of this phase are aligned parallel with basal (0001) planes of the reactant Mg(OH)2. This closest match of lattices minimizes interfacial energy. Growth proceeds until accumulated strain results in detachment of a product crystallite. Kinetic measurements were made using powdered Mg(OH)2and also using single crystals of known masses and areas. In the lowest temperature experiments, the initiation of reaction required a short induction period followed by a brief acceleratory process, indicative of a nucleation and growth mechanism. Dehydroxylations were, however, predominantly deceleratory and well described by the first-order equation. Rate coefficients diminished with increasing thickness of the reactant sample layer. Kinetic characteristics are significantly influenced by physical factors, notably particle disintegration resulting from strain at the reactant-product interface, which changes during the progress of reaction, and the availability of water at the site of dehydroxylation, which reduces the dissociation rate. The kinetics of dehydroxylation of large crystals could not be satisfactorily represented by the interface model since cracking could be seen to propagate more rapidly than interface advance and behaviour also depended, to some extent, on crystal thickness. Mechanistic features of brucite, Mg(OH)2, dehydroxylation have been discussed in detail by Brett et al. [92,1265] and Freund et al. [610]. A list of reported E values is given and discussed by Sharp [611]. The rate of water release from Mg(OH), is sensitive to PHZoand, in experiments where the magnitude of this parameter is controlled at a constant and homogeneous value, it must be specified for each reported E . For reaction in vacuum, E is comparable with, or slightly greater than, the reaction enthalpy, AH (measured values of E AH have been reported for several other endothermic and reversible rate processes [64]). The rate of brucite dehydroxylation is perceptibly increased and the value of E slightly reduced by an electric field [612] (-lo5 V m-'). Water loss is inhibited by the presence of various stable inorganic ionic impurities [ 6131 (aluminate, phosphate, silicate or sulphate). The decomposition of Mg(OH)2 yields appreciable amounts of hydrogen at >570 K [ 12661.

-

2.1.2 Other inorganic hydroxides Several other hydroxides of divalent metals crystallize in the same Cd12 type structure as brucite, notably [610] those of Ca2+,Mn2+,Fe2+,Co2+, Ni2+ and Cd2+.The rates of dehydroxylation of these solids have, how-

139

ever, been less intensively studied. Poorly oriented product CaO is given [92] by the decomposition of Ca(OH)2in air, which occurs at a relatively higher temperature (-720 K ) than that in vacuum (-500 K). The deceleratory dehydroxylations of Fe(OH)2 and Ni(OH)2 obeyed [614] the contracting area equation [eqn. (7), n = 21 a < 0.6 with E 92 kJ mole-', whereas the activation energy for the comparable change in C O ( O H )was ~ somewhat lower, -75 kJ mole-'. It is suggested [260] that Ni(OH)2undergoes rapid and complete nucleation at all edges of the platelike crystallites and the subsequent advance of the coherent interface is a topotactic process yielding a pseudomorphic product, within which the pores are disposed in a regular manner. Surface area changes and splitting of crystals during reaction have been discussed by Cronan et al. [ 12671. Bertrand et al. [615] report a kinetic study of Cd(OH)2dehydroxylation, supplemented by crystallite size determinations for both reactant platelets and product CdO. Vacuum reactions at -360-420 K of samples consisting of the larger particles were deceleratory throughout and the rate diminished markedly before attainment of complete reaction [ 6161. This effective cessation of product release at a < 1.00 was shown by microscopic examination t o be due to inequalities of reactivity: some crystals had been converted to CdO while others, within the same heated sample, remained intact and unaltered. Reaction in water vapour = 18.6 Torr) occurred in the higher temperature interval, 450-480 K; the rate of dehydroxylation of the largest crystallites was again deceleratory throughout and again a = 1.00 was not achieved. In contrast, smaller crystallites underwent an initial deceleratory process, followed by a sigmoid a-time relation leading t o complete dehydration. Kinetic characteristics are thus seen t o be controlled to some extent by PHZO, temperature, and crystallite size and, therefore, no attempt was made to report conventional kinetic data [the f(a)-time relation, A, E l . Instead, the observations were compared with those for the dehydrations of CuS04 5 H 2 0 and BaC204* H2CZO4 2 H20 in a general consideration of the mechanisms whereby water may be removed from solids. It was concluded that four steps may contribute to the overall change: (i) formation of the water molecule within the crystal, (ii) water elimination at the gassolid interface, (iii) fragmentation of the reactant crystal, and (iv) reorganization of the vacancy structure. Isothermal decomposition [617] of COO OH

-

-

-

1 2 COO * OH = 4 Co304+. 6 H2O + 0

2

in air, in the temperature range 533-583 K, yielded deceleratory a-time curves obeying the contracting area equation [eqn. (7), n = 21 0.00 < a < 0.80. The Arrhenius plot showed a discontinuous change of slope at 553 K. Values of E were 145 and 79 kJ mole-' below and above this temperature, respectively. It is concluded that the reaction proceeded by an advancing interface mechanism in the brucite-type structure of the

140

reactant and both proton transfer ( 2 OH- HzO + 0,-) and electron transfer ( 2 Co3++ 0,- + 2 Co2++ 0,) steps were involved. The higher value of E found for the lower temperature range was ascribed t o participation of the electron transfer step, whereas above the transition temperature (>553 K) water escape became inhibited so that dehydroxylation exerted the dominant influence on reaction rate. The high-temperature value of E found here was almost identical with that reported [614] earlier for C O ( O H )dehydroxylation. ~ Giovanoli and Brutsch [264] studied the kinetics of vacuum dehydroxylation of y-FeO OH(+? Fez03).It was not possible to demonstrate satisfactory obedience to a single kinetic expression. Microscopic examinations detected the occurrence of random nucleation over reactant surfaces and crystallographic indications of the specific structural reorganization steps, which occur at the reaction interface, are discussed. The sequence of the transformations which follow the dehydroxylations of the three forms of Al(OH)3 (i.e. gibbsite, bayerite and norstrandite) and of A10 * OH (boehmite), yielding the various forms of Alz03(X, K, y, 8 and, ultimately, a, corundum) have been qualitatively summarized with approximate reaction temperatures, by Brett et al. [ 921. Kinetic measurements for each of these transformations are not currently available. There are indications that the dehydroxylations may be sensitive to prevailing conditions, so that meaningful rate studies would require control of PHZoin the vicinity of the reaction interface, including water evolved by the reaction, and particle sizes. Thermal analysis was used [618] (inter alia) to investigate the mechanism of conversion of gibbsite to boehmite and it was concluded that the reaction rate was controlled by the diffusion of water along structural channels and by the desorption step. The dehydroxylation of P-U02(0H)z occurs [ 6191 by nucleation and growth of a- and y-U03 at reactant surfaces. The value of E for the linear rate of interface advance in the [ l o o ] direction underwent a change at 613K [ E = 19OkJ mole-' (573-613K) and 122 kJ mole-' (613673 K)]. It is suggested that bulk diffusion of water was significant in the lower of the two temperature intervals. The initial stage of vacuum dehydroxylation of P-Be(OH), (408493 K) [620] was deceleratory ( E 59 kJ mole-'), ascribed t o diffusion control. During the subsequent main stage of reaction, interface penetration (E = 115 kJ mole-') was rate-determining. +

-

-

2.1.3 Hydroxyhalides and related salts Interest in the dehydroxylation of metal hydroxy salts has hitherto largely centred on the hydroxyhalides. Studies of the relative reactivities of comparable salts of this type have included measurements of the influences of the constituent halide and of variations in the ratio of

141

halogen to hydroxide extended, in some instances, to include the metal hydroxide and perhaps also to certain hydrated halides [621]. Some limited qualitative generalizations have emerged from such comparisons. The sequence of compounds Cd(OH)z, Cd4(0H)J2, Cd7(0H)lo13, Cd3(0H)4I2, Cd(0H)I and CdIz show [622] a progressive increase of stability as the OH groups are replaced by I. The temperatures of reaction [621,623] of the copper (and also Cd and Zn) oxyhalides, Cu(OH)X, increased in the sequence X = OH < I < Br < C1< F. Analyses of rate measurements for the decomposition of a large number of basic halides of Cd, Cu and Zn did not always identify obedience to a single kinetic expression [ 623-6251 , though in many instances a satisfactory fit t o the first-order equation was found. Observations for the pyrolysis of lead salts were interpreted as indications of diffusion control. More recent work [625] has been concerned with the double salts XM(OH)~yMeClz where M is Cd or Cu and Me is Ca, Cd, Co, Cu, Mg, Mn, Ni or Zn. In the M = Cd series, with the single exception of the zinc salt, reaction was dehydroxylation with concomitant metathesis and the firstorder equation was obeyed. Copper (=M) salts underwent a similar change but kinetic characteristics were more diverse and examples of obedience t o the first order, the phase boundary and the Avrami-Erofe'ev equations [eqns. (7) and (6)] were found for salts containing the various cations (=Me). The reports cited above contain a wealth of kinetic information concerning diverse reactions in a field that is experimentally difficult to investigate. However, the significance of the often reported obedience to the first-order equation [eqn. (15)] has not always been satisfactorily established and the fit to other relationships, characteristic of solid phase reactions, cannot be accepted as unambiguous evidence for the operation of specific nucleation and growth processes. More microscopic and/or diffraction observations and investigations of the possible influence of PHZo(including water released during reaction) on the kinetic characteristics [f(a)-time, A and E l would be valuable. Ball and Casson [ 12681 have studied the decomposition of laurionite, which they represent as

-

4 Pb(OH)Cl+ 3 PbC12 * 2 PbO + PbClz + 2 PbO + 2 HzO This deceleratory reaction obeyed the parabolic law [ eqn. (lo)] attributed t o diffusion control in one dimension, normal t o the main crystal face. E and A values (92-145 kJ mole-' and 109-1015 s-l, respectively) for reaction at 490-520 K varied significantly with prevailing water vapour pressure and a plot of rate coefficient against PHZo(most unusually) showed a double minimum. These workers [1269] also studied the decomposition of PbzCl2CO3 at 565-615 K, which also obeyed the parabolic law at 565 K in nitrogen but at higher temperatures obeyed the Jander equation [eqn. (14)]. Values of E and A systematically increased

142

(from 130 t o 215 kJ mole-' and 8 X 1 0 1 kN m-2).

lo9 t o

7 X 10l6 s-l) with Pco, (0 t o

2.1.4. Clay minerals

Many studies have been made of the rates of water evolution from layer-type silicate minerals which contain structural hydroxyl groups (clays and micas). Variations in composition of mineral specimens from different sources hinders comparison of the results of different workers. Furthermore, the small crystallite sizes and poor crystallinity that are features of clays limit and sometimes prevent the collection of ancillary observations (e.g. microscopic examination and diffraction measurements). Dehydroxylation of the clay mineral kaolinite [ 71,626-6291 is predominantly deceleratory and sensitive to PHZo(Table 11).Sharp and co-workers [ 71,6271 conclude that water evolution is diffusion controlled and that an earlier reported obedience to the first-order equation is incorrect. A particularly critical comparison of a-time data is required t o distinguish between these possibilities. Anthony and Garn [629] detected a short initial acceleratory stage in the reaction and concluded that at low PHZothere is random nucelation, which accounts for the reported TABLE 11 Kinetic data for dehydroxylation of representative clay minerals (See also ref. 36.) Mineral

Kaolinite

Water vapour Activation pressure, P H 2 0 energy, E (kJ mole-') (Torr)

<10-3 4.6 14 47

Kaolinite

300 2400

Kaolinite

Vacuum

Kaolinite

4.3

Preexponential factor, log1oA (molecules m-2 s - l )

Temperature range (K)

Ref.

210 346 371 461

32.7 41.8 43.2 48.7

663708723743-

723 748 753 768

621

257 1060

37.2 76.8

693- 753 953-1033

629

169

29.5

690-

753

628

104

24.5

676-

704

626

Montmorillonite

Vacuum 4.5

16.1 62.6

19.3 24.1

363375-

493 463

630

Illite

Vacuum 4.5

12.3 51.9

18.2 23.1

355311-

573 465

630

Muscovite

Vacuum

31.2

818-

847

631

222

143 500r

x/ 0'2'0

i5 3b ;5 o; Log ( A/molecules rn'* s-' 1

45

5'0

Fig. 14. Compensation plot for dehydroxylation of kaolinite ( 0 )and other layer-type silicates ( x = montmorillonite, illite and muscovite): data and sources given in Table 11. (Redrawn, with permission, from Advances in Catalysis, ref. 36).

first-order behaviour. With increasing availability of water, there is a rise in the rate of nucleation (this step possibly involves proton transfer) though later the influence of the reverse reaction may become significant. The very considerable variations in the apparent magnitude of E with P H are~ identified as arising as a result of changing mechanism and it is considered that a single mathematical description of the reaction rate cannot be formulated. Some representative values of E for this reaction and the dehydroxylations of related minerals are summarized in Table 11, together with estimated values of A (as molecules m-? s-') calculated from assumptions concerning crystallite sizes. These data exhibit a pronounced compensation effect (Fig. 14) which may be a consequence of the participation of adsorbed water in interface equilibria which precedes the desorption step. These coupled variations of A and E are explained [36] by similar surface interactions of comparable intermediates occurring within an approximately constant temperature interval for the different reactants. The large range of values of E cannot, however, be attributed t o differences of the energy barrier in a rate-limiting step and the changes in magnitude of A cannot be ascribed t o similar dehydroxylation processes. Kodama and Brydon [631] identify the dehydroxylation of microcrystalline mica as a diffusion-controlled reaction. It is suggested that the large difference between the value of E (222 kJ mole-') and the enthalpy of reaction (43kJ mole-') could arise from the production of an amorphous transition layer during reaction (though none was detected) or an energy barrier t o the interaction of hydroxyl groups. Water vapour reduced the rate of water release from montmorillonite and from illite and

~

144

varied kinetic characteristics [ 6301 : apparent values of A and E were close to the compensation line on Fig. 14. Daw et al. [632] made a microscopic and crystallographic study of talc dehydroxylation. Nucleation, to yield enstatite, occurs inhomogeneously within the particles, perhaps at dislocations. Later, this product is topotactically orientated with respect to the reactant lattice, though with extensive faulting on the (010) plane owing t o misfit, in addition to the attempt t o preserve the oxygen lattice. In an isothermal study (11001160K) of the same reaction, Ward [633] found first-order obedience and the value of E determined (422 kJ mole-') is close t o that estimated for Mg-OH (g) Mg (g) + OH (g) Accordingly, the mechanism of reaction proposed is Mg-OH bond scission followed by migration of the magnesium released. While there is agreement that the rates of clay dehydroxylations are predominantly deceleratory and sensitive t o there is uncertainty as to whether these reactions are better represented by the first-order or by the diffusion-control kinetic expressions. In the absence of direct observational evidence of interface advance phenomena, it must be concluded that the presently available kinetic analyses do not provide an unambiguous identification of the reaction mechanisms. The factors which control the rates of dehydroxylation of these structurally related minerals have not been identified. -+

2.2 OXIDES

The simple metal oxides, M,O,, containing the 02-ion only, appear, at first sight, t o be an exceptionally favourable group of solids for the study of thermal dissociation reactions. Many of these binary compounds are amongst the most fully characterized crystalline solids and large single crystals of simple and accurately known structures are often available. Oxide phases are usually readily identified by diffraction methods and this facilitates the detection of topotactic relationships between reactant and product, where these occur. Much detailed information concerning thermodynamic properties of oxide phases has been published and defect and non-stoichiometric properties have been characterized. However, many of the favourable circumstances mentioned above are effectively offset by limitations inherent in the systems, since oxides are frequently refractory and many are capable of existing over an appreciable composition range. It is, therefore, necessary to determine whether a given release of oxygen is a consequence of a change of the M : 0 ratio of an existing phase or results from the appearance of a new phase, a lower oxide or a metal. Kinetic investigations of such rate processes are sometimes complicated by the occurrence of changes of both types which may proceed

145

concurrently or consecutively. In addition, many oxygen dissociation reactions are reversible, so that rate characteristics are sensitive t o the prevailing oxygen pressure ( P o , ) . Furthermore, many metal-oxygen systems form several distinct compounds and some of these may be polymorphic. It is, therefore, necessary t o identify the phases present at appropriate stages during the reaction by diffraction and/or compositional measurements. There are reviews on the topic of decomposition reactions of oxides by Dollimore [ 791 and by Malinin and Tolmachev [634]. In addition to the simple oxides, the present survey includes reference t o the higher oxides, in which the anions contain inter-oxygen linkages: peroxides (O:-), superoxides (0;) and ozonides (0;).

2.2.1 Extended imperfections in oxides Recent developments in the theory of extended imperfections in oxides, notably crystallographic shear (CS) and Wadsley defects [635--639], while largely concerned with the significance of these imperfections in accounting for departures from stoichiometry, can also be expected to prove important in studies of reactivity, as suggested by Anderson [ 6351. The lattice vacancy and line and screw dislocations were stimuli for the development of models for decomposition of solids. The more sophisticated structures recently recognized (or developments arising from them) can be expected t o increase the accuracy with which the mechanism of reactions in a wider range of compounds may be portrayed. Several excellent recent accounts of crystallographic shear are available [635-639]. Crystallographic shear (CS) has not yet been utilized t o provide mechanistic explanations of observed kinetic behaviour but must exert an influence on the progress of certain reaction interfaces. The crystallographic shear plane can be schematically represented as a laminar lattice plane within the crystal, along which one constituent ion (e.g. the cation in Ti02) is co-ordinated with its neighbours differently from that characteristic of the stoichiometric compound. Each such plane can be regarded alternatively as an array of defects or a “single lattice layer” of a lower oxide accommodated within, and bearing a coherent crystallographic relationship with, the host phase. The generation of CS planes from “perfect” lattices can be schematically represented as the production of a regular array of vacancies of one ion at the plane. Slip along the plane then represents an alternative rematching of adjoining layers whereby the vacancies are filled and the cations are displaced to antiphase disposition across the line of slip (see diagrams given by Hyde [637]). Anderson and Tilley [6391 discuss critically the possible mechanisms whereby CS development occurs in real crystals. A complete kinetic investigation of dissociations involving CS formation would require separate rate studies of the production of new CS planes (a nucleation process) and their subsequent advance into the reactant bulk (a growth

146

process) including any changes in their orientation. Changes in composition of phases containing CS planes can be accommodated by changes in their orientation and at high concentration ordering may result in the development of regular superlattice features. 2.2.2 Mechanisms and products of oxide decomposition The dissociation of an oxide may, in general, be represented as a twostep process, involving both electron transfer and dimerization 202--4ee-+ 2 0 + 0 2 The steps do not necessarily, however, proceed as simply as indicated but may also involve the formation of additional intermediates, such as adsorbed 0 - , O,; etc., and/or the generation and migration of defects at a surface, interface or in the bulk. The chemical properties of oxide surfaces have been studied by several methods, including oxygen exchange. This method has been used t o investigate the mechanisms of heterogeneous reactions for which oxides are active catalysts [36]. The dimerization step does not necessarily precede desorption and Malinin and Tolmachev [634], in one of the few reviews of decomposition kinetics of solid metal oxides, use this criterion to distinguish two alternative reaction mechanisms, examples being (a) reactions yielding molecular oxygen only : dimerization before desorption Ag2O * Ag; Cr02 Cr203;P-Mn02 * a-Mn203 P-Mn304;UO, * uo2.9 * u308 (b) reactions yielding both atomic and molecular oxygen c0@4 COO; CuO * Cu20; Pb304 PbO; U 3 0 8 * U8OZl It is concluded [634] that, so far, rate measurements have not been particularly successful in the elucidation of mechanisms of oxide dissociations and that the resolution of apparent outstanding difficulties requires further work. There is evidence that reactions yielding molecular oxygen only involve initial interaction of ions within the lattice of the reactant and kinetic indications are that such reactions are not readily reversed. For those reactions in which the products contain at least some atomic oxygen, magnitudes of E , estimated from the somewhat limited quantity of data available, are generally smaller than the dissociation enthalpies. Decompositions of these oxides are not, therefore, single-step processes and the mechanisms are probably more complicated than has sometimes been supposed. +

+

-+

+

2.2.3 Dissociation of oxides (a) Silver oxide The dissociation of Ag,O in oxygen was an early (1905) example (Lewis [640]) of a kinetic study of a solid state reaction and interest in

147

the system has continued. Allen [641]has particularly drawn attention to the spread of values of E (-43-192 kJ mole-') to be found in different reports. The observations described are, however, seldom strictly comparable, since measurements refer to various chemical processes (nucleation and/or growth), have been made in different temperature intervals, and the data analyzed by alternative rate expressions. In considering his own observations, Allen [ 6411 distinguished two initial rate processes occurring in the ranges 373-473 and 473-573 K for which the values of E were 125 and 208 kJ mole-', respectively, attributed to contributory steps in the generation of stable particles of silver. Above 573 K, reaction proceeded at an oxide-metal interface with E 150 kJ mole-'. Dubinin et al. [642] showed that deposited silver (or nickel) metal catalyzed the decomposition of Ag,O at 603 K (but not the breakdown of AgzC03). Since the presence of metallic particles in a mechanical mixture exerted no perceptible acceleratory effect, it is concluded that the formation of an effective reaction interface requires very close contact between reactant and product. The reaction of Ag20 at >550 K required a considerable induction period and the product silver was identified as possessing catalytic properties for the oxide decomposition. Lagier et al. [643]showed that the kinetics of Ag20 decomposition were sensitive to the number of silver nuclei present initially. When Ag nuclei were present, a parabolic a-time curve was observed ( E = 111 kJ mole-'), but with less excess silver, E = 136 kJ mole-'. In the deceleratory period, E = 121 kJ mole-' but this value was reduced t o 100 kJ mole-' by traces of mercury. Again, the catalytic properties of the product silver are confirmed. Nakamori et al. [402]showed that the sigmoid a-time curves for Ag20 decomposition obeyed by the Avrami-Erofe'ev equation [eqn. (6)]and that the reaction temperature was diminished by the presence of reducing gases (H,, CO and CzH4). Scanning electron micrographs indicated the occurrence of melting (the m.p. of Ag is 1234 K) or sintering during the decomposition but not during the lower temperature reduction reactions. The crystallization of silver is identified as the rate-limiting step. Progress in the collection of reliable kinetic data and in the interpretation of observations has been slow during the long period of interest in this reaction due to the sensitivity of rate characteristics t o the presence of constituent impurities, reactant pretreatment and especially the availability of COz. Herley and R o u t [644]attributed marked differences in kinetic behaviour of different preparations of Ag20 t o the extremely high reactivity of this oxide with carbon dioxide. Ag,C03 in the reactant could be removed by preheating for 3 h in vacuum at 553 K and thereafter the reproducible decomposition of Ag20 (603-653K) exhibited a sigmoid a-time curve. The acceleratory reaction obeyed the power law [eqn. (2), n = 21, attributed to growth of a fixed number of two dimensional nuclei, followed by first-order decay. Similar values of E were found for both intervals (121k 6 kJ mole-') and kinetic behaviour was not sensitive to

-

148

pre-irradiation. Young [29] believes that the power law [eqn. (2), n = 31 may provide a more satisfactory fit to the acceleratory period. While general agreement has been reached concerning the catalytic behaviour of the product metal in promoting reaction, other aspects of the rate process have been less satisfactorily characterized : these include the changes which precede nucleus formation, the distribution of such sites and development of the reaction interface. The decomposition of silver(I1) oxide in vacuum at 356-407 K exhibits a sigmoid a-time curve in which the deceleratory period predominates [645]. Arrhenius parameters were shown t o be consistent with the Polanyi-Wigner model, eqn. (19), and E = 125 kJ mole-’. ( b ) Lead oxides

The sequence of decomposition intermediates formed varies with the particular preparation of reactant being studied. Gillibrand and Halliwell [646] conclude that the course of oxygen loss is controlled by the defect structure of the reactant and may proceed through all, or some, of the steps PbO2 -+ Pb12019

+

Pb1201,

--t

Pb304

+

PbO

The second and the final changes may involve more than a single polymorph. There is thus the problem of identifying each rate process with a particular chemical transformation, and many reported inconsistencies remain to be resolved. Malinin et al. [634,647] have studied rates of decompositions of lead oxides. The reaction of Pb304 at -840 K yields some 15%atomic oxygen, obeys the Avrami-Erofe’ev equation [eqn. (6), n = 21 and values of E are -320 and 190 kJ mole-’ at atmospheric pressure and in vacuum, respectively.

( c ) Mercury(II) oxide Taylor [648] has shown that the deceleratory decomposition of HgO is satisfactorily described by the contracting volume equation [eqn. (7), n = 31. Calculated values of E (162-201 kJ mole-’) rise with increasing crystallite size and are somewhat greater than the enthalpy of dissociation (160 kJ mole-’). Since estimated values of A are consistent with the predictions of the Polanyi-Wigner equation, eqn. (19), it is concluded that breakdown involves the detachment of individual molecules rather chains than the “unzipping” of the long zig-zag polymeric -Hg+ which constitute the reactant lattice. Pavlyuchenko and co-workers [ 6491 have shown that mercury is a more effective inhibitor of HgO decomposition than oxygen. Apparent values of E for the reaction of red HgO at 0.01Torr vary with temperature;

149

magnitudes determined within the intervals 430-490,510-650 and 670770 K were -84, -0 and 170 kJ mole-', respectively. There was also evidence that reaction advanced in different directions in variously shaped reactant crystals. ( d ) Umnium oxides There is an extensive literature concerned with the decompositions of uranium oxides, certain of which exist in polymeric forms, and reports sometimes also include observations for the dehydroxylations of allied hydroxides. It is difficult to assess the value of some non-isothermal kinetic data, in the absence of information concerning the influence of rate of product withdrawal. Beketov and Vlasov [650]have studied the decompositions of a-U03, y-U03, and U308. Reaction of a - U 0 3involves transformation, at the composition U02.8a, from the hexagonal structure of the reactant to the orthorhombic lattice of the product, U308;E is 168 kJ mole-' during the initial, almost constant, rate of reaction between 800 and 875 K. y U 0 3 decomposition proceeds through a two-phase reaction when 01 < 0.1 and E = 178 kJ mole-' (-870450 K). E , during the early stages of decomposition of U 3 0 8 t o U 0 2 , was 105 kJ mole-', but later fell to -50 kJ mole-'. A comparative study [ 6511 of the relative stabilities of various forms of U 0 3 by DTA methods lists the temperatures of onset of reaction in the sequence 01 < E < amorphous < p < U02.9< 6 < y (673,733, 773, 803, 853, 863 and 903 K, respectively). Themal stabilities, as measured by the first-order reaction rate coefficient, magnitudes of E or enthalpies of reaction, increased with increasing structural symmetry.

(e) Chromium(IV) oxide A study by Shannon [652] of the kinetics of the decomposition of C r 0 2 ( +CrzO3), which included microscopic observations, indicated the

initiation of reaction at surfaces, with subsequent advance of the interface developed towards crystallite centres. A topotactic relationship was maintained between reactant and product phases, both of which contain hexagonal close packed oxygen layers, though the cation distributions differ. Reaction occurred with minimum structural disturbance through the removal of half of the constituent oxide ions in alternate rows (a process which resembles, in some respects, the generation of crystallographic shear planes). Oxygen removal became appreciable at comparatively low temperature (the reaction was studied at 723-823 K) and the apparent value of E (=200kJ mole-') was relatively low. (f) Cob& oxide

The decomposition of Co304 (+COO) obeyed [653] the contracting volume equation [eqn. (7),n = 31 between 970 and 1070 K with E =

150

367 kJ mole-'. The same kinetic fit was found for oxide containing Alz03 or Inz03 as additive, but on addition of LizO or NazO there was an induction period to the formation of COO nuclei. ( g ) Copper oxide The dissociation of CuO (+CuzO) is a slow [654]reaction with a high apparent E (=205kJ mole-'). However, the reduction of both of these oxides occurs at a lower temperature and with a diminished E (-56 kJ mole-'). ( h ) Vanadium(V) oxide Reference t o this oxide is included here t o indicate a possible complication that may appear in kinetic and mechanistic studies of sublimationtype reactions, since the vacuum dissociation of VzOs has been shown [655] t o produce a variety of molecular entities: V4010, v 6 0 1 4 y V6O12, V 4 0 8 and Vz04. Allowance for the complexity of the product mixture must be made in the design of experiments. (i) Higher oxides Few kinetic studies of the decompositions of higher oxides have been reported; one probable reason is that the preparation of pure samples of these highly reactive compounds is difficult. Accordingly, interest has been largely restricted to the most readily available substances which are the alkali and alkaline earth peroxides (0;-), superoxides ( 0 ; ) and ozonides (Oi). Some of these may be hydrated. E values reported [656] for the dehydrations of M O z - 8 H z 0 (288-313K) were 96, 163 and 63 kJ mole-' for the CaySr and Ba compounds, respectively. The vacuum decomposition [657]of Li2OZ( +LiZO)at 553-593 K was a zero-order reaction for which E = 234 kJ mole-'. It was suggested that a large part of the energy required t o rupture the peroxide (0-0) link was compensated by the decrease in the Li' to 0'- spacing in the product. In a different study [658],but within a comparable temperature interval, the rate-limiting step was identified as 0-0 bond rupture ( E = 209 kJ mole-'), and from X-ray evidence it was concluded that solid solution (Liz02-LizO) occurred when (11< 0.5.Taran and Karpenko [659]found marked differences in the rates of decomposition of various preparations of NaOz ranged from the onset of reaction at -413 K in the most labile salt ( E 117 kJ mole-') to breakdown initiated at >453 K in the most stable sample ( E 155 kJ mole-'). These variations were ascribed to differences in defect structure. The stabilities of the alkaline earth peroxides, MOz - 2 HzOz increased in the sequence Ca > Sr > Ba. Values of E for the autocatalytic reactions

-

-

151

of the latter two are 96 and 125 kJ mole-' respectively. The observed increase in relative yield of product superoxide in the same sequence is ascribed to diminishing polarity of the cationanion interaction. Decomposition of CaO, - 2 H 2 0 z is believed to propagate along hydrogen bond chains within the solid. Reaction is initiated inhomogeneously on crystal faces and later results in particle disintegration. Isotopes have been used [660] to determine the incidence of 0-0 peroxide linkage rupture during oxygen release. The oxygen bond is retained in gas evolved on reaction of Ba02 - 2 H 2 0 , whereas rupture occurs during pyrolyses of CaO, * 2 H 2 0 2 , CaO,, LizOzand others. ( j ) Alkali carbonate perhydrates and alkali peroxycarbonates

These substances are included here t o emphasize their close relationship with other peroxycompounds. KzC03 3 H 2 0 2 contains hydrogen peroxide of crystallization and the solid phase decomposition involves the production of the free radicals OH' and HO;, detected by EPR measurements [661]. a-Time curves were sigmoid and E = 138 kJ mole-' for reactions in the range 333-348 K. The reaction rate was more rapid in vacuum than in nitrogen, possibly through an effect on rate of escape of product water, and was also determined by particle size. From microscopic observations, it was concluded that centres of decomposition were related to the distribution of dislocations in the reactant particles. a-Time curves for the decompositions of sodium and potassium peroxydicarbonates (Na2C206and K2C206) [662] had short acceleratory reactions prior to onset of the deceleratory processes which constituted the greater part of the decompositions and fitted the contracting volume equation [eqn. (7), n = 31 for 0.1 < (Y < 0.7. Values of E for the two salts were 89 and 97 kJ mole-' in the ranges 373-393 and 393-413 K, respectively. Reactions were identified as topochemical processes, though no microscopic evidence in support of this interpretation was provided. 2.3 HYDRIDES, CARBIDES, NITRIDES AND RELATED SUBSTANCES

Of the many known hydrides, carbides, nitrides and related substances, only a few undergo solid state decomposition and few kinetic and mechanistic studies have been reported. Compounds of the non-metals are covalent, those of strongly electropositive elements are ionic, and almost all members of both groups melt prior t o decomposition. Another large group, the interstitial substances (NbC, Tic, TiN, WC, etc.) are characterized by great stability and melting points are often very high (>3000 K). The restricted group of compounds which undergo decomposition without melting at comparatively low temperature are often non-stoichiometric interstitial phases that possess some metallic character. Those

152

hydrides, carbides and nitrides, whose thermal stability and reactivity have been studied, were selected because they have been postulated as intermediates, either as surface or as bulk phases (e.g. palladium and nickel hydrides [ 6631) in heterogeneous catalytic reactions. Nickel carbide has been postulated [36] as a possible intermediate in hydrocarbon cracking reactions on the metal, and iron nitride may be formed during ammonia synthesis [61]. While some kinetic data for decompositions of these possible participants are available, the mechanistic interpretation of the observations is not always straightforward. When the overall dissociation is rate-limited by a surface process, the step concerned may not always be identified unambiguously. The kinetics of decomposition of these solids may be classified according to the process which has been identified as rate-limiting. This criterion allows a more concise presentation but is not completely satisfactory since some reactions show a sensitivity of behaviour to the conditions prevailing [ 12701. Furthermore, certain of the reactions discussed are reversible. Reference to the extensive literature devoted to the thermodynamic properties of these solids and phase stabilities and interactions will only be made where kinetic observations or arguments have been used. Carbide decompositions yield no volatile product and, therefore, many of the more convenient experimental techniques based on gas evolution or mass change cannot be applied. This is a probable reason for the relative lack of information about the kinetics of reaction of these and other compounds which are correctly classifed under this heading, such as borides, silicides, etc. 2.3.1 Decompositions rate-limited by a surface or desorption step: comparable in some respects with heterogeneous catalytic processes Decompositions rate-limited by a surface process or the product desorption step are kinetically similar in form to those envisaged as operating in many heterogeneous catalytic reactions. Participants located within the bulk of reactant particles must diffuse to the surface sufficiently rapidly to sustain the rate of product evolution. The rates of decompositions of this type may be proportional to the reactant surface area and sensitive to product removal due to the possible effects of readsorption on phase boundary equilibria. Extraneous adsorbed materials (e.g. poisons) may exert a profound influence on surface reactivity and reproducible behaviour can be obtained only when surface conditions are standardized. There are difficulties in identifying, unambiguously, the rate-limiting step from the several concurrent and/or consecutive processes which may participate. Indeed, the mechanisms of such decompositions are usually formulated through reference to data available for related heterogeneous catalytic processes.

153

( a ) Palladium hydride Hydrogen is lost from palladium hydride at 393-473 K [664]. The ready inhibition of the rates of adsorption and desorption reactions in slightly contaminated systems is regarded as a great convenience in the preparation and study of solids of high H : Pd ratio. The very factor which is advantageous in thermodynamic studies hinders identification of the controlling parameters in the kinetic process. As a result, therefore, much is known about the properties of hydrogen in this solid but the mechanisms of its incorporation or removal have been much less fully characterized and the rate-limiting step remains unidentified [ 6641. The catalytic properties of palladium hydride have recently been reviewed [ 6631. ( b ) Titanium hydride and related compounds

The rate of decomposition of titanium hydride in vacuum at 523773 K was slower than that predicted from diffusion calculations and was sensitive t o the presence of gaseous hydrogen [665]. Helium reduced the ease of escape of the volatile product but the reaction was insensitive t o the presence of traces of oxygen. The rate-controlling process was identified as a surface step, probably the combination of hydrogen atoms t o yield molecules. The decompositions of TiH2, ZrH2, NbH0.g5and TaH0., exhibited more complicated behaviour at the upper end of the temperature ranges studied [ 6661. This is attributed t o the occurrence of two consecutive reactions, hydride decomposition (first order) followed by combination of hydrogen atoms (second order). ( c ) Nitrides The kinetics of nitrogen evolution from e-iron nitride have been shown by Goodeve and Jack [667] t o be second order in concentration of interstitial nitrogen, and E = 175 kJ mole-'. The rate of diffusion of nitrogen to particle surfaces was very much greater (by at least X104) than the rate of release of the product gas. The controlling factor in the decomposition is identified as the bimolecular combination of nitrogen atoms to yield p r o d x t molecules and this is consistent with theoretical calculations for the surface collision frequency between adsorbed atoms. These conclusions are supported by Logan et al. [61] who report a slightly lower value of E (161 kJ mole-'). Reaction of gaseous hydrogen with constituent nitrogen of the solid proceeds relatively more rapidly since ammonia formation does not necessitate the slow bimolecular combination of nitrogen, and the magnitude of E for this process is very much lower (58 kJ mole-'). The significance of these observations in the synthesis and decomposition of ammonia on iron is discussed [611. Dreger et al. [668] have pointed out that nitrogen release can occur

154

more readily from the nitrides of TiN and ZrN, where lattice defects are present, than from the more strictly stoichiometric phases BN, A1N and Mg3N2.Nitride decompositions are believed to involve three steps: transfer of the nitrogen atom t o a surface, production of a nitrogen molecule and the metal and, finally, N2 desorption. The significance of these steps in decompositions of the phases mentioned is not, however, discussed.

( d ) Nickel carbide Ni3C decomposition is included in this class on the basis of Dorkmieux's conclusion [669] that the slow step is the combination of carbon atoms on reactant surfaces. The reaction (543-613 K) obeyed first-order [eqn. (15)] kinetics. The rate was not significantly different in nitrogen and, unlike the hydrides and nitrides, the mobile lattice constituent was not volatilized but deposited as amorphous carbon. The mechanism suggested is that carbon diffuses from within the structure to a surface where combination occurs. When carbon concentration within the crystal has been decreased sufficiently, nuclei of nickel metal are formed and thereafter reaction proceeds through boundary displacement. Escoubes and Eyraud [ 6701 find the vacuum decomposition of Ni3C t o be deceleratory throughout the range 533-583 K. The contracting volume [eqn. (7), n = 31 and first-order [eqn. (15)] equations were obeyed between 0.10 < a < 0.65 and 0.10 < a < 0.85, respectively, with E = 208 kJ mole-'. In contrast t o observations by Dorkmieux [669], the reaction in 200 Torr argon was different; in the higher temperature range (603-629 K) there was a marked induction period, the Prout-Tompkins equation, eqn. (9), was obeyed for 0.1 < a < 0.9, and E fell somewhat t o 167 kJ mole-'. Hofer et al. [671] observed that the decompositions of Ni3C and C02C (the iron compounds melt) obeyed the zero-order equation for 0.3 < a < 0.9 (596-628 K and E = 255 kJ mole-') and 0.2 < a < 0.75 (573-623 K and E = 227 kJ mole-'), respectively. The magnitudes of the rate coefficients for the two reactions were closely similar but the nickel compound exhibited a long induction period and an acceleratory process which was not characteristic of the reaction of the cobalt compound. Decomposition mechanisms were not discussed. The first-order reaction of hydrogen with Ni3C at 443 K is relatively more rapid than the decomposition [669], indicating facile hydrogenation of the residual carbon at the reactant surface and the possibility of diffusion control is mentioned.

( e ) Caesium-raphite

compound

Caesium-aphite decomposes [ 6721 in a sequence of identifiable steps, each involving a reduction in the Cs : C ratio. The rate-limiting process is

155

identified as the desorption of metal from the surface, the consequent loss being replenished by diffusion from within the structure. Values of E were greater for reactants with larger Cs contents.

2.3.2 Reactions rate-limited by an interface process There have been few satisfactory demonstrations that decompositions of hydrides, carbides and nitrides proceed by interface reactions, i.e. either nucleation and growth or contracting volume mechanisms. Kinetic studies have not usually been supplemented by microscopic observations and this approach is not easily applied t o carbides, where the product is not volatile. The existence of a sigmoid a-time relation is not, by itself, a proof of the occurrence of a nucleation and growth process since an initial slow, or very slow, process may represent the generation of an active surface, e.g. poison removal, or the production of an equilibrium concentration of adsorbed intermediate. The reactions included below are, therefore, tentative classifications based on kinetic indications of interface-type processes, though in most instances this mechanistic interpretation would benefit from more direct experimental support. Kinetic data for the decompositions of several metal hydrides are summarized in Table 1 2 t o which the following information can be added. The acceleratory period in the decomposition of BeHz ( a < 0.35) is ascribed [673] t o the random formation of metal nuclei followed by linear growth. The increase in rate consequent upon exposure to X-irradiation is attributed to enhanced nucleation. Grinding similarly increased the

TABLE 12 Summary of kinetic characteristics for decompositions of some metal hydrides (interface reactions) Kinetic characteristics

BeHz

Power law [eqn. (2),n 61 (0.1< (Y < 0.35) Contracting volume [eqn. (7),n = 3](a > 0.35) Zero-order Contracting area [eqn. (7),n = 21 Sigmoid Order =

478- 523

Order = Modified [eqn. (9)]

873-1073 400- 432

137 100

676 677

First-order

490- 520

196

671

CrH MgH ZnHz ThH3

-1 ThH1.S LiAlH4

Temperature range (K)

E (kJ mole-' )

Reactant

-

5

673

478- 523

108

213608333483-

9 120-126 116 58

304 641 373 663

Ref.

673 674 1294 675 676

-1 LiAlHz (?)

156

rate of decomposition but the power law [eqn. (2)] exponent, n , was reduced from 6 to 5. The irreversible decomposition of chromium hydride [674] results in the formation of a defective hexagonal phase (CrH CrHoal)and at lower proportions of hydrogen there was recrystallization. Thorium hydride decomposition is identified [676] as being controlled by an interface rather than a diffusion process. The reaction of LiA1H4 proceeds t o completion in three stages and aspects of the proposed mechanisms require further investigation [677]. The initial process may be a consequence of impurities in the reactant. There have been several studies of the pyrolyses of complex metal hydrides; see, for example, ref. 678. Silver acetylide decomposition was studied [ 6791 by X-ray diffraction and microscopic measurements and, although the a-time relationship was not established, comparisons of intensities of diffraction lines enabled the value of E t o be estimated (170 kJ mole-'). The rate-limiting step is believed t o involve electron transfer and explosive properties of this compound are attributed to accumulation of solid products which catalyze the decomposition (rather than t o thermal deflagration). -+

2.3.3 Reactions rate-limited b y a diffusion process

The role of bulk diffusion in controlling reaction rates is expected t o be significant during surface (catalytic-type) processes for which transportation of the bulk participant is slow (see reactions of sulphides below) or for which the boundary and desorption steps are fast. Diffusion may, for example, control the rate of Ni& hydrogenation which is much more rapid than the vacuum decomposition of this solid. Baranowski [6801 concluded that the decomposition of nickel hydride was rate-limited by a volume diffusion process; the first-order equation [eqn. (15)] was obeyed and E = 56 kJ mole-'. Later, Pielaszek [681], using volumetric and X-ray diffraction measurements, concluded from observations of the effect of copper deposited at dislocations that transportation was not restricted to imperfect zones of the crystal but also occurred by diffusion from non-defective regions. The role of nickel hydride in catalytic processes has been reviewed [663].

2.3.4 Transition metal sulphides Kinetic observations for decomposition of some representative transition metal sulphides are summarized in Table 13. Several instances of an advancing interface [contracting volume, eqn. (7), n = 31 rate process have been identified and the rate may be diminished by the presence of sulphur. Diffusion control is, however, believed t o be important in the reactions of two lower sulphides (Nio.P5S,[687] and C U ~ . [688]). ~S These solids have attracted particular interest since both are commercially valuable ores and pyrolysis constitutes one possible initial step in metal extraction.

TABLE 13 Summary of kinetic characteristics for decompositions of some transition metal sulphides Reactant

Product

Kinetic characteristics

FeS2

FeS 1.08 5

Pyrite FeS2

Pyrrhotite

Contracting volume [eqn. (7),n = 31 Interface advance Contracting volume [eqn. (7),n = 31

(Y

- 0.1-0.9

Pyrite

cosz

COSl.2

Co3S.9 NiS2 NiS2

NiS Nil --x S

Ni0.95S

cus Covellite

CU1.8S

Contracting volume [eqn. (7),n = 31 Linear Parabolic Linear Order = Deceleratory Diffusion control Contracting volume [eqn. (7),n = 31 Diffusion control

3

range considered

-

0.2 0.6 0.75 0.1-0.9

<0.1 0.1-0.35 0.35-0.9

E (kJ mole-' )

Ref.

