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Physical Chemistry of Solid-Gas Interfaces
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Physical Chemistry of Solid-Gas Interfaces Concepts and Methodology for Gas Sensor Development
René Lalauze Series Editor Dominique Placko
First published in France in 2006 by Hermes Science/Lavoisier entitled “Physico-chimie des interfaces solide-gaz 1 et 2” First published in Great Britain and the United States in 2008 by ISTE Ltd and John Wiley & Sons, Inc. Translated from the French by Zineb Es-Skali and Matthieu Bourdrel. Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address: ISTE Ltd 6 Fitzroy Square London W1T 5DX UK
John Wiley & Sons, Inc. 111 River Street Hoboken, NJ 07030 USA
www.iste.co.uk
www.wiley.com
© ISTE Ltd, 2008 © LAVOISIER, 2006 The rights of René Lalauze to be identified as the author of this work have been asserted by him in accordance with the Copyright, Designs and Patents Act 1988. Library of Congress Cataloging-in-Publication Data Lalauze, René. [Physico-chimie des interfaces solide-gaz. English] Physical chemistry of solid-gas interfaces : concepts and methodology for gas sensors development / René Lalauze. p. cm. Includes bibliographical references and index. ISBN 978-1-84821-041-7 1. Gas-solid interfaces. 2. Gas detectors. I. Title. QD509.G37L3513 2008 681'.2--dc22 2008022737 British Library Cataloguing-in-Publication Data A CIP record for this book is available from the British Library ISBN: 978-1-84821-041-7 Printed and bound in Great Britain by Antony Rowe Ltd, Chippenham, Wiltshire.
Table of Contents
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii Chapter 1. Adsorption Phenomena . . . . . . . . . . . . . . . . . . . . . . . . . .
1
1.1. The surface of solids: general points . . . . . . . . . . . . . . . . . . . . 1.2. Illustration of adsorption . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.1. The volumetric method or manometry . . . . . . . . . . . . . . . . 1.2.2. The gravimetric method or thermogravimetry. . . . . . . . . . . . 1.3. Acting forces between a gas molecule and the surface of a solid. . . . 1.3.1. Van der Waals forces . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.2. Expression of the potential between a molecule and a solid. . . . 1.3.3. Chemical forces between a gas species and the surface of a solid 1.3.4. Distinction between physical and chemical adsorption . . . . . . 1.4. Thermodynamic study of physical adsorption . . . . . . . . . . . . . . . 1.4.1. The different models of adsorption . . . . . . . . . . . . . . . . . . 1.4.2. The Hill model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.3. The Hill-Everett model . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.4. Thermodynamics of the adsorption equilibrium in Hill’s model . 1.4.4.1. Formulating the equilibrium . . . . . . . . . . . . . . . . . . . 1.4.4.2. Isotherm equation . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.5. Thermodynamics of adsorption equilibrium in the Hill-Everett model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5. Physical adsorption isotherms . . . . . . . . . . . . . . . . . . . . . . . . 1.5.1. General points. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5.2. Adsorption isotherms of mobile monolayers . . . . . . . . . . . . 1.5.3. Adsorption isotherms of localized monolayers . . . . . . . . . . . 1.5.3.1. Thermodynamic method . . . . . . . . . . . . . . . . . . . . . 1.5.3.2. The kinetic model . . . . . . . . . . . . . . . . . . . . . . . . . 1.5.4. Multilayer adsorption isotherms . . . . . . . . . . . . . . . . . . . . 1.5.4.1. Isotherm equation . . . . . . . . . . . . . . . . . . . . . . . . .
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1 2 3 4 4 4 6 7 8 8 8 9 10 10 10 11
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1.6. Chemical adsorption isotherms . . . . . . . . . . . . . . . . . . . . . . . . . 23 1.7. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 Chapter 2. Structure of Solids: Physico-chemical Aspects . . . . . . . . . . . . 29 2.1. The concept of phases . . . . . . . . . . . . . . . . . . . . 2.2. Solid solutions . . . . . . . . . . . . . . . . . . . . . . . . 2.3. Point defects in solids . . . . . . . . . . . . . . . . . . . . 2.4. Denotation of structural members of a crystal lattice. . 2.5. Formation of structural point defects . . . . . . . . . . . 2.5.1. Formation of defects in a solid matrix . . . . . . . 2.5.2. Formation of defects involving surface elements . 2.5.3. Concept of elementary hopping step . . . . . . . . 2.6. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . .
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Chapter 3. Gas-Solid Interactions: Electronic Aspects . . . . . . . . . . . . . . 39 3.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. Electronic properties of gases . . . . . . . . . . . . . . . . . . . . . . 3.3. Electronic properties of solids . . . . . . . . . . . . . . . . . . . . . . 3.3.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.2. Energy spectrum of a crystal lattice electron. . . . . . . . . . . 3.3.2.1. Reminder about quantum mechanics principles . . . . . . 3.3.2.2. Band diagrams of solids . . . . . . . . . . . . . . . . . . . . 3.3.2.3. Effective mass of an electron . . . . . . . . . . . . . . . . . 3.4. Electrical conductivity in solids . . . . . . . . . . . . . . . . . . . . . 3.4.1. Full bands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.2. Partially occupied bands . . . . . . . . . . . . . . . . . . . . . . 3.5. Influence of temperature on the electric behavior of solids . . . . . 3.5.1. Band diagram and Fermi level of conductors . . . . . . . . . . 3.5.2. Case of intrinsic semiconductors . . . . . . . . . . . . . . . . . 3.5.3. Case of extrinsic semiconductors . . . . . . . . . . . . . . . . . 3.5.4. Case of materials with point defects. . . . . . . . . . . . . . . . 3.5.4.1. Metal oxides with anion defects, denoted by MO1x . . . 3.5.4.2. Metal oxides with cation vacancies, denoted by M1xO . 3.5.4.3. Metal oxides with interstitial cations, denoted by M1+xO 3.5.4.4. Metal oxides with interstitial anions, denoted by MO1+x . 3.6. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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39 39 40 40 41 41 45 52 55 55 56 57 57 61 62 64 65 66 67 67 68
Chapter 4. Interfacial Thermodynamic Equilibrium Studies . . . . . . . . . . 69 4.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2. Interfacial phenomena . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3. Solid-gas equilibriums involving electron transfers or electron holes . 4.3.1. Concept of surface states . . . . . . . . . . . . . . . . . . . . . . . .
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69 70 71 72
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4.3.2. Space-charge region (SCR) . . . . . . . . . . . . . . . . . . . . . . . 4.3.3. Electronic work function . . . . . . . . . . . . . . . . . . . . . . . . 4.3.3.1. Case of a semiconductor in the absence of surface states . . 4.3.3.2. Case of a semiconductor in the presence of surface states . . 4.3.3.3. Physicists’ and electrochemists’ denotation systems . . . . . 4.3.4. Influence of adsorption on the electron work functions . . . . . . 4.3.4.1. Influence of adsorption on the surface barrier VS . . . . . . . 4.3.4.2. Influence of adsorption on the dipole component VD. . . . . 4.4. Solid-gas equilibriums involving mass and charge transfers . . . . . . 4.4.1. Solids with anion vacancies . . . . . . . . . . . . . . . . . . . . . . 4.4.2. Solids with interstitial cations . . . . . . . . . . . . . . . . . . . . . 4.4.3. Solids with interstitial anions. . . . . . . . . . . . . . . . . . . . . . 4.4.4. Solids with cation vacancies . . . . . . . . . . . . . . . . . . . . . . 4.5. Homogenous semiconductor interfaces. . . . . . . . . . . . . . . . . . . 4.5.1. The electrostatic potential is associated with the intrinsic energy level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.2. Electrochemical aspect . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.3. Polarization of the junction . . . . . . . . . . . . . . . . . . . . . . . 4.6. Heterogenous junction of semiconductor metals . . . . . . . . . . . . . 4.7. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
vii
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73 77 77 78 79 80 80 90 91 92 94 94 96 97
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103 104 107 107 108
Chapter 5. Model Development for Interfacial Phenomena . . . . . . . . . . . 109 5.1. General points on process kinetics. . . . . . . . . . . . . . . . . . . . 5.1.1. Linear chain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.1.1. Pure kinetic case hypothesis . . . . . . . . . . . . . . . . . 5.1.1.2. Bodenstein’s stationary state hypothesis . . . . . . . . . . 5.1.1.3. Evolution of the rate according to time and gas pressure 5.1.1.4. Diffusion in a homogenous solid phase. . . . . . . . . . . 5.1.2. Branched processes . . . . . . . . . . . . . . . . . . . . . . . . . 5.2. Electrochemical aspect of kinetic processes . . . . . . . . . . . . . . 5.3. Expression of mixed potential . . . . . . . . . . . . . . . . . . . . . . 5.4. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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109 111 114 118 119 121 125 126 133 136
Chapter 6. Apparatus for Experimental Studies: Examples of Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 6.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2. Calorimetry . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.1. General points. . . . . . . . . . . . . . . . . . . . . . . 6.2.1.1. Theoretical aspect of Tian-Calvet calorimeters 6.2.1.2. Seebeck effect. . . . . . . . . . . . . . . . . . . . 6.2.1.3. Peltier effect . . . . . . . . . . . . . . . . . . . . . 6.2.1.4. Tian equation . . . . . . . . . . . . . . . . . . . .
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137 138 138 139 139 140 140
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6.2.1.5. Description of a Tian-Calvet device. . . . . . . . . . . . . . . . 6.2.1.6. Thermogram profile . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.1.7. Examples of applications . . . . . . . . . . . . . . . . . . . . . . 6.3. Thermodesorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.2. Theoretical aspect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.3. Display of results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.3.1. Tin dioxide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.3.2. Nickel oxide. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4. Vibrating capacitor methods . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.1. Contact potential difference . . . . . . . . . . . . . . . . . . . . . . . 6.4.2. Working principle of the vibrating capacitor method . . . . . . . . 6.4.2.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.2.2. Theoretical study of the vibrating capacitor method . . . . . . 6.4.3. Advantages of using the vibrating capacitor technique . . . . . . . 6.4.3.1. The materials studied . . . . . . . . . . . . . . . . . . . . . . . . 6.4.3.2. Temperature conditions . . . . . . . . . . . . . . . . . . . . . . . 6.4.3.3. Pressure conditions. . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.4. The constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.4.1. The reference electrode . . . . . . . . . . . . . . . . . . . . . . . 6.4.4.2. Capacitance modulation . . . . . . . . . . . . . . . . . . . . . . . 6.4.5. Display of experimental results . . . . . . . . . . . . . . . . . . . . . 6.4.5.1. Study of interactions between oxygen and tin dioxide . . . . . 6.4.5.2. Study of interactions between oxygen and beta-alumina . . . 6.5. Electrical interface characterization . . . . . . . . . . . . . . . . . . . . . . 6.5.1. General points. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5.2. Direct-current measurement . . . . . . . . . . . . . . . . . . . . . . . 6.5.3. Alternating-current measurement . . . . . . . . . . . . . . . . . . . . 6.5.3.1. General points. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5.3.2. Principle of the impedance spectroscopy technique . . . . . . 6.5.4. Application of impedance spectroscopy – experimental results . . 6.5.4.1. Protocol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5.4.2. Experimental results: characteristics specific to each material 6.5.5. Evolution of electrical parameters according to temperature . . . . 6.5.6. Evolution of electrical parameters according to pressure . . . . . . 6.6. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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142 144 146 156 156 157 161 161 163 172 172 176 176 176 179 179 179 181 181 181 182 182 184 185 187 187 189 191 191 191 196 196 197 202 208 212
Chapter 7. Material Elaboration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215 7.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2. Tin dioxide . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.1. The compression of powders . . . . . . . . . . . . . 7.2.1.1. Elaboration process and structural properties
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215 216 216 216
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7.2.1.2. Influence of the morphological parameters on the electric properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.2. Reactive evaporation. . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.2.1. Experimental device . . . . . . . . . . . . . . . . . . . . . . . . 7.2.2.2. Measure of the source temperature . . . . . . . . . . . . . . . 7.2.2.3. Thickness measure . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.2.4. Experimental process . . . . . . . . . . . . . . . . . . . . . . . 7.2.2.5. Structure and properties of the films . . . . . . . . . . . . . . 7.2.3. Chemical vapor deposition: deposit contained between 50 and 300 Å. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.3.1. General points. . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.3.2. Device description . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.3.3. Structural characterization of the material . . . . . . . . . . . 7.2.3.4. Influence of the experimental parameters on the physico-chemical properties of the films. . . . . . . . . . . . . 7.2.3.5. Influence of the structure parameters on the electric properties of the films . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.4. Elaboration of thick films using serigraphy . . . . . . . . . . . . . 7.2.4.1. Method description. . . . . . . . . . . . . . . . . . . . . . . . . 7.2.4.2. Ink elaboration . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.4.3. Structural characterization of thick films made with tin dioxide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3. Beta-alumina . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3.1. General properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3.2. Material elaboration . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3.3. Material shaping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3.3.1. Mono-axial compression . . . . . . . . . . . . . . . . . . . . . 7.3.3.2. Serigraphic process. . . . . . . . . . . . . . . . . . . . . . . . . 7.3.4. Characterization of materials . . . . . . . . . . . . . . . . . . . . . . 7.3.4.1. Physico-chemical characterization of the sintered materials 7.3.4.2. Physico-chemical treatment of the thick films. . . . . . . . . 7.3.5. Electric characterization. . . . . . . . . . . . . . . . . . . . . . . . . 7.4. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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254 255 255 257 261 261 262 263 263 266 273 275
Chapter 8. Influence of the Metallic Components on the Electrical Response of the Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277 8.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2. General points. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.1. Methods to deposit the metallic parts on the sensitive element . 8.2.2. Role of the metallic elements on the sensors’ response . . . . . 8.2.3. Role of the metal: catalytic aspects . . . . . . . . . . . . . . . . . 8.2.3.1. Spill-over mechanism . . . . . . . . . . . . . . . . . . . . . .
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277 278 278 279 282 283
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8.2.3.2. Reverse spill-over mechanism . . . . . . . . . . . . . . . . . . . 8.2.3.3. Electronic effect mechanism . . . . . . . . . . . . . . . . . . . . 8.2.3.4. Influence of the metal nature on the involved mechanism. . . 8.3. Case study: tin dioxide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3.1. Choice of the samples . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3.2. Description of the reactor . . . . . . . . . . . . . . . . . . . . . . . . . 8.3.3. Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3.3.1. Influence of the oxygen pressure on the electric conductivity 8.3.3.2. Influence of the reducing gas on the electric conductions . . . 8.4. Case study: beta-alumina . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.4.1. Device and experimental process . . . . . . . . . . . . . . . . . . . . 8.4.2. Influence of the nature of the electrodes on the measured voltage . 8.4.2.1. Study of the different couples of metallic electrodes . . . . . . 8.4.2.2. Electric response to polluting gases . . . . . . . . . . . . . . . . 8.4.3. Influence of the electrode size . . . . . . . . . . . . . . . . . . . . . . 8.4.3.1. Description of the studied devices . . . . . . . . . . . . . . . . . 8.4.3.2. Study of the electric response according to the experimental conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.5. Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.6. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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284 284 286 288 288 289 291 291 295 296 297 298 299 301 303 303
. 304 . 306 . 307
Chapter 9. Development and Use of Different Gas Sensors . . . . . . . . . . . 309 9.1. General points on development and use . . . . . . . . . . . . . . . . . . 9.2. Examples of gas sensor development . . . . . . . . . . . . . . . . . . . . 9.2.1. Sensors elaborated using sintered materials . . . . . . . . . . . . . 9.2.2. Sensors produced with serigraphed sensitive materials . . . . . . 9.3. Device designed for the laboratory assessment of sensitive elements and/or sensors to gas action . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.3.1. Measure cell for sensitive materials . . . . . . . . . . . . . . . . . . 9.3.2. Test bench for complete sensors . . . . . . . . . . . . . . . . . . . . 9.3.3. Measure of the signal . . . . . . . . . . . . . . . . . . . . . . . . . . 9.3.3.1. Measure of the electric conductance . . . . . . . . . . . . . . 9.3.3.2. Measure of the potential. . . . . . . . . . . . . . . . . . . . . . 9.4. Assessment of performance in the laboratory . . . . . . . . . . . . . . . 9.4.1. Assessment of the performances of tin dioxide in the presence of gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.4.2. Assessment of beta-alumina in the presence of oxygen . . . . . . 9.4.2.1. Device and experimental process . . . . . . . . . . . . . . . . 9.4.2.2. Electric response to the action of oxygen. . . . . . . . . . . . 9.4.3. Assessment of the performances of beta-alumina in the presence of carbon monoxide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.4.3.1. Measurement device . . . . . . . . . . . . . . . . . . . . . . . .
. . . .
. . . .
309 310 310 312
. . . . . . .
. . . . . . .
316 317 319 319 319 322 322
. . . .
. . . .
322 327 327 327
. . 329 . . 329
Table of Contents
9.4.3.2. Electric results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.5. Assessment of the sensor working for an industrial application . . . . . 9.5.1. Detection of hydrogen leaks on a cryogenic engine . . . . . . . . . 9.5.1.1. Context of the study . . . . . . . . . . . . . . . . . . . . . . . . . 9.5.1.2. Study of performances in the presence of hydrogen . . . . . . 9.5.1.3. Test carried out in an industrial environment . . . . . . . . . . 9.5.2. Application of the resistant sensor to atmospheric pollutants in an urban environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.5.2.1. Measurement campaign conducted at Lyon in 1988 . . . . . . 9.5.2.2. Measurement campaign conducted at Saint Etienne in 1998 . 9.5.3. Application of the potentiometric sensor to the control of car exhaust gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.5.3.1. Strategy implemented to control the emission of nitrogen oxides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.5.3.2. Strategy implemented to control nitrogen oxide traps . . . . . 9.5.3.3. Results relative to the nitrogen oxides traps . . . . . . . . . . . 9.6. Amelioration of the selectivity properties . . . . . . . . . . . . . . . . . . 9.6.1. Amelioration of the selective detection properties of SnO2 sensors using metallic filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.6.1.1. Development of a sensor using a rhodium filter. . . . . . . . . 9.6.1.2. Development of a sensor using a platinum filter . . . . . . . . 9.6.2. Development of mechanical filters . . . . . . . . . . . . . . . . . . . 9.6.2.1. Development of a sensor detecting hydrogen . . . . . . . . . . 9.6.2.2. Development of a protective film for potentiometric sensors . 9.7. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . .
xi
329 332 333 333 333 337
. 341 . 342 . 345 . 347 . . . .
347 349 350 352
. . . . . . .
352 352 354 356 356 356 359
Chapter 10. Models and Interpretation of Experimental Results . . . . . . . 361 10.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2. Nickel oxide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2.1. Kinetic model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2.2. Simulation of a kinetic model using analog electric circuits. . . . 10.2.2.1. Simulation of the curves displaying a maximum . . . . . . . 10.2.2.2. Simulation of the curves displaying a plateau . . . . . . . . . 10.2.3. Physical significance of the measured electric conductivity . . . . 10.3. Beta-alumina . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3.1. Physico-chemical and physical aspects of a phenomenon taking place at the electrodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3.1.1. Oxygen species present at the surface of the device. . . . . . 10.3.1.2. Origin of the electric potential . . . . . . . . . . . . . . . . . . 10.3.2. Expression of the model . . . . . . . . . . . . . . . . . . . . . . . . . 10.3.2.1. The electrode potential. . . . . . . . . . . . . . . . . . . . . . . 10.3.2.2. Expression of the coverage degree . . . . . . . . . . . . . . . .
. . . . . . . .
361 362 365 370 370 377 380 380
. . . . . .
380 380 384 385 385 389
xii
Physical Chemistry of Solid-Gas Interfaces
10.3.2.3. Expression of the theoretical potential difference at the poles of the device. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3.3. Simulation of the results obtained with oxygen . . . . . . . . . . . . 10.3.3.1. Behavior as a function of temperature and pressure. . . . . . . 10.3.3.2. Behavior as a function of electrode size. . . . . . . . . . . . . . 10.3.3.3. Evolution of the surface potential . . . . . . . . . . . . . . . . . 10.3.4. Simulation of the phenomenon in the presence of CO . . . . . . . . 10.3.4.1. Description of the mechanisms considered . . . . . . . . . . . . 10.3.4.2. Oxidation mechanisms of carbon monoxide . . . . . . . . . . . 10.3.4.3. Results of the simulation. . . . . . . . . . . . . . . . . . . . . . . 10.4. Tin dioxide. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.4.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.4.2. Proposition for a physico-chemical model . . . . . . . . . . . . . . . 10.4.3. Phenomenon at the electrodes and role of the thickness of the sensitive film . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.4.3.1. Calculation of the conductance G as a function of the thickness of the film . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.4.3.2. Mathematical simulation. . . . . . . . . . . . . . . . . . . . . . . 10.5. Bibliography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
394 395 395 397 399 401 401 402 405 409 409 410 415 416 423 428
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 431
Preface
Produced with the collaboration of Christophe Pijolat and Jean Paul Viricelle, this book is the fruit of research carried out over a long period of time by the Microsystems, Instrumentation and Chemical Sensors department at the Ecole des Mines, Saint Etienne, France. The abilities of this laboratory on the subject of modeling and instrumentation on heterogenous systems have enabled us to develop and study different devices for the detection of gas. The theoretical models based on kinetic concepts constitute the course of reflection and progress in a scientific area that is still little understood. A large part of this book refers to PhD and scientific reports. My thanks go out to all the authors. I would also like to thank the translators of this book from French, Zineb EsSkali and Matthieu Bourdrel.
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Chapter 1
Adsorption Phenomena1
1.1. The surface of solids: general points The concept of form, which can be associated with that of surface, is characteristic of a solid. On a crystallographic level, every solid can be identified by its atomic or molecular arrangement. This arrangement, which is specific to each solid, constitutes a solid phase. Generally, the identification of such a structure (atomic positions, cohesive energy) is defined in the hypothesis of an infinite crystal, which implies a similar environment for all atoms. Near the surface, this is no longer true and it is important to imagine a new local structure of atoms or electrically charged species. In the particular case of ionic species, to submit to the local electroneutrality, it will often be necessary to take the solid’s environment into account. The material and the different phases in contact with it will thus reach equilibrium. Thus appears the concept of interface: a privileged area of the solid, from which all interactions likely to occur between a solid and different surrounding compounds upon its contact will start and develop. Depending on the nature of these compounds, there will be talk of solid-solid, solid-liquid or gas-solid reactions.
2
Physical Chemistry of Solid-Gas Interfaces
To conceptualize the solid-gas reactions on which we will concentrate, it is essential to start by simply picturing a molecule of gas bonding with a solid. The bonded molecule could remain independent from its support or react with it. In the first hypothesis, the reversible process at work is one of adsorption, which then constitutes the overall reaction. It is called the adsorption-desorption phenomenon (see Figure 1.1a). In the second hypothesis, adsorption will be the first step of a more complex process. It has, in this case, a non-reversible character due to which a new compound, GS for instance, will form. The nature of the observed phenomenon will depend on the thermodynamic conditions (pressure, temperature) as well as on the chemical affinity of the present species. It is also possible in adsorption phenomena to distinguish between physical and chemical adsorption. Chemical adsorption or chemisorption is characterized by a simple electron transfer between the gas in physisorbed state and the solid. This transfer results in the forming of a reversible chemical bond between the two compounds (see Figure 1.1b). Once again, the appearance of the chemisorption process is directly related to the environment’s thermodynamic conditions.
Figure 1.1. The different interaction modes between a gas and a solid: a) physical adsorption, b) chemisorption, c) non-reversible reaction
1.2. Illustration of adsorption Volumetric and gravimetric methods are the most explicit and common methods used to display and quantify adsorption.
Adsorption Phenomena
3
1.2.1. The volumetric method or manometry In a closed system, the bonding of a gas molecule with a solid contributes to lowering the partial pressure of the gas and measuring the variation of this pressure is enough to access the necessary information. To conduct an experiment, one uses two containing vessels A and B (see Figure 1.2) are used. Vessel A is connected to a device that measures pressure in it or in vessel A+B if A and B are joined by a valve V1. Gas is introduced in vessel A using valve V2 under pressure Pa . The solid sample is put in vessel B. A simple gas expansion in vessel A+B is enough to allow us to measure pressure Pa b .
Figure 1.2. Adsorption-measuring device using the volumetric method
Generally, the number of gas molecules introduced, n, is given, either by:
n1
PaVa
when vessel A is isolated from vessel B, or by:
n2
Pa b (Va Vb )
after the expansion of the gas in vessel A+B.
Va and Vb are, respectively, the volumes of vessel A and B. If there is no solid sample in vessel B, we naturally find that:
n1 = n2
4
Physical Chemistry of Solid-Gas Interfaces
If there is a solid sample, we generally note that:
n1 > n2 The difference n1-n2 is the amount of gas bonded to the solid. This experiment, if conducted under different gas pressure conditions, gives us adsorption isotherms, which plot n against P at a given temperature. 1.2.2. The gravimetric method or thermogravimetry When a molecule of gas bonds with a solid, it changes the mass of the solid and simply weighing the solid gives us information about the bonded amount given the system’s parameters. This method allows us to easily verify that the process is reversible (see Figure 1.3).
Figure 1.3. Evolution of a solid sample’s mass gain ǻm under changing pressure: if t < t0: P = P0 if t0 < t < t1: P = P1 > P0 if t > t1: P = P0 a) reversible process; b) non-reversible process
1.3. Acting forces between a gas molecule and the surface of a solid 1.3.1. Van der Waals forces By analogy with molecular interactions, we can use forces known as Van der Waals forces to interpret the source of the physical adsorption processes which are G favored by very low temperatures. These forces, denoted by F for instance, are associated with a scalar potential ij:
G F
grad M
The scalar potentials are additive and the global scalar potential is the sum of the potential of attraction M a and the potential of repulsion M r :
Adsorption Phenomena
M
5
Ma Mr
where:
C r6
Ma
Mr
B rn
and:
r represents the intermolecular distance, while the constant C consists of three contributions: – the Keesom interaction or Keesom force, which only applies to polar molecules and originates from the attraction between several molecules’ permanent dipoles; – the induction interaction or Debye force, which originates from a molecule’s polarizability. It is caused by the attraction between permanent dipoles and other dipoles that are induced by the permanent dipoles; – London’s dispersion force, which originates from the attraction between molecules’ instantaneous dipoles. This is generally the most powerful attraction. As for the expression of M r , this is an empirical expression for which we generally choose n = 12. The global scalar potential M between two molecules is thus given by:
M
B C r 12 r 6
If we take into account the fact that the potential reaches a minimal value, M 0 , at equilibrium, meaning for an intermolecular distance r0, we then obtain:
ª § r0 · 6 § r0 ·12 º ¸ ¨ ¸ » «¬ © r ¹ © r ¹ »¼
M M 0 «2¨
6
Physical Chemistry of Solid-Gas Interfaces
1.3.2. Expression of the potential between a molecule and a solid In the hypothesis that all of the supposed semi-infinite crystal’s n molecules interact with the gas molecule, and that the potentials are additive, the global potential ĭ can be expressed as follows:
)a
¦M
a
for the attraction potential
)r
¦M
r
for the repulsion potential
n
and: n
These summations can be replaced with integrals:
)a
³ M dn
)r
³ M dn
a
and: r
where dn = N dv, and N represents the number of molecules per volume unit. The volume element used in the integrals is the volume between the spherical caps of radius r and r+dr, (see Figure 1.4), so: dV
Sdr
:r 2 dr
ȍ is the solid angle, and if Į is the maximum angle formed by the sphere’s radius and the solid’s surface normal, then:
:
2S (1 cos D )
where cos Į = Z / r , and Z is the distance between the molecule G and the solid.
Adsorption Phenomena
7
Figure 1.4. Domain of integration in solid
The potential of attraction then becomes: )a
SNC 6Z 3
and the potential of repulsion now is: )r
SBN 45Z 9
Thus, in the case of a gas molecule interacting with a solid, the 1/r3 Van der Waals potential becomes a 1/r6 potential of attraction, and a 1/r12 potential becomes a 1/r9 potential of repulsion. The solid seems to be a thousand times more attractive or repulsive than a simple molecule. 1.3.3. Chemical forces between a gas species and the surface of a solid In an upcoming chapter, we will go into more detail about this physico-chemical aspect, which is crucial in explaining the workings of chemical sensors. For now, we will merely point out that if a gas atom has free electrons, a chemical bond between the gas and the solid becomes a possibility, and there are two extreme polarization possibilities that can be observed, either:
G e G or:
G G e
-
8
Physical Chemistry of Solid-Gas Interfaces
1.3.4. Distinction between physical and chemical adsorption The difference between physical and chemical adsorption is due to the difference between the natures of forces that keep the gas molecules on the solid’s surface. Let us analyze the ĭ = f ® curve: it goes through a minimum defined by ĭ0 and r0. In physical adsorption (see Figure 1.5), the value of ĭ0 is so much smaller than that observed for chemical adsorption (1 instead of 5 or 6 Joules per mole); r0, on the contrary, is lower for chemical adsorption. At last, physical adsorption can be represented as a non-activated and therefore spontaneous process that is likely to take place at very low temperatures. On the contrary, chemisorption is an activated process and the ĭ = f ® curve goes first through a maximum marked by the activation energy value EA. The necessity of activation is related to the fact that electron transfer, from the gas or the solid, requires an energy input; this implies the existence of a kinetic process.
Figure 1.5. Plot aspect of ĭ = f ® in case of a): physisorption; b): chemisorption
1.4. Thermodynamic study of physical adsorption 1.4.1. The different models of adsorption In order to build a thermodynamic model of physical adsorption, it is important to take note of a few experimental results. The adsorption isotherms acquired through the volumetric or the gravimetric method allow us to make sure that the
Adsorption Phenomena
9
quantity n of bonded molecules is a function of gas pressure and temperature. These results involve a divariant system. Thereby, at the very least, all proposed models will have to meet this condition. It is important to note that the adsorption process can in no case whatsoever be identified with a simple condensation process. Indeed, condensation is a monovariant process that owes its origin to gas saturation. Saturation is achieved at a pressure P greater than or equal to the saturation vapor pressure P0, which varies with temperature only. On the other hand, adsorption is observed at gas pressure values that are lower than P0. The various thermodynamic models that have been proposed are grounded on such considerations. 1.4.2. The Hill model To take into account a system’s divariance, Hill deems it necessary to take surface effects into consideration. With this aim in mind, he supposes that the adsorption film, that is to say the adsorbent + adsorbed block, is easily assimilated to a solution where the adsorbent is formed by the free sites on the solid’s surface, and the adsorbed species are the gas molecules that have settled on those sites. In this case, the possible variables are pressure, temperature and the quantities of matter for the adsorbent (ns) and the adsorbed (na) species. There are 2 independent components (adsorbent + adsorbed + gas – an equilibrium relation between these three components). There are 2 exterior parameters (P and T) and there are 2 phases (solid and gaseous). Thus, the variance v is:
v 1 3 2
2
We can therefore plot: – isotherms na = f (P) where T = constant; – isobars na = f (P) where P = constant; – isosters P = f (T) where na = constant.