724- 749

313

682

873- 926 759- 851

284 113

683 684

747- 776

263 196 142 242

685 685 685 682

1393-1678 1393-1678 1393-1678 668- 699 673- 723 680- 803 583- 611

75 163 200 244 234 251

686 686 686 682 687 687 687

618- 673

100

688

Temperature range (K)

158

Although not strictly included within the scope of the present review, decompositions have been considered in the context of related rate processes including sulphide oxidations, sulphidation of oxides and/or metals and diffusion in sulphide phases [ 6891. 2.3.5 Related reactions

From kinetic measurements of the sublimation of GeSe ( E = 135 kJ mole-'), it was concluded [690] that desorption involved multi-step surface processes; no residual product remains. From a study of the kinetics of volatilization of zinc phosphide (Zn3P2-+ Zn, P2 and P4, 620-820 K), it is argued [691] that the breakdown step must involve considerable changes in the separation distances of the participating atoms during activation of the lattice constituents. The dissociation of Th14 yields [1271] I2 (vapour) and, successively, the solid lower iodides Th13, Th12, ThI and, finally, the metal. 2.4. AZIDES

Kinetic and mechanistic studies of azide decompositions have contributed significantly towards an understanding of the fundamental principles which control reactions occurring in solids. Attention has largely centred on the azides of Groups IA and IIA metals, BaN6 in particular, and also some of the more stable of the heavy metal azides (e.g. Ag, Pb and Tl). Information from photolysis studies has often been usefully combined with observations on the thermal decomposition. Several reviews of the structures, properties and reactions of azides have appeared [ 232,350, 354,692495,12721. The azide ion generally decomposes irreversibly to gaseous nitrogen, although the formation of nitrides has sometimes been described [696,697]. 2.4.1 Group 11 azides

It is appropriate t o start with BaN6 since this compound has been studied particularly intensively and has been regarded as a model in the development of the theory of kinetics of decompositions of solids. The sigmoid a - t i m e curves for BaN6 pyrolyses, Fig. 15, are typical examples of solid state autocatalytic behaviour. From microscopic measurements of the rates of nucleation and of growth of particles of barium metal product, Wischin [201] observed that the number of nuclei present increased as the third power (-2.5-3.5) of time and that the isothermal rate of radial growth of visible nuclei was constant. During the early stages of reaction, the acceleratory region of the a-time plot obeyed the power law [eqn. (2)] with -6 < n < 8. The temperature coefficients of these processes were used by Wischin [2011

159

Time / min

Fig. 15. Isothermal cY--time curves for the decomposition of barium azide [696]. (Reproduced, with permission, from Monatshefte fur Chemie.)

t o calculate “activation energies” of 309,98 and 694 kJ mole-’ for the nucleation, growth and overall reaction rates, respectively. As pointed out by Prout and Moore [698], however, the rate coefficients from which conventional activation energies should be calculated have dimensions (time)-’ and f(a) = h’t” should be written as f(a) = h”t”. When Wischin’s data are reanalyzed with due allowance for this change in exponent of h , E values for nucleation, growth and the initial rate of the overall reaction are found to be 103, 98 and 116 kJ mole-’, respectively. This suggests that a similar process is rate-determining throughout and means that the mechanisms devised by Mott [699] and by Thomas and Tompkins [430] to explain the high values of E reported by Wischin [201] should now be reconsidered. There is good agreement between conventional activation energies, determined by different workers, for decomposition of both unirradiated and irradiated BaN6. The reaction mechanism has been discussed in considerable detail by Tompkins [ 3501. R o u t and Moore [698,700] found that the acceleratory period in BaN6 decomposition was well described by the power law [eqn. (2)] but the exponent, n = 4, was significantly lower than that mentioned above (n 6) and the contracting volume relation [eqn. (7), n = 31 was obeyed in the later stages: values of E were 112 and 102 kJ mole-’, respectively. Strontium azide also obeyed the power law [eqn. (2)] but with n = 3 and in the later stages data fitted the first-order equation. The behaviour of calcium azide [701] was similar in that n = 3 during the acceleratory process but the contracting volume relation [eqn. (7), n = 31 was obeyed later and values of E were 113 and 79 kJ mole-’, respectively. Tompkins and Young [354,692] also find that the decomposition of caN6 is described by the cubic law, but the magnitude of E is influenced by thermal treatment of the reactant and rate behaviour is sensitive t o the presence of contaminants and to salt ageing. Pre-irradiation of all three (Ca, Sr and Ba)

-

160

azides reduced the induction period and accelerated the rate of subsequent decomposition. Pai Verneker and Kannan [1273] observe that data for the decomposition of BaN6 single crystals fit the Avrami-Erofe'ev equation [eqn. (6), n = 31 for 0.05 < a < 0.90. Arrhenius plots (393-463 K) showed a discontinuous rise in E value from 96 t o 154 kJ mole-' at a temperature that varied with type and concentration of dopant present: Na' and C0:impurities increased the transition temperature and sensitized the rate, whereas A13+ caused the opposite effects. It is concluded, on the basis of these and other observations, that the rate-determining step in BaN6 decomposition is diffusion of Ba" interstitial ions rather than a process involving electron transfer. Torkar et al. [696,702] have also made a detailed kinetic study of BaN6 decomposition. The acceleratory period (a < 0.1) was again shown to obey the power law with the lower exponent, n = 4; this agrees with observations by Prout and Moore [700] referred t o above. The AvramiErofe'ev equation [eqn. (6), n = 31 described the data for 0.1 < a < 0.8, the Prout-Tompkins equation [eqn. (9)] was satisfactorily fitted for 0.05 < a < -1.0 and the contracting volume relation [eqn. (7), n = 31 applied when a > 0.6. Nucleation was confined t o outer (100) crystal surfaces and (001) planes; basal planes of growing nuclei were diamondshaped. Nuclei were randomly distributed and the number present increased according t o an exponential law. The rate of interface advance varied slightly with crystallographic direction and E for growth was 109 kJ mole-'. Once again, a complicated set of reaction mechanisms was proposed as a result of unconventional activation energies (see above). On recalculation of rate coefficients t o dimensions (time)-', there were only minor differences in magnitudes of E for the various processes and these were within the range of other reported values. The decomposition rate was increased by crushing, but kinetic characteristics were largely unchanged. From measurements of product yields, X-ray diffraction studies and the enthalpy of reaction, it was concluded [696] that the decomposition gave a large yield of residual nitride, the proportion, 75% Ba3N2 and 25% Ba metal, is attributable t o the intervention of the unstable intermediate Ba2N2. Reaction is identified as an interface process, rather than product evolution through diffusion control. It is also supposed that nucleation follows an irreversible electron transfer step at appropriate surface sites and that growth involves electron transfer with the production of nitrogen gas following combination of two azide radicals. Nitride formation has also been detected [697] in BaN6 decomposition under liquid hydrocarbons at 420-470 K. Although there have been several independent, careful kinetic studies of the reactions of BaN6 and a-time measurements have been supplemented by quantitative microscopic observations, there remain a number of points of significant disagreement concerning the rate laws obeyed. The nuclea-

-

161

tion process has been alternatively described as fitting the power law [201,430] [eqn. (2)] and the exponential law [696] [eqn. (8)], and although the acceleratory process fits the power law [eqn. (2)], different workers have found the exponent (n)to be four [696,700,702] and six [201,403]. It is desirable that the reasons for these apparent discrepancies should be identified, since a satisfactory reconciliation of the differences could help to clarify the nature of the problems and limitations inherent in such kinetic analyses. Indeed, it is surprising that these apparent disagreements should remain unresolved for so long in such a well-defined and extensively studied reaction. This emphasizes the exceptional care that is required in the collection and analysis of kinetic data for solid state decompositions. 2.4.2 Group IA azides ( a ) Lithium azide Satisfactory reproducibility for the decomposition of LiN3 at 483 K [703] was only obtained with salt which had been ground and pelleted. a-Time curves were sigmoid, the reaction obeyed the Avrami-Erofe'ev equation [eqn. (6), n = 31 for 0.02 < a < 0.58 and the contracting volume equation [eqn. (7), n = 31 for 0.05 < a < 0.95 and E = 119 kJ mole-'. It is concluded that reaction was initiated at a fixed number of nuclei which grow in three dimensions. The reproducibility achieved by grinding and pelleting was attributed to the production of a uniform distribution of a large number of defects throughout the reactant. Pre-irradiation accelerated decomposition. ( b ) Sodium azide

The vacuum decomposition of sodium azide obeyed the AvramiErofe'ev equation [eqn. (6), n = 21, though the range of a over which the fit could be regarded as satisfactory varied with reactant mass owing to the influence of product gas pressure on the ease of volatilization of the sodium metal formed. In 500Torr argon, the kinetic behaviour was independent of mass and E = 159 kJ mole-'. In the initial stages of reaction, metal product evaporation opposed the generation of nuclei, but if conditions favoured the retention of this metal, an acceleratory period could be observed. After reaction had penetrated the intermosaic network of the crystal [705], linear filaments of sodium were developed which grew in two dimensions, thus accounting for the observed kinetic obedience. Later, however, when a 0.6-0.7, the molten sodium could no longer be retained within the disintegrating crystal and so the kinetic characteristics changed. Walker et al. [119] found that the rate of NaN3 decomposition was proportional t o the surface area of the crystals and the

-

162

interface developed advanced into the reactant particle in a preferred crystallographic direction. Torkar et al. [ 702,706-7081 identified nucleation as an autocatalytic process at the (hhO) planes of hexagonal platelets of NaN3. The deceleratory reaction fitted the first-order equation [eqn. (15)]. Values of E tended to be irreproducible for the pure salt; E was about 180 kJ mole-’ but this was reduced to about half by doping. This influence of an additive and the observed similarities in magnitudes of E for decomposition and for diffusion were interpreted as indicating that growth of nuclei was controlled by a diffusion process. In another study [393] of the effect of dopants on NaN3 decomposition, it was observed that Fe3+ ions, potential electron traps, sensitized reaction [704], indicative of an electron transfer mechanism. It is also believed that the diffusion mechanism proposed by Torkar et al. [702, 706-7081 is not supported by the concentration-dependent effect of doping with the carbonate ion, since at low concentrations (0.01 mol%) the rate is reduced, whereas at higher concentrations (0.1 and 1.0 mol%) it is increased. Univalent cation additives, for which the radius is greater than that of the host ion, decrease the induction period t o the onset of salt decomposition, an effect attributed [ 7091 t o induced strain. The influence of strain in defect generation is supported by observations [393] on the broadening of absorption peaks in the infrared spectra of NaN3 doped with divalent cations. Both precompression [ 3931 and grinding [710] increased both the concentration of defects in the solid and the rate of decomposition, while annealing [393] (420 K for 1 h), expected to reduce the concentration of defects, decreased the reaction rate. It is suggested [393] that the effects of gross imperfections overshadows that of point defects. The role of “dipoles”, involving the defect structure of the solid, during the early stages of decomposition (a < 0.02) has also been discussed [ 3681. The kinetics of NaN3 decomposition are sensitive to both pressure and composition of the surrounding atmosphere. The influence of an inert gas in suppressing sublimation of product metal has been mentioned already. The reaction of NaN3 at 623 K was strongly inhibited [711] by NO and by H2.The possible formation of transient decomposition intermediates could not, however, be distinguished from the direct interaction of added gas and azide. ( c ) Potassium azide

An initial deceleratory process (-1%) in KN3 decomposition is ascribed to reaction at superficial imperfections [ 7121. The subsequent ‘constant rate of product evolution corresponds to an interface process but this is not a nucleation and growth mechanism since the product metal is volatile (as in NaN3). The catalytic properties of potassium vapour are attributed

163

to a reduction in E by the provision of electron traps other than vacant anion sites. In the high vacuum system used by de Panafieu et al. [3721, decomposition at relatively low temperature could be studied by mass spectrometry and electrical conductivity measurements. The correlation found between E values for decomposition and for conduction was similar to that referred t o above for NaN, [702,706-7081. These observations, together with the enhancement of the decomposition rate resulting from the influence of an electric field and the results of conductivity [ 7131 and of photolytic studies [349] suggest that the rate-controlling step for the decomposition of this, and indeed other azides, is more complex than that of exciton formation.

( d ) Rubidium and caesium azides Caesium azide melts with a little decomposition (<1%)at 598 K. There is slow decomposition of the solid when large amounts of NiO are present [714]. Observations on the photolyses of RbN, and CsN, have been discussed [ 7151 with reference to the pyrolyses of other alkali azides.

2.4.3 Other azides ( a ) Thallium azide a-Time curves for the decomposition of TlN, obeyed the zero-order equation [119,503,716] and slopes were directly proportional to the surface areas of the reactant, with E = 150 kJ mole-' between 507 and 529 K. Microscopic examination revealed that decomposition involved the boring of holes into reactant crystals, or surface etching, interface advance being [119] predominantly in the [110] direction, but also parallel to the (001) layer structure. The articles cited include photographs of partially reacted salt and the geometry of interface advance is discussed.

( b ) Silver azide There is no induction period to the decomposition of AgN3, the reaction is deceleratory throughout and a kinetic order of 2/3 is found [ 7171 [identical with the contracting volume equation, eqn. (7), n = 31 and E = 150 kJ mole-' at 515-555 K. (The melting point of AgN3 is listed [693] as -523 K.) In their discussion of the reaction mechanism, Gray and Waddington [717] contrast certain properties of AgN, and TlN, with the alkali metal azides and the differences in behaviour of the two groups of solids are identified with the properties of the excitons. In the silver and thallium salts, positive holes and electrons are formed by exciton dissociation, whereas no such separation occurs in azides of the alkali metals. The first step in AgN, decomposition is identified as exciton dissociation and

164

many of the positive holes and electrons so formed recombine directly, though a proportion of the electrons are trapped at suitable cations which are thereby converted to metal. Product particle growth continues through aggregation of mobile interstitial metal ions (see also ref. 718). Bartlett e t al. [719] also report obedience of AgN3 decomposition at 463-523 K to eqn. (7), n = 3, though a slightly lower value of E (130 kJ mole-') is found. The mechanism of reaction has been discussed by Young [ 291. The importance of electron mobility in the reaction is further confirmed by the observed ability of many additives (including semiconducting oxides, organic dyes, etc .) to accelerate salt decomposition. The steps leading to nucleation have been discussed by Zakharov et al. [ 12741. (c) Lead azide

The a - t i m e curve for the decomposition of PbN6 is predominantly deceleratory [ 281 ; the induction and acceleratory periods are relatively short. Griffiths and Groocock [720] distinguish three regions of the reaction (-540 K). The initial process, a rapid evolution of gas for which E = 63 kJ mole-', is attributed to the breakdown of superficial basic carbonate. The acceleratory process in the main reaction obeyed the power law, n = 5, and the reported value of E , 1095 kJ mole-', is equivalent (i.e. X i ) t o a conventional activation energy of 219 kJ mole-' (with rate coefficients in units of time-'). This kinetic obedience was attributed t o a rate of production of nuclei directly proportional t o time followed by three-dimensional growth ( p = 2, X = 3 so that n = 5). The final deceleratory period obeyed the contracting volume equation [eqn. (7), n = 31 resulting from continued advance of a coherent reaction interface. Both nucleation and growth processes were ascribed to reactions of positive holes (N; + N3 + eand 2 N3 + 3 NZ). The kinetic observations reported by Young [721] for the same reaction show points of difference, though the mechanistic implications of these are not developed. The initial limited (- 2%) deceleratory process, which fitted the first-order equation with E = 1 2 1 kJ mole-', is (again) attributed to the breakdown of superficial impurities and this precedes, indeed defers, the onset of the main reaction. The subsequent acceleratory process is 'well described by the cubic law [eqn. (2), n = 31, with E = 233 kJ mole-', attributed t o the initial formation of a constant number of lead nuclei (i.e. instantaneous nucleation) followed by three-dimensional growth (0 = 0, X = 3). Deviations from strict obedience to the power law ( n = 3) are attributed t o an increase in the effective number of nuclei with reaction temperature, so that the magnitude of E for the interface process was 209 kJ mole-'. The influence of pre-irradiation on a-PbN6 decomposition kinetics was studied by Jach [722]. The initial acceleratory process in untreated solid [eqn. (2), n = 21 was ascribed t o surface and three-dimensional growth

165

reactions, and when a > 0.4 the first-order equation [eqn. (15)] was approximately obeyed in the deceleratory period. Irradiation decreased the contribution of the acceleratory period and reduced the magnitude of E from 152 kJ mole-' (468-526 K) in the unirradiated solid to 107 kJ mole-' (446-512K). This reduction in E is believed to be due to changes in the electronic excitation energy and the accompanying diminution in A to structural changes on irradiation. There have been several studies of the effects of additives (Fe, Ag, Cu and Bi ions) on the kinetics of PbN6 decomposition. Hutchinson and Stein [723] make some critical comments concerning the shortcomings of earlier work and describe an investigation of the influence of iron impurities on the kinetics of reaction, including due allowance for variations in particle size distributions of the preparations used. At equal impurity concentrations, Fe3+ increased the rate of interface advance more than that which resulted from the incorporation of (FeN3)'+, but the latter produced the greater shortening of the induction period: neither additive caused an appreciable change in the calculated values of E. (It is of interest to note here that the same foreign ion is believed [350]to participate in the nucleation step of BaN6 pyrolysis.) ( d ) Copper(I) azide The acceleratory period for the decomposition of CuN3 obeyed the cubic law [eqn. (2),n = 31 and E = 110 kJ mole-' (442-467 K) [724]. ( e ) Decomposition reactions of azides Characteristically, the mechanisms formulated for azide decompositions involve [693,717]exciton formation and/or the participation of mobile electrons, positive holes and interstitial ions. Information concerning the energy requirements for the production, mobility and other relevant properties of these lattice imperfections can often be obtained from spectral data and electrical measurements. The interpretation of decomposition kinetics has often been profitably considered with reference to rates of photolysis. Accordingly, proposed reaction mechanisms have included consideration of trapping, transportation and interactions between possible energetic participants, and the steps involved can be characterized in greater detail than has been found possible in the decompositions of most other types of solids. 2.5 FULMINATES AND CYANAMIDES

The fulminates (containing the CNO group or ion) and the cyanamides (CNZ-) bear some structural similarities to the azides.

166

2.5.1. Fulminates The decomposition kinetics of mercury fulminate [ 7251 are significantly influenced by ageing, pre-irradiation and crushing; these additional features of reaction facilitated interpretation of the observations and, in particular, the role of intergranular material in salt breakdown. Following a slow evolution of gas (-0.1%) during the induction period, the acceleratory process for the fresh salt obeyed the exponential law [eqn. (S)]when a < 0.35. The induction period for the aged salt was somewhat shorter and here the acceleratory process obeyed the cube law [eqn. (2),n = 31 and E = 113 kJ mole-'. Singh and Palkar [ 7261 identified an initial deceleratory reaction in the decomposition of silver fulminate. This obeyed first-order kinetics (E = 27 kJ mole-') and overlapped with the acceleratory period of the main reaction, which obeyed the power law [eqn. (2),n = 21 with E = 119 kJ mole-'. The mechanism proposed included the suggestion that twodimensional growth of nuclei involved electron transfer from anion t o metal. Boddington and Iqbal [ 7271 have interpreted kinetic data for the slow thermal and photochemical decompositions of Hg, Ag, Na and T1 fulminates with due regard for the physical data available. The reactions are complex; some rate studies were complicated by self-heating and the kinetic behaviour of the Na and T1 salts is not described in detail. It was concluded that electron transfer was involved in the decomposition of the ionic solids (i.e. Na' and T1' salts), whereas the rate-controlling process during breakdown of the more covalent compounds (Hg and Ag salts) was probably bond rupture.

2.5.2 Cyanamides The vacuum decomposition of cadmium cyanamide in the range 830950 K yielded [728]Cd, C2N2and N2, was controlled by the rate of interface advance, and obeyed the contracting volume equation [eqn. (7),n = 3]and E = 159 kJ mole-'. The decomposition of dried thallium(1) cyanamide proceeds [729] t o completion in four distinct stages. Only the first stage is completed before melting at 793 K. This stage obeys the firstorder equation [eqn. (15)]in the temperature range 733-813 K with E = 129 kJ mole-'. 3. Decompositions of metal salts of oxyacids Diverse and sometimes contrasting types of kinetic behaviour have been described for the decompositions of salts in this class, which includes the metal carbonates, sulphates, nitrates and nitrites, phosphates, oxyhalides, permanganates and chromates (Sects. 3.1-3.7, respectively). It is con-

167

venient to discuss ammonium salts together (Sect. 4) since the NH; cation is capable of interacting with the anion to yield volatile products. Separate subsequent sections consider carboxylates (Sect. 5) and co-ordination compounds (Sect. 6), other than the hydrates. The various factors identified as controlling the rates of breakdown of salts of oxyacids have been characterized by detailed investigations of the reactions of particular, conveniently studied (i.e. model) compounds. Thus, the reaction of CaC03 is an endothermic and reversible process and similar behaviour is apparent for other carbonates [ 641. In contrast, the decomposition of KMnO, is exothermic and irreversible and comparable behaviour is found for certain other salts containing transition metals in the higher oxidation states. The properties of NH4C104are different again; here, there is the possibility of proton transfer and concurrent sublimation, the salt is stabilized by NH3, and onset of decomposition is accelerated by HC104. The reactions of the sulphates, nitrates, etc., have attracted relatively less interest, probably because of the difficulties which attend the collection of meaningful kinetic data due to dissociation of the volatile oxides (of sulphur or of nitrogen, etc.). The kinetic behaviour of metal salts of oxyacids may be influenced by water of crystallization. Where complete-dehydration precedes decomposition, the anhydrous material is the product of a previous rate process and may have undergone recrystallization. If water is not effectively removed, there may at higher temperature be the transient formation of a melt prior to decomposition. The usual problems attend the identification of partial or transient liquefaction of the reactant in the mechanistic interpretation of kinetic data. 3.1 METAL CARBONATES

Metal carbonate decompositions proceed t o completion in one or more stages which are generally both endothermic and reversible. Kinetic behaviour is sensitive to the pressure and composition of the prevailing atmosphere and, in particular, t o the availability and ease of removal of COz. The structure and porosity of the solid product and its relationship with the reactant phase controls the rate of escape of volatile product by interand/or intragranular diffusion, so that rapid and effectively complete withdrawal of COz from the interface may be difficult t o achieve experimentally. Similar features have been described for the removal of water from crystalline hydrates and attention has been drawn to comparable aspects of reactions of both types in Garner’s review [ 641. The kinetics of carbonate decompositions have been studied for both their technical importance and their theoretical interest. While both isothermal and non-isothermal techniques have been used, data obtained by rising temperature methods may be unreliable where the influence on the reverse reaction of COz gas present has not been positively characterized.

TABLE 14 Selected kinetic characteristics for the decomposition of metal carbonates ~~

~~~

~

Compound

Temperature range (K)

Atmosphere

AH&,

E (kJ mole-' )

Remarks

Ref.

(kJ mole-' )

Single (1011)face Contracting volume equation [eqn. (7),n = 31 Non-isothermal analysis based on contracting volume equation [eqn. (7),n = 31 Single (001)face Contracting volume equation [eqn. (7),n = 31 Pellets (I.R.) (Y 4 0.1, First stage Second stage Contracting volume equation [eqn. (7),n = 31 Prout-Tompkins equation [eqn. (911

121 734

2 9 8 ~ a

CaC03 MgC03

934-1013 813- 873

Vacuum Vacuum

178 116.9

205 150

SrC03 BaC03

1023-1 293 11 03-1 373

Vacuum Vacuum

234.5 269.2

222 283

- 1160-1 210

Vacuum

(252.1)

Vacuum He

81.3 81.3 94.0 -6.4 87.6

96 75-84 105 126 168-1 74

116.3

123

99.0 99.0 71.1

151 96 96

BaCO3 Ag2 co3 (active) (inactive) PbC03 PbC03 . PbO PbC03 MnC03

500 421 473 473 608

N2

611- 661

N2

N2 Vacuum

Vacuum

CdC03 ZnC03 ~~

a From ref.

420384463463509-

733.

225.9

I

735 736 458 288 737 737 738, 739 740 741 47 740

169

Accordingly, the present survey is mainly concerned with constant temperature methods, though thermal analysis [730] has been shown to be most valuable in identifying the temperature range of stability and the compositions of decomposition intermediates. Zawadski and Bretsznajder [731] have shown that the value of Ef, for the forward reaction of the reversible decomposition

increases with rising pressure from a minimum value in vacuum. Pavlyuchenko and Prodan [ 7321 distinguish two methods of measuring Ef: (i) at constant partial pressure of C02, Pcoz and (ii) at a constant ratio PC02/Pe,where P, is the equilibrium partial pressure of COz. For method (i), Ef increases as Pco2 approaches P,, while for method (ii), Ef is independent of the value of the ratio and will have the same value as that for the vacuum reaction. The more usual use of method (i) accounts [730] for some of the variation in reported values of E for the same reaction. Activation energy values for the recombination of the products of carbonate decompositions are generally low and so it is expected that values of Ef will be close t o the dissociation enthalpy. Such correlations are not always readily discerned, however, since there is ambiguity in what is t o be regarded as a “mole of activated complex”. If the reaction is shown experimentally t o be readily reversible, the assumption may be made that Ef = n,AH and the value of n, may be an indication of the number of reactant molecules participating in activated complex formation. Kinetic parameters for dissociation reactions of a number of carbonates have been shown t o be consistent with the predictions of the Polanyi-Wigner equation [eqn. (19)]. Much detailed information concerning the decompositions of carbonates is to be found in the review by Stem and Weise [733] and selected kinetic data are summarized in Table 14. 3.1.1. Calcium carbonate From the more recent reports cited below, further references to the extensive literature concerned with calcite decomposition may be traced. Other modifications of CaCO, (aragonite and vaterite) undergo solid phase transitions t o calcite at temperatures of 728 K and 6 2 3 4 7 3 K respectively [733], below those of onset of decomposition (>900K). There is strong evidence [ 7421 that the reaction CaCO,(s) + CaO(s) + C02(g) takes place at an interface between calcite and residual oxide, which may first appear in a metastable form [121].

170

Beruto and Searcy [ 1211 have eliminated those complications in kinetic analysis which arise from variations in particle size and the changing geometry of reaction by sheathing all surfaces of the reactant sample, which was in the form of a thin slice (-1 mm thickness), except the (1011) cleavage face at which reaction was initiated. The interface developed advanced into the reactant bulk at constant rate up t o a > 0.8, while the pressure in the reaction vessel was maintained below -5 X Torr, removing the possible influence of the reverse process. The value of E (205 kJ mole-') was somewhat greater than the enthalpy of decomposition (178 kJ mole-'). Optical and electron microscopy revealed two distinguishable product layers. The outer layer was identified as polycrystalline CaO, while that nearer the reactant, constituting -10% of the thickness at high a , showed structural differences, supporting the suggested [ 7431 production of a metastable modification, represented as CaO *. Towe [1275] attributes metastability of CaO t o small crystallite size and crystallite shape rather than a basic structural difference. (It was not stated [121] whether kinetic characteristics A and E varied with the crystallographic surface of reactant exposed t o the vacuum.) Thomas and Renshaw [ 207,5741 concluded that decomposition in deformed calcite crystals can be initiated at particular dislocations only, namely those which glide on (100) and (21T ) planes but not those which glide on (113) planes. The value of E (210 kJ mole-') determined for the very early stages of reaction (0.002 < a < 0.01) was close t o that (205 kJ mole-') mentioned [121] above. There has been speculation that the elastic energy associated with strain in the vicinity of the dislocation may be the cause of the increased reactivity (i.e. preferred nucleation) in these zones. Fox and Soria-Ruiz [ 5751, however, conclude that the effect arises from changes in the stereochemical environment of the carbonate ion due to the presence of the imperfection rather than from stored core energy. Some influence may also arise from the impurities preferentially incorporated in the disorganized regions of the reactant [ 7441. In reviewing reported values of E for calcite decompositions, Beruto and Searcy [121] find that most are close to the dissociation enthalpy. They suggest, as a possible explanation, that if product gas removal is not rapid and complete, readsorption of C02 on CaO may establish dissociation equilibria within the pores and channels of the layer of residual phase. The rate of gas diffusion across this barrier is modified accordingly and is not characteristic of the dissociation step at the interface. A critical examination of the literature shows that few studies have measured Pcoz within the reactant mass, and other important parameters such as particle sizes and distributions, interface geometry, annealing [575] and the effects of self-cooling, which may be significant in large samples, are not always fully characterized. It is hardly surprising, therefore, that very different kinetic parameters (and mechanistic conclusions) are t o be found in the literature. The problems which arise in interpreting

171

non-isothermal measurements are nowhere more apparent than in the unreasonable spread of values of A (102-106') and E (108-1600 kJ mole-') summarized by Zsak6 and Arz [ 5161. Hashimoto [ 7451 has also determined high values of E for decomposition in C02, but data were more consistent with the vacuum reaction on extrapolating measurements to zero pressure [ 7321. The decomposition rate decreases linearly with Pco, at low temperature but the relationship is non-linear at higher temperatures [745]. The linear dependence has been used by Ingraham and Marier [191,746] in support of their proposal that the rate was limited by diffusion of C02 through a layer of CaO and by Hyatt et al. [ 7471 for a surface reaction mechanism involving CaCO,, CaO, CaO * and adsorbed COz. Where large samples of reactant are used and/or where C02 withdrawal is not rapid or complete, the rates of calcite decomposition can be controlled by the rate of heat transfer [748] or C02 removal [749]. Draper [748] has shown that the shapes of a-time curves can be altered by varying the reactant geometry and supply of heat t o the reactant mass. Under the conditions used, heat flow, rather than product escape, was identified as rate-limiting. Using large (-100 g) samples, Hills [749] concluded that the reaction rate was controlled by both the diffusion of heat t o the interface and CO, from it. The proposed models were consistent with independently measured values of the transport parameters [750-7521; whether these results are transferrable t o small samples is questionable. 3.1.2 Other Group IZA carbonates

The decomposition of MgC03 (magnesite) is an interface process [734] between 813-873 K and E = 150 kJ mole-'. In the presence of CO,, E was increased t o 234 kJ mole-' but was reduced slightly on the addition of ZnO or NiO. Admixture with CaO reduced the value of E t o 54 kJ mole-'. This is a surprising result since the value of E for decomposition [734,753] of the mixed carbonate (Ca, Mg)C03, dolomite, is 220 kJ mole-', larger than the value for each constituent. The influence of Pcoz and of alkali metals on MgC03 decomposition has been the subject of a DTA study [ 4041. Basu and Searcy [736] have applied the torsion--effusion and torsionLangmuir techniques, referred t o above for calcite decomposition [1211, to the comparable reaction of BaCO,, which had not been studied previously. The reaction rate at the (001) faces of single crystals was constant up to a product layer thickness of -1 mm. The magnitude of E (225.9 kJ mole-') was appreciably less than the enthalpy of the reaction (252.1 kJ mole-'). This observation, unique for carbonates, led to the conclusion that the slowest step in BaC03 vacuum decomposition at -1160-1210 K is diffusion of one of the reaction components in a condensed phase or a surface reaction of C02 prior t o desorption.

172

Judd and Pope [735] conclude that mechanisms of decompositions of SrC03 and BaC03 are similar to that described by Hills [749] for the calcium salt, and non-isothermal measurements, using the contracting volume equation [eqn. (7), n = 31, yielded values of E as 222 and 283 kJ mole-’, respectively. The former is in good agreement with 230 f 20 kJ mole-’ found [754] using the zero-order equation followed (a > 0.5) by first-order dependence. Decomposition studies of both solids are complicated by phase transitions [733] and there is melting of SrC03 [755]. The reactions of co-precipitated composite (Ca, Sr, Ba)C03 crystals have been investigated [756] because of the applications found for the mixed residual oxide product. 3.1.3 Silver carbonate Ag2C03 can be prepared in two forms described [757] as “active”, readily decomposed at 439 K, and “inactive”, which achieved the same rate of decomposition only at 593 K. Reaction yielded Ag20 and C02or, at higher temperature (>-520 K) Ag, O 2and C02. a-Time curves for both active and inactive preparations are predominantly deceleratory , with only brief induction periods: curves for inactive samples are characterized by a marked decrease in rate at a 0.1. Activation energies for decomposition of the inactive form [288], from infrared measurements on pressed discs, were 75 f 13 and 84 f 1 5 kJ mole-’ for the induction periods and the subsequent firsborder reactions, respectively. A value of 96 kJ mole-’ has been reported for the deceleratory process [eqn. (7), n = 31 with the active preparation. The high reactivity of the active form of Ag2C03is attributed to the retention of water, incorporated during preparation, in the form of the ions HCO; and OH-, with corresponding cation vacancies (VA,+),viz.

-

H2O + Ag2C03

+

2 Ag’ + HCO, + OH- + 2 V A g +

Such defects facilitate movement of C 0 2 within the crystal by transfer from HCO; to OH- and of Ag’ in the cation vacancies. This interpretation is supported [758,759] by the observed increase in reactivity resulting from doping of Ag2C03 with Cd2+,Y3+ or Gd3+,where incorporation of the additive is accompanied by the creation of cation vacancies. Differentiation between the two forms of Ag2C03is not easy and, from the many methods used, electron spin resonance spectroscopy and thermal analysis have been most successfully applied [ 7571. The imperfections mentioned above occur in the low temperature decomposition product and are identified as being responsible for enhanced activity in readsorbing CO,. Annealing of the residue removes these defects and reduces the reversibility of reaction.

173

3.1.4 Lead carbonate

An important feature of the decomposition of PbC03 is that COz evolution proceeds to completion in distinct steps. Although various intermediates having PbC03 : PbO ratios between 5 : 1 and 1 : 2 have been reported [760], Ball and Casson [403] found no evidence from X-ray diffraction measurements for the existence of compounds other than PbC03: PbO and PbC03: 2 PbO. They suggested that the inferred existence of other intermediates arose from the influence of Pcoz on the rate of decomposition of the 1 : 1compound. The degree of perfection of the reactant PbC03 crystals has also been shown to be important [761]. Vacuum decomposition (509-608 K ) occurred [738,739] in a single stage and obeyed the contracting volume equation [eqn. (7), n = 31 with E = 168-174 kJ mole-'. Both grinding and ageing influenced the reaction rate. Kodama et al. [737] found only two stages in the isothermal decomposition in nitrogen at 463-673 K, viz. 2 PbC03 = PbC03 * PbO + COZ PbCO3 PbO = 2 PbO + COZ a-Time data for the first stage, identified as an interface reaction, obeyed the contracting volume equation [eqn. (7), n = 31 and E = 105 kJ mole-'. The second stage proceeded at a constant rate, E = 126 kJ mole-'. The value of Pcoz at the surface of the reactant pellets was estimated from the Also included in effects of varying the rate of flow of the carrier gas (Nz). the study [737] were the decomposition reactions of 2 PbC03 * Pb(OH)2 and of 2 PbC03 PbO. The former was converted into the latter on dehydroxylation, viz.

-

-HzO

2 PbCO3 * Pb(0H)z +2 PbCO3 * PbO + 3 PbO + 2 COZ The first reaction was studied in 760 Torr COz (493-623 K) and the second step in vacuum (513-553 K). Both a-time curves obeyed the contracting volume equation [eqn. (7), n = 31 and E values were 125 and 172 kJ mole-', respectively. 3.1.5 Manganese(II) carbonate The reaction of MnC03 is of particular interest because of the possibility of the formation and interconversion of the various oxides of manganese [733,1276]. Westerdahl and Leader [762] identify the initial process as

3 MnC09 = Mn304+ CO + 2 COz However, within appropriate conditions of temperature and Pco, reduction can occur, viz. Mn304+ CO = 3 MnO + COz

174

MnO is the overwhelmingly predominant product in inert [763,764] and in static [762] atmospheres. In nitrogen at 611-661 K, the sigmoid atime curve obeys [765] the Prout-Tompkins equation [eqn. (9)] and E = 123 kJ mole-'. 3.1.6 Carbonate decompositions

The above studies (Table 14) and related measurements for certain other salts (e.g. ZnCOB [765,766] and CdC03 [47,741,767-769]), characterize carbonate decompositions as both endothermic and reversible [64]. The recent work by Searcy et al. [121,736], in which the influence of the reverse reaction was effectively eliminated by the use of very low pressures (-5 X 10-5Torr), showed that individual values of E for carbonate decompositions could be appreciably greater than, or (in one instance) lower than the dissociation enthalpy. This careful work and detailed mechanistic consideration of the data draws attention to shortcomings in certain previous experimental investigations. Effective measurements of Pco, were not always included and this omission is particularly significant during application of the rising temperature technique t o kinetic studies of decompositions of this group of solids. Equilibration processes within the layer of solid product are believed [121] to be a possible cause of the often reported similarity between a measured value of E and the dissocation enthalpy. 3.2 METAL SULPHATES

The decompositions of anhydrous metal sulphates are often endothermic and usually reversible MS04 * MO + SO3 However, unlike the carbonates discussed above, the reaction is further complicated by the dissociation of the gaseous product

SO3 * SO2 + f O2 for which [770] AH&, is 99 kJ, thus increasing the endothermic nature of the overall reaction, and equilibrium constants rise [770] from -4 X at 298 K to 1at -1050 K and 180 at 2000 K.Rates of salt dissociation are reduced by the presence of gaseous or adsorbed SO3 and the proportion of these species can be expected t o be increased when oxygen is available. It is also possible that decomposition may proceed to completion through the intermediate formation of one (or more) basic salts or (and) the oxidation state of the cation may be changed. Stern and Wise [ 7701, in the first of a series of reviews concerned with the high temperature properties of inorganic salts, summarize much of the thermodynamic and kinetic data available (1964) for the metal sulphates. Many of these

175

salts, including the alkali sulphates, melt before or during reaction. Representative kinetic data for sulphate decompositions are summarized in Table 15. 3.2.1 Group IIA sulphates

Probably the most reliable kinetic investigation of the decomposition of a metal sulphate presently available is that by Mohazzabi and Searcy [140] for the reaction of BaSO,. The technique used has been referred to above for the similar study of calcite dissocation [121]. Decomposition was initiated at a single cleaved (001) surface of a BaSO, crystal, thus eliminating systematic changes in area of the interface during subsequent advance. The reaction rate was constant up to a product layer thickness of at least 1mm. Since mass spectrometric measurements showed that the ratio of peak intensities SO; : SO; from decomposition was always > l o 0 : 1,the principal reaction is identified as BaS04 = BaO + SO2 + f O2 The solid product, BaO, was apparently amorphous and porous. Decomposition rate measurements were made between the phase transformation at 1422 K and 1550 K (the salt melts at 1620 K). The enthalpy and entropy of activation at 1500 K (575 f 13 kJ mole-' and 200 f 8 J K-' mole-') are very similar to the standard enthalpy and entropy of decomposition at the same temperature (588 f 7 kJ and 257 f 5 J K-', respectively, referred to 1mole of BaS04). The simplest mechanistic explanation of the observations is that all steps in the reaction are in equilibrium except for desorption of the gaseous products, SO2 and 02.Desorption occurs over an area equivalent t o about 1.4% of the total exposed crystal surface. Other possible models are discussed. Kinetic data available for the reactions of other metal sulphates refer t o reaction conditions closer t o those of actual pyrometallurgical processes [ 7901. Magnesium sulphate (m.p. 1403 K ) decomposes at 1193-1353 K obeying the contracting volume equation [eqn. (7), n = 31 and E = 312 kJ mole-' [ 7721. This value is in agreement with that reported by Brownwell [773] (343 kJ mole-') for the approximately constant rate during the initial period (a < 0.25), but is very different from the value reported by Pechkovskii et al. [774] (661 kJ mole-') for a similar temperature range. Increasing the sample mass or compressing the sample into pellets reduces the reaction rate [772] by increasing the magnitude of PsoBdeveloped within the reactant. Calcium sulphate (anhydrite) melts at 1723 K. Decomposition of BeS04 (either reagent grade or freeze-dried) yielded Be0 [771] and kinetic analyses based on the contracting area equation [eqn. (7), n = 21 for 875-990 K gave values of E from 213 to 226 kJ mole-'. Under non-isothermal conditions, the values of E varied between

TABLE 15 Selected kinetic characteristics for the decomposition of metal sulphates Reactant

Solid product

Temperature range (K)

E (kJ mole-' )

8

AHdecomp.29s~a

990

219

191

1193-1 353

312

285

1293-1333

343 661

1422-1 550

575

923-1223

268

512 (588 at 1500 K) 580

910-1 040

310

(526 at 1000 K )

875-

289 792

1073-1 27 3 1073-1 173 1123-1 173 748- 848

213 259

748- 848 9 53-1 003

210 253

973-1 07 3

83 154

823-

923

107

Remarks

Ref.

Contracting area [eqn. (7), n = 21 Contracting volume [eqn. (7), n = 31 Constant rate (a< 0.25) Constant rate and [eqn. (7), n = 31 (001) face, constant rate

771

(kJ (mole reactant)-' )

305 289

230

*

*I *

526(1000 K )

772 773 770,774 140

Contracting volume 775 [eqn. (7), n = 31 Reagent grade 776 [eqn. (7), n = 31 Freeze dried [eqn. (7), n = 21 Avrami-Erofe 'ev 777 n = 1.0-1.6 Initial rates 778 Contracting area [eqn. (7), n = 21 ( N 2 or vacuum) Contracting volume [eqn. (7), n = 31 (air) N, ,contracting volume [eqn. (7), n = 31 vacuum, contracting volume [eqn. (7), n = 31 Air, contracting volume [eqn. (7), n = 31

779 381 780 775 781 782

C0S04

coo

1008-1098( N2 )

222

209( 1000 K)

1088-1 178(0 2 )

222

252

1113-1 153

318

252

1083-1 133 968-1 083 1273-1423 1053-1 123

963-1083 1133-1 193 1033-1 073 963-1 083

356 269 255 212 238 238

351(1000 K ) 236

262 219 357 t 10 1 7 4 t 20 267 f 9 212 77 271 385

1133-1 573 912- 994

385 245

geometry

235 305 400

783

geometry volume 31

774

=

Constant rate

Contracting volume [eqn. (7), n = 31 Constant rate

281 t 36 346 268 280

923-1023 1023-1123 1023-1123 1113-1173 1233-1 293 1148-1 163

Contracting [eqn. (711 Contracting [eqn. (711 Contracting [eqn. (7), n

Contracting volume [eqn. (7), n = 31 Parabolic rate law (Overall value) Parabolic rate law Constant rate Parabolic rate law Non-isothermal Non-isothermal Unspecified intermediate Unspecified intermediate (Overall value) Constant rate Nucleation and growth

783 784 785 786 774 787,788 784 786 774 787,788 784 770 784 784 784 781 781 774 774 770 781 789

a Enthalpies of decomposition, AH~w,,,, .298K,refer [ 7701 to 1 mole of the reactant specified (crystalline) with evolution of SO3 gas, except where marked * where the product is SO2 gas and an appropriate yield of oxygen. AH& for the reaction

S03(P) SOz(g) is 99 kJ mole-' . +

+

$2

178

197 and 247 kJ mole-' but values were not directly correlated with heating rates, sample masses or the method of analysis used. 3.2.2 Group IIIA sulphates The kinetic characteristics of A12(S04)3decomposition in nitrogen between 910 and 1040 K varied somewhat with the salt preparation studied [776]. The reaction of the reagent grade material obeyed the contracting volume equation [eqn. (7), n = 3; E = 310 kJ mole-'], while atime data for freeze-dried samples obeyed the contracting area relation [eqn. (7), n = 2; 0.15 < a < 0.90; E = 289 kJ mole-'] or the first-order relation (within the less extensive interval 0.3 < a < 0.9, E = 347 kJ mole-'). Ingraham [791] has identified the residual product from reaction in vacuum or in air as 77-A1203,but there is a lack of agreement [ 7921 on the composition of the gaseous products and on the significance of E values determined by non-isothermal methods [ 524,7931. Indium sulphate is slightly more stable than the aluminium salt and decomposition curves (1073-1273 K) fitted [ 7771 the Avrami-Erofe'ev equation [eqn. (6)] with values of n increasing with temperature from 1.0 to 1.6. Gallium sulphate is less stable and decomposes between 833 and 973 K [ 7701.

3.2.3 First period transition metal sulphates Rising temperature measurements, supplemented by isothermal studies, gave values of E , based on obedience to the contracting volume equation [eqn. (7), n = 31, ranging from 96 t o 123 kJ mole-' and increasing in the sequence Zn < Fe(II1) < C o < Ni < Cu. CrS04 decomposes [794] t o Cr203 in hydrogen at 648 K, but t o Cr2O3 and &2(s04)3 in oxygen at -770 K. Margulis et al. [795] find appreciable decomposition of Cr2(S04)3in air at 720 K. MnS04 decomposes in nitrogen (1073-1173 K) to Mn304 and in oxygen (1123-1173 K) to Mn203; values of E , based on rates of initial reaction, were 213 and 259 kJ mole-', respectively [ 7781. Although the decompositions of FeSO, and Fe2(S04)3have received considerable attention, there is a lack of close agreement between isothermal and non-isothermal measurements [ 5281. Kinetic parameters are sensitive to the nature of the prevailing atmosphere and the particular salt preparation used [ 3811. The decomposition of iron(I1) sulphate [ 319, 381,5241 in vacuum or in an inert atmosphere (748-848 K) proceeds with the transitory formation of the intermediate Fe2Oz(SO4),viz.

2 FeS04

+

Fe202(S04)+ SO2

Fe202(S04) Fe203+ SO3 -+

179

A detailed kinetic study of these reactions has been given by Johnson and Gallagher [ 7791, in which consecutive half-order (contracting area) obedience was found. Results were in good agreement with an analysis [381] based on the assumption that the first step was effectively complete before the second reaction started. E values were 260 and 210 kJ mole-'. In oxygen, FeS0, - H 2 0 undergoes concurrent oxidation and hydrolysis to yield Fe20(S 0 4 ) 2 + Fe(OH)S04 and subsequently Fez(SO& [ 7961. Valence changes have been determined by Mossbauer spectroscopy (Chap. 2, Sect. 10.2). Decomposition of Fe2(S04)3between 973 and 1073 K obeyed the contracting volume equation [eqn. (7), n = 31 [775] and values of E for reaction in dry nitrogen [775] and in vacuum [781] were 8 3 and 154 kJ mole-'. The value E = 289 kJ mole-' for reaction in air [780] was not confirmed by Kolta and Askar [782] who report E = 107 kJ mole-' (823-923 K ) using the contracting volume model [eqn. (7), n = 31. Most of these values are significantly less than the decomposition enthalpy which at 1000 K is 526 kJ [mole Fe2(S04)3]-1or 176 kJ (mole SO3)-' [781]. No intermediate oxysulphate is formed [774,783] in the decomposition of CoSO,; the rate-determining step is identified as the direct dissociation t o COO and SO3. If Po, is sufficiently large, COO may be oxidized to Co304. There is, therefore, a complex dependence of the overall reaction rate on the prevailing pressures of 02,SO2 and SO3. The value of E , based on obedience t o the contracting geometry equations, was 222 kJ mole-' for reactions in nitrogen at 1008-1098 K and in oxygen at 1088-1178 K. E for the decomposition of Co304 to COO is 356 kJ mole-'. Both values of E are close to the corresponding enthalpies of reaction [783] (Table 15). NiS0, decomposes directly to NiO between 968 and 1083 K [784] (the oxide product may undergo some further dissociation [770]). The value of E determined from the region of constant reaction rate (269 f 8 kJ mole-') is in satisfactory agreement with that reported by Ingraham and Marier [785] (225 f 12 kJ mole-') at 1273-1423 K. Decomposition of anhydrous [774,784,786,787] CuS04 proceeds t o completion in two stages; there is general agreement that the intermediate is an oxysulphate, Cu20(S04).This intermediate recrystallizes at 1100 K (AH= 12 f 1kJ mole-') [787]. Ingraham and Marier [787] conclude that reaction in the pelleted salt proceeds at a well-defined interface which advances at a constant rate. [This results in obedience to the contracting geometry equations, eqn. (7), with an "order" of or but not t o the often-quoted zero order.] Reaction is retarded by either SO3 or 0 2 [787, 7881. The fair agreement between reported values of E is evident from Table 15. Cu2S04 undergoes partial decomposition at -500 K t o Cu and CuS04

180

[ 7971,and around 720 K

3 cu2so4 = 2 c u s o 4 + 2 c u z o + so2 The reaction in air at 400-490 K gives CuS04 and Cu20. The intermediate formed in the two-stage decomposition of ZnS04 t o ZnO has been variously reported as Zn502(S04)3[ 781,7981 and reported values of E (Table 15) show little conZ I I ~ O ( S O ~[784,799]: )~ sistency. Decomposition has been described [ 7991 as a topochemical reaction and the reverse process is slow if the ZnO (product) is not finely divided. 3.2.4 Other metal sulphates Relatively little kinetic information is available concerning the decompositions of other metal sulphates. Decomposition of the lanthanide sulphates [800,801]proceeds to completion in two stages. M2(S04)3

+

MzOz(S04)

Mz03

Sulphate stability decreases with increase in atomic number of the lanthanide cation: gas diffusion may be rate limiting. The decomposition of U 0 2 S 0 4 to U 3 0 8 at 912-994 K [789]is identified as a nucleation and growth process for which E = 245 kJ mole-'. The decomposition of PbS04 is complicated by the melting of intermediates [770,798],though an activation energy ( E = 385 kJ mole-', 1133-1573 K ) has been reported [781]from a study in which no intermediates were detected. The reaction of HgS04 is complicated by reactant sublimation. Thermal analyses of some divalent metal selenates and their hydrates have been reported [ 8021. 3.2.5 Metal salts of other sulphuroxyacids Few kinetic studies of the decompositions of these salts are available and, of those which have been investigated, the sulphites have received greatest attention. In general, sulphites disproportionate [ 8031 in an inert atmosphere to sulphides and sulphates, the latter decomposing at a higher temperature. The decomposition of silver sulphite to Ag2S04+ Ag between 403 and 440 K is complicated by the occurrence of a crystallographic transformation and the value of E is stated [804]to change from 83 t o 164 and to 54 kJ mole-' within this temperature range. Gilevich and Pavlyuchenko [805]found E = 178 kJ mole-' from the observed obedience of the latter stages of reaction (433453K) t o the contracting volume equation [eqn. (7),n = 31. The rate of decomposition was reduced by the addition of Pb2+ and VO,, presumably by altering the defect concentration. The reaction rate of the salt was increased by grinding or by addition of Hg,

181

CU, Al, SnC12, CuC1, Na2S03 and PO:-; E in the presence of PO:- was reduced to 138 kJ mole-'. A decomposition mechanism involving the intervention of SO; radicals has been proposed. The first step in barium sulphite disproportionation in dry nitrogen [806], 803-1073 K, is considered [807] to be BaS03

+

BaO + SO2

followed by

2 BaS03 + SO2 = 2 BaS04 + 4 S2 2 BaO + 4 S2 = 2 Bas + SO2 Susumov et al. [806] report an activation energy of 99 kJ mole-', which is far below that found by Mocek and Erdos [808] ( E = 257 kJ mole-') based on the temperature dependence between 951 and 967 K, of k in the rate equation

At 951 K, the reaction rate is directly proportional t o PHZ0,a catalytic effect that is attributed [808]to the role of water as an oxygen carrier. The reaction rate was also influenced by the method of salt preparation but for a given sample the effect of particle size was small. ZnS03 decomposes between 473 and 613 K t o ZnS203,ZnS04 and SO2 [ 8091. In sodium thiosulphate crystals, interionic S exchange occurs [ 8101 between 563 and 623K without detectable decomposition and the reported activation parameters are AH# = 245 kJ mole-' and AS' = 74 J K-' mole-'. Values of the same parameters for the first-order disporportionation

4 Na2S203= Na& + 3 Na2S04 are 312 kJ mole-' and 164 J K-' mole-'. Mechanisms proposed for both processes, based on application of the activated complex theory, are found to give good agreement with the experimental observations. Metal dithionates decompose [811,812] t o the corresponding sulphate and SO2. The decomposition [811] of BaS20d in vacuum at 453-483 K obeys the Prout-Tompkins equation [eqn. (9)] and E = 129 kJ mole-'; the reaction [812] of Ag2S20, at 373-398 K fits the contracting area equation [eqn. (7), n = 21 and E = 93-105 kJ mole-'. Grinding accelerates decomposition. A mechanism involving S-S bond rupture and the participation of SO; and SO; radicals has been proposed [811]. The decomposition of solid potassium peroxydisulphate [ 12771

182

was accompanied by extensive fragmentation: values of E reported for this and the corresponding reaction of the ammonium salt were 361 and 273 kJ mole-', respectively. Thermal analyses of the sodium salts of several sulphuroxyacids, including some non-isothermal kinetic data, have been reported [ 8131. Evidence for the formation of SO; radicals during such reactions has been obtained [ 3481 by electron spin resonance measurements. 3.3 METAL NITRATES AND NITRITES

Studies of the thermal decompositions of metal nitrates and nitrites are complicated by the occurrence of interactions between the evolved oxides of nitrogen [814] and the possibility of phase transitions [815] which may alter the behaviour of the original reactant. It is not always clear from literature reports whether the reaction considered proceeded exclusively in the solid or if there was melting. Overall decompositions are often exothermic; the kinetics sometimes vary with reaction conditions and the rate process studied is not always reversible. Gaseous products which have been identified include 02,N2, NO, NO2, N203, N204 and N205.Guides to the probable compositions of product mixtures, based on thermodynamic data, provided by Stem [814] are (i) N 2 0 5is unstable at >298 K and reacts t o form N204 or N203. (ii) N 2 0 4 dissociates (*2 NO2) with increasing temperature and at >400 K the partial pressure of N204 is negligible. (iii) N203is unstable at >400 K, decomposing to NO2 and NO. (iv) NO2 predominates in the equilibrium NO+f02*NO2

up to 500 K, but at higher temperatures both NO and NO2 are present in significant amounts. (v) N2 is stable with respect t o NO and NO2, while O2 may react with NO, (iv) above, or NO2. (vi) The rates of decomposition of NO2 and of NO to N2 and O2 are negligible at < l o 0 0 K. Nitrites generally decompose at lower temperatures than the corresponding nitrates. The formation of nitrites as intermediates during the decomposition of nitrates is doubtful (or difficult t o demonstrate). However, with nitrites, the decomposition is supposed to take place according to the scheme

A

2 MNO2 = M2O + NO + NO2 Accumulation of gaseous products may result [814] in oxidation of the nitrite t o the nitrate (if the latter is stable at the reaction temperature). Anhydrous nitrates and nitrites are often difficult to prepare and residual water can hydrolyze the reactant with the formation of basic

183

salts [816,817]. Interest in the field has largely been directed towards the qualitative characterization of the reactions involved and it is not at present possible t o associate most measured values of E with a specific chemical change. Studies of the radiolysis of nitrates [818-8211 have provided some information concerning possible decomposition mechanisms. Patil et al. [821] used infrared spectroscopy and thermogravimetry to study the decompositions of silver, lead and rare earth nitrates and nitrites. AgN03 decomposes in the melt (m.p. 485 K ) only at >720 K. Pb(NO& Torr, 538-583 K ) in a single stage, decomposes in a vacuum (-3 X yielding the residual non-stoichiometric phase PbOl.,. The initial fast process and the subsequent slow deceleratory parts of the a-time curve were fitted t o first-order equations from which the values of E determined were 155 and 188 kJ mole-'. These are significantly different from those found (251 and 46 kJ mole-', respectively) using evolved gas pressure measurements [822]. An average value of E of 238 kJ mole-' was determined [823] by nonisothermal methods. Vratny and Gugliotta [824] report sigmoid a-time curves for the decomposition between 523 and 708 K. Margulis et al. [825] identify both dissociation and autoxidation steps during Pb(N03)2decomposition, in which there was melting of the eutectic formed between reactant and the initial product, 2 PbO * PWNO 312. Decomposition of the rare earth nitrates proceeded [821] through the intermediate formation of oxysalts of the form MONO3 and E values were low: Nd(NO&, 33 kJ mole-', 663-703 K; Dy(NO&, 23 kJ mole-', 583-633 K; Yb(N03)3, 46 kJ mole-', 563-598 K. Thermogravimetric curves showed that the formation of anhydrous salts was possible, in contrast to observations by Wendlandt and Bear [826]. In a similar study [827] of the reaction of h ( N 0 3 ) 3 at 558-758 K, the intermediate formation of a nitrite is postulated during decomposition to a non-stoichiometric residual oxide, (the actual composition depends on temperature). Barium and lead nitrites [ 8211 decompose t o yield nitrates [ 8281

2 Ba(NOz)z= Ba(N03)?+ BaO + NO + Nz 3 Pb(N0Z)z = Pb(N03)Z + 2 PbO + 4 NO The behaviour [821] of AgN02 is closer to that expected of a nitro compound than a nitrite. Decomposition (308-363 K) yields Ag metal and NOz. a-Time curves are sigmoid with a prominent linear region (0.15 < a < 0.45) but the Arrhenius plot was curved at >333 K. This was attributed t o inadequate gaseous product removal. In contrast to the behaviour observed for most other solids, pre-irradiation with y-rays inhibits subsequent thermal decomposition [8291. Rare earth nitrites decompose at lower temperatures [821] and with

184

even lower values of E (5-15 kJ mole-') than the corresponding nitrates (25-45 kJ mole-'). 3.4 METAL PHOSPHATES

Most of the decompositions of metal phosphates considered here involve the elimination of water from acid salt with concurrent anion condensation. Such chemical transformations often proceed t o completion in more than a single step; hydrogen bonds are replaced by oxygen bonds [ 8301 and behaviour is sometimes complicated by the occurrence of phase changes which may, or may not, involve variations in anion composition [831]. Studies in this large and technologically important field have hitherto been concerned primarily with the qualitative identification of the chemical steps involved and there have been relatively few detailed kinetic studies. Griffith [831] has reviewed some of the chemical and physical properties of the condensed phosphates; Osterheld et al. [ 830, 8321 have studied polymerization and depolymerization in phosphatemetaphosphate systems. Reactions of all salts containing the NH; ion are discussed in Sect. 4, below, and simple loss of water of crystallization (i.e. dehydration without anion condensation) is not considered here. 3.4.1 Group IA phosphates

The rate-limiting step in the reaction

2 NaH2P04= Na2H2P207+ H20 has been identified [833] from thermogravimetric studies as a surface process below 470 K ( E = 158 kJ mole-'), whereas above this temperature product diffusion becomes rate-limiting. The salts MH2P04, where M = Li, K, Cs and also (',)Ba, (i)Pb, similarly decompose initially to M2H2P2O7.Since reaction occurs within approximately the same temperature interval (462-516 K ) as that of the sodium salt, it is concluded that bond structures of the reactant and decomposition mechanisms are comparable. Stages in the pyrolyses of MH2P04and MD2P04to MP03 (M = K or Rb) were not fully resolved [199] by thermogravimetry (5 K min-' t o 773K). The behaviour of the arsenates (MH2As04 and MD2As04) under similar conditions was simpler in that no intermediate stages were detected. Salts containing H (rather than D) and K (rather than Rb) were the most stable [ 1991. Phase transformations preceding the decomposition of the alkali metal salts, MH2P04have received considerable attention [834]. It is believed [1278] that an amorphous phase is transiently formed during the vacuum decomposition of P-Na2H2P207(and probably also on reaction of the p' form) and this is responsible for the slow reaction rate. Crystallization of the disorganized phase into condensed polyphosphates

185

is catalyzed by low vapour pressures of water but, at higher pressures, water vapour exerts on inhibitory effect due to equilibria displacements. Decomposition of K2HP04 [832] commences at 555 K to yield the intermediate 2 K2HP04.K$207 and reaction subsequently (-670 K ) proceeds t o K4P207. The dehydration of Na2HP04is catalyzed [835] by the addition of H3P04 (<2% molar) or NH; salts, through operation of a proton transfer mechanism, and the salt is stabilized by the addition of similar quantities of Na3P04,which introduces anionic defects. 3.4.2 Group IIA phosphates

From infrared and thermogravimetric studies, Pechkovskii et al. [836] identify the following steps in the decomposition of Mg(H2P04)2* 2 HzO.

-

633-873 K

MgHzP207

[Mg(PO,),] (amorphous)

-

873-1273 K

[Mg(PO,),] (crystalline) The reaction of Ca(H2P04), H20 is even more complicated [836], involving the formation of Ca2P20, and Ca5(P3010)2. Anhydrous CaHP04 (monetite) decomposes [837] to y-Ca2P207(-770 K, E = 213 kJ mole-') and is transformed to the P-modification at higher temperatures. 3.4.3 Other metal phosphates

The water elimination reactions of cO,(P04)2 8 H20 [838], zirconium phosphate [839] and both acid and basic gallium phosphates [840] are too complicated t o make kinetic studies of more than empirical value. The decomposition of the double salt, Na3NiP3010* 1 2 H 2 0 has been shown [593] to obey a composite rate equation comprised of two processes, one purely chemical and the other involving diffusion control, for which E = 38 and 49 kJ mole-', respectively. There has been a thermodynamic study of CeP04 vaporization [841]. Decomposition of metal phosphites [842] involves oxidation and anion reorganization. 3.5 METAL PERHALATES, HALATES AND HALITES

It is convenient t o classify here the decompositions of metal salts of the various oxyhalogen acids on the basis of the oxygen content of the anion, with subsections devoted t o the metals of a particular sub-group of the Periodic Table. Again, consideration of the ammonium salts is deferred to Sect. 4. As noted elsewhere in this review, some reports are not explicit as to whether or not melting accompanies reaction: thermal analysis studies can be valuable [843].

186

A comprehensive and detailed review of the literature relating to the decomposition reactions of the salts of halogen oxyacids has recently been given by Solymosi [1279].This book discusses many aspects of the chemical characteristics of this group of compounds. It includes a large amount of kinetic data and provides access to the original publications. An important source of reference is another excellent review by Stern [844];this one is concerned with the high temperature properties of oxyhalides. The following general trends are found in salts containing an XO; anion (X = C1, Br and I): there are variations in stabilities in the sequences (i) (X =) C1> Br > I for halogens in the same oxidation state, and (ii) XO, > XO; > XO; > XO- for the different oxidation states of a particular halogen. Decomposition often proceeds by the stepwise release of oxygen, viz. MX04

- - _ -21

0 2

MX03

-2

1

02

MX02

_ -21

0 2

MXO

_ -21

0 2

MX

although some of the intermediates may not be formed at all, or only in small quantities. Alternatively, an oxide may be the residual product (with consequent release of halogen) or disproportionation may be involved, for example

4 M X 0 3 = 3 M X 0 4 + MX 3 MXOl

=

2 M X 0 3 + MX

3.5.1 Perhalates

( a ) Perhalates of the Group IA metals During the initial stages (when a < 0.04)of the thermal decompositions of the alkali (Na, K , Rb, Cs) perchlorates [845](giving MC103),the rates of oxygen evolution from all four salts were approximately the same and independent of particle size and sample mass. Experimental values of E (-190 kJ mole-') were low compared with those found by Solymosi [846] for the overall reaction (250-290 kJ mole-') and also lower than the standard enthalpies for anion breakdown (276-289 kJ mole-') for MC104 (s) MClO3 (s)+ 0 (g) -+

To explain the observed magnitude of E and other kinetic features of reaction, a homogeneous bimolecular interaction between neighbouring C1Oi ions in the crystal structure was postulated and application of the activated complex theory t o this model gave good agreement with the experimental observations. The reaction products, MC103 and MC1, reduce the melting point of the alkali perchlorate reactant by eutectic formation and, at high a, the accumulation of MC1 results in resolidification. Since reaction proceeds

187

relatively more rapidly in the fused state, the a-time curves are sigmoid. Precompression sensitizes the low temperature decompositions of the alkali perchlorates [ 392,8471 but, except with NaC104, inhibits the high temperature reaction. The addition of NaC103 increases the rate of breakdown of NaClO, whereas, in contrast, KCIOBreduces the rate of reaction of KC104: this effect is attributed [392,847] t o the relatively lower stability of the former additive. Values of E reported by Cabank and Bknard [848] for the decompositions of Na, K and Cs perchlorates (117146 kJ mole-') are in close agreement with the measured activation energies for ClO, ion diffusion in these crystals. Many oxides catalyze decompositions of perchlorates [ 849,8501. Hisatsune and Linnehan [ 2991 have used infrared measurements to study the decomposition of C10, in a KC1 matrix. Despite the differences in the environment of the perchlorate ion, the kinetics of reaction were similar to those reported by Cordes and Smith [845] for pure Kclo,. The reaction was second order and E was 185 kJ mole-'. Comparable behaviour was observed for C10; in KC1, except that E was lower (-125 kJ mole-') and when both ions (ClO; and C10,) were present the reaction was approximately first order. Only a few perbromates have so far been prepared [844]; the stability of BrO, is about the same [851] as C104 and 10,. KBr0, decomposes (548-553 K) exothermally to KBr03 which is stable [852]. Potassium metaperiodate decomposes [853] (529-561 K ) KIO4 = KI03 + O2 and the value of E (192 f 17 kJ mole-') is identified with 1 - 0 bond rupture. ( b ) Perhalates of the Group IIA metals

Vacuum decomposition [ 8541 (609-711 K ) of anhydrous Mg(C104)2 involves the stepwise release of oxygen, in which the initial steps are identified as

c10;

+

c10; + 0

c10, + 0 + c10; + 0

2

The rate of reaction diminishes at a

=

0.575 due to the occurrence of

2 c10- -+ Cl2 + 02-+ 0 Chloride is the predominant residual product from reactions at low temperature and in contact with the gaseous products, whereas in vacuum and at high temperature, MgO is formed. It has also been s u g gested that MgO - Mg(C104)2is a decomposition intermediate [855]. Ca(C104)2 decomposes in the solid phase (666-678 K), E = 260 kJ

188

mole-') [856], but at higher temperatures a melt is formed and E is reduced (226 kJ mole-'). Similarly, the onset of reactions of Sr(C104), to SrCl, [857] is detected at -688 K and the salt melts at 723 K. The decomposition of Ba(C104), has been the subject of several studies [858]. It is believed that during the initial acceleratory process, reactions are analogous to those cited above for Mg(C1O4),. After a series of several successive bond scissions, the accumulating concentration of chloride product participates in the equilibrium

c1- + 0 * c10and, if the gaseous products are not removed, there is a marked diminution in reaction rate at a 0.52.

-

( c )Perhalates of other metals The decomposition of Al(c104)3 [859] (to A1203,C120 and 0 2 ,513563 K) obeyed the Avrami-Erofe'ev equation [eqn. (6)] with E = 83 kJ mole-'. Similar kinetic behaviour was found [859] for the reactions of several lanthanide perchlorates in nitrogen at 513-643 K, viz. 2 M(C104)3= MOCl + MC13 + Cl,O + 11O2 Values of E were 105-143 kJ mole-' and 87 kJ mole-' for scandium perchlorate, i.e. for the process

3 S C ( C ~ O=~ScOCl ) ~ + Sc2O3 + 4 C120 + 1 4 0

2

The decomposition of T1C104 is autocatlytic [860] above 680 K, yielding T1203 and volatile TlC1; E = 227 kJ mole-'. This reaction was catalyzed [861] by Cr203. Limited information concerning the decompositions of a number of other perchlorates is to be found in the literature: Cd, Pb, Zn (553-676 K) [846]; Co, Fe, Mn, Ni (363-458 K) [862], Ag (687-718 K) [863], and Ni, Cu, Co, Mn (518-538 K) [1280]. AgI04 decomposes [864] at >473 K t o AgI03, AgI and 0,; the reaction is explosive in vacuum. 3.5.2 Halates

(a) Halates of the Group IA metals The alkali chlorates melt before decomposition [844]. The catalytic properties of c0304 in promoting [865] the solid phase decomposition of NaC103 are attributed to the ability of the oxide t o donate an electron to an oxygen atom, temporarily accepted at its surface from a C10, ion, prior to molecular oxygen formation and desorption. The progressive increase in E during reaction (from 120 t o 200 kJ mole-') is associated with systematic deactivation of the surface.

189

The decomposition of potassium bromate [ 8661 KBr03 = KBr + 1; O 2 obeyed first-order kinetics in two temperature ranges, separated by a transition region: E values for reactions between 615 and 640 K and from 652 to 685 K (where melting occurs) were 260 and 221 kJ mole-', respectively. These rate characteristics were ascribed t o a nucleation and growth process leading to crystallite cracking. Similar results were obtained for NaBr03 [866]. Pre-irradiation enhanced melting, with a consequent increase in the rate of decomposition. ( b ) Halates of the Group IIA metals

Between 650 K and melting at 669 K, Ba(C103)? disproportionates [867,868] to Ba(C104)2and BaC12 with some direct decomposition to K in air and 538-588 K in BaC12. The reactions of B ~ ( B I - O (563-653 ~)~ vacuum) may involve the formation of BrO, and BrO;; E values reported [867,869] are 209 and 218 kJ mole-'. Calcium and strontium bromates behave similarly, but the reaction of Mg(BrO& [870] gives MgO as the predominant residual product. The solid decomposition of Ba(Br03)2has been described [1283] as proceeding consecutively through (i) an initial fast process, (ii) a short induction period, (iii) a slow linear reaction, (iv) an accelerating stage, and finally (v) a deceleratory period. The activation energy during nucleation (159 kJ mole-') was smaller than that for the main reaction (191 kJ mole-'). Irradiation enhanced rate coefficients, the effect increasing with irradiation dose. The decomposition of Ba(I03)2above -850 K [871,872] proceeds by the Rammelsberg reaction [ 8731

10 Ba(I03)2= 2 Ba5(106)2+ 8 I2 + 18 0

2

Ba5(106)2is stable to -770 K in vacuum and t o -1220 K in air, and decomposition t o BaO, I2 and O 2 is reversible. Calcium [874] and strontium [871] iodates behave similarly, while Mg(I03)2[875] reacts at >848 K to give MgQ . (c) Halates of other metals

The decomposition of Pb(C103)2 [868] (467-489 K) is complex, yielding both PbC12 and PbO. Following an initial rapid deceleratory process, the sigmoid a-time curve for the main reaction obeyed the Prout-Tompkins equation [eqn. (9)] (0.35 < a < 0.85) with E = 180 kJ mole-'. AgC103 reacted [863] in a melt (589-612 K) with solidification at a 0.8 as the residual product (AgC1) accumulates ( E = 239 kJ mole-'). The decomposition [826] of thallium(1) chlorate (423-443 K) may be

-

190

represented as

7 TlC103 = 3 T1203+ TlCl + 6 C102 and the mechanism is complicated. The breakdown of TlBr03 [876] also yields T1203, proceeding through an initial (a < 0.05) rapid first-order process ( E = 150 kJ mole-') followed by a sigmoid a-time relation. The acceleratory and deceleratory parts of this process obeyed the ProutTompkins equation (a < 0.35 and E = 209 kJ mole-') and the contracting volume ( E = 150 kJ mole-') equations [eqns. (9) and (7), n = 31, respectively. It is suggested that rapid decomposition at sub-grain boundaries is followed by advance of the reaction interface into the reactant particles. Bancroft and Gesser [870] conclude that kinetic factors are predominant in determining whether decomposition of a metal bromate yields residual bromide or oxide. The thermal stabilities of the lanthanide bromates [877] and iodates [877,878] decrease with increase in cationic charge density, presumably as a consequence of increased anionic polarization. Other reports in the literature concern the reactions of bromates of Ag, Ni and Zn [870] and iodates of Cd, Co, Mn, Hg, Zn [871], Co and Ni [872], Ag [864], Cu [867], Fe [879], Pb [880] and T1 [874].

3.5.3 Metal halites The most frequently encountered reaction on heating metal chlorites is disproportionation

3 MClO2 = 2 MClO3 + MC1 reported for salts of the following metals: Na, Ba [881], Li, K , Rb, Sr, Ba [ 8821, K [ 8831, Cs, Ca [ 8841, Ag [ 8631 and Pb [ 8851. Rapid heating t o a higher temperature caused explosion of the Ba and Pb [881] salts. The decompositions of NaC10, (>413K) and of AgClO, (>358K) are first order and the values of E are 227 and 109 kJ mole-', respectively. The major products of AgCIOz decomposition above 373 K are Ag, AgzO and Cl02. B~(BIO~ is) formed ~ [886] during decomposition of the bromate in oxygen at 523 K.

3.5.4 General comments The high values of E generally characteristic of the decomposition reactions of metal oxyhalides are widely interpreted as evidence that the initial step in anion breakdown is the rupture of the X-0 bond and that the energy barrier to this reaction is not very sensitive t o the properties of the cation present. Information of use in the formulation of reaction mechanisms has been obtained from radiolytic studies of oxyhalogen salts [887-8891. In many of the reactions discussed above, little is known about whether

191

or not discrete nuclei exist or about the kinetics of initiation and development of any reaction interface present. There have been remarkably few microscopic investigations of the decompositions of metal salts of oxyhalogen acids. 3.6 METAL PERMANGANATES

3.6.1 Potassium permanganate

Reference t o the decomposition of KMn04 has already been made in the discussion of chain branching reactions (Chap. 3, Sect. 3.2) in which the participation of a highly reactive intermediate was postulated. This work provided a theoretical explanation of the Prout-Tompkins rate equation [eqn. (9)]. Isothermal decomposition in vacuum of freshly prepared crystals at 473-498 K gives symmetrical sigmoid a-time curves which are described by the expression lOg[a/(l - a ) ] = k t + c

(9) From microscopic examination of the partially decomposed salt, Prout and Tompkins [465] concluded that reaction was initiated at lattice imperfections, later identified [ 8901 as line dislocations, where the activation energy for anion breakdown was relatively low. The solid products (of uncertain composition, but containing MnOz) are formed on reactant surfaces and cause strain, evident in X-ray diffraction photographs for partially decomposed salt [891], and this induces cracking of the reactant crystallite. Such generation of new surfaces can be regarded as a form of “branching” and this explanation has superseded the earlier assumption that energy chains were involved. Visual studies have confirmed [465] that crystallite disintegration ceases at the inflection point of the a-time curve (i.e. a 0.5). Hill et al. [117] extended the lower end of the temperature range studied (383-503 K) t o investigate, in detail, the kinetic characteristics of the acceleratory period, which did not accurately obey eqn. (9). Behaviour varied with sample preparation, For recrystallized material, most of the acceleratory period showed an exponential increase of reaction rate with time ( E = 155 kJ mole-’). Values of E for reaction at an interface and for nucleation within the crystal were 130 and -210 kJ mole-’, respectively. It was concluded that potential nuclei are not randomly distributed but are separated by a characteristic minimum distance, related to the Burgers vector of the dislocations present. Below -423 K, nucleation within crystals is very slow compared with decomposition at surfaces. Rate measurements are discussed with reference to absolute reaction rate theory. Marked differences in the decomposition kinetics of fresh and aged KMnO, are attributed [464] t o slight decomposition at surfaces and grain

-

192

boundaries of the older material during storage. The variations in reported kinetic obediences during the acceleratory period, i.e. the Prout-Tompkins equation [465] [eqn. (9)], the power law [892] [eqn. (2)], and the Avrami-Erofe’ev equation [448] [eqn. (6), n = 21, can be traced to sample age and pretreatment. From measurements for eighteen preparations of KMn04 with different initial specific surface areas, Protashchik [893] found that the rate of reaction during the acceleratory period increased with increase in surface area, but the maximum decomposition rate decreased. From these results, he concluded that the sites of initial decomposition are within, rather than at the surfaces of the crystals. Conduction in KMn0, is believed [894] t o proceed through electron transfer within the anionic lattice and the possibility that this step is involved in salt decomposition has been investigated through studies of the pyrolysis of KMn04-KC104 solid solutions [894,895]. The ClO; ion will not accept an electron during KMn0, decomposition (460-510 K). Reaction, for the various proportions of the components, in general involves a series of successive processes [895]; sigmoid, constant rate, power law [eqn. (2), n = 21 followed by the main acceleratory reaction. In dilute solid solution at 508 K, decomposition of KMnO, is incomplete and the extent of reaction is related [894] to the proportion of MnO; present in the host lattice as other than isolated units [896]. Groupings of MnO; ions, such as dimers or more extensive associations, are required in order to permit decomposition to proceed through an electron transfer step, e.g. 2 MnO,

k2 * MnOz- + MnO, MnOi- + Mn02 + O2 k-1 kl

+

Using a steady-state argument, Boldyrev derived the rate expression klk2[Mn0i1 Rate = k-,[MnO:-] + k 2 where [MnOi-] is a measure of the number of electrons present in the lattice and [MnO;] is the concentration per unit area of interface. Additives either catalyze or inhibit decomposition according to whether their electronic work function is greater than or less than that of the reactant KMnO,, as shown [894] for a range of different Mn02 preparations. Kabanov and Zharova [ 3621 concluded from conductivity studies in the early stages of decomposition (a < 0.16) that K2Mn04is formed in solid solution with KMnO,. The double salt, K3(Mn04)2,prepared by co-precipitation of KMn04 and K2Mn04, is more stable than KMnO,. Thus, one of the solid decomposition products of KMnO,, MnOz catalyzes the reaction, while the other MnO:-, is an inhibitor (see also refs. 897, 898). The decomposition of KMn0, is sensitive to pre-irradiation [899] by UV [396], X-rays, y-rays, protons and neutrons. The effects of such pretreatment, which increase with dosage, are to reduce the induction period

193