10
Physical Chemistry of Solid-Gas Interfaces
1.4.3. The Hill-Everett model Unlike the previous model, where the surface acts through the surface ns of its species, Hill and Everett describe surface effects using a physical parameter, namely the force field of the solid. In effect, this model considers that adsorption can be described as a localized condensation process that tends to progressively cover the entire surface when the gas pressure increases. A fluctuation in the fraction of covered surface necessarily induces a fluctuation in the energy of the contact between the two phases. This energy term is the product of an extensive quantity AS, which is the contact surface between the two phases, with an intensive quantity PS, which is comparable with a surface pressure. PS is identified with the variation of the surface tension coefficient Ȗ during the covering, that is to say: PS
Ȗ0 Ȗ
In this case, there are 3 exterior parameters: pressure, temperature and surface pressure. Assuming that there is only one independent component, the variance is given by:
v 1 3 2
2
There is in effect only one component: a solid + a gas – an equilibrium relation. At P = P0 (saturation vapor pressure), we will assume that the entire surface is covered and that there is no longer any change in the solid’s force field; the conditions we now have are those of a simple condensation, for which v = 1 + 2 – 2 = 1. 1.4.4. Thermodynamics of the adsorption equilibrium in Hill’s model 1.4.4.1. Formulating the equilibrium In the adsorbed phase, the change dG in enthalpy G is given by Gibbs’ equation:
dG where: μ1
Sdt VdP P1dn1 dn2
§ GG · and: μ2 ¨ Gn ¸ 1 ¹ P ,T , n2 ©
§ GG · ¨ Gn ¸ 2 ¹ P ,T , n1 ©
Adsorption Phenomena
11
For component 1 (the adsorbed species) in the solution, we have:
§ Gμ · S1dT V 1dP ¨¨ 1 ¸¸ dn1 © Gn1 ¹ P ,T ,n2
dμ1
S1 being the differential molar entropy of component 1, and V1 the differential molar volume of component 1, we know that:
dP1
d(
GG G ) (dG ) , S1 Gn1 Gn1
GS1 and V1 Gn1
GV1 Gn1
Let us suppose that dn2 = 0, which would imply that the quantity n 2 of adsorbent is a constant. This assumption works all the better for the fact that the value of n 1 is very much lower than that of n 2 . As to the gas phase, it is pure, so we have:
dPG
SG dT VG dP
SG and VG representing the molar entropy and the molar volume of the gas. At equilibrium, necessarily, d ȝ1 = d ȝG, hence the following equilibrium equation:
S
G
§ Gμ · S1 dT VG V 1 dP ¨¨ 1 ¸¸ dn1 © Gn1 ¹ P ,T ,n2
0
1.4.4.2. Isotherm equation To make things simpler, we will make a few hypotheses: – the volume of the gaseous phase is far greater than that of the adsorbed phase:
VG !! V1 – the gas is ideal:
PVG
RT
12
Physical Chemistry of Solid-Gas Interfaces
The process being isothermal dT = 0 leads to:
RT
§ Gμ1 · ¨¨ ¸¸ dn1 © Gn1 ¹ P ,T ,n2
dP P
if: ȝ1 = ȝ0 + RT Ln nS, where nS is the number of fixed moles per surface unit. Then:
§ Gμ1 ·§ GnS ¸¸¨¨ ¨¨ © GnS ¹© Gn1
§ Gμ1 · ¸¸ ¨¨ © Gn1 ¹
· ¸¸ ¹
thus:
RTd ( LnP)
RT ( LnS )
which brings us to:
nS
DP
in which we recognize Henry’s law. 1.4.5. Thermodynamics of adsorption equilibrium in the Hill-Everett model In this case, the effects due to the surface tension between the condensed phase and the solid need to be taken into account when using Gibbs’ equation. To this end, we can start by expressing the internal energy changes dUS of the condensed phase:
dU S
TdS S PdVS PS dAS P S dnS
A new additional energy term appears when we distance ourselves from the classic model, which is a function of P and T only, that is, PS dAS. SS, VS, AS and dnS stand for entropy, volume, contact surface and the condensed phase’s number of moles. We can finally give the expressions for US and GS using the fact that, for a compound in a pure phase, GS = ȝS nS:
Adsorption Phenomena
US
TS S PVS PS AS P S nS
GS
U S TS S PVS PS AS
13
and:
If we consider G to be an exact differential, then we arrive at:
s s dT v s dP a s dPS P s dn s
dG S Since:
dG
nS dP S P S dnS
dμS
s s dT v s dP a s PS
then:
where s s
SS
nS
, vs
VS
nS
and a s
AS
nS
.
If ī denotes the quantity of matter per surface unit, as in 1/aS, the equilibrium condition:
dP S
dPG
becomes:
S G s S dT VG v S dP
1 dPS *
0
This equation expresses the equilibrium condition in a Hill-Everett system. 1.5. Physical adsorption isotherms 1.5.1. General points Physical adsorption isotherms are generally obtained experimentally using a volumetric or gravimetric method. Before we try to obtain meaningful results from the theoretical expressions we have arrived at using Hill’s or Hill and Everett’s
14
Physical Chemistry of Solid-Gas Interfaces
hypotheses, we can already point out a few things concerning the mobility of the layers that become adsorbed on the surface of a solid. There are two borderline cases to be considered: – molecules that are adsorbed in the form of mobile layers; – molecules that are perfectly located on some of the solid’s sites. The existence of these borderline cases can be explained by the non-uniformity of the solid’s surface potential and the fact that this is typically related partly to the periodicity of a crystal lattice and the nature of the solid’s constituents. This periodicity (see Figure 1.6) can be described as there being E1 sites of lower energy, separated by higher E2 energy levels. The probability of a molecule moving from one stable site to another is thus proportional to E2 – E1. The E2 – E1 difference represents the energy barrier related to this species’ surface movement. If kT >> E2 – E1, the probability of a hopping step is high, and it is then said that the layer is mobile. If kT << E2 – E1, the probability of a hopping step is low, and it is then said that the layer is localized.
Figure 1.6. Periodic change in surface energy of crystal of parameter a
Beyond this classification, it is also relevant to consider the case of monolayer adsorption as well as that of multilayer adsorption.
Adsorption Phenomena
15
1.5.2. Adsorption isotherms of mobile monolayers In such a case, the solution analogy is perfect. Hill’s model can therefore be applied here. The equation for the isotherm is as previously stated, that is to say:
nS
ĮP
In fact, this model does not take into consideration the interaction between adsorbed molecules. However, the truth is that, generally, the hypothesis of a dilute solution cannot be used when studying adsorption phenomena; therefore, the thermodynamic model for solutions will rarely be of any help to us. 1.5.3. Adsorption isotherms of localized monolayers The adsorbed molecule is bound in a low energy position; this position constitutes an active site. The solid’s surface is now made up of identical active sites that we will assimilate to active species, which we will denote by s. Adsorption can then be expressed as an actual chemical reaction for which we will use the following notations: – [A] stands for a compound A in gaseous state; – << A >> is for a constituent A in a solid or liquid solution; – < A > is for a pure solid or liquid phase of a compound A. In the situation we are considering, the adsorption reaction is expressed by:
s G s << G – s >> appears here as the new species, and we therefore have a G – s solution in s. This model is fully compatible with Hill’s model. To express the equation of the isotherm, there are two complementary and equally effective methods available.
16
Physical Chemistry of Solid-Gas Interfaces
1.5.3.1. Thermodynamic method If we apply the mass action law to the previous equilibrium, we have:
K
G s !! P s !!
where K is the equilibrium constant. It is given by:
K
§ 'H q · K 0 exp¨ ¸ © RT ¹
Adsorption is an exothermic process, which leads to ǻH° < 0. A negative value for ǻH° means that it is the reverse reaction that takes place if the temperature increases; therefore, adsorption is more likely to take place at low temperatures. In an ideal solution, if S denotes the number of free sites, S0 denotes the number of sites, and ș represents the fraction of sites that are in use, which is expressed as:
T
S0 S S0
G s !!
then:
s !!
S S0
1T
which brings us to:
K
T 1 T P
Thus:
T
KP 1 KP
This relation, which is called the Langmuir isotherm, demonstrates that the percentage coverage of the surface is a homographic function of pressure. This
Adsorption Phenomena
17
function is an accurate way to represent most adsorption-related experimental results. Note that, at low surface coverage fractions ( ș << 1), a proportionality law not unlike Henry’s law is obtained:
T
KP
1.5.3.2. The kinetic model An equilibrium is reached if the variable resulting from two dynamic processes is brought to zero: – adsorption, which has a rate RF; – desorption, which has a rate RD. These two processes can be seen as two elementary steps that do not involve any intermediate reactions. In such a case, the RF rate is proportional to the number of shocks ȣ, which is the number of molecule and surface impacts per time unit, as well as to the number of free sites on the surface. Thus:
RF
DX 1 T
where:
X
P
2S m kT
.
Therefore:
RF
D ' P (1 T )
Rd is proportional to the number of already adsorbed molecules, so:
RD
ET
At equilibrium, VF = VD, which leads to:
18
Physical Chemistry of Solid-Gas Interfaces
T
KP 1 KP
where:
K
D'
E
1.5.4. Multilayer adsorption isotherms During physical adsorption, each adsorbed molecule forms a new active site for the remaining gas molecules, but there is no reason why this process should limit itself to only one layer. The Brunauer-Emmet-Teller theory, which originates from the Langmuir theory, allows us to obtain a relation (BET equation) involving a parameter that expresses the influence of the solid’s global surface area, that is to say, the area exposed to gas action. 1.5.4.1. Isotherm equation This derives from the application of the Langmuir theory to the piled up layers. A given site can be covered by 0, 1, 2,… i,… layers of localized gas molecules that do not interact. We will denote by S0, S1, S2,… Si the respective fractions of surface covered by 0, 1, 2,… i layers (see Figure 1.7). We will also hypothesize that the number of layers can be infinite. We will discuss the latter point further in a following section. At equilibrium, each fraction is constant. Now we must consider the different layers: – Layer 0 The rate of the disappearance of S0 (condensation over S0) is equal to the rate of adsorption over S0, which is a1PS0. The rate of the appearance of S0 is equal to the rate of desorption of S1, which is b1S1.
Adsorption Phenomena
19
Figure 1.7. Parceling of the solid’s surface depending on the number of layers
At equilibrium, the rates of appearance and disappearance of S0 are equal, so:
a1 PS0
b1S1
a1 and b1 are kinetic constants relative to adsorption and desorption. This equation is similar to that obtained using the monolayer model and the Langmuir hypothesis. – Layer 1 The rate of the disappearance of S1 is equal to the rate of adsorption over S1, which is a2PS1, to which the rate of desorption of S1 is added, that is: b1S1. The rate of the appearance of S1 is equal to the rate of adsorption over S0, which is a1PS0, to which the rate of desorption of S2 is added, that is: b2S2. At equilibrium:
a1 PS 0 b2 S 2
a2 PS1 b1S1
which, given the relation obtained for layer 0, becomes:
a2 PS1
b2 S 2
– Layer i-1 The same reasoning as before leads to:
ai PSi 1
bi Si
We therefore have a system of i equations and i + 1 variables S0, S1, S2,… Si, where:
20
Physical Chemistry of Solid-Gas Interfaces
S1
(a1 / b1 ) P0
S1
(a 2 / b2 ) P0
" " " " " " Si
(ai / bi ) P0
In addition: i f
¦S
i
S the global surface area of the solid.
i 0
Moreover, if V0 is the volume per cm2 of fixed gas for an assumed complete theoretical monolayer, then the total volume is:
V
i f
0 1.V0 S1 2.V0 S 2 ... i.V0 S i ... V0 ¦ iS i i 0
If Vm refers to the SV0 product, which is the theoretical volume obtained in the case of a monolayer that is assumed complete, then:
V
Vm S
¦ iS
i
i
Vm
¦ iS ¦S
i
i
To find the solutions, we will assume that ai and bi are respectively equal to a and b for every i but 1. Thus:
x
a P b
for i z 1 and by analogy:
cx
a P b
for i = 1 where:
c
a b1 / a1b
Adsorption Phenomena
21
if we consider that when i = 1, a = a1 and b = b1. The first layer is different from the rest by the fact that the solid is in direct contact with the gas. The system of equations then becomes:
S1
cxS 0
S2
xS1
cx 2 S 0
" " " " " " " Si
xS i 1
cx i S 0
Thus:
S
>
@
S 0 1 c x x 2 x 3 ... x i ...
Assume that 0 < x < 1 (we will soon explain why). We therefore have:
x x 2 x 3 ....... x i
x 1 x
which leads to:
S
cx · § S 0 ¨1 ¸ © 1 x ¹
§ 1 c 1 x · S0 ¨ ¸ © 1 x ¹
In a similar way, we arrive at:
¦ iS
i
cxS 0 1 2 x 3 x 2 ... ix i 1 ...
since, if 0 < x < 1:
1 2 x 3 x 2 ...... ix i 1 which gives us:
¦ iS
i
cxS0 (1 x) 2
1 (1 x) 2
22
Physical Chemistry of Solid-Gas Interfaces
thus:
V
Vm
cx 1 x >1 c 1 x@
We must now analyze the role of x. If: x o 1, we note that in effect V o f, which means that the gas liquefies and that P = P0 at infinite V. This brings us to:
a P0 1 b thus:
a b
1 P0
which leads to:
x
P P0
Since P is necessarily less than P0 during adsorption, then we meet the requirement of x being less than 1. The isotherm equation is therefore expressed as follows:
V
Vm
cP ª º P0 P «1 c 1 P » P0 ¼ ¬
It is possible, by applying the appropriate mathematical transform to this equation and making comparisons with the experimental results, to prove the validity of such an expression and also calculate the values of the related parameters, namely Vm and c. It is important to note that knowing Vm gives us access to the value of the solid’s specific surface area. Moreover, the BET equation allows access to the porosity of the solid. This book will not go into details on these two points. Overall, the previous expression’s domain of validity is limited by the following condition:
Adsorption Phenomena
23
0.05 d P / P0 d 0.35 This restriction is due to the fact that, at too low x values, there are not nearly enough adsorbed molecules, which makes multilayers very unlikely to form. At very high values for x, though the number of layers increases, it is difficult to imagine there being an infinity of layers, which is what the theoretical expression predicts. 1.6. Chemical adsorption isotherms As we have already mentioned, only chemical adsorption can be the source of an electric disturbance. That is why these processes constitute the basis of a resistive or potentiometric sensor’s working mechanism, in which we will take an interest. Chapter 4 is therefore devoted entirely to this subject. However, we can start already by presenting some facts: a) Chemisorption isotherms have an asymptotic form and Langmuir-type equations are perfectly compatible with experimental results. However, in such a case, the equilibrium constant K may be dependent on the fraction of covered surface. We already know that the equilibrium constant is related to the molar heat of adsorption 'H0. However, this quantity is not necessarily constant, mainly for two reasons: – firstly, because the surface might be heterogenous in terms of energy; – secondly, because of surface charge effects, which are induced by chemisorption itself. This aspect will be developed further in Chapter 4. Whichever is the case, it is possible to solve this problem using a site distribution based on the heat of adsorption. We may then apply the Langmuir theory to the sites that are of category i and heat of adsorption 'Hi, to obtain:
Ti
K i Pi 1 K i Pi
There are different types of distributions we can now use: – Assume that we have an exponential distribution: ni
n0 exp( 'H i / 'H 0 )
A summation for all values of Ti gives, at low values of Tv, the following expression:
24
Physical Chemistry of Solid-Gas Interfaces
LnT f
RT / 'H 0 LnP C st
thus
Tf
aP n
which is the equation of the Freundlich isotherm. – Assume that the heat of adsorption is related to the fraction of covered surface. This hypothesis is perfectly satisfactory in case surface electrical effects are present. In fact, the rigorous relationship that has been established between the fraction of covered surface and the heat of adsorption is not simple. It is however possible, using some hypotheses, to reach simpler solutions. That is how some linear approximation laws, for instance 'H = 'H0 (1 – ET), were discovered. The following expression was therefore reached:
LnP
Ln(T f / 1 T f ) LnA 'H 0 ET f / RT
For average coverage fractions, namely Tv = 0.5, the first term is negligible, so we have:
Tf
RT / 'H 0 ET f LnAP
that is, the equation of the Temkin isotherm. b) We have already mentioned that chemical adsorption processes had to be activated, which brings us to the kinetic aspect of such a process, which does not necessarily have just one elementary step anymore. Rather, it is more realistic to think of this as a process with two elementary steps: – the first step constitutes the physisorption process; – the second step represents the electron transfer from the gas to the solid or from the solid to the gas. During adsorption, only the second step has an activation energy (see Figure 1.5), so it is therefore the step that controls the kinetic process. Desorption’s two steps, however, have to be activated. Yet it is obvious in Figure 1.5 that the chemisorption process takes over. That is because its activation energy value ED is much higher than that of physisorption. c) Moreover, it appears that in the case of chemisorption, it is quite difficult to conceptualize an electron transfer from a stable diatomic molecule such as oxygen.
Adsorption Phenomena
25
We can thus imagine a preliminary step representing the molecule’s dissociation in its gaseous or adsorbed state. For oxygen, for instance, the global process including a gas dissociation would be written as:
O2 2O with K1 as the equilibrium constant. Then:
O 1 electron s (O s) with K2 as this equilibrium’s constant. Thus:
K1
PO2 PO2
and:
K2
T PO (1 T )
therefore:
T
K 2 K1 PO2 1 K1 PO2
In this case, the law for diatomic molecules is no longer a function of PO2 but it is now a function of PO12/ 2 . More generally, for a gas whose atomicity (the number of atoms that form the molecule) is i, we have:
Gi iGi
26
Physical Chemistry of Solid-Gas Interfaces
with:
T
K 2 i K1 PO2 1 i K1 PO2
d) The case of gas mixtures: suppose we have a mixture of two gases A and B that could be adsorbed by a particular solid. These gases are characterized by their equilibrium constant of adsorption KA and KB, and by their fraction of covered surface TA and TB. Under these conditions, the number of available sites on the surface is 1 – TA – TB, and the equilibrium conditions are expressed as follows:
T A /(1 T A T B )
K A PA
on the one hand, where:
1T A TB
T A / K A PA
and on the other:
T B /(1 T A T B )
K B PB
This leads to:
T A /TB
K A PA / K B PB
By transferring this expression to one of the two previous expressions, we obtain:
T A T A / K A PA (1 K A PA K B PB ) In general, and for multiple gases, we would obtain:
TA
K A PA /(1 ¦ K i Pi )
Adsorption Phenomena
27
1.7. Bibliography 1. D.M. YOUNG, A.D. CROWELL, Physical Adsorption of Gases, Butterworths, London, 1962. J.E. GERMAIN, Catalyse hétérogène, Dunod, Paris, 1959. E.A. FLOOD, The Solid Gas Interface, Marcel Dekker, Inc, New York, 1967. T. WOLKENSTEIN, Théorie électronique de la catalyse sur les semi-conducteurs, Masson, Paris, 1961. J. BESSON, M. AZZOPARDI, M. CAILLET, M. SOUSTELLE, P. SARRAZIN, J. Chimie. Physique, 1964, p. 1018.
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Chapter 2
Structure of Solids: Physico-chemical Aspects
2.1. The concept of phases Before addressing the subject of the electronics of the sensors we have chosen to study in this book, we will first briefly concentrate on some physico-chemical aspects of solid materials, but more specifically of metal oxides. We will limit the topic to crystalline solids. Therefore, every solid can be identified by its crystal structure. The crystal structure is formed by a pattern: it could be an ion, an atom or a complex molecule. This pattern is duplicated in space G G G using three vectors a, b, c (see Figure 2.1). The crystal lattice is therefore composed G G G of nodes, directions and planes (see Figure 2.2). The primitive vectors a , b, c are defined by their magnitudes a, b, c and by the measure of the angles Į, ȕ, Ȗ formed by the three vectors. The values of these parameters are accessible using Bragg’s law, which has to be applied to the diffraction patterns obtained using X-ray scattering. Bragg’s law is defined by: 2dSinT
kO
where d is the distance between two planes from the same family of reticular planes in the crystal, ș is the diffraction angle of soft X radiation on this family of planes and Ȝ is the associated beam’s wavelength.
30
Physical Chemistry of Solid-Gas Interfaces
Figure 2.1. Definition of the three primitive vectors
Figure 2.2. Concept of nodes, directions and planes
The relative or absolute value of these different parameters allows us to define seven base lattices or Bravais lattices, which are: – the cubic lattice, where a = b = c and Į = ȕ = Ȗ = 90°; – the tetragonal lattice, where a = b c and Į = ȕ = Ȗ = 90°; – the hexagonal lattice, where a = b c and Į = ȕ = 90°, Ȗ = 120°; – the trigonal or rhombohedral lattice, where a = b = c and Į = ȕ = Ȗ 90°; – the orthorhombic lattice, where a b c and Į = ȕ = Ȗ = 90°; – the monoclinic lattice, where a b c and Į = Ȗ = 90° ȕ; – the triclinic lattice, where a b c and Į = ȕ = Ȗ 90°. Knowing the values of a, b, c, Į, ȕ and Ȗ for a given chemical compound makes it completely possible to identify it. Conversely, a chemical compound can crystallize in different forms, that is to say with different values for a, b, c, Į, ȕ and Ȗ.
Structure of Solids
31
Therefore, knowing a solid’s chemical formula is no longer enough to identify and describe a compound from a physical or physico-chemical point of view. If a compound crystallizes in different forms, then this compound is said to have different allotropes, and each allotrope constitutes a separate phase. Overall, there are as many solid phases as there are different crystal systems in a given system. 2.2. Solid solutions A solid compound constitutes a pure phase if all the patterns of its lattice are identical. The nature of the patterns depends on that of the compounds: an atom in metallic compounds, the association of an anion and a cation in an ionic compound, and a group of atoms or ions in the case of a more complex compound. As a matter of fact, we can rarely come across a situation as ideal as this one in a natural environment. Other chemical elements often settle on a crystal lattice. These foreign elements can either occupy the lattice’s normal sites (this is called a substitutional defect) or other sites in interstitial positions. The initial phase stays the same if the presence of foreign elements only causes a simple local distortion of the lattice. The foreign elements can then be viewed as a solute, and the elements that constitute the lattice as the solvent. This kind of situation will be defined by many parameters. Picture an element A, forming a pure phase, and crystallizing in the form of a cubic-type lattice LA (see Figure 2.3a), as well as an element B, also forming a pure phase but crystallizing as a tetragonal lattice LB (see Figure 2.4a). If a quantity of B is introduced in the LA lattice and this lattice’s structure is preserved, then it is said that A and B form a solid solution (solubility of B in A; see Figure 2.3b). Similarly, if a quantity of A is introduced in the LB lattice and this lattice’s structure is preserved, then A and B form a solid solution (solubility of A in B; Figure 2.4b). It is possible, under the hypothesis that the B element has reached a substitutional or interstitial position, to define, by analogy with liquid solutions, a concentration CA for A and a concentration CB for B: CA
Number of sites containing A Total number of sites
32
Physical Chemistry of Solid-Gas Interfaces
CB
Number of sites containing B Total number of sites
with: C A CB
1.
Figure 2.3. Diagrammatic plane representation of cubic lattice LA a) compound A in pure phase, b) solution of B in A
Figure 2.4. Diagrammatic plane representation of tetragonal lattice LB a) compound B in pure phase, b) solution of A in B
Actually, the solubility of B in LA is necessarily limited since in the possibility that CB = 1, there has to be an LB-type lattice, and the same reasoning also applies to A. In the simplest case, where CBl = CAl, we go directly from having a LA structure to having a LB structure. In a more complicated situation, it is possible to observe the existence of multiple intermediate phases (see Figure 2.5).
Figure 2.5. Phase diagram
Structure of Solids
33
Moreover, the solubility limit CBl of B in LA is dependent on temperature. The same reasoning applies to the B phase. All of this information is usually presented and illustrated for each element or compound, using a specific phase diagram. 2.3. Point defects in solids1, 2, 3 In the hypothesis of a perfect crystal lattice defined by a single pattern present on all of the lattice’s nodes, it is difficult to imagine an atom or ion moving around in the structure of the solid. Yet, experience shows scattering of chemical species in most materials. To explain this movement and to conceptualize some heterogenous reactions involving solid compounds, it was necessary to imagine the existence of point defects in solids. In the case of metallic solids, these defects consist either of the presence of metallic atoms in interstitial positions of the lattice or the absence of a few atoms from the nodes of the lattice. In the case of ionic solids and according to the Wagner classification, there are four kinds of point defects, that is to say: – anion vacancies, meaning that some anions are missing from their anion sites on the lattice; – cation vacancies, meaning that some cations are missing form their cation sites on the lattice; – interstitial anions, meaning that some anions moved from their regular sites into an interstitial position in the lattice; – interstitial cations, meaning that some cations moved from their regular sites into an interstitial position in the lattice. To make sure the electroneutrality principle is respected in the lattice, these defects have to be associated with charge carriers: electrons or electron holes. These carriers can be trapped in the defects or free to move around in the lattice. The release of a charge carrier by a defect is identified with an ionization of the defect (see Figure 2.6).
34
Physical Chemistry of Solid-Gas Interfaces
(a) Ionization of an anion vacancy
(b) Ionization of an interstitial anion
(c) Ionization of a cation vacancy
(d) Ionization of an interstitial cation Figure 2.6. Diagrammatic description of four Wagner-type defects
2.4. Denotation of structural members of a crystal lattice1, 2 To describe and make efficient use of point defects in reaction processes, it was necessary to set up a specific denotation that would be able to express the nature of the defect, and its environment, as well as the effective charge it represents. The effective charge “qe” is defined as a change in charge, which conveys the fact that there is a charge input or deficiency compared to the reference of a lattice that respects the principle of electroneutrality. If qn is the regular charge attributed to an ideal lattice’s site and qr is the real charge allocated to that site, the charge deficiency or excess is then expressed by the following relationship:
qe
q r qn
Structure of Solids
35
The denotation suggested by F.A. Kröger and H.J. Vink3 is now used by all scientists. Thus, in binary ionic crystal AB (A+n, B-n) where each site of the ideal lattice carries a +n or –n charge, we will have structural member X for each lattice: – information concerning the nature of the element based on its chemical symbol: Cl, Na, V, for instance (V refers to a vacancy, which means that an element is missing from that position), the electrons and electron holes are referred to using respectively the e- or h+ symbols; – information concerning the nature of the occupied crystal site: - A is for a regular site containing A, - B is for a regular site containing B, - I is for an interstitial position. This information is given in the index position of the nature of the element: - AA represents an A element on a regular A site, - BB represents a B element on a regular B site, - AI represents an A element on an interstitial site I, - BI represents a B element on an interstitial site I; – information concerning the site’s effective charge qe. This information is given in exponent position after the element. In order to present the information in a clear way, the positive charge’s value will be expressed by the number of dots in the exponent position of the element and the negative charge’s value by the number of commas. Thus, in a lattice A+nB-n where n = 2, for example, an A2+ element in its regular position on its site is denoted by AA, and: qe
qr qn
22 0
An A in interstitial position is denoted by AI, and: qe
qr qn
00 0
An A2+ element in interstitial position is denoted by A DI D , and:
qe
qr qn
20 2
36
Physical Chemistry of Solid-Gas Interfaces
A non-ionized A vacancy is denoted by VA, and:
qe
qr qn
22 0
A singly ionized A vacancy is denoted by VA' , and:
qe
qr qn 1 2 1
A fully-ionized A vacancy is denoted by VA" , and:
qe
qr qn
0 2 2
A non-ionized B vacancy is denoted by VB, and:
qe
qr qn
2 2 0
A singly ionized B vacancy is denoted by: VBq , and:
qe
qr qn
1 2 1
A fully-ionized B vacancy is denoted by VBD D , and:
qe
qr qn
0 2 2
2.5. Formation of structural point defects3 The formation of structural defects can take place inside the crystal matrix itself or it can require the surface structural elements; these elements are likely to establish equilibriums with the gaseous phase. 2.5.1. Formation of defects in a solid matrix The only way to cause a point defect in a crystal lattice is to imagine the jump of an element from a regular position into an interstitial position. This jump allows the formation of an interstitial element as well as a vacancy. In the case of a cationic element, we have a positive effective charge in interstitial position AI0 associated with a vacancy V ' with a negative effective charge. Obviously, for an anionic element, we can observe the opposite. We should note here that the charge neutrality
Structure of Solids
37
is maintained. Both defects are Frenkel defects: cation Frenkel defect in the first case, and anion Frenkel defect in the second case (see Figure 2.7).
Figure 2.7. Cation Frenkel defect
2.5.2. Formation of defects involving surface elements A solid’s surface, which is the manifestation of a crystal lattice’s discontinuity, can be described as a set of free potential sites capable of receiving the lattice’s anions and cations. Therefore, a lattice anion that is near the surface can move on such a site by simultaneously creating a vacancy under the surface and a new element on the surface (see Figure 2.8). Such a vacancy will make it possible for the lattice anions to scatter progressively towards the surface. Anionic vacancies formed near the surface will thus be able to move to the lattice’s core. This process, which also applies to cations, results in the formation of cationic as well as anionic vacancies, making it possible to respect the electroneutrality principle inside the lattice. The compounds featuring this characteristic are of the Schottky type.
Figure 2.8. Anionic Schottky-type defect
Note that the formation of such vacancies necessarily leads to an electrical disturbance on the surface. For a Schottky-type compound, we might think that these effects cancel out just on the surface of the material. It is no longer necessarily the
38
Physical Chemistry of Solid-Gas Interfaces
case if only one type of defect is predominant. This kind of situation can arise when the formed defect is caused by an equilibrium between the solid and the surrounding gaseous phase. This situation will be more closely examined in the section about interface equilibriums. 2.5.3. Concept of elementary hopping step2 We have just seen that the existence of elementary defects allows the ions to move inside the crystal lattice. Their movement can be described as a sequence of elementary hopping steps. There are two distinct types of hopping steps: – hopping steps that require an element to move from a regular site on the lattice to another neighboring regular site, a hopping step of type N o N (Schottky defects); – hopping steps that require an element to move from a regular site on the lattice to a neighboring interstitial site, a hopping step of type N o I (Frenkel defects). In both situations, these moves are activated processes (an energy barrier has to be overcome). In the presence of a chemical force (a concentration gradient for instance) and/or an electric force (an electric field for instance), these moves will be oriented in the direction of the effective force. All of these hopping steps are identical and are characterized by the same energy barrier or activation energy value. Such a process, which identifies with a scattering process in a solid phase, is therefore athermal (ǻH=0). Note finally that equilibriums can form between different structural elements of the lattice, and that such equilibriums follow the classical rules of thermodynamics. For further details, refer to Kröger’s or Soustelle’s work.2, 3 2.6. Bibliography 1. C. DESPORTES, M. DUCLOT, P. FABRY, J. FOULETIER, A. HAMMOU, M. KLEITZ, E. SIEBERG, J-L. SOUQUET, Electrochimie des solides, Collection Grenoble Sciences, 1994. 2. M. SOUSTELLE, Modélisation macroscopique des transformations physico-chimiques, Masson, Paris, 1990. 3. F.A. KRÖGER, The Chemistry of Imperfect Crystals, Amsterdam, North Holland Co., 1974.
Chapter 3
Gas-Solid Interactions: Electronic Aspects
3.1. Introduction Before going into a description of electron transfers between a gas and a solid, it is necessary to present some general physical or physico-chemical properties of the constituents, that is to say gases and solids. We will limit our study of gases to a few random points. 3.2. Electronic properties of gases Depending on its nature, a gas element interacting with a solid can act as an electron acceptor or donor. If its orbitals are full, then the gas is necessarily an electron donor, and this property will be characterized by the energy the system needs to extract an electron from the molecules or atoms of gas. This energy is the ionization potential, denoted by Ii. The same gas element can successively free many electrons, and each extraction will be characterized respectively by its ionization potential: I1, I2, I3, etc. If the orbitals of the gas molecule or the gas atom are empty, then they will be able to accept electrons, and the corresponding energy then identifies with an electron affinity Ai. In such a case, there are multiple possible energy configurations. Oxygen is the perfect example, with: O 2 , O , O 2 .
40
Physical Chemistry of Solid-Gas Interfaces
3.3. Electronic properties of solids1 3.3.1. Introduction A given isolated metal atom A (metal vapor for instance) has electrons with predetermined energy levels E iA . This is due to the fact that these electrons’ energy interactions only concern one nucleus; the nucleus-electron distances are indeed greatly lower than the internuclear distances. The soft X-ray spectrum is thus composed of distinct and very thin lines (see Figure 3.1a). If N atoms are compressed to form a crystal, then most outer atoms, and especially the valence electrons, will interact with the neighboring atoms. These electrons of energy E V A are no longer subject to the influence of only one nucleus but to that of the entire crystal, consequently forming an electron cloud which will ensure the cohesion of the solid. Each electron will be characterized by a trajectory which passes through the entire crystal. We will then have N electrons with the same energy level. This conclusion is not compatible with the Pauli exclusion principle, which states that two electrons cannot have the same energy level unless their spin values are opposites. Therefore, we have to imagine that the isolated atom’s discrete energy levels will expand in the crystal and form energy bands (see Figure 3.1b). Each band will possess N / 2 levels and be able to accept N electrons. Historically, it is Drude who, in around 1900, first speculated that valence electrons could form a gas, and a classical theory based on the kinetic theory of gases made it possible to explain the high electrical conductivity of metals. However, since this theory was not in agreement with many experimental results, the calculations had to be redone using the principles of quantum mechanics.1
Figure 3.1. Energy diagram of electrons: a) in isolated atoms, b) in a solid
Gas-Solid Interactions
41
3.3.2. Energy spectrum of a crystal lattice electron Energetically speaking, a crystal lattice has a periodic potential, and the issue we are facing is to know how an electron behaves in such a lattice. In theory, it would also be necessary to take into account the movement of all the other electrons. However, for the sake of simplicity, we will adopt a 1D lattice model, and we will suppose that the movement of the electron is not affected by the presence of other electrons. This simplified model, though, is a good means of describing the electronic properties that interest us in this book. This model will particularly allow us to demonstrate the concept of the electron’s effective mass. 3.3.2.1. Reminder about quantum mechanics principles Quantum mechanics are based on the three following postulates: 1) Everything there is to know about a system of n particles boils down to a function \ (xi, yi, zi, t), of the coordinates xi, yi, zi of each particle and of time t; this function is a mathematical tool that makes it possible to calculate dynamic quantities such as a system’s location, energy or moment. 2) The probability dp of finding a system in a volume element dW of the configuration space is II*dW where I* is the complex conjugate function of I (i becomes –i). The complex conjugate function is chosen so as to obtain a II* product that is always positive and therefore a positive probability value. According to the definition of probabilities, we must obtain:
³ II dW ³ I *
2
dW
1
This relationship expresses the fact that a particle must necessarily be inside the configuration space. 3) Each dynamic quantity l (energy, moment, etc.) corresponds to a linear operation L. The only observable results are the eigenvalues O of L, which verify:
L<
O<
[3.1]
L is an operator and \ an eigenfunction of L, is a state function of I 2 Thus, if L w
wt 2
and I
sin Zt , then:
42
Physical Chemistry of Solid-Gas Interfaces
w2 sin Zt wt 2
Z 2 sin Zt
Therefore, the eigenvalue O associated with the operator L is equal to –Z2. As far as we are concerned, the only dynamic quantity we will take some interest in is the energy E, and in that case, relationship [3.1] can be written as:
h2 8S 2
ª 1 § w 2\ w 2\ w 2\ ¨¨ 2 2 2 wyi wz i ¬ i © wxi
¦ «« m
·º ¸¸» V\ ¹»¼
E\
that is to say:
H<
E<
[3.2]
Equation [3.2] is the Schrödinger equation, where H is the operator (Hamiltonian operator) whose eigenvalues have the dimensions of energy. It is expressed in the following way:
H {
ª 1 § w 2 w 2 w 2 ·º h2 ¦ « ¨ ¸» V 8S 2 ¬ mi ¨© wxi wyi wz i ¸¹¼
V represents the periodic potential of the crystal. H, the Hamiltonian operator, must be hermitic, which means that:
³\
1
H\ 2 dW
³\
2
H\ 1dW
[3.3]
Remember, additionally, that: E
hQ
h
Z 2S
, because Ȟ
Ȧ . 2ʌ
3.3.2.1.1. Expression of energy E eigenvalues The eigenvalues of the energy E must be real. To express them using equation [3.2], we have to multiply the two members by \* and integrate over the entire space domain. We obtain:
³\
*
H\dW
E ³\ *\dW
Gas-Solid Interactions
43
(we must not forget that H is an operator and that E is a physical quantity). However, since according to the second postulate, we have:
³\ \dW *
1
then:
³\
E
*
H\dW
[3.4]
Using the hermitic property, we can demonstrate that E = E*, which means that E is necessarily a real value. 3.3.2.1.2. Orthogonality of eigenfunctions Suppose we have two eigenfunctions <1 and <2* with two different eigenvalues E1 and E*2 ; using [3.2], we obtain: H<1
E1<1
H\ 2*
E 2*\ 2*
and: E 2\ 2*
because we have already shown that E2*
* E2 . Multiplying the first equation by \ 2
and the second one by <1 and integrating over the entire space domain yields:
³\
* 2
H\ 1 dW
E1 ³\ 1\ 2* dW
[3.5]
E 2 ³\ 1\ 2* dW
[3.6]
and:
³\ H\ 1
* 2
dW
Since the operator is hermitic:
³\
* 2
H\ 1 dW
³\ H\ 1
* 2
dW
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Physical Chemistry of Solid-Gas Interfaces
subtracting [3.5] from [3.6] gives us:
E1 E 2 ³\ 1\ 2* dW
0
Thus, in general:
Ei E j
³<
i
< *j dW
There are two possibilities here: – First possibility: i = j: The condition i = j leads to Ei E j and, as a result, to the following condition, which is in agreement with the second postulate:
³ < < dW * i
i
1
Here, the condition:
( Ei E j ) ³
0
is fulfilled by the condition Ei E j . – Second possibility: i z j: in this case, the condition:
( E i E j ) ³
0
cannot be fulfilled unless:
³ < < dW i
* j
0
[3.7]
These are the fundamental results concerning the conditions which have to be fulfilled by \ functions that have to be determined. These are general conditions; each particular problem will create new ones, and this way, we will approach the ideal function that is a solution of the given system. Actually, the function we will arrive at will always be only an approximation of the ideal solution.
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45
3.3.2.2. Band diagrams of solids If we have a wave function \ that is a solution to our problem, then it should necessarily fulfill the following equation:
H<
E<
This equation should also express the fact that the electron is subjected to the influence of all the atoms in the chain (hypothesis of a linear lattice restricted to a chain of atoms; see Figure 3.2).
Figure 3.2. Location of atoms in a linear chain
In the hypothesis that there is only one atom g, the corresponding wave function Mg would meet the condition:
H gM g
E0M g
E0 is identified with the energy of an isolated atom as it is represented by one of the discrete levels in Figure 3.1a. Finally, we will suppose that the function Mg has already been determined. If there are N atoms, we can then consider that the function \ we are looking for is a linear combination of the N discrete solutions, that is to say:
<
g N
¦a
g
Mg
g 1
The knowledge of \ is directly related to that of all of the ag, and to that of some conditions that have to be met by Mg : 1) The ag coefficients must be a function of the wave vector kg (the wave vector describes a wave’s capability of moving in a given environment and direction). In the simple case of a sine-wave propagation, we would have for instance:
Mg
M g0 sin Zt M M g0 sin Zt k g x
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Physical Chemistry of Solid-Gas Interfaces
where kg is the wave vector in the x direction.
\ describes wave propagation, and we have already seen that the \\* product represented a presence probability. In our case, there is only one particle and we hope to achieve a near-zero value for the probability on the entire space domain, except a very small area around the particle. This result cannot be obtained mathematically unless the Mg function wave vectors are slightly different, which boils down to an interference problem. As an example, we can easily deal with the case of the function:
Mg
M 0 sin> k 0 g'k x @
The wave vector kg varies from: k0 =
' k to k0 + N'k when g ranges from 1 to
N. If N tends to infinity, the aspect of the solution <
g N
agMg ¦ g 1
at constant ag is
shown on Figure 3.3a. There are still many maxima, which is prejudicial to a unique location of the phenomenon. This result can be improved by making the minimum amplitude ag vary with k, that is to say ag = f(k). If we choose an exponential function for f(k), the shape of the solution curve is shown in Figure 3.3b and constitutes an adequate result. 2) The ag coefficients have to be chosen so as to minimize the energy value E corresponding to the function. Thus, according to [3.4], we have:
E
³\
*
H\dW
which means that E = f(ag). _
We use the notation E because it represents an intermediate energy value. 3) The ag coefficients have to be chosen so that the \ function meets the normalization condition:
N
³\\
*
dW
1
Once again, this leads to N = f ‘(ag). Mathematically, conditions 2) and 3) are expressed in a simple way by the N following equations, N being the number of atoms involved (Lagrange multiplier method2).
Gas-Solid Interactions
47
Figure 3.3. Shape of the curves depending on the chosen mathematical solution. st Curve a, ak c , curve b, ak f (k )
GE GN K Gag Gag
0
Let us express how E and N are related to the Mg functions:
E
³\
*
³\
*
³¦a
H\dW
g
* g
M g* H ¦ a g 'M g ' dW
[3.8]
g'
and:
N
\ dW
³¦a g
* g
M g* ¦ a g 'M g ' dW g'
Equation [3.9] can also be written:
N
¦a
* g
gg '
a g ' ³ M g* M g ' dW
Consider that:
S gg '
³M M * g
g'
dW
[3.9]
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Physical Chemistry of Solid-Gas Interfaces
it follows that:
¦a
N
* g
[3.10]
a g ' S gg '
gg '
However, the orthogonal property leads to:
S gg ' 1 with N
¦a
* g
a g ' if g = g’
gg '
and:
S gg '
0 with N
0 if g z g’
As regards equation [3.8], if we consider that the operator H only acts on variables depending on coordinates, then, by isolating the ag terms that do not depend on the coordinates: _
¦a
E
* g
gg '
a g ' ³ M g* HM g ' dW
If we assert that:
³M
* g
HM g ' dW
H gg '
then: _
E
¦a a * g
g'
H gg '
[3.11]
gg '
We are going to expand this expression: 1) Suppose only that atom g is taken into account in the chain; in that case g = g’ and:
H gg
³M
* g
HM g dW
This term identifies with energy value E1 ([3.4]) which represents one of the chain atoms’ contributions, that is to say the periodic potential. This value is different from E0 because this solution is relative to an isolated atom whose potential is no longer periodic. We can verify that:
Gas-Solid Interactions
³M
E0
g
H g M g* dW z W1
³M
g
49
HM g* dW
that is, that the difference between Hg and H lies in the nature of the potential. 2) If we only take into consideration atom g’s right and left hand neighbors, with: g’ = g+1 or g’ = g-1, (this symmetric double positioning will be denoted g' g r 1 ) it follows that:
H gg '
H gg r1
³M
* g
HM g r1dW
This expression has the dimension of energy and we will denote its value by E2. It expresses the energy contribution of the interaction between the two closest neighbors of g. We can therefore go on denoting these contributions by E3, E4 … Ei. We will consider that from E3 onwards Ei becomes negligible. Given [3.10] and [3.11], the relation: _
wN wE K wa g wa g
0
becomes:
¦ a H * g'
gg '
KS gg ' 0
[3.12]
If we only take into consideration the close neighbors of g, this relation can be written:
a g ( H gg KS gg ) a g r1 ( H gg r1 KS gg r1 ) If we introduce the fact that H gg
0
E 1, H g (g r1)
E 2 , Sgg = 1 and Sgg r1 = 0,
then we obtain:
a *g E1 K a *g 1 E2 a *g 1 E2 0 Indeed, K has the dimension of energy, which can be quickly verified.
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Physical Chemistry of Solid-Gas Interfaces
Using [3.12] and multiplying the two terms by ag yields the relation:
E
KN
Since N = 1, K has the dimension of an energy E, hence the new relation:
a *g E1 E E 2 a *g 1 a *g 1
0
If we choose the energy of the electron in the isolated atom E0 as the energy reference, then:
a *g D E0 E E a *g 1 a *g 1
0
[3.13]
where:
D
E1 E0
E
E2
and:
However, we have already seen that ag is related to the wave vector k using a relation of the form:
ag
a0 exp igk
a *g
a 0* exp igk
and:
Substituting this expression in [3.13] yields: a 0 exp igk >D E 0 E @ E >a 0 exp igk ik a 0 exp igk ik @ 0
which becomes, after eliminating exp igk :
D E0 E E >exp(ik ) exp( ik )@ 0 then: E
E0 D 2E cos k
[3.14]
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51
and:
\
a 0 ¦ e ikg M g g
[3.15]
These results are the solutions to our problem. However, new conditions must now be set. 1) \ must have a finite value when g tends to infinity (concept of probability). For that to be true, the value of k must be real. 2) The term cos. k implies the requirement:
S d k d S 3) \ must be a periodic function and of the same periodicity l as the lattice:
\ x nl \ x The previous condition can also be expressed: a0 ¦ expik g n M g x nl a0 ¦ exp>ik g @M g x
Since:
M g ( x nl ) M g ( x) it follows that:
exp>ik g n @ exp>ik g @ and:
k
2 KS n
If there are N atoms in the chain, we can see that k can assume N values. As for the energy, note that its maximum value EM is reached for k = 0:
EM
E0 D 2 E
and that its minimum value Em is reached for k = rS:
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Physical Chemistry of Solid-Gas Interfaces
Em
E0 D 2E
We therefore have an energy band whose width is 4E and whose midpoint is located at:
E
E0 D
Thus, an electron with an initial energy E0 in the isolated atom will be able to move inside the crystal if the energy value ranges from:
E0 D 2E to E0 D 2E (see Figure 3.4)
Figure 3.4. Evolution of the energy state of a solid’s electron in a state of isolation
3.3.2.3. Effective mass of an electron We have demonstrated that the wave function \ is a linear combination of N periodic functions, and we have seen that we would be well-advised to use a distribution of the wave vector’s values. If N tends to infinity and \ is expressed:
\
³a M g
0
exp> i 2SQt kx @ dk x
We now have a wave packet whose maximum is characterized by the multiple waves being in phase, which means that the quantity y 2SQt kx does not depend on the variations of k3, which means that:
dy dk
0
Gas-Solid Interactions
53
Thus:
2S
dQ tx dk
0
We therefore obtain:
x t
2S
dQ dk
V
The term x / t has the dimension of velocity; it represents the velocity V of the wave packet and therefore, the speed of the particle. On the other hand, we know that: E = hQ. It follows that:
V
2S dE h dk
In the presence of an external force F taking its origin from, for instance, an electric field, we will write:
dE
FVdt
Given the expression for V, we arrive at:
dE
F
2S dE dt h dk
Thus:
F
h dk 2S dt
If we wish to obtain results that are similar to those of classical mechanics, we only have to turn to the fundamental law of mechanics, that is:
F
mJ
h dk 2S dE
This relation constitutes the link between classical and quantum mechanics; we will see here what conditions this requires.
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Physical Chemistry of Solid-Gas Interfaces
Thus:
2S d 2 E dk h dk 2 dt
J
dv dt
m
h2 § d 2E · ¨ ¸ 2S 2 ¨© dk 2 ¸¹
so: 1
Using the result established in the previous section: E
E0 D 2E cos k
we can write: d 2E dk 2
2 E cos k
and:
m
h2 8S 2 E cos k
Note that the fundamental law of classical mechanics may apply, provided we assign an effective mass to the particle whose value and sign depend on cos k. This implies that m can assume negative values, depending on the value of k. Only quantum mechanics could have introduced such a concept. We will see in the next sections that we can dispose of the negative effective masses by introducing new particles or electron holes. In conclusion, we will retain the following results: 1) With an initial energy E0 in an isolated atom, an electron inside a crystal carries the energy:
E
E0 D 2E cos k
which corresponds to an allowed energy band whose width is of 4E. Between two allowed energy bands is a forbidden band whose width is represented by a gap in energy.
Gas-Solid Interactions
55
2) An electron located in the lower half of an allowed energy band has a positive effective mass. In the presence of a positive external force, it will be subjected to a positive acceleration value, which is in accordance with the findings of classical mechanics. 3) An electron located in the upper half of an allowed energy band has a negative effective mass. In the presence of a positive external force, it will be subjected to a negative acceleration value. 3.4. Electrical conductivity in solids3
Suppose we have an allowed band of n electrons, the current I flowing during dt is the sum of the n electron contributions. If [ denotes the electric field, then:
qe ¦Ve
I
qe ¦ J e dt
n
n
because:
F
qe[
meJ e
I
qe ¦
q e[ dt me
and:
n
qe2[dt ¦ n
1 me
me represents the effective mass of the electron. 3.4.1. Full bands
In the case of a full band, we would have: N ªN2 1 1 º q [dt «¦ ¦ » «¬ 1 me N 2 me »¼ 2 e
I
However, for reasons of symmetry, and because m e N
1 ¦1 m e 2
N
¦ N
2
1 me
m e :
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Physical Chemistry of Solid-Gas Interfaces
which means that I = 0. Thus, a band that is fully occupied by electrons does not contribute to the electrical conductivity of a material. 3.4.2. Partially occupied bands
In the case of a partially occupied band, two cases can occur: a) n N
2
Every electron is assigned a positive mass value: I
n
qe2[dt ¦ 1
1 me
Classical mechanics easily apply here. b) n ! N
2
It is then important to count the electrons with positive mass value and those with negative mass value. To deal with this difficulty, we will introduce the concept of electron holes. To do so, let us go back to the general expression for the current I, which can be written, if we take into account the available locations in the band:
I
º ª » «N2 n N N 1 1 1 1 qe2[dt «¦ ¦ ¦ ¦ » » « 1 me N me n me n me » « 2
»¼ «¬ 0
It is possible to verify that the sum of the first three terms gives us a full band, and therefore corresponds to a zero electrical contribution. This leads to: I
N
qe2[dt ¦ n
1 me
Gas-Solid Interactions
57
This amounts to accounting for only those electrons missing from the band, which necessarily have a negative mass. The expression here of the current I is assigned a negative sign. Suppose there exists a particle h, carrying a positive charge qh and with an
effective mass m h ; then:
I
q 2 [dt ¦
1 me
q 2 [dt ¦
1 m h
This last expression is perfectly compatible with the laws of classical mechanics. Thus, in the case of a band with an occupancy value higher than N / 2 , and to avoid having to work with negative effective masses, we will choose to use the concept of electron holes. 3.5. Influence of temperature on the electric behavior of solids 3.5.1. Band diagram and Fermi level of conductors
When retaining the hypothesis of a partially occupied band of n electrons occupying N energy levels, we encounter the problem of accessing the distribution of electrons in the different levels according to temperature. The probability f(E) of finding an electron with an energy level E is given by the Fermi-Dirac distribution function, which is written: f E
1 E EF 1 exp kT
T represents the absolute temperature, while k is the Boltzmann constant. The function brings into play the parameter EF, which has the dimension of energy: this is the Fermi energy. The variations of the occupancy probability f(E) of an energy level E depending on the distance to the Fermi level E – EF are plotted in Figure 3.6 at different temperature values.
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Physical Chemistry of Solid-Gas Interfaces
At absolute zero temperature f (E) = 1 where E < EF and f (E) = 0 where E > EF. This means that at absolute zero temperature, the Fermi energy EF represents the energy of the last occupied level. When the temperature rises, the discontinuity disappears and the function is symmetric around the point where E = EF and whose occupancy probability f (EF) is 0.5. In most occurances, we can approximate that f (E) | 1 where E – EF < -3kT, and that f (E)|0 where E – EF > 3kT. We can therefore draw the conclusion that the levels notably lower than the Fermi level are fully occupied; while the notably higher levels are empty (see Figure 3.5).
Figure 3.5. Variation of the occupancy probability of an energy level E 4 depending on its distance to the Fermi level (according to Vapaille )
If, at absolute zero temperature, the Fermi level EF is located in an allowed band, then we are in the presence of a metallic element and the conduction band is partially occupied. The energy value EF, which represents the energy of the last occupied level, is the energy necessary to extract an electron from a solid. In the case of a semiconductor or an insulator, the last occupied band is full at absolute zero temperature, and the Fermi level is located at the top of this band, which is called the valence band.
Gas-Solid Interactions
59
The next band, known as the conduction band, is empty. Figure 3.6 gives a diagrammatic representation of the bands filling up at absolute zero temperature.
Figure 3.6. Occupancy of bands at absolute zero temperature
If the valence and conduction bands are separated by an energy interval Eg = Ec – Ev that is short enough (on the order of an electron-volt), and if kT is high enough compared to Ec – Ev at non-zero temperature, then there is a possibility of electronic transitions between the conduction and the valence band. Then, electrons appear on the conduction band and electron holes on the valence band. Under such conditions, we find ourselves with two incomplete bands, which poses the problem of electronic distribution. Here, the position of a given solid’s single Fermi level is not obvious. We will see how to tackle this problem while taking into account electrons as well as electron holes. The probability of finding an electron in a conduction band denoted by fn(E) is given by: f n E
1 E EF 1 exp kT
[3.16]
The probability of finding a hole in a valence band denoted by fp(E) is complementary to that of an electron in the same band: f p E 1 f n E
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Physical Chemistry of Solid-Gas Interfaces
which yields:
f p E
1 E E 1 exp F kT
[3.17]
In a non-degenerate semiconductor – where there are few electrons or holes compared to the available locations in the conduction or valence bands – the Fermi level is located on the forbidden band and there is enough spacing between it and the conduction and valence bands. In such a case, the energy levels E of the bands are such that: E E F !! kT , and the Fermi-Dirac distribution laws, which apply to electrons and holes, are reduced to Boltzmann statistics. The possibilities of finding electrons in the conduction band and holes in the valence band respectively become: f n E exp
EF E kT
[3.18]
f p E exp
E EF kT
[3.19]
and:
The concentrations in carriers are obtained by multiplying the band density of states by the occupancy probability of the states. The free electron concentration n in the conduction band is given by:
n
³
f
Ec
nc E f n E dE
[3.20]
nc(E) represents the density of states in the conduction band. Similarly, the free hole concentration p in the valence band is written:
p
³
Ev
f
nv E f p E dE
nv(E) represents the density of states in the valence band.
[3.21]
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61
3.5.2. Case of intrinsic semiconductors
An intrinsic semiconductor does not possess impurities. Each valence band electron that is excited enough to transfer to the conduction band leaves behind a hole carrying a positive charge; as a result, the concentrations in electron n and in hole p are equal, which is expressed as n = p = ni; ni is the intrinsic carrier concentration. Integrating [3.20] and [3.21] yields the following relations for electron and hole concentrations: – Either: n where: N c
N c exp
2
h3
EF Ec for the electrons, kT
2Sm c kT 3 / 2 ,
while mc is the effective mass of the integral electronic density, and h is the Planck constant. – Or: p N v exp where: N v
2
h3
EV E F for the electron holes, kT
2Sm v kT 3 / 2 ,
and mv is the effective mass of the integral hole density. If we take into account the fact that n = p stemming from the intrinsic property, then the intrinsic Fermi level EF = Ei is given by: Ei
1 Ec Ev 1 kT log N c 2 2 Nv
If the effective mass of the integral electronic density mc is equal to that of the holes mv, then Nc = Nv and the intrinsic Fermi level Ei is located at the middle of the forbidden band (see Figure 3.8a): Ei
Ec Ev 2
We can also conclude that:
Ei Ec
E v Ei
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Physical Chemistry of Solid-Gas Interfaces
3.5.3. Case of extrinsic semiconductors
This is the case of a semiconductor holding impurities whose energy levels are located on the forbidden band. If these impurities have excess electrons compared to the lattice element, then electronic donor levels ED are assigned to them. If these impurities have an electronic deficit compared to the lattice element, then electronic acceptor levels EA are assigned to them. In the hypothesis of donor type impurities that can be ionized according to the reaction:
A A e Suppose NA is the global concentration in A, N 0A is the concentration in levels at an electrically neutral state and N A is the concentration at an electrically charged state, such that:
NA
N A0 N A
If we do not take into consideration the possibility of extrinsic level degeneration, the concentrations N 0A and N A are expressed by the following relations:
N A
f n E A N A
NA E EF 1 exp A kT
[3.22]
N A0
f p E A N A
NA E EA 1 exp F kT
[3.23]
and:
If EF < EA – 3kT, it is reasonable to suppose that all EA levels are in a neutral state, and in that case: N A | N A0 !! N A . Conversely, if EA- EF > 3kT, all EA levels are in an excited state, and: N A | N A !! N A0 . A similar reasoning applied to ED donor levels of global concentration ND leads, for neutral state and charged state level concentrations N 0D and N D , to the following expressions:
Gas-Solid Interactions
63
N D0
f n E D N D
ND E EF 1 exp D kT
[3.24]
N D
f p E D N D
ND E ED 1 exp F kT
[3.25]
and:
In the hypothesis of a non-degenerate semiconductor, the concentrations in electron n and in hole p are once again given by Boltzmann statistics, and are written:
n
N c exp
E F Ec kT
[3.26]
p
N v exp
Ev E F kT
[3.27]
The Fermi energy value can be expressed using the electroneutrality equation which, for a semiconductor with only one type of donor level and one type of monovalent acceptor, is written:
n N A
p N D
Using [3.24], [3.25] and [3.26], it is possible to solve the previous equation and express EF. Qualitatively speaking, it is possible to say that introducing donor type impurities, whose energy levels are generally located near or beneath the conduction bane, contributes to raising the electronic concentration in that same band. This results in the band diagram in the Fermi level rising above its initial position, that of the intrinsic regime (see Figure 3.7a). This behavior is that of an extrinsic semiconductor of type n, such that n > p (see Figure 3.7b). Conversely, acceptor-type impurities induce a rise in positive hole concentration in the valence band. The Fermi level goes down and approaches the top of the valence band; this is for a semiconductor of type p, such that p > n (see Figure 3.7c).
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Physical Chemistry of Solid-Gas Interfaces
Figure 3.7. Band diagram of semiconductors
3.5.4. Case of materials with point defects
By way of example, we will address the question of a metal oxide denoted by M2+O2- (a divalent metal). From the electronic point of view, we can consider that the metal’s oxidation was caused by electron transfers from the metal to the molecule of oxygen. In fact, the initial metal has free electrons in its conduction band, while non-saturated oxygen had electron holes in its valence band. As a result, the oxide’s conduction band is empty and its valence band is full at 0°K (see Figure 3.8). This ideal material seems to act like an intrinsic semiconductor.
Figure 3.8. Energy diagram of an electron transfer during the oxidation of a metal
In actual fact, these metal oxides can present point defects. In the hypothesis that these are majority defects, there are four possibilities (Wagner classification).
Gas-Solid Interactions
65
3.5.4.1. Metal oxides with anion defects, denoted by MO1 x x represents the stoichiometry deviance. To fulfill the electroneutrality conditions, an oxygen vacancy will necessarily accompany the presence of two electrons. At low temperatures, these electrons are trapped in the vacancy. The discrete energy states of the vacancies are different from those of the missing oxygen. These states position themselves in the energy gap (see Figure 3.9), appearing as electronic donor type impurities.