and increase the maximum reaction rate, though in general there is no significant change in the kinetic obedience or the magnitude of E . (Comparable behaviour has been described for the other alkali permanganates [ 900-9021 .) There is some controversy about the mechanism whereby irradiation influences reactivity. Prout [ 8991 favours a displacement model in which multiple ionization of Mn04 groups lead t o random formation of interstitial cations. During thermal decomposition, these defects are annealed in the vicinity of dislocations and the release of stored (Wigner) energy (-100 kJ mole-') may then rupture bonds in an adjacent Mn04 ion. The products formed cause structural deformation and enhance the annealing process through the development of decomposition spikes which eventually lead to fracture of the crystal. Irradiation nuclei are distinct from the thermal nuclei. Boldyrev et al. [903,904] believe that the radiolysis products catalyze decomposition. Protashchik and Erofe'ev [905] take an intermediate view. 3.6.2 Other Group IA metal permanganates All alkali metal permanganates decompose with sigmoid a-time curves [900,901]. LiMnO, (>380 K) [900] shows an initial linear process ( E = 95 kJ mole-'). The subsequent reaction obeys eqn. (9) ( E = 138 kJ mole-') and the first-order decay with E = 130 kJ mole-'. The ProutTompkins equation was obeyed over virtually all of the reaction of NaMn0, (>400 K) [900] with two rate coefficients but a single value of E (128 kJ mole-'). The reaction of the rubidium salt at 488-528 K [901] resembled that of the lithium salt but E = 167 k 7 kJ mole-'. The decomposition of CsMn04 at 513-558 K [900] involved an initial slow process, which obeyed the power law [eqn. (2), n = 2 and E = 141 kJ mole-'], and, thereafter, fitted the Prout-Tompkins equation with E = 167 and 1 4 1 kJ mole-' in the acceleratory and deceleratory periods, respectively. Manganates have been identified [902] in the decomposition products of RbMn04 and CsMnO,. 3.6.3 Barium permanganate Hardy [906] has proposed that the steps for the decomposition of Ba(Mn04)2are Ba(Mn04)*= BaMn0, + Mn02 + 0

2

( E = 142 f 4 kJ mole-')

( E = 126 2 BaMnO, = 2 a-BaMn03+ O 2 4 P-BaMn03 * BaMn03 (1)

+_

4 kJ mole-')

Rienaecker and Werner [907] suggest that Ba3(MnO& is the initial decomposition product, by analogy with results for KMnO,. Isothermal a-time curves for vacuum decomposition at 413-463 K were sigmoid

194

[908] following an initial burst of gas (to (Y = 0.04). The acceleratory process was fitted by the Prout-Tompkins equation [eqn. (9)] ( E = 151 kJ mole-') and the power law [eqn. (2), n = 2, see CsMnO, above] and fragmentation into thin platelets was observed. The deceleratory period obeyed the first-order equation with E = 124 kJ mole-'. The effects of pre-irradiation [ 9081, although still marked, were less for a given dose than those observed for the alkali metal permanganates. The other Group IIA permanganates are obtained as hydrates. 3.6.4 Silver permanganate

The kinetics and mechanism of vacuum decomposition of AgMn04 at 378-393 K [466] are believed to differ from the behaviour of KMn04 in that the effective chain branching coefficient diminishes with time and this leads (Chap 3, Sect. 3.2) t o the modified form of the Prout-Tompkins equation log[cY/(l - a ) ]

=

k log t + c

This expression fitted the acceleratory period of the &-time curves, followed by first-order decay and E = 122 f 2 kJ mole-'. No disintegration of small crystals was observed but pre-irradiated crystals [909] shattered on completion of the induction period. X-ray diffraction studies [910] confirm the existence of strain during the formation of decomposition product. Addition of small amounts (5%by mass) of ZnO or T h o 2 accelerated the decomposition of AgMn04 at 388 K. T i 0 2 reduced the rate, while NiO and Co304had no effect [911]. Attempts to relate the kinetic characteristics of permanganate decompositions to the nature of the constituent cation have been discussed by Young [ 291. 3.7 METAL CHROMATES

The decomposition of magnesium chromate(V1) [912] 2 MgCr04 = MgCr204+ MgO + 1; O2 obeys the contracting volume equation [eqn. (7), n = 31 and E = 331 f 1 7 kJ mole-'. The reactions of the chromates(V1) of lanthanum, neodymium and samarium proceed in two stages M2(Cr04)3= 2 MCr0, + 4 Cr203+ 1: O2 2 M C r 0 4 = 2 MCr03 + O2 Kinetic characteristics for the different compounds are given by Darrie et al. [912]. It was concluded, from comparisons of the values of E found with spectroscopically determined charge transfer energies, that the activa-

195

tion step in the decomposition involved the transfer of one electron from oxygen to chromium. Analogous studies [913,914] were made for the reactions of the lanthanide chromates(V), which form the second step in the decompositions of the chromates(V1). It was concluded that the breakdown of LaCrO, and of PrCrO, involved the transfer of energy between the CrO, units. In the other lanthanide chromates, however, energy was transferred by exchange from an activated C r 0 4 group to an adjacent cation. CrO, groups at a surface act as energy sinks by absorbing energy reaching the surface and then decompose. The ammonium chromates, which have been studied more extensively than any other salts of these anions, are considered in the next section. 4. Decompositions of ammonium salts

The grouping of ammonium salts in a separate section serves to emphasize the similarities of behaviour which are apparent in reactions yielding the volatile NH3 molecule, following removal of a proton from the NH; cation. This property is not unique; indeed, many cations are volatile and numerous salts leave no residue on completion of decomposition. Few kinetic investigations have, however, been reported for other compounds, in contrast t o the extensive and detailed rate measurements which have been published for solid phase decompositions of many ammonium salts. Comparisons with the metal salts containing the same anion are sometimes productive, so that no single method of classification is altogether satisfactory. Ammonium salts resemble hydrates in several respects since, like water, the NH3 molecule may occupy a variety of bonding situations from which it may be removed unchanged. There is general agreement that, for most ammonium compounds, the first step is proton transfer. The consequent accumulation of H' in the neighbourhood of the oxygen network of oxyanions results in the elimination of water, accompanied by condensation (or continued condensation) of these anions. Since the decompositions of many ammonium salts evolve NH3 and H 2 0 simultaneously (or consecutively) in a 2 : 1 molar ratio, it is often convenient t o represent the formula of such salts in the form ~ I ( N H , ) ~*On(metal oxide) * r H 2 0 where rn, n and x are integers (see ammonium vanadates, tungstates and molybdates below). Determination of the influence of crystal structure and reactant environment on deammination and dehydration processes is complicated by the several solid phase transformations that are a characteristic feature of many ammonium salts. Sublimation and/or melting may also occur. Deammination and dehydration steps are generally reversible. A t high temperatures, however, particularly in the presence of a residual oxide

196

product or a strongly oxidizing anion, some of the ammonia initially released may be oxidized. The final composition of the volatile substances formed may thus be sensitive to the effective contact between gaseous and solid products during reaction. Such variations in composition cause difficulties in defining and determining values of a . Thermal analyses of 26 ammonium salts are reported by Erdey et al. [915] and more references to ammonium salts are to be found in Duval’s book [ 9161. Calculations of the enthalpies of formation have been used to predict the thermal properties of these compounds [917]. (See also refs. 918,919.) Most of the compounds considered here are ammonium salts of oxyanions and, for convenience of reference, the classification sequence adopted is based on the position in the periodic table of the anionic constituent. 4.1. AMMONIUM SALTS CONTAINING OXYANIONS OF THE NON-METALS

4.1.1 Ammonium perchlorate

The thermal reactions of ammonium perchlorate (AP)are unusually complicated. On account of the importance of this compound as a solid propellant and also its intrinsic interest, an intensive and widespread series of studies has been completed using various experimental approaches. The main kinetic characteristics of the reactions involved and the mechanistic explanations of these observations are largely agreed. There have been two detailed reviews of the literature to mid-1968 [ 59,3571. On heating AP, cation oxidation is accompanied by sublimation of unchanged reactant at low pressures and decomposition is incomplete during the low temperature reaction (420-600 K). Total conversion of the salt to gaseous products only occurs above -600 K (the high temperature reaction). Particular interest has been concerned with the nature of the residue from the low temperature reaction since the composition and structure of this material are identical with those of the reactant from which it is derived. The only significant change occurring as a result of the partial (-30%) decomposition is a marked increase in surface area. There have been several quantitative studies of the compositions of the volatile reaction products and the variations which result from changes of reaction temperature, fraction decomposed (a), or the presence of additives [ 9201.

( a ) Low temperature reaction (-420-600 K ) a-Time curves are sigmoid and obey the Avrami-Erofe’ev equation [eqn. (6)] [59,120,268], though the value of n depends on whether the reactant is a single crystal, a powder, or a pellet. Many of the published values of E are within the range 100-140 kJ mole-’ [59]. The kinetic

197

characteristics of the reaction (shape of the a-time curve, rate coefficients and the magnitudes of A and E) are significantly influenced by the orthorhombic t o cubic phase transition at 513 K. This is about mid-way through the temperature range for which kinetic measurements are usually made. Above the transition temperature, there is a reduction in the rate coefficients for reaction. The review by Jacobs and Whitehead [ 591 tabulates data and discusses results up to 1968. Since then, Jacobs and Ng [452,921] have applied statistical methods t o curve fitting of a-time data for low temperature AP decomposition. Several distinct rate processes were identified. On heating of gas was immedia single crystal of reactant, a small volume (a < ately evolved, probably by desorption from salt surfaces, and the linear was identified rate of product evolution which followed t o a < a < 4 X lo-’ there was an [211] as surface nucleation. Between exponential acceleratory period, attributed to more rapid nucleation, following the generation of dislocations produced by local strain in the vicinity of existing nuclei. Thereafter, 0.01 < a < 1.0, data fitted the extended form of the Avrami equation [eqn. (4)] and this representation was more satisfactory than that found using the approximate forms usually employed. This quantitative description of the a-time measurements for the overall reaction required a total of 10 parameters. Arrhenius parameters reported in this study [ 4521 for the nucleation (N), branching (B) and growth (G) processes in the low temperature decomposition of

-

E

11

100

G I

8

I

10

I

I

1

1

12 14 Log ( A / min-’ )

I

I

16

Fig. 16. Graphical representation of Arrhenius parameters for the low temperature decomposition of ammonium perchlorate (pelleted, orthorhombic, 0 , and cubic, 0, forms). Compensation behaviour is observed. Data from Jacobs and Ng [452]. N = nucleation, B = branching, G = growth processes.

198

orthorhombic ( 0 ) and of cubic ( 0 ) AP are summarized in Fig. 16, which also indicates the occurrence of compensation behaviour [eqn. (21)]. Microscopic examination has shown [ 102,9221 that the compact nuclei, comprised of residual material [211], grow in three dimensions and that the rate of interface advance with time is constant [ 9221. These observations are important in interpreting the geometric significance of the obedience t o the Avrami-Erofe’ev equation [eqn. (6)] [ 59,9231. The rate of the low temperature decomposition of AP is influenced by the particle ageing [ 9241 and irradiation [ 451, the presence of gaseous products [924], ammonia [ 1201, perchloric acid [ 1201 and additives [ 591. The first step in the low temperature reaction of AP is proton transfer [ 46,5 9,9 15,92 5-9 301 NH; C10,

+

NH3 + HC104

This explains the increase in the induction period which is apparent after exposure of the salt to ammonia, and the decrease in the induction period found for samples which contain traces of HC104, identified as the unstable species [ 59,9251. In the low temperature range, the presence of an outer layer of adsorbed NH3 and/or NHf ions suppresses the formation of HC104 and, in consequence, the decomposition reaction.

( b ) Sublimation and the high temperature reaction (>-600 K ) At low pressures, NH3 is desorbed and HClO, is also volatilized. Both may rapidly diffuse from the heated zone and recombine elsewhere on the cool walls of the vacuum envelope as sublimate. The kinetics of sublimation, which may accompany the low temperature reaction [ 9261, have been studied and discussed in detail [931,932]. The rate of this process is deceleratory throughout, empirically obeying eqn. (7) [931]

1 - (1 -(Y)1’7

= ht

where y = 3 in vacuum but reduces to 2 as the pressure of inert gas present is increased. From consideration of surface diffusion and diffusion in the gas phase, Jacobs and RussellJones [931] developed an appropriate rate equation. If at high temperatures (>-600 K ) the volatilized NH3 and HClO, are prevented from leaving the heated zone by the presence of an inert gas, decomposition in the homogeneous phase follows. This is the high temperature (gas phase) reaction in which there is complete conversion of the reactant t o volatile products and no residue remains.

( c ) A unified reaction scheme The relationships between the several rate processes referred t o in (a) and (b), above, are given in the unified reaction scheme proposed by

199 PRODUCTS High temperature reaction

SUBLIMATE

(g 1

NH.,+CIO,(Reactant)

NIH, ( a )

+

I I I

NH,

I

(Adsorbed)

t

I

L

HCLO, ( a )

( Gaseous)

(a)

Xl

"

I

Low temperature reaction

PRODUCTS

Fig. 17. Unified reaction scheme for the thermal decomposition o f ammonium perchlorate, proposed by Jacobs et al. [59,925,926]. In the low temperature reaction, the interaction occurs between adsorbed species (a) whereas the high temperature reaction and sublimation process involved volatilization intermediates (g). X I and Xz represent mixtures of intermediates.

Jacobs e t al. [59,925,926] (Fig. 17). While this scheme conveniently summarizes many features of the observed behaviour, a number of variations or modifications of the mechanisms indicated have been proposed. Maycock and Pai Verneker [924,933] emphasize the possible role of point defects and suggest, on the evidence of conductivity measurements, that the initial step may be the transfer of either a proton or an electron. Boldyrev et al. [46] suggest that proton conduction permits rapid migration of HC10, within the reactant and this undergoes preferential decomposition in distorted regions. More recently, the ease of proton transfer and the mobilities of other species in or on AP crystals have been investigated by a.c. [360] and d.c. [934] conductivity measurements. Owen et al. [ 9341 could detect no surface proton conductivity and concluded that electron transfer was the initial step in decomposition. At the present time, these inconsistencies remain unresolved. The decomposition of a number of perchlorates containing substituted ammonium groups (various methylamines, guanadine etc.) [935-9391 resemble the mechanism proposed for AP decomposition in that proton transfer is identified as the initial step. 4.1.2 Ammonium halates

The stabilities of the ammonium halates increase in the sequence N H 3 r O 3 < NH4C103< N H d 0 3 [940]. Decompositions of the chlorate

200

[941]and bromate [942]yield residual NH.,N03, but explosion gives no residue and, in contrast, the non-volatile products of reaction of NH4103 are H1308and 1205. The first step in the reactions of all three substances is identified [940] as proton transfer (cf. AP above) and the acid released subsequently decomposes. Microscopic measurements have shown [9401 that the ratio of the rate of nucleus formation to the rate of their growth increases in the sequence NH4C103> NHJ3r03 > NH4103. The sigmoid a-time curve for NH4C103decomposition obeys [941]the Avrami-Erofe'ev equation [eqn. (6), n = 21 with E 96 kJ mole-' (-320-345 K). Explosion occurred at >363 K for freshly prepared material but at a lower temperature for slightly older salt. a-Time plots for NHJ3r03 were also sigmoid [942] for reaction at -270 K; the exponential law [eqn. (8)]in the early stages was followed by a long linear region (0.2< a < 0.8 and E 120 kJ mole-'). This compound exploded at >327 K. Decomposition of NH4103in the range 418438K was deceleratory throughout [943] and obeyed either the contracting volume equation [eqn. (7),n = 31 or the first-order equation (E = 276 kJ mole-'): the salt exploded at >453 K.

-

-

4.1.3 Ammonium sulphate

According to Erdey et al. [915],ammonium sulphate releases ammonia in an endothermic reaction commencing above 523 K, viz. (NH4)2S04.+NH4HS04 + NH3 This temperature is higher than those given in other reports, 383 K [944] and 413-513 K [ 9451 indicating the possible influence of retained water on the onset of reaction. Although ammonium sulphate does not melt, the product NH4HS04 does and decomposes to NH3 and H2S04 at higher temperatures (623-723 K). A review of earlier results is included in a paper by Kiyoura and Urano [946] on the decompositions of (NH.J2S04 (413-513 K) and NH&S04 (433-473 K). The intermediate formation at 433 K of the double salt (NH4)3H(S04)2was detected by X-ray diffraction and this salt decomposed to NH&S04 at 453 K. Decomposition of the ammonium hydrogen sulphate at 473 K proceeded through the formation of molten sulphamic acid N H a S 0 4 -+ NH2S03H + Ha0 which then reacted t o form the pyrosulphate NH2S03H + NHfiSO4 (NH4)2S20, with evolution of SO3 at >523 K. Values of E for the first-order deammination and dehydration processes were [945] 67 and 54 kJ mole-', respectively, indicating possible diffusion control. Decomposition was generally inhibited by water vapour. +

201

(NH4)2S03sublimes unaltered [ 9461 but the monohydrate undergoes partial decomposition to HzO, NH3 and (NH4)?S207.Decomposition of ammonium thiosulphate is inhibited by the addition of other ammonium salts, e.g. (NH4)2C03,and by briquetting [947]. Most mixed and complex ammonium metal sulphates (and selenates) [948,949] lose NH3, H 2 0 and SO3 (or Se03) t o form the simple metal sulphate (or selenate); some of the ammonia may be oxidized [949]. The basic aluminium ammonium sulphate [950], (NH4)2O - 3 A1203 - 4 SO3 * xHzO ( x = 6-8), loses water at -473 K. Deammination and complete dehydration commences at >673 K, and SO3 evolution starts at about 873 K to yield residual A1203 which contains traces of SO3.&-Time data for most of the stages obeyed the contracting volume equation [eqn. (7), n = 3 ] [951]. 4.1.4 Ammonium nitrate

Following three phase transformations [951] (>298 K), NH4N03 decomposition begins [915] in the solid phase at -423 K but only becomes extensive well above the melting point (-440 K). Decomposition with the evolution of N 2 0 and H 2 0 from the melt is first order [952,953] (E = 153-163 kJ mole-'), the mechanism suggested involving intermediate nitramide formation. Other proposed schemes have identified NO; [954] ortheradical NHzNO' [955] (<473 K) as possible participants. Studies [956,957] have been made of the influence of additives on NH4N03 decomposition. UV photolysis [958] of NH4N03 yields N 2 0 , H 2 0 , N2, 02,and traces of NO, while the same products, with the exception of O2 were detected in gases evolved during y-radiolysis [959]. No NO; was detected in the irradiated salt. In general, ammonia is evolved before anion breakdown in the decompositions of ammonium metal nitrates [960,961]. Decomposition of hydrazonium nitrate [9621 obeys second-order kinetics and presumably occurs in a melt. 4.1.5 Ammonium phosphates

Kubasova [963] has reviewed the chemistry of the ammonium salts of polyphosphoric acids. Much interest in the field derives from the agricultural uses of these substances as fertilizers. Both NH3 and H 2 0 tend to be eliminated simultaneously on heating, but dehydration alone may be achieved in an atmosphere of NH, [ 9631, e.g.

Thermal analyses, [915,9644661 supported by chemical analyses and

202

X-ray diffraction [ 9651 measurements, show that (NH4)3P04 and (NH4)2HP04both lose NH3 in a manner analogous t o the dehydration of hydrates to form NH4H2P04. (All three salts are isostructural.) Above -420 K, water elimination is accompanied by anion condensation t o form (NH4)2H2P20, and (NH4)3H2P3010,proceeding t o N H $ 0 3 at higher temperatures. A glassy melt is formed after an exothermic transition at 553 K. The relative thermal stabilities of condensed ammonium phosphates have been studied [967]; most fuse t o a glass-like substance but some polymerize slowly in the solid phase (-450 K) [967,968]. Liteanu e t al. [969] have studied the isothermal dehydration of (NH4)2HP04 in a fluidized bed. The reaction obeyed the contracting volume equation [eqn. (7), n = 31 and the rate in air increased with decreasing particle size; for a fixed particle size, the rates and E increased with variation in carrier gas in the sequence air < methane < hydrogen; the values of E were 80 4, 93 3 and 104 3 kJ mole-', respectively. The reaction rate also increased with P H Z oin the air, but E decreased from 84.5 f 0.5 in dry air to 64.0 f 0.5 kJ mole-' when PHZ0= 17.7 Torr. Water vapour on grain surfaces promoted hydrolysis _+

_+

_+

(NH4)2HP04 + H2O * NHJI2PO4 + NH3 + H2O Small amounts (<3.5%) of ammonium salts markedly accelerate [970] the dehydration of Na2HP04 * 1 2 H 2 0 t o Na2P207. This is attributed t o an increase in the concentration of delocalized protons in the structure, as a consequence of the proton donor properties of NH;, and this promotes dehydration. Although many ammonium metal phosphates are known, few kinetic studies of their decompositions have been reported and no systematic investigations of the influence of metal ion or structure on the deammination reactions are available. Thermal analyses [971] of compounds of the type MNH4P04 x H 2 0 (where M is a divalent metal) show that, after dehydration, there is a continuous and simultaneous evolution of NH3 and H 2 0 [137], maintained until crystalline M2P20, is formed, e.g.

-

CONH~PO * 6~ H2O

-+

CoNHJ04

*

H2O * CONH$O~ * C02P207

U 0 2 * NH4 * PO4 - 3 H 2 0 is dehydrated [972] in two stages (<420 K , E = 69-72 kJ mole-') and between 523 and 746 K loses NH3 to form U 0 2 H P 0 4 (E = 143 k 8 kJ mole-'). This is further dehydrated at 746863 K t o form (UO2)2P2O7 ( E = 260 k 1 2 kJ mole-') and at higher temperatures (1003-1137 K) loses oxygen to give U 2 0 3 P 2 0 7( E = 583 f 71 kJ mole-').

4.1.6 Ammonium carbonate

(NH4)2C03decomposes [ 9151 without melting but with some sublimation 293-373 K.

203

Pavlyuchenko et al. [973] have made a kinetic study of the decomposition of NHJIC03 in which gravimetric measurements were supplemented by, and were consistent with, quantitative microscopic observations. The rate of linear displacement of surfaces of cavities (analogous t o nuclei since no solid product was formed) was constant. &-Time curves were predominantly deceleratory . Measured values of E were generally 6970 kJ mole-', though rates varied somewhat with the atmosphere present within the temperature range studied (293-343 K). Ammonia exerted a marked inhibitory effect and, when present, E = 142 kJ mole-' for reaction in the higher temperature interval (360-387 K). It was concluded that the initial step is decomposition of the salt to NH3 + H2C03. 4.1.7 Ammonium carboxylales Many of these salts melt or sublime before or during decomposition and reaction temperatures generally increase with molar mass. Thermal analyses for a selection of ammonium carboxylates have been given by Erdey et al. [915] who conclude that the base strength of the anion increases with temperature until it reaches that of NH3. Decompositions of ammonium acetate (>333 K) and ammonium oxalate (>473 K) proceed through amide formation. Ammonium benzoate and ammonium salicylate sublime (>373 K) without decomposition but ammonium citrate decomposes (>423 K) t o yield some residual carbon. Hijek et al. [173] have reported a detailed kinetic study of the solid phase decomposition of the ammonium salts of terephthalic and isophthalic acids in an inert-gas fluidized bed (373-473 K). Simultaneous release of both NH3 molecules occurred in the diammonium salts, without dehydration or amide formation. Reactant crystallites maintained their external shape and size during decomposition, the rate obeying the contracting volume equation [eqn. (7), n = 31. For reaction at 423 K of material having particle sizes 0.25-0.40 mm, the rate coefficients for decompositions of diammonium terephthalate, monoammonium terephthalate and diammonium isophthalate were in the ratio 7.4 : 1.0 : 134 and values of E (in the same sequence) were 8 7 , 1 0 8 and 99 kJ mole-'. 4.2 AMMONIUM SALTS CONTAINING OXYANIONS OF THE METALS

4.2.1 Ammonium permanganate There have been two studies of the vacuum decomposition of NHJ4n04, the results of which differ in a number of important respects. Bircumshaw and Tayler's preparation [ 9741 exploded in the temperature range 343-384 K unless reactant self-heating was reduced by immersion of the salt in an inert oil. Pavlyuchenko et al. [975] describe the reaction as slow between 343 and 363 K, very fast at 2 3 6 9 and explosive at

204

2373K. Solid and gaseous products identified were Mn02, Mn2O3, NH$J03, H20, N2, 0 2 ,NO2, N 2 0 [974]and Mn02, MnO (in a 1 : 1 ratio), 02,H20, NO2 (traces of NO), NH3 [975]with the (NO2 + NO): NH3 ratio 1 : 1.a-Time curves were different, though values of E were in agreement at 109 kJ mole-'. The exceptional behaviour of a reaction rate, continually accelerating almost to a = 1.00, described by Bircumshaw and Tayler [974] may be a consequence of decomposition involving several rate process with only a small proportion of the reactant being converted to gaseous product (anion oxidation yielded NHf103). Pavlyuchenko et al. [975]observed a maximum reaction rate and proposed a radical chain mechanism. The decomposition rate was reduced in the presence of H20 and NH3 but increased by 02. UV pre-irradiation [976] increased the rate of NHyInO, decomposition at 351 K up to a maximum, followed by a decrease in rate with a further exposure. A similar maximum was observed for samples which had been aged for various times. These effects are ascribed to partial decomposition with the formation of products which, at low concentration, accelerate decomposition but at higher concentrations increase the stability of the reactant by effectively opposing self-heating during reaction. 4.2.2 Ammonium perrhenates Decomposition of NH,Re04 occurs in two steps [977].Below 633 K, in dry nitrogen, the first step is NH4Re04= Re02 Noes+ N2 + 2 H20 where the product is poorly crystalline and decomposes in a second step to monoclinic Re02 (+) N2) above -633 K.At higher temperatures, there is a crystallographic transformation to orthorhombic R e 0 2 (-873 K) which decomposes t o Re207and Re at >-1123 K. a-Time curves for the decomposition of N H a e O , are deceleratory and obey both the contracting volume equation [eqn. (7),n = 31 and the Avrami-Erofe'ev equation [eqn. (6)]with n = 1.0-1.3 (i.e. close to firstorder behaviour), 0.2 < a < 0.9. Values of E based on these models were 151 and 113 kJ mole-', respectively. Surface nuclei were detected in electron microscopic examinations. Closely similar kinetic characteristics were found for the decomposition of the intermediate R e 0 2 * Noes.Equation (7) (n = 3) was obeyed (0.08< a < 0.6) with E = 180 kJ mole-', and the Avrami-Erofe'ev equation [eqn. (6),now with n = 1.71 fitted from 0.1 < (Y < 0.7 with E = 255 kJ mole-' and n = 1.0 thereafter (E = 176 kJ mole-'). The decomposition of Re02(+Re207and Re) was also deceleratory and was found t o fit the contracting volume equation [eqn. (7),n = 31 from 0 < a < 0.5 with E = 423 kJ mole-' and (somewhat inappropriately) the Prout-Tompkins equation [eqn. (9)] was applied t o the rather flat decay period (E = 318 kJ mole-'). These observations are consistent with DTA results [ 9781.

-

a

205

The above results correlate well with studies by Ratner et al. [979,980] who used samples of defined particle size and surface area. They report the rapid formation at 503-523 K of nuclei of a new phase on NH4Re04 surfaces and that decomposition is accompanied by a surface area increase. There is a marked reduction in conductivity (X-10-8) near the onset of reaction. Structures and compositions of the product phases are discussed. &-Time curves for decomposition in hydrogen [ 979,9801

2 NH&e04+ 7 H 2 = 2 Re + 2 NH3 + 8 H 2 0 were deceleratory and between 473 and 623 K obeyed the contracting volume equation [eqn. (7), n = 31 when a < 0.75, though the value of E (80 kJ mole-') was less than that found for the reaction in N2. The reaction rate varied with PHZ0in the hydrogen, being a maximum at about 5% water vapour. Above 548 K, intermediates ( R e 0 3 , etc.) were volatilized and reduced in the gas phase. 4.2.3 Ammonium chromates The first step in the decomposition of ammonium chromate is conversion t o the dichromate [981] (-375 K), the rate of this process being reduced by oxygen [ 9821 (1-100 Ton). Thermoanalytical measurements have identified four stages in the decomposition [983]. A t 508 K

3 (NH4)2e@, = 3 (Q@s

*

NH3) + N2 + 6 H2O + NH3

followed at 533 K by

-

3 (Cr205 NH3) = [ ( C r 0 2 ) 6- H 2 0 ] + N2 + 2 H20 + NH3 The hydrated oxide loses water at -570 K and later oxygen, giving Cr203. The nature and properties of the final solid product have received considerable attention [ 280,9841 on account of its activity as catalyst. Three consecutive stages were identified [ 4631 for the decomposition of single crystals of (NH4)2CrzO7 at 453-488 K. (i) An induction period corresponding to nucleation; this decreased on ageing. (ii) The accumulatory evolution of N2(+N20),which obeyed the Prout-Tompkins equation [eqn. (9)] with a single rate coefficient (E = 138 kJ mole-'). (iii) A zeroorder rate process thereafter was ascribed to a constant area of interface advance, for which E was 159-172 kJ mole-' depending on particle size. The evolution of NH3 and H 2 0 occurred until completion of the acceleratory stage. These compounds inhibited reaction and it was concluded (by analogy with other ammonium compounds) that the first step is proton transfer. The ammonia released was oxidized. There was infrared evidence for the intermediate formation of NO; or NO;, with the maximum concentration occurring at the end of the acceleratory period, though the reaction temperature was somewhat above the stability range of NH&03. Fischbeck and Spingler's (earlier) kinetic analysis [985] of the sigmoid

206

curve (461-491 K) found obedience to the power law [eqn. (2), n = 41 during the acceleratory period followed by the contracting volume equation [eqn. (7), n = 31 with E = 205 kJ mole-'. In a study [986] of the effect of particle size on the kinetics of (NH4)2Cr21)7decomposition and the composition of gaseous products, Erofe'ev found one maximum only in the isothermal (473K) a-time curves for samples of small surface area. However, on increasing the specific surface area of the reactant, a second and earlier maximum appeared due mainly t o the evolution of NH3 and N 2 0 . It is suggested that the reaction involved generation of nuclei on surfaces and also in the bulk [ 4631. The surface process becomes more significant as the particle size diminishes. The surface area increases were achieved by grinding. which may, however, have also introduced imperfections. The role of dislocations in promoting reaction has been the subject of a more recent publication [987].

4.2.4 Ammonium molybda tes and tungstates Complete agreement on the steps involved and intermediates formed during the decompositions of various ammonium molybdates has not yet been reached and little kinetic information is available. Some rate measurements [988] have been obtained for the reactions of (NH4)20 4 Moo3 2 H20 which reacts in several steps [989] and may oxidize ammonia in the later stages [990]. Some inconsistencies are apparent in the literature [ 171,915,9911 concerning the intermediates formed during the decomposition of 3 (NH4)20 * 7 Moo3 4 H20, which is the usual commercial product. Similarly, although there have been several structural and stoichiometric investigations of the decompositions of ammonium tungstates, little kinetic information is available and some of the rate processes involved are sensitive to prevailing reaction conditions. Kinetic and thermodynamic measurements for the decompositions of ammonium di- and tetrathiomolybdates and tungstates have been reported by Miiller et al. [992,993]. (NH4)2M~S4 decomposes at 414-430 K to MoS3, NH3 and H2S;values of E based on initial rates and from DTA were 138 and 188 kJ mole-', respectively, the corresponding values for the reactions of (NH4)2WS4at 453-473 K being 88 and 117 kJ mole-'. Decompositions of (NH4)2M02S2(M = Mo or W ) are believed 19931 t o involve intermediate formation of MOS2, which is later decomposed t o MS2 accompanied by some oxidation to M 0 2 . Activation energies and decomposition enthalpies determined from DTA curves were E = 230 f 1 7 and 163 f 13 kJ mole-' and AH,,, = 151 f 17 and 176 f 21 kJ mole-' for the Mo (-433 K) and W (-493 K) salts, respectively.

-

-

-

4.2.5 Ammonium vanadates Decomposition of NH4V03proceeds t o completion in several successive stages, some of which are reversible, so that thermal behaviour is sensitive

207

to the composition and pressure of the prevailing atmosphere [405,994, 9951. Decomposition can be represented as the stepwise decrease in the (NH4)20 : V 2 0 5ratio. The first step (432-453 K) yields (NH4)20 - 2 V z 0 5 which reacts further at 453-483 K t o (NH4)20 * 3 V2OS(both steps occur as a single stage in moist ammonia) and between 533 and 573 K, decomposition yields V205.The overall reaction is readily reversible [995], viz.

2 NH4VO3 + VzO5 + 2 NH:, + H2O The kinetics of the contributory rate processes could be described [995] by the contracting volume equation [eqn. (7), n = 31, sometimes preceded by an approximately linear region and values of E for isothermal reactions in air were 175, 133 and 143 kJ mole-'. It was concluded [995] that the rate-limiting step for decomposition in inert atmospheres is NH evolution while in oxidizing atmospheres it is the release of HzO. A detailed discussion of the reaction mechanisms has been given [995]. Thermal analyses for the decomposition in air [991,996] revealed only the hexavanadate intermediate and values of E for the two steps detected were 180 and 163 kJ mole-'. 4.2.6 Ammonium uranates While Cordfuncke [997] believes that there are only four stable compounds in the U03-NH3-HzO system, the results of Stuart et al. [998, 9991 indicate the existence of a continuous non-stoichiometric phase containing the NH; ion and possessing zeolitic properties: U0z(0H)2-x * (ONH4 )x * YH2O. Ammonium diuranate, identified as U 0 3 - NH3 * 2 HzO, decomposed by two rate processes [ 10001. From thermogravimetric measurements, the first stage, completed at -500 K, was identified as a one-dimensional diffusion process, by its obedience t o a parabolic rate law ( a = h'" t'I2) and E = 42 f 4 kJ mole-'. This is consistent with a zeolite-type reactant structure. The product U 0 3 - 2 HzO is dehydrated at 500-600 K to @ - U 0 3and this reaction obeys the contracting volume equation [eqn. (7), n = 31 with E = 75 f 8 kJ mole-' and an increase of surface area. U 0 3 decomposes to U 3 0 , above -600 K and again eqn. (7) ( n = 3) is obeyed but E is increased t o 92 f 8 kJ mole-'. Price [1001] investigated the influence of salt preparation and reaction atmospheres on the decomposition of ammonium diuranate. Davidovich et al. [lo021 have studied the complex behaviour of ammonium oxofluorouranates on heating. 4.3 OTHER AMMONIUM COMPOUNDS

4.3.1 Ammonium azide

Small pellets of NH&J3sublime in an inert atmosphere below 523 K [ 10031. At higher temperatures and/or pressures, there is slow decompo-

208

sition, but above limits represented by 7 2 3 K at 10 Torr and 583 K at 150 Torr, the reaction is explosive yielding N2, H2, NH3 and HN3.

4.3.2 Ammonium complex salts Anhydrous (NH4)4[Fe(CN)6] decomposes [lo041 in air at >423 K; at -573 K, the solid product is cubic Fe203. In oxygen at 473-523 K , the reaction is explosive. The violet exothermic breakdown [ 10051 of (NH4)2 [ Fe(CN),NO] is due t o reaction between the NH3 and the NO evolved.

4.3.3 Ammonium zeolites Ammonium salts of the zeolites differ from most of the compounds containing this cation discussed above, in that the anion is a stable network of A104 and Si04 tetrahedra with acid groups situated within the regular channels and pore structure. The removal of ammonia (and water) from such structures has been of interest owing to the catalytic activity of the decomposition product. I t is believed [lo061 that the first step in deammination is proton transfer (as in the decomposition of many other ammonium salts) from NH', to the (Al, Si)04 network with -OH production. This reaction is 90% complete by 673 K [lo071 and water is lost by condensation of the - O H groups (773-1173 K). The rate of ammonia evolution and the nature of the residual product depend to some extent on reactant disposition [ 1006,10081.

4.3.4 Ammonium thiocarbamate From a kinetic study [ 1 2 8 1 ] of the reaction NHzCOSNH4 = 2 NH3 + COS the specific rate expression a = -2k ( t - t , ) { a + b - 2k(t - t , ) } ab was developed, where a and b are the dimensions of the crystal and t, is the time required t o attain a constant rate of growth of nuclei. The value of E , measured for the vacuum reaction (303-353 K), was 43 kJ mole-'. 5. Decompositions of metal carboxylates

Metal salts of carboxylic acids obviously possess some organic character, but decompositions of these substances can be considered in the present context. Many metal carboxylates decompose at a reactant-product interface and their nucleation and growth processes are similar t o the behav-

209

iour of the various inorganic reactants discussed here. The several mechanistic studies which have been made of the decompositions of the representative compounds Ca, Ag and Ni oxalates and Ni formate have been theoretically interpreted by the same principles applicable t o the consideration of the reactions of perchlorates, permanganates, azides etc. The generalization of results obtained for all reactants available has contributed towards the advancement of the subject. Those metal carboxylates which decompose in the solid state differ from most organic compounds which characteristically either melt or sublime unchanged or at least undergo partial melting during pyrolysis [ 10091. As with many other solids, decompositions of the carboxylates may first involve water removal from a hydrate, reaction may proceed to completion through more than a single step, and mechanistic studies must always include consideration of the possible occurrence of melting. Reference has been made in Sect. 1 t o kinetic studies of the dehydration of various formates and oxalates. These reactions are entirely comparable with the elimination of water from inorganic solids. Dehydration may or may not be accompanied by recrystallization [ 971 or extensive lattice reorganization. After water removal, many nickel salts are largely amorphous t o X-rays [502]. Accordingly, for such substances large single crystals of reactant cannot be prepared. Complete dehydration is sometimes difficult and is not always achieved before the onset of anion breakdown. There is evidence that nickel oxalate tenaciously retains a small amount of water [286] and that dehydration may control nucleation in the decomposition of nickel formate [375,433]. The products of decomposition of metal carboxylates vary t o some extent with the constituent cation and the final residue is usually either the metal or an oxide, occasionally the carbide and sometimes some elemental carbon deposit. Dollimore et al. [94] have described the use of Ellingham diagrams for the prediction of the composition of the solid products of oxalate decompositions. The complete characterization of residual material can be difficult, however, since the solids may be finely divided, pyrophoric [ 10101, metallic and amorphous t o X-rays. Changes in the composition of gaseous products as reaction proceeds may make definition of the fractional decomposition, a, difficult. For example, product CO and residual carbon may be capable of reducing a metallic oxide, particularly at high a ; and the catalytic properties of an accumulating solid product may result in promotion of secondary gas reactions. Kinetic studies of the decomposition of metal formates have occasionally been undertaken in conjunction with investigations of the mechanisms of the heterogeneous decomposition of formic acid on the metal concerned. These comparative measurements have been expected t o give information concerning the role of surface formate [ 5221 (dissociatively adsorbed formic acid) in reactions of both types. Great care is required,

210

however, in the interpretation of rate data and many outstanding problems remain unresolved [ 891. Metal carboxylates featured among the first investigations of the changes in kinetic characteristics which result from systematic variations of the cation [89] or the anion. Recent work has included the effects of cation changes in the oxalates of Mg, Mn and Fe(l1) [ l o l l ] and of Mg and Zn [1012]. Variations of the anion in a series of nickel carboxylates [88] and cobalt carboxylates [ 10131 resulted in different modifications of the kinetic characteristics [f(a),A and El. Various rate-limiting chemical steps have been identified for carboxylate breakdown [32]. These include rupture of each of the principle linkages in the R-CO-O-M group, i.e. the R-C bond [ 1014-10161, the S-0- bond [ 409,10171, or the -0M bond [88,1018]. Alternatively, the rate may be controlled by charge transfer [ 1012,1017,1019] or by interface strain or catalysis by the solid products [ 286,375,10201. Much of the interest in the field has been concentrated on the simplest reactants and especially the formates and oxalates. 5.1 METAL ALKANOATES

5.1.1 Metal forma tes

( a ) Group IA metal formates It is apparent from DTA studies [lo211 of the decompositions of Group IA formates in inert or oxidizing atmospheres that reaction is either preceded by or accompanied by melting. Anion breakdown leading to carbonate production may involve formation of the oxalate, through dimerization [ 10221 of the postulated intermediate, CO;, especially during reaction of the Na and K salts in an inert atmosphere and under isothermal conditions. Oxalate production is negligible in reactions of the Li and Cs formates. Reference to oxalate formation is included here since this possibility has seldom been considered [ 10141 in discussions of the mechanisms of decompositions of solid formates.

( b ) Group IIA metal formates The decompositions of these compounds are of interest since they are used as binders in electron-emissive coatings [1023]. The initial stage of the endothermic reaction in vacuum or nitrogen (520-820 K) yields residual carbonate and a small quantity of carbon. Changes in surface area during reactions have been measured. The main volatile product is HCHO, but secondary, exothermic reactions occur on the surface of the product carbonate so that the overall reaction is 2 M(HC02)2 = 2 MCOB + H2 + f C02 + 1; C + H2O

211

Magnesium formate decomposes (613-723 K) directly t o the oxide [ 10241 and the barium salt melts prior to anion breakdown. Isothermal a-time curves were sigmoid [lo241 for the anhydrous Ca and Ba salts and also for Sr formate, providing that nucleation during dehydration was prevented by refluxing in 100% formic acid. From the observed obedience to the Avrami-Erofe'ev equation [eqn. (6), n = 41, the values of E calculated were 199, 228 and 270 kJ mole-' for the Ca, Sr and Ba salts, respectively. The value for calcium formate is in good agreement with that obtained [292] for the decomposition of this solid dispersed in a pressed KBr disc. Under the latter conditions, concentrations of both reactant (HCO;) and product (COi-) were determined by infrared measurements and their variation followed first-order kinetics.

( c ) Transition metal formates There have been wide variations in the interest shown in the salts of this group. Nickel formate and, to a lesser extent, copper formates have been the subject of particularly detailed investigations. For other solids, little information is available. ( i ) Scandium formate. This salt decomposes (-470-670 K) t o give principally ScZO3, CO and HzO and smaller yields of COZ, Hz,CHI, HCOOCH3 [ 10251. No carbonate was detected. ( i i ) Manganese(l1) formate. During the initial stage (a < 0.2) of the decomposition of manganese(I1) formate [ 1691 (491-563 K), the reaction was autocatalytic and obeyed the exponential law [eqn. (S)], E = 96 kJ mole-'. Thereafter, there was a temperature-independent zero-order reaction to a 0.8, when the rate process became strongly deceleratory.

-

( i i i ) Cobalt formate. There is evidence that the kinetics of decomposition of cobalt formate [1026,1027] are similar to those of the nickel salt, considered in some detail below. A significant point of difference, however, is that metal production during reaction of the former is preceded by formation of cobalt oxides [ 10281.

(iu) Nickel formate. The decomposition of anhydrous nickel formate can be represented by the concurrent occurrence of the two reactions Ni + H, + 2 CO, Ni + H 2 0 + CO + CO, with that which gives Hz predominating [ 10291. The composition of the product gases may vary as a consequence of secondary reactions on the metal surface [ 375,10301.

212

Bircumshaw and Edwards [lo291 showed that the rate of nickel formate decomposition was sensitive t o reactant disposition, being relatively greater for the “spread” reactant. a-Time curves were sigmoid and obeyed the Prout-Tompkins equation [eqn. (9)] with values of E for spread and aggregated powder samples of 95 and 110 kJ mole-’, respectively. These values are somewhat smaller than those subsequently found [ 3751. The decreased rate observed for packed reactant was ascribed t o an inhibiting effect of water vapour which was most pronounced during the early stages. References to a number of other kinetic studies of the decomposition of Ni(HC02)2have been given [ 3751. Erofe’ev et al. [ 10261 observed that doping altered the rate of reaction of this solid and, from conductivity data, concluded that the initial step involves electron transfer (HCOO- + HCOO - +e-). Fox et al. [118], using particles of homogeneous size, showed that both the reaction rate and the shape of a - t i m e curves were sensitive to the mean particle diameter. However, since the reported measurements refer t o reactions at different temperatures, it is at least possible that some part of the effects described could be temperature effects. Decomposition of nickel formate in oxygen [ 601 yielded NiO and COz only; the shapes of the a-time curves were comparable in some respects with those for reaction in vacuum and E = 160 15 kJ mole-’. Criado et al. [lo311 used the Prout-Tompkins equation [eqn. (9)] in a non-isothermal kinetic analysis of nickel formate decomposition and obtained E = 100 f 4 kJ mole-’. Microscopic observations [ 3751 confirmed that the sigmoid a-time decomposition curves for Ni(HCO& were due t o the production and development of discrete nuclei, comprised of approximately spherical metallic particles 20-50 nm in diameter. The appearances of such nuclei suggested their preferred, but not exclusive development across surfaces, so that 2 < h < 3. Since the nickel particles which make up the nucleus were small compared with the volume of the nucleus, it was suggested [433] that the product crystallites (Ni) possessed some mobility. During the initial acceleratory period of reaction, the power law [eqn. (2)] was obeyed, though difficulties were experienced in determining the value of n , and E = 124 kJ mole-’ (0.1 < a < 0.3). Thereafter, data fitted the contracting volume equation [eqn. (7), n = 31 and E = 194 kJ mole-’ (0.5 < a < 0.7). The length of the induction period and the shapes of the a-time curves varied with reaction conditions [ 4331 ; this was attributed t o variations in the rate of surface dehydration and ease of removal of water vapour, identified as strongly inhibiting the nucleation step, but not the growth process. The several A and E values cited apply t o the overall reaction, which involves composite nucleation followed by growth. Attempts were made t o measure individually the kinetic characteristics of these steps from examination of electron micrographs for salt decomposed (a < 0.2). Such

*

213

material contained areas of dense nucleation on some crystallite faces while other particles remained completely unreacted. The local variations in numbers of nuclei per unit area were so great that trends with change in a or reaction temperature could not be discerned. Onset of reaction within any crystallite assemblage was markedly inhomogeneous and was identified as occurring preferentially within those zones from which water can escape most easily. The rate of nucleation is a function of the locally prevailing pressure of water, and this may be expressed in the form k N = kf(PH20)

f(x)

where f(x) reflects spatial changes of PH20throughout the reactant mass (a further geometric factor which is not readily determined). f ( P H 2 0 ) is the dependence of nucleation rate on PH20and has not yet been established. Overall kinetic characteristics [f(a), A and El depend on sample disposition and further studies will be required to determine the rates of formation and growth of nuclei. ( u ) Copper formate. The decompositions of both formates of copper have been studied by Schuffenecker et al. [1032]. The reaction of copper(I1) formate is autocatalytic (368-436 K) and obeys the ProutTompkins equation [eqn. (9)](thus resembling early reported behaviour for nickel formate [1029]) and E = 67 kJ mole-'. The autocatalytic process is believed t o involve transfer of an electron from the anion t o the metallic products and the possible intermediate formation of copper( I) formate. Decomposition of copper(1) formate occurred in a somewhat lower temperature interval (351-385 K) and the slightly acceleratory reaction obeyed the exponential law [eqn. (8)]with E = 107 kJ mole-'. Three different crystalline forms of anhydrous copper(11) formate have been identified [lo331 and these three variations provide a convenient group of reactants for an investigation of the influence of lattice structure on the kinetics and mechanisms of the decomposition. Erofe'ev and Kravchuck [ 10341 showed that kinetic characteristics for the decompositions of two of these forms were appreciably different, an effect attributed t o different relative dispositions of the cations in the two reactant structures. Galwey et al. [97] supplemented kinetic measurements for the isothermal decompositions (-430-500 K) of the three different forms of copper(11) formate with electron microscopic examinations of surface textures. Sigmoid a - t i m e curves obeyed the power law [eqn. (2)]in the early stages with n = 2 for the salt having a laminar structure and n = 3, corresponding to three-dimensional growth of nuclei, for the other two salts. E = 115 kJ mole-' for all three reactants. The deceleratory reactions obeyed the contracting area expression [eqn. (7),n = 21 for the laminar structure (E= 115 kJ mole-') and the contracting volume equation [eqn. (7),n = 31 for the other two solids with E = 146 and 132 kJ mole-'.

214 Nucleation

cu

(adsorbed on nucleus

- 1

I

growth of nuclei

Fig. 18. Schematic representation of the mechanism of decomposition of copper( 11) formate, proposed by Galwey et al. [97 1. (Reproduced, with permission, from Journal of Physical Chemistry.)

Significant differences in rate behaviour are thus related t o structural features of the reactant. Decomposition of copper(11) formate was accompanied by sublimation of copper metal and the residual product from the partial or completed reaction gave the appearance of having sintered. These indications of the mobility of copper during reaction are attributed to the intermediate formation of a volatile and very unstable cation-containing entity, identified as copper(1) formate, since a dimer of this compound may briefly exist [lo351 in the gas phase prior to breakdown. The reaction mechanism proposed [97] is given in schematic form in Fig. 18. It is suggested that effective nuclei are developed within the reactant crystallites and interaction of the metal produced with the reactant yields the volatile copper(1) formate. This unstable participant may (i) decompose within the crystal, and the metal produced become incorporated in the growth of an existing nucleus, (ii) decompose at or near a surface of the salt, with which the metal released reacts t o further development of an existing nucleus or t o establish a new one, or (iii) escape from the reactant and breakdown elsewhere, depositing sublimed metal. The relative contributions from these processes change with variations in reaction conditions (e.g. reaction rate was increased by pelleting, since the relative ease of escape of the volatile active intermediate was decreased as a result of the reduction of the surface/volume ratio of the compressed aggregate) or during reaction [e.g. particle disintegration at high a, with greater ease of volatilization of copper( I) formate]. Nucleation and growth processes are here closely interconnected, since the mobile intermediate is not localized at an inter-

215

face, but may migrate elsewhere and possibly initiate reaction. Accordingly, the rate characteristics are not completely represented by the theory developed for an interface advance process and the value of E cannot be associated with a specific bond redistribution step. Since copper is similarly volatilized during the heterogenous decomposition of formic acid on copper metal [1036], it seems probable that copper(1) formate is again an intermediate. The mechanism may, therefore, contain similar features to that operating during the decomposition of copper(I1) formate (Fig. 18).

(ui) Zinc formate. The kinetics of decomposition of zinc formate El691 differ from the behaviour of manganese(I1) formate, above, with which it is prob’ably isostructural. The a-time curves for reaction (463528 K) of the zinc salt were deceleratory throughout, though approximately linear between 0.3 < a < 0.8 (E= 67 kJ mole-’). This behaviour is ascribed to initial instantaneous nucleation followed by obedience t o a contracting volume model (a < 0.3). After a 0.3, interfacial strains induce reactant cracking and the area of active reaction interface remains approximately constant t o a 0.8.

-

-

(uii) General comments. According to Kornienko [ 10371, decompositions of the transition metal formates may involve cleavage of both C - O and M - O bonds to yield metal oxide and the unstable formic anhydride. Oxide reduction by CO and/or Hz may then yield residual metal. Shishido and Masuda [lo381 conclude, from evolved product analyses, that the decompositions of Co, Ni, Cu and Pb formates yield mixtures of metal and metal oxide by concurrent reactions. (uiii) Silver forrna te. Solid silver formate explodes “with intense detonation” on heating t o -365 K [1039]. Decomposition products are mainly Hz and CO, and small quantities of metal may be sublimed in vacuum. A kinetic study of the decomposition of this salt would be valuable since extensive rate studies have been made [ 361 of the silver-catalyzed decomposition of formic acid.

( d ) Lanthanide formates The lanthanide formates decompose above -670 K [lo401 and the chemical changes proceed through the oxyformate [ 10411 and the oxycarbonate t o Ln203. Values of E determined by non-isothermal methods [lo401 decreased with increase in atomic number for reaction in air but were approximately equal for reactions in vacuum.

( e ) Actinide formates ( i ) Thorium tetraformate. The decomposition of Th(HC02)4 [ 10201 obeyed the Prout-Tompkins equation [eqn. (9)] and E = 150 kJ mole-’

216

between 498 and 553 K. No solid intermediates were found in the reaction which yielded Tho2, HCHO, and C02. These primary gaseous products underwent a series of secondary catalytic reactions on the oxide surfaces, giving Hz, CO, H 2 0 , etc. The incorporation of nickel in the reactant substantially increased both the decomposition rate and the relative yields of CO, C 0 2 , and H2 (which are the predominant products of nickel formate decomposition).

(ii) Uranium tetraformate. At 453 K under inert conditions, this salt decomposes [lo141as follows

2 U(HC02)4 = 3 HCOOH + 4 CO + Hz + C02 + 2 UOZ Zero-order kinetic obedience is found and E = 119 kJ mole-'. In air at 493 K, U(HC02)4 is very largely converted t o U0z(HC02)2and reaction of this compound is almost identical with that of the solution-prepared specimens, viz.

3 U0z(HC02)2= 2 HC02H + 4 CO + HzO + 3 a - U 0 3 The Prout-Tompkins equation [eqn. (9)] was obeyed ( E = 169 kJ mole-'). The first step in the reaction was identified as

HCO;

-+

H' + CO',-

and further steps have been discussed [lo141 with reference t o the kinetic data. ( f ) Surface formates