Figure 3.9. Energy diagram representing the double ionization of an anion vacancy
At higher temperature, there is a state of first ionization: VO VOq e
then a state of second ionization: VOq VOqq e
The freed electrons will thus contribute to the electrical conductivity of the oxide. If K1 and K2 represent the constants relative to the two previous equilibriums, then: K1
[V q ][e ] [VO ]
and: K2
[V qq ][e ] [V q ]
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Physical Chemistry of Solid-Gas Interfaces
thus, for a singly ionized vacancy: [e ]
K1 [VO ] [V q ]
and for a doubly ionized vacancy:
[e ] 2
K 1 K 2 [VO ] [V qq ]
In both cases, the concentration of free electrons, and therefore the electrical conductivity, is related to the defect concentration, which is the concentration in ionized oxygen vacancies. This material’s behavior is that of a n-type semiconductor. 3.5.4.2. Metal oxides with cation vacancies, denoted by M 1 x O In this case, the cation vacancy goes along with the presence of two electron holes. Once again, the energy states associated with this vacancy position themselves on the energy gap and appear as electron acceptor states (see Figure 3.10). A rise in temperature facilitates an electron transfer from the valence band to the vacancy’s energy levels. This induces the presence of holes in the valence band, and therefore conductivity by holes in the material, whose behavior is then that of a material of type p. The equilibriums are expressed by: VM o VM' h
and: VM' o VM'' h
Figure 3.10. Energy diagram representing the double ionization of a cation vacancy
Gas-Solid Interactions
67
3.5.4.3. Metal oxides with interstitial cations, denoted by M 1 xO The interstitial metal elements appear to act here as electron donors (see Figure 3.11) that, under the influence of temperature, free electrons in the conduction band. This transfer ensures a conductivity of type n for the material, just as for anion vacancies. The equilibriums are expressed by:
M I o M Iq e ' and:
M Iq o M Iqq e
Figure 3.11. Energy diagram representing the double ionization of an interstitial cation
This material is quite similar to an n-type semiconductor material. 3.5.4.4. Metal oxides with interstitial anions, denoted by MO1+x In this case, the interstitial oxygen ions form an electronic acceptor center at the expense of the valence band (see Figure 3.12). This material is a p-type semiconductor. The equilibriums are expressed by:
OI o OI' h and:
OI' h o OI'' h
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Physical Chemistry of Solid-Gas Interfaces
This material’s behavior is that of a p-type semiconductor material.
Figure 3.12. Energy diagram representing the double ionization of an interstitial anion
Thus, the semiconductor type of a material allows us to choose the right formula for the oxide, that is to say, either M1+xO or MO1-x, if the material is of type n, M1-xO or M1O1+x, if the material is of type p. 3.6. Bibliography 1. G. BRUHAT, Cours de physique générale : électricité, Masson, Paris, 1959. H.Y. BERNARD, Initiation à la mécanique quantique, Hachette, Paris, 1960. S.N. LEVINE, Electronique quantique, Masson, Paris, 1968. P. KIREEV, La physique des semi-conducteurs, MIR, Moscow, 1975. 2. J. GILBERT, Chimie physique I : atomistique et liaisons chimiques, Masson, Paris, 1963. 3. A. VAPAILLE, Physique des dispositifs à semi-conducteurs, vol. 1, Masson, Paris, 1970.
Chapter 4
Interfacial Thermodynamic Equilibrium Studies
4.1. Introduction By definition, a device derives from the association of multiple elements in order to achieve a given purpose. Such an association necessarily involves the existence of bonds, of interfaces between the different elements that constitute the device, and it is through these interfaces that the function we are aiming at will be accomplished. Interface processes therefore seem to be fundamental in the workings of a device. To be convinced of such a thing, we have only to mention, by way of example, the case of optical or electronic devices. In an optical device, the expected function is to control the propagation of light rays in transparent media. To do so, it is necessary to combine at least two transparent media characterized by distinct refractive indexes and by contact surfaces that are most often hemispherical. Thus, the light rays’ direction of propagation is fully controlled by the change in light propagation velocity at the interfaces. In terms of electronics, it is important when dealing with electrical charges to control their flow, their location and their concentration. All of this is made possible by the creation of junctions made by associating different semiconductor materials or semiconductor and metallic materials.
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Physical Chemistry of Solid-Gas Interfaces
Such junctions, whose effects can be limited to a depth of a few dozen angstroms, will make it possible to accumulate charges and to regulate electrical flows. The art of microelectronics then consists of minimizing the volume of materials used, in favor of the interface regions. This makes it possible for junctions to pile up within a minimum width. In the area of gas detection – regardless of the type of device used – we will once again be addressing interfacial problems, most often resulting from physicochemical processes which we will study from a thermodynamic or kinetic aspect. 4.2. Interfacial phenomena1 Generally, the systems used for gas detection are heterogenous, that is to say of solid-liquid or gas-liquid type. However, since this book in only interested in devices using solid materials, we will not deal with the gas-liquid aspects particular to some electrochemical devices. We can also consider homogenous systems formed by at least two materials that are identical from a chemical and crystallographic point of view, and that differ from each other only in terms of the composition of the foreign elements, the impurities, and the dopants they contain; such is the case for p-n junctions. Such interfaces are often made use of in electric or optical transducers, which are then used in some gas sensors. From the point of view of their physico-chemical properties, all of these interfaces are characterized by a sudden discontinuity in the chemical or electrochemical potential of at least one of the neutral or charged elements present. The resulting chemical and/or electrical gradients are at the origin of an exchange of matter between the two adjoining phases. These transfers will allow an interface thermodynamic equilibrium to occur. From an electrochemical viewpoint, the equilibrium condition is always expressed by the following relation:
¦Q
i
P~i
0
i
P~i represents the electrochemical potential of a charged species, i, subjected to an electric field.
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71
This relation is associated with Poisson’s equation: d 2V ( x)
dx 2
U
HH 0
This relation makes it theoretically possible to solve the problem and to express all the chemical and electrical quantities that characterize the interface. V represents the potential corresponding to the presence of a charge density ȡ. However, solving this system, and especially Poisson’s equation, is not always so easy, so some simplifying hypotheses have to be formulated, depending on the nature of the system we are studying and the physical or chemical quantities we wish to express. Moreover, every element on a crystal lattice is located at a low-level energy site, and its movement through the lattice or through the interfaces confining it necessarily implies that it will overcome an energy barrier. The condition for the transfer is thus related to the nature of the phases present, to the concentration and the nature of the electrical and chemical species, as well as the temperature. We can therefore establish a classification of interfaces based on the nature of the moving species and/or charges, as well as the nature of the phases which are present. In this book, we will first explore solid-gas equilibriums and distinguish between the equilibriums that only involve electron transfers and/or electron holes and those that involve charge and mass transfers. The solid-solid aspect involving electron and/or electron hole transfers will be dealt with afterwards. In the case of metallic or semiconductor solids, we can imagine that electron transfers and/or electron holes will most often be involved. Conversely, for purely ionic solids, it will most often involve mass and charge transfers. 4.3. Solid-gas equilibriums involving electron transfers or electron holes As we have already mentioned in the previous chapters, it is difficult to formulate solid-gas equilibriums without referring to the concept of surfaces and therefore that of surface states.
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Physical Chemistry of Solid-Gas Interfaces
4.3.1. Concept of surface states2 Extrinsic energy states, which we presented when exploring the electrical properties of solids, are states relative to the bulk of the semiconductor-type material. They are the result of stoichiometry deviances or impurities introduced by doping. In the case of a finite-dimension semiconductor, the existence of the surface brings in additional energy or surface states. Among surface states, there are some that originate simply from the sudden discontinuity in the crystal lattice; these are intrinsic surface states. They are sorted, depending on their source, into two categories: Tamm states, which are caused by lattice deformation, and Schockley states, caused by the unsaturated bonds on the surface. There also appears on the real surfaces extrinsic surface states due to the presence of foreign species on the surface of the solid, namely adsorbed atoms or molecules originating from a gaseous phase. The energy states of the surface, denoted by ES, are located with respect to the Fermi energy value EF, which corresponds to the reference state of the solid. In a similar way to the bulk states, each surface state can be empty or occupied by an electron. The ratio of surface states ES occupied by electrons, denoted by ft (ES), is given by the Fermi-Dirac distribution function: f t E S
1 E EF 1 exp S kT
We are led to make a distinction between electron-acceptor-type and electrondonor-type surface states: 1) Acceptor-type surface states ESA are such that ESA < EF. On the energy diagram of a semiconductor, they are located below the Fermi level (see Figure 4.1a). As soon as they form, they trap electrons that are coming from the solid. The surface then carries a negative charge. Therefore, the electron concentration in the semiconductor decreases near the surface, which causes the relative position of the Fermi level to the conduction band to vary locally. An electron impoverishment in the solid thus contributes to a localized lowering of the Fermi level and increasing the electronic work function. To keep the Fermi level constant in the entire solid, we prefer representing the surface disturbance by a band curvature pointing towards the opposite direction. In this case, the energy band curvature is pointing upwards (see Figure 4.1b). Both configurations express a rise in the electronic work functions.
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73
Figure 4.1. Semiconductor with surface states of acceptor-type (a, b) or donor-type (c, d)
2) The donor-type surface effects ESD are characterized by an energy value ESD higher than the Fermi level EF. They are located on the band diagram above the Fermi level (see Figure 4.1c). They can donate electrons to the semiconductor; under these conditions, the surface acquires a positive charge, and the electron concentration near the surface increases, which is shown by the localized downward bending of the energy bands (see Figure 4.1d). The electronic work functions are therefore lowered. In both situations, the localized deformation of the solid’s energy bands (near the surface) leads to the formation of a region in which the electron concentration varies: this is the SCR. 4.3.2. Space-charge region (SCR) We have just seen that the electron transfers between the solid and the surface states simultaneously created both a surface charge, caused by the ionization of impurities, as well as an SCR in the solid. For a semiconductor, this region has a depth l, the order of which can reach that of a few hundred interatomic distances. The parameters used to describe the SCR should be specified. They are represented using a diagram in Figure 4.2.
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Physical Chemistry of Solid-Gas Interfaces
Usually, the surface is the plane of abscissa x = 0 and the x-axis is pointing towards the interior of the semiconductor. The electronic electrostatic potentials in the semiconductor are given by the relation:
I
E F Ei q
[4.1]
M MV EF: Fermi energy; Ei: intrinsic Fermi energy; q: absolute value of the electron’s charge. The electrostatic potential I varies depending on the distance x to the surface of the semiconductor. When x t l:
M MV where MV is the bulk potential. When x = 0:
M M S where M S is the surface potential. In the SCR, the potential I varies, differing from the bulk potential IV, which leads us to define the potential barrier V as:
V
I IV
[4.2]
The value of V on the surface, that is to say when x = 0, is that of the surface barrier VS:
V
IS IV
[4.3]
If we use relations [3.26] and [3.27] in Chapter 3, and write, on the one hand:
E F EC
EF Ei Ei EC
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75
and on the other hand:
EV EF
EV Ei Ei E F
Figure 4.2. Energy representation in the SCR of a semiconductor
The concentrations in electrons n(x) and in holes p(x) at a distance x from the surface are expressed, for a non-degenerate semiconductor:
n( x )
ni exp
qI ( x ) kT
p ( x)
pi exp
qI ( x ) kT
nV exp
qV ( x) kT
pV exp
[4.4]
qV ( x) kT
[4.5]
where:
ni
pi
N C exp
Ei EC
kT
NV exp
EV Ei
kT
ni and pi represent the intrinsic carrier densities. qIV
nV
ni exp
pV
ni exp
kT represents the bulk concentration of electrons.
qIV
kT represents the bulk concentration of electron holes.
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Physical Chemistry of Solid-Gas Interfaces
The potential V(x), which is characteristic of the space charge, must obey Poisson’s equation:
d 2V ( x) dx 2
U ( x)
HH 0
[4.6]
H0: permittivity of vacuum; H: dielectric constant; U(x): local charge density at a distance x from the surface. If we suppose that there is, in the semiconductor, an acceptor-type impurity A as well as a donor-type impurity D, that their concentrations at charged state are respectively N A and N D , and that the charge density U(x) is written:
U ( x) q>N D N A p ( x) n( x)@
[4.7]
The electroneutral condition in the bulk:
N D N A
nV pV
[4.8]
then makes it possible to rewrite [4.7] in the following way:
U ( x) q>nv pv n( x) p( x)@
[4.9]
at equilibrium; the general expression for Poisson’s equation becomes:
d 2V ( x) dx 2
q ª § qV ( x) ·º qV ( x) · § nV ¨1 exp ¸ pV ¨1 exp ¸ « kT ¹»¼ kT ¹ HH 0 ¬ © ©
[4.10]
Solving this equation yields the expression of the potential barrier V(x) as a function of the characteristic quantities of the system. We are going to show how the surface potential barrier VS (and consequently the electronic work function), which is obtained using the expression for V(x) when x = 0, is related to the surface charge and the concentration in adsorbed species.
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77
4.3.3. Electronic work function The electronic work function ) in a solid is defined as the difference between ~ of the electrons in the solid and the electrostatic the electrochemical potential μ potential –qVe of the electrons in the vacuum near the surface of the solid:
ĭ
~ qV μ e
[4.11]
~ μ
§ wG · ¨ ¸ © wn ¹ P ,T
[4.12]
where
G being the free enthalpy of the system. Statistical thermodynamics make it possible to demonstrate that the Fermi energy EF is equal to the partial derivative of the free enthalpy G:
EF
§ wG · ¨ ¸ © wn ¹ P ,T
[4.13]
Using [4.12] and [4.13], we arrive at the conclusion that the Fermi energy is equal to the electronic electrochemical potential. Under such conditions, the work function is the amount of energy required by an electron trapped in the solid, and whose energy is equal to the Fermi energy, in order to reach the vacuum with a zero velocity. The Fermi level is the highest energy level occupied by electrons at 0°K temperature; the work function, as we have defined it above, therefore represents the lowest amount of energy that has to be supplied so that one of the solid’s electrons is extracted without gaining kinetic energy. 4.3.3.1. Case of a semiconductor in the absence of surface states In this ideal case, where there are not any surface or space charges, the energy bands are horizontal. The work function )0 is the sum of two contributions (see Figure 4.3a):
)0
F HV
[4.14]
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Physical Chemistry of Solid-Gas Interfaces
where F referred to as the electron affinity of the semiconductor, represents the difference between the energy of the electrons in a vacuum and at the bottom of the conduction band.
HV represents the difference between the energy corresponding to the bottom of the conduction band and the Fermi energy, that is HV = EC – EF. HV is sometimes referred to as the work function in the bulk. The quantity HV is mainly dependent on the doping process and the temperature; we will see that this is one of the characteristics of the bulk of the solid.
Figure 4.3. Formation of potential barrier in the presence of surface states
4.3.3.2. Case of a semiconductor in the presence of surface states The presence of charged surface states leads to the formation of a barrier potential VS at the surface; in the hypothesis that the surface states are due to adsorbed species. A dipole layer can form, which leads to an additional energy jump –qVD. The electron affinity of the semiconductor becomes F – qVD. The work function ) is then expressed (see Figure 4.3b):
)
F H V q(VS VD )
[4.15]
The quantities F and HV, which are characteristic of the ideal semiconductor with no surface states, are not affected by the adsorption of foreign species at the surface. Consequently, the change in the electron work function ') during adsorption is written:
')
q ( 'V S 'V D )
[4.16]
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79
where 'VS and 'VD denote the corresponding variations of the surface barrier and the dipole component. 4.3.3.3. Physicists’ and electrochemists’ denotation systems Physicists and electrochemists do not necessarily use the same symbols and/or the same designations, particularly to describe the energy quantities involved in the use of semiconductors. Figure 4.4 and Table 4.1 present the two systems generally used.
Figure 4.4. Energy quantities involved in semiconductors
Table 4.1. Matching of denotations
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Physical Chemistry of Solid-Gas Interfaces
4.3.4. Influence of adsorption on the electron work functions We have just seen that the adsorption of foreign species (atoms or gas molecules) on the surface of the semiconductor shows in the band diagram, where surface states appear, and that the presence of these states causes a change in the electronic work function ) because of a variation of the surface VS and the appearance of a dipole component VD. We intend to relate these two quantities to the concentration in chemisorbed species N, which is expressed in the number of atoms per surface unit. 4.3.4.1. Influence of adsorption on the surface barrier VS Boundary layer theory The electronic transfers between solids and surface states are at the root of the first electronic theories about chemisorption, which were simultaneously developed by Aigrain and Dugas2, Weisz, Hauffe and Engell3. Suppose there is, on the surface, an electronegative species X (or electronacceptor) like oxygen and whose electron affinity A is greater than the electronic work function ) of a semiconductor: it will tend to trap an electron coming from the solid, according to the following equation:
X e o X The difference A-) represents the adsorption energy. During this chemisorption process, the surface acquires a negative charge and the bands bend upwards. The potential barrier VS decreases, causing a rise in the electronic work function ) until the Fermi level and the energy level of the gas become the same, which would mean that the equilibrium had been reached and the chemisorption process had stopped. Figures 4.5a and 4.5b represent the bands of a semiconductor n in the presence of electron acceptor-type molecules at the beginning of adsorption and at adsorption equilibrium. The chemisorption of an electropositive molecule results in an electron transfer towards the solid, provided that the work function ) is greater than the ionization energy I of the adsorbed gas. The adsorption energy is )-I. The surface acquires a positive charge during the process of chemisorption which leads to a rise in the potential barrier VS, and therefore a decrease of the work function ).
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81
Figure 4.6 shows the energy diagrams of p-type semiconductor in the presence of donor-type molecules.
Figure 4.5. Semiconductor n in the presence of acceptor-type molecules: (a) at beginning of adsorption, (b) at adsorption equilibrium
Figure 4.6. Semiconductor p in the presence of donor-type molecules
Within the framework of the boundary layer theory, Aigrain and Dugas4 solved the Poisson equation for an n-type semiconductor with fully-ionized donor-type impurities, the boundary conditions being:
U ( x) qN D U ( x) 0
when 0 x 1 when x ! l
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Physical Chemistry of Solid-Gas Interfaces
Moreover, we will suppose that all impurities are fully ionized at working temperature, which, for the electron concentration, means that:
n
N D
ND
over the entire domain, that is to say: 0 < x < l. In such a case, the electroneutral condition is written:
N
xN D
xN D
N represents the concentration in surface states and is expressed in number of atoms per surface unit. Solving equation [4.6] results in a parabolic variation for VS:
VS
aN 2
This is the Schottky barrier. There is a second possibility where the ionization of the impurity levels is no longer considered to be full when x < l and which yields a linear relation between VS and N:
VS
aN
This is the Mott barrier. Some authors consider that, during the chemisorption process, the Mott barrier intervenes at the beginning of adsorption, when the levels are not all ionized, while the Schottky barrier is involved at the end of the process, when the ionization is almost complete. Theoretical study of the surface barrier VS A full mathematical processing performed by Wolkenstein5 allows us to estimate the variations of the surface barrier VS depending on the surface charge, then depending on the surface concentration N of the adsorbed species. 4.3.4.1.1. Variations of the potential barrier VS as a function of the surface charge V Let us briefly recall the calculations leading to the expression for VS as a function of ı, which represents the surface charge and is expressed in number of charges per surface unit.
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83
The Poisson equation can be written:
U
d 2V dx 2
HH 0
The potential V(x) at a depth x is expressed, according to [4.2], by:
V ( x ) I ( x ) IV when x = f:
M ( x) MV and:
V(x) 0 when x = 0:
M ( 0) M S and:
V(0)
VS
The volume charge density U is a function of x; it can also be expressed as a function of the potential I, which is related to x. Integrating Poisson’s equation with I gives us: IV
³I
H 0H ³
U (M )dI
f
X
2 f d V dV d 2V dI dx H H dx 0 ³ X dx 2 dx dx 2 dx
If we consider that dV / dx x
f
0 and express
IV
³I
U (M )dI as a function of V
by a variable transformation V = I - IV, integrating the previous expression yields the relation:
§ dV · ¨ ¸ © dx ¹
2
2
V
HH³ 0
0
U (V )dV
[4.17]
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Physical Chemistry of Solid-Gas Interfaces
when x = 0, V = VS, and equation [4.17] leads to: 2
§ dV · ¨ ¸ © dx ¹ x
0
2
VS
HH³ 0
0
U (V )dV
[4.18] is a first relation between dV / DX x
[4.18]
0
and VS.
We will demonstrate that we can obtain a second relation between dV / dx x and V .
0
The electroneutrality condition at the interface is expressed by the fact that the surface charge V and the volume charge ȡ are equal, hence:
V
f
³ U ( x)dx 0
However, integrating Poisson’s equation leads to: f
§ dV · H 0H ¨ ¸ © dx ¹ 0
f
³ U x dx 0
Combining the two previous relations gives us:
§ dV · ¨ ¸ © dx ¹ x
0
V H 0H
[4.19]
Relations [4.18] and [4.19] thus make it possible to write the following relation between the potential barrier at the surface VS and the surface charge V:
V2 2H 0H
VS
³ U (V )dV 0
[4.20]
For a semiconductor containing both a singly-ionized donor-type impurity D, of concentration ND, as well as a singly-ionized acceptor-type impurity A, of concentration NA, the density U(V) can be expressed using relation [4.7]:
U (V ) q>N D N A p(V ) n(V )@
[4.21]
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85
The concentrations of electrons n(V) and of holes p(V) are given by [4.4] and [4.5], while [3.23] and [3.25], found in Chapter 3, yield the concentrations of
ionized acceptor-type species N A and in ionized donor-type species N D . This means that the ionization state of donors and acceptors changes according to the band curvature and therefore according to the value of x. We are going to
express N A and N D as functions of V; note therefore that relation [3.23] of Chapter 3 involves the difference EA – EF, which breaks down into:
E A EF
E A Ei Ei E
which, according to [4.1], yields:
E A EF
E A Ei qMV qV
Consequently, the concentration N A is related to V through: N A
NA 1 § qV · 1 exp¨ ¸ a © kT ¹
[4.22]
where: a
§ E Ei qIV · exp¨ A ¸ kT © ¹
Similarly, the concentration N D is: N D
ND 1 § qV · 1 exp¨ ¸ b © kT ¹
where:
b
§ E ED qIV · exp¨ i ¸ kT ¹ ©
[4.22]
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Physical Chemistry of Solid-Gas Interfaces
Using [4.5], [4.6], [4.22] and [4.23], which relate n(V), p(V), N A and N D to V, the integration of equation [4.20] leads to a general formula relating to the surface barrier VS to the surface charge:
§ § qV · · § § qVS · · V2 nV ¨ exp¨ S ¸ 1¸ pV ¨ exp¨ ¸ 1¸ 2H0H kT © © kT ¹ ¹ © © kT ¹ ¹ § qV · 1 a exp¨ S ¸ © kT ¹ NA log 1 a
[4.24]
§ qVS · 1 bexp¨ ¸ © kT ¹ ND log 1 b Two borderline cases present themselves: – 1st case The impurities are virtually non-ionized, hence the following conditions: qV qV << ND and N A << NA, resulting in: b exp 1 and a exp 1 . kT kT
N D
Formula [4.24] becomes:
2sh
qVS kT
V V*
[4.25]
where:
V*
2HH 0 kTn *
n*
pV N D ( f )
and:
nV N A( f )
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87
N A (f) and N D ( f) represent the values of N D and N A in the bulk and far enough from the interface that we can consider that V = 0 in this space region:
N D ( f )
N D exp
N A( f )
N A exp
Ei E D qIV kT
and: E A ED qIV kT
– 2nd case The impurities are fully ionized. The conditions N D | N D and N A | N A lead to the following relations:
b exp
qV qV !! 1 and a exp !! 1 kT kT
The electroneutrality condition in the solid is written:
nV pV
ND N A
Using [4.24], we then arrive at: nV
ª § qVS «exp ¨ © kT ¬
qVS · ¸ 1 kT ¹
º ª § qVS » pV «exp ¨ © kT ¼ ¬
qVS º · ¸ 1 kT » ¹ ¼
[4.26] nV
§ V · n *¨ ¸ ©V *¹
2
Wolkenstein considers the variations of VS depending on the surface charge V in each of the two following situations: – in case of a low band curvature, which means that: qVS kT ; – in case of a high band curvature, which means that: qVS !! kT .
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Physical Chemistry of Solid-Gas Interfaces
In the hypothesis of low band curvature, whether the impurities’ ionization is low or full, we obtain:
VS
kT V q V*
in the hypothesis of strong band curvature; a) if there is low ionization, relation [4.25] yields:
VS
kT §V · r log¨ ¸ q ©V *¹
2
– with a + sign when V > 0, – with a - sign when V < 0; b) if the impurities are fully ionized, relation [4.26] brings to light two possibilities: – the SCR becomes poorer in majority carriers; the band curvature is depletive. Such is the case of n-type semiconductors in the presence of acceptor molecules:
VS
kT § V · r ¨ ¸ q ©V *¹
2
– the SCR grows richer in majority carriers; the band curvature is of the accumulative type. Such is the case for a p-type semiconductor in the presence of acceptor molecules:
VS
kT §V · log¨ r ¸ q ©V *¹
2
The relations previously established between VS and V will enable us to relate the surface concentration of adsorbed species N to the barrier VS by expressing the surface charge V as a function of N.
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89
4.3.4.1.2. Variation of the surface potential VS depending on the surface concentration N The surface charge V is due to a charge VA carried by the adsorbed species as well as a charge VB resulting from the presence of surface states that are different from those due to adsorption and which may be structural defects or surface impurities. As a result:
V
V A V B
In the hypothesis where the adsorbed species are singly ionized, we will have, for an acceptor-type species:
VA
qN
For a donor-type species:
VA
qN
The relations between VS and V make it possible to estimate the variation 'VS of the surface barrier caused by the adsorption of N particles depending on the relative values of VA and VB. There are a few different possibilities summarized below: – case of strong band curvature, which means:
VS !! kT . q – case of low band curvature, which means:
VS kT
q
Therefore:
'VS
kT N V*
We therefore obtain the following.
[4.27]
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Physical Chemistry of Solid-Gas Interfaces
Table 4.2. Relationships between ǻVS and N, according to degree of impurity ionization
4.3.4.2. Influence of adsorption on the dipole component VD6 During adsorption, there is, at the surface, a decrease in the potential of the double electronic layer. This decrease is represented by the dipole component VD of the work function. The double electronic layer may be due to polar molecules, induced dipoles, or dipoles created by the polarization of the bonds between the adsorbed species and the solid. Adsorption of polar molecules A number of molecules have, when they are free, a non-negligible dipole moment, for example the sulfur dioxide molecule SO2, whose dipole moment is μ = 1.61 debye. The dipole component is related to the dipole moment of adsorbed molecules through:
'V D
Nμ
HH 0
where N is the density of adsorbed molecules at the surface.
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91
Actually, according to a few other authors, the interactions between adsorbed molecules cause the dipole moment value μ to vary depending on the fraction of covered surface. In the hypothesis of a high fraction of covered surface, a mutual depolarization of the dipoles occurs, which tends to lower the value of their dipole moments. Adsorption of polarizable molecules The crystal lattice’s field, or the electric field caused by the space charge near the surface, can induce the polarization of non-polar free molecules. Quantum dipole moment Some weakly chemisorbed atoms – meaning that the bond between the atom and the lattice does not involve any electron or electron hole of the crystal lattice – can be found to be in a more or less highly polarized state. Thus, it appears that an electric field is equivalent to a field generated by a dipole whose moment μ is a normal surface, such that:
P
qGr
where r is the distance between the atom and the surface, and G represents the probability for one of the atom’s electrons to be captured by the lattice. 4.4. Solid-gas equilibriums involving mass and charge transfers
Next we demonstrate that some materials, particularly metal oxides, tend to facilitate mass and charge transfers with the surrounding gaseous phase. However, three conditions have to be fulfilled: – the existence of a chemical species that is present in both the solid and the gaseous phase, which in this case happens to be oxygen; – the presence of point defects that are capable, after being ionized, of supplying free carriers, as is the case for semiconductors; – the presence of point defects capable of accepting the gas species in question on the surface and/or facilitating its insertion in the lattice. The oxygen molecule will be received through the point defects that are characteristic of oxygen, that is to say either interstitial sites or sites with anion vacancies.
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Physical Chemistry of Solid-Gas Interfaces
The point defects that are characteristic of metal cations, which are cation vacancies and interstitial cations, make it easier for the oxygen to access its assigned lattice sites. In any case, the first step towards equilibrium is always adsorption, whose electrical and electrochemical aspects we have already described. During this step, we can imagine that the electrons involved result from the ionization defects of the solid and that the oxygen species’ degree of ionization is the same in its chemisorbed state as it is in its solid phase. The value for oxygen is two. The second step represents the transfer of the chemisorbed species from the surface to one of the solid’s sites that is near or on its surface (see Figures 4.7, 4.8, 4.9 and 4.10). We can also assume that the first step is often quick to be completed and is therefore always at equilibrium, at all pressure and temperature values. This causes the creation of a surface potential that we have already expressed for adsorption. We will make these equilibriums more specific to each type of Wagner defects. 4.4.1. Solids with anion vacancies (see Figure 4.7)
In this case, the two steps are: O2 4e 2 s l 2(O s)2
and: 2(O s)2 2V qq l 2OO 2 s
The global process is written: O2 4e 2V qq l 2OO
Note that, in this case, the presence of oxygen causes a decrease in the concentration of defects caused by the annihilation of anion vacancies and the electrons that are associated with them. The electrical conductivity of the material decreases as a result. Actually, the global equation does not express a real charge transfer because the electrons involved are obtained through a vacancy’s ionization, these two species being initially in the same phase.
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93
Thus, the only charge transfer to be considered at equilibrium takes place during the first step, which is adsorption. Experimentally, this kind of situation is not at all realistic when sensors are concerned, since sensors necessarily use metallic electrodes.
Figure 4.7. Insertion mechanism of an oxygen atom inside the lattice of a MO1-x type oxide
Electrochemists suggest then the use of a system containing three phases: the metal oxide, the gas and the metal, which acts through its electrons. The equation is therefore: O 4e 4s 2(O s)2 2 metal
The application of the electrochemical equilibrium condition, that is: yields the expression for the Galvani potential of the metal and the oxide: 1 (4P metal 2P P gas ) g metal Ox e O s O 4q 2
¦i QiP~i
0,
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Physical Chemistry of Solid-Gas Interfaces
4.4.2. Solids with interstitial cations (see Figure 4.8)
In this case, the two steps are written:
O2 2 s 4e l 2(O s ) 2 and: 2(O s)2 2M Iqq 2s l 2OO 2M M 4s
yielding the following global equation: O2 4e 2 M Iqq l 2OOsurface 2 M Msurface
We have here defect annihilation and a decrease in electrical conductivity as a result. 4.4.3. Solids with interstitial anions (see Figure 4.9)
In this case, the two steps are written:
O2 2 s 4e l 2(O s ) 2 and:
2(O s)2 2 I O l 2OI'' 2s yielding the following global equation:
O2 4e 2 I O l 2OI'' Note that, in this case, the presence of oxygen helps create a defect, or more specifically an interstitial anion. These electrons being from the material’s valence band, there is an electron hole conduction.
Interfacial Thermodynamic Equilibrium Studies
95
Figure 4.8. Insertion mechanism of an oxygen atom in the lattice of a M1+x O-type oxide
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Figure 4.9. Insertion mechanism of an oxygen atom in the lattice of a MO1+x-type oxide
4.4.4. Solids with cation vacancies (see Figure 4.10)
O2 2s 4e l 2(O s) 2 2(O s)2 2M Mvolume 2s l 2OMsurface 2M Msurface 2VM'' the global equation being:
O2 4e 2M Mvolume l 2OMsurface 2M Msurface 2VM''
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97
or:
O2 2M Mvolume l 2OMsurface 2M Msurface 2VM'' 4h Once again, the electrons are from the material’s valence band, therefore causing an electron hole conduction. As for the surface potentials, the remarks made about the first case apply for all other cases.
Figure 4.10. Insertion mechanism of an oxygen atom in the lattice of a M1-x O-type oxide
4.5. Homogenous semiconductor interfaces
This is about interfaces formed by two materials that are initially identical and only differ through the nature and/or the concentration of introduced doping species. The most typical example is that of a junction formed by an n-type and a p-type semiconductor material (see Figure 4.11).
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Figure 4.11. Homogenous semiconductor interfaces
During this study we will assume that all defects are ionized at working temperature. There is simply a charge transfer through the junction, involving electrons and electron holes. Influenced by the concentration gradient, the electrons resulting from the presence of electron donors in the n-type material will migrate towards the p-type material. Conversely, the electron holes resulting from the presence of electron acceptors in the p-type material will move to the n-type side. At the junction, electrons and electron holes will react through the annihilation reaction:
h e 0 This relation leads to n = p = 0 in the exchange region, if n and p are, respectively, the concentrations of electrons and electron holes. In such a situation, the junction is characterized by the presence of positive charges due to the presence of ionized donors in the n-type material, and the presence of negative charges due to that of ionized acceptors in the p-type material. This region, called the space-charge region (SCR) or depletion region, is characterized at equilibrium by the absence of free carriers: electrons or electron holes. The charges, as we have just seen, will generate an electric field [ that will oppose any new transfer of electrons or electron holes. At equilibrium, the chemical forces created by the concentration gradients equal the electric forces. The physical and mathematical processing of this system is identical to that suggested for chemisorption in section 4.3.4.1.
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99
In the present case, given the physical conditions, the mathematical processing may be considerably simplified if we suppose that the concentration of charges in the SCR is constant over its entire depth l (see Figure 4.12a). There is then talk of an abrupt junction. Whether it will extend through the n and p-type materials will depend on the concentration of electron donors and acceptors. Note that the lower the donor and acceptor concentrations are, the larger the SCR will be (see Figure 4.12b).
Figure 4.12. Outline of the charge concentration in the hypothesis of an abrupt junction a) symmetric junction, b) asymmetric junction
In the case of an abrupt junction, if NA and ND respectively denote the concentration of ionized acceptors and donors, then the system can be described by the following equations:
G[ Gx
U H SC H 0
q N D p N A n
H SC H 0
(Poisson’s equation)
Since n = p = 0 in the SCR, the previous equation becomes:
G[ Gx
U H SC H 0
q N D N A
H SC H 0
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Physical Chemistry of Solid-Gas Interfaces
The hypothesis of an abrupt junction, which implies that the charge concentration is constant in the SCR, also implies for a unit section that:
xp N A
xn N D
xp and xn stand for the expansion of the SCR in the p and n materials. Thus:
xp xn
ND NA
This relation shows that, at equilibrium, the charges are equal in both centers, and that the lower the concentration of donors or acceptors, the larger the SCR is in the corresponding center. On the acceptor side, where the charge density is qN A , integration leads to:
[
qN A
H SC H 0
(x xp )
with: [ = 0 when x = -xp. Similarly, on the donor side, where the charge density is qN D we obtain:
[
qN D
H SCH 0
( x xn )
with [ = 0 when x = xn. Note that the electric field, which is negative over the entire domain, has a triangular profile (see Figure 4.13). The maximum value [ M of the field is given by:
[M
[ (0)
qN A
H SCH 0
xp
qN D
H SCH 0
xn
[4.28]
Integrating over the triangle area leads to the expression of ) as a function of x (see Figure 4.14), and therefore to its maximum value between –xn and xp.
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This value represents the diffusion potential VD, which is expressed:
VD
1 [ M xn x p 2
[4.29]
This potential is electrostatic in nature, so it cannot be measured directly. As for the energy diagram, it should show that at equilibrium, if a diffusion potential VD exists, the electronic and electron hole functions should be identical in both materials. This means that the Fermi levels should be equal, at least when x = 0, and also that there is a non-zero variation of the electron function in both materials. Indeed, we have to remember that the extraction work function value in n-type materials is lower than in p-type materials. There are two types of representation that can be adopted to take the previous two conditions into account. These two types are related to the arbitrary choice of the energy level E, which is related to the potential ), and therefore the profile of the diffusion potential VD. We already know that in effect E = -q ).
Figure 4.13. Outline of the electric field ȗ in the SCR
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Physical Chemistry of Solid-Gas Interfaces
Figure 4.14. Outline of the electric potential V and energy in the SCR
The electrostatic potential is associated with the Fermi level. Under these conditions, the band diagram is flat and only the Fermi levels vary according to the potential. Thus, the Fermi levels are only equal when x = 0. Note that the extraction work function value gradually rises in the n-type material as we get closer to the junction. When x = 0, the extraction work value in the n-type material equals the initial Fermi level ( nF added to a fraction of –qVD: -DqVD. The D coefficient equals 0.5 for a symmetric junction; it will be less than 0.5 if the SCR extends more in the p-type material than in the n-type material, and higher than 0.5 for the opposite condition. On the p side, the work function decreases until it reaches the value of ( pF , from which is subtracted the following quantity:
q (1 D )VD
qE V D
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The work functions being equal, we obtain:
q ) n x
qVD
xn
) p x
x p
( nF x
xn
( Fp x
x p
4.5.1. The electrostatic potential is associated with the intrinsic energy level
It is interesting to note that, for such a junction, the two materials are identical before the doping process, as are their intrinsic energy levels. This level is therefore an excellent reference for physicians. Here, unlike before, it is the energy bands that will be associated with the profile of the potential. The Fermi level is flat and is equal in both materials (see Figure 4.15).
Figure 4.15. Evolution of the potential barrier according to the distance: case of an asymmetric junction where x(p) < x(n)
The work functions being equal, we obtain:
qVD
q ĭn x
xn
ĭ p x
x p
Ǽin x
xn
where:
Ǽin x
xn
Ǽip x
x p
§ N D x ǼF kT Log ¨¨ © ni
xn
· ¸¸ ¹
and:
§ N A x ǼF kTLog ¨¨ © ni
x -p
·¸
¸ ¹
Ǽip x
x p
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It is now possible to express VD or qVD as a function of the concentration of electron donors and acceptors. Using the previous relations, we arrive at:
qVD
kT Log
N D x n N A -x p ni2
This relation expresses the fact that, at equilibrium, the forces of chemical and/or electrical origin are equal. The previous relations [4.28] and [4.29] allow us to finally express the total width l of the SCR:
1
2İSC İ0 § 1 1 · ¨¨ ¸VD q © N A N B ¸¹
Knowing that, for silicon:
H0 = 8.85x10-14 Fcm-1 HSC = 12 q = 1.6 10-19 C we also pose: NA = 1018 atoms per cm3 NB = 1015 atoms per cm3 We obtain VD = 0.75 volt and 1 = 0.96 Pm, which yields xn = 0.96 Pm and xp = 1 Å. Thus, if the concentration ratio of acceptors compared to donors reaches 103, we note that the SCR is almost completely located in one material alone, which happens to be the n-type material. 4.5.2. Electrochemical aspect
The expression of the potential VD can be directly obtained using the electrochemical equilibrium condition corresponding to the reaction:
e h 0
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105
To clarify the condition of such an equilibrium, we will first express the electrochemical potential of the electrons and electron holes:
P~e
P e0 RT ln nn qe M n
for the n side and, for the p side:
P~h
P h0 RT ln p p q pM p
Moreover, we are going to demonstrate that:
Pe0
P h0
knowing that:
Pe
E F EC
RT ln
nn NC
P e0 RT ln n n
and that:
Ph
EV E F
RT ln
pp NV
P h0 RT ln p p
We obtain, for the intrinsic regime, the following relations for each carrier:
P ei
E I EC
RT ln
n ni NC
P e0 RT ln n ni
and:
P
i h
EV E I
RT ln
Since:
EI EC
EV EI
p ip NV
P h0 RT ln p ip
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Physical Chemistry of Solid-Gas Interfaces
then:
P ei
P hi
Actually, this relation implies that NC = NV Furthermore, since ni = pi, then:
P e0
P h0
Under such conditions, the equilibrium condition
RTln
nn pp
¦i Qiμ~i
qe M n qh M p
Since:
qh
qe
it follows that:
RTln
nn pp
qe (M p M n )
qe VD
In the hypothesis where all defects are fully ionized:
nn
ND
pp
NA
and:
Moreover, we have:
nn p p
ni2
0 is written:
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107
therefore:
RTln
ND N A ni2
qeVD
This is obviously the same expression as before. 4.5.3. Polarization of the junction
It is possible, using an external energy source, to supply the system with electrical charges, which will push it towards a new equilibrium that, unlike the initial one, is not solely the result of the presence of donors and acceptors. The evolution of the equilibrium will depend on the nature of the introduced changes. The simplest case involves externally connecting the junction to a direct potential power supply. Positively polarizing the p-type material helps strengthen its p-type material characteristics. It boils down to extrinsically increasing the concentration of acceptors. From the n side, we can then observe an artificial increase in the concentration of donors. All of this leads to a reduction of the potential barrier, the width l of the SCR and the electric field. Conversely, a positive polarization of the n-type material increases the potential barrier, the width of the SCR and the electric field. 4.6. Heterogenous junction of semiconductor metals
Such a junction is found in all electrical connections on devices that use semiconductor materials. Given the extremely high concentration of electrons inside the metal, in the order of 1022 to 1023 electrons/cm3, we find ourselves in a situation where the SCR is entirely supported by a semiconductor whose donor or acceptor concentration does not exceed 1018/cm3. Generally, the potential barrier only depends on the donor or acceptor concentration inside the semiconductor. These junctions are also used in electronics, particularly in rectifier devices. To conclude, we gather from all these results that all interfaces combining chemical elements and/or two non-insulating materials induce potential barriers. These potential barriers are associated with insulating SCR whose width depends on the donor and acceptor concentration as well as on the possible external input of charges into the considered device. Given the insulating property of the SCR, modulating its width can in some cases make it possible to modulate a material’s electrical conductivity.
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Physical Chemistry of Solid-Gas Interfaces
Chemisorption thus induces in the material concerned the creation of an SCR whose width depends on the gas pressure. For a ceramic material with intergranular porosity and which is characterized by the presence of grains that are in contact with the gas atmosphere, the intergranular interface and the SCR will both have control over the ceramic’s electrical properties. Indeed, we have to remember that the SCR is a particularly insulating region and that, depending on its depth, its conductance value can affect its volume. Once again, the pressure value of the surrounding gas will influence the process (see Figure 4.16).
Figure 4.16. Evolution of the potential barrier according to the distance at the grain boundary
4.7. Bibliography 1. J-P. COUPUT, Réalisation d’un dispositif de mesure du travail de sortie des électrons, Application à l’étude des systèmes dioxyde d’étain - oxygène et dioxyde d’étain - dioxyde de soufre, Thesis, Grenoble, 1982. 2. P. AIGRAIN, C. DUGAS, “Adsorption sur les semi-conducteurs”, Z. Elektrochimie, 56, 363, 1952. 3. P.B. WEISZ, K.J. HAUFFE, H.J. ENGELL, “Relation between the interaction energy and the surface potential of some films”, Chem. Phys., 21, 15, 1953. 4. P. AIGRAIN, C. DUGAS, “Adsorption sur les semi-conducteurs”, Z. Elektrochimie, 56, 363, 1952. 5. Th. WOLKENSTEIN, Physico-chimie de la surface des semi-conducteurs, MIR, Moscow, 1977. 6. A. CLARK, The Theory of Adsorption and Catalysis, Academic Press, 1970.
Chapter 5
Model Development for Interfacial Phenomena
5.1. General points on process kinetics Every charge or mass transfer we have mentioned previously represents one or many steps of a more or less complex process. Modeling, however, is the anticipation, interpretation, description and then simulation of the course of these processes over time. This is all carried out using the information we have about the system being studied: information about the nature and concentration of the present species, the nature and location of the phases, parameters such as temperature and partial gas pressure. Generally, the model of a process can also be expressed by a number of equations that relate these parameters to each other over time. To obtain these relations, the entire process has to be clearly described. If the simulation and experimental results are compatible, the model will be validated, allowing us to interpret the observed phenomena. Although thermodynamics makes it possible to relate the concentration of chemical species in the inflow to the concentration in the outflow, which corresponds to the initial and final states, it does not allow us to take into account the intermediate steps that form the links in the chain and constitute the process being studied. These intermediate states, which have to be considered when modeling a process, cannot be observed. They can, however, be imagined or guessed at using experimental results, then be validated with kinetic-type information.
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Physical Chemistry of Solid-Gas Interfaces
Each step of the process will have to be identified with an elementary step that consumes and/or produces one or multiple intermediate compounds. Consequently, the expression for the rate of each step generally obeys van’t Hoff’s law. This rate, as with adsorption, is the product of a kinetic constant k and the concentration of reactant species, the respective order of each species being equal to its stoichiometric coefficient. In fact, the global rate V of the reaction o
appears as the difference between two terms, which are the rate V of the forward m
reaction and the rate V of the reverse reaction. Thus, for an elementary step such as:
DA EB l JC GD the rate V is:
V
o
m
V V
o
m
k >A@ >B @ k >C @ >D @ D
E
J
G
where: o
k
o
o
kO exp(
o
m
m m E E ) and k kO exp( ) RT RT
m
E and E represent the respective activation energies of the forward and reverse reactions. These energy values, in a solid medium, are representative of the energy needed to cause the transfer of an electrically neutral particle in the crystal lattice (scattering process) or through interfaces. In the case of electrically charged particles, there might be electrical barriers that should be taken into account, as we have already seen in section 4.5, when we discussed heterogenous junctions. Therefore, a corrective term of the DqVD or EqVD type will have to be added or subtracted from the activation energy. Generally speaking, the elementary steps form linear chains with branched possibilities.
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111
5.1.1. Linear chain1, 2 Suppose we have a global reaction of the following kind:
A1 A2 ...... Ai ..... An B1 B2 .....Bi ....Bn From all the possible configurations of linear chains, we have chosen the following:
A1 X 1 B1
for step 1
A2 X 1 X 2 B2
for step 2
………………………. Ai X i 1 X i Bi ………………………. An X n 1 Bn
for step i for step n
We will suppose, for simplicity’s sake, that this reaction has n elementary steps and that each step consumes and produces a single, distinct, intermediate species X. Thus, each intermediate compound Xi is produced during step i; it is then consumed during the following step i+1. Therefore, we can suppose that there cannot be any interaction between the reaction intermediates. The Ai and Bi compounds respectively represent the reactants and products of the reaction. The rate Vi of each step i considered separately is:
Vi
o
m
k i > Ai @>X i 1 @ k i >Bi @> X i @
The kinetic system can therefore be represented by the reaction path that can be seen in Figure 5.1.
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Physical Chemistry of Solid-Gas Interfaces
Figure 5.1. Reaction path of a chain process
As well as the following system of differential equations:
dX 1 V1 V2 dt - - - - - - dX i Vi Vi 1 dt - - - - - - dX n 1 Vn 1 Vn dt To complete the system, we have to express the variations of the reactants (Ai) or products (Bi). Thus, we would have for each step i:
d [ Ai ] dt
d [ Bi ] Vi J A and Vi J B i i dt
JA represents a possible external input of Ai species, and JB a possible consumption of Bi species by a system that is external to the considered system. The concept of external systems induces for each step that of an open or closed system for inlet and outlet reactants. The system will be considered open for inlet reactants if the inlet concentration of reactants is constant over time. The system therefore has a permanent supply.
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113
The system will be considered closed for inlet reactants if the reactants introduced in the beginning are depleted. The reaction is therefore limited in time. The system will be considered open for outlet products if the outlet concentration of products is constant over time. Such a condition can be fulfilled if, for instance, the products of the reaction are continually removed from the system or if the concerned reactant is already present and with a high concentration in the medium that constitutes the system’s outlet. Desorption of oxygen in air is a good example of that. The system will be considered closed for outlet products if the products formed accumulate over time in the system’s outlet. Thus, for a system that is open to Ai and Bi, we would have:
d > Ai @ dt
d >Bi @ dt
0 Vi
J Ai and Vi
J Bi
This relation implies that Ai and Bi are constant throughout the process. Such a situation is typical of an industrial process during which the reactants are continuously supplied and the formed products are continuously evacuated. From the previous system of equations, we have noted that a process may never be described by only one expression of its rate. The kinetic evaluation of a process can therefore depend on the nature of the species to be analyzed and, as a result, on the analytical tools and methods that are used. The evolution curves of the gaseous mass bound to the solid sample, which can be obtained by thermogravimetry, will be identified with the rate of adsorption step Va or desorption step Vd. If ǻm represents the mass variations over time, then:
d ('m) dt
DVa or - DVd
depending on whether V represents an adsorption or desorption step. Generally speaking, adsorption and desorption processes take place most often at the chain’s end, and their respective rates are V1 and Vn.
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Physical Chemistry of Solid-Gas Interfaces
However, during calorimetric experiments, if we assume that each step is characterized by a molar reaction enthalpy value ǻHi which has the dimension of a molar heat Qi, then:
dQ dt
i n
¦V 'H i
i
i 1
Q represents the total amount of heat that is produced or consumed simultaneously by the n process reactions. This amount may be directly measured by calorimetric apparatus. Let us go back to the system of differential equations and note that it is rarely possible to solve mathematically. To overcome this, we can contemplate making simplifying hypotheses that are realistic and take into account some physical or physico-chemical aspects of the process. The nature of such hypotheses could depend on the relative values of the kinetic constants or on the experimental conditions. We will distinguish, to that end, between reactions in an open or closed system for inlet and for outlet reactants. 5.1.1.1. Pure kinetic case hypothesis The pure kinetic case hypothesis consists of supposing that there is, among the different steps, a step that can be considered much slower than the other ones. To go further, we will also suppose that all of the other steps are fast enough to be considered at equilibrium. Suppose the pure kinetic case is controlled by step j; all kinetic constants o
m
o
m
k i and ki therefore tend to infinity for every i value but j, while constants k j and k j o m
have finite values. If we take into consideration the fact that the fraction k / k represents the equilibrium constant K of the step in question, we will have to suppose that, when i and j have distinct values, this fraction of two infinite quantities necessarily has a finite value. In the pure kinetic case controlled by step j, the process can be described by a sequence of steps at equilibrium prior to step j and by a second sequence of steps at equilibrium following j. The equilibrium condition for the upstream sequence is here expressed by the following relations:
Model Development for Interfacial Phenomena
>X 1 @
K1 > A1 @ >B1 @
for step 1;
>X 2 @
K1K 2 >A1 @>A2 @ >B1 @>B2 @
for step 2;
115
---------------------------i j 1
>X @
K i > Ai @
i 1 i j 1
j-1
for step j-1.
>B @ i
i 1
Similarly, starting from the last step n of the downstream sequence, we have:
K n An Bn
1 X n 1
for the last step;
and: i j 1
1 Xj
> @
K >A @ i
i
i n i j 1
>Bi @
for step j.
i n
These relations allow us to express the concentration of all the intermediate species, and those of step j in particular. In the hypothesis of an open system for inlet and outlet reactants, which must be constant and independent of time concentrations for all reagents Ai and all products Bi, we note that the concentration of all intermediate species Xi are independent of time, which leads to:
d >X i @ 0 dt
for any value of i.
This relation, if associated with the previous system of differential equation, makes it possible to state that:
V1 V2
..... V j
..... Vn 1 Vn
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Physical Chemistry of Solid-Gas Interfaces
The entire system will thus be controlled by the slowest process, that is to say step j. This step is referred to as the rate limiting process. Although the other steps are intrinsically quite fast to achieve equilibrium, they are controlled by the rate limiting process. The designation of process kinetics is therefore preferred to that of a process rate. Using the previous relations, we can now express the rate of the limiting process, and therefore the kinetics of the process: i j-1
Vj
G kj
i j
K A i
i 1
i 1
i j-1
B
i j
i
H -kj
i
B
i i n i j 1 i j 1
K A i
i 1
i n
i
i n
This expression allows us to express the variation of physical parameters such as mass or heat effect as functions of the kinetic and thermodynamic system parameters: d('m) dt
D Vj and
dQ dt
E Vj
i n
¦ 'H
i
i 1
Under these conditions, the process kinetics are perfectly described based on the system data, that is, temperature and reagent concentrations. a) Influence of temperature on the process kinetics We know that only equilibrium and kinetic constants are functions of temperature. Indeed, we have: K K 0 exp(
'H 0 ) RT
G k
G G E k 0 exp( ) RT
H k
H H E k 0 exp( ) RT
and:
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117
As a result, Vj appears as a particularly complex function of temperature. That is due to Vj being the difference between two terms that involve exponential functions. This difficulty can be overcome if the rate limiting process is considered to be much more advanced in the forward direction; we therefore have to suppose that:
G H G H k j k j or k j ! k j Such a hypothesis makes it possible to eliminate a term in the expression of Vj.
G H Thus, if k j ! k j, it follows that: i j-1
i j
K i Ai G i 1 i 1 kj i j-1 Bi
Vj
i 1
with: G j 1 k j Ki
O exp(-
j 1 G E j ¦ 'H i0 1
RT
1
)
Under such conditions, the process kinetics obey a 1/T exponential law. The Arrhenius law applies here, and if we plot the logarithm of Vj according to 1/T, we obtain a line whose slope A is:
A
(
j 1 G E j ¦ 'H i0 1
R
)
We note that the slope value depends on the nature of the rate limiting process. Indeed: G E1 ; – if the rate limiting process is step 1, we will have: A = R G E ǻH1 – if the rate limiting process is step 2, we will have: A = - 1 , etc. R
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Physical Chemistry of Solid-Gas Interfaces
b) Influence of the reactant and product concentrations on the process kinetics This is much easier to deal with from a mathematical standpoint. The influence of reactants and products depends once again on the nature of the rate limiting process. To be convinced of such a thing, we only have to compare the expressions of step 1 and step n in the hypothesis that these are limiting processes: G H >B @..... >B @ V1 k1>A1 @ - k1 n >A n @.... >A 2 @
and:
Vn
G >A @..... >A @ H n kn 1 k >B @ >B1 @.... >Bn-1 @ n n
Note that, for this type of species, A1 and Bn do not influence V1 and Vn in the same way. Based on this type of consideration, and after making a comparison between some experimental results, we will be able to validate the working hypotheses and therefore also validate a kinetic process. To make this task easier, we must choose the nature of the experiments to be conducted and the parameters that will control these experiments with great care. 5.1.1.2. Bodenstein’s stationary state hypothesis This hypothesis consists of supposing that after a period of time during which the reaction takes off, steady-state conditions will establish themselves, characterized by constant intermediate compound concentrations. Such a hypothesis implies that the reaction time is long enough for the steady-state conditions to be reached, and this is especially true for systems that are open to inlet and outlet reactants. Mathematically, we only need to express the condition:
d >X 1 @ d >X i @ d >X n 1 @ ----------dt dt dt
0
Just as for the pure kinetic cases, this relation naturally results in V1 = V2 = … Vn, but the processes are no longer necessarily at equilibrium. We are then led to solve a system of algebraic equations with n-1 undetermined variables:
V1 V2 ………….
Vi 1 Vi ………….
Vn 1 Vn
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119
Solving this system makes it possible to express all the concentrations of intermediate species as functions of the physico-chemical system’s parameters. The rates all being equal, the kinetic process can be described by either one of them by copying out, in the expression of its rate, the rates of the affected intermediate species Xi. The solutions are necessarily different from those we have obtained using the hypothesis of pure kinetic cases because they only involve kinetic constants ki, unlike the pure cases which bring into play the kinetic constants ki as well as the equilibrium constants Ki. The stationary state hypothesis therefore supplies us with a more general solution without requiring any details of the nature of a possible rate limiting process. 5.1.1.3. Evolution of the rate according to time and gas pressure We will deal with this kinetic aspect using the two examples that are the most appropriate for this book, that is to say that of chemisorption and that of an adsorption-reaction type of process. – Case of chemisorption Suppose we have the reaction:
Gs Gs Since it is an elementary step, we can write:
dș dt
V
G H k P( 1 ș) k ș
In such a case, the mathematical solution is easy to find. We have:
dT G G H k P (k P k )
dt
and:
ș
G G H kP G H 1 exp ( (k P k )t kP k
>
@
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Physical Chemistry of Solid-Gas Interfaces
With the knowledge of T, we can relate the rate to time. We therefore arrive at:
V
>
G G H k P exp (k P k )t
@
if we consider that:
t
ti
0 Vi
G kP
and that:
t
tf
f Vf
0
Vi representing the initial process rate. Also note that the maximum rate value is reached immediately, and that the rate decreases non-stop over time. In that case, the changes in the rate according to P are relatively complex. – Case of an adsorption-reaction process If we assume that the adsorption process, as we have just described it, is associated with a chemical reaction, and if we hypothesize that there is a rate limiting process and that the reverse reaction is distinctly advanced, then we can write that:
Gs Gs If the step is at equilibrium, it follows that:
T
K1P 1 K1P
Moreover, for the second step that imposes its rate, we will have:
(G s ) A AG s and:
G V2 k 2T >A @
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121
If the system is open for A, we will also have:
>A @
C te
Under such conditions, the rate of the global process is expressed by:
V
V2
G k 2 >A @K1 P 1 K1 P
The rate here is independent of time (the process is equivalent to a stationary state), rather, it is a homographic function of pressure. 5.1.1.4. Diffusion in a homogenous solid phase3,4,5 Within the context of linear processes, it is necessary to mention the case of diffusion processes in a homogenous phase. The most typical case involves the migration of a chemical species in a solid phase. It can be, for example, the migration of an oxygen ion through the lattice of a metallic oxide thanks to the oxygen vacancies. In such a case, the positions occupied by oxygen are of the same nature for all of the hopping steps. Consequently, these lattice positions are characterized by the same energy value. Every hopping step that corresponds to an elementary step is characterized by G H identical activation energy values ( and ( , the former being for the forward reaction and the latter for the reverse one. It is therefore an athermal reaction for which (see Figure 5.2):
ǻH q
G H EE
Every hopping step being the same, all kinetic constants are identical and are identified with a diffusion coefficient D expressed by:
D
G E D0 exp ( ) RT
H E D0 exp ( ) RT
We will retain D as the dimension of a kinetic constant.
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We can also suppose that such a process will generate a diffusing species concentration gradient with boundary conditions fixing the concentration values at the inlet and outlet interface of the homogenous scattering region. Under such conditions, the concentration of the scattering species C(x,t) is a function of time and of the diffusion distance x, which is initialized at the inlet interface (see Figure 5.3). Note that if we suppose the system to be open at x=0, the vacancy concentration will be kept constant. If J(x, t) represents the flow of particles crossing the energy barrier E per time unit between two stable lattice positions, then (see Figure 5.2):
J x,t
G H J x,t J x,t
This flow, which is identified with the rate of an elementary step, is expressed by:
G J x,t
DC (x,t) for the forward reaction
and by:
H J x,t DC xa ,t
DC(x,t) aD
į C x,t įx
for the reverse reaction
a, which represents here the distance between two consecutive hopping steps, can be identified with a crystal lattice parameter.
Figure 5.2. Energy diagram of a hopping step in a crystal lattice
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To be more precise, a coefficient D has to be added to the expression of the flow. This takes into account the probability of finding a free site; it follows that:
J x ,t
DaD
į C x,t Gx
This relation is the first Fick’s law. Moreover, at the t + įt instant, we will have: J x ,t Gt
DaD
G C x,t Gt Gx
§ GC G 2C x ,t · dt ¸¸ DaD¨¨ x ,t G x2 © Gx ¹
Figure 5.3. Evolution of the vacancy concentration gradient according to the x coordinates and time t
We can then perform a mass balance for a volume element of a single unit section and of a width dx, during a time duration dt (see Figure 5.4). In our case, dx will be considered as equal to the lattice parameter a.
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Figure 5.4. Element of a scattering zone
Thus, the number of particles going into this volume element at the abscissa x and at the instant t equals that of the outgoing particles at the abscissa x+a and at the instant t+dt added to that of the particles that have accumulated or been depleted inside the volume element:
J x,t įt ĮaD
J x,t
įC x,t įt
dt
Using the previously established relations, we obtain:
DaD
GC x ,t Gt
DaD
G 2C x ,t dx 2
dt
which leads to:
GC x ,t Gx
G 2 C x ,t Gt 2
This is the second Fick’s law. In the hypothesis of a stationary state, which requires a system that is open for inlet and outlet reactants, C0 and Ce being the respective constant inlet and outlet concentrations, we obtain:
GC x ,t Gx
0
G 2 C x ,t Gt 2
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which leads to:
GC x ,t Gt
C 0 Ce e
that is to say a constant linear concentration gradient:
C0 Ce e
A
This result only applies in the hypothesis of an open system to inlet and outlet reactants. “e” represents the distance between the system’s inlet and outlet. 5.1.2. Branched processes
In some cases, the process can no longer be described as a simple linear process, as multiple chains appear and sometimes split into branches. The approach for linear processes does stay the same when applied to each chain. However, the ramification nodes have to be taken into account as they are presented in Figure 5.5.