There is an extensive literature relating t o the role of surface intermediates in the heterogeneous catalytic decomposition of formic acid on metals and oxides (see Refs. 36,522,1030,1042-1045). 5.1.2 Metal acetates There have been relatively few detailed kinetic studies of the decompositions of metal acetates, which usually react to yield [lo461 either metal oxide and acetone or metal and acetic acid (+CO2+H2+ C). Copper(I1) acetate resembles the formate in producing a volatile intermediate [copper(I) acetate] [152,1046,1047].

(a) Nickel acetate a-Time curves for the vacuum decomposition of Ni(CH3C0& (562610 K) obeyed the Proutl?ompkins equation [eqn. (9)]with two linear regions for both of which E = 95 ? 8 kJ mole-'. This value of E is close to that found for nickel formate by Bircumshaw and Edwards [lo291 and

217

also for reaction in air (94 ? 5 kJ mole-', 555-631 K. The a-time curves were approximately linear 0.1 < a < 0.8). The external crystal shape was maintained during preliminary dehydration and decomposition, though reaction resulted in a marked increase in surface area [273]. The final product of vacuum decomposition [669,1049] (2613 K) was a mixture of the f.c.c. and hexagonal forms of nickel and the decomposition of the Ni3C intermediate was first order. Admixture of Ni3C with the reactant did not catalyze the breakdown of the salt. Dorbmieux [669,1049] from TG and DTA measurements (529-619 K), has suggested additional detail for the mechanism of decomposition of Ni(CH3C02)2.

( b ) Cobalt acetate a-Time curves for the decomposition of cobalt acetate [lo481 were irreproducible (563-613 K), possibly due t o sublimation which occurred under vacuum conditions.

( c ) Uranyl acetate Isothermal a-time curves for the decomposition of UOz(CH3C02)2in air (513-573 K) [lo181 showed two approximately linear regions, 0.0 < a < 0.2 and 0.2 < a < 0.9, for which the values of E were 107 and 165 kJ mole-', respectively. In nitrogen, the earlier portion of the curve was not linear and E = 151 kJ mole-' for the later interval. The zero-order kinetic behaviour was explained by growth of nuclei in thin, plate-like crystals, which were shown by microscopic and surface area measurements to fragment when a > 0.85. The proposed initial step in the decomposition was fission of bonds between the UOy and the (OCO - CH3)- species [ 10181. ( d ) Barium acetate

Barium acetate decomposes [lo501 with growth of planar product nuclei, E = 167 kJ mole-' (720-750 K). Reactions of other Group I1 acetates are reported [lo511 as being accompanied by at least partial melting. 5.1.3 Other metal alkanoates

Comparative studies [ 1028,1052,10531 of the decompositions of Ni, Co and Cu alkanoates from formate to valerate showed that both the cation present and the length of the alkane chain influenced the temperature and enthalpy of decomposition. No such relationship was found [1048], however, between chain length and temperature of reaction of a series of nickel salts between the propionate and the stearate in a study which included some qualitative identifications of the products. Mass

218

spectrometric examination of the volatile products of decomposition of copper(I1) alkanoates indicated the participation of the copper( I) compounds in the pyrolysis processes [1035]. The reaction of magnesium propionate is accompanied by melting [ 10541. 5.2 METAL ALKANDIOATES AND RELATED COMPOUNDS

5.2.1 Metal oxalates There have been many extensive and intensive studies of metal oxalate decompositions. Boldyrev et al. [lo151 have suggested that these may be classified according t o the three principle reactions

MCz04

fMC03 + co MO + CO + COZ -+

M ‘

+ 2 COz

Despite the differences in final products formed, these workers identify the initial step in the breakdown of all oxalates as C - C bond rupture in the anion (C2O;- + 2 COZ). This intermediate may be converted to the carbonate (through the carbonyl-arbonate intermediate) or t o COz (by electron transfer), viz.

co; ir

[ococoz]’--c0:- + co oz-+ coz + co -+

\COz + 2 e- and {MZ’ + 2 e - + M}

Reaction of CO; with H 2 0 may yield formate and/or bicarbonate ions. The activation energy found for the decomposition of an individual oxalate ion in a KBr matrix (270 15 kJ mole-’) [292,294] is regarded as the energy requirement for C - C bond rupture. The generally lower values of E observed for many oxalates (-165-175 kJ mole-’) are attributed to the facilitation of reaction at the reactant-product interface.

*

( a ) Group IA metal oxalates These salts decompose [39] to the carbonates in the temperature intervals Li, 811-826 K; Na, 737-814 K; and K, 754-798 K (from DTA measurements, 5 K min-I). The reaction of lithium oxalate [98] (742765 K) obeyed the contracting volume equation [eqn. (7), n = 31 with E = 223 k 1 3 kJ mole-’. A marked increase in surface area during the initial stages of decomposition was later followed by extensive sintering.

( b ) Group IIA metal oxalates

-

BeC,O, H 2 0 decomposes [lo551 at 473-593 K t o give the basic intermediate 8 BeC204* 5 Be(OH)z, which is converted t o Be0 between 593

219

and 623 K; the CO2/CO ratio is unity throughout. The deceleratory region of magnesium oxalate decomposition [ 10561 (677-745 K) obeyed the contracting volume equation [eqn. (7), n = 31 and the first-order equation from which the average value of E was 297 k J mole-'. Reaction was believed t o proceed through the growth of nuclei formed randomly during the dehydration of MgC204* 2 H 2 0 . Danforth and Dix [ 10121, however, regard the composite equation da - _ - hl(1 - a) + h,cY(l - a ) dt

as providing a more satisfactory representation of the data. The first term can be regarded as a primary thermal decomposition process while the second is ascribed to reaction catalyzed by product oxide. The CO2/CO ratio was initially as high as 3 and decreased thereafter, though it remained greater than 1. Separate measurements of the yields of both products were made and a values calculated from the cumulative yields. The value of E = 201 ? 8 kJ mole-' was obtained from the temperature variations, 708-733 K, of both rate coefficients (i.e. h l and h 2 ) .The ratecontrolling step in the decomposition of MgC204 (and also ZnC204 [1012]) was identified as electron transfer C20$- + M2+

-+

C204 + M'

The positive hole (C20;) migrated rapidly to a surface where subsequent decomposition may proceed either by the thermal or the catalytic path. The adsorbed species CO, has been identified [lo571 by ESR in the decomposition of MgC204. The thermal reactions of CaC204 H 2 0 have been very fully investigated and this substance has been used as a thermal analysis reference material [ 10581. Dehydration, decomposition to the carbonate, and dissociation to CaO are all well separated, though kinetic characteristics are influenced by the presence of C02, O2 and H 2 0 as well as by the reaction conditions, including heating rate, sample size, and sample container. Kinetic parameters for the oxalate decomposition reaction have been summarized by Gurrieri et al. [1059]. Values of E are close to 314 f 8 kJ mole-'. Decompositions [1057,1060,1061] of Sr (643-743 K ) and Ba (663-743 K) oxalates involves some disproportion of CO, yielding residual carbon. (c) Zinc oxalate

The rate equation [eqn. (26)], given above for the reaction of magnesium oxalate, is also obeyed [lo121 by the decomposition of zinc oxalate (620-646 K), although here the catalytic (second) term is dominant, so that behaviour approximated to the Prout-Tompkins equation [eqn. (9)]. The value of E (201 ? 8 kJ mole-') was the same as that found

220

[lo621 in an earlier study (209 f 13 kJ mole-') but greater than a value [lo631 (169 f 11 kJ mole-') obtained from non-isothermal measurements. The structural changes which accompany reaction have been discussed [1063,1064]. The measured increase in area during reaction was proportional to a, attributed [267,10651 t o the production of small nonporous ZnO particles, accompanied by some sintering. The rate of surface area increase is proportional t o the remaining reactant, i.e. to (1-a), while the probability of sintering is proportional t o a, leading to ProutTompkins behaviour [eqn. (9)Jas found by Danford and Dix [1012]. ( d ) Transition metal oxalates

(i) Chromium oxalate. Between 623 and 648 K, some of the Cr3+in Ck2(C204)3 * 6 H 2 0 [lo661 undergoes reduction (to Cr"), at -700 K a Cr3+hydroxy-compound is formed, and above 713 K the final product is Cr203. (ii) Munganese(1I) oxalate. The rates of both vacuum decomposition and of oxidation of anhydrous manganese(I1) oxalate are appreciably influenced [408] by the conditions of dehydration of the prepared dihydrate. Dehydration exhibited Smith-Topley behaviour (see Sect. 1.4) and subsequent reactions were more rapid (X-2.5-3) in the less perfect anhydrous material prepared in vacuum than that resulting from heating in air. The shapes of the a-time curves for all four rate processes studied (decomposition and oxidation reactions of reactant dehydrated in vacuum and in air) were closely similar. The power law [eqn. (2),2 < n < 31 was obeyed ( a < -0.2) following an initial reaction completed at a 0.02, and the deceleratory period fitted the contracting volume equation [eqn. (7), n = 31. This model is supported by electron microscopic observations, which indicated surface nucleation leading t o the establishment of a superficial product layer and subsequent advance of the interface into reactant particles. The oxidation reaction occurs in a lower temperature range (500590 K) and with a lower value of E (100 f 6 kJ mole-') than the vacuum decomposition (616-636 K and 141 f 4 [272] or 180 f 4 kJ mole-' [1067], respectively). From this observation and the analytical evidence that the initial gaseous products contain a higher proportion of CO than that formed subsequently, it is suggested [408] that the interface reactions involved a chain-type mechanism, with regeneration of an active Mn3+ intermediate. This model is described in greater detail in ref. 408, which includes citations of many studies of the decomposition of manganese(I1) oxalate.

-

(iii) Iron oxakrtes. Many decomposition studies of FeCZO4* 2 HzO are cited by Carib et al. [lo681 in an investigation using Mossbauer spectroscopy with an oxidizing atmosphere, t o which the reaction is very sensitive [409,1069]. No intermediates are found, as microcrystalline a-Fe203

221

is formed at reactant crystallite surfaces. Macklen [ 1069J has suggested that the initial step is oxidation of Fez+t o Fe3' followed by rapid rupture of the weakened F e - 0 and C - C bonds to release COz. Reactions of the various iron( 111) oxalates have also been studied [ 1070J .

(iu) Cobalt oxalate. Broadbent et al. [43] have shown that the kinetics of decomposition of anhydrous cobalt oxalate are sensitive to the temperature at which the salt has been previously dehydrated. Water removal at 423 K yielded a reactant possessing considerable lattice strain. Decomposition in vacuum (570-588 K) involved an initial deceleratory process (a < 0.025), an induction period (E = 204 kJ mole-') leading to an exponential [eqn. (S)] acceleratory process (a< 0.5), a linear period to a 0.95 (for which the rate coefficient was almost temperature-independent) and, finally, a first-order decay. Dehydration at higher temperature (473 K) yielded smaller but more perfect CoC204crystallites. The linear region was absent from the a-time curve, following the exponential acceleratory process, and the Prout-Tompkins equation [eqn. (9)] was obeyed when 0.25 < a < 0.97, E = 167 kJ mole-'. Reference has been made in Chap. 3, Sect. 4.5 to the mechanistic explanation provided [43] for zero-order reaction; interfaces proceed outwards from the central axis and inwards from the surfaces of cylindrical particles. Recently, it has been shown [lo711 that CoCz04* 2 H 2 0 exists in two crystalline modifications, a and p. Taskinen et al. [lo721 prepared anhydrous cobalt oxalate of different particle sizes by dehydration of the 0 (coarser grained) phase and the a/P mixture (finer grained). The coarser grained preparation decomposed at 590-700 K with a sigmoid a-time curve fitted by the Avrami-Erofe'ev equation [eqn. (6),n = 21 and below and above 625 K, E values were 150 and 57 kJ mole-', respectively. Reaction of the fine preparation obeyed eqn. (6) (n = 3) and below and above 665 K, values of E were 120 and 59 kJ mole-', respectively. Catalytic properties of the products of decomposition of cobalt oxalate have been investigated [ 10731.

-

( u ) Nickel oxalate. The a-time curves for the decomposition of nickel oxalate have been the subject of particularly detailed scrutiny and the kinetic analysis is one of the most complete available [40,286,107410791. The initial deceleratory reaction (0 < a < 0.0085) is well described [40] by the contracting area formula [eqn. (7), n = 21 with E = 141 kJ mole-' and is identified as surface decomposition following nucleation at crystallite surfaces and edges. After due correction for the initial process and the induction period, the subsequent reaction, under conditions such that product gases are allowed to accumulate, obeys the AvramiErofe'ev equation [eqn. (6), n = 21 for 0.10 < a < 0.85 with E = 210 kJ mole-'. Similar obedience was found (0.20 < a < 0.88) for reaction under conditions where produced gases were removed intermittently for gas

222

chromatographic analysis (differential conditions) but the magnitude of E was significantly less (130 kJ mole-'). The induction period is identified as an interval of slow growth. From a detailed theoretical consideration, it is concluded that nucleation is instantaneous (0 = 0) and that the observed kinetic exponent ( n = 2) is due to twodimensional growth ( h = 2). Since the difference in values of E for reaction under accumulatory and under differential conditions (210 - 130 = 80 kJ mole-') is close t o that characteristic of dehydration of the hydrate, it is concluded that water removal is efficient during differential reactions but for accumulatory processes the activation step also involved dehydration. The proposed mechanism of reaction involves electron transfer C20i- + C204+ 2 e-1 2 coz Ni2' + 2 e- + Ni Dominey et al. [lo741 generally confirm this pattern of kinetic behaviour but ascribe the induction period to migration of nickel atoms across surfaces, resulting in the production of nuclei along linear imperfections. Initial three-dimensional growth of nuclei in this distribution results in the generation of cylindrical particles of product. This pattern of behaviour is entirely consistent with electron micrographs obtained for reacted salt [ 2861. Some fragmentation of the reactant occurs during decomposition [ 1076,10771. Pre-irradiation of the salt with X-rays [lo751 increased the extent of the initial deceleratory rate process, an effect attributed to the promotion of the electron transfer step. Neutron irradiation [lo741 accelerated the decomposition rate and reduced the magnitude of E for the induction period from 216 to 159 kJ mole-'.

( e ) Heavy metal oxalates ( i ) Silver oxalate. The kinetics of decomposition of AgC204are sensitive to a variety of influences, including the method of preparation [435], doping [ 10801, ageing, grinding, pre-irradiation [ 1081,1082], the surrounding atmosphere [54] and, in the initial stages, the presence of an electric field [ 1083,10841. The initial step in the reaction has been identified as electron transfer and the mechanism of this process has been discussed in detail by Boldyrev [ 10851 and by Leiga [ 10861. Decomposition yields CO, and finely divided silver metal [1087], the structure of which depends on the thermal treatment of the solid. The presence of excess C2024- in the reactant promotes breakdown whereas the reaction is inhibited by the presence of excess Ag' or O2 or NO [lo881 (COZhas no effect). The acceleratory period of the vacuum decomposition of AgC204 at 385-410K obeys either the power law [eqn. (2), n=3.5-4.01 or the

223

exponential law [eqn. (S)]. Derek and Mania [lo841 used the AvramiErofe'ev equation [eqn. (6), n = 0.5-2.01 and found E = 172 ? 21 kJ mole-'. In the presence of an electric field, E for the initial stage was increased to 230 f 21 kJ mole-'. From optical and electron microscopic observations [ 10861, it was shown that during vacuum decomposition compact nuclei are formed on surfaces and at defective regions [1089, 10901 and grow in three dimensions. Kolesnikov et al. [1087], however, have described the development of two-dimensional layers of product which lead to reactant fragmentation.

(ii) Mercury(II) oxalate. The a-time curves for the vacuum decomposition at 453-478 K of mercury(I1) oxalate 4 HgC204= 2 Hg + 2 HgO + C + 7 C02 fitted [1091,1092] the power law [eqn. (2), n = 21 during the acceleratory period and the contracting volume equation [eqn. (7), n = 3, but applied in the differential form, (da/dt)"2 = k t + c ] during the decay period. This behaviour was attributed to the rapid two-dimensional growth of nuclei over the surfaces of approximately spherical particles ( E = 107 kJ mole-') followed by inward interface advance ( E = 169 kJ mole-'). Reaction was retarded by water vapour [1091], but was insensitive to Hg vapour and other decomposition products. Decomposition kinetics were very sensitive to reactant pre-irradiation.

(iii) Lead(II) oxalate. I t is concluded [ 10931 that defects are important participants in the decomposition of lead(I1) oxalate, since the reaction rate is decreased by ageing, UV irradiation and thermal annealing. Decomposition is catalyzed by lead metal [lo931 and the C02/C0 ratio in the product gases (623-898 K) has been the subject of a detailed study by Yankwich and Copeland [ 10841. Bircumshaw and Harris [ 10951 analyzed their kinetic data (582-623 K) by the Prout-Tompkins equation [eqn. (9)], E = 151 kJ mole-'. Decomposition in air at 643-673 K was expressed as [lo961 PbC204 = PbO + C02 + CO and the value of E was unaltered. ( f ) Lanthanide oxalates

While there have been many non-isothermal studies of the decompositions of lanthanide oxalates, fewer detailed kinetic investigations have been reported. The anhydrous salts are difficult to prepare. La, Pr and Nd oxalates decompose [lo971 t o the oxide with intervention of a stable oxycarbonate, but no intermediate was detected during decomposition of the other lanthanide oxalates. The product CO disproportionates exten-

224

sively [ 10981. Horsley et al. [ 10991 have studied the catalytic properties of the residual solid obtained from the reaction of cerium( 111) oxalate. The a-time curves for the vacuum decomposition at 5 9 3 - 6 9 3 K of lanthanum oxalate [ 10981 are sigmoid. Following a short induction period (E = 164 kJ mole-'), the inflexion point occurred at a 0.15 and the Prout-Tompkinsequation [eqn. (9)] was applied (E = 133 kJ mole-'). Young [29] has suggested, however, that a more appropriate analysis is that exponential behaviour [eqn. (8)] is followed by obedience t o the contracting volume equation [eqn. (7), n = 31. Similar kinetic characteristics were found [lo981 for several other lanthanide oxalates and the sequence of relative stabilities established was Gd > Sm > Nd > La > Pr > Ce. The behaviour of europium(II1) oxalate [1100] is exceptional in that Eu3+is readily reduced

-

E~Z(C204)a= 2 E ~ C 2 0 4+ 2 C02 and breakdown of EuC204to the carbonate at 633-693 K is inhibited by

co2.

(g) Actinide oxalates In an inert atmosphere, the decomposition at 573-623 K of uranyl(V1) oxalate [1101]obeys the Proutl'ompkins equation [eqn. (9)] with E = 261 k 4 kJ mole-'. The residual product is U 0 2 and, under low pressure accumulatory conditions, the final CO2/CO ratio is -9. In air,the reaction proceeds in two stages. The initial process obeys the Prout-Tompkins equation and is identified as a surface reaction. Thereafter, decomposition fits the Avrami-Erofe'ev equation [eqn. (6), n = 21, involving isolated disc-like grains of reactant, to yield amorphous U 0 3 as the final product. Values of E for both stages of reaction are close to that found for reaction in the inert atmosphere (-260 kJ mole-') and comparable with theoretical predictions [ 881. There was no pattern of systematic variations in values of E (251326 kJ mole-') for the decompositions [ 11021 of various actinide oxalates [Th(IV), U(IV), Np(IV), Pu(1V) and Pu(VI)] in air, from non-isothermal measurements based on apparent orders of reaction ranging from 0.8 to 1.9.

5.2.2 Metal malonates and succinates There have been comparatively few kinetic studies of the decompositions of solid malonates [1103]. The sodium and potassium salts apparently melt and non-isothermal measurements indicate second-order rate processes with high values of E (962 ? 125 and 385 f 84 kJ mole-', respectively). The reaction of barium malonate apparently did not involve melting and, from the third-order behaviour, E = 481 125 kJ mole-'.

*

225

Malonic acid decomposed in a KBr matrix at 413-440 K to acetic acid and C02 by a first-order process with E = 96 kJ mole-'. Isothermal a-time plots for the vacuum decomposition of nickel malonate [502] at 543-613 K included an initial deceleratory process completed at a 0.11. The subsequent acceleratory period obeyed the Avrami-Erofe'ev equation [eqn. (6), n = 31 t o a 0.5, and thereafter the rate of reaction was unchanged (zero-order obedience) to a = 0.9 (E = 179 kJ mole-'). The kinetic behaviour (a > 0.1) is ascribed to the threedimensional growth of nuclei disposed in regular laminar arrays, so that overlap results in the formation of rectangular aggregates of product which grow by advance in a single dimension (Chap. 3, Sect. 4.5). (This mechanistic representation provides an interesting parallel with conclusions [ 286,10741 for nickel oxalate, where overlap of nuclei disposed in linear array results in the growth of cylindrical assemblages of product. For both salts /3 = 0, and with nickel malonate X = 3 + X = 1, whereas with nickel oxalate X = 3 + X = 2.) The kinetic characteristics of the oxidation of nickel malonate were closely similar to the vacuum reaction. The shapes of the a-time curves were only slightly different but the activation energy was reduced t o 157 12 kJ mole-' (522-593 K), as a consequence of the formation of NiO instead of Ni&. The kinetics of cobalt malonate decomposition at 572-600 K [lo131 were sensitive t o the prevailing reaction conditions and two regions of zero-order dependence ( 0 . 0 6 4 . 3 0 and 0.45-0.72) were found; the latter process was the slower (X-0.2) but both values of E were 181 15 kJ mole-'. The residual products contained Co, COO and Coz03. It was concluded that this reaction was autocatalytic, though the activity of the poorly crystallized residual material was sensitive t o the availability of one or more gaseous products at the reactant-product( s) interface. Reaction proceeded more rapidly in oxygen (524-575 K) particularly in the latter stages, though the shapes of the a-time curves were not consistent with a single interface advance mechanism.

-

-

*

*

5.2.3Metal tartrates Anhydrous sodium and potassium tartrates decompose [1104] at >520 K t o the carbonates through the intermediate oxalate MZC&I406= MzCz04 + 2 C + 2 HzO From non-isothermal measurements, based on apparent first-order obedience, values of E for the overall reactions were 528 and 302 kJ mole-' for the Na and K salts, respectively. During dehydration at 450 K, Rochelle salt formed [1104] a mixture of separate crystallites of the Na and K salts which then decomposed as above. From DTA studies [1105] of the decompositions of Ni, Co and Cu tartrates, the temperatures of onset of reaction and values of E were

226

found to be 583,563 and 493 K and 247, 192 and 151 kJ mole-', respectively.

5.2.4 Metal citrates Decomposition of lead citrate [221] proceeds t o completion in two stages, studied at 488-558 and 553-598 K, yielding C02 as the major gaseous product (
-

5.2.5 Metal maleates and fumarates The vacuum decomposition [1106] of nickel maleate at 543-583 K was predominantly a deceleratory process. Following an initial surface reaction, data fitted the kinetic expression

(1- a ) - 2 ' 3- 0.91

=

kt

based on continued first-order nucleation on small reactant crystallites, the size of which progressively diminish as reactant is converted t o product. The almost amorphous reactant yielded a finely divided Ni + C residue, the growth of the metallic particles being inhibited by deposited carbon. The value of E found, 188 f 1 2 kJ mole-', is similar to that for decomposition of the maleate ion in a KBr matrix [ 2951. The temperature range for the decomposition of nickel fumarate [1107] was somewhat higher (573-613 K) that that of the maleate and Ni3C was detected in the residual product by X-ray diffraction. An initial (-2%) deceleratory reaction was followed by a sigmoid curve which fitted the power law [eqn. (2), n = 21 from 0.03 < a < 0.5. This kinetic behaviour is consistent with nucleation at dislocation lines, overlap of closely spaced particles and growth of cylindrical nuclei (comparable with the mechanism proposed [lo741 for the reaction of nickel oxalate). It was concluded [1107] that anion breakdown occurred at the surfaces of Ni3C particles. The relatively high activation energy (208 f 8 kJ mole-') was

227

attributed to steric factors which preclude the approach of two carboxyl groups to a single nickel atom. The &-time curves for the oxidation reactions [60] of both nickel maleate (534-568 K ) and nickel fumarate (548-583 K) were similar to those characteristic of each reactant in vacuum, though E values were reduced to 150 f 10 kJ mole-'. It was concluded that the distributions of nucleation sites and subsequent patterns of product development were little altered by the change in composition of product from Ni/C (and Ni3C) to NiO. This difference, however, significantly changed the temperature coefficient and stoichiometry of the interface processes, since all carbonaceous material in the reactants was converted t o COz. A constant value of E (150 kJ mole-') was thus found for the oxidations of the four nickel salts studied [60], the maleate, fumarate, formate and malonate. The predominant gaseous products of the decomposition [1108] of copper maleate at 443-613 K and copper fumarate at 443--653 K were C 0 2 and ethylene. The very rapid temperature rise resulting from laser heating [1108] is thought t o result in simultaneous decarboxylation to form acetylene via the intermediate - C H = CH-. Preliminary isothermal measurements [487] for both these solid reactants (and including also copper malonate) found the occurrence of an initial acceleratory process, ascribed to a nucleation and growth reaction. Thereafter, there was a discontinuous diminution in rate (a 0.4), ascribed to the deposition of carbon at the active surfaces of growing copper nuclei. Bassi and Kalsi [ 12821 report that the isothermal decomposition of copper(I1) adipate at 483-503 K obeyed the Prout-Tompkins equation [eqn. (9)] with E = 191 kJ mole-'. Studies of the isothermal decompositions of the copper(I1) salts of benzoic, salicylic and malonic acids are also cited in this article.

-

5 . 3 METAL SALTS OF AROMATIC CARBOXYLIC ACIDS

Kinetic studies of the decompositions of these substances have usually been concerned with the simplest compounds available, notably the benzoates (some of which melt), phthalates and the mellitates (which resemble the oxalates in that they are often prepared as hydrates and, after dehydration, contain no hydrogen). Several of the anhydrous transition metal salts of aromatic carboxylic acids are amorphous t o X-rays, presumably due to the difficulties experienced in the generation of a regular lattice for compounds in which both cations and anions tend to form two or more bonds possessing appreciably covalent character. Accordingly, decompositions proceed in a disordered phase and some reactants may not be correctly classified as solids but may be more accurately regarded as glasses or vitreous material. Kinetic characteristics of the decompositions of these substances resemble reactions proceeding in the homogeneous phase in that yield-time data fit rate equations of the first, second or third orders [eqns. (15)-(17)]. A second reason for the

228 TABLE 1 6 Summary Qf kinetic results for the decomposition of metal salts of aromatic carboxylic acids [88,460,1109,1110] Most processes were deceleratory throughout, fitting a rate equation based on the reaction order eqns. (15)-(17). ( * indicates a nucleation and growth reaction.) B = Basic salt; M = melting. Results expressed as (order) activation energy/kJ mole-' (temperature range/K) Cation

Mellitate

Benzoate

Phthalate

( 0 , l ; M ) 158 (573-673)

(1)168 (593-673)

Cr(II1) B

(2) 126 (573-643) { ( 3 )208 (743-823)j (2) 254 (733-853) Mn(I1) (0) 224 (773-853) Fe(II1) B (2) 182 (493-573) ( 0 ) 172 (693-823) co (2) 276 (663-728)

I I

1

1

(M)

195 (>630)

174 (553-643) I ((1) 161 (673-773) 1 2 ) 193 (573-723) (*)

Ni Cu(11) Zn A1

I

(0;M) ( 2 ) 191 (591-668) (1)162 (526-558) (3) 210 (733-853) (3) 190 (655-758) (3) 190 (798-866) (0, *) 167 (468-523)

190 (581-643)

1

Several reactions proceed to completion in two stages, shown bracketed { }.

pronounced deceleratory nature of some reactions is the relatively large carbon yield retained in the residue. Deposition of such material may inhibit the growth of metallic particles so that the observed rate process is controlled by a maintained nucleation step in a reaction for which growth of the nuclei is effectively prevented. Published kinetic observations [88,460,1109,1110] for a number of decompositions are briefly summarized in Table 16. Sigmoid curves, attributable t o nucleation and growth reactions, were observed for the decompositions of cobalt phthalate and silver mellitate: these are marked * in Table 16. The decomposition of nickel terephthalate [88]obeys the Avrami-Erofe'ev equation [eqn. (6)],for which n is 1.01.5 and E = 226 ? 8 kJ mole-'. Decompositions of Co-Ni mixed mellitates are discussed in Sect. 7. 5.4 GENERAL DISCUSSION

The literature available constitutes neither a comprehensive nor a particularly systematic investigation of the kinetics of decompositions of metal carboxylates. (A comparable remark could also be made at the end of each of the Sections 1-4 and 6.) The simplest reactants have naturally been accorded the greatest interest. Reactions of certain formates and

229

oxalates and nickel salts have been the subject of detailed scrutiny. These results have contributed to the general understanding of the thermal behaviour of solids. Many decompositions of metal carboxylates proceed by nucleation and growth processes in which the surface of the solid product may be an active catalyst for anion breakdown. While different studies of the same compound have often reported obedience to the same kinetic expression [f(a)-time], agreement between Arrhenius parameters has usually been less than satisfactory and this has made discussions concerning the mechanisms of reactions proceeding at the interface rather speculative. Such uncertainties also make it more difficult t o identify trends in kinetic behaviour through comparisons of observations for a series of related compounds in which either the cation or the anion is systematically varied. Marked changes, in A , E and/or f(a) are sometimes apparent between members of such a series and are not easily explained, whereas similarities are found between substances which are not chemically or even structurally related. The sensitivity of kinetic characteristics t o features of the reactant or reaction conditions (e.g. disposition of Ni(HC02)2within the reaction vessel [433] or pelleting of C U ( H C O ~[97]) )~ makes it most important that these features should be carefully defined when reporting rate data and drawing mechanistic conclusions. The reactions of some aromatic metal carboxylates are on the borderline of classification as solid-state processes. While there is no evidence of liquefaction, rates of decomposition in the poorly crystallized or vitreous reactant obey kinetic expressions more characteristic of reactions proceeding in a homogeneous phase. Pyrolyses of formates, oxalates and mellitates yield CO and C02 (H2, H2O etc.) as the predominant volatile products and metal or oxide as residue. It is sometimes possible to predict the initial compositions from thermodynamic considerations [ 94 J , though secondary reactions, perhaps catalyzed by the solids present, may result in a final product mixture that is very different. The complex mixtures of products (hydrocarbons, aldehydes, ketones, acids and acid anhydrides) given [1109] by reactants containing larger organic groupings makes the collection of meaningful kinetic data more difficult, and this is one reason why there are relatively few rate studies available for the decompositions of these substances. Although some progress has been made in determining the geometry of interface advance through interpretation of observed f(a)-time relationships for individual salts, the reasons for differences between related substances have not always been established. Nickel carboxylates, for which the most extensive sequence of comparative rate studies has been made [40,88,375,502,1106,1107,1109],show a wide variety of kinetic characteristics, but the controlling factors have not yet been satisfactorily determined. Separate measurements of the rates of nucleation and of growth are not usually practicable.

230

Factors proposed as determining the thermal stability of metal carboxylates include the radius [ 10401, electronegativity [ 409,10691 or ionization energy [ 10791 of the cation, the covalent character [ 10401 or strength of the M - O bond, the enthalpy of formation of the metal oxide [88], crystal field stabilization energies [lo791 and, where appropriate, the length of an alkane chain [1052,1053]. Some of these are interdependent or derived from a common factor. Where reaction proceeds in oxygen, there is fairly wide agreement that the initial step is cation oxidation [409,1069]. From a study of the decompositions of several rhodium(I1) carboxylates, Kitchen and Bear [llll]conclude that in alkanoates (e.g. acetates) the a-carbon-H bond is weakest and that, on reaction, this proton is transferred to an oxygen atom of another carboxylate group. Reduction of the metal ion is followed by decomposition of the a-lactone to CO and an aldehyde which, in turn, can further reduce metal ions and also protonate two carboxyl groups. Thus reaction yields the metal and an acid as products. In aromatic carboxylates (e.g. benzoates), the bond between the carboxyl group and the aromatic ring is the weakest. The phenyl radical formed on rupture of this linkage is capable of proton abstraction from water so that no acid product is given and the solid product is an oxide. Identification of E values for carboxylate decompositions with the energy barrier to a specific chemical step at the reaction interface (the rate-determining process) is difficult. In such rate processes, a variety of steps may, in principle, occupy this role including (as pointed out above) fission of the bonds M - O , C-0 or R - C in the R-CO-O-M group, or electron transfer. If the reaction is catalyzed by the surface of a metal or an oxide product, the value of E determined may be a composite parameter [ 361, including contributions from temperaturedependent changes in concentrations of surface (interface) participants. There is uncertainty regarding the significance t o be attached to the temperature coefficient of many heterogeneous rate processes. From the correlations found [88] between magnitudes of E for the decompositions of oxalates and mellitates and the enthalpy of formation of the appropriate metal oxides, it was concluded that the activation step in carboxylate breakdown was rupture of the M - O linkage. This approach was applied [88] to the range of nickel salts for which E values were available, assuming that this parameter contained contributions from the following terms. (i) An energy requirement for the dissociation of each -C02-Ni- bond participating (113 kJ mole-'). (ii) A reduction of the energy barrier by -20 kJ mole-' resulting from autocatalysis where the anion was chemisorbed on a metal particle. (iii) A reduction in the energy barrier by -40 kJ mole-' where resonance stabilization of the activated anion complex was possible. This model was consistent with the observations available [88,1106,1107], but may require modification when an agreed value of E for the decomposition of nickel formate [375] is obtained.

231

6. Decompositions of coordination compounds

It is not easy to provide a rigorous, yet comprehensive, definition of that group of substances which are most usually referred to as “coordination compounds”, “coordination complexes” or “complex compounds”. With certain qualifications, Cotton and Wilkinson [ 11121 recognize the formation of substances of this type when a central atom or ion (M) combines with one or more ligands (L, L’ L” etc.) to form a species [ML,LLLK]”. M, the ligands, and the resulting species may or may not bear a charge, n can be a positive or negative integer or zero. Those ligands in the inner coordination sphere are distinguished from those ions, counter ions or ligands (X) in the outer coordination sphere, where X may be ions, polyatomic or coordinated groupings. The overall compound may, therefore, be represented generally as

[ML,LkL: ...I” [X,,Xh ,X: ...]”“Classical complexes” are identified [1112] as those species in which the central metal ion possesses a welldefined oxidation number and a set of ligands with a discrete electron population. “Non-classical complexes”, in contrast, involve highly covalent and/or multiple metal-ligand bonding resulting in indistinct oxidation numbers for both participants. This section is almost entirely concerned with the kinetics of solid phase decompositions of classical coordination compounds, since most of the information available refers t o these substances. The hydrates, in which the ligands are water only, are correctly classified under the present heading, but as their dehydrations have been so intensively studied, a separate section (Sect. 1 ) has been devoted to the removal of water from crystalline hydrates. A separate water elimination step also preceeds many decomposition reactions. There is an extensive literature devoted t o the preparation and structure determination of coordination compounds. Thermal analysis (Chap. 2, Sect. 4 ) has been widely and successfully applied in determinations [1113, 11141 of the stoichiometry and thermochemistry of the rate processes which contribute t o the decompositions of these compounds. These stages may overlap and may be reversible, making non-isothermal kinetic data of dubious value (Chap. 3, Sect. 6). There is, however, a comparatively small number of detailed isothermal kinetic investigations, together with supporting microscopic and other studies, of the decomposition of coordination compounds which yields valuable mechanistic information. As with other crystalline substances, on heating coordination compounds may melt, sublime, decompose, or undergo a solid phase transition. The greater complexity of the constituents present increases the number of types of bond redistribution processes which are, in principle, possible within and between the coordination spheres. The following solidstate transitions may be distinguished; (i) changes in relative dispositions

232

of the lattice components, without modification of the inner coordination sphere, (ii) stereochemical changes within the inner coordination sphere, (iii) structural rearrangement of the inner sphere, (iv) exchange of ligands between the inner and the outer coordination spheres, (v) reaction within the inner sphere, which may include changes in oxidation state of the central ion, and (vi) intermolecular reaction between coordination spheres (e.g. as in the solid-state polymerization of vinyl complexes [1115]). There is also the possibility that changes of more than one type may proceed concurrently. The chemical changes, which occur during decomposition, are similarly complicated by the increased possibilities of bond reorganization which exist in reactants which contain a greater number of participating groups. Thermal stability will be influenced by the chemical properties of all components, the central ion (atom) M, the several ligands (L,L',L'' ...) and any counter ions (X,X',X" ...), and their possible interactions. As with other solids, reactivity and kinetic behaviour may be significantly influenced by particle size, presence and concentrations of impurities and imperfections, pretreatment, prevailing atmosphere, etc. There is also the possible occurrence of melting, which is less than adequately considered in many reports. Many investigations of the decompositions of coordination compounds have been concerned with the qualitative identification of the steps involved, characterization of any intermediates formed and comparisons of reactivities of related salts containing systematically varied constituents. Observations and conclusions from such work [1113,1114] are outside the scope of this review, though the results can serve to identify systems worthy of more detailed investigation. The content of this section, reflecting the content of the relevant literature, is restricted to accounts of the behaviour of a number of representative substances. Features distinguishing these reactions from those of simple salts are emphasized. 6.1 METAL AMMINE COMPOUNDS

Decomposition of the metal ammines have probably been most extensively investigated. Some qualitative features of the thermal decomposition of metal ammine compounds are conveniently illustrated [111611181 by the somewhat contrasting behaviour of the compounds [Cr(NH&]X, and [CO(NH&,]X3where X is C1- or Br-. During decomposition of the chromium compound, the oxidation number of the metal remains unchanged, viz.

233

Values of E for the first reaction were [1118] 124 and 180 kJ mole-' for X = C1- and Br-, respectively. For comparison, activation energies for the deaquation [1119] of [Cr(NH,), (HzO)]X3were 110, 120, 128 and 9 1 kJ mole-' for X = C1-, Br-, I-, and NO,, respectively. The overall reaction of the cobalt compound, however, involves metal ion reduction and may be represented as 6 [CO(NH,),]X, = 6 COXZ+ Nz + 6 NH& + 28 NH3 Reaction involves more than a single step. The relative thermal stabilities of the hexammine salts, as determined by the temperatures of onset of the reaction, are C1- > Br- for the cobalt compounds but Br- > C1- > I- for the chromium compounds. When X = NO,, rapid oxidation developed into an exothermic explosive reaction of both the Cr and the Co salts. 6.1.1 Cobalt(III) ammine azides

Isothermal studies at 370-420 X have been made of the kinetics of decomposition of [ C O ( N H ~ ) , ] ( N ~[CO(NH,),(N,)](N~)~ )~, and both cisand trans-[Co(NH,),(N3),](N3) [1120]. Results are interpreted as indicating the operation of a common reaction mechanism which is not greatly influenced by either the constituents or the stereochemistry of the complex cation. The reactions of all four compounds may yield either CON or C O ( N H , ) ~ ( Nas ~ )the ~ residual product: the alternative decompositions may be represented as

(Analogous expressions may be written for the other reactants.) The reaction yielding CON is characterized by an induction period which is reduced by the addition of the solid product and prolonged by the presence of NH3. Following a rapidly completed acceleratory process, the main reaction is predominantly deceleratory and satisfactorily described by the first-order equation. Values of E for both induction periods and the main reactions of the four compounds mentioned were in the range 84-109 kJ mole-'. The alternative reaction, yielding C O ( N H & ( N ~ ) ~ , exhibited simoid a-time curves and values of E were greater, 170-230 kJ mole-'. The marked sensitivity of reaction rate t o the prevailing pressure of ammonia reduced the accuracy of kinetic analyses. The discussion [1120] considers reasons for this unusual feature whereby the salt may decompose by alternative stoichiometrically and kinetically different processes. It is concluded that the chemical change occurring in any particular sample is determined during the induction period. The first step in reaction is identified as electron transfer (also found for decomposi-

234

tions of other ionic azides)

[cO(NH3)6]3' + e -

+

[CO(NH3)6]2'

followed by

[CO(NH3)6]" + 2 N3

-+

{ C O ( N H ~ ) Z ( N ~+) ~4)NH3

where the bracketed, {}, product is an unstable, disorganized material which may either decompose further t o give CON or recrystallize to form a stable crystalline phase of the same composition, i.e. solid C O ( N H ~ ) ~ ( N ~ ) ~ . The balance between these alternatives is apparently influenced only by factors operating within a highly localized zone at the reaction interface. 6.1.2 Ammine cobalt thiocyanates The solid state isomerizations of the thiocyanates [ Co(NH,),( SCN)]Xz (where X = C1- or SCN-) t o the corresponding isothiocyanates [Co(NH3),(NCS)]XZ have been studied in detail [1121,1122]. The reactions are topotactic and the well-oriented products are similar t o the salts prepared from solution. The mechanism suggested [ 11211 involved the intermediate formation of [CO(NH,),]~' which then reacted with the nitrogen of a neighbouring SCN-. This model was tested by studies of the reaction of [Co(NH,),(SCN)]( S'4CN)2, from which it was concluded that >45% of the cations isomerize by the dissociative path. N o exchange was observed in similarly treated [CO(NH,),(NCS)](S'~CN),.Isomerizations of [ Co( NH3),(NOz)](N03)2 to [ Co( NH3)5(ONO)] (NO & [ 1122,11231 and of Pd [As(C6H5),]z(SCN)2 to the corresponding isothiocyanate [ 11241 are believed t o be largely intramolecular solid-state processes. The rate of isothermal decomposition of [ C O ( N H ~ ) ~ ( N C S ) ] ( C I O ~ ) ~ depends on the particle size of the reactant [486]. When (Y < 0.09, the decomposition of large particles is relatively rapid and the value of E (138 kJ mole-') is independent of crystallite size. However, for a > 0.09, small particles decompose more rapidly and, although the activation energy is generally reduced, values increase with increasing particle sizes from 88 to 1 1 7 kJ mole-'. The explanation provided for these observations is that, owing t o strain, the large particles possess the greater number of nucleation sites. However, when ar > 0.09, escape of ammonia from the larger particles is restricted and the rate of decomposition reduced accordingly. This interpretation was confirmed by the observed inhibiting effect of NH3 on the decomposition of small crystals.

6.1.3 Ammine aquo cobalt salts Dynamic and isothermal thermogravimetric measurements [ 12841 for the olation reactions

2 [CO(NH,)~(OH)(OH~)]XZ = [(NH~)~CO(OH)~CO(NH~)~IX~ + 2 HzO

235

with X = C1-, Br- and SO',- gave E = 84, 180 and 105 kJ mole-', respectively. For the analogous reaction of ~is-[Co(en)~(OH)(0H~)]S~0~, the activation energy found was 205 kJ mole-'. 6.1.4 Ammine nickel salts The vacuum decomposition of [Ni(NH3)6](C104)2proceeds t o completion in two stages [1125]. In the lower temperature reaction (353413 K), 4 NH3 are lost by a reversible process for which E = 71 kJ mole-'. The a-time curves are predominantly deceleratory though, at the lowest temperatures, a short induction period was found. The rate of the recombination reaction was apparently diffusion controlled ( E 10 kJ mole-'). The second stage of the reaction, decomposition of [Ni(NH3)2](C104)2, was studied at 513-553 K and above this range became explosive. Isothermal a-time curves for the irreversible rate process were sigmoid and the reaction fitted the Avrami-Erofe'ev equation [eqn. (6), n = 21 and E = 137 kJ mole-'. The kinetic characteristics of this reaction were very similar to the behaviour of NH4C104over the same temperature interval. The stoichiometry of decomposition of [Ni(NH3)4](NCS)2was dependent on the method of salt preparation [1126]. Ammonia was lost in three successive steps (-NH3, -NH3, -2 NH-J from the solution-prepared salt, but the first intermediate could not be isolated from the similar reaction of material prepared by heterogenous reaction. The difference in behaviour was ascribed to differences in perfection of the crystallites resulting from the alternative preparative methods.

-

6.2 METAL PYRIDINE COMPOUNDS

Comparative studies [1127] of the kinetics of decomposition of similar salts containing related pyridine ligands have been used to investigate the strength of M-N bonds in coordination compounds. Non-isothermal DSC measurements were used to determine values of E for the reactions NiL,Cl,(c)\

/NiL2C12(c) + 2 L(g)[L = pyridine(py) or 3-methylpyridine] NiLC12(c)+ 3 L(g)[L

=

4-methylpyridine]

(c = crystal and g = gas) Activation energies were in the sequence py < 4-mepy < 3-mepy which is the order of M-N bond strengths. Isothermal a - t i m e curves for the decomposition at 363-464 K of the pseudo octahedral compounds NiL2(NCS)2 (L = py, 3-picoline or quinoline) to NiL(NCS)2and volatilized L, obeyed the contracting volume equation [eqn. (7), n = 31. E values decreased in the sequence L = py > 3-picoline > quinoline and this order was ascribed t o the effect of increasing ligand volumes [ 11281.

236

Liptay et al. [1129] used DTA and DTG peak temperatures as a measure of the relative thermal stability for the compounds ML,X, (with M = Mn(II), Co(II), Ni(II), Cu(II), Zn(II), or Cd(I1); L = py, 2-, 3-, or 4picoline; X = C1-, Br-, I-, OCN-, SCN-, NO;, or SO:-; n = 2, 3, 4, or 6; and z = 1 or 2). Thermal stabilities were related t o the strengths of the M-N bonds. 6.3 COMPOUNDS CONTAINING POLYDENTATE LIGANDS

Coordination compounds containing bidentate ligands are often thermally more stable than those comprised of related monodentate ligands, e.g. ethylenediamine (en) complexes dissociate at a higher temperature than those of ammonia or pyridine. Compounds containing a ring structure, such as coordinated salicylaldehyde (sal) and acetylacetonate (acac), are particularly stable, and may often be sublimed without melting.

Sal

acac

[ C ~ ( e n ) ~ complexes lX~ [1113,1130] decompose in nitrogen to yield Coxz and give c0304 in air, the sequence of stability with variation in X is SCN- < C1- < I- = Br- < SO:- < NO,. Mass spectrometric analysis of the products of reaction in vacuum indicated the formation of large quantities of NH3 and no ethylenediamine. Decomposition does not, therefore, involve stepwise release of the ligand. The corresponding chromium compounds [ Cr(en)3]X3 evolve ethylenediamine [1131] and the values of E determined using non-isothermal measurements were 105 and 182 kJ mole-' for X = C1- and SCN-, respectively. Hughes [1132] reported a value of E = 175 kJ mole-' for X = C1and showed that the decomposition rate is sensitive t o sample disposition. Amine evolution from both the (en) and propenediamine (pn) compounds was catalyzed by NH4C1 [1132,1133] or NHSCN [1133,1285], addition of small amounts of these substances resulting in a substantial reduction of E. The influence of NH4C1is ascribed [1132] t o the dissociation products, since HCl promoted the reaction but NH&r and NH41 showed no such effect. Isothermal and dynamic studies [ 12861 of the thermal deamination and racemization reactions of (+)ssp-[Cr(en)3](NCS)3gave activation energy values 113 and 100 kJ mole-', respectively. The mechanisms of these and

237

related reactions are discussed with reference t o the crystal structures of the compounds concerned. The compounds FeA312, FeB312 and FeC312, where A = 1,lO-phenanthroline (phen), B = 4,7-dimethyl(phen) and C= 4,7-diphenyl(phen), lose ligands in a stepwise manner on heating [1134] The first dissociation step obeyed the rate equation of order 0.7 (approximately the contracting volume expression [eqn. (7), n = 31) and values of E ranged from 92 to 264 kJ mole-', indicating that the stability of the compounds increased in the order A < C < B. The first stage of reaction on heating the various mixed compounds FeA2B12, FeA2C12, FeB2A12 and FeC2A12 was the release of one mole of ligand A(phen). The increase in values of E to between 117 and 222 kJ mole-', from 92 kJ mole-' for FeA312, was ascribed t o a strengthening of the Fe-N bond resulting from 4,7-substitution in the (phen) ligand. It is believed [1135,1136] that the decomposition of metal complexes of salicyaldoxime and related ligands is not initiated by scission of the coordination bond M-L, but by cleavage of another bond (L-L) in the chelate ring which has been weakened on M-L bond formation. Decomposition temperatures and values of E, measured by several non-isothermal methods were obtained for the compounds M(L-L)2 where M = Cu(II), Ni(I1) or Co(I1) and (L-L) = salicylaldoxime. There was parallel behaviour between the thermal stability of the solid and of the complex in solution, i.e. Co < Ni < Cu. A similar parallel did not occur when (L-L) = 2-indolecarboxylic acid, and reasons for the difference are discussed [ 11361. Where M = Cu(II), Ni(II), and Pd(I1) and (L-L) = resacetophenoneoxime [1135], the solid state sequence of stabilities (Pd > Ni > Cu) differs from that in solution (Pd > Cu > Ni). It appears that decomposition of the Pd(I1) compound is initiated by M-L bond scission. The first reaction in the decomposition of trans-[ CoL2X2](H502)X2, where L = (en) or (pn) and X = C1-, is the evolution of H20 and HC1 [ 11371. The (en) compound developed nuclei which advanced rapidly across all surfaces of the reactant crystals and thereafter penetrated the bulk more slowly. Kinetic data fitted the contracting volume equation [eqn. (7), n = 31 and values of E (67-84 kJ mole-') vaned somewhat with the particle size of the reactant and the prevailing atmosphere. Nucleus formation in the (pn) compound was largely confined t o the (100) surfaces of reactant crystallites and interface advance proceeded as a contracting area process [eqn. (7), n = 21. It was concluded that layers of packed propene groups within the structure were not penetrated by water molecules and the overall reaction rate was controlled by the diffusion of H 2 0 to (100) surfaces. Decomposition of trans-[Co(pn),Cl,] (H502)C12[ 11381 is accompanied by some solid state isomerization t o the cis form. Reported values of E, based on first-order behaviour, were 138 and 500 kJ mole-' for decomposition and isomerization, respectively. The rate of isomerization in the

238

corresponding bromide, t o the cis form, is greater [1139] than the rate of evolution of HzO and HBr: all three reactions obeyed first-order kinetics does not with E = 117 kJ mole-'. Anhydrous tran~-[Co(pn)~Br~]Br isomerize. The related chromium compound [1140], trans-[Cr(pn),Br,]Br * HzO, undergoes rapid dehydration at 395-419 K by a first-order process for which E = 96 kJ mole-' and this is accompanied by some 10%isomerization to the cis compound. At higher temperatures, 433-473 K, the residual anhydrous trans compound isomerizes in the solid state; this is also a first-order process and E = 180 kJ mole-'. 6.4 OTHER KINETIC STUDIES

Values of E and enthalpies of decomposition of PtXz(C3H6), PtXz(C3H6)Lzand PtXz(C3H6)(L-L) (where X = C1- or Br-, L = pyridine or 4-methylpyridine, and (L-L) = 2,2'-bipyridyl or ethylenediamine) have been determined [1141]. Results were used t o measure P t - C bond strengths in these trismethyleneplatinum( IV) compounds. These were found to be in the range 112-124 kJ mole-'; the slightly higher values for the bromo compounds were attributed to the cis influence of the halide ligands. Decomposition products included both propene and cyclopropane and detailed reaction mechanisms are discussed. The decomposition of Ir0zCOC1(PPh3)z in nitrogen at 379-397 K [1142] yields O 2 by a nucleation and growth reaction which obeys the Avrami-Erofe'ev equation [eqn. ( 6 ) , n = 21 and E = 232 kJ mole-'. At higher temperatures (405-425 K), a phase boundary mechanism is rate controlling, the contracting area equation [eqn. (7), n = 21 is obeyed, and E = 180 kJ mole-'. Ball and Pope [ 11431 have h a d e a detailed study of the reversible reaction [IrC1CO(PPh3)z](s)+ HCl(g) * [IrHC1zCO(PPh3)z](s) The rate of the addition reaction is determined by a phase boundary process, the contracting area expression [eqn. (7), n = 21 is obeyed and E = 37 kJ mole-'. The value of E for decomposition of the trans-chloro isomer (right-hand side of above equation) is 51 kJ mole-', which is less than that (130 kJ mole-') for HC1 elimination from the cis-chloro isomer. An unusual variation in kinetics and mechanisms of decomposition with temperature of the compound dioxygencarbonyl chloro-bis(tripheny1phosphine) iridium(1) has been reported by Ball [1287]. In the lowest temperature range, 379-397 K, a nucleation and growth process was described by the Avrami-Erofe'ev equation [eqn. (6), n = 21. Between 405 and 425 K, data fitted the contracting area expression [eqn. (7), n = 21, indicative of phase boundary control. At higher temperatures, 426443 K, diffusion control was indicated by obedience to eqn. (13). The

239

two-dimensional formal geometric parameter apparent in each of these rate equations suggests that the kinetics of decomposition were powerfully influenced by the plate morphology of the reactant. Increasing temperatures resulted in significant reduction in the magnitude of the apparent activation energy: for the three ranges mentioned above, values 1014-2 and 10’ s-l, of E and A were 232,180 and 84 kJ mole-’ and respectively. The rate of isotopic exchange in the solid state, between cobalt in the cation and in the anion of [60Co(H20)6] [Co(edta)] - 4 H20, was increased [1144] by irradiation (100 Mrad) of the reactant. It was concluded that exchange occurred via vacancies, rather than through motion of a “ring” of cobalt atoms, one from a cationic site and the other from a neighbouring anionic site. 6.5 GENERAL COMMENT