Figure 5.5. Branched processes
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As an example, we will present the two cases seen in Figure 5.5 with the hypothesis that the forward reactions are distinctly advanced, which amounts to completely disregarding the reverse reactions. In the first case, there is no interaction between the intermediate species (see Figure 5.5a): d>X 2 @ dt
G G G V1A V1B V2
thus:
d>X 2 @ Į X1A ȕ X1B Ȗ>X 2 @ dt
> @ > @
In the second case, there are interactions between the intermediate species and therefore: d>X 2 @ G G V1 V2 dt
d <X2 > dt
Į ¢¡ X1A ¯±° ¢¡ X1B ¯°± Ȗ < X 2 >
Here we are presented with quadratic expressions that make this case harder to solve mathematically. In conclusion we hold that expressing the kinetics of a reaction process is a relatively difficult approach which will require the researcher to: – acquire as much information as they can about the experimental results obtained through different analysis techniques; – imagine a realistic kinetic process and its experimental conditions; – introduce hypotheses also compatible with the nature of the process; – simulate and validate the obtained kinetic models. 5.2. Electrochemical aspect of kinetic processes We have previously mentioned that the activation energy value can be changed when there is movement of charged species. In such a case, an electrochemical
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phenomenon is observed. We will explore this subject through an oxidationreduction reaction which brings into play a solid-gas interface. This case is typical of chemisorption. Generally speaking, the reaction is: oxidizing agent De reducing agent
The rate V of this reaction is defined as the number of electron grams dn extracted from the reducing agent during dt and per surface unit, therefore:
V -
1 dn G H V V Vred Voxy D dt
dn/dt is therefore proportional to the density of the current i, for which the following convention was adopted: the current is considered to be positive in the case of an oxidation, and negative in the case of a reduction, thus leading to:
i
q
dn dt
iOx iRe d
where:
iox
qGk ox >Re d @
and:
ired
qGkRe d >Oxy @
~ ~ Suppose EOx and ERe d are the energy values that define the activation energies respectively corresponding to the kinetic constants k Ox and k Red , where:
kOx
~ EOx ) k exp( RT 0 Ox
and: k Re d
0 k Re d exp(
~ ERe d ) RT
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As a result of the existence of an electrically charged interface, these energy quantities have to take the diffusion potential VD into account or rather take into account the fractions ĮVD or ȕVD as they are expressed and presented in Figure 4.15. Thus: H E ȕqVD
~ E Ox
and:
G E ĮqVD
~ E Red
It follows that:
H ( E EqVD ) k exp( ) RT 0 Ox
k Ox and:
0 k Re d exp(
k Re d
G ( E DqVD ) ) RT
It is now possible to choose: G k1
k
kRe d
0 Re d
G H E1 exp( ) and k 2 RT
H E2 k exp( ) RT 0 Ox
G DqVD ) k exp( RT
and: kOx
H EqVD k exp( ) RT
The global current is then expressed as: i
G EqVD DqVD ªH º ) Re d k exp( ) Ox » qG «k exp( RT RT ¬ ¼
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Thus, at equilibrium, which is when i = 0, we have:
VD
G >Ox@ ) RT k (ln H ln * * >Re d @ q (D E ) k
This expression leads us to Nernst’s law. Į* and ȕ* stand for the value of these coefficients at equilibrium, considering that Į + ȕ* = 1. *
The idea that D and E are functions of time is based on the fact that the surface potential value, and therefore the curve V = f(x,t), changes during the shift towards equilibrium. Therefore, the coefficients D and E which describe this curve, may from now on be associated with such an evolution type. Given the extent to which these coefficients affect kinetic parameters, we will clarify them for two particular cases: that of an abrupt junction in a closed medium, and then in an open medium – the latter being typical of adsorption. – First case: abrupt junction in a closed medium, case of the p-n junction Suppose we have an oxidant medium as medium 1 and a reducing medium as medium 2:
Q t
U1 x1
U 2 x2
with Q t charge per surface unit and
U
the charge density.
If –x1 d x d 0, we will have:
U1 0 and
d 2V dx 2
U 1 HH 0
If 0 d x d +x2, we will have:
U2 t 0 and
d 2V dx 2
U 2 HH 0
Q(t) denotes the charge initiating at the interface as charge transfers are taking place and until the system reaches equilibrium.
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G
If [ stands for the electric field, then we have, for medium 1 and 2 (see Figure 5.6):
G
[1
G U1 ( x x1 ) and [ 2 HH 0
dV dx
dV dx
U2 ( x x2 ) HH 0
therefore:
G
[1 max
G U1 ( x1 ) [ 2 max HH 0
U2 ( x2 ) HH 0
However, we have: x xp
V
G
³ [ dx = area of triangle ABC
x xn
and:
DV
x 0G ³ [ dx = area of triangle AOC x xn
Figure 5.6. Outline of the electrical field at the interface (see Figure 4.13)
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Under such conditions:
D
surface of triangle A, 0, C surface of triangle A, B, C
S1
U1 ( x12 ) 2HH 0
S1 S0
where:
with x1 = xn and: S0
U1
2HH 0
( x12 x1 x 2 )
with x2 = xp which yields:
D
1 x 1 2 x1
1 1
U1 U2
and:
E 1-D
1 1
x1 x2
1 1
U1 U2
Note that U1 and U 2 , which here represent the volume concentration of defects in the two considered mediums, keep the same value even while the external parameters change. These results lead to the conclusion that the D and E coefficients, at least for a closed system and in the case of an abrupt junction, are independent of the charge value and consequently of time. – Second case: abrupt junction in an open medium In the particular case of an adsorption process that is characterized by a system that is open to the gas and a single chemisorbed layer, medium 1 can be described
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using a surface density of charges q N(P, t), as well as the width of a space-charge region x1, which is limited by that of an adsorbed monolayer. We will adopt that width value as a reference, keeping it constant and equal to a single unit. Consequently, N(P, t) represents the number of chemisorbed molecules in the monolayer per surface unit at the point in time t. Thus:
Q( P , t )
qa
N ( P ,t ) a
qN ( P ,t )
Ux 2
As for medium 2, nothing has changed since the previous situation: it is now the x2 parameter that varies according to the carried charge value and the charge density, which is related to the concentration of intrinsic defects in the oxide, is constant. Under such conditions, the D coefficient, which is the ratio:
D
area of triangle A, 0, C area of triangle A, B, C
S1 S0
can be expressed as:
D
1 1 x2
1
1 qN ( P , t )
U2
In such a case, the D and E coefficients are functions of the chemisorbed amount N(P, t) and, as a result, of gas pressure and time. However, this situation allows us to suppose that x2 is much larger then x1. Indeed, if we suppose that the medium fraction of covered surface is 0.5, and that the ratio of defects in the oxide is in the order of 1%, then the x2 / x1 ratio is in the order of 20. This calculation is done on the hypothesis that the molecular volume of the considered species is the same in both phases. Under such conditions, we can consider that D is negligible compared to E, and go back to a situation similar to the one we found ourselves in with heterogenous junctions of semiconductor metals, whose space charge region and, as a result, its potential barrier, is fully supported by the semiconductor.
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5.3. Expression of mixed potential The same solid-gas interface can be the scene of multiple simultaneous and independent oxidation-reduction reactions. This has to be taken into consideration when modeling the electrical response of some electrochemical sensors, particularly those located in a gaseous atmosphere containing oxidant and reducing gases. We will approach this study by considering two electrochemical reactions of the following type:
Ox1 įe Re d1 1 where VD is the scattering potential of reaction 1, and:
Ox2 įe Re d 2 where VD2 is the diffusion potential of reaction 2. The catalytic oxidation of carbon monoxide by oxygen on metallic oxide, is a typical example. Thus, Rideal’s hypothesis, which supposes the presence of interactions between the adsorbed oxygen and the carbon monoxide, leads to:
O2 2e 2s 2(O s ) and:
2CO2 2e 2s l 2CO 2(O s) the global reaction being:
Ox1 Re d 2 l Ox2 Re d1 and also, in the present case:
CO O2 l CO2
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Let us go back to the global system and consider separately the two reactions out of equilibrium. They are each at the origin of an electric current characterized by: i10
G ªH º E qV 1 D qV 1 qG «k exp( 1 D )>Re d1 @ k exp( 1 D )>Ox1 @» RT RT ¬ ¼
i20
G ªH º E qV 2 D qV 2 qJ «k exp( 2 D )>Re d 2 @ k exp( 1 D )>Ox2 @» RT RT ¬ ¼
If both reactions are taken into account, then the current i will represent the summation of both phenomena. However, it should be made clear that there is only one possibility for the electrical diffusion barrier potential and the profile of V=f(x). This results in the same value VM for the potential barrier as well as the Į and ȕ coefficients in both cases, so:
D
D1 D 2
E
E1 E 2
and:
VM is referred to as the mixed potential. We can now express i as i = i1 + i2, where: i1
G EqVM DqVM ªH º qG «k exp( )>Re d1 @ k exp( )>Ox1 @» RT RT ¬ ¼
i2
G EqVM DqVM ªH º qJ «k exp( )>Re d 2 @ k exp( )>Ox2 @» RT RT ¬ ¼
and:
To reach a simple expression of VM using i1 and i2, it is necessary, from a mathematical standpoint, to suppose that the forward global reaction is distinctly advanced. We will therefore only use the first term of i2 and i1 while expressing this condition:
Ox1 Re d 2 o Ox2 Re d1
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135
and: i
G EqVM DqVM ª H º q «Jk2 exp( )>Re d 2 @ Gk1 exp( )>Ox1 @» RT RT ¬ ¼
The i = 0 condition, which expresses the stationary character of the process, yields the expression for VM: G Gk >Ox @ RT ln H 1 1 q(D E ) Jk2 >Re d 2 @
VM
If we take into account the fact that Į + ȕ = 1, we obtain, for the present case:
G RT Gk1 >Ox1 @ ln( H ) q Jk2 >Re d 2 @
VM
This model applies to the catalytic oxidation of CO. It is however advisable to take into consideration the fact that, in such a case, the two reactions are not independent, and have a shared reaction intermediate that is the chemisorbed species (O s ) , whose concentration is denoted by ș. It is possible here to express the stationary character of the reaction using the reaction intermediate. Thus, we have:
>
1 d (O s) dt 2
@
V1 V2
i1 i2
0
In the present case, making the same hypotheses as before, and considering that Ȗ = į = 2, we arrive at:
VM
G k1 PO2 (1 T ) RT ln( H ) q k 2 PCOT
Note that VM depends on the concentration of the involved species, on the values of the kinetic constants and therefore on the nature of the solid.
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5.4. Bibliography 1. M. SOUSTELLE, Modélisation macroscopique des transformations physico-chimiques, Masson, Paris, 1990. 2. A. SOUCHON, Utilisation de la microcalorimétrie pour l'étude des réactions hétérogènes Application à l’oxydation du niobium par les gaz, Thesis, Grenoble, 1977. 3. M. SOUSTELLE, “La théorie des sauts élémentaires dans les réactions gaz-métal, résolution par la méthode des zones”, C.R. Acad. Sci., 270C, 2-032, 1970. 4. M. SOUSTELLE, “Etude théoriques des demi-réactions d’interfaces en cinétique hétérogène gaz-solide, I – les demi-réactions d’interface externe”, J. Chim. Phys., 67, 240, 1970. 5. M. SOUSTELLE, “Etude théoriques des demi-réactions d’interfaces en cinétique hétérogène gaz-solide, I – les demi-réactions d’interface interne”, J. Chim. Phys., 67, 1173, 1970.
Chapter 6
Apparatus for Experimental Studies: Examples of Applications
6.1. Introduction A physico-chemical approach to phenomena relating to the behavior of materials, and more specifically to that of interfaces associated with a gas detection device, demands the use of specific methods of investigation and analysis. The gaseous atmosphere is an important determining factor so it is essential to be able to conduct the investigations in the presence of a gas. Many analysis techniques for solids use methods involving radiation-matter interactions, which requires us to operate under ultra vacuum. However, this state of the art technology, including ESCA and ionization probes, is not necessarily the most appropriate to deal with this type of situation. Nowadays, however, physico-chemists do have some particularly effective tools at their disposal, which allow them to study phenomena that involve heterogenous equilibriums affecting at least one gaseous element. The purpose of this chapter is to describe and illustrate using concrete examples some methods that could supply us with relevant data, at least within the investigative field of this book. Moreover, we will see in Chapter 10 how these results can be utilized in order to model certain phenomena.
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Regarding the investigative methods specific to this type of study, there are four techniques used by the “laboratory of processes granular mediums”, which are: – calorimetry using a Tian-Calvet calorimeter; – surface potential using a vibrating capacitor apparatus; – temperature programmed desorption; – complex impedance spectrometry. 6.2. Calorimetry 6.2.1. General points As we have already mentioned, it is reasonable to believe that measuring the heat released during a physico-chemical process through time yields useful information about process kinetics. Thus, in the case of solid-gas heterogenous interactions, the calorimetric method seems to be a particularly appropriate solution. In general, if W denotes the heat released in a calorimetric cell over time, which is expressed in Joules/second, then we can assume that a fraction W1 of this amount raises the internal enclosure’s temperature, while the remainder W2 is evacuated from the internal to the external enclosure, constituting what we refer to as a thermal leak. We thus have: W
W1 W2
From a technological point of view, it is possible to distinguish three types of calorimeters: – isothermal calorimeters, in which we attempt to fulfill the condition W1 = 0. The heat flux W2 is then measured, leading to W; – adiabatic calorimeters, in which we attempt to fulfill the condition W2 = 0. The rise in temperature is proportional to W1 so measuring it leads to W; – conduction calorimeters of the Tian-Calvet kind, which constitute an intermediate solution to isothermal and adiabatic calorimeters. We will limit our interest in this book to the study of the Tian-Calvet calorimeter.
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6.2.1.1. Theoretical aspect of Tian-Calvet calorimeters1, 2 The microcalorimetric cell, which is where the process we are studying takes place, is connected to the external enclosure through a thermoelectric cell. The cell contains platinum – rhodium-coated platinum thermocouples connected in series and electrically isolated from the cell. There must be enough thermocouples to record the entire flux emitted by the internal enclosure (see Figure 6.1).
Figure 6.1. Diagrammatic representation of a flux calorimeter
We will see how it is possible to measure W1 and W2 using these thermocouples. 6.2.1.2. Seebeck effect Suppose we have a conductor chain A/B/A that is closed using a voltmeter. If the two metal junctions A/B and B/A are not at the same temperature, we note the formation of an electromotive force E that is proportional to the temperature difference 'T:
E D 'T
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Physical Chemistry of Solid-Gas Interfaces
6.2.1.3. Peltier effect If the temperature values of the same chain’s two junctions A/B and B/A are identical, and we have a current i, there is a power transfer W from one junction to the other, which results in a difference in temperature between the two junctions. 6.2.1.4. Tian equation In the case of a Tian-Calvet calorimeter, we note that the presence of a temperature difference between the internal and external enclosure will lead to the creation of an electromotive force that is proportional to this difference (Seebeck effect). Consequently, a current will flow in the thermocouples between the internal and external enclosure. There is then a thermal exchange that is proportional to i (Peltier effect). Thus, the two effects add up and the expression of the flux W2 exchanged between the internal and external enclosure is obtained:
W2
I
P(T i T e )
ș e and ș i respectively denote the temperature of the external and internal enclosure. We then only have to calibrate the current i generated by the thermocouples using a known power to obtain the value of the flux I. In this case, a percentage of the released heat W1 contributes to raising the internal enclosure’s temperature by dș during the time dt. Knowing that μ denotes the internal enclosure’s heat capacity, we have:
W1
P
dT dt
P
d ('T ) if T e = constant dt
This relation is due to the fact that Q the exchanged heat. In these circumstances, the condition W
mc'T and that W1
dQ / dt , Q being
W1 W2 obviously becomes:
Apparatus for Experimental Studies
W
P'T P
141
d ('T ) dt
This relation is referred to as the Tian equation. It allows us to relate the total energy to only one variable ș. If we assume that the signal Ȝ provided by the calorimeter is proportional to the electromotive force E, and therefore to ǻș, then the Tian equation becomes:
W
D ('O W
d ('O ) ) dt
As a result, determining W is determining Į, W and d ('O ) / dt . ǻȜ represents the change in calorimetric signal between the equilibrium and outof-equilibrium states Ȝ0 and Ȝ. As for d ( 'O ) / dt , there are two possible cases to be considered: – the process is slow enough that we can consider IJ d ( 'O ) / dt to be negligible compared to 'O , and, under such conditions, the measured flux leads to W; – the process is rapid, and we have to calculate d ( 'O ) / dt first using the slope of the recorded signal ǻȜ = f(t) at multiple points in time. As for Į and W , it is important to conduct a calibration using a known thermal power. The easiest method consists of producing an electrical Joule effect EJ inside the calorimeter’s measurement cell (see Figure 6.2). Under steady-state conditions, when the delivered power is constant, the calorimeter produces a constant signal equal to Ȝp and is therefore proportional to EJ. As a result:
D
EJ where 'O 'O
O p O0
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Physical Chemistry of Solid-Gas Interfaces
Figure 6.2. Set-up for the calibration of a calorimeter
To access the value of IJ, we have to reach steady-state conditions and record the curve obtained during the shift toward equilibrium after we achieve the condition EJ = 0. The equation of this curve is:
'O W
d ('O ) dt
0
Integration then yields:
Ln('O )
t c st
W
It is possible, using the response curve, to plot Ln(ǻȜ) according to t. The slope of the obtained line equals: 1 .
W
6.2.1.5. Description of a Tian-Calvet device Some of the devices produced by the SETARAM company make it possible to work at temperatures that reach 800°C; the thermostated calorimetric block contains two identical microcalorimetric cells set up to form a differential system (see Figure 6.3).
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143
access to the reactor cell
Figure 6.3. Section of a Tian-Calvet microcalorimeter as produced by the SETARAM company
The importance of such a set-up lies in its allowing us to avoid the effect of any possible changes in external temperature, șe being the temperature of the reference enclosure. The reactor is made up of two identical quartz tubes immersed in the two microcalorimetric cells, thus preserving the symmetry of the equipment (see Figure 6.4). At the microcalorimeter’s outlet, the tubes can be connected to the same gas pumping or gas admittance equipment.
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Physical Chemistry of Solid-Gas Interfaces
Figure 6.4. Schematic view of the gas admittance set-up
6.2.1.6. Thermogram profile We have just seen that the recorded calorimetric signal is representative of the process rate. Yet, for many processes including adsorption, the initial rate value is the highest. This value Vi = Į decreases with time to finally reach a zero value at equilibrium (see Figure 6.5, curve b, which shows the reality of the thermal process that takes place inside the cell). To express such behavior, the calorimetric signal must shift, starting from the initial instant, from a value representing a post-reaction equilibrium where V = 0 to the value corresponding to the initial rate Vi = Į, which in this case equals 40. The time W of this transient state will depend on the response time of the equipment. Concretely speaking, the signal will increase from a zero value representing the equilibrium to a maximum value VM = 20 where it will meet the real curve, b.
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145
Figure 6.5. Evolution of the calorimeter’s response to the action of an adsorbed gas
The thermogram, which is obtained using curves a and b, will therefore contain a curve that shows a maximum, as can be seen in Figure 6.5.
Figure 6.6. Evolution of the calorimeter’s response in case stationary conditions have been reached
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After the reaction has taken off, it is possible to observe other situations due especially to the existence of a stationary process. In such a case, the calorimetric signal will be constant at a value lower than or equal to the initial value. If the time duration t needed to reach the stationary state is higher than IJ, the response curve will look like curves a and c of Figure 6.6. In the opposite situation, the response curve will look like curves a and d. 6.2.1.7. Examples of applications To illustrate the importance of this technique, we will present some experimental results regarding three types of materials. These studies deal with: – interaction between oxygen and nickel oxide; – interaction between oxygen and beta-alumina associated with metals; – interaction between oxygen and tin dioxide associated with metals. 6.2.1.7.1. Study of interaction between oxygen and nickel oxide3 The conducted physico-chemical research concerning the interaction between this material and oxygen has yielded some original electrical responses to the effect of this gas. To complete these observations from a kinetic angle, these experiments were conducted again using calorimetry. – Process conditions The sample, which is in pulverulent form, is first degassed for two days under a residual pressure of 1.33x10-4 Pa at 800°C. It is then admitted into the calorimeteric cell, which is at a controlled temperature of 700°C. Having achieved thermal equilibrium, we successively insert multiple amounts of oxygen under pressures ranging from 0.133 to 300 Pa. – Experimental results Figure 6.7 perfectly illustrates the observed results. Note first that these results could very well be of a mere adsorption process. The kinetic processes become relatively fast as soon as the gas is admitted then progressively decrease until equilibrium.
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As a matter of fact, beyond 7x10-2 Pa, the results start to become more and more complex, at least when it comes to this experiment. Indeed, we note the appearance of an incipient stationary state characterized by a constant signal whose value differs from the one corresponding to the equilibrium. A point worth noting is that introducing additional oxygen has practically no effect on the calorimetric signal. Other results, presented in Figure 6.8, confirm this tendency and show that the time duration of the state we assumed to be stationary can reach three days when the oxygen pressure is 13.3 Pa. We will also note that once the equilibrium value has again been reached, the situation is similar to the initial one, and there is another peak in the device’s response after it has admitted a gas that is under a pressure of 106 Pa.
Figure 6.7. Calorimetric response of nickel oxide to the action of oxygen 8x10-3 < P < 0.4 Torr (1 Torr = 133 Pa)
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Figure 6.8. Calorimetric response of nickel oxide to the action of oxygen 0.05 < P < 1.5 Torrs (1 Torr = 133 Pa)
Such phenomena can be interpreted as a reaction mechanism, involving an adsorption step associated with the formation of cation vacancies that diffuse inwards from the oxide’s surface until the cation vacancies are uniformly distributed in the bulk. The presence of stationary conditions as they have been presented in Chapter 5 corresponds to the period of time where cation vacancies are filling up the bulk. All of these results are perfectly compatible with such kinetic laws, and especially with the pressure laws. What is more, they confirm the tendencies we have observed in the electrical results of Figures 6.9 and 6.10, that is to say the presence of a transient state, accompanied by a peak and a shift towards equilibrium under oxygen pressure lower than 13.3 Pa, the presence of a more complex state accompanied by a peak and an evolution towards a stationary state under oxygen pressure higher than 13.3 Pa.
Apparatus for Experimental Studies
Figure 6.9. Evolution of nickel oxide’s electrical conductivity as a function of time and for different oxygen injections: curve a: P = 8 Pa , curve b: P = 10.6 Pa
Figure 6.10. Evolution of nickel oxide’s electrical conductivity as a function of time after the injection of oxygen at 40 Pa (1 torr = 133 Pa)
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6.2.1.7.2. Study of interaction between oxygen and beta-alumina associated with metals4 The research conducted on the development of an electrochemical sensor made of ionic materials led to many investigations concerning beta-alumina associated with metallic elements, such as gold or platinum and used in electrodes. In order to locate and count the different oxygen species found on the surface of the materials in question, calorimetric experiments were conducted on different samples. These samples are made with beta-alumina only, beta-alumina associated with gold or platinum, with gold and with platinum. The purely metallic samples appear as foils with a surface in the order of 10 cm2, and a width of 0.1 mm. The alumina samples appear as sintered pellets made using 200 mg of alumina. We can associate alumina with metals by cathode sputtering of the metal in question. The 500 nm thick sputtering partially covers the surface of the alumina pellet. The most typical results are presented in Figures 6.11 and 6.12. Observing Figure 6.11 leads us to the conclusion that the interaction between oxygen and beta-alumina is a perfectly reversible endothermic process at temperatures between 200 and 400°C.
Figure 6.11. Corrected thermograms obtained at 300°C using beta-alumina for different changes in oxygen pressure (10 to 104 Pa)
The endothermic character of the process is a particularly interesting fact that excludes the possibility of a mere adsorption process, which is usually associated
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with an exothermic reaction. A plausible explanation of this phenomenon would be that the adsorbed oxygen has dissolved in the crystal lattice. Figure 6.12 illustrates the effect of gold and platinum on the thermograms. There is quite a significant decrease of the heat produced by oxygen in the presence of a metal, the platinum having a bigger effect than gold.
Figure 6.12. Comparison between the thermograms obtained with beta-alumina only and those obtained with alumina and gold or platinum for a change in oxygen pressure of 10 to 104 Pa
The histogram in Figure 6.13 sums up this kind of situation, leading us to the conclusion that the effects of gold or platinum are all the more visible since the working temperature is low. Moreover, it confirms the fact that the effects we observed on the beta-alumina only as the temperature varied are suggestive of an endothermic process, which is characterized by an increase in the amount of formed species, and as a result, by an increase of the matching heat quantity as temperature rises. The role played by metals can be interpreted by considering the formation of a new exothermic oxygen species whose bound amount constantly decreases while the temperature rises. The exothermic nature of this species makes it possible to explain why its contribution to the heat exchange continually decreases with temperature; the calorimetric signal corresponding to the composite material of alumina + metal then joins up with the signal corresponding to alumina alone.
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Figure 6.13. Heat exchange of the different samples, and at different temperatures, for a change in oxygen pressure of 10 to 104 Pa
6.2.1.7.3. Study of the interaction between oxygen and tin dioxide associated with metallic elements We have just seen that the presence of a metal could have direct consequences on the nature of surface chemical states for an ionic oxide. These results, which are particularly interesting when it comes to understanding the kinetic processes of gas-solid interactions, have led us to conduct similar investigations on tin dioxide. These experiments are related to those we will present in Chapter 7 and which concern the role of electrodes. Once again, we will study tin dioxide, tin dioxide associated with gold or platinum, gold and finally platinum. – Experimental protocol The experiments are conducted on tin dioxide samples that were initially sintered at 800°C under a residual oxygen pressure of 10 Pa. The samples used weighed 150 mg, and the specific surface of this material was in the order of 5 m2/g. Regarding tin dioxide associated with gold or platinum, we used 150 mg plates covered with a 450 nm-thin layer of metal that was deposited by cathode sputtering.
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Gold and platinum are used in the form of metal foils with a 2.10-2 m² surface area and a 0.1 mm width. – Results obtained with the different samples a) Tin dioxide only The interaction between tin dioxide and oxygen has been studied for three different changes in oxygen pressure ranging from 10 to 200 Pa, from 10 to 2x103 Pa, and from 10 to 5x103 Pa. These experiments were conducted in isothermal conditions at 300 and 400°C. We have plotted the thermograms we obtained at 400°C under three different oxygen pressure values in Figure 6.14. We can see that an increase in oxygen pressure yields an exothermic signal, and that the signal amplitude increases with pressure.
Figure 6.14. Thermograms obtained with a tin dioxide sample at a temperature of 400°C and for different changes in oxygen pressure (10 to 5x103 Pa)
We can also see that the process is relatively fast and that its time duration, which is in the order of 300 seconds, does not seem to be affected much by the admitted amount of oxygen. The reverse process, which is much slower but perfectly reversible, has a duration in the order of 30 minutes.
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These results perfectly fit those of an adsorption process. b) Pure metals Unlike the previous results, those obtained with gold or platinum-only metal foils have not shown any sign of heat exchange during the multiple gas injections, at least not with the experimental conditions and sensitivity ranges used for the tin dioxide samples. c) Gold or platinum-covered tin dioxide The effects of gold or platinum, which are presented in Figure 6.15, result in a noticeable increase of the emitted heat, platinum having a bigger effect than gold.
Figure 6.15. Thermograms obtained with the different types of samples at a temperature of 400°C and for changes in oxygen pressure of 5x103 Pa
The influence of oxygen pressure confirms this tendency, as can be seen in Figure 6.16
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Figure 6.16. Heat exchange (-Q in mJ) with the different types of samples for changes in oxygen pressure ranging from 10 to 5x103 Pa, at 400°C
It is tempting to take into consideration the results we obtained using pure metals and come to the conclusion that oxygen is more reactive towards tin dioxide associated with metals because of a synergic effect between metal and oxide. In order to eliminate the exclusive action of metal, complementary experiments were conducted using equal metal surface areas in both cases, that is to say for pure metals and also for metal associated with tin dioxide. In the second case, it comes down to sputtering the metal on a 1 mm x 10 mm surface; the metal then appears as a line. If we take into account the sintered material’s specific surface area, we obtain a surface area of approximately the same magnitude as the metal-only sample, that is to say 2 dm2. Figure 6.17 clearly confirms the influence of the oxide-supported metal even when the oxide and metal are present in equal amounts. Indeed, just as we expected, the interaction between oxygen and tin dioxide results, using an exothermic process, in the formation of at least one chemisorbed oxygen species on the surface of the oxide.
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Figure 6.17. Thermograms obtained with the different types of samples at a temperature of 400°C and for changes in oxygen pressure of 20 Pa
In order to interpret the role of deposited metal, we can imagine the creation of a new chemisorbed oxygen species of exothermic nature but whose formation enthalpy is higher in absolute value than the other species. This hypothesis could be correlated to the fact that the oxide-metal interface can induce the creation of new adsorption sites with higher energy than that of tin dioxide. 6.3. Thermodesorption 6.3.1. Introduction This technique, which is based on the exothermic nature of adsorption, allows us, by using a programmed temperature increase, to analyze the chemical species initially bound to the surface of a solid and which are desorbed under the influence of temperature. Detecting and/or analyzing desorbed molecules is possible with the use of different detectors, such as thermistors, or analyzers, such as chromatography or mass spectrometry. This analysis could also be conducted by maintaining the sample under a dynamic vacuum or inert gas vector flow.
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The choice of a detector depends most often on the nature and the quality of the expected information: – thermistors provide only quantitative information, without specifying the nature of bound species; – chromatography provides quantitative as well as qualitative information, but in a discontinuous way; – mass spectrometry provides continuous quantitative and qualitative information using samples that are, usually, maintained under a dynamic vacuum of 10-4 Pa. These devices are designed to analyze charged species obtained after the desorbed element is ionized. The gathered information is therefore characterized by a m/e ratio where m is the mass of the element chosen by the experimenter and charge e is identified with the ionicity degree of the element in question. Some elements can thus appear with different ionicity degrees. The experimental results presented in this chapter were all obtained through mass spectrometry. The equipment we used consisted of 5 (see Figure 6.18): – a heating reactor made up of a laboratory tube and a programmed temperature furnace which reaches a temperature of 900ºC; – a mass spectrometer chosen based on its performances and the nature of species to be detected. The information delivered by this analyzer is representative of an ionized material flux marked by the m/e ratio. Through a continuous scan adapted to the m/e ratio, we will be able to monitor all of the masses, or even continually monitor one or multiple m/e ratios that the experimenter will have had to provide; – two turbomolecular pumps capable of creating a separate residual atmosphere. Note that turbomolecular pumps maintain atmospheres with no trace of oil in them, which averts hydrocarbon pollution. The first vacuum pump controls the gaseous atmosphere of the reactor, and allows us to degass the solid sample beforehand at a moderate temperature. The second pump controls the residual pressure in the mass spectrometer. 6.3.2. Theoretical aspect 6, 7 We have just seen that the information delivered by the mass spectrometer is representative of a material flux and therefore, in this case, of a desorption rate.
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We have seen, however, that a desorption process can be considered an elementary step:
n( X s ) X n ns [X] represents the concentration of the species X - s in its adsorbed state, and n is its stoichiometric coefficient.
Figure 6.18. Diagrammatic representation of a thermodesorption set-up associated with a mass spectrometer
The rate Vd is therefore:
Vd
H Ed d >X @ )>X @ n k d exp( dt RT
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Given the temperature and pressure range of study, we will assume that the adsorption component Va is negligible compared to Vd. Thus, concerning the monoatomic adsorbed oxygen, we will have:
2(O s ) O2 2 s where n = 2 X also being a function of temperature T, the changes in desorption rate can be expressed as:
dVd dT
H H H E Ed Ed dX 2 )>X @ 2kd exp( )>X @ k exp( 2 d RT RT RT dT
It is possible, using this relation, to prove that the rate reaches a maximum value that corresponds with the temperature. To do so, we will choose a variation law for temperature as a function of time:
T
T0 at
a being the heating rate. It follows that:
dVd dT
dVd dt dt dT
1 dVd a dt
The maximum rate VdM is obtained using the equation:
dVd dT
0
This maximum rate will therefore correspond to a temperature value T = TM and a concentration value [X] = [XM]. We will thus have:
H E >x@ RT 2
2 Vd a M
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Therefore:
H E RTM2
H 2H E )> X M @ k0 exp( a RTM
We can also demonstrate, using some mathematical approximations, that when n = 2:
>X M @ >X 0 @ 2
The previous expression can be written a different way:
a Ln 2 TM
H H E E Ln H Ln> X 0 @ RTM Rk0
Determining the system’s parameters, and especially the activation energy requires an analysis of multiple spectra obtained with different heating rates. This
procedure 2 M
Ln(a / T )
easily
leads
us
to
the
value
of
H E
by
H E,
plotting
f (1 / TM ) . A specific temperature value TM indeed corresponds to
each value of a. The slope of the obtained line equals
L E/R.
In fact, observing noticeable variations of the rate curve as temperature changes requires there to be very high variations of the heating rate. Ratios of the order of 100 are sometimes necessary, which can pose some technological problems. On a purely qualitative level, this procedure is not necessary. We can then analyze two types of spectra: – those obtained through a scan of the m/e ratio. Such spectra make it possible for us to quickly analyze the nature of present species; – those obtained using a chosen value of the m/e ratio. Since they are more precise, such spectra allow us, if need be, to better describe the species, particularly when it comes to their binding energy to the solid. It is important to note that depending on the diversity of adsorption sites and/or
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temperature, a species of a given chemical nature can be differently adsorbed; each possibility being characterized by the value of its binding energy to the solid. Thus, a mere perusal of the spectra obtained using the same sample but different values of the m/e ratio will lead us, on the one hand, to information of a chemical nature and, on the other, to information concerning energy; both with regards to the entire set of adsorbed species on the solid’s surface. Based on a few experimental results, we will show the importance of this technique in solving the problems regarding the analysis of surface chemical states. 6.3.3. Display of results These are experimental results from, on the one hand, a study on tin dioxide and, on the other, a study on nickel oxide. These two materials are studied here under different oxygen pressure values and either have or have not been subjected to some gaseous treatments. 6.3.3.1. Tin dioxide8 Particularly used as the sensitive element in gas sensors, this material has been the subject of a large number of investigations in the thermodesorption field. This presentation will focus more specifically on the effect the presence of adsorbed sulfur dioxide has on the binding energies of the hydroxyl groups present on the tin oxide’s surface. The experiments were conducted on two types of sintered samples. These two samples differ from one another in respect of a sulfur dioxide gaseous treatment that was conducted upon one, but not the others, at 500°C for 15 minutes. Generally, the surface of a material that has not been subjected to a sulfur dioxide treatment is rich in hydroxyl groups, and the thermodesorption spectrum presented in Figure 6.19 is typical of this kind of situation. The desorption of these species, which is marked by the ratio value m/e = 18, takes place over a temperature ranging from 100 to 800°C, with a very noticeable peak around 550°C. There are also three slight bumps located at 180, 380 and 750°C. Figure 6.19 also indicates an oxygen spectrum characterized by m/e = 32. Weak traces of carbon monoxide and carbon dioxide were also detected but are not presented in this diagram.
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We note a profound change in the water spectrum of the sample that was subjected to a sulfur dioxide treatment (see Figure 6.20). We observe, indeed, that the peak at 550°C has practically disappeared, contrary to the peak corresponding to 180°C. We also note that there are, at high temperatures, new species marked by the ratio value m/e = 48.
Figure 6.19. Thermodesorption spectrum of the hydroxyl groups (m/e = 18) and oxygen (m/e = 32) bound to tin dioxide prior to treatment
These species are characterized by a sharp thermodesorption peak located between 700 and 800°C. This peak is very clearly associated with a simultaneous oxygen desorption. The signal corresponding to m/e = 48, which can be attributed to the SO+ ion, expresses the presence of a sulfur compound that is surely different from sulfur dioxide. This is based on the fact that the ratio of the m/e = 32 and m/e = 48 is about 2 in the present case, while it is around 0.4 when it comes to sulfur dioxide. The value of 0.4 was determined during the calibration of the mass spectrometer.
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Figure 6.20. Thermodesorption spectrum of the hydroxyl groups (m/e = 18) and oxygen (m/e = 32) bound to tin dioxide after the sulfur dioxide treatment
The sulfur compound present on the tin dioxide’s surface could be SO or SO3. These results therefore seem to indicate that sulfur dioxide reacts with tin dioxide and produces a relatively stable species that is only desorbed once high temperatures are reached. This species, which causes the changes we observed on the spectrum marked by m/e =18, could therefore compete with hydroxyl groups by occupying sites that were initially occupied by the hydroxyl groups, which would be forced to occupy sites of lower energy. 6.3.3.2. Nickel oxide9 It was deemed necessary, in a study on the evolution of the electrical behavior of this material in the presence of gases, and particularly in the presence of sulfur dioxide, to better analyze and control its chemical surface states under different temperature and oxygen pressure conditions. The samples studied were in pulverulent form and weighed 1 g. The heating rate was 14°C/min.
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A preliminary analysis (see Figure 6.21) leads to the observation that there is large water desorption at 180 and 470°C. The two peaks probably express a dehydration followed by a dehydroxylation of the oxide. The m/e = 48 ratio value corresponds to the carbon dioxide, which is desorbed at 180, 410 and 610°C. Desorption of oxygen leads to a much more intense and complex spectrum. It reaches its maximum at 520°C, and also presents many oscillations that show the presence of multiple adsorbed species with different energies.
Figure 6.21. Thermodesorption spectrum of nickel oxide sinters exposed to air
To better grasp and characterize these different species, we adopted a protocol that consisted of controlling the temperature TA that corresponds to oxygen admittance on a perfectly degassed sample. It is reasonable to think that the concentration of each adsorbed species, which is related to its adsorption or desorption rate, is a function of temperature and oxygen treatment time. – Influence of temperature and adsorption time From a practical standpoint, the sample that is degassed for one night at 750°C is subjected to 100 Pa pressure oxygen at the temperature TA and for a time t. After that, the sample is quickly cooled, then degassed at degassing temperature TD.
10-3 Pa for an hour at the
The effects of introducing the gas at the temperature TA are shown in Figure 6.22 for four different temperature values, with an oxygen exposure time t of one hour and a degassing temperature of 20°C.
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These results perfectly display the considerable evolution of the oxygen’s energy state depending on the adsorption temperature. Moreover, they allow us to observe the evolution of multiple coexisting species according to temperature.
Figure 6.22. Oxygen thermodesorption spectrum as a function of adsorption temperature TA
Figure 6.23 presents the results obtained with a sample that was exposed to oxygen at 500°C, and for a time duration of 1, 15 and 60 minutes. This particularly interesting spectrum shows that, in this case, the oxygen exposure time causes the disappearance of a species, marked by a peak at 400°C, apparently to the benefit of the species corresponding to the peak located around 500°C.
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Figure 6.23. Oxygen thermodesorption spectrum as a function of adsorption time
Using these results, which show how complex this oxide’s surface chemical states are, six different oxygen species were identified and marked by the temperature of their desorption peak TM (see Table 6.1). Adsorbed species
01
02
03
04
05
06
TM(ºC)
320
410
520
640
740
860
Table 6.1. Desorption temperature of the different species
It is possible, by identifying each desorption curve with a Gaussian curve, to “decompose” each spectrum and evaluate the effect of each species as a function of time and temperature of adsorption TA. Figures 6.24 and 6.25 give two examples of the “decomposition” of spectra, each corresponding to a different adsorption temperature: TA= 750 and 400°C, and with respective exposure times of 30 seconds and 15 minutes.
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Figure 6.24. “Decomposition” example where the adsorption temperature is 750°C
Figure 6.25. “Decomposition” example where the adsorption temperature is 400°C
Figures 6.26 and 6.27 give the evolution model of species “320” and “410” for different adsorption temperature values; we will note that species “300” is still present when the sample is exposed to oxygen at 750°C. – Influence of desorption temperature It is possible, based on the previously obtained results, to prepare various samples characterized by the number of species on their surface by choosing the right values for the desorption temperature TD. The method consists of successively eliminating some species by desorption, starting with the most weakly bound ones.
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Figure 6.26. Amount of chemisorbed oxygen in the “320°C” form: adsorption kinetics as a function of TA
Figure 6.27. Amount of chemisorbed oxygen in the “410°C” form: adsorption kinetics as a function of TA
Figure 6.28 gives the thermodesorption spectrum of four samples that were degassed at 250, 400, 500 and 600°C. These samples had initially been exposed to oxygen at 600°C.
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Figure 6.28. Thermodesorption spectrum of oxygen obtained with nickel oxide at 600°C and degassing at different temperatures TD
Table 6.2 sums up the surface states specific to each sample that is referred to by a number from 1 to 5. sample
TD
species bounded at the surface
1
250
06 + 05 + 04 + 03 + 02
2
400
06 + 05 + 04
3
500
06 + 05
4
600
06
5
750
no adsorbed species
Table 6.2. Evolution of the nature of adsorbed species as a function of desorption temperature
– Reactivity to sulfur dioxide In order to better interpret nickel oxide’s reaction to sulfur dioxide, it might be interesting to consider this problem from the angle of the selective contribution of one or multiple oxygen species. Selecting 5 different sample types enables us to
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conduct a certain number of tests. Each sample is subjected to the action of pure sulfur dioxide at 250°C and is then analyzed by thermodesorption. The spectra retained are those corresponding to the ratio values m/e = 32 and 48. Regarding samples 2 to 5, the spectrum in Figure 6.29 shows simple desorption of sulfur dioxide, the mass ratio keeping a constant value of 0.4. The interaction between nickel oxide and sulfur dioxide therefore comes down to a simple adsorption process. The results we obtained for sample 1 (see Figure 6.30) are much more interesting if we consider the appearance of new species on the spectrum beyond 600°C. In such a case, the signal ratio is no longer constant, and its value greatly exceeds 1. This leads to the idea that a species that is much more stable than adsorbed sulfur dioxide is present on the nickel oxide’s surface, and that this species, which is present in sample 1 only, is a result of the interaction between sulfur dioxide and the oxygen species that is most weakly bound to the solid.
Figure 6.29. Thermodesorption spectrum obtained with nickel oxide after sulfur dioxide adsorption at 250°C: samples 2 to 5
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Figure 6.30. Thermodesorption spectrum obtained with nickel oxide after sulfur dioxide adsorption at 250°C: sample 1
.
.
.
Figure 6.31. Heat exchange during adsorption of sulfur dioxide at 250°C as a function of its pressure and for different nickel oxide pretreatments
In addition, this difference of behavior was brought forth by calorimetric experiments conducted at 250°C (see Figure 6.31). The results show that the heat of reaction between oxygen and nickel oxide is distinctly higher for sample 1. This confirms the fact that sample 1 has a much greater reaction to sulfur dioxide.
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6.4. Vibrating capacitor methods As we have already mentioned with regard to adsorption processes, the formation of new surface states, such as atomic rearrangements or the presence of chemisorbed gaseous species, influences the equilibrium states of this same surface. These surface states generally lead to the creation of a potential barrier VS at the surface of the material. This potential can vary according to experimental conditions, particularly the partial pressure of the gases present in the gaseous environment. There are various experimental methods that can lead us to the value of VS. Physico-chemists consider the vibrating capacitor method to be one of the most efficient because it allows us to work under gas and at different temperature. In general, this method allows us to measure the work function of a solid or its variations simply by measuring the contact potential between the concerned solid and a reference solid. 6.4.1. Contact potential difference10 Suppose we have two solids R and S characterized by their respective ~ and P ~ (see Figure 6.32a) and that when thermal electrochemical potentials P R S equilibrium is reached – considered separately in each phase – we have:
P~R ! P~S If the ends of these two solids are electrically connected, the system approaches a state of thermodynamic equilibrium whereby electrons in both solids will have the same electrochemical potential, thus:
P~R
P~S
It is possible to demonstrate that the shift of the system towards equilibrium generates an electron flux from the solid with the highest electrochemical potential towards the other solid. This electron transfer comes with the appearance of a negative charge on the solid S, and a positive one on the solid R, revealing a difference in potential between two solids.
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The difference in potential between two points M and P on the surface of solids R and S is referred to as the Volta potential difference or the contact potential difference; it is expressed using the relation:
VRS
VeR VeS
where VeR and VeS represent the electrostatic potential of electrons on the nearsurface layer of solids R and S. Figure 6.32b represents the energy diagram of the two solids R and S at thermodynamic equilibrium. According to the definition of the electronic work function (see Chapter 4), the electrostatic potentials VEr and VeS are expressed the following way:
VeR
1 (IR ~ ȝR ) q
Figure 6.32. Energy diagram of solids R and S
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and:
VeS
1 (IS ~ ȝS ) q
which yields the following expression for the contact potential difference:
VRS
VeR VeS
1 IR IS q
The contact potential difference between two solids R and S equals the difference between their work functions multiplied by 1 / q . Depending on each case, measuring the contact potential difference can yield either the absolute value of the work function or the work function changes of a solid: – if solid R’s work function has been precisely determined using another method, we can deduce the value of the work function IS of solid S using the contact potential difference VRS between R and S:
IS
qVRS IR
– if the work function of one of the two solids, say solid R, is stable under the chosen experimental conditions, then we have:
IR
0
As a result, the changes ') S in work function of the solid S equal those of the contact potential difference multiplied by the factor q:
'IS
qVRS
In the particular case of a metal semiconductor system, whose energy diagram is given in Figure 6.33, the contact potential difference is obtained using the relation:
VRS
IS I R q
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where:
IS
F H V q(VS VD )
(see Chapter 4, equation [4.15])
As a result:
VRS
F HV q VS VD IR q
We have already seen that the only parameter of a semiconductor that can vary during the adsorption of gases on its surface is the surface barrier VS and the dipole component VD; therefore, choosing a metal R whose work function IR is constant under the working conditions leads to:
'VRS
(VS VD )
Figure 6.33. Energy diagram of a metal semiconductor system
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6.4.2. Working principle of the vibrating capacitor method11, 12 6.4.2.1. Introduction In this method, solids R and S constitute the electrodes of a capacitor whose capacitance will be denoted by C. When the two electrodes are electrically connected through a resistance R, the capacitor charges up with the potential difference VRS, which is the contact potential difference between the two solids. We will denote it by VDPC throughout this chapter. Under such conditions, the electrical charge Q carried by the capacitor’s electrodes equals:
Q CVDPC The principle method, owed to Kelvin, consists of distancing one of the capacitor’s electrodes from the other; the subsequent change in capacitance ǻC leads to a change in carried charge ǻQ while the electrode is moving:
'Q VDPC 'C If an opposite direct voltage is added to the circuit and fixed at a value U0 so that distancing the electrodes will no longer create a charge variation, then we are allowed to say that U0 has the algebraic value of the opposite of the contact potential difference VDPC. The vibrating capacitor method known as the Kelvin-Zisman method was developed by Zisman based on the previous method. Instead of simply distancing the electrodes from each other, Zisman periodically vibrates an electrode, thus creating an alternating current that is easier to detect. 6.4.2.2. Theoretical study of the vibrating capacitor method Suppose we have a plane capacitor, whose section area is denoted by S and whose electrodes are l0 apart from each other and made of solids R and S. Its capacitance C0 is:
C0
H 0H
S l0
İ represents the dielectric constant of the medium between the two electrodes.
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When an electrode is moved according to a sinusoidal law of amplitude l1 and (mechanical) pulsation Z, the distance between electrodes l varies as a function of time according to:
l
l0 l1 sin Zt
Inserting the modulation amplitude m
l
l1 / l0 leads to:
l0 (1 m sin Zt )
Under such conditions, the capacitor’s capacitance C equals:
C
H 0HS
l0 1 m sin Zt
At low modulation amplitudes, that is to say when m << 1, we will assume the following expression for C:
C C 0 (1 m sin Zt ) Figure 6.34 presents the working principle of the vibrating capacitor method; U is an opposite electromotive force that is inserted in the measurement circuit, VDPC is the change in contact potential between the solid that forms the electrodes of capacitor C (previously denoted by VRS), and R is an electrical resistance. The current i generated by the vibrating capacitor is:
i
dQ dt
d VDPC U Ri C dt
Hence:
i
VDPC U Ri ZC0 m cos Zt RC
di dt
When m << 1, an approximate solution of this equation is:
i
VDPC U mZC0 cos Zt 4 1 Z 2 R 2C02
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The experimental conditions are such that: Ȧ R C0 << 1, so the expression for the current i is simply:
i
VDPC U mZC0 cos Zt 4
Figure 6.34. Set-up diagram for the Kelvin method
The vibrating capacitor method is a zero-determining method, where measuring the contact potential difference VDPC amounts to measuring the opposite voltage U that leads to a zero current. Compared to other methods, this one has some interesting characteristics which we will develop throughout this study.
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6.4.3. Advantages of using the vibrating capacitor technique The vibrating capacitor method, or Kelvin-Zisman method, is a non-destructive method that does not disturb the surface using photon or electron beams. It can be used for a large number of materials, and in a wide temperature and pressure range. It is therefore highly appropriate for the study of surface properties of polycrystalline metal oxides. 6.4.3.1. The materials studied Although the Kelvin method is generally used by some authors to study the electronic work function of monocrystals, it is also appropriate for studying metallic or non-metallic polycrystalline materials. In the case of a heterogenous surface of polycrystalline materials, the work function of the grains depends on their crystal orientation: it has been demonstrated that the work function measurements obtained by the Kelvin method led to the mean value I of the work function values Ii of each grain i:
I where: f i
6 i f iIi Si / ¦ iSi : Si: grain surface area.
6.4.3.2. Temperature conditions Such a method does not require high working temperatures, making it possible to avoid thermodesorption processes. It also enables us to conduct measurements over a wide range of temperatures. Some authors have chosen to work at very low temperatures, while others have used the Kelvin method at a temperature of a few hundred degrees in the framework of studies on catalysts. If the system is no longer isothermal, it is possible to demonstrate that the experimentally measured potential difference is the contact potential difference added to the electromotive force of thermoelectric origin. Figure 6.35 gives a diagrammatic representation of the system when its components are not at the same temperature.
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Figure 6.35. Diagrammatic representation of the system’s multiple parts
We successively have: – the surface of the reference solid R. Its thermoelectric power is Į, and it is at the temperature T1; – the junction between the reference solid and the connecting metal conductor at the temperature T2; – the connecting metal conductor whose thermoelectric power is Į’; – the junction between the connecting metal and the solid S, which is studied at the temperature T3; – the surface of the semiconductor solid being studied, whose thermoelectric power is Į”, and which is at the temperature T4. The electromotive force E of thermoelectric origin equals:
E D (T1 T2 ) D ' (T2 T3 ) D '' (T3 T4 ) If the thermal gradient at the electrodes is weak, which is usually the case, the terms Į(T1 T2 ) and Į (T3 T4 ) are negligible. Moreover, since the conductor ''
connecting the two solids R and S is metallic, its thermoelectric power Į’ is weak and the term Į ' (T2 T3 ) is small. This electromotive force, for systems at a temperature lower than 360°C, was estimated at a few mV by J.P. Beaufils.
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Because we are only interested in the variations of the work functions, and since the electromotive force of thermoelectric origin is stable when the temperature conditions are also stable, the problem concerning its influence on the “contact potential difference” information becomes irrelevant. 6.4.3.3. Pressure conditions The vibrating capacitor method does not require high vacuums; it measures work function values over a wide range of pressures and in various atmosphere types. The method can be used to evaluate the work function of some solids in ultravacuum as well as monitor solid-gas reactions under pressure lower than or equal to atmospheric pressure. This method is recommended for monitoring surfaces under gaseous atmospheres and static pressures, or under gas flow. 6.4.4. The constraints 6.4.4.1. The reference electrode The Kelvin-Zisman method makes it possible to monitor the variations in a sample’s work function, provided the reference electrode’s work function is stable under the chosen experimental conditions. It is therefore important to choose the right reference electrode depending on the gas atmosphere and the temperature. The materials most commonly employed as a reference are metals, metal oxides, glasscoated metals and graphite. Metals, especially noble metals, have the advantage of being able to support treatments at high temperatures. Tungsten is a good reference in a vacuum, but it cannot be used in the presence of a gas. Noble metals are therefore often used under gaseous conditions, either because they do not react with gases, or because they produce a stable compound. The latter case mostly concerns platinum and gold, which can be used as a reference at temperatures reaching 400°C and under oxygen if they have been subjected to oxygen treatment at 400°C. Regarding glass-coated metals, recall the example of molybdenum, which is a stable reference under a hydrocarbon-air mix at temperatures below 300°C. Lastly, metal oxides are a suitable choice at very low temperatures.
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6.4.4.2. Capacitance modulation Although periodically modifying the permittivity of the dielectric located between the two electrodes allows us to vary the capacitance, most studies prefer to modify capacitance geometrically by distancing one of the capacitor’s electrodes from the other. A change in the surface area of the capacitor can be caused by moving one electrode sideways from the other. This is used in systems with electrodes in rotational or pendular motion. The most commonly used principle for geometrically modifying the capacitance is to change the distance between electrodes. To do so, Zisman used a vibrating electrode jointed with a metal rod whose end is moved mechanically. In fact, most systems used are of the electromagnetic type. The vibrating electrode is either joined to the coil of a speaker powered by an alternating current, or bound to a metal rod that vibrates because of a piezoceramic electromagnet. The vibrating electrode is generally also the reference electrode. 6.4.5. Display of experimental results Most of the devices used by laboratories are home-made. The results we present in this book have been obtained using two types of equipment. The first was made by the laboratory of processes in granular mediums at the Ecole des Mines de Saint Etienne13 and uses piezoelectric ceramics (see Figure 6.36). The upside of this device is its small size at the measurement level; it is therefore very sensitive when it comes to adjusting the settings and reproducing the electrode positioning. This device (see Figure 6.37) has been used to study the interaction between oxygen and tin dioxide. The reference electrode is made of gold and was treated at 400°C. The second device was made by the “University of Lille catalysis laboratory” and uses a speaker membrane as a vibrating element. The reference electrode is a graphite disk. This device has been used to study the interaction between oxygen and beta-alumina (see Figure 6.38).
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Figure 6.36. Diagrammatic representation of a Kelvin probe
Figure 6.37. Diagrammatic representation of a device using a ceramic material as a vibrating element
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Figure 6.38. Diagrammatic representation of a device using a speaker membrane as a vibrating element
6.4.5.1. Study of interactions between oxygen and tin dioxide The most meaningful results were obtained using mechanically sintered tin oxide samples which were thermally treated at 500°C. The electrical contact is a back-side contact – relative to the sintered pellet – and it is made of gold paste. The results we have obtained at 340°C under oxygen pressure values ranging from 1.33 to 2 Pa can be found in Figure 6.39. They are typical of this type of material. The response curves show a peak whose amplitude and time duration depend on the pressure of the oxygen introduced. An evolution such as this one is typical of complex kinetic processes. This one can be attributed to the adsorption-diffusion of the oxygen species in the material. To explain these results along the entire curve, it is necessary to rigorously deal with this kinetic system by eliminating any simplifying hypotheses, particularly that of stationary conditions.
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Detailed calculations can be found in J.P. Couput’s thesis13.
Figure 6.39. Work function evolution of SnO2 at 380°C: a) after the introduction of oxygen under 0.133 Pa, b) after the introduction of oxygen under 0.6 Pa
These results confirm the complexity of the surface phenomena involved during such interactions, and therefore also confirms that some of the gas sensors use such materials. 6.4.5.2. Study of interactions between oxygen and beta-alumina The goal of this study is to validate the calorimetric results obtained using this same material, namely the existence of two different oxygen species on the surface, one being endothermic and the other being exothermic. In order to achieve this, our study exclusively considers the case of beta-alumina only and that of beta-alumina associated with gold or platinum. The samples here are in pulverulent form. The metal coating was realized by cathode sputtering (200 Å) of the metal on the powder. After the deposit, it appears that powder grains are only partially covered with metal. These experiments were conducted under oxygen pressure ranging from 5x103 to 4x104 Pa, and at temperatures between 50 and 400°C.
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– Beta-alumina only While conducting the required measurements, we did not note any surface potential change on the beta-alumina, whatever the pressure and temperature conditions. This total absence of information leads us to the idea that the endothermic oxygen species we have observed in calorimetry, if it is under the same experimental conditions, stays electrically neutral upon contact with the material. Thus, the hypotheses we have previously made concerning either the existence of a physisorbed species or the dissolution of the gas in the material seem perfectly reasonable. – Gold-covered beta-alumina The study of this type of sample showed large variation in surface potential when experimental conditions altered. The results in Figure 6.40 show an increase in surface potential value when the oxygen pressure rises. This logarithmic evolution is visible for experiments performed at 300 and 400°C. – Platinum-covered beta-alumina The results, which can be found in Figure 6.41, are relatively similar to those of gold-covered beta-alumina: once again, the surface potential increases with oxygen pressure. However, in this case the change in surface potential is slightly higher than for the gold-covered sample. This observation seems to confirm that platinum’s affinity for oxygen is higher than gold’s.
Figure 6.40. Evolution of surface potential as a function of oxygen pressure (1mbar = 100 Pa): beta-alumina – gold structure
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Figure 6.41. Evolution of surface potential as a function of oxygen pressure (1 mbar = 100 Pa): beta-alumina – platinum structure
Thus, the results we obtained using gold or platinum once again confirm the formation of an additional charged species that induced the surface electrical effects. Moreover, such experiments confirm the importance of this technique in the study of surface phenomena in physico-chemistry. 6.5. Electrical interface characterization 6.5.1. General points The electrical characteristics of heterogenous interfaces renders them very good candidates to be used in gas sensor applications. Indeed, we often find that the electrical or electrochemical nature of the data supplied by such sensors depends on the nature and intensity of the processes taking place at the interfaces of the device. There are usually three types of electrically active interfaces on each device (see Figure 6.42). They are as follows. – Metal-sensitive element interfaces The presence of a metal on the sensor’s sensitive element is usually simply related to the presence of electrodes, which guarantee the electrical continuity of the data-recording system. These electrodes, however, do have an active role in the setup, although their physico-chemical role is not always clear.
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In some cases, the metals are scattered in the sensitive material, especially near its surface. This situation increases their catalytic role in some possible reactions with the sensitive element. – Intergranular interfaces We know that most of the materials used to develop gas sensors appear as an assembly of grains. This assembly is characterized by the presence of grain boundaries ensuring the cohesion and electrical continuity of the material. These grain boundaries result in as many interfaces, and therefore potential barriers in the electrical circuit. The latter will be characterized by a number of resistive and/or capacitive elements. – Solid-gas interfaces As we have already seen, the presence of chemisorbed gases can either generate new potential barriers upon contact with the concerned solids, or modify the intensity of the ones already existing at the solid-metal or intergranular interfaces. Thus, it is important, whatever the case, to have the means to assess and quantify effects of these interfaces on the sensor recorded data. We will distinguish, throughout this study, between a semiconductor and ionsensitive materials.
Figure 6.42. Diagram representing the electrical behavior of a ceramic material associated with two electrodes
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6.5.2. Direct-current measurement This method consists of measuring the electrical current generated in the material when we position potential differences at its terminals. In the case of electronic conductors, this technique is perfect for determining resistance values; here, the direct current flowing through the material is constant over time. If the electrolyte is solid, the results will mostly depend on the nature and quality of the electrodes we are using. Indeed, an electric field will cause the mobile ions in the solid to shift towards the anode or the cathode, depending on the nature of the charge they are carrying. When they arrive at the electrode, there are two possibilities to be considered: 1) First, we can assume that there will be no possible ionic or electronic charge transfer between the material in question and the electrode or the surrounding medium. In that case, we see the charges accumulate near the electrode, which induces a capacitive effect that tends to block any charge flow in the electrical circuit. A constant electrical potential then generates an electrical current that decreases exponentially with time. Reciprocally, if we short-circuit the initially charged electrodes, a reverse current appears and decreases until equilibrium is reached. In the case of ideally polarizable electrodes, the charge and discharge currents must correspond to the same amount of carried charge. This is an ideal situation that is difficult to verify in reality. Indeed, it would be necessary to estimate the amount in question. As can be seen in Figure 6.43, this operation might be relatively easy during the charge, but that is not the case during discharge, which takes a very long time before the system reaches equilibrium. As a result, it is difficult for the experimenter to correctly determine the end of the process, and therefore the involved charge amount. Furthermore, the process is not always purely capacitive. During polarization, there can also be irreversible electrochemical reactions at the electrodes. This will depend on the nature of the materials we are using and the value of the applied potential.
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2) The solid electrolyte’s charge carrying ions can fully react with the electrode or the environment of the material. There is no longer any charge accumulation, and we are therefore back to a situation where the measured current keeps a constant value over time. The electrodes are then defined as non-polarizable.
Figure 6.43. Evolution of the current flowing through the material over time during the polarization of a device made up of two metal electrodes on a solid electrolyte (300 mV)
It is conceivable that direct-current measurement, which is a perfectly valid method for solid electrolytes associated with non-polarizable electrodes, would only allow us to access qualitative information if the electrode is ideally or partially polarizable. Furthermore, as we have already mentioned, this method can induce irreversible parasitic reactions for ionic materials, which is unacceptable. To overcome these problems and be able to specify whether the electrodes are polarizable or not, we will use another characterization technique which involves measuring the alternating current.
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6.5.3. Alternating-current measurement14 6.5.3.1. General points The use of an alternating current will let us avoid the problems we had to face with a direct current. In order to avoid those inconveniences, we will have to work at high frequencies, which is to say at a few Hertz. Working with high frequencies will also make it possible for us to characterize the resistive and capacitive behavior of the set up we are studying. This technique, called impedance spectroscopy, has found wide application in electrochemistry of liquids and was later adapted to the study of solids by J.E. Bauerle. 6.5.3.2. Principle of the impedance spectroscopy technique15, 16 This technique consists of working with an alternating current I = I0 exp. i(Zt+M) produced by the presence of a sinusoidal voltage U of pulsation Z. This sinusoidal current sustains a phase shift M in the material because of the present capacitive elements. The impedance Z (Z ) Z 0 exp( iM ) is therefore defined as the ratio I/U, so it is a complex number with a real part Re(Z) and an imaginary part Im(Z), thus:
Z (Z )
Re ( Z ) iI m ( Z )
We will use, during the following applications, a Cartesian representation of Z in the complex plane (real part as x-coordinate, imaginary part as y-coordinate). This representation is also called the Nyquist representation. In the case of materials made up of sintered and electrically conductive powders, we will distinguish charge carrier movement in the solid from movement at grain boundaries. The former is considered to be a purely resistive phenomenon while the latter is viewed as a resistive-capacitive system (see Figure 6.44).
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Figure 6.44. Illustration of interface phenomena modeled using electrical circuits (left-side). Nyquist representation
Thus, in general: – low frequencies are essentially representative of capacitive phenomena that could take place at the electrodes; – moderate frequencies are essentially representative of capacitive and resistive phenomena that could take place at the grain boundaries; – high frequencies are essentially representative of resistive phenomena that could take place in the solid: intragranular phenomenon. In order to illustrate and simulate such behavior, we can build and calculate the parameters of an electrical circuit made up of two resistances R and r, and a capacitance C (see Figure 6.44). To approach the conditions that characterize a sintered material, we connect R and C in parallel, while r and the RC circuit are connected in series; the impedance of the circuit is calculated in the following way:
1 Z //
1 ZC R i
Z tot
r Z //
and:
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We therefore have:
Z (Z )
§ · § RZW · R ¨¨ r ¸ i¨¨ ¸ 2 ¸ 2 ¸ © 1 (ZW ) ¹ © 1 (ZW ) ¹
Re( Z ) i Im(Z)
where W = RC is the time constant of the parallel RC circuit. In the Cartesian representation of the complex plane, this equation is represented R by a R/2 radius semicircle whose center is on the x-axis at ( r ). 2 In the case where we have ideally polarizable electrodes, the material-electrode interface has to be characterized at low frequencies by a purely capacitive effect. The S / 2 phase shift caused by a capacitor is therefore represented on the Nyquist diagram by a vertical line. Consequently, it will be necessary, in order to obtain information about the electrodes’ polarizability, to work at low frequencies where there is more chance of ion accumulation at the electrodes. The accumulation of charges near the electrodes, however, has to be associated with ion diffusion phenomena inside the material. The lower the measurement frequency, the higher the depth reached inside the material of the disturbance caused by the alternating current, and the greater the amplification of the electrode polarization process. The mobilization of these charge carriers, which are no longer necessarily available for current conduction, then leads to an increase in the material’s resistance at low frequencies. Expressing the impedance of this system is now possible if we consider its behavior as equivalent to that of a Warburg impedance21 in a semi-infinite medium, so:
Z Z
Vw 1 i Z
where Vw is the Warburg coefficient, which takes into account the concentration of charge carriers and their diffusion coefficient inside the material. Such an expression is represented in the Nyquist plane by a line inclined by 45° as can be seen in Figure 6.45, the 45° angle being a result of the 1/2 pulsation power. This line will be considered as representing an electrode polarization process.
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In reality, the angle value might diverge slightly from 45° for reasons concerning material inhomogenity or material-electrode interface quality. As for the intrinsic electrical properties of the materials, there are three regions in the diagram to be considered. First of all, the intersection points of the semicircle and the x-axis. This semicircle intersects with the x-axis at (r+R) for a zero Z, and once again at x = r when Z tends to infinity. This information makes it possible to determine the contribution of each resistive element to the set up, meaning either r or R.
Figure 6.45. Nyquist representation of an R/C circuit associated with a Warburg-type diffusion process
The top of the semicircle’s arc is another interesting point: it corresponds to the maximum amplitude of In(Z) (that is, In(Z) = R / 2 ), which is reached when Z0RC = 1. This useful pulsation value helps us determine the relaxation frequency f0 of the electrical circuit, where f0 =1/ 2S RC . Knowing f0 and R thus leads us to C. This method allows us to distinguish and evaluate the equivalent resistive and capacitive effects attributed to the various constituents of the material. A sufficient difference between the relaxation frequencies of the various electrical circuits is enough to obtain multiple semicircles that will allow us to distinguish the contribution of each RC system.
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The third point is related to the quantization of the polarization effects at the electrodes, which are due to the accumulation of carriers inside the material. It is therefore important to establish a model and a variation law depending on frequency. We will here employ a more general expression than Warburg’s by involving an element with a constant phase, which takes into account the material’s inhomogenity:
Z Z
i *.Z n
The properties of the material are defined by two parameters. The first one (*) is similar to capacitance, the second (n) controls the slope of the line, and its value lets us know how far we are from an ideal case, which corresponds to n = 1/ 2 . Just as the previous experimental results recommend, we fix the value of n to around 0.5 so that the slight variations of the linear part’s slope is taken into account. The global electrical properties of materials can be approximately modeled by using equivalent electrical circuits, which present themselves as follows (see Figure 6.46).
Figure 6.46. Equivalent circuits
Simulating the experimental results consists of adjusting the values of R and C for the semicircles, and those of * and n for the linear part. This was done using a commercialized program called Zview, version 2.1b, written by Dereck Johnson and developed by Scribner Associates Inc. An example is presented in Figure 6.47.
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Figure 6.47. Nyquist representation and computer simulation
This tool will make it possible to quantitatively determine the electrical characteristics of each material and easily compare them according to experimental conditions. 6.5.4. Application of impedance spectroscopy – experimental results17
A number of results, more specifically those concerning beta-alumina, zirconia and tin dioxide when they are associated with gold electrodes, will help us illustrate the importance of complex impedance spectroscopy. These materials were chosen because of their importance in sensor applications; moreover, they make it possible to explore semiconductors and ionic conductors. 6.5.4.1. Protocol The analyses were conducted using an impedance spectrometer of the HP4192A LF type. This machine allows us to use a frequency scan from 5 Hz to 13 Mhz, and measure impedance values between 0.1 M: and 1.3 M:. The experiment consists of recording the real and imaginary part values of the impedance according to the alternating current’s frequency. Most often, the data is represented in a Nyquist diagram. The measurements were conducted using a sinusoidal alternating current whose maximum amplitude was set at 100 mV. This value allows us to produce a current that is high enough for us to obtain precise impedance measures.
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6.5.4.2. Experimental results: characteristics specific to each material The experimental results presented in Figures 6.48, 6.49 and 6.50 help us understand the importance of the data gathered, as well as the influence the nature of the material has on the complex impedance spectrum. a) Sintered beta-alumina This material is an ionic conductor due to the presence of sodium ions. It is therefore capable of inducing a polarization process at the electrodes. The samples studied appear here as 10 mm diameter sintered pellets associated with two gold electrodes and made by cathode sputtering of a 400 nm-thick layer. Impedance spectroscopy analysis, conducted at various temperatures and under air, yields the results presented in Figure 6.48. We note the presence of a semicircle, which is characteristic of a RC circuit and can be attributed to the presence of grain boundaries. When temperature increases, the semicircle’s diameter is lowered, and consequently the electrical resistance of the material as well. This result confirms the activated nature of the ionic conductivity. Furthermore, we note the existence of a linear part appearing at low frequencies, which is caused by electrode polarization.
Figure 6.48. Nyquist representation of the impedance spectrum obtained with sintered betaalumina associated with two gold electrodes, at various temperatures, and under air
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The value of the tilt angle is independent of temperature; it is estimated for this material at 55°, therefore at a slightly higher value than the expected theoretical 45°. b) Sintered zirconia This material is an ionic conductor due to the presence of oxygen vacancies that are at equilibrium with the surrounding oxygen. The samples appear as 10 mm diameter sintered pellets. The electrical contacts are produced using gold electrodes deposited by cathode sputtering. The complex impedance spectroscopy results in Figure 6.49 show that this material has some characteristics related to electrode polarization, at least in the temperature range we are working on, that is to say between 200 and 600°C, and under air.
Figure 6.49. Nyquist representation of the impedance spectrum obtained with two gold electrodes deposited on zirconia, at 400°C and under air
Indeed, we note that on the impedance spectrum there is a linear curve appearing at low frequencies and whose slope is about 50°. This result was not necessarily predictable since the charge and mass transfers taking place between the gaseous and the solid phase is not necessarily conducive to polarization effects. In the case of zirconia, however, the impedance spectrum is more complex than beta-alumina’s. There is, at high measurement frequencies, an additional semicircle that might be due to intragranular conduction, which is an intrinsic conduction mechanism.
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c) Tin dioxide: n-type semiconductor Tin dioxide is characterized, just like zirconia, by the presence of oxygen vacancies. However, its electrical properties lead to it being sorted in the electronicconduction semiconductor category. Such behavior might be caused by lower defect mobility, which would weaken the ionic behavior of the material.
Figure 6.50. Nyquist representation of the impedance spectrum obtained with two gold electrodes deposited on tin dioxide, at 300°C and under air
We have conducted the study of this material through complex impedance spectroscopy using sintered pellets on which gold electrodes were deposited. In this case, the obtained results only show a semicircle that is characteristic of this material’s intrinsic and intergranular properties. The linear part previously obtained using solid electrolytes is no longer there (see Figure 6.50), leading us to conclude that there are no polarization processes at the electrodes. Thus, these results confirm the electronic nature of this material which makes it very unlikely to have any electrode polarization. This material, whose electrical sensitivity towards gas is a particularly common subject of study, is characterized by unique and sometimes complex behavior.
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Regarding the thermodesorption experiments, we have already seen that, under chemical treatment of 1,000 ppm pressure, sulfur dioxide deeply alters the chemical state of the surface, especially the binding energy of the hydroxyl groups on the material’s surface. Such change in the surface states does have its consequences on the performance of tin dioxide when it is subjected to the action of some gases. Thus, this material’s electrical response to the action of benzene at 150°C is significantly more amplified than that of a material that has not been treated18 (see Figure 6.51).
Figure 6.51. Influence of sulfur dioxide treatment: 1) pure air, post treatment, 2) benzene (500 ppm) prior to treatment, 3) benzene (500 ppm) post treatment
The results obtained through complex impedance spectroscopy for various samples are presented in Figure 6.52 in two representation modes, that is to say the variations of the resistance Y and the capacitance X as a function of frequency, and the variations of Y according to X at various frequency values (Nyquist diagram). These results are interpreted based on the equivalent circuit in Figure 6.53. The curves presented in Figure 6.52a correspond to a sample that was not treated under air. They are representative of a potential barrier at the grain boundaries. The electrical properties of this material are therefore characterized by a preponderant effect at the grain boundaries: R1 = 105 :, R = 4x105 : and C = 5x10-11 F.
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The effects of the sulfur dioxide chemical treatment appear on the curves of Figure 6.52b. Note that the intrinsic conductivity of the material is particularly affected, resulting in a noticeable decrease of R1 (5x103 : instead of R1 = 105 :). Finally, we note that the action of benzene on a treated material leads to a pure resistive effect that is mostly due to a high contribution of gas at the grain boundaries (see Figure 6.54c). The diagrams of Figure 6.54 sum up all our remarks from a macrophysical and energetic point of view.
Figure 6.52. Complex impedance diagram obtained at 150°C with a polycrystalline SnO2 sample (powder sintered at 500°C)
Figure 6.53. Equivalent electrical circuit
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Figure 6.54. Electrical conduction model for polycrystalline SnO2: evolution of the SCR at the grain boundaries in the presence of gas
6.5.5. Evolution of electrical parameters according to temperature
Determining the influence of temperature on the electrical parameters is essential if we want to accurately define devices that will work under different temperature conditions. Moreover, we will see that this information can allow us to access some physicochemical quantities such as activation energy values. The results presented in this section concern materials that are known to be ionic conductors, that is to say: – beta-alumina in sintered form; – beta-alumina in thin screen-printed films; – sintered zirconia; – sodium-ion conducting glass in thin screen-printed films.
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As for the conducting glass, it is made of a sodium aluminosilicate whose composition is as follows: 26.1% of Na2O, 61.6% of SiO2 and 12.3% of Al2O3. a) Evolution of electrical resistance We have presented the measures of resistance according to temperature in Figure 6.55. Concerning zirconia, we see the contribution of both the intragranular and the intergranular electrical properties deduced from the two semicircles. These results demonstrate perfectly the influence of temperature on the resistance of these materials as their conductivity increases with this parameter.
Figure 6.55. Evolution of the resistance value of the materials’ contributions with temperature and under air
We generally assume, for this type of material, that conductivity varies with temperature according to a law that corresponds to a process of conduction by thermally activated hopping:
V .T
§ - Ea · ¸¸ © k bT ¹
V 0 exp¨¨
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where VT denotes the conductivity of the material, T is the temperature in Kelvin degrees, kb is the Boltzmann constant, and Ea represents the activation energy characterizing the ionic conduction process. The value of this activation energy, which is independent of the geometrical parameters characterizing each sample, is perfectly representative of the material’s intrinsic electrical properties. Knowing that the conductivity V is inversely proportional to the resistance R, the previous relation becomes:
§T · ln¨ ¸ ©R¹
§ - Ea · 1 ¨¨ ¸¸ Cst k © b ¹T
To make sure that this relation is valid, we only need to plot, the natural logarithm of the T/R ratio as a function of the inverse temperature, as shown in Figure 6.56. The results we have obtained are satisfactory for all the materials, so we can calculate, for each material, the activation energy corresponding to its ionic conduction mode.
Figure 6.56. Arrhenius diagram representing the evolution of the studied materials’ resistance
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These values are given in Table 6.3. b-AI2O3 Sintered material
b-AI2O3 Screen-printed material
glass
ZrO2 - HF
ZrO2 - BF
slope
-6.745
-8.945
-9.996
-11.617
-13.062
Ea (kJ/mole)
56.0
74.3
83.0
96.5
108.5
Ea (eV)
0.58
0.77
0.86
1.00
1.13
Table 6.3. Values of activation energy graphically determined using the Arrhenius diagram
Note that beta-alumina has the lowest activation energy value. The activation energy determined for this material is higher than those found in scientific literature: 0.58 eV compared to 0.33 eV, 0.27 eV, 0.26 eV or 0.28 eV, depending on the bibliographical source. This quite significant difference is either due to a difference in crystallographic structure between the samples (single crystal or, as in the present case, sintered powder), or to a difference in the exact composition of the material, particularly in the stoichiometry deviance. Regarding the glass material in the Na2O-SiO2 system, the activation energy values usually range from 0.62 to 0.74 eV depending on their composition, against 0.86 eV in the present case. Actually, this difference might be explained by the presence of alumina in the studied samples. In the case of the material that was produced by screen printing with 60% of ȕ-alumina and 40% of glass, we obtained a value between that of beta-alumina only and glass material only. However, we note that it is closer to that of glass material despite the much higher percentage of beta-alumina. On the other hand, the values for zirconia are very close to those found in scientific literature: from 1.0 to 1.1 eV against 1.1 eV, 1.15 eV, 1.12 eV, 0.98 eV, 0.93 eV, 1.16 eV. We can also see that the measured activation energy reading on the semicircle we obtained at high frequencies is lower than the one we observed on the low frequency semicircle. This could mean that the ion transport mechanism functions with greater ease in the bulk than it enjoys at the grain boundaries.
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b) Evolution of equivalent capacitance according to time Using the relaxation frequency: f0 = 1/(2SRC), which corresponds to the maximum value on the semicircle, it is possible, knowing R, to obtain C at different temperature values. As can be seen in Figure 6.57, temperature effects on capacitance values are very weak whatever the studied material. The measured values are in the order of 10-5 μF. Some studies conducted on pulverulent zirconia post hot sintering, mention a slight decrease as temperature rises, while others give constant values in this temperature range. Concerning beta-alumina, Armstrong and Archer19 have established a law that slightly increases with temperature. Whatever the case, the variations in this temperature range are low, and we can assume that, broadly, the capacitance is independent of measurement temperature. This lack of evolution is not surprising, considering that the measured capacitance corresponds to intergranular discontinuities in the material. At temperatures of the order of 200 to 600°C, the grain boundaries do not sustain any major alteration. On the other hand, when we reach very high temperatures, a partial sintering process could step in and alter the capacitive effects.
Figure 6.57. Evolution of the equivalent capacitance as a function of temperature
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c) Evolution of parameters * and n according to temperature The simulations, which are obtained using the equivalent electric scheme containing a constant-phase element, allow us to compare the electrical properties at the electrode-material interface. Such properties are characterized by two quantities * and n. The first one, as we have already seen, is easily assimilated to the capacitance produced by the interface, and the second one is related to the formation of a charge carrier diffusion layer in the material. Concerning *, this parameter’s order of magnitude is a microfarad. As shown in Figure 6.58, where we represented the natural logarithm of * as a function of temperature, this parameter increases exponentially with temperature, and depends on the nature of the material. The slope D of these lines is given in Table 6.4.
Figure 6.58. Evolution of parameter * with temperature
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glass
b-AI2O3 screen-printed
ZrO2
D (u.a.)
0.0083
0.0115
0.0126
0.0162
Ea (eV)
0.58
0.77
0.86
1.13
Table 6.4. Values of activation energy graphically determined using the Arrhenius diagram: confrontation of the activation energy of the ionic conduction process and the evolution slope D of parameter * according to temperature
These results seem to indicate that the capacitive phenomenon at the materialelectrode interface is strongly related to the mobility of the ion charge carriers in the material. d) Evolution of parameter n As for n, which is the parameter that provides the gap between the actual capacitace and a pure capacitance, it is independent of temperature. The values are close to 0.5 (Warburg diffusion mechanism), slightly higher for sintered betaalumina and sintered zirconia (0.62 and 0.59), slightly lower for glass and the serigraphed material (0.45). The gaps are difficult to explain. The only difference comes from the fact that the first two materials are in a crystallized state, while the other two are partially or fully amorphous. However, we have found that this parameter does not have any significant effect on the intrinsic electrical properties of materials. 6.5.6. Evolution of electrical parameters according to pressure
Under a pressure between 10 and 104 Pa, and at a temperature in the 300 to 600°C range, analysis of the complex impedance spectrums show that, whatever the studied material (beta-alumina, glass, zirconia), oxygen pressure does not influence at all the parameters ī and n which characterize the electrode-material interface. The capacitive effect and charge carrier diffusion in the material stay the same under all oxygen pressure values. It is the same for the capacitive effects due to the presence of structural defects in the materials. In fact, oxygen probably does influence the capacitive effect, but it is surely hidden, at least partially, by the charge we placed on the electrodes using the measurement system. It is therefore not surprising that oxygen action on the capacitive effect cannot be measured.
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It seems that only global resistance is affected and slightly increases with oxygen pressure. The results we have obtained with screen-printed ȕ alumina are presented in Figure 6.59, where we plotted log (1/R) as a function of oxygen pressure. 1/R represents the conductivity of the material.
Figure 6.59. Evolution of conductivity as a function of oxygen pressure
We see a very slight decrease in conductivity as oxygen pressure goes up. We have tried to quantify this change using an expression of the following type:
V
P
1 / n
O2
This type of expression is often adopted to express the change in material conductivity according to oxygen pressure. In the simple cases where the gas adsorption reaction is controlled by the adsorbed-phase electron transfer, the value of n depends on whether or not the adsorption process is dissociative. Generally, in the case of oxygen adsorption, n assumes the value 1 if adsorption is not dissociative, and assumes the value 2 if it is. In our case, whatever the material, the electrodes or the temperature, n only assumes values between 24 and 70. We note that this value cannot, in any case, correspond to conduction by vacancy ionization produced electrons.
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Thus, our results confirm that these are ionic materials, whose conductance is little affected by the changes in oxygen pressure. In the case of solid electrolytes, the electrical conductivity is usually described using the Patterson diagram, which is represented in Figure 6.60. This diagram, which is an application of the Brouwer diagrams, makes it possible to separate the ionic conductivity areas from those where electronic conduction is dominant. It gives a theoretical representation of conductivity as a function of temperature and the pressure of the gas at equilibrium with the compound we are studying.
Figure 6.60. Patterson diagram, representing the variations of the conductivities due to ionic and electronic carriers as a function of the temperature T and the partial pressure PX2, for a binary compound MaXb20
The central region denoted by I represents the predominance area of ionic conductivity, where conductivity is independent of oxygen pressure. Above a certain pressure value (PX2)sup, the conduction process is operated by free electrons, while it is operated by electron holes below (PX2)inf.
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Some experiments that have been conducted with direct current also confirm the ionic nature of the conductivity. Using measures on serigraphed beta-alumina (see Figure 6.61), it is indeed possible to estimate the ratio R of the hatched surface areas during discharge and charge. These surface areas respectively equal the amount of charges Qd restored to the system and the amount of accumulated charges Qc. For a perfectly reversible ionic conductor, this ratio must equal 1. In the present case, this ratio is at 60% after only 15 minutes of discharge. This relatively high value leads us once again to the conclusion that there is much more ionic transport than electron transport, electronic conduction therefore being rendered negligible.
Figure 6.61. Evolution of the current flowing through the material over time during the polarization of a device containing two metal electrodes deposited on a solid electrolyte (300 mV)
Thus, studying the electrical properties of these materials has helped us to highlight a notable capacitive effect at the interfaces between solid electrolytes and metal electrodes. Impedance spectroscopy has shown us that there is accumulation of the material’s charge carriers near the electrodes. Furthermore, experimental conditions, specifically temperature and the gaseous environment, seem to have only a very limited influence upon the capacitive effect resulting from this charge accumulation.
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Thus, there is no exchange of matter, nor is there any ionic charge carriers between the electrodes and the solid electrolytes we have studied under the specified pressure and temperature conditions. Such properties are, however, characteristic of “blocking” electrodes, which are permeable to electrons. The last direct-current experiment indicates that ionic conduction in these materials is predominant compared to electronic conduction under these experimental conditions. We can therefore assume that this behavior is compatible with that of “ideally polarizable” electrodes. 6.6. Bibliography 1. E. CALVET, H. PRAT, Microcalorimétrie, Masson, Paris, 1956. 2. A. SOUCHON, Utilisation de la microcalorimétrie pour l'étude des réactions hétérogènes Application à l'oxydation du niobium par les gaz, Thesis, Grenoble, 1977. 3. J. MEUNIER, Mécanisme de l’interaction oxygène-oxyde de Nickel – Etude de la conduction électrique et des effets thermiques, Thesis, Grenoble, 1979. 4. N. GUILLET, Etude d’un capteur de gaz potentiomètrique, influence et rôle des espèces oxygénées de surface sur la réponse électrique, Thesis, INPG-ENSMSE, Saint-Etienne, 2001. 5. J.-L. Le THIESSE, Détermination de la nature des différentes espèces formées par adsorption d’oxygène ou de dioxyde de soufre à la surface de l’oxyde de nickel, Application à l’étude des mécanismes réactionnels dans les systèmes O2/NiO et O2/SO2/NiO, Thesis, Grenoble, 1985. 6. A. CLARK, The Theory of Adsorption and Catalysis, Academic Press, 1970. 7. V.N. KONDRAT’EV, Chemical Kinetics of Gas Reaction, Pergamon Press, 1964. 8. C. PIJOLAT, Etudes des propriétés physico-chimiques et des propriétés électriques du dioxyde d'étain en fonction de l’atmosphère gazeuse environnante. Application à la détection sélective des gaz , Thesis, Grenoble, 1986. 9. J.-L. LE THIESSE, Détermination de la nature des différentes espèces formées par adsorption d’oxygène ou de dioxyde de soufre à la surface de l’oxyde de nickel, Application à l’étude des mécanismes réactionnels dans les systèmes O2/NiO et O2/SO2/NiO, Thesis, Grenoble, 1985. 10. J.A. CHALMERS, “Contact Potentials: General Principle”, Phil. Mag., 33, 1942. 11. L. LASSABATERE, Mecanismes d’adsorption et propriétés des surfaces de germaniumantimoniure de gallium, Thesis, Montpellier, 1969. 12. J.P. BEAUFILS, Nouvelle méthode de mesure des potentiels de Volta, potentiométrique. Application à l’oxyde de zinc, Thesis, Lille, 1964.
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13. J.-P. COUPUT, Réalisation d’un dispositif de mesure du travail de sortie des électrons : Application à l’étude des systèmes dioxyde d’étain-oxygène et dioxyde d’étain-dioxyde de soufre, Thesis, Grenoble, 1982. 14. J.E. BAUERLE, “Study of solid electrolyte polarization by a complex admittance method”, J. Phys. Chem. Solids, 30, p. 265, 1969. 15. E. SCHOULER, M. KLEITZ, C. DESPORTES, “Application selon BAUERLE du tracé des diagrammes d'admittance complexe en électrochimie des solides”, J. Chimie Physique, 70, no. 6, p. 923-935, 1973. 16. C. DESPORTES, M. DUCLOT, P. FABRY, J. FOULETIER, A. HAMMOU, M. KLEITZ, E. SIEBERG, J.-L. SOUQUET, Electrochimie des solides, Collection Grenoble Sciences, 1994. 17. N. GUILLET, Etude d’un capteur de gaz potentiomètrique, Influence et rôle des espèces oxygénées de surface sur la réponse électrique, Thesis, INPG-ENSMSE, Saint-Etienne, 2001. 18. R. LALAUZE, C. PIJOLAT, J.-P. COUPUT, Procédé, capteur et dispositif de détection de gaz dans un milieu gazeux, patent: French (8119536,1981), European (77,724), US (428438, 1984), Japanese (753 030, 1993). 19. R.D. ARMSTRONG, W.I. ARCHER, “The double layer capacity of the Au/Na-b-alumina interface-variation with temperature”, J. Electroanal. Chem., 87, 221-224, 1978. 20. C. DESPORTES, M. DUCLOT, P. FABRY, J. FOULETIER, A. HAMMOU, M. KLEITZ, E. SIEBERG, J.-L. SOUQUET, Electrochimie des Solides, Collection Grenoble Sciences, 1994.
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Chapter 7
Material Elaboration
7.1. Introduction The choice of a material fit to be used as a gas sensitive element depends on certain properties, which naturally include sensitivity and selectivity. Sensitivity, which is generally given by the expression G-G0/G0, where G and G0 are the electric response in the presence of gas and air respectively, expresses the relative variation of the signal due to different gases. Selectivity, which appears most often as a parameter relative to the desirable level of accuracy, expresses the sensor’s capacity to detect different gases. The relative nature of this parameter is linked to the fact that the physicochemical interactions between gas and solid are very likely and that only the intensity of the phenomenon can vary. Still, there are other criteria that are just as important. These materials, which are often powders, have to be considered with particular regard to these properties: – their aptitude to being shaped; – their mechanical stability after shaping; – their chemical stability given the gases present in their environment; – their capacity to receive mechanically and electrically stable electrodes.
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Such a high number of conditions will limit the number of candidates for such an application. Thus, tin dioxide is most often used to make sensors based on electric resistance, and zirconium to make electrochemical based sensors. However, there is fruitful and ongoing research into new materials. Thus, this chapter will be devoted to the assessment of these two types of materials: a commonly used material, like tin dioxide, and a more innovative one, like beta-alumina. Since both are sensitive to certain gases, we will see how different configurations of these materials can be exploited. We will distinguish ceramic materials stemming from compressed powder from materials deposited on a substrate shaped as thin or thick films. Generally, the films whose thickness is contained between 100 A° and 700 A° are considered thin; the films whose thickness is contained between 500 A° and 2000 A° are considered intermediate; lastly, the films whose thickness is greater than 1 μm are considered thick. 7.2. Tin dioxide As far as tin dioxide is concerned, the different technological possibilities of shaping have been exploited in the granular environment processes laboratory of the Ecole des Mines de Saint Etienne. 7.2.1. The compression of powders 7.2.1.1. Elaboration process and structural properties Generally, common powders are used. They are sifted in order to keep only those particles whose diameter is less than 100 μm. This material is then cold-compressed under a pressure of 2 tons/m3. This operation can be achieved in two different ways: – the first, which is coaxial, consists of using a cylindrical and metallic mold. We then obtain a pastille. A gram of product makes it possible to obtain a 1 mm-thick pellet whose diameter is 13 mm. The sample is then sintered during 10 minutes at a temperature above 500°C; – the second is isostatic. The powder is, in this case, contained in a flexible rubber mold, which is placed in a bath of oil. The compression of oil then allows
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217
effects of isostatic compression on the powder. The samples are then sintered in the same conditions as previously. The second method, which uses a large quantity of material, is better adapted to mass production. However, the samples have to be cut out of the obtained block. The sintering temperature determines the porosity, the size of the grain and the specific surface area of the material. The results obtained for temperatures from 800°C to 1,300°C (see Table 7.1) allow us to confirm that the diameter of the pores and the diameter of the grains increases considerably with the temperature. Annealing temperature
Grain diameters nm
Pore radius nm
Specific area m2/g
without annealing
<100
20
7
800ºC
<100
25
4
1,100ºC
100
60
2.5
1,200ºC
240
80
1.1
1,300ºC
550
250
0.5
Table 7.1. Variation of the relative density. Evolution of the morphological parameters as a function of the annealing temperature
7.2.1.2. Influence of the morphological parameters on the electric properties Furthermore, the microstructure of the materials (size of the grains, porosity) has a great effect on the electric properties of a semiconductor oxide and on its electric sensitivity toward gas action.1, 2, 3 Figure 7.1 illustrates the influence of the size of the grain on the conductance of the sintered material.
Figure 7.1. Influence of the grain size and sintering temperature on the electrical conductance3
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Physical Chemistry of Solid-Gas Interfaces
To interpret such results, N. Yamazoe2 suggests a model based on the relation between the diameter L of the crystallites and the depletion width Ld, which the author estimates at 3 nm. The sensitive element is represented by a 1D string of crystallites bonded mostly by necks stemming from sintered grains, and the rest of the crystallites are bonded by grain boundaries stemming from a simple mechanical contact, as presented in Figure 7.2. In this case, the oxidizing gases cause an increase in the width of the space-charge layer:
Figure 7.2. Necks and grain boundaries in a polycrystalline material
– if L>>2Ld, the conduction canals through the neck are too wide to be influenced by the reactions at the surface. The grain boundaries are, in this case, the most resistant element of the conduction string: the conductivity