It is apparent, from the above short survey, that kinetic studies have been restricted t o the decomposition of a relatively few coordination compounds and some are largely qualitative or semi-quantitative in character. Estimations of thermal stabilities, or sometimes the relative stabilities within sequences of related salts, are often made for consideration within a wider context of the structures and/or properties of coordination compounds. However, it cannot be expected that the uncritical acceptance of such parameters as the decomposition temperature, the activation energy, and/or the reaction enthalpy will necessarily give information of fundamental significance. There is always uncertainty in the reliability of kinetic information obtained from non-isothermal measurements. Concepts derived from studies of homogeneous reactions of coordination compounds have often been transferred, sometimes without examination of possible implications, to the interpretation of heterogeneous behaviour. Important characteristic features of heterogeneous rate processes, such as the influence of defects and other types of imperfection, have not been accorded sufficient attention. Formulation of the detailed mechanisms of decomposition of coordination compounds are likely to remain difficult. Reliable kinetic and supporting observations are not easily obtained where several initiating reactions are possible and subsequent chemical changes may occur, before the first-formed product has left the crystallite of reactant.

7. Decompositions of solid solutions and double salts Double salts and solid solutions exist as a single phase, but contain two components. Such reactants incorporate certain features in common with two phase systems which interact on heating (discussed in Chap. 5): in

240

principle two compounds are present and mixtures of solids sometimes form solid solutions as a necessary precursor step in product formation. The reactivity of an existing, relatively well-crystallized two-component material is likely to be appreciably less than that of the finely divided, defective, transient and probably inhomogeneous solid solution which may be produced briefly at a reaction interface. Some properties of such dynamic intermediates, which provide the contact and reaction path between two crystalline reactants, will be discussed in Chap. 5. The kinetics of the chemical changes which occur on heating a solid solution are frequently different from those characteristic of the individual components and measured variations of such effects have provided insight into the mechanisms of decompositions of pure salts. References have been made to the influence of homogeneously incorporated additives in the previous survey. The doping of solids, the controlled admission of selected impurities into the crystalline host lattice, has, for example, been exploited as a convenient method of varying the concentration of electronic imperfections in the reactant. From the observed influence of changes in concentration of the additive, the roles of such participating species as electrons or positive holes in the reaction can be deduced. The kinetics of decomposition of some double salts are characteristic of that particular solid alone, and, in this respect, such a reactant resembles a simple salt. Other substances react through two, or more, distinct steps and the rate processes involved resemble the behaviour of the separate pure components. In principle, the components of a double salt may separate before, during or after the breakdown of the less stable constituent and catalytic influences may be apparent. While the terms “solid solution” and “double salt” provide convenient descriptive titles for the groups of compounds considered here, these are not mutually exclusive. The number of possible reactants is obviously very large and for every mechanistic study of the decomposition of a pure solid, it could be worthwhile t o determine the influence on the kinetics of a variety of additives over a range of concentrations. The consequences of changes in reactant composition on rate behaviour must obviously be distinguished from the variations which arise from other sources, including sizes, perfection and damage t o surfaces of crystals in different preparations, unintentional impurities, the availability of products during successive processes, etc. The addition of a second component to a solid generally reduces the melting point and the possible development of a liquid phase must be considered in the interpretation of rate observations. It is premature t o attempt to identify, from the few kinetic studies reported, generalized conclusions on patterns of behaviour, but certain characteristic features of the rate processes are apparent. The few systems t o which reference is made below illustrate certain characteristics of the decompositions of these reactants. Some of the examples referred t o explore the influence of additives in studies primarily concerned with the mechanism

24 1

of decomposition of a particular solid while others are concerned with the preparation of a two-component solid product. Few studies have been aimed directly at determining kinetic features of the decompositions of solid solutions. 7 . 1 DECOMPOSITIONS OF TWO-COMPONENT SOLID SOLUTIONS

Many of the most detailed kinetic studies of the reactions of these solids have been concerned with mixtures containing a common ion, (AJ3)X.

7.1.1Dolomite, (Ca,Mg)C03 There have been several kinetic studies of the calcination of dolomite [29], a reaction of considerable technological importance. As in many reversible reactions, the rate of carbon dioxide release is sensitive t o the prevailing pressure of this product (Pco2) in the vicinity of the reaction interfaces. At low pressures (Pco2 < 1 2 Torr), reaction proceeds to completion in a single stage between 900 and 950 K CaMg(C03)2= MgO + CaO + 2 COz When Pco2 > 24 Torr, a higher decomposition temperature (-960 K) is required and the reaction is CaMg(C03)2= CaC03 + MgO + C 0 2 Even higher temperatures are required for calcite dissociation. As Pco2 is increased to 760 Torr, the reaction temperature rises t o 1170 K and the extent of dissociation is diminished [29]. The rate of decomposition of dolomite in vacuum [734] was intermediate between those for magnesite and calcite. Ranges of study were: magnesite 810-870 K, dolomite 910990 K, and calcite 990-1050 K. Values of E were in the different sequence, magnesite < calcite < dolomite. Magnesite, which would decompose very rapidly at the temperature of dolomite dissociation, is, therefore, relatively stabilized, whereas the reactivity of calcite is enhanced in the mixed crystal. It was concluded [ 7341 from visual inspection and chemical analysis of partially decomposed dolomite, that reaction was initiated at the outer surfaces of the crystallites and the interface established advanced thereafter into the bulk. The deceleratory a-time curves obeyed the contracting volume equation [eqn. (7), n = 31 and the values of E determined were between 206 and 232 kJ mole-'. These values of E were generally greater than those reported for other studies (-190 kJ mole-') which are in the range mentioned [121] for CaC03 dissociation and slightly larger than the enthalpy of that reaction. On exposure of the residue from vacuum decomposition of dolomite t o C02, the gas uptake at 1070 K was

242

somewhat less than the quantity required t o convert all the CaO present to CaC03. Dolomite decomposition is, therefore, identified as an interface reaction yielding, as the initial residual product, the solid solution (Ca,Mg)O. This mixed oxide subsequently separates and CaO may react with COz if the latter is available. The decomposition of dolomite shows many points of similarity with the reactions of calcite and of other single carbonates of Group IIA metals (Sects. 3.1.1 and 3.1.2): the reaction is reversible, occurs at an interface, and both apparent kinetic parameters and reactivity are influenced by the prevailing COz pressure. Powell and Searcy [1288], in a study of CaMg(CO& decomposition at 7 5 0 4 0 0 K by the torsion-ffusion and torsion-Langmuir techniques, conclude that dolomite and COz are in equilibrium with a glassy phase having a free energy of formation of (73 600 - 36.8T)J from 0.5 CaO + 0.5 MgO. The apparent Arrhenius parameters for the decomposition are calculated as E = 194 kJ mole-' and activation entropy = 93 JK-' (mole

coz)-l.

Thermal analysis has been widely and usefully applied in the solution of technical problems concerned with the commercial exploitation of natural dolomite including, for example, the composition of material in different deposits, the influence of impurities on calcination temperatures, etc. This approach is not, however, suitable for the reliable determination of kinetic parameters for a reversible reaction (Chap. 3, Sect. 6). The mechanism of dolomite decomposition contrasts, in some respects, with the behaviour of other mixed carbonates containing Group IIA cations. The reactions of SrC03 : CaC03 solid solutions (95 : 5, 50 : 50 and 40 : 60 molar ratios) have been described by Zemtsova et al. [ 12891. The constituents of the (1: 1) double carbonate SrBa(CO& separate [1145] and the onset of decomposition of SrC03precedes that of BaC03, though the two rate processes overlap t o some extent [ 11461. The initial reaction of the triple (Ca, Sr, Ba) carbonate yields CaO and a double (Sr, Ba) salt which does not contain the individual carbonates (SrC03and BaC03). 7.1.2 Mixed hydroxides

Decompositions of crystalline mixed hydroxides t o mixed oxides often occur at temperatures lower than those required t o produce the same phases through the direct interaction of metal oxides. This route thus offers an attractive approach for the preparation of catalysts of high area and activity [1147]. Detailed kinetic investigations comparable with those for the dehydroxylations of a number of pure hydroxides (Sect. 2.1) are not, however, available. Yur'eva et al. [1147] prepared Cu, Ni, Co, Mn, Zn, Fe and Mg chromites of areas 1 0 - 6 0 mz g-' by heating mixtures of hydroxides to

243

-870-1170 K. The more usual method of preparing these compounds by heating mixtures of oxides at 1270 K yields a low area product. Makarova and Zorya [1148] detect ZnCr204as the only phase present after heating E-Zn(OH), + 2 Cr(OH)3 at 670 K and there was infrared evidence for the formation of NiCr204 and MgCr204after heating appropriate mixtures of the oxides to 593 and 623 K, respectively. Roginskii et al. [1149] conclude that precipitation of Ni(OH)2 and Mg(OH)2 (from a solution of the nitrates) yields the solid solution and, on heating, this is transformed from the hexagonal lattice of the mixed hydroxide to the cubic mixed oxide in a single stage. It is suggested that the nickel component participates in initiation of dehydroxylation since this reacts at a lower temperature than Mg(OH),. Maksimov et al. [1150] find that the mixed oxide produced by the decomposition of C U ( O H )+~ Mg(OH), contains a relatively higher proportion of Cuz+ in the surface than in the bulk and that the distribution of this cation in the product is inhomogeneous. 7.1.3Mixed carboxylates ( a ) Mixed formates

The addition of nickel formate t o magnesium formate significantly reduced the decomposition temperature [ 11511. The acceleratory period characteristic of the decomposition of pure Mg(HCO 2)2 was eliminated and the value of E was substantially diminished. For the double (Zn,Ba) and (Cu,Ba) formates, the rate of decomposition [1152] of the less stable component (Zn or Cu) was slower and that of the more stable component (Ba) more rapid than the values characteristic of pure preparations of these substances. ( b ) Mixed oxalates

Decompositions of oxalates containing the strongly electropositive metals yield an oxide product but the more noble elements yield the metal. Discussion of the mechanisms of these reactions and, in particular, whether metal formation necessarily involves the intermediate production of oxide which is subsequently reduced by CO has been extended t o consideration of the kinetics of pyrolysis of the mixed oxalates [32]. Kadlec and Rosmusovi [1153] believe that both Ni and Co oxalates initially yield product oxide and that the proportion of metal increases with a . Since nickel oxalate decomposes at temperatures -60 K lower than those for C0C204,even a small proportion of Ni2+markedly increases the rate of decomposition of cobalt oxalate. The effect was attributed to the catalytic properties of the preferentially formed Ni metal. The a-time curves were generally sigmoid and showed only slight deviations in shape with changes in the Ni : Co ratio. In the decomposition of a mechanical

244

mixture of salts, there was evidence of an initial rapid decomposition of NiC204.the value of E for the decomposition of cobalt oxalate (-180 kJ mole-') was readily reduced by the incorporation of the nickel salt, reaching the value characteristic of NiC204 (-138 kJ mole-') at some 20 at.% of Ni2+. Kadlec and Danes [1154] studied the decompositions of (Ni,Mg) and (Co,Mg) mixed oxalates. The magnesium salt is the more stable constituent in both and the products are MgO and Ni or Co. Decomposition rates decrease from the values for the pure nickel and cobalt oxalates as the MgC204 content increases. The acceleratory periods of reaction are most pronounced in the Ni and Co pure oxalates but are less significant in the mixtures. The most strongly deceleratory behaviour was found for reactants containing either 46.2 mole% Ni or 15 mol% Co. Values of E for the decompositions of (Co,Mg)C204 solid solutions were all close to 184 kJ mole-' and not greatly different from those for both pure components. However, for the (Ni,Mg)C204 solid solutions, there was a decrease in E with addition of NiC204towards the value characteristic of nickel salt. Guslev et al. [1155] confirm the increase in stability of (Ni,Mg) oxalates with increase in magnesium content. These workers suggest that the impurity cation in the solid solution (i.e. that which is present at the lower concentration) disturbs the symmetry of the oxalate ion, so promoting its breakdown.

0.8-

solid solution nickel salt ( ~ 0 . 5 )

__--__-_---

cobalt salt ("0.5) nickel salt ( ~ 0 . 5 )

_ _ _ _ _ - - -_-_-_ _ _ _ _ - - c o b a l t

salt (aO.5)

Time I min

Fig. 19. The rate of decomposition of a 1 : 1 N i - C o mixed mellitate at 663 K was appreciably greater than that expected from the sum o f the contributions from the pure individual components. (Reproduced, with permission, from the Journal of the Chemical Society.)

245

(c) (Ni,Co) mixed mellitates

Decomposition rates of (Ni,Co) mellitates [ 11101 increase with increase in nickel content. The a-time curves for the pure components and the mixed mellitates were deceleratory throughout and there was no discontinuity in shape with changes in composition. Rates of decomposition of the solid solutions were appreciably greater than those expected from the decomposition of the individual components present (Fig. 19).The values of E determined for the initial stages of the decomposition of mixtures were close to that found for the nickel salt (184 kJ mole-') and in the latter stages tended to increase towards that for cobalt mellitate (251 kJ mole-'). Values of A showed a systematic decrease with increase in cobalt content. 7.1.4 Other solid solutions

Reference has already been made t o the dehydration of alums (Sect. 1.2 and Table lo), decomposition of ammonium metal phosphates (Sect. 4.1.5) and the use of KMn0,-KC104 solid solutions in mechanistic studies of the decomposition of potassium permanganate (Sect. 3.6). The dehydration of the double salt Na2Ca5(S04)a 3 HzO obeyed [1290] the contracting area equation [eqn. (7),n = 21 and the Arrhenius parameters tended to increase with water vapour pressure from E = 75 kJ mole-' and A = 9.2 X lo3 s-l at 0.013 N m-' to 159 kJ mole-' and 2.05 X 1014 s-l, respectively, at 2.6 kN m-'. This behaviour resembles that of hydrated calcium sulphate (Sect. 1.5.2) t o which the reactant is closely related.

-

7.1.5 Discussion

Most of the decompositions referred t o in this section concern solid solutions containing a common anion which is chemically reorganized during reaction. From the restricted range of systems for which reliable kinetic data are available, it is apparent that reactivity and kinetic characteristics (the magnitudes of A and E and the shapes of the a-time curves) generally change continuously with progressive changes in chemical composition (i.e. cation ratio). The reactivities of solid solutions usually appear to lie between those of the pure constituents. This conclusion, although still t o be generally established, is of considerable potential significance in the formulation of mechanisms for reactions between solids (Chap. 5), since intermediate formation of a solid solution will not be readily apparent from kinetic data. The participation (or absence) of such phases at the reaction zone would have t o be demonstrated by techniques such as X-ray diffraction or elemental analysis by electron probe at polished sections of reactant-product interfaces.

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7.2 DOPING

References t o doping studies have been made at appropriate places in the earlier text. Interest in the additive, which is usually present in dilute solid solution, is concerned with the influence it exerts on the decomposition of the particular reactant in which it is incorporated. The incorporation of Fe3+ ions, which provide potential electron traps, sensitized NaN3 decomposition [ 393,7041, while lattice strain resulting from the presence of large univalent ions is believed [709] t o be the reason for a reduction in the induction period t o reaction. Fe3+and other ionic impurities facilitate the decompositions of PbN6 and of AgN3 (Sect. 2.4). The rate of Ag2C03 decomposition is sensitive t o the concentration of lattice vacancies [757-7591: this can be controlled by the incorporation of appropriate ionic impurities such as water (as HCO; and OH-), Cd2+,Y 3 + , or Gd3+ (Sect. 3.1). The influence of various additives on the decomposition of NH,C104 has been discussed [46,59] (Sect. 4.1). Erofe'ev et al. [lo261 observe that doping (with Li', Mn2+ or A13+) influenced both the rate of decomposition and the conductivity of Ni(HC02)2,and conclude that the primary step in the reaction is electron transfer (Sect. 5.1). Non-stoichiometry, an excess of one or other ionic component of the reactant solid, can also influence the kinetics of decomposition: such effects have been noted for silver oxalate [lo881 and for ammonium perchlorate [ 591.

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Chapter 5

Reactions between Inorganic Solids

As emphasized in previous chapters, the concept of the reaction interface is a generally unifying characteristic feature of the literature concerned with the mechanistic interpretation of kinetic observations for decompositions of single solids. The numbers and dispositions of growth product nuclei generated in the reactant particles and their subsequent development control the geometry of interface advance and thus the shape of the a-time curve. A and E values have been associated with interface processes (Chap. 4). Reactions between two (or more) solids also occur at interfaces and, for product formation t o be maintained, a process is necessary whereby reactant species, separated and largely immobilized in different particles, can be transported t o the active reaction zone. Characteristically, such chemical changes involve minimum displacements of lattice components of the interacting solids so that, frequently, a product phase (or phases) is developed and grows in the immediate vicinity of the original intercrystalline contacts between reactants. For the reaction A + B --* AB, this may be schematically represented as AIB+ AIABIB where each vertical line represents an interface between solids. The rate of product formation in such reactions is often controlled by a diffusion process. The necessary movements of material may include migration across surfaces, or in the gas phase, but the determining step is more usually the migration of entities A and/or B through the barrier layer AB by diffusion in the bulk or along preferred paths of imperfection. Since the overall rate of mass transfer diminishes as the thickness of the interposed layer increases, such reactions characteristically exhibit deceleratory behaviour (Fig. 3, p. 75). Accordingly, the overall kinetics of many reactions between solids are controlled by the rate of diffusion of one or more participating species across the product barrier and many mechanistic studies are directed largely towards the identification of these diffusing species. A kinetic analysis must, however, also include considerations of the geometric factors since, in addition t o the thickness of the barrier (product) layer, rates are also appreciably influenced by changes in shape and disposition of the reaction interface (Table 5, p. 74). In general, no induction period or acceleratory process is discerned in these reactions since interaction at sites of initial A IB contact (nucleation) tends t o occur readily at temperatures significantly below the range conveniently used in

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rate measurements for the main process. Nucleation is, therefore, effectively instantaneous. Other factors have been identified as rate controlling in other types of solidsolid interaction, and some of these are described in subsequent sections. These include, for example, the decomposition of a solid catalyzed by a (different) solid and rate processes in which one reactant is volatilized, e.g. reaction of carbon (+ COz) with a solid oxidizing agent. Rate studies currently available represent a restricted selection from the very large number of possible combinations of solid reactants which could be expected to interact chemically at temperatures below the melting point. The techniques of kinetic analysis are less straightforward than those used in studies of the decomposition of a single solid. The a-time data for reactions between solids are not always amenable to a sensitive comparison with the appropriate rate expressions. Some progress is being made in the interpretation of kinetic behaviour in a number of particular systems (some of which are described below) and such fundamental work may be expected t o proceed towards the recognition of concepts of more general applicability. While there have been several discussions of the mechanisms of solidsolid interactions (see, for example, refs. 1, 66, 77, 111, 1156), the kinetic characteristics of such rate processes have been less comprehensively reviewed (Chap. 3, Sect. 3.3). This account of the kinetics of reactions between (inorganic) solids commences with a consideration of the reactant mixture (Sect. l),since composition, particle sizes, method of mixing and other pretreatments exert important influences on rate characteristics. Some comments on experimental methods are included here. Section 2 is concerned with reaction mechanisms formulated t o account for observed behaviour, including references to rate processes which involve diffusion across a barrier layer. This section also includes a consideration of the application of mechanistic criteria to the classification of the kinetic characteristics of solidsolid reactions. Section 3 surveys rate processes identified as the decomposition of a solid catalyzed by a solid. Section 4 reviews other types of solid + solid reactions, which may be conveniently subdivided further into the classes

A(s) + B(s) + C(s) (Sometimes referred to as an addition reaction, discussed in Sect. 4.1.) +

B(s)

+

C(S)

+

D(g)

(Includes decomposition reactions, discussed in Sect. 4.2.)

AB(s) + CD(s) + AD(s) + CB(s) (Can be specified as substitution or as double decomposition reactions, discussed in Sect. 4.3.) A short account of other and more complicated reactions is given in Sect. 4.4.

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1. Reactant mixtures and experimental methods The retarding influence of the product barrier in many solidsolid interactions is a rate-controlling factor that is not usually apparent in t,he decompositions of single solids. However, even where diffusion control operates, this is often in addition to, and in conjunction with, geometric factors (i.e. changes in reaction interfacial area with a ) and kinetic equations based on contributions from both sources are discussed in Chap. 3, Sect. 3.3. As in the decompositions of single solids, reaction rate coefficients (and the shapes of a-time curves) for solid + solid reactions are sensitive t o sizes, shapes and, here, also on the relative dispositions of the components of the reactant mixture. Inevitably as the number of different crystalline components present initially is increased, the number of variables requiring specification t o define the reactant completely rises: the parameters concerned are mentioned in Table 17. The overall composition of any reactant mixture, i.e. the total quantity of each component present, is of little practical use in kinetic studies since such (concentration-type) terms are not meaningfully related to magnitudes of rate coefficients or shapes of a-time curves. Of greater signifi-

TABLE 1 7 Reactions between solids. Parameters requiring consideration in the description of any reaction mixture and in the measurement of interaction kinetics

Specification of the reactant mixture including the identities, compositions and relative quantiReactant components: ties of all solids present. Particle sizes:

sizes, size distributions and shapes of each solid component.

Mixing:

the relative dispositions of all solid components present, including any pretreatment (grinding, compaction, ageing, etc.) of the constituents, either individually or collectively.

Measure me nt o f kine tic behaviour identification of all solid products of reaction, including Products: solid solutions. Yield-time data:

quantitative measurement of the changes with time of the amounts of all reactant and product phases present.

Topochemistry :

determination of the relative dispositions and spatial relationships developed between reactants and products, including identification of zones of preferred reaction, directions and rates of interface advance, compositions of phases concerned with any significant directional variations, cracking and surface area changes.

Temperature :

effects on the above parameters.

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cance in rate analyses are particle sizes, considered here rather generally t o include such factors as the area of initial contact between appropriate participants and also the shapes and dimensions of the crystallites concerned, since these control the directions of and limits t o interface advance. The area of initial contact may be markedly modified by any pretreatment that the reactant mixture has received. Grinding or crushing will result in fracture of and surface damage to crystallites. Compaction is likely to increase the total area of interparticle contacts between reactants. The effectiveness of this will depend on the severity of the mechanical treatment and on the physical properties (hardness, ease of deformation, etc.) of the solids concerned. Compaction may also vary the concentrations, distributions and intensities of crystal imperfections; the effect on any particular solid is difficult to predict since the numbers of defects present are reduced by cracking across defective zones, but can also be increased by cold-working. The complete investigation of a particular reaction may require quantitative measurements of the separate variations in kinetic behaviour which result from systematic changes in reactant composition, particle sizes and pretreatment. Great care must be taken in the preparation of reactant mixtures if these are to yield reproducible and reliable a-time data. Reactantreactant interaction, within a loose powder, may vary with the shape and constraints imposed by a containing vessel (i.e. thickness of the powder layer) and constant remixing is a possible consequence of vigorous gas evolution (in appropriate reactions). In addition, changes can occur during storage (i.e. ageing) when slow reaction may be initiated, resulting in recrystallization or reorganization of the surfaces of the particles. Impurities, notably water and sometimes carbon dioxide, may facilitate reorganization of those zones of the reactant at which reaction preferentially commences. Techniques proposed for preparing mixtures of more reproducible or defined properties include the following. One reactant may be crushed to a very fine powder and mixed with the coarser particles of a second reactant so that, at least initially, the former is in contact with all surfaces of the latter (including surfaces in interparticulate spaces, pores, surface cracks, etc.). It is also possible t o use one reactant in large excess so that on compaction the more “dilute” component is suspended in a continuous matrix of that present in greater amount. Individual flat cylindrical pellets or single crystals of each of the two pure reactants can be prepared and the planar faces held in contact (as in electrical conductivity experiments). A defined initial contact is thereby established and the influence of geometric changes is absent from the ensuing reaction of particles which originally met at a planar interface. Experimental techniques used in the kinetic investigation of solid decompositions (described in Chap. 2) may need modification for the study of rate processes which yield no gaseous products. Measurements

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are, therefore, less straightforward and the collection of accurate data may be more difficult. In principle, quantitative kinetic investigations of reactions between solids require the identification of every product phase formed and of each participating reaction interface, together with the influences of reaction time , temperature, and any other relevant variables (particle size, reactant composition, compaction, etc.) on the movements of interfaces (both rates and directions) during product formation (Table 17). Solid products may be identified qualitatively, and, in favourable systems, the yields measured quantitatively from X-ray diffraction data. This technique is, however, of restricted value where some (or all) of the product is poorly crystallized and this often occurs in the early stages of solid + solid interactions at low temperatures. Solid solution formation, particularly when the distribution of elements in the host crystal is inhomogeneous, also introduces uncertainties which reduce analytical accuracy, since diffraction maxima become broadened. A systematic variation in the composition of a solid solution with distance from a reaction interface (the compositional gradient) may be an important parameter in diffusion-controlled reactions. Phase and compositional variations can be measured, by diffraction or other methods, in selected small volumes of solid serially removed from appropriate points in a polished section cut normally to a reaction interface. This is clearly a prolonged and laborious process. Optical microscopic examination of these polished sections can yield useful information, providing that the phases present and their boundaries can be recognized. Sometimes the position of the initial reactantieactant contact surface can be conveniently defined through the incorporation of inert markers which do not move with the advancing reactant-product interface. A more convenient method for the characterization of compositional changes occurring in the vicinity of and accompanying the advancing interface( s) is afforded by electron probe microanalyses of sectioned reaction zones. Through the use of a number of reactant samples previously heated for appropriate time intervals at various temperatures within a suitable interval, kinetic data concerning the development and advance of reaction interfaces is obtained. This approach is capable of application to the more complicated reactions in which two, or more, product phases are formed (e.g. A lA2B IAB lAB2 IB) and may also enable the inhomogeneity of solid solutions, arising from diffusion of participating species towards a reaction interface, t o be examined. Rate processes of the type illustrated cannot always be quantitatively described by a single parameter (say a ) , since the extent of each contributingreaction requires individual specification and measurement. However, the present survey is largely concerned with fundamental kinetic studies of some of the simplest solidsolid interactions known and, for many of these, the extent of reaction can be expressed satisfactorily through the use of a single parameter, a . The full potential of the more sophisticated techniques has yet t o be realized.

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Rates of relatively simple solid + solid interactions have been measured using appropriate properties including gas evolution, mass loss and the enthalpy of reaction (by non-isothermal methods, DTA and DSC). More specialized approaches have been concerned with magnetic properties [1157,1158], EPR [347], and electrical conductivity [418,1159] (the last-mentioned has also been used to detect local melting [111,417]). Evidence concerning the onset of surface migrations and the adsorption interactions which precede the development of product particles during the main reaction has been obtained from measurements [1,111] of surface area and chemical properties such as catalytic behaviour and adsorption. Microscopy, electron microscopy, and scanning techniques can provide evidence of textural variations, before, during, and after reaction; the combination of scanning microscopy with crystal or energy dispersive X-ray spectrometry offers great potential. Other references to experimental techniques are given in Chap. 2, in particular Sect. 15, and in the text below. With the continuing interest in the development of solid materials possessing specific properties for specialized technological uses (such as electrical components, cements for building, parts for space-craft, etc.), it is probable that the well-established interest in solidsolid reactions and solid-state reactivity will be accelerated. 2. Mechanisms of reaction

As with the decompositions of single solids, rate data for reactions between solids may be tested for obedience to the predictions of appropriate kinetic expressions. From the identification of a satisfactory representation for the reaction, the rate-limiting step or process may be identified and this observation usually contributes to the formulation of a reaction mechanism. It was pointed out in Sect. 1, however, that the number of parameters which must be measured to define completely all contributory reactions rises with the number of participating phases. The difficulties of kinetic analyses are thereby also markedly increased and the factors which have to be considered in the interpretation of rate data include the following. (i) There is the possibility that a series of product layers may be interposed between the reactants, e.g. A IA,Bb I ...IA,B, IB. (ii) There are considerable difficulties in identifying the rate-controlling step in a multiphase system [e.g (i), above]: the rate-limiting process in the reaction may be adsorption, i.e. transfer of a participant from the active surface of one phase to another, or diffusion. Moreover, the phases present and their relative thicknesses may vary during the progress of reaction. (iii) Appreciable concentration gradients may be established in reactant I intermediate(s) I product solid solutions, during migration of participants towards and across the reaction zones.

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(iv) Migration of participants may proceed by preferred paths in a barrier layer, or other participant phase, within which there are locally high concentrations of lattice imperfections or, indeed, these zones of the solid may be poorly crystallized. Growth of a product phase can be accompanied by lattice reorganization with consequent diminution in the ease of diffusion, and thus reactant transport. (v) The development of local strain can lead t o a loss of contacts between reactant particles as product layers become separated. In loose powders, the movement of particles can result in the establishment of new contacts and the continuation of product formation. (vi) Topotactic relationships may be established and maintained between adjoining solids. During migrations of the smaller lattice constituents (normally the cations) the more bulky anion structure may undergo less extensive reorganization and thus a topotactic relationship between the crystals concerned can be maintained across an advancing interface. (vii) Gaseous additives may influence reaction rates. Few quantitative investigations have, however, been made of the kinetic consequences of the presence of active additives, e.g. the influence of oxygen on the interactions of oxides or the participation of water. (viii) The controlling factor in any rate process may vary with temperature, time, and/or the extent of product formation and the influence of any of the effects mentioned above may be restricted to specific conditions. During the early stages of reaction between two different solids, product formation may be rate-limited by either a surface (interface) adsorption step or by the vapour or surface diffusion of one reactant to the other. The extent of this stage may be limited. Later, the diffusion of one or more reactant species across the barrier layer may become ratedetermining. Examples of reactions in which there are changes from sublimation to diffusion control and from reaction at an interface to diffusion control are [l] CaC03 + MooBand Na2C03+ S O z , respectively. Sections 2.1-2.3 give accounts of kinetic and mechanistic features of the three rate-limiting processes: (i) diffusion at a surface or in a gas (including the nucleation step), (ii) reaction at an interface, and (iii) diffusion across a barrier phase. [(ii) and (iii) are growth processes.] In any particular reaction, the slowest of these processes will, at any particular instant, control the rate of product formation. (A kinetic analysis of rate measurements must also incorporate an allowance for the geometric factors.) 2.1 SURFACE OR GAS-PHASE DIFFUSION

2.1.1 Area of interparticulate contact between reactants

The zone within which reaction is most probably initiated is that at which particles of the two reactants present (A and B) are in direct

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contact. Chemical interaction is possible only if the separation of the participants is less than the distance across which bonding forces normally operate, i.e. -0.1 nm. This constraint restricts the onset of product formation to a very small fraction of the surface, as is apparent from the following estimations based on idealized calculations [ 11. In a 1 m3 volume occupied by smooth 1mm diameter spheres, the total contact area m2 (defined as surface separations GO.1 nm) amounts t o only -3 X and to -0.3 m2 for the same volume filled with equivalent smooth spheres of the total surface of these particles is of 0.01 mm diameter. Only within the range of possible influence of the chemical forces of a neighbouring crystallite and thus constitutes the zone of effective initial reaction. Although this model is an unrealistic representation of real systems, where the crystallites are not usually spherical, atomically smooth or of homogenous sizes, and reaction mixtures contain two different components, it is nevertheless believed that the qualitative conclusion retains general validity. The zones of effective chemical contact between neighbouring particles in a reactant mixture comprised of loose particles constitutes but a minute fraction of the total surfaces of the crystallites concerned. Ruzek [ 3761 concludes that this area increases sharply on grinding, slowly on mixing, and negligibly under compaction. Some aspects of the influence of reactant pretreatment on subsequent reaction have been investigated [1160].

2.1.2 Initial formation (nucleation) and growth o f the product phase While it is inherently probable that product formation will be most readily initiated at sites of effective contact between reactants (A IB), it is improbable that this process alone is capable of permitting continued product formation at low temperature for two related reasons. Firstly (as discussed in detail in Sect. 2.1.1) the area available for chemical contact in a mixture of particles is a very small fraction of the total surface (and, indeed, this total surface constitutes only a small proportion of the reactant present). Secondly, bulk diffusion across a barrier layer is usually an activated process, so that interposition of product between the points of initial contact reduces the ease, and therefore the rate, of interaction. On completion of the first step in the reaction, the restricted zones of direct contact have undergone chemical modification and the continuation of reaction necessitates a transport process to maintain the migration of material from one solid t o a reactive surface of the other. On increasing the temperature, surface migration usually becomes appreciable at temperatures significantly below those required for the onset of bulk diffusion within a product phase. It is to be expected that components of the less refractory constituent will migrate onto the surfaces of the other solid present. These ions are chemisorbed as the first step in product formation and, in a subsequent process, penetrate the outer layers of the

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initial small area of reactant-reactant contact interface 0 surface of

thin mobile layer of reactant A on surface of product AB

reaction rate controlled by diffusion across b a r r i e r product layer

eliminate local thin regions of barrier product b y e r

Fig. 20. Schematic representation of the solid + solid reaction A + B -+ AB in which constituents of the relatively mobile reactant (A) are transported t o the outer surfaces of the product phase (AB) and rate is controlled by diffusion of constituents of A and/ or B across the barrier layer AB.

underlying lattice leading towards bulk product formation. Adsorption and catalytic properties of the surfaces of solid reactant mixtures are changed [1,111], relative to those of the pure constituents, at temperatures appreciably below those of the onset of the bulk reaction. This coverage of crystallites of one reactant by the chemical constituents of the other, corresponds to the complete and rapid nucleation of all surfaces before occurrence of the more difficult growth step requiring bulk diffusion. If this “main” reaction, proceeding at higher temperature, is controlled by bulk diffusion across an adherent, coherent, and non-porous barrier layer of product, the kinetic characteristics are independent of the state of subdivision of the more mobile constituent (or, indeed, whether it is a solid, liquid or gas) always providing that the outer surface of the barrier is maintained in a saturated condition. This reaction path uses the maximum available cross-section of the reaction zone, following effectively instantaneous nucleation. Some features of this model are schematically represented in Fig. 20. While it is possible that surface defects may be preferentially involved in initial product formation, this has not been experimentally verified for most systems of interest. Such zones of preferred reactivity would, however, be of limited significance as they would soon be covered with the coherent product layer developed by reaction proceeding at all reactant surfaces. The higher temperatures usually employed in kinetic studies of diffusion-controlled reactions do not usually permit the measurements of rates of the initial adsorption and nucleation steps.

2.1.3 Melting Discussion of the significance of melting in solidsolid interactions raises difficulties of definition. To allow product formation, one or more

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components of the reactant must be capable of movement such as the migration across a surface, and this can be regarded as a two-dimensional liquid, or by sublimation into the gas phase. In either case, the restrictions imposed by the crystal structure are at least temporarily relaxed for a proportion of one participant. Therefore, if one reactant does not melt and the rate process is controlled by diffusion across a product barrier layer, the kinetic characteristics are not influenced by the state of the second reactant (solid, liquid or gas), provided that the outer surface of the product barrier is maintained in the saturated condition. Kinetic parallels are thus found between solidsolid and solid-as [ 31-38] reactions and also with the less intensively investigated solid-liquid reactions. Systems considered here will be restricted to those in which both reactants remain nominally solid. 2.1.4 Reactant mobility and particle coarsening

Surface migration and/or homogeneous phase diffusion are also capable of crystallite surface reorganization and, in particular, a reduction in total surface free energy by growth of the larger, more perfect particles at the expense of the smaller and less perfect. This physical change is mentioned here as a possible concurrent process, accompanying reactions between solids which possess restricted surface mobility. The kinetics of changes in sizes of particles have been discussed in several reports. (i) Catalyst sintering: particle growth by coalesence or Ostwald ripening [1161] has been the subject of two recent publications [1162,1163]. (ii) Homogeneous phase diffusion: Ardell and Nicholson [ 11641 have applied the Lifshitz-Wagner theory to the coarsening of an alloy phase. (iii) Particle size distributions and changes during growth in MgO and MgO-Fe203 solid solutions have been discussed [11651. 2.2 INTERFACE REACTIONS

The kinetic principles operating during the initiation and advance of interface-controlled reactions are identical with the behaviour discussed for the decomposition of a single solid (Chaps. 3 and 4). The condition that overall rate control is determined by an interface process is that a chemical step within this zone is slow compared with the rate of arrival of the second reactant. This condition is not usually satisfied during reaction between solids where the product is formed at the contact of a barrier layer with a reactant. Particular systems that satisfy the specialized requirements can, however, be envisaged; for example, rate processes in which all products are volatilized or a solid additive catalyzes the decomposition of a solid yielding no solid residue. Even here, however, the kinetic characteristics are likely t o be influenced by changing effectiveness of contact as reaction proceeds, or the deactivation of the catalyst surface.

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Another possibility is that one of the reactants is particularly mobile, this reactions, such as the reduction of NiO is apparent in certain solid-as with hydrogen, which is a well-characterized nucleation and growth process [30,1166]. Attempts have been made t o use the kinetic equations developed for interface reactions t o elucidate the mechanisms of reactions between the crystalline components of rocks under conditions of natural metamorphism [1167,1168]. 2.3 DIFFUSION ACROSS A BARRIER LAYER

An important insight into the kinetics and mechanisms of diffusion across barrier layers was afforded by Wagner's quantitative measurements [ 11691 of the rate of synthesis of AgZS from the elements. Although this is a solid-liquid reaction (the sulphur is molten) the conclusions are also significant in quantitative discussions of solid-gas [ 371 and solidsolid reactions. Some important features of this model are summarized in Fig. 21. The mobile participant is identified as Ag' and this migrates through both barrier blocks so that total product formation is effectively localized at the one interface, AgZS IS. Slight modifications to the Wagner theory have been proposed, but its general validity remains acceptable and recent results [ 11701 are in excellent agreement with predictions based on the model. The relative displacement rates of the interfaces AIAB and ABIB in any particular system will, of course, depend on the relative migration velocities of all mobile participants across the barrier layer and reaction will continue while appropriate reactant constituents remain available. Such migrant entities travel by the most efficient route and therefore overall rates of such reactions are frequently sensitive to the concentration of imperfections in the product crystal lattice [1171]. One possible

Weight change after l h ( m g )

SULPHUR

(Liquid)

1 Interface advance Diffusion d interstitial Ag+

2 Ag* + 2 +~5-

Ag2S

t rate-limiting Ag

-

Ag*

+ E

Fig. 21. Schematic representation of the Wagner experiment [ 11691 on the formation of silver sulphide at 493 K from the elements (2 Ag + S + Ag2S).

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influence of changes in the number of defects present with time has been mentioned [ 771 in the derivation of the Carter-Valensi kinetic expression (Chap. 3, Sect. 3.3). Significantly different values of E were found for the diffusion-controlled oxidation of nickel [ 11721 proceeding by “leakage path” (155 kJ mole-’) and by lattice diffusion modes (217 kJ mole-’). Different diffusion processes may be rate-controlling over different temperature intervals [77], e.g. at lower temperatures diffusion may be mainly along extended defects, changing to bulk lattice diffusion in a relatively defect-free phase formed at some higher temperature. (A parallel is seen here with solid phase electrical conductivity and this is to be expected since, in a number of systems, migrations of the same charged species are rate-limiting.) A detailed account of transport phenomena in crystals is outside the scope of the present review, though it is relevant t o point out that factors which determine the rate at which reactants penetrate a barrier layer include the numbers, distributions and mobilities of vacancies. Oleinikov et al. [1173] conclude that Arrhenius parameters are devoid of any physical significance if due allowance is not made for imperfection concentration, which may vary with temperature (and (Y [77]). Solid solution formation also exerts a control over kinetic characteristics of the reactions between solids. Pelton et al. [1174] classify rate processes as being of two kinds: in the first kind, the starting material is a mixture comprised of the pure reactants, while in the second kind, each component has been presaturated with the other. Their theoretical discussion of the rates of formation of the spinels NiCrz04 and MgCr204 includes consideration of the influence of mutual solubilities, interface progression, and the dependence of interdiffusion rates on concentrations of participants. Leute and Kalb [1175] also consider the significance of concentration profiles and thermodynamic controls on solidsolid interactions. Some kinetic features of reversible solid state reactions, involving solid solution formation, have been explored by Strunin et al. [1176]. Solid solution production is determined to some extent by sintering, crystallite growth, creep, surface relaxation, and other high temperature phenomena [1177]. Schmalzried [66,1178,1179] has given a detailed, critical discussion of the assumptions which underlie the development, from first principles, of rate laws applicable to one-dimensional solidsolid reactions. (This treatment does not, therefore, require consideration of the influences of a changing geometry of reaction interface.) Transport dynamics are based on the thermodynamic properties of defects. The theoretical conclusions are examined with reference to observations on reactions between oxides, again including spinel formations, and citations give access to recent literature. Spinel formation, involving cation diffusion in an oxide matrix, is a simple solid state reaction, resembling, in certain respects, homogeneous rate processes, and is conveniently selected as a model system.

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In reactions of the type discussed, the more bulky anions are often regarded as an immobile framework within the solid through which the cations diffuse. Some experiments have been directed towards investigation of the significance of anion migration but results are restricted in scope and more work is clearly desirable. It is possible that anion migrations may occur along dislocation lines, at surfaces, or even by desorptionadsorption, and may be sensitive t o the presence of specific impurities. In a study of the spinel formation reaction COO + A1203= COA1204 Holt [1180] concluded that cation counterdiffusion using labelled l80, proceeded in a rigid lattice (the Wagner mechanism) and that the transport of aluminium was rate-limiting. He suggested that it would be desirable that similar determinations should be made for all those reactions in which a high mobility of oxygen is proposed. Perrichon [1181], in a study of the reaction COO + W 0 3 = C0W04 at 823 K, identified the rate-limiting step as grain boundary migration of oxide ions and ascribed the large increase in rate found when water vapour was present to OH- formation, which greatly enhances the mobility of oxide ions in the crystal. (This explanation is reminiscent of that advanced 17571 to account for the influence of structural water on Ag2C03decomposition.) The kinetic expressions applicable to diffusion-controlled reactions have been discussed in Chap. 3, Sect. 3.3. Mass transport in ionic solids has been reviewed by Steele and Dudley [ 11821. 2.4 CLASSIFICATION OF SOLID-SOLID INTERACTIONS

No single criterion has yet been found to provide a satisfactory basis for the classification of solidsolid reactions. Budnikov and Ginstling 113 (see also Rastogi [ 11831)discuss several possible divisions which include: (a) chemical criteria: e.g. reaction of (i) basic oxides with acidic oxides, (ii) an oxide with a salt, (iii) a metal with an oxide, (iv) exchange decompositions, etc., or the compositions of reactant constituents. (b) physical criteria: the state of matter (i.e. solid, liquid or gas) of the product phases resulting from solidsolid interaction. (c) mechanistic criteria: reaction rate is controlled by (i) a chemical step, or sequence of changes, including contributions from autocatalytic behaviour, recrystallization, etc.,

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(ii) a diffusional limitation, (iii) the simultaneous operation of (i) and (ii), (iv) a rate of vaporization or sublimation. Classification of experimental observations using these criteria, sometimes with appropriate modifications or developments, have contributed towards advancement of the topic. This framework does not, however, provide a comprehensive and generally acceptable basis for the ordering of kinetic phenomena in this large and incompletely explored field. Early discussions, by Tammann and by Hedvall, considered the possible existence of a common characteristic (approximate) temperature for a solid at which chemical interactions with other reactants became detectable. For example [ 1111, such a characteristic temperature for CaO, measured in various reactions with CuS04, C O ~ ( P O ~MgC03, ) ~ , and MnSi03, was found t o be 788-838 K. Similarly, the onset of reaction of BaO with the sulphates of Mg, Ca, Sr, Co, Cu, and Zn occurred between 601 and 645 K. In the latter example, it has been shown that the fusion of Ba(OH)2 (an impurity not easily excluded from BaO) could contribute to the initiation of reaction. Eutectic formation during the reactions of BaC12with alkali metal sulphates M2S04 + BaClz = 2 MCl + BaS04 has been investigated [417] by the simultaneous measurement of electrical conductivity and DTA and the observations discussed with reference to the relevant phase diagrams. The concept of a “characteristic” reaction temperature must, therefore, be accepted with considerable reservation and as being of doubtful value since the reactivity of a crystalline material cannot readily be related to other properties of the solid. Such behaviour may at best point towards the possible occurrence of common controlling factors in the reaction, perhaps related to the onset of mobility, e.g. melting of one component or eutectic formation, onset of surface migration or commencement of bulk migration in a barrier phase. These possibilities should be investigated in detail before a mechanism can be formulated for any particular chemical change.

3. Decomposition of a solid catalyzed by a solid Systems for consideration under this heading are conveniently classified into two groups, distinguished by the relationship existing between the reactant and the additive considered, which may be (i) a product of the decomposition process or (ii) a substance chemically different from all the participating phases. In certain important respects, reactions of type (i) may be regarded as specific instances of the autocatalytic behaviour characteristic of the reactantderived product in many nucleation and

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growth processes. Investigations of the influence, in promoting product formation, of an additive, separately prepared and introduced, is a possible route to the study of phenomena occurring at, or properties of, an active interface. Reports in the literature include descriptions of decompositions of both types (i) and (ii) in which the rate processes Concerned are promoted by an additive under such conditions that it is known that the “catalyst” is not in direct mechanical contact with the reactant. For example, the dehydrations of CuSO, - 5 H20 and of NiSO, - 7 H20are accelerated by the close proximity of the corresponding monohydrates, even when crystals of the two substances were prevented from touching [ 11841. This effect is ascribed to a reduction in the water vapour pressure prevailing within the reactant mass, leading to an acceleration in the rate of its release from the higher hydrate. The catalytic actions of copper chromite, of copper(I1) oxide and of potassium dichromate in the high temperature decomposition of NH4C104are ascribed [1185] to promotion of HClO, pyrolysis during dissociative sublimation of the reactant. In both of these examples, the detected catalytic effect is traced t o the behaviour of a gaseous participant and, as is apparent in the articles cited, the observations are of value in the elucidation of the decomposition mechanism of the salt concerned. Such systems are, however, outside the scope of the present account since the reactions are not a direct consequence of solidsolid interaction. 3.1 DECOMPOSITION REACTIONS CATALYZED BY THE SOLID PRODUCT

The important characteristic feature of the interfacial reactions discussed in Chap. 3, Sects. 1 and 2 is the promotion of the chemical change within a reactant-product contact zone (Fig. 8, p. 112). Investigation of the conditions required to generate artificially an effective reaction zone through the introduction of pure product provides a method for determining certain characteristic features of that interface. Moreover, if such preliminary treatment results in the development of an active zone before the reactant is heated, the form of the a-time relationship is modified by the elimination of any induction period and perhaps also the acceleratory process. Such pretreatment, leading t o the attainment of maximum rate immediately on reaching reaction temperature, is not, perhaps, to be regarded as true catalysis since the rate of subsequent interface advance is unaltered and the increase in overall rate is a consequence of an effective increase in the participating product area at low a. Any specific promotional effect of the additive is here restricted t o the early stages of reaction (nucleation) since active participation by introduced, but immobile, material is rapidly lost immediately upon movement of the interface into the reactant crystallites. Representative examples of kinetic studies concerned with the accelerated initiation of solid decomposition through introduction of product are given below.

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Dehydration reactions. In early studies of dehydration reactions (e.g. of CuSO, 5 H 2 0 [400]), the surfaces of large crystals of reactant were activated through the incorporation of product into surfaces by abrasion with dehydrated material. An advantage of this pretreatment was the elimination of the problems of kinetic analysis of the then little understood relationship between a and time during the acceleratory process. Such surface modification resulted in the effective initiation of reaction at all boundary surfaces and rate studies were exclusively directed towards measurement of the rate of interface advance into the bulk.

-

Decomposition of A g 2 0 . Dubinin et al. [642] have shown that the induction period to Ag20 decomposition at 603 K is reduced and the initial reaction rate is increased by the deposition of a thin film of Ag (or of Ni) on the reactant surface. Close contact between reactant and additive must be established for the effective promotion of salt breakdown since no activating influence was detected during reactions of mechanical mixtures of A g 2 0 and Ag. Decomposition of KMnO,. Boldyrev [894] has shown that decomposition of KMnO, is catalyzed by Mn02, which is also known t o be a decomposition product. The activities, in this reaction, of different preparations of the additive varied markedly, the most active forms of Mn02 being capable of eliminating the induction period and accelerating the initiation of decomposition. This catalytic influence is attributed to the ability of MnOz to facilitate the electron transfer step, an interpretation that is also consistent with the inhibitory influence known t o be exerted by K3(Mn04)2.The acceleratory effect of pre-irradiation on KMn04 decomposition has also been ascribed [894] t o the catalytic properties of radiolysis products retained within the reactant crystal (Chap. 4, Sect. 3.6). It is seen from these examples that, in appropriate systems, it is possible to introduce product into the reactant in such a manner that an effective reaction interface is established before the reactant has been heated to the decomposition temperature. Accordingly, the induction period is removed and the acceleratory process may be less pronounced or eliminated altogether. Artificial nucleation results in changes in reaction geometry with consequent variation in the a-time curve shape and the maximum value of da/dt but does not enhance the rate of interface advance. We have found no studies in which increases in reaction rates were quantitatively correlated with the increased interfacial area and/or density of nucleation which resulted from the reactant pretreatment. 3.2 DECOMPOSITION REACTIONS CATALYZED BY A SOLID ADDITIVE

Studies of the influence of additives on rates of salt decompositions are often directed towards the formulation or confirmation of a mechanism

263

for the decomposition of the pure compound. Such observations are frequently qualitative only and kinetic conclusions may not extend beyond the comment that a particular additive accelerates, inhibits or is without influence on the rate process of interest. The methods of reactant preparation can sometimes introduce difficulties in quantitative rate measurements since rate characteristics are sensitive to physical parameters of the reactant, including particle sizes, mixing, compaction, etc. There is also always the possibility that reaction may be accompanied by partial or localized melting. Systems selected for mention here are largely concerned with those decomposition reactions which have been most intensively studied: the decomposition of NH4C104(in which the reactant yields no barrier phase between salt and additive) and of a number of silver salts: the oxalate, the carbonate and the azide (which do yield residual products).

3.2.1 Decomposition of NH4C104 Jacobs and Whitehead [59] conclude that no single mechanistic explanation accounts for the effects of various catalysts in accelerating the decomposition rate of NH4C104. They identify three distinct modes of action (see also Chap. 4,Sect. 4.1). (i) The activities of certain oxides have been ascribed [1185] to their ability to promote the decomposition of perchloric acid and thus at temperatures above those at which NH4C104commences sublimation the catalyst does not need to be in direct contact with the salt. These observations have resulted in the specific investigations [1186,1187] of the kinetics of HC104 breakdown on the catalysts concerned. (ii) Incorporation of certain ions (including Ag', Cd2+,I-, C10, and MnOi) in the reactant crystal has been shown to promote the low temperature decomposition of NH4C104 . The mode of action of these additives has not been completely elucidated, although a suggestion that has found some support is that ammine formation by the cations concerned may facilitate the proton transfer step. (iii) A number of metal oxides (e.g. CdO, MgO, and ZnO) are converted to the corresponding perchlorate and decomposition proceeds more rapidly in the resulting melt (again, it is possible that proton transfer occurs more readily). In none of these examples is there any evidence that the catalytic behaviour results from direct chemical interaction between the solid reactant and the solid additive. In an earlier study of the decomposition of NH4C104in the presence of MnOz, Galwey and Jacobs [1188] noted the sensitivity of kinetic behaviour to the degree of compaction of the reactant mixture. Reproducible results could be obtained only by using fragments of hard compressed pellets composed of a rigid matrix of (i) excess MnOz (go%), in

264

which the salt particles were embedded, and (ii) excess NH4C104, with Mn02 embedded (90% : 10%). The later stages of reactions of the mixtures containing excess oxide were deceleratory and obeyed the contracting volume equation [eqn. (7),n = 31; this later product evolution was ascribed to decomposition of NH4C104alone after Mn02 activity or saltloxide contact had been lost. The initial stage of reaction of the preparatioris containing the excess NH4C104was zero order. Reproducible kinetic behaviour was thus obtained by immobilization of the components of the mixture on compression. Mass spectrometric analyses of the products of reaction catalyzed by “0-enriched oxide and analytical investigations of the catalyst gave no evidence t o indicate that the oxide participated chemically in salt breakdown. Mn02 markedly promoted the onset of reaction and since the value of E for the catalyzed decomposition, -134 kJ mole-’, was close t o that characteristic of the reaction of pure NH4C104, it must be concluded that the additive increased the frequency factor. It was suggested [1188] that a Mn4+ion at the oxide surface stabilized an intermediate complex, approximately represented as [Mn3+C10.,NH‘4].Since this proposal was made, however, the existence of such a complex has become less acceptable due t o changes in the generally agreed mechanism of NH4C10 decomposition (see the “unified scheme” in Fig. 17). Accordingly, it now seems more realistic to associate the activity of MnOz with facilitation of proton transfer, modification of surface equilibria (perhaps with ammine formation), or promotion of HC1o4 decomposition. Kishore et al. [ 12911 suggest electron transfer. Pelleting also achieved reproducible kinetic behaviour in the reaction of NH4C104+ C mixtures [1189], the salt always being present in excess. Carbon was not oxidized and below 513 K exerted little influence on the rate of NH4C104decomposition. Above 533 K, however, the rate of reaction was substantially greater than that in the absence of additive, and NH4C10 reactant pellets containing 20% C underwent mild explosion. Kinetic characteristics between 513 and 533 K were sensitive both to temperature and t o reactant mass, behaviour which was ascribed t o selfheating. It is suggested that ammonia adsorption on the carbon reduces the inhibition offered by this constituent to HC104decomposition and so salt pyrolysis is more vigorous. Acheson and Jacobs [I3541 used DSC measurements to supplement an isothermal kinetic study of the decomposition of NH4C104+ Mg(C104)2 mixtures. An endotherm close t o the onset of salt breakdown was attributed to local melting and a later sharp exotherm, towards completion of reaction, was ascribed to solidification. It was suggested that within the molten layer, between NH4C104and MgO particles, the C10, ions undergo stepwise deoxygenation t o yield (inter alia) 02-.Oxide ions act as proton acceptors capable of reacting with NHf to form NH3. Solymosi and Rasko [1190] conclude that the influence of Zn(C104)2 in accelerating the decomposition of NH4C104is a consequence not only of melting, but also of the marked polarizing property of Zn2+.

265

3.2.2Decompositions of other salts of oxyhalogen acids

Several alkali chlorates and perchlorates undergo fusion during the onset of decomposition, the autocatalytic character of reaction then being attributable to the greater rate of reaction in the melt. Khorunzhii and Il'in [849], from work on the reactions of Na' and K' salts of chloric and perchloric acids, conclude that surface and grain boundary diffusion exert an essential role in decomposition rate control. Wydeven [865] concludes that, in the presence of Co304(6.8%), up to 60% of the reactant NaC103 decomposed in the solid state. During subsequent melting, there was an increase in reaction rate. The catalytic activity of the additive was ascribed t o the electron accepting properties of the oxide (Co304 is a p-type semiconductor). The apparent value of E increased from 120 to 200 kJ mole-' between a = 0.05 and 0.5. Solid KC104 oxidizes lauryl aldehyde to lauric acid by a second-order rate process [eqn. (16)] under the influence of ultrasonic irradiation [ 11911. The reaction rate is directly proportional to radiation intensity and, as in most other reactions of solids, increases as the crystallite size is reduced. 3.2.3Decomposition of silver oxalate

The addition of dyes, or other molecules in which there is extensive delocalization of orbitals, results in significant changes in the rate of Ag2C204decomposition [ 1019,1086,1192]. Legia [lo861 reports that the decomposition of the pure salt obeys the power law [eqn. (2)] with n = 3 or 4 and that this kinetic behaviour does not change on the addition of donor-type molecules. In the presence of electron acceptors, however, the exponent is increased t o n 5. In the expression a = Ct", the magnitude of C (a composite parameter including kinetic contributions from both nucleation and growth steps) decreased in the sequence: Ag2C204 containing donor-type additives > pure salt > Ag2C204 containing acceptor-type additives. The influence of the additive is ascribed to the activity of the surface trapping sites that it offers: donor traps are believed to accumulate (interstitial) Ag', whereas acceptor sites stabilize excited oxalate ions. Electronic interactions between salt and additive surfaces are identified as exerting a significant influence over the relative stabilities and concentrations of those species (i.e. interstitial Ag' and excited C20$-) which participate in salt breakdown (Chap. 4, Sect. 5.2). Boldyrev et al. [ 11921 have correlated the inhibiting influences of various polyacetylenes on Ag2C204decomposition with the estimated energies of the lowest unoccupied molecular orbitals. Later work [ 10191 related the promoting action of ten dyes with their ability to facilitate electron transfer (from C20',- to Ag'), measured by the redox potential of the additive. The method used t o introduce the dye did not influence reactant stability.

-

266

3.2.4 Decomposition of silver carbonate In a DTA study [1193] of decomposition reactions in Ag2C03+ CaC03 mixtures, the presence of a response peak, absent on heating the silver salt alone, resulted in the identification of the double salt Ag2C03 : 2 CaC03, stable at <420 K. One important general consideration which arises from this observation is that the formation of a new phase, by direct interaction between the components of a powder mixture, could easily be overlooked and, in the absence of such information, serious errors could be introduced into attempts t o formulate a reaction mechanism from observed kinetic characteristics. Due allowance for this possibility must be included in the interpretation of experimental data. 3.2.5 Decomposition of silver and other azides The influence of added dyes on AgN3 decomposition resembles closely the behaviour of Ag2Cz04 described above (Sect. 3.2.3). The catalytic activity of additives (5%)on silver azide decomposition at 508 K depended on the lability of their 7r electrons, which increased somewhat with chain length but was reduced by the presence of electron attracting substituents [ 1 1 9 4 . A comparable pattern of behaviour was apparent [ 3691 in the influences of semi-conducting oxides (CdO, COO,C0203, Co300,NiO, Ni203, or ZnO) on the same reaction, The catalytic activity of the additives increased with increase in the work function, measured under the conditions of decomposition. The rates of decomposition of barium azide and of copper azide were accelerated [1195] by electron acceptors and inhibited by electron donors; this was attributed to the provision of electron traps or modification of the role of impurities. The electronic properties of the additive were, therefore, identified as influencing the ease of the electron transfer step, which is a controlling feature of the reaction mechanism. The catalytic activity of doped nickel oxide on the solid state decomposition of CsN, decreased [714] in the sequence NiO(l% Li) > NiO > NiO(l% Cr) > uncatalyzed reaction. While these results are in qualitative accordance with the assumption that the additive provided electron traps, further observations, showing that ZnO (an n-type semi-conductor) inhibited the reaction and that CdO (also an n-type semi-conductor) catalyzed the reaction, were not consistent with this explanation. It was noted, however, that both NiO and CdO could be reduced by the product caesium metal, whereas ZnO is not, and that the reaction with NiO yielded caesium oxide, which is identified as the active catalyst. Detailed kinetic data for these rate processes are not available but the pattern of behaviour described clearly demonstrates that the interface reactions were more complicated than had been anticipated.

267

4. Reactions between solids 4.1 REACTIONS OF THE TYPE A(s) + B(s) -+ AB(s)

The most extensively studied rate processes in this group are those which yield spinels [ 11 (ferrites, chromites, etc.), molybdates and tungstates, and complex iodides. These types are conveniently exemplified by the representative systems ZnO + A 1 2 0 3 = ZnA1204 COO + W 0 3 = C o W 0 4 2 AgI + HgIz = Ag2HgI4 An important characteristic feature, common to all these reactions, is the formation of a single product (barrier) phase. In addition, the lattice structures of both reactants and products are relatively simple and information on appropriate physical and chemical properties of these substances is available. Complex iodide formation is of particular interest because of the exceptionally large cation mobilities in these phases. Experimental methods have been described in Sect. 1and Chap. 2. 4 . 1 . 1 Zinc ferrite formation ZnO + Fe203 = ZnFe204 Reports of the early and extensive studies of this reaction by Huttig [ 11961 have been cited at considerable length in subsequent reviews [ 1,1111.This work places particular emphasis on the changes in surface properties of the solids of the reactant mixture that occur at temperatures well below the range in which bulk product formation becomes detectable. The capacity of the crystals t o adsorb ions from solution is appreciably varied by simply mixing the oxides at ambient temperature. On heating a reactant mixture (ZnO + Fez03)to 500-670 K, there is an increase in the catalytic activity (for the heterogeneous reaction: 2 CO + O2 2 CO,) attributable t o the localized surface formation of product spinel at favourable sites, following phase boundary migration of appropriate species. A diminution in the catalytic properties after heating the reaction mixture to 670-770 K is attributed to the formation of a complete and coherent product layer. The onset of lattice penetration becomes detectable between 770 and 880 K and is accompanied by further changes in surface properties. In the range 900-1200 K, product phase formation becomes measurable by X-ray diffraction methods and further temperature increase reduces imperfection through the growth of product crystallites. One of the most significant conclusions is that extensive surface reaction, arising from the mobility of one or both reactants, generates a coherent product layer, corresponding t o complete +

268

surface nucleation, at temperatures well below those required for the production of appreciable amounts of crystalline ZnFezO4. Duncan et al. [325,1197] considered the influence of the physical form of the reactant on the kinetics of low temperature (963-1033 K) zinc femte formation. The rate process obeys the Jander expression [eqn. (14)] and other related rate equations with E = 300 kJ mole-'. The reaction is influenced by the prevailing atmosphere. It is concluded that ZnO is the more mobile constituent of the reactant mixture and this migrates t o coat the Fez03 particles. The rate-limiting step thereafter is diffusion of cations within the barrier product phase, probably accompanied by 0'- displacements. Since Zn2+ migration is expected to be relatively rapid, it is suggested that the overall rate of product formation is controlled by Fe3+movement. There are some indications that a change of mechanism occurs at higher temperatures (>1470 K). Parker et al. [1158] believe that an initial change in iron oxide composition precedes Zn'' incorporation. From gravimetric, X-ray diffraction, and magnetic measurements, it was concluded that between 670 and 770 K there was a substantial oxygen loss (0.070-0.075 atom per molecular formula). This was accompanied by the production of a spinel phase through which Zn'' may readily diffuse. The oxygen released may be readsorbed at the same temperature. Zinc migration may occur within the total volume of each iron oxide crystal and subsequent oxidation yields zinc ferrite and y-FezO3 with Zn2' in solid solution. In this interpretation, the important feature of the mecahnism is identified as the variation in stoichiometry. Further measurements on the system would be desirable, notably of the influence of oxygen pressure on reaction rate. 4.1.2 Other spinel formation reactions

Armijo [1198] has discussed a number of features of the kinetics and mechanisms of spinel formation. Under suitable conditions, the rates of some high temperature spinel syntheses can be studied gravimetrically [1199]. Holt [1180] has been concerned with the role of oxygen diffusion in C0A1204formation. Parker et al. [ 11581, considering observations for the reaction NiO + Fe203= NiFez04 conclude that the mechanism is similar to that operating in ZnFezO, production. Earlier work on the same system by Szabo et al. [1157] showed that doping of the reactants changed the reaction rate and the apparent activation energies. Values of E for the interaction of pure oxides and mixtures containing the doped oxides (NiO + 1%Li20), (NiO + 1%Crz03),and (Fez03+ 1%TiOz) were 397, 334,247 and 552 kJ mole-', respectively. It was concluded, from the influence of the additive on cation diffusion, that a quantitative description of the reaction required

269

information concerning the mobilities of both cations (i.e. Fe3+and NiZ+) in the oxide ion lattice. Cerovit et al. [1200] have prepared the mixed Ni-Zn ferrite by reaction of Fez03with a NiO-ZnO solid solution. The rate-controlling process was identified as cation diffusion, Ni2+and ZnZ+ in one direction and Fe3+and Fez+in the other (E = 250-288 kJ mole-'). Electron probe microanalyses revealed the establishment of concentration gradients across the product phase. From a kinetic study of the reaction MgO + Fez03 = MgFez04 in pelleted mixtures (1248-1373 K), Hulbert et al. [1201] identified iron oxide as the host lattice. The rate of product diffusion progressively decreased with time and E = 222 kJ mole-'. Beretka et al. [1202] showed that due allowance for the particle size distribution must be included in the kinetic analysis; fine powder reacted more rapidly than larger crystals. Yield-time data for the smaller crystallites (<1 pm) obeyed the empirical rate expression (Y = k log t, while for larger particles, rate measurements fitted the Jander equation [eqn. (14)]. Laqua et al. [1292] have made a detailed kinetic study of the interaction between COO and @-Ga203.In this reaction of the second kind (i.e. each reactant has been presaturated with the other), growth of the spinel product layer is parabolic and E = 300 kJ mole-'. The autocatalytic behaviour found [ 12031 for chromite formation, through the reactions of Crz03 with various oxides (CdO, CuO, MgO, NiO, and ZnO) in air, was attributed t o the intermediate production of the chromate which later decomposed to MCr204. Haber [1204] concluded that during the reaction MgO + CrzO3 = MgCrz04 the MgO particles were initially covered with a thin layer of spinel and that the subsequent increase in thickness of this phase proceeded by a process involving cation migration across it. At high temperature, there may be counter diffusion of both Mgz+ and Cr3+. Hulbert et al. [422] found evidence that Cr3+may enter MgO in solid solution, prior t o spinel formation, at the MgCr,O,-MgO interface. Below 1370 K, the most probable mechanism was identified as unidirectional lattice diffusion of Cr3+ with gas phase transport of oxygen. The reaction rate depended on the temperature at which MgO was precalcined, and E = 170 kJ mole-'. Further investigations of spinel formation reactions are to be found in the literature [ 11, but the above representative selection illustrates a number of typical features of these rate processes. Following migration of cations from one constituent onto the surfaces of the other, the process is limited by the rate of diffusion across a barrier layer. While obedience t o a particular kinetic expression is sometimes reported, the data available are not always sufficiently precise to enable the fit found t o be positively

270

preferred to those given with alternative related expressions. The effects of particle size distribution and of thermal pretreatments have not always been quantitatively determined. Some reactions are clearly more complicated than is indicated by the overall stoichiometry: there may be solid solution formation and the above account has included reference to systems in which there is evidence that one reactant may be oxidized (e.g. Cr2O3) or reduced (e.g. oxygen release from Fe203). While the diffusing cation(s) have been reliably identified in many specific reactions, other aspects of the mechanisms of spinel formation await more detailed characterization.

4.1.3 Calcium silicate formation and related reactions The interaction between CaO and Si02 at 1470 K occurs [ l ] in stages which may be represented schematically as CaO ICa2Si04lSi02 CaO ICa3SiOsICa2Si04ICa3Si207lSi02 CaO ICa2Si04ICa3Si207 ICaSi03ISi02 The stable end-product (CaSi03) is formed through a sequence of binary interactions, involving the intermediates and interfaces shown. This, and related reactions, are of particular significance in the cement and ceramic industries where interest has extended to ternary systems, also including A1203. Some progress has been made in the qualitative recognition of routes to the production of particular phases, usually involving binary interaction, e.g. anorthite (CaA12Si208)can be formed from the reactions of gehlenite (Ca2A12Si07)with Si02, or with ($ A1203 + S O 2 ) , but is not formed from CaA120, + 2 S O 2 . These, and allied rate processes of greater complexity, are of considerable technological importance but are difficult to study and there has been little progress in making quantitative kinetic measurements. It is not appropriate to review here the specialist field of cement formation reactions.

4.1.4 Tungstate and molybdate formation reactions The general conclusions of the preceding paragraphs are equally applicable to the reactions of a number of oxides with Moo3 or W 0 3 . In such processes, the Moo3 or W 0 3 is often the more mobile. Many solidsolid interactions of the type

R ~ +O3 MOO^ ~

=

~

~

(

~

0

0

~

)

~

(where R is, for example, La3+ or Fe3') obey [1205] the Jander equation [eqn. (14)]. Diffusion processes have also been identified in the reactions COO + W 0 3 = CoWO, SrO + Moo3 = SrMoO, CdO + Moo3 = CdMo04

(ref. 1206) (ref. 1207) (ref. 1208)

271

4.1.5 Double iodide formation

The exceptionally large ionic conductivities characteristic of certain double iodides [1182] make them particularly attractive systems for kinetic and mechanistic studies of s o l i d s o l i d interaction. Countercurrent migration of Ag’ and Hg2+ in the product phase has been identified as the rate-controlling process for [ 12091 2 AgI + HgI2 = Ag2HgI4 The interface reactions for AgI IAg2HgI4 lHgI2 can be represented as 4 AgI - 2 Ag’ + Hg2+

+

Ag2HgI4 + 2 Ag’ + 2 HgI2 - Hg2’

The rate of product formation can be predicted from a knowledge of the conductivity and transport numbers of cations in the product barrier phase and appropriate thermodynamic data. This interpretation is based on the Wagner model (Sect. 2.3). [In principle, reaction schemes similar to that given in the preceding paragraph may be developed for other comparable rate processes, for example spinel formation. However, Stone [27] has pointed out that, where the barrier phase is not an efficient ionic conductor, the overall reaction may be controlled by the movement of a single cation and anion. In addition, there is the probability that lattice imperfections (internal surfaces, cracks, “leakage paths” [ 11721, etc.) may provide the most efficient route t o product formation.] In the reaction [418] KI + 4 AgI = KAgJ5 the thickness of the product layer increased linearly with time and values of E for y- and a-AgI were 135 and 90 kJ mole-’, respectively. A marked reduction in rate occurred on increasing the temperature across the AgI phase transition a t 420 K. The analogous reaction of y-AgI with RbI (-+RbAgd,) was very much slower ( E = 190 kJ mole-’). While this reaction did not yield Rb2Ag13, the use of this compound as an alternative reactant yielded RbAg415 a t a rate which was only slightly slower than that using RbI. Since, in both these reactions (i.e. KI o r RbI and AgI), product formation occurs on both sides of the original contact interface, it is believed that there is migration of both alkali metal and silver ions across the barrier layer. Alkali metal movement is identified as rate limiting and the relatively slower reaction of the rubidium salt is ascribed to the larger size and correspondingly slower movement of Rb’. The measured values of E are not those for cation diffusion alone, but include a contribution from

272

the heat of solution. Rates of reaction of mixed crystals (K,Rb)I with yAgI were somewhat higher than those predicted from consideration of the behaviour of the single constituents and rates were deceleratory with product layer thickness proportional to (time)"2. The K' ions migrate more rapidly than the larger Rb' ions, and the consequent partial separation of cations is compared with chromatographic frontal analysis. Flor et al. [ 12101 identify countercurrent migration, with diffusion of the monovalent cation, as the rate-limiting process in the reactions 4 0-AgI + MI = MAg& (M = K',Rb'

or NH',)

4.1.6 Other reactions

Numerous intercalation reactions are known in which one reactant enters the lattice of the other. Such behaviour is conveniently illustrated by reference to two recent studies. Lithium undergoes a low temperature (298 K) topochemical reversible reaction with transition metal compounds (e.g. TiS2, NbSe3) [1211] in which the host lattice structure may be partially retained (e.g. in Li,TiS2, Li3NbSe3).The reaction [ 12121 Ti + TiB2 = 2 T B proceeds by surface migration of titanium, followed by diffusion-controlled growth of product TiB into the TiB2. 4.2 REACTIONS OF THE TYPE A@) + B(s) -+ C(s) + D(g)

Such systems have the experimental advantage that kinetic data may be obtained by gravimetric or evolved gas pressure measurements. However, these data must be interpreted with care, since gas release is not necessarily concurrent with the solidsolid interaction but may, in principle, be a distinct rate process under independent kinetic control and occur either before or after reaction between the solids. Possible mechanisms to be considered, therefore, include the following. (i) A single step reaction, in which measurements of the yield of C also determines the quantity of D formed concurrently [410]. (ii) Initial dissociation of one reactant followed by interaction of the residual phase with the second reactant A(s) + E(s) + D(g) (dissociation) E(s) + B(s)

+

C(s) (interaction)

If both steps are kinetically distinct, measurement of gas evolution (D) does not give any information concerning the rate of the subsequent interaction (formation of C). If E is produced in a finely divided state, it may be appreciably more reactive than alternative bulk preparations of the

273

same compound. There is also the possibility that the presence of B (C or E) may influence the kinetics of dissociation of A. An example [1213] of a two-step process is the interaction between c0304 and A1203 above 1170 K, which occurs as COO + A1203since Co304dissociates at <1120 K. (iii) Double salt formation could also occur prior t o gas evolution and it is possible to represent the two-step consecutive reactions as A(s) + B(s) + AB(s) + C(s) + D(g) While many reactions are undoubtedly of these three types, few kinetic studies are available. There are, however, close resemblances between specific rate processes in which a gas is evolved and the more intensively studied spinel formation reactions (Sect. 4.1). 4.2.1 Reaction o f lithium carbonate with ferric oxide Johnson and Gallagher [410] showed that, in finely divided powder mixtures, Li2C03 and Fe203react significantly below the usual temperature of carbonate dissociation, so that C 0 2 evolution can be used in kinetic studies of the solid state reaction Li2C03+ Fe203= 2 LiFeOz + C 0 2 The rate data fitted the Ginstling-Brounshtein equation [eqn. (ll)] (threedimensional diffusion) and E 210 kJ mole-' (653-783 K). The magnitude of A increased somewhat as the particle size of Fe203 was reduced. It is suggested that Li2C03 can migrate t o cover the Fe203 particles, react t o release C02, and the rate-limiting process is diffusion of Li' across the LiFe02 product layer. Oleinikov and Shumyantsev [ 12141 report E = 226 and 255 kJ mole-' for simultaneous interactions at Fe203 dislocations and the diffusion-controlled reaction, respectively.

-

4.2.2 Reactions of barium carbonate with various oxides The reactions of BaC0, with a number of oxides are accompanied by the evolution of C02. Attention has often been focussed on the identification of the several product phases, though some kinetic information is available. (i) S i 0 2 . The reaction between BaC03 and Si02 finally yields BaSiO, and the following reaction mechanism has been proposed [ 12151. SiOzIBaCO,

(equimolar reaction mixture)

SiOzIBaSiO, IBaCO,

(BaC0, + SiOz -+ BaSi0, + C 0 2 )

Si02IBaSi031BazSi041BaC03 (BaSiO, + BaCO,

+

Ba2Si04+ C 0 2 )

Si02IBaSi0, IBa2Si04

(Ba2Si04+ Si02+ BaSiO,)

BaSi0,

(final product)

274

In a non-isothermal study of this reaction, Kato and Suyama [1216] found that the Si02 particle size markedly influenced the reactivity of this component, the formation of the intermediate (BazSi04),and the value of E . One value of E found here (226 kJ mole-') was close to that reported earlier by Jander. Yamaguchi et al. [1217] identify the partially overlapping steps in the formation of Ba2Si04as BaC03 + Si02 = BaSi03 + C 0 2 BaC03 + BaSi03 = Ba2Si04+C 0 2 From isothermal measurements at 1123-1223 K , it was shown that the first step was a strongly deceleratory reaction and the a-time curves for the second step were sigmoid. Values of E were 136 and 85 k J mole-', respectively, and were in approximate agreement with those determined using the equimolar mixtures (BaC03 + Si02) and (BaC03 + BaSi03), for which the E values were 116 and 74 kJ mole-', respectively. Ball milling of the reactant mixture (2 BaC03 + S O 2 ) preferentially diminished the BaC03 particle size so promoting the initial formation of BaSi03 and accelerating the onset of the second step. It was concluded that the rates of formation of the two silicate phases are determined by the migration rates of Ba" in these phases and by the interfacial rate processes. (ii) T i 0 2 .In the presence of C 0 2 , the reaction

BaC03 + Ti02 = BaTi03 + C 0 2 proceeds quantitatively to completion [go], but if the C 0 2 is removed, the BaO formed reacts further t o give Ba2Ti04. Carbonate decomposition is an independent step which precedes titanate production. Yamaguchi et al. [1218] report values of apparent activation energies of 200-280 kJ mole-' for this reaction, but express reservations about their mechanistic significance. (iii) F e 2 0 3 and AL2O3.To gain further insight into the mechanisms of reactions between powdered solids, Beretka et al. [1219] studied the interaction of an equimolar mixture of BaC03 and Fe203. Evolution of COz, probably due to BaC03 decomposition, was a deceleratory process. None of the usual rate laws was obeyed, though a fit was obtained to the empirical expression, (Y = k log t , between 933 and 1033 K. There was evidence that surface interactions occurred at significantly lower temperatures. Electron micrographs revealed the development of high area features (spikes, platelets, etc.) during the course of reaction and it was concluded that the mechanism is complex. Just how complicated the participating chemical processes are was revealed by Wilson et al. [424] who made electron probe microanalyses of the product phases formed during reactions at 1220-1520 K. The reactant samples studied consisted

275

of a sintered Fez03 pellet surrounded by BaC03 and, after heating, the adherent assemblage was sectioned normally to the original BaC03-Fe203 interface for analysis. Five different product phases were identified and, although not all were detected in every experiment, substances always appeared in the same sequence Ba5Fe208IBa3Fez06IBa2Fez05lBaFe20 lBaFelzO1 9 IFe20 Similar experiments with Alz03 in the range 1300-1570 K yielded the products Ba 5A1208I Ba 3A1206IBaA120 I “BaA1 zO

9”

IAlzO

where “BaA112019”was composed of two different substances. While the rate processes occurring at each interface may obey simple laws, the overall reactions are clearly complicated. A full kinetic analysis would require information concerning the rate and geometry of advance of each interface. It would also be necessary t o determine the influence of stresses and strains on the development of cracks and internal surfaces, the generation of lattice imperfections and other changes which can exert a control over the ease of diffusion of participants across each barrier phase. The appearance of several distinct products in both reactions (i.e. BaC03 + Fez03 or A1203) indicates that neither can be regarded as a particularly suitable system for fundamental kinetic and mechanistic studies. If such information was required concerning these reactions, a more profitable approach would appear to be through individual studies of the constituent binary systems, e.g. BasFezOB+ Ba~FezO6,etc. 4.2.3 Molybdate and tungstate formation reactions Some of the reactions which yield MMo04 or MW04, referred to in Sect. 4.1.4, are closely related t o those discussed here in which a carbonate or higher oxide is used as reactant. For example, the solid state reaction c0304 -t 3 MOO3

=

3 COMOO4 -I- 0

2

(and related processes) have been particularly extensively studied [ 12201 owing to the importance of cobalt molybdate as an active and selective catalyst for organic reactions. (The feature which distinguishes this reaction of Co304from the temporary and partial reduction of Fe,O,during zinc ferrite formation [1158],Sect. 4.1.1,is that here the divalent cation is retained in the solid product and the oxygen permanently released.) The evidence indicates that there is rapid surface diffusion of Moo3 or W 0 3 onto appropriate oxides and the product may catalyze oxidation or reduction of the reactant. Haber and co-workers [1220] have studied the kinetics of C o 3 0 4 + Moo3interaction for an unusually wide range of compositions of mixtures,

276

having Co : Mo molar ratios in the range 9 : 1 t o 1 : 9. The isothermal reaction rates were measured from gas evolution and solid product compositions (the polymorphic forms a-CoMo0, and b-CoMoO,) were determined from X-ray diffraction maxima. Yield-time data fitted the parabolic law [eqn. (lo)] and the Jander equation [eqn. (14)] more satisfactorily than other kinetic expressions. For the reactions (793-923 K) of mixtures having compositions (Co : Mo) 3 : 7, 1 : 1 and 7 : 3, values of E were close t o 220 kJ mole-’. Rate coefficients increased with area of the Co304 reactant and variations with composition of the mixture were shown t o be due entirely to changes in the numbers of intergranular contacts. MOO, was identified as the mobile participant and diffusion of the molybdenum ion was rate limiting. The initial product of reaction at 823 K was identified as a-CoMo04, formed on c0@4 surfaces, with a defective lattice which facilitates the polymorphic transition to b-CoMo04. Further discussion of the mechanism of reaction was given in the article cited [ 12201. Kononyuk [1221] reports obedience to the Jander equation [eqn. (14)] for the solid state interaction of a CoCO, + MOO, (15 : 1)mixture. Haber and co-workers [1220] have made a parallel study of the reaction Mn203 + 2 MOO, = 2 MnMo04 + O2 between 753 and 963K. Again, MOO, was identified as the mobile participant, enveloping Mn203 particles with a coherent layer of product, so that the sequence of phases along any radius was Mn203IMnMoO IMoO, This is the Jander model and E for the diffusion limited reaction is 140 kJ mole-’. This rapid establishment of a complete coherent film of product on Mn2O3 contrasts with the behaviour of Co304where product formation was apparently initiated only at points of Co304-Mo03 contact and the MOO, does not migrate to cover all Co304 particles. (This accounts for kinetic obedience t o the parabolic law.) It is suggested that Moo3 is capable of “wetting” (and, therefore, migrates readily across) Mn@3 surfaces, but does not so “wet” the Co304. This work has been extended [1220] to the formation of the corresponding tungstates through the interactions of WO, with Co304and with Mn2O3. Again, the mechanism is identified as surface migration, followed by bulk diffusion which is considered to be rate-limiting. Reactions proceed to completion in two stages. Reported values of E are 297, (no value); 184, 52 kJ mole-’ for c0304 and Mn203,respectively. Zukhovskii et al. [1222] conclude that the reaction MgC03 + MOO3 = MgM004 + C02 is complicated and involves a number of distinct steps. Initially, particles of the reactant mixture become adherent and a barrier layer of MgMo04 is

277

formed across which diffusion is rate-limiting. From non-isothermal measurements of the rates of reactions of Moo3 with the oxides, hydroxides, and carbonates of calcium, strontium, and barium, it was concluded that initial surface-controlled reactions (0.04< a < 0.4, E = 104 k J mole-') were followed by diffusion-limited processes (0.4 < a < 0.9,E 230 kJ mole-'). In satisfactory agreement with this value of E , Flor et al. [1223] report E = 250 kJ mole-' for

-

Moo3 + SrC03 = SrMoO, + C 0 2 and identify Mo6+as the migrating entity in the diffusioncontrolled reaction. Jander (see ref. [l]) showed that the reaction CaC03 +Moo3 (793-823 K) obeyed the kinetic equation (14). The solid state formation of T12W04occurs [1224]in two steps T12C03= T120 + C 0 2 T120 + W 0 3 = T12W04

(330-570 K) (670K)

At high temperatures, the product loses oxygen and there is discoloration of the residual non-stoichiometric T12W04. 4.2.4 Oxidation of carbon

There have been many studies of the reduction of oxides and of oxyacid salts with elemental carbon, some of which are of great technological importance. Although both reactants may be solids MO, + C + M + (CO,CO2) the mechanisms proposed usually involve gaseous intermediates and gassolid processes rather than direct solidsolid interaction. This is because there are rapid and facile interconversions of the highly mobile and reactive products (CO and C02) at reaction temperature which permit the efficient transfer of carbon t o and oxygen from the oxide or oxyacid phase. Such rate processes are outside the scope of this survey. The theory of the kinetics of metal oxide-arbon interaction has been discussed by Sohn and Szekely [1225]. CO and C 0 2 have been shown t o be intermediates in the reduction of Fe203 [1226],c0304 [1227],and Si02 [ 12281.

The reaction of Si02 with Sic [ 12291 approximately obeyed the zeroorder rate equation with E = 548-405 kJ mole-I between 1543 and 1703 K. The proposed mechanism involved volatilized SiO and CO and the rate-limiting step was identified as product desorption from the Sic surface. The interaction of U 0 2 + Sic above 1650 K [1230]obeyed the contracting area rate equation [eqn. (7),n = 21 with E = 525 and 350 kJ mole-' for the evolution of CO and SiO, respectively. Kinetic control is identified as gas phase diffusion from the reaction site but E values were largely determined by equilibrium thermodynamics rather than by diffusion coefficients.

278

The reduction of calcium phosphate with carbon [ 12311 Ca3(P04)2+ 5 C = 3 CaO + P2 + 5 CO obeyed the first-order equation [eqn. (15)] and was accelerated by the addition of A1203 or Si02 (which resulted in the production of residual CaA1204 or CaSi03). Values of E for the reaction alone and in the presence of these additives were 227, 265, and 184 kJ mole-', respectively, at -1320-1670 K. Hoffmann and Patai [ 11601 have investigated the influence of various pretreatments and ageing on the solidsolid interactions between KClO and KI03 and carbon. The process KC104 + 2 C = K C l + 2 C02 was shown to obey the empirical rate expression

for wide variations in composition of the reactant mixtures. The carbon particles were relatively small, thus surrounding each crystallite of oxidant, and the rate is proportional to the area of KC104represented by the term (1- a)2'3in the rate equation.

4.2.5 Other reactions Between 1093 and 1123 K, the solid state process [1232] CuCr204+ CuO = Cu2Cr204+

0 2

consists of the following steps: decomposition of CuCr204t o Cu2Cr204 and volatilization of CrOBwhich then reacts with CuO t o form Cu2Cr204. Initially, the rate-limiting step is Cr03 evolution and the reaction obeys the contracting volume equation [eqn. (7), n = 31. Subsequently, however, the reaction becomes diffusion-controlled and is described by the kinetic relation

(1- ( 1 - ( Y ) ~ ' ~ =} ~k log t Reactions of alkaline earth carbonates with V2OS [1233] occur in the solid phase and are limited by diffusion of ions in the oxide lattice. A suggested catalytic effect by V205 on the carbonate decomposition was not confirmed. The formation [1234] of Tl3V5OI4from T1NO3 + V205 proceeds stepwise through the intermediates Tl2V6OI6and T1V03. Since the reaction [1235] TlCO3 + I2 = T12012 + C02 obeys zeroarder kinetics in the range 298-348 K ( E = 58 kJ mole-'), it is concluded that the product layer does not remain coherent.

279

4 . 3 REACTIONS OF THE TYPE AB(s) + CD(s) + AD(s) + CB(s)

This solid state double decomposition may be schematically represented by AB ICB IAD ICD Two product barrier layers are formed and the continuation of reaction requires that A is transported across CB and C across AD, assuming that the (usually smaller) cations are the mobile species. The interface reactions involved and the mechanisms of ion migration are similar to those already described for other systems. (It is also possible that solid solutions will be formed.) As Welch [lll]has pointed out, reaction between solids, however complex they may be, can (usually) be resolved into a series of interactions between two phases. In complicated processes an increased number of phases, interfaces, and migrant entities must be characterized and this requires an appropriate increase in the number of variables measured, with all the attendant difficulties and limitations. However, the careful selection of components of the reactant mixture (e.g. the use of a common ion) or the imaginative design of reactant disposition can sometimes result in a significant simplification of the problems of interpretation, as is seen in some of the examples cited below. Kinetic studies of the reactions Cu + AgCl = CuCl + Ag and AgCl + NaI = NaCl + AgI have been simplified by careful consideration of the experimental procedures; these are schematically represented in Fig. 22. The interpretation of the rate data has been discussed by Wagner [ 12361. The presence of the common ions permits the use of a system that corresponds to a galvanic cell with closed circuit. In the first example [Fig. 22(a)], the electron mobility in the metals is large, the ionic conductivity of AgCl is greater than that of CuC1, so that it is possible t o calculate the rate coefficient for the overall chemical change from the resistance of the CuC1. In the second example [Fig. 22(b)], the reaction rate is controlled by the migration of two ions each in two different phases. The rate-controlling process in the solid state displacement reaction CsCl + NaI = CsI + NaCl was [1293] diffusion of the iodide ion in CsCl and the parabolic rate equation was obeyed. Leute and Stratmann [1237] have shown that the double conversion between CdTe and HgSe is strongly influenced by intrinsic doping. The pathway for reaction is identified as the movement of interstitial species,

280

..\

/ z cu-CU'

+

n g + + r- - a g

E

1

C u ' + AgCI

Na'

+ AgCI

t

-

CuCl

Ag*

NoCl + Agt

(b)

Ag*+NaI-AgI+Na'

Fig. 22. Schematic representation of the solid phase double decomposition reactions (a) Cu + AgCl = CuCl + Ag (b) AgCl + NaI = NaCl + AgI

possibly vacancies, and quantitative data are given for the dependence of diffusion coefficient on metal content. Deb [1238] prepared thin films of inorganic azides (for optical studies) by reaction of an alkali metal azide with a heavy metal iodide, e.g. CUI + KN3 = C U N +~ K I While kinetic investigations of these reactions were incomplete, it was shown that the deceleratory process obeyed the Jander equation [eqn. (14)] approximately. Kutty and Murthy [1159] have made a kinetic study of the solidsolid reaction between tricalcium phosphate and urea nitrate, a process of possible technological importance. A reduction in particle size, notably of Ca3(PO&, increased the rate of reaction in powder mixtures and also changed the kinetic characteristics (318-338 K). Reaction in relatively coarse material (between -180 and +200mesh) obeyed the parabolic

28 1

relation [eqn. (lo)] and E = 76 kJ mole-', whereas in fine powder (between -300 and +320 mesh), the first-order equation described the data and E was larger, 119 kJ mole-'. Kinetic measurements were interpreted with reference to evidence from microscopic examination of sections of reaction interfaces, developed on heating composite pellets in which a layer of urea nitrate was sandwiched between layers of Ca3(P04)2. The first step in the reaction was identified as proton transfer t o the phosphate, producing HPO$-, followed by the slow step involving combination of Ca2' and NO,. Results of etching of interface sections suggested that dislocations provide pathways for NO 3 movements. The first-order obedience of reaction rate (in small particles) was attributed t o control by Ca(N03)2 nucleation whereas, in the larger crystallites, it was concluded that the rate process was subject t o diffusion control. High temperature reactions between solids containing no common ions can result in such complicated behaviour that it is difficult t o elucidate the stoichiometry and kinetic measurements are unlikely to be meaningful. For example, from consideration of the interactions of NiS with the oxides of manganese and of iron, Gladman and Buttler [1239] list 38 stoichiometric equations representing possible chemical changes involving various degrees of reactant oxide reduction and oxidation of NiS (with the formation of NiO, SOz, SO$-, etc.). The products obtained depended on the ratio of reactants used and attempts were made to identify the reactions occurring by TG, DTA, X-ray diffraction, and analytical measurements. Kochkin et al. [ 12401,working with the relatively simpler binary mixtures CdS + ZnS04 and ZnS + CdS04, identified several reaction steps on heating. Secondary sulphates are formed which subsequently decompose. The temperatures and stoichiometries of some solid state reactions of sodium oxide with Cr and Zr are given by Barker and Wood [ 12411. Although not strictly encompassed within the scope of this review, it is appropriate to make a brief reference to those rapid and highly exothermic rate processes capable of sustaining themselves through selfheating. Reaction propagates by rapid transfer of energy or reactive intermediate at a high temperature interface. The theory of the propagation of gasless reactions in solids has been discussed recently by Hart et al. [ 1242, 12431 (see also Ubbelohde [1244]).Hill [185,1245]has discussed the physics and chemistry of the self-sustaining reaction between KMnO and iron, approximately expressed as

-

2 KMn04 + 2.42 Fe = 0.81 Fe304+ K 2 0 2 MnOl.8g In low density reactant compacts, the reaction is believed to involve gas phase oxygen diffusion whereas under conditions of improved contact, in highdensity material, the mobile species is identified as Fez+.The metal catalyzes decomposition of the oxidant (KMn04), an effect that is inhibited by small quantities of certain additives (e.g. NaF). There is a large and specialist literature devoted t o self-heating reactions.

282

4.4 MORE COMPLICATED REACTIONS

The simplest solidsolid reactions are those involving two solid reactants and a single barrier product phase. The principles used in interpreting the results of kinetic studies on such systems, and which have been described above, can be modified for application to more complex systems. Many of these complex systems have been resolved into a series of interconnected binary reactions and some of the more fully characterized examples have already been mentioned. While certain of these rate processes are of considerable technological importance, e.g. to the cement industry [l], the difficulties of investigation are such that few quantitative kinetic studies have been attempted. Attention has more frequently been restricted t o the qualitative identifications of intermediate and product phases, or, at best, empirical rate measurements for technological purposes.

283

Chapter 6

Conclusions

There have been remarkably few reviews of the chemistry of decompositions and interactions of solids. The present account is specifically concerned with the kinetic characteristics described in the literature for the reactions of many and diverse compounds. Coverage necessarily includes references to a variety of relevant and closely related topics, such as the background theory of the subject, proposed mechanistic interpretations of observations, experimental methods with their shortcomings and errors, etc. In a survey of acceptable length, however, it is clearly impossible to explore in depth all features of all reports concerned with the reactivity and reactions of all solids. We believe that there is a need for separate and more detailed reviews of topics referred to here briefly. The value of individual publications in the field, which continue t o appear in a not inconsiderable flow, would undoubtedly be enhanced by their discussion in the widest context. Systematic presentation and constructive comparisons of observations and reports, which are at present widely dispersed, would be expected t o produce significant correlations and conclusions. Useful advances in the subject are just as likely t o emerge in the form of generalizations discerned in the wealth of published material as from further individual studies of specific systems. Perhaps potential reviewers have been deterred by the combination of the formidable volume and the extensive dispersal of the information now available. Numerous and varied conclusions have been stated explicitly or implied in the text of Chaps. 2-5. These include mechanistic deductions, references to inconsistencies or irreconcilable interpretations found in different studies, recommendations for the re-analysis of certain experimental data etc. These will not be repeated in detail in the present chapter, which summarizes only the most significant and general conclusions relating t o the kinetics of decompositions and interactions of solids.

1. Decompositions of solids The reliability of mechanistic deductions, based on kinetic analysis of &-time data, depends mainly on the following. (i) Accurate knowledge of the occurrence (or absence) of melting, perhaps partial or local. This is sometimes not clearly discussed in published reports.

284

(ii) Accurate specification and measurements of a, particularly when reversible, concurrent, consecutive, or secondary reactions are involved. (iii) The availability of supporting evidence, such as microscopic measurements, which can provide more detail on the individual contributions from the separate and distinct processes of nucleation and of growth. (iv) Quantitative allowance for the influences of additional factors which exert some control over kinetic behaviour; these include particle sizes, reactant self-heating (or cooling), defect content, pretreatment, atmosphere, recrystallization, preliminary dehydration, etc. While non-isothermal measurements can provide a rapid and useful qualitative indication of the occurrence of one or more reactions and the main features of behaviour (such as reaction temperatures, phase transitions, melting etc.), the method cannot be recommended as providing the most accurate kinetic data, particularly when the reaction is reversible. Kinetic analysis of a-time measurements usually involves curve-fitting of the data t o a theoretical expression [f(a)-time] based on geometric considerations. Different workers studying the same reaction have frequently (though not invariably) reached exact, or close, agreement concerning the kinetic expression that describes the yield-time observations most satisfactorily. Conclusions are in many instances supported by microscopic observations. Differences of interpretation of a particular fit can arise where the kinetic expression concerned can be derived from alternative interface advance models and microscopic examination is incapable of resolving the ambiguity due to properties of the reactant such as fine particles, opaque crystallites, etc. Apart from these unusual or specific difficulties, considerable progress has been achieved in obtaining agreement concerning the characteristic shapes of a-time curves for decompositions of many and diverse solids. However, the quantitative criteria used in identifying a particular rate law are not always stated and the subject would benefit from a critical reassessment using a more rigorous statistical approach. The next stage of interpretation in analysis of rate data, the identification and characterization of processes occurring at the reaction interface, is considerably more difficult. There is, therefore, correspondingly less agreement concerning the quantitative data upon which conclusions may be based. The kinetic parameters most frequently used to provide information concerning the step identified as rate-limiting are A and E . Values of these parameters reported by different workers for nominally the same chemical change often show significant deviations. These inconsistencies make it difficult t o use such data in the formulation of reaction mechanisms, particularly since the theoretical justification for associating A and E values with a single step in the reaction is incomplete and relies partly on the analogy with homogeneous rate processes. Arrhenius parameters for many reactions do not show acceptable conformity with the predictions of the Polanyi-Wigner equation [eqn. (19)] and have, in conse-

285

quence, been described as “abnormal”. Obviously, identification of significant participants and their roles and concentrations within a reaction zone which is inaccessible to direct study must lead to discrepancies, since the relevant information must be derived indirectly from measurements and may, therefore, be of limited reliability. Some of the difficulties which are inherent in attempts to portray the sequence of molecular events through which the components of a solid reactant are converted into products are illustrated in the following examples. Reference has already been made above to the difficulties which have arisen concerning the value of E for the relatively simple decomposition reaction of BaN6. These apparent inconsistencies emphasize the need for care in the design of experimental and interpretive procedures used in the measurement of activation energies required for the formulation of reaction mechanisms. In reversible decompositions, such as the reaction of CaC03, reported values of E equal to the dissociation enthalpy should be treated with reserve, unless experimental conditions were such that possible readsorption of product gases has been completely precluded. Ammonium perchlorate decomposition, which is one of the most exhaustively investigated solid state reactions, is now regarded as being controlled by the breakdown of an adsorbed species (HC104)on the crystal surfaces. Mechanistic studies have advanced beyond investigation of the overall reaction and recent work has been concerned with electrical conductivity (identification of mobile entities) and the catalytic breakdown of perchloric acid. In the long history of study of this, admittedly relatively complicated, reaction a large number of different kinetic characteristics [f(a!)--t obediences, magnitudes of A and E l have been reported. As in other heterogeneous rate processes, the significance to be attached to the magnitudes of Arrhenius parameters has yet to be agreed. It may also be pointed out that sigmoid-shaped a-time curves are not necessarily indicative of a reaction controlled by a simple nucleation and growth process; the mechanism may be more complicated. (For example, the decomposition of nickel formate is probably a two-step rate process in which productcatalyzed anion breakdown follows dehydration and the growth of nuclei during copper formate decomposition occurs during concurrent sintering and sublimation of the metallic product phase.) The central role of imperfections in mechanistic interpretations of decompositions of solids needs emphasizing. Apart from melting (which requires redistribution of all crystal-bonding forces, by a mechanism which has not yet been fully established) the decompositions of most solids involve the participation of atypical lattice constituents, structural distortions and/or surfaces. Such participants have, in particular instances, been identified with some certainty (e.g. excitons are important in the decompositions of some azides, dislocations are sites of nucleation in dissociations of a number of hydrates and carbonates). However, the

286

quantitative appraisal of the role of such species in particular reactions requires much more detailed knowledge of their precise structures and properties, including concentrations, reactivities, mobilities, etc. Because these essential participants are atypical, their characteristics are not readily measured and there is not usually sufficient information available for the quantitative prediction of kinetic characteristics of decomposition of a particular reactant sample. Whether studies of chemical reactivity will increase our understanding of the properties of crystal imperfections or vice versa remains t o be seen; at present it is clear that atypical lattice zones provide the route for many chemical reactions of solids. The concept of the reaction interface is the central feature of the interpretation of shapes of a-time curves; as yet comparatively little information is available concerning the steps which culminate in its generation (nucleation) or the steps which contribute to and control its advance (growth). 2. Interactions of solids

The involvement of two (or more) solid reactants increases the number of parameters which must be measured t o determine quantitatively the progress of all reactions occurring. In multicomponent mixtures, factors possibly influencing kinetic behaviour include overall composition, ratio of quantities of phases present, the absolute and relative sizes of all crystalline participants, the degree of compaction and mixing, etc. In addition, there are the effects of conditions within the reaction vessel, gases present, etc. During the course of reaction each barrier product phase must be recognized and the rates and extents of movement of each individual interface determined at appropriate time intervals for reactions at various temperatures. Many of the systems which have been successfully studied in detail have been particularly selected t o exploit simplifying characteristics, so that fundamental rate investigations have been concerned with reactant combinations involving a minimum number of experimental variables. The maintenance of product formation, after loss of direct contact between reactants by the interposition of a layer of product, requires the mobility of at least one component and rates are often controlled by diffusion of one or more reactant across the barrier constituted by the product layer. Reaction rates of such processes are characteristically strongly deceleratory since nucleation is effectively instantaneous and the rate of product formation is determined by bulk diffusion from one interface to another across a product zone of progressively increasing thickness. Rate measurements can be simplified by preparation of the reactant in a controlled geometric shape, such as pressing together flat discs at a common planar surface that then constitutes the initial reaction interface. Control by diffusion in one dimension results in obedience to the

287

parabolic law [eqn. (lo)]. Reactions in powders are often described as obeying the Jander equation [eqn. (14)], though kinetic analyses are not always precise since yield-time data are not particularly accurate. The increased ease and flexibility of making chemical analyses of material in the vicinity of reaction interfaces, which has resulted from the development of microanalytical instruments, is expected to facilitate the more rapid development of understanding of reactions between solids. Measurements of composition-distance profiles in selected sections of a reaction zone combined with conductivity data and transport numbers offers a most powerful approach to the identification of mobile constituents in the barrier phase. Other factors which may exert some control on reaction rates are solid solution formation, lattice imperfections, impurities present and changes in valency (perhaps only temporary) of the ions participating. The controls of reaction may also be changed or influenced appreciably by variations in temperature, product yield, sintering, annealing, phase transformation, strain-induced cracking, etc. Thus, the formulation of reaction mechanisms cannot be based on kinetic evidence alone but requires the support of all other relevant information available. As with solid phase decompositions (Sect. l), the kinetic characteristics of solidsolid interactions are controlled by the properties of lattice imperfections, though here many systems of interest involve the migration, in a crystal bulk of a mobile participant, from one interface to another. Kinetic measurements have been determined for reactions in a number of favourable systems, but there remain many possibilities for development in a field that is at present so largely unexplored.

288

Acknowledgments

It is a particular pleasure to express our thanks to the authors, editors, and publishers who so readily granted us permission to reproduce diagrams from their publications. These are as follows: Fig. 4, Thermochimica Acta, ref. 73; Fig. 9 and Table 9,International Union of Crystallography, ref. 580; Fig. 12, Pergamon Press, ref. 596; Fig. 14, Academic Press, ref. 36; Fig. 15, Osterreichische Akademie der Wissenschaften, ref. 696; Fig. 18, American Chemical Society, ref. 97;and Fig. 19,The Chemical Society, London, ref. 1110.

M.E.B., D.D. and A.K.G.

289

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323

A acceleratory period, in decomposition of Mg(OH)2,138 -,-, NHdC104,197 -, in solid reactions, 41, 42, 44, 51, 58, 60, 80,81 -, in solidsolid interactions, 261, 262 actinide formates, decomposition of, 215, 216 actinide oxalates, decomposition of, 224 activated complex, and solid reactions, 89,93,94,230 activation energy, and solid reactions, 6, 7, 29, 42, 8 3 , 8 8 , 89, 92, 94-96, 230, 284,285 -, determination of, 87,97,99-108 -, of BaC03 + SiO2, TiOz, 274 -, of Ca3(P04)2 + C, 278 -, of Ca3(P04)2 + ureanitrate, 281 -, of decomposition of alkandioates, 218-227,244,245 -, -,alkanoates, 211-213, 215-218 -, -, ammines, 233-235 -,-,ammonium salts, 196, 197, 200208,264 -, -, azides, 159-165 -, -,CaMg(C03)2, 241,242 -, -, carbides, 154, 156 -, -, carbonates, 95, 168-174 -,-, chlorites, 190 -, -,chromates, 194 -, -, CzOi-, 218 -,-, complexes, 236-238 -, -, cyanamides, fulminates, 1 6 6 -, -, halates, 188-190, 265 -, -, hydrides, 1 5 5 , 1 5 6 -, -, hydroxides, 138-140 -,-, maleate ion, 226 -, -, malonic acid, 225 -, -, NazCas(S04)6, 245 -, -, nitrates, nitrites, 183, 184 -,-, nitrides, 153 -, -, oxides, 146-151

_ ,- , oxyhalides,

141, 142

-, -, perhalates, 186-188 -, -, permanganates, 191,193, 194 -, -, phosphates, 184, 1 8 5 -, -, pyridine complexes, 235 -, -, salts of sulphur acids, 175-182 -,-, sulphides, 157 -, of dehydrations, 123, 124, 126, 130135,150 of dehydroxylation of clays, 142-144 of LizCOJ + Fe203,273 of Ni + 0 2 , 2 5 8 of oxide-xide reactions, 276, 277 of Sic + SiO2, UO?, 272 of spinel formation, 268, 269, 271 of TlC03 + 12,278 ageing, and solid reactions, 77, 159, 166, 173, 191, 198, 204, 205, 222, 223, 249,278 alloys, 56, 57, 256 aluminium, effect on decomposition of AgzSOj, 181 aluminium ammonium sulphate, decomposition of, 201 aluminium hydroxide, decomposition of, 140 aluminium mellitate, decomposition of, 228 aluminium oxide, effect on Cas(P04)~+ C, 278 -, effect on decomposition of C0304, 150 -, reaction + BaC03, 275 -, -, COO, 2 5 9 , 2 6 8 , 2 7 3 -, -, SiO?/CaO, 270 -, -, Z n 0 , 2 6 7 aluminium perchlorate, decomposition of, 188 aluminium sulphate, decomposition of, 176,178 alums, decomposition of, 4 7 , 4 8 , 93, 245 -, dehydration of, 121,122, 124, 131 ammonia, and decomposition of cobalt ammine thiocyanates, 234

-, -, -, -, -, -, -,

3 24

-, -, iron nitride, 153

-, determination of, 22, 23 -, effect on decomposition of ammines, 74,233

-, -,ammonium salts, 36, 167, 195, 198,199,201,203-205,264

-, reaction + SO2 in solid, 39

ammonium acetate, decomposition of, 203 ammonium azide, decomposition of, 207, 208 ammonium benzoate, decomposition of, 203 ammonium bromate, decomposition of, 199,200 ammonium carbonate, decomposition of, 202 -, effect on decomposition of (NH4)2S2043 201 ammonium chlorate, decomposition of, 199,200 ammonium chloride, effect on decomposition of chromium complexes, 236 ammonium chromates, decomposition of, 205,206 ammonium citrate, decomposition of, 203 ammonium hydrogen carbonate, decomposition of, 203 ammonium hydrogen sulphate, decomposition of, 200 ammonium iodate, decomposition of, 199,200 ammonium iodide, reaction + AgI, 272 ammonium iron cyanides, decomposition of, 208 ammonium nitrate, decomposition of, 201 ammonium oxalate, decomposition of, 203 ammonium perchlorate, decomposition of, 19, 26, 32, 58, 59, 83, 115, 167, 196-199, 235, 246, 261, 263, 264, 285 ammonium permanganate, decomposition of, 203 ammonium peroxydisulphate, decomposition of, 182 ammonium perrhenates, decomposition of, 204,205 ammonium phosphates, decomposition of, 201,202 ammonium phthalates, decomposition of, 203

ammonium salicylate, decomposition of, 203 ammonium sulphate (sulphite), decomposition of, 200, 201 ammonium thiocarbamate, decomposition of, 208 ammonium thiocyanate, effect on decomposition of chromium complexes, 236 ammonium thiosulphate, decomposition of, 201 ammonium tungstates, decomposition of, 206 ammonium uranates, decomposition of, 207 ammonium vanadates, decomposition of, 206,207 ammonium vanadyl oxalate, decomposition of, 79 ammonium zeolites, decomposition of, 208 annealing, and decomposition of carbonates, 170, 172 _ ,- , K M n 0 4 , 1 9 3 -,-,NaN3,162 _ ,- ,PbC204,223 argon, effect on decomposition of NaN3, 161 -,-,Ni3C, 154 Arrhenius equation, and solid reactions, 87-92,95,99 Austin-Rickett equation, 68 Avrami-Erofe'ev equation, 57, 59, 67, 74, 75, 7 8 , 8 1 , 8 5 , 8 6 -, and decomposition of AI(C104)3,188 -, -, ammines, 235 -, -, ammonium salts, 79, 196-198, 200,204 -, -, azides, 160, 1 6 1 -, -, carboxylates, 211, 221, 223-225, 228 -, -, K M n 0 4 , 1 9 2 -, -,organometallic compounds, 238 - ,_ ,oxides, 147, 148 -,-,oxyhalides, 1 4 1 _ ,- ,sulphates, 176, 178 -, and dehydrations, 131, 132, 1 3 4 azides, decomposition of, 29, 31-33, 35, 47,48,50,85,158-166,285

B barium acetate, decomposition of, 217 barium azide, decomposition of, 25, 47, 48,50,115,158--161,266,285

325 barium bromate, decomposition of, 189, 190 barium carbonate, decomposition of, 168,171,172 -, reaction + oxides, 273-275, 277, 278 barium chlorate, decomposition of, 189 barium chlorate monohydrate, dehydration of, 134 barium chloride, reaction + sulphates, 266 barium chloride hydrates, dehydration of, 24,29, 122, 134 barium chlorite, decomposition of, 190 barium dihydrogen phosphate, decomposition of, 184 barium dithionate, decomposition of, 181 barium formate, decomposition of, 211, 243 barium hydrogen oxalate hydrate, dehydration of, 123, 135, 139 barium hydroxide, reaction + MoOa, 277 barium iodate, decomposition of, 189 barium malonate, decomposition of, 224 barium nitrite, decomposition of, 183 barium oxalate, decomposition of, 219 barium oxide, reaction + MoO3, 277 -, -, sulphates, 260 barium perchlorate, decomposition of, 188 barium permanganate, decomposition of, 193,194 barium peroxide, decomposition of, 150, 151 barium peroxide octahydrate, dehydration of, 150 barium strontium carbonate, decomposition of, 242 barium sulphate, decomposition of, 175, 176 barium sulphite, decomposition of, 181 barrier layer, and dehydrations, 122 -,and solid reactions, 6, 7, 10, 13-15, 37, 68, 69, 72, 111 -, and solidsolid interaction, 247-249, 253, 255-259, 267-269, 271, 276, 279,286 beryllium hydride, decomposition of, 155,156 beryllium hydroxide, decomposition of, 140 beryllium oxalate, decomposition of, 218,219 beryllium sulphate, decomposition of, 175,176,178

BET theory, 28 bond strength, in Pt(1V) cyclobutanes, 238 branching, and decomposition of permanganates, 191, 194 -, of nuclei, 48, 6 6 C

cadmium carbonate, decomposition of, 168,174 cadmium cyanamide, decomposition of, 166 cadmium hydroxide, decomposition of, 138,139,141 cadmium iodate, decomposition of, 190 cadmium oxide, effect on decomposition of azides, 266 -,-, NH4C104,263 -, reaction + Cr2O3, 269 -, -,MoO3,270 cadmium oxyhalides, decomposition of, 141 cadmium perchlorate, decomposition of, 188 cadmium pyridine compounds, decomposition of, 236 cadmium sulphate, reaction + ZnS, 281 cadmium sulphide, reaction + ZnS04,281 cadmium telluride, reaction + HgSe, 279, 280 caesium azide, decomposition of, 163, 266 caesium chloride, reaction + NaI, 279 caesium chlorite, decomposition of, 1 9 0 caesium dihydrogen phosphate, decomposition of, 184 caesium formate, decomposition of,210 caesium-graphite, decomposition of, 154, 155 caesium perchlorate, decomposition of, 186,187 caesium permanganate, decomposition of, 193,194 calcium azide, decomposition of, 159 calcium bromate, decomposition of, 189 calcium carbonate, decomposition of, 24, 92, 93, 95, 111, 113, 115, 167-171, 241,285 -, reaction + Ag2C03, 266 -, -, M O O ~253,277 ,

- -, V 2 0 5 , 2 7 8 9

calcium carbonate hexahydrate, dehydration of, 63,64, 1 2 4 calcium chlorite, decomposition of, 190

326 calcium dihydrogen phosphate, decomposition of, 185 calcium formate, decomposition of, 211 calcium hydrogen phosphate dihydrate, dehydration of, 123, 124, 133 calcium hydroxide, decomposition of, 24, 138,139 -, reaction + Mo03, 277 calcium iodate, decomposition of, 189 calcium magnesium carbonate, decomposition of, 241, 242 calcium oxalate, decomposition of, 106, 219 calcium oxalate hydrates, dehydration of, 123,124,126,134,135 calcium oxide, reaction + solids, 260, 270,277 calcium perchlorate, decomposition of, 187,188 calcium peroxide, decomposition of, 150, 151 calcium peroxide octahydrate, dehydration of, 150 calcium phosphate, reaction + C, 278 _ ,- , urea nitrate, 280, 281 calcium sulphate, decomposition of, 175 -, reaction + BaO, 260 calcium sulphate hydrates, dehydration of, 123,124,126,132,133,245 carbon, and decomposition of carbides, 154 -, -, Ni maleate, 226 -, oxidation of, 15, 277, 278 -, reaction + NH4C104, 264 carbon dioxide, and BeC03 + TiOz, 274 -, and decomposition of AgzO, 147 -, -,azides, 29 -,-,cdg(co3)z,241,242 -, -, carbonates, 36, 167, 169-173 - ,_ ,oxalates, 219, 222, 224 -, and LizC03 + Fe203,37,38 carbon monoxide, and decomposition in matrices, 29 -, and decomposition of AgzO, 147 -, -, MnC03,173 -, -,oxalates, 219,223 -, determination of, 22 cerium(II1) oxalate, decomposition, of, 224 cerium(II1) phosphate, vaporization of, 185 chain branching, and solid decomposition, 65-68, 192, 194

characteristic temperature, and solidsolid interactions, 260 charge transfer, and decomposition of carboxylates, 210 -, and reaction interface, 110 chlorate ion, decomposition of, 187 chlorine, reaction + solids, 14, 1 5 chromium, reaction + NazO, 281 chromium ammines, decomposition of, 232,233 chromium ethylenediamines, decomposition of, 236, 237 chromium hydride, decomposition of, 155,156 chromium hydroxide, decomposition of, 243 chromium mellitate, decomposition of, 228 chromium oxalate, decomposition of, 220 chromium(II1) oxide, and chromite formation, 269 -, and decomposition of TlClO4,188 -, reaction + MgO, 38 chromium(IV) oxide, decomposition of, 146,149 chromium propenediamines, decomposition of, 236 chromium sulphates, decomposition of, 178 clays, dehydroxylation of, 142-144 coal, pyrolysis of, 102 coalescence, of nuclei, 51 cobalt acetate, decomposition of, 217 cobalt ammines, decomposition of, 232235 cobalt benzoate, decomposition of, 228 cobalt carbide, decomposition of,154 cobalt ethylenediamines, decomposition of, 236,237 cobalt formate, decomposition of, 211 cobalt hydroxide, decomposition of, 138, 139,242 cobalt 2-indolecarboxylic acid complex, decomposition of, 237 cobalt iodate, decomposition of, 190 cobalt malonate, decomposition of, 225 cobalt mellitate, decomposition of, 228, 244,245 cobalt oxalate, decomposition of, 84, 221,243,244 cobalt oxalate hydrates, dehydration of, 134

327 cobalt oxides, decomposition of, 146, 149,150,177 -, effect on decomposition of AgMn04, 194 -, -, AgN3,266 -, -, NaCI03,188 -, reaction + A1203, 259, 267, 268, 273 - , ,C,277 - , ,Ga203,269 -, -, MoO3,275,276 _ ,- , NaC104, 265 _ ,- , WO3,259,270,276 cobalt perchlorate, decomposition of, 188 cobalt phosphate, reaction + CaO, 260 cobalt(I1) phosphate octahydrate, decomposition of, 1 8 5 cobalt phthalate, decomposition of, 228 cobalt propenediamines, decomposition of, 237, 238 cobalt pyridine complexes, decomposition of, 236 cobalt salicylaldoxime complexes, decomposition of, 237 cobalt(I1) sulphate, decomposition of, 177-179 -, reaction + BaO, 260 cobalt sulphides, decomposition of, 157 cobalt tartrate, decomposition of, 225, 226 cold-working, 8, 77, 113, 250 collision number, and reaction interface, 110 colour centres, 5 compensation effect, 95-97 -, and decomposition of NH4C104, 197, 198 -, and dehydration, 134 -, and dehydroxylation of clays, 143 computers, and solid reactions, 24, 59, 82,106 contracting area equation, 74, 75, 78 -, and decomposition of Ag2S206,181 -, -, carboxylates, 213, 221 -, -, hydrides, 155 -, -, hydroxides, 139 -, -, sulphates, 175, 176, 178, 179 -, and dehydration, 134 -, and organometallic reactions, 238 -, and S i c + U02, 277 contracting volume equation, and decomposition of ammonium salts, 200207, 264

_ ,- , azides, 159, 161, 163, 164 -, -, CaMg(C03)2, 241 -, -, carbides, 154

-, -, carbonates, 168, 172, 173

-, -, carboxylates, 212, 218-220, 223 -, -, chromates, 194 -, -, Co propenediamines, 237 -, -, CuCr204 + CuO, 278 -, -, cyanamides, 166 -, -, hydrides, 155 -, -, Ni pyridines, 235 -, -, oxides, 148, 149, 1 5 1 -, -, sulphates, 175-180 -, -, sulphides, 156, 157 -, -, TIBr03,lgO -, and dehydration, 132-134 -, and diffusion, 69, 74, 75 -, and nucleation, 60, 64 -, and particle size, 72 -, applicability of, 77, 78, 8 1 coordination, of H2O in hydrates, 118, 119 coordination spheres, and solid decomposition, 231, 232 copper, effect on decomposition of AgzS03,181 _ ,- ,NiH2,156 -, reaction + AgCl, 279, 280 copper acetate, decomposition of, 216, 217 copper adipate, decomposition of, 227 copper azide, decomposition of, 165, 266 copper(I1) benzoate, decomposition of, 227 copper(1) chloride, effect on decomposition of Ag2S03, 181 copper chromite, effect on decomposition of NH4C104,261 -, reaction + CuO, 278 copper formates, decomposition of, 213215,229, 285 copper(I1) formate tetrahydrate, dehydration of, 85, 120-122, 124, 126, 128, 134, 243 copper fumarate, decomposition of, 227 copper hydroxide, decomposition of, 242,243 copper 2-indolecarboxylic acid complexes, decomposition of, 237 copper iodates, decomposition of, 190 copper(1) iodide, reaction + KN3, 280 copper maleate (malonate), decomposition of, 227

328 copper mellitate, decomposition of, 228 desorption, 9,84, 93, 111,112 copper(I1) oxide, decomposition of, 146 j -, and decomposition of BaS04, 175 -, effect on decomposition of NHaClOo. .. -, -, carbides, hydrides, nitrides, 152, 261 154-156 -, reaction + Cr2O3, 269 -, -, GaSe, 158 -, -, CuCrzO4,278 -, -, hydroxides, 140 copper oxyhalides, decomposition of, -, -, NH4C104,197,198 -, and dehydrations, 127, 130, 133 141 copper perchlorate, decomposition of, -, and Sic + SiO2,277 -, and spinel formation, 259 188 copper pyridine complexes, decomposi- dieletric constant, and solid reactions, 32, 33 tion of, 236 copper resacetophenoneoxime complexes, differential scanning calorimetry, 23, 24, 29, 38, 98, 235, 252, 264 decomposition of, 237 copper salicylaldoxime complexes, decom- differential thermal analysis, 23, 24, 38, 39, 98, 149, 171, 204, 206, 210, 217, position of, 237 225,236,252,260,266,281 copper(I1) salicylate, decomposition of, 237 diffusion, 6, 7, 9, 12-15, 19, 20, 37,41, copper sulphate, decomposition of, 17748,65,68-76,78,95,111 -, and decomposition of ammines, 235, 180 -, reaction + BaO, CaO, 260 237 copper sulphate pentahydrate, dehydra- -, -, ammonium salts, 198, 200, 207 tion of, 48, 92, 115, 117, 121-126, -, -, azides, 160, 162 .128--131,139,261,262 - ,_ , carbonates, 167, 170, 171 -, structure of, 118 -, -, hydroxides, 140 copper sulphides, decomposition of, 156, -, -, IrOzCOCI(PPh3)2, 238 157 -, -, Ni&, NiH2,156 copper tartrate, decomposition of, 225, -, -, oxyhalides, 141 226 -, -, phosphates, 184, 185 cracking, 47, 55, 66, 110-113, 249, -, -, sulphates, 180 250,275,287 -, -, sulphides, 157 -, and decomposition of carboxylates, -,and dehydrations, 117, 122, 123,129, 215 132,133 -, -,hydroxides, 137, 138 -, and dehydroxylation of clays, 143, -,-,KBr03,189 144 -,-,KMn04,191 -, and solidsolid interaction, 247-249, -,and dehydrations, 118, 122, 123, 251-260, 265, 268-273, 275, 277128 279,281 -, and double iodide formation, 271 -, and sublimation, 3 crushing, and solid reactions, 8, 160, 166, dioxy gencarbonylchloro-bis( triphenyl250 phosphine) iridium(I), decomposition crystal field stabilization energy, and of, 238 dipole-dipole interaction, and dehydradecomposition of carboxylates, 230 Curie point method, 20 tion, 126 dipotassium hydrogen phosphate, decomposition of, 185 D dislocations, 5,85, 113, 285 decay period, see deceleratory period -, and decomposition of ammonium deceleratory period, in solid reactions, salts, 197, 206 42, 52, 58,59, 6 8 , 8 1 -, -, CaC03,170 deformation strain energy, and nuclea- -,-,KMn04,191,193 tion, 43 -,-, Ni fumarate, 226 degrees of freedom, and solid reactions, -,-,NiHz, 156 -, -, oxides, 145, 151 92,93

329 - , and dehydration, 1 2 1 -, and Li2CO3 + Fe2O3,273 -, and melting, 2 disodium hydrogen phosphates, decomposition of, 184, 185 dithionates, decomposition of, 31, 181 doping, 30, 31, 34-36, 39, 240, 246,

266,268,279 Dunwald-Wagner equation, 70 dyes, effect on decomposition of AgzCz04,265 -, -, AgN3,266 dynamic scanning calorimetriy, 23 dynamic reflectance spectroscopy, 23 E edges, initiation of nucleation at, 55, 221 electrical conductivity, 18, 32, 38, 39, 111,250,252,258,260 -, and decomposition of ammonium salts, 199, 205 -,-,KN3,163 -, and dehydrations, 120 -, and melting, 3 electrical field, and solid reactions, 32, 33,138,163,222,223 electromotive force, and solid reactions, 39 electron diffraction, and solid reactions, 27,138,274 electronegativity, of cation and decomposition of carboxylates, 230 electron microscopy, 25, 26, 28, 39, 43, 170, 212, 213, 220, 222, 223, 226, 251,252 electrons, and decomposition of azides, 163-1 65 electron transfer, 1 4 -, and decomposition ofAgZCz,l56 -,-,ammines, 233 -, -,ammonium salts, 199, 264 -,-,azides, 160,162, 266 -,-, carboxylates, 212, 213, 219, 222 -,-, fulminates, 166 -,-,hydroxydes, 1 4 0 -,-, KMn04,192,262 -, -,oxides, 146 Ellingham diagrams, 209 enthalpy change, 8, 18, 24, 27, 76, 80, 89,96,98,230 -, and decomposition of ammonium salts, 206 '-, -, azides, 1 6 0

, -, carbonates, 95, 167-171, --

174

, ,ClO,, 186 -, -, Mg(OH)z, 138

-, -, oxides, 146, 148, 149 -, -, sulphates, 174-177, 179 -, and dehydrations, 117, 120, 123, 124, 131

-, and dehydroxylation of mica, 1 4 3 enthalpy of activation, of decomposition of BaS04,175 -, -, Na2S203, 181 entropy change, and dehydration, 124 -, for decomposition of BaS04,175 entropy of activation, for decomposition of BaS04,175 -, -, CaMg(CO3)2,242 -, -,Na2Sz03,181 -, for dehydration, 134 -, nucleation and, 45, 96 equilibrium constant, and temperature, 87 -, for SO3 dissociation, 174 etching, and solid reactions, 25,163, 281 ethylene, effect on decomposition of AgzO, 147 europium iron cyanides, decomposition of, 30 europium(111) oxalate, decomposition of, 224 eutectic formation, 1, 8, 116, 183, 186, 260 evolved gas analysis, 20-23, 272 excitons, and solid decompositions, 5 , 4 6 , 163,165,285 exponential law of nucleation, 45, 47, 50, 51, 6 3 exponential rate law, 66, 67,74, 8 0 -, and decomposition of ammonium salts, 197, 200 -,-, carboxylates, 211, 213, 221, 223 -,-, fulminates, 1 6 6 extended fractional decomposition, 52 extent of reaction, see fractional reaction

F Faraday method for magnetic susceptibility, 31 F'-centres, and decomposition of LiAIH4, 32 fluidized bed, 23, 202 flux, of product gas, 2 0 , 2 1 formic acid, and decomposition of formates, 209, 211, 215, 216

330 fractional reaction, 6-10, 12, 13, 17, 42

-, and decomposition of BaN6, 159 _ , _ , carboxylates, 209, 244

-, and diffusion, 69-71

-, and growth of nuclei, 44, 50-52, 5462,64,66--68

-, and particle size, 72, 7 3 -,and rate equations, 74-83, 90, 91, 99-109 -, and solidsolid reactions, 269, 274 -,determination of, 18, 19, 24, 25, 27, 41,76,284 free energy, see Gibbs free energy freeze-drying, and sample preparation, 34,175,176,178 frequency factor, see reaction frequency factor

G gadolinium oxide, reaction + COO, 269 gallium phosphates, decomposition of, 185 gallium selemide, decomposition of, 158 gallium sulphate, decomposition of, 178 gamma distribution, and nucleation, 56 gas chromatography, 18, 22, 221, 222 germ nuclei, 5, 8 , 4 4 , 46, 4 7 , 4 9 Gibbs free energy, and nucleation, 4345,59 -, and melting, 2 -, and solid decomposition, 15, 21 -, of formation of CaMg(C03)z, 242 Ginstling-Brounshtein equation, 69, 74, 75, 273 gold films, and solid reactions, 25 grinding, and solid reactions, 29, 34, 35, 155, 161, 173, 180, 181, 206, 222, 249,250,254 growth nuclei, 5, 44, 4 6 , 4 7 H half-life, and solid decompositions, 55, 56 helium, and decomposition of Ag2C03, 168 Hertz-Knudsen-Langmuir equation, 21 hexammine nickel perchlorate, reaction + H*O, 8 4 holes, 5, 32 -, and decomposition of azides, 163165 -, -, MgCz04, 219 -, -, N H ~ C 1 0 4 , 2 6

hydrazonium nitrate, decomposition of, 201 hydrogen, effect on decomposition of AgzO, 147 - ,_ , ammonium salts, 202, 205 -, -, N a N 3 , 1 6 2 - ,_ ,NiCzO4,37 -, -,sulphates, 178 -, -, T i H z , l 5 3 -, from decomposition of Mg(OH)z, 138 -,reaction + FeN, NiO, 15, 257 - ,_ ,Ni3C, 154 hydrogen chloride, effect on decomposition of Cr ethylenediamines, 236 -, reaction + IrCICO(PPh3)2, 238

I impedance, by HzO and dehydration, 117 impingement of nuclei, 51 indium oxide, effect on decomposition of C03O4,150 indium sulphate, decomposition of, 176, 178 induction period, 41, 42, 59, 71, 73, 74, 78,80 -, in decomposition of ammines, 233, 235 -, -, ammonium salts, 198, 205 -, -, azides, 160,162-165 -, -, carbides, 154 -, -, carbonates, 172 -, -, carboxylates, 212, 221, 222, 224 -, -, fulminates, 1 6 6 -, -, Mg(OH)z, 138 -, -, oxides, 147, 1 5 0 -, -, permanganates, 192, 194, 262 -, in dehydrations, 1 2 0 -, in solidsolid reactions, 26 1 infra-red spectroscopy, 23, 29, 30, 39, 119 -, and decomposition of AgZC03, 172 -, -, cnrboxylates, 211 -, -, C104.187 -, -, NaN3,162 -, -, ( N H 4 ) ~ C r 2 0 7205 ~ -, -, nitrates, nitrites, 183 -, -, phosphates, 1 8 5 -, and dehydrations, 120 ingestion of nuclei, 51, 52, 57 instantaneous nucleation, 45, 62, 164 interface,see reaction interface interface potentials, 32, 3 3 interfacial energy, and recrystallisation, 3

331 interferometry, 25 intermediates, and the reaction interface, 109,111 -, in BaC03 + Si02, 274 -, in decomposition of ammonium salts, 199,200,206,207,264 -, -, azides, 160, 162 210, 216, 218, 223 _ ,,-_ ,,Pcarboxylates, _ bC03,173 -, -, perhalates, 186, 187 _ ,- , sulphates, 174, 178-180 -, in dehydrations, 117, 118, 131 -,in isomerisation of Co ammine thiocyanates, 234 ion exchange, 29 iron, reaction + KMn04, 281 iron(I1) hydroxide, decomposition of, 138--140,242 iron iodates, decomposition of, 190 iron(II1) mellitate, decomposition of, 228 iron nitride, decomposition of, 153 -, reaction + Hz , 1 5 iron oxalates, decomposition of, 210, 220,221 -,hydrated, dehydration of, 1 3 4 iron(II1) oxide, decomposition of, 30, 31 -, reaction + A1203, 275 -, -, BaCO3, 214, 215 _ ,- , C , 2 7 7 __,-, LizC03, 38, 273 _ ,- , MgO, 3 9 , 2 5 6 , 2 6 9 _ ,- , M o 0 3 , 2 7 0 _ ,- , NiO, 268,269 -, -, N i S , 2 8 1 -, -, ZnO, 267-269 iron perchlorates, decomposition of, 188 iron phenanthroline complexes, decomposition of, 237 iron(II1) phthalate, decomposition of, 228 iron( 11) sulphate heptahydrate, dehydration of, 1 3 2 iron sulphates, decomposition of, 176, 178,179 iron sulphides, decomposition of, 157 irradiation, and decomposition of ammonium salts, 198, 201, 204 _ , _ , carboxylates, 222, 223 -, -, permanganates, 192-194, 262 -, and isotope exchange, 239 -,effect on solids, 8, 113, 148, 155, 159, 161,164-166,183,189,190 isomerisation, and solid decomposition, 13

-,

of cobalt complexes, 234, 237, 238 isothiocyanatopentammine cobalt( 111) perchlorate, decomposition of, 74 isotope exchange, and cobalt complexes, 239

J Jander equation, 69, 287 -, and CuI + KN3, 280 -, and decomposition of PbzClzCO3,141 -, and Mn2O3 + Moo3, 276 -, and spinel formation, 268, 269

K krypton, and surface area measurement, 28

lanthanide bromates, decomposition of, 190 Ianthanide chromates, decomposition of, 94,195 lanthanide formates, decomposition of, 215 lanthanide iodates, decomposition of, 190 lanthanide oxalates, decomposition of, 223,224 lanthanide perchlorates, decomposition of, 188 lanthanide sulphates, decomposition of, 180 lanthanum carbonate octahydrate, dehydration of, 124, 1 3 3 lanthanum(II1) oxide, reaction + Moo3, 270 lasers, and solid decomposition, 227 lattice defects, and doping, 35, 36 -, and melting, 2 --,and solid reactions, 4, 5, 10, 14, 18, 109,111,113 lauryl aldehyde, reaction + KClO4, 265 lead, effect on decomposition of PbCz04, 223 lead azide, decomposition of, 29, 35, 72, 164,165, 246 lead carbonate, decomposition of, 168, 173 lead chlorate, decomposition of, 189 lead chlorite, decomposition of, 190 lead citrate, decomposition of, 226

332 lead dihydrogen phosphate, decomposition of, 184 lead iodate, decomposition of, 190 lead nitrate (nitrite), decomposition, 183 lead(I1) oxalate, decomposition of, 223 lead oxides, decomposition of, 146, 148 lead oxyhalides, decomposition of, 1 4 1 lead perchlorate, decomposition of, 188 lead sulphate, decomposition of, 177, 180 linear law of nucleation, 45, 66 lithium aluminium hydride, decomposition of, 32, 155, 1 5 6 lithium azide, decomposition of, 161 lithium carbonate, reaction + Fe203, 38, 273 lithium chlorite, decomposition of, 190 lithium dihydrogen phosphate, decomposition of, 1 8 4 lithium formate, decomposition of, 210 lithium oxalate, decomposition of, 218 lithium oxide, effect on decomposition of c0304,150 lithium permanganate, decomposition of, 193 lithium peroxide, decomposition of, 1 5 0 lithium sulphate monohydrate, dehydration of, 1 2 6 , 1 2 8 , 1 3 2

M magnesium bromate, decomposition of, 189 magnesium carbonate, decomposition of, 93,168,171,241 -, reaction + CaO, 260 _ ,- , M O O ~276,277 , magnesium chromate, decomposition of, 194 magnesium dihydrogen phosphate, decomposition of, 1 8 5 magnesium formate, decomposition of, 211,243 magnesium hydride, decomposition of, 155 magnesium hydroxide, decomposition of, 137,138,242,243 magnesium iodate, decomposition of, 189 magnesium oxalate, decomposition of, 210,244 magnesium oxalate hydrates, dehydration of, 134 magnesium oxide, effect on decomposition of NH4C104,263

-, reaction + Cr2O3, 38, 269 -, -, Fe2O3,39,256,269 -, -, NiS, 281 magnesium perchlorate, decomposition of, 187 -, reaction + NH4C104, 264 magnesium propionate, decomposition of, 218 magnesium sulphate, decomposition of, 175,176 -, reaction + BaO, 260 magnesium sulphate hydrates, dehydration of, 118, 123, 126, 1 3 2 magnetic susceptibility, 23, 31, 38 maleate ion, decomposition of, 226 malonic acid, decomposition of, 225 manganese(I1) carbonate, decomposition of, 1 6 8 , 1 7 3 , 1 7 4 manganese dioxide, effect on decomposition of KMn04,192, 262 -, -, NH4C104,263,264 manganese(I1) formate, decomposition of, 211 manganese(I1) formate dihydrate, dehydration of, 120-122, 124, 126, 128, 134 manganese(I1) hydroxide, decomposition of, 138, 242 manganese iodate, decomposition of, 1 9 0 manganese mellitate, decomposition of, 228 manganese oxalate, decomposition of, 210,219,220 manganese oxalate dihydrate, dehydration of, 124-126,134 manganese(II1) oxide, decomposition of, 146 manganese perchlorate, decomposition of,188 manganese pyridine complexes, decomposition of, 236 manganese(I1) silicate, reaction + CaO, 260 manganese(I1) sulphate, decomposition of, 1 7 6 , 1 7 8 markers, 38, 251 Marquardt algorithm, and kinetic data, 83 mass spectrometry, 1 8 , 21, 22, 163, 175, 217,218,236,264 melting, and solid reactions, 1-3, 6, 8 , 11, 13, 18, 24, 38, 56, 110, 116, 147, 166, 167, 172, 175, 180, 182, 183, 185, 188, 189, 200-203, 210, 218, 224,227,228, 231, 232, 283-285

333

-, and solidsolid interaction, 252, 255, 256,260,264,265 -, and solid solutions, 240 mercury, effect on decomposition of AgzO, 147 -, - AgzS04,180 -,-,HgCz04,223 -,-, H g 0 , 1 4 8 mercury fulminate, decomposition of, 65, 66,166 mercury iodate, decomposition of, 190 mercury(I1) iodide, reaction + AgI, 267 mercury(I1) oxalate, decomposition of, 223 mercury(I1) oxide., decomposition of, 148,149 mercury(I1) selenide, reaction + CdTe, 279,280 mercury(I1) sulphate, decomposition of, 180 methane, determination of, 22 -, effect on decomposition of NH4HP04, 202 mica, dehydroxylation of, 143, 144 microbalance, and solid decomposition, 19-21,31 microcinematography , and solid reactions, 25 microscopy, 17, 18, 24-26, 28, 37, 38, 47, 48, 58, 66, 80, 84, 99, 110, 111, 251,252,281,284 -, and decomposition of AgzCZ, 156 -, -, ammonium salts, 198,203,204 -, -, azides, 158, 160, 163 -, -, carbonates, 170 -, -, carboxylates, 212, 217, 223 -, -, hydroxides, 138, 139 -, -, KMn04,191 -, -, oxides, 149, 151 -, -, salts of oxyhalogen acids, 191 -, and dehydrations, 120, 130, 131, 134 -, and dehydroxylation of clays, 142, 144 molybdenum( VI) oxide, reaction + CaC03,253,277 -,-, CdO, SrO, 270 -, -,CoCO3,276 -,-, c0304,275,276 _ ,- , MgCOj, 276,277 -, -, MnzO3,276 -, -, SrCOj, 277 Mossbauer spectroscopy, and solid reactions, 30, 31, 38,179, 220 I

N nickel, effect on decomposition of AgzO, 147,262 -,-,TI(HCOz)4, 216 -, oxidation of, 69, 258 nickel acetate, decomposition of, 216, 217 nickel ammines, decomposition of, 235 nickel benzoate, decomposition of, 228 nickel bromate, decomposition of, 190 nickel carbide, and decomposition of Ni fumarate, 226, 227 -, decomposition of, 154, 156, 217 nickel formate, decomposition of, 36,48, 209, 211-213, 216, 227, 229, 230, 246,285 -, effect on decomposition of Mg(HCOz)z, 243 nickel formate dihydrate, dehydration of, 134 nickel fumarate, decomposition of, 226, 227 nickel hydride, decomposition of, 152, 156 nickel hydroxide, decomposition of, 138, 139,242,243 nickel 2-indolecarboxylic acid complexes, decomposition of, 237 nickel iodate, decomposition of, 190 nickel maleate, decomposition of, 226, 227 nickel malonate, decomposition of, 84, 225,227 nickel mellitate, decomposition of, 228, 244,245 nickel oxalate, decomposition of, 7, 37, 85,115,209, 221,222,225,243,244 nickel oxalate hydrates, dehydration of, 95,124,134,135 nickel oxide, effect on decomposition of AgMn04,194 -,-,azides, 266 -I -,MgC03,171 -, reaction + CrzO3, 269 -,-, FezO3,268,269 -, -, Hz, 1 5 , 2 5 7 nickel perchlorate, decomposition of, 188 nickel phthalate, decomposition of, 228 nickel pyridine complexes, decomposition of, 235, 236 nickel resacetophenoneoxime complexes, decomposition of, 237

334 nickel salicylaldoxime complexes, decomposition of, 237 nickel sulphate, decomposition o f , 24, 178,179 nickel sulphate hydrates, dehydration of, 121-124,131,132,261 nickel sulphide, decomposition of, 156, 157 -, reaction + Fe2O3, Mn2O3, 281 nickel tartrate, decomposition of, 225, 226 niobium hydride, decomposition of, 1 5 3 nitrogen, and decomposition of alkanoates, 217 - , , carbonates, 168, 173, 174 _ ,- , sulphates, 176-179 -, and surface area determination, 28 -, determination of, 22 nitrogen-15, and decomposition of azides, 29 nitrogen oxides, and decomposition of &2C204, 222 -,-,NaN3,162 - -, nitrates and nitrites, 182 , nuclear magnetic resonance, and solid reactions, 31, 39, 1 2 0 nucleation, 5-7, 10, 12-15, 17, 24, 25, 33, 36, 37, 41, 42, 76, 77, 84, 229, 248,254,255,286 -, and Ca3(P04)2 + ureanitrate, 2 8 1 -, and decomposition of alkandioates, 219-223,225-227 -, -, alkanoates, 209, 212-215, 217,

285 ammonium salts, 197, 200, 204-206,208 -, -, ArCO? salts, 228 -, -, azides, 158-162,164, 1 6 5 -, -, caibonates, 170 -, -, Co propenediamines, 237 - ,_ , fulminates, 166 -, -, hydrides, 155 -, -, hydroxides, 138-140 -, -, KMn04,191,193

-, -,

_ , _ , LiAlH4, 32

-, -, NH4C104,26

-, -, oxides, 145, 148 -, -, salts of oxyhalcgen acids, 189, 191 -, -, sulphates, 179 -, and dehydration, 117, 120-123, -, -,

129-1 32,134-136 and dehydroxylation of clays, 142, 143 and diffusion, 71, 72

-, -, -, -,

and kinetics, 84-86 and melting, 2 and particle size, 74 and reaction interface, 112, 1 1 3 -, and spinel formation, 268 -, laws of, 42-47

0 order of reaction, and mechanism, 8486 -, and rising temperature method, 101, 104,105 -,determination of, 74, 75, 104, 106109 -, for Ca3(P04)2 + urea nitrate, 281 -, for decomposition of ammines, 233 -, -, ammonium salts, 200, 201, 205, 2 64 -, -, azides, 159, 162-165 -, -, carbides, 154 -, -, carbonates, 172 -, carboxylates, 211, 216, 217, 219, 221, 224, 225,227, 228 -, -, chlorites, 1 9 0 -, -, complexes, 238 -, -, cyanamides, 166 166 -, -, hydrides, 153, 1 5 5 , 1 5 6 -, -, MdOHIz, 138 -> -> oxyhalides7 14' - , , Pb(N03)z, 1 8 3 -' -'sulphates9 178, -, -, sulphides, 157 -j-*

->

->

-, for dehydrations, 134, 135 -, for dehydroxylation of clays, 142144

-, for KMn04 + lauryl aldehyde, 265 -, for TIC03 + 1 2 , 278

overlap of nuclei, 51, 52, 57 oxalate ion, decomposition of, 218 -, effect o n decomposition of Ag2C204, 222 oxygen, and solid reactions, 37, 145, 146, 148, 175, 177-179, 204, 205, 212, 219,220, 2 2 2 , 2 2 5 , 2 2 7 , 2 3 0 , 2 5 3 -, reaction + Ni, 258

P palladium hydride, decomposition of, 152,153 palladium resacetophenoneoxime complexes, decomposition of, 237

335 parabolic law, 69, 287 -, and Ca3(P04)2 + urea nitrate, 280, 281 -, and COO,MnzO3 + MOOS,276 -, and CsCl + NaI, 279 -, and decomposition of Ag,O, 147 -, -, ammonium salts, 207 -, -, Pb(OH)Cl, 1 4 1 -, -, sulphates, 177 -, -, sulphides, 157 -, and spinel formation, 269 particle size, 72-74, 84, 232, 249-251, 256,284 -, and BaC03 + Si02,274 -, and Ca3(P04)2+ urea nitrate, 280, 281 -, and decomposition of ammonium salts, 202, 205, 206 -, -, CaC03, 170 -, -, carboxylates, 221 -, -, cobalt ammine thiocyanates, 234 - ,_ , perchlorates, 170 -, and diffusion, 70 -, and Fez03 + LiZCO3,273 -, and KClO4 + lauryl aldehyde, 265 -, and spinel formation, 269, 270 partition function, and solid reactions, 92,93 perchlorate ion, decomposition of, 186, 187 perchloric acid, and decomposition of NH4CIO4, 167, 198, 199, 261, 263, 264,285 phantom nuclei, 5 1 phases, 1-3, 18, 27, 33, 34, 37, 38, 71, 80, 110, 111, 231, 249, 251, 252, 254, 255, 260, 266, 279, 281, 284, 286 -, and BaC03 + SiOz, 274 -, and decomposition of ammines, 234 _ , _ ,ammonium salts, 195, 197, 204, 207 -, -, ArCO; salts, 227 _ ,- , carbonates, 169, 172 - ,_ , hydrides, 156 _ ,- , Ir02COCI(PPh3)2, 238 - ,_ , nitrates and nitrites, 182 -, -, oxides, 149 _ , _ , phosphates, 1 8 4 _ ,- , sulphates, 175 -, and dehydrations, 117, 123, 126, 128, 130,131,135,136 -, and oxide-oxide reactions, 276 -, and spinel formation, 267, 271

phonons, and solid decomposition, 5 photoconductivity, 32 platinum, as reactant support, 20 point defects, and solid decomposition, 5 Polanyi-Wigner model, 92, 96, 284 -, and decomposition of AgzO, 148 _ , _ , carbonates, 169 -, and dehydrations, 118, 123, 124, 130 polyacetylenes, effect on decomposition of A g ~ C 2 0 4 , 2 6 5 pores, 28, 38, 61, 250 -, and decomposition of carbonates, 167, 170 -, and dehydrations, 1 1 8 , 1 2 8 potassium azide, decomposition of, 29, 33,162,163 -, reaction + CuI, 180 potassium bromate, decomposition of, 189 potassium bromide, decomposition of CH3COONa in, 29 _ , _ , Cz 03- in, 218 -- ,_ _ , maleate ion in, 226 , , malonic acid in, 225 potassium carbonate perhydrate, decomposition of, 1 5 1 potassium chlorate, effect on decomposition of KC104, 187 potassium chlorite, decomposition of, 190 potassium dichromate, effect on decomposition of NH4CI04,261 potassium dihydrogen arsenate (phosphate), decomposition of, 184 potassium hydrogen oxalate hydrate, dehydration of, 48, 124 potassium iodide, decomposition of CH3COONa in, 29 -, reaction + AgI, 38 potassium malonate, decomposition of, 224 potassium oxalate, decomposition of, 218 potassium perbromate, decomposition of, 187 potassium perchlorate, decomposition of, 186,187 -, effect on decomposition of KMn04, 192,245 -, reaction + C, 278 -, reaction + lauryl aldehyde, 265 potassium periodate, decomposition of, 29,187 -, reaction + C, 278 potassium permanganate, decomposition

336 of, 29, 32, 67, 167, 191-194, 245, 262 -, reaction + Fe, 281 potassium peroxydicarbonate, decomposition of, 151 potassium peroxydisulphate, decomposition of, 181, 182 potassium tartrate, decomposition of, 225 power law, 74, 80, 86, 89 -, and decomposition of AgzO, 147, 148 -, -,azides, 158-161, 164 ,-,carboxylates, 212, 220, 222, 223 -,-,fulminates, 166 -,-, hydrides, 155, 156 -, -, (NH4)zCrz07,206 -,-, permanganates, 192-194 -, and nucleation, 46, 50, 51,57, 67 pre-exponential factor, see reaction frequency factor proton mobility, and dehydration, 119 proton transfer, and Ca~(P04)z+ urea nitrate, 281 -, and decomposition of ammonium salts, 195, 198-200, 205, 208, 263, 264 -,-,hydroxides, 137, 140 -,-,phosphates, 185 -, and dehydroxylation of clays, 143 Prout-Tompkins equation, 67, 74, 75, 81 -, and decomposition of azides, 160 - -v BaZS2069181 -,-,carbonates, 168, 174 -, -,carboxylates, 212, 213, 215, 216, 219,221,223,224,227, -, -, (NH4)zCrzO7,205 -, -, N ~ J C154 , -, -, Pb(C104)~,189 -, -, permanganates, 191-194 -, -, ReOz, 204 -, -,TIBrO3,190 pseudomorphism, and solid reactions, 27,139 9

R radiolysis, see also irradiation

-, and Mossbauer spectroscopy, 30 -, in electron microscope, 26

-, of azides, 31

radius, of cation and decomposition of carboxylates, 230 Raman spectroscopy, and solid reactions, 29

random nucleation, 50, 51, 62, 63 rare earth nitrates (nitrites), decomposition of, 183,184 rate coefficient, and decomposition of ammonium phthalates, 203 -, -, carbides, 154 -, -, Mg(OH)z, 138 -, and temperature, 87-92 -, calculation of, 81-83, 99 rate controlling step, 12, 41, 77, 84, 88, 94,112,249,252,253 -, and COO + MoO3,276 -, and CsCl + NaI, 279 -, and decomposition of azides, 159, 160,163 -, -, Be(OH)Z, 140 -, -, carbides, hydrides, nitrides, 152156 -, -, carbonates, 171 -, -, fulminates, 166 -, -, 1 r O ~ C O C l ( P P h ~ ) ~ , 2 3 8 -,-, oxides, 147, 150 -, -, sulphates, 180 -, and dehydration, 124, 133 -, and Fez03 + LizC03,273 -, and Ni + 0 2 ,258 -, and Sic + SiOz, 277 -,and spinel formation, 259, 268, 271, 272 rate equation, 74-76, 78, 79, 90-92, 284 -, and diffusion, 69-71 -, and interface advance, 50, 52, 54, 55, 57-61,63,64,66-68 -, and nucleation, 45-47 -, and particle size, 73 -, and temperature, 99-102, 104-109 -, for BaC03 + FezO3,274 -, for CuCrz04 + CuO, 278 -, for decomposition of MgCz04, 219 -, -,NHzCOSNH4,208 -, -,Ni maleate, 226 -, -, permanganates, 191, 192, 194 -, for KC104 + C, 278 -, for MgO + Fe203, 269 -, for sublimation of NH4C104,198 reaction frequency factor, 6, 7, 28, 42, 88,89,92,94-97,99,100,102,106 -, for decomposition of azides, 165 -, -,CaC03,95 -, -, carbonates, 171 -, -,HgO,148 -, - NaZCo5(S04)6, 245 -, -, oxyhalides, 141, 142 I

337

-, for dehydrations, 126,130 -, for dehydroxylation of clays, 142 reaction interface, 4-6, 8, 9, 12, 13, 15,

17, 18, 20, 24, 25, 28, 38, 39, 75, 109-113,229,284 -, and decomposition of ammines, 234, 237 -, -, azides, 163,164 -, -, CaMg(C03)~,241,242 --,--,carboxylates, 214, 215, 220, 223, 225,245 -, -, cyanamides, 166 -, -, hydroxides, 137,140 -, -, KMn04,191 -, -, oxides, 148 -, -, salts of oxyhalogen acids, 190,191 -, -, sulphates, 179 -, and dehydration, 117,121,122,127130 -, and diffusion, 71,72 -, and nuclei growth, 44,47,58,59 -, and solidsolid interactions, 247,251, 256-259,261,270,271 -, and zero-order kinetics, 84,85 -, processes at, 92-95 real space crystallography, 27 recrystallisation, 1, 3, 9, 13, 28, 167, 259,284 -, and decomposition of sulphates, 179 -, -,ThH3,156 -,and dehydrations, 123, 127,128, 131, 136,209 reduced time, and rate laws, 75, 77-79, 82 reflectance spectroscopy, 39 resonance stabilization, and decomposition of carboxylates, 230 rhenium dioxide, decomposition of, 204 rhodium carboxylates, decomposition of,

230 roughness factor, and solid reactions, 28 rubidium azide, decomposition of, 163 rubidium chlorite, decomposition of, 190 rubidium dihydrogen arsenate (phosphate), decomposition of, 284 rubidium iodide, reaction + AgI, 38 rubidium perchlorate, decomposition of,

186,187 rubidium permanganate, decomposition of, 193

S scandium formate, decomposition of, 211 scandium perchlorate, decomposition of,

188

selenates, decomposition of, 180 shape factor, and nucleation, 49,50,56 shear, and decomposition of oxides, 145,

146 silica gel, and sample preparation, 34 silicon carbide, reaction + SiOz, 277 silicon dioxide, effect on Ca3(P04)2 +

C, 278

-, reaction + BaC03, 273, 274 -, -,Ca0,270 -, -, Na2C03,253 -, -, S i c , 277 silver, effect on decomposition of AgzO,

147,148,262

-, reaction + S, 257 silver acetylide, decomposition of, 156 silver azide, decomposition of, 29, 33,

163,164,246 silver bromate, decomposition of, 190 silver carbonate, and decomposition of Ag20, 147 -, decomposition of, 29, 147, 168, 172,

246 siIver chlorate, decomposition of, 189 silver chlorite, reaction + Cu, NaI, 279,

280 silver dithionate, decomposition of, 181 silver formate, decomposition of, 215 silver fulminate, decomposition of, 166 silver iodate, decomposition of, 190 silver iodide, reaction + HgI2, 267,271 -, -, KI, RbI, 38,271,272 silver mellitate, decomposition of, 84,

228 silver nitrate (nitrite), decomposition of,

183 silver oxalate, decomposition of, 222,

223,246,265 silver oxide, decomposition of, 146-148,

262 silver perchlorate (periodate), decomposition of, 188 silver permanganate, decomposition of,

67,68,194 silver sulphite, decomposition of, 180,

181 sintering, 12, 13, 24, 28, 38, 77, 111,

147, 214, 218, 220, 256, 258, 275, 285,287 slip, and decomposition of oxides, 145 Smith-Topley effect, and decomposition of hydroxides, 137 -, and dehydrations, 118,125-131,220 sodium, and decomposition of NaN3, 161

338 sodium acetate, decomposition of, 29 sodium azide, decomposition of, 35, 161-163,246,266 sodium calcium sulphate, decomposition of, 245 sodium carbonate, reaction + CaC03, 266 - ,_ , S i 0 2 , 2 5 3 sodium chlorate, decomposition of, 188 -, effect on decomposition of NaC104, 187 -, reaction + C0304, 265 sodium chloride, melting of, 3 sodium chlorite, decomposition of, 190 sodium dihydrogen phosphate, decomposition of, 184 sodium fulminate, decomposition of, 166 sodium iodide, reaction + AgCl, CsCl, 279,280 sodium malonate, decomposition of, 224 sodium oxalate, decomposition of, 218 sodium oxide, effect on decomposition of c0304,150 -, reaction + Cr, Zn, 281 sodium perchlorate, decomposition of, 186,187,265 sodium permanganate, decomposition of, 193 sodium peroxide, decomposition of, 1 5 0 sodium peroxydicarbonate, decomposition of, 1 5 1 sodium phosphate, effect on decomposition of Ag*S03, 181 -, -, Na2HP04, 185 sodium sulphite, effect on decomposition of AgzS03,181 sodium tartrate, decomposition of, 225 sodium thiosulphate, decomposition of, 181 solid solutions, 32, 33, 71, 241-245, 251,252, 2 5 6 , 2 5 8 , 2 7 9 , 2 8 7 -, and d'ecomposition of Li202, 150 -, and dehydrations, 122 -, and spinel formation, 269 spinel formation, 70, 258, 259, 267-272 split temperature method, 8 6 statistics, and kinetics of solid reactions, 81-83 steps in crystals, and nucleation, 113 storage, of solids, and reactions, 29, 34 strain, and decomposition of carboxylates, 210 _ ,- , cobalt ammine thiocyanates, 234 _ ,- , K M n 0 4 , 1 9 1 -, -,NaN3,246

_ , _ , NH4C104,197 -, and nucleation, 47, 66, 74, 162 -, and reaction between solids, 253, 287 -, and reaction interface, 109, 110, 112, 113, 1 3 7 , 1 3 8 stress deformation, and nucleation, 47 -, and reaction interface, 1 1 0 strontium azide, decomposition of, 159 strontium bromate, decomposition of, 189 strontium carbonate, decomposition of, 168,172 -, reaction + Moo3, 277 _ _ , ,V20~,278 strontium chlorite, decomposition of, 190 strontium formate, decomposition of, 211 strontium hydroxide, reaction + Moo3, 277 strontium iodate, decomposition of, 189 strontium oxalate, decomposition of, 219 strontium oxalate hydrate, dehydration of, 1 3 5 strontium oxide, reaction + Moo3, 270, 276 strontium perchlorate, decomposition of, 188 strontium peroxide, decomposition of, 150,151 strontium peroxide octahydrate, dehydration of, 150 strontium sulphate, reaction + BaO, 260 sublimation, 1, 3, 9, 13, 18, 19, 24, 36, 47,150,180,195,231 -, and decomposition of ammonium salts, 198, 202, 203, 207, 261 -, -, carboxylates, 214, 217, 285 -, and solidsolid interaction, 256, 260 sulphamic acid, and decomposition of NHqHS04,200 sulphur, effect on decomposition of sulphides, 1 5 6 -, reaction + Ag, 257 sulphur dioxide, and decomposition of sulphates, 174, 175, 177, 179 -, reaction + NH3 in solid, 39 sulphur trioxide, and decomposition of sulphates, 174, 177, 179

T talc, dehydroxylation of, 144 tantalum hydride, decomposition of, 1 5 3

339 tetra-n-amylammonium thiocyanate, melting of, 2 thallium azide, decomposition of, 29, 35, 85,163 thallium(1) bromate, decomposition of, 192 thallium(1) carbonate, reaction + Moo3, 272 thallium(1) chlorate, decomposition of, 189,190 thallium(1) cyanamide, decomposition of, 166 thallium fulminate, decomposition of, 166 thallium iodates, decomposition of, 190 thallium iodides, decomposition of, 158 thallium oxalate hydrates, dehydration of, 134 thallium(1) perchlorate, decomposition of, 188 e thermal analysis, 10, 23, 38, 39 -, and decomposition of ammonium salts, 196, 201-203, 205 _ _ 9 c a g ( c o 3 ) 2 , 242 --,_-, carbonates, 169, 172 , , oxyhalogen salts, 185 _ , _ , sulphoxyacid salts, 182 -, and dehydrations, 120 thermal emission, and electron microscopy, 26 thermistor, and temperature measurement, 20 thermogravimetry, 10, 20, 21, 23, 1831 8 5 , 2 1 7 , 2 3 4 , 281 thorium dioxide, effect on decomposition of AgMn04,194 thorium hydride, decomposition of, 155, 156 thorium(1V) oxalate, decomposition of, 224 thorium tetraformate, decomposition of, 215,216 tin(I1) chloride, effect on decomposition of AgzS03,181 tin(1V) sulphide, decomposition of, 27 titanium, reaction + TiBz, 272 titanium boride, reaction + Ti, 272 titanium dioxide, and shear, 1 4 5 -, effect on decomposition of AgMn04, 194 -, reaction + BaC03, 274 titanium hydride, decomposition of, 1 5 3 titanium nitride, decomposition of, 154 titanium sulphide, reaction + Li, 272 3

topotactic relations, and solid reactions, 27, 111, 134, 137, 144, 149, 234, 253,272 trimethyleneplatinum(1V) compounds, decomposition of, 238 tungsten(V1) oxide, reaction + COO, 259, 267, 270 _ , _ , Co304, Mn203,275,276 -, -, T12CO3,277 U ultrasonic irradiation, and KC104 + lauryl aldehyde, 265 uranium oxides, decomposition of, 146, 149 -, reaction + Sic, 277 uranium tetraformate, decomposition of, 216 uranyl acetate, decomposition of, 217 uranyl ammonium phosphate, decomposition of, 202 uranyl hydroxide, decomposition of, 140 uranyl nitrate hexahydrate, dehydration of, 3 6 , 8 4 , 1 2 1 , 1 2 4 , 1 2 6 , 1 3 3 uranyl oxalate, decomposition of, 224 uranyl sulphate, decomposition of, 177, 180 urea nitrate, reaction + Ca3(P04)2, 280, 281 V vanadium(V) oxide, decomposition of, 150 -, reaction + carbonates, 278 van’t Hoff relation, 87, 8 8 vaporisation coefficient, and solid decomposition, 21 vapour pressure measurement, and solid reactions, 20, 21 vibration frequency, and dehydrations, 123,124 -, and rates of interface advance, 92, 94

W water, and decomposition in matrices, 29 of, 22, 23 -, effect on decomposition of ammonium salts, 195, 200, 202, 204, 205 -,-, B a S 0 3 , 1 8 1 -, -, carbonates, 167

-, determination

340

-, -, carboxylates,

209, 212, 213, 219, 221,223 _ , _ ,hydroxides, 137-139

- ,_ , NazCas(S04)6,245 -,-, oxides, 151 _ , _ , Pb(OH)CI, 141

-, -, phosphates, 185 -, -, propenediamine complexes, 237

-,effect on dehydration, 28, 34, 36, 47, 61, 62, 80, 117, 120, 121, 123, 125-130,133,135,261 -, effect on dehydroxylation of clays, 142-144 -, effect on reactions between solids, 253 -, effect on spinel formation, 259 -, in crystalline hydrates, 118-120 Weibull distribution, and solid reactions, 55,56,83 work function, and AgN3 + oxides, 266 X X-ray diffraction, 18, 27, 28, 31, 37, 39, 111,251,281 -, and decomposition of AgZC2,156 -,-,ammonium salts, 200, 202 _ ,_ ,azides, 160 , carboxylates, 209, 226 _ _ ,,-_ , hydroxides, 137 -,-, oxides, 150 _ ,_ ,PbC03,173 _ ,- ,permanganates, 191,194 -, and dehydrations, 120, 131 -, and oxide-oxide reactions, 276 -, and spinel formation, 267, 268 X-ray fluorescence, 38 X-ray photoelectron spectroscopy, 3 0 Z

zeolites, and decomposition of ammonium salts, 207, 208

zinc bromate, decomposition of, 190 zinc carbonate, decomposition of, 168, 174 zinc formate, decomposition of, 215, 243 zinc hydride, decomposition of, 155 zinc hydroxide, decomposition of, 242, 243 zinc iodate, decomposition of, 190 zinc mellitate, decomposition of, 228 zinc oxalate, decomposition of, 210, 219, 220 zinc oxide, effect on decomposition of AgMn04,194 -,-, azides, 266 _ 3 _ ,MgC03,171 _ , _ , NH4C104,263 -, reaction + FezO3, 267-270 zinc oxyhalides, decomposition of, 141 zinc perchlorate, decomposition of, 188 -, reaction + NH4C104, 264 zinc phosphide, decomposition of, 158 zinc pyridine complexes, decomposition of, 236 zinc sulphate, decomposition of, 177, 178,180 -, reaction + BaO, 260 _ , _ ,CdS,281 zinc sulphate heptahydrate, dehydration of, 123,126 zinc sulphide, reaction + CdS04, 281 zinc sulphite, decomposition of, 181 zirconium, reaction + NazO, 281 zirconium hydride, decomposition of, 153 zirconium nitride, decomposition of, 154 zirconium phosphate, decomposition of, 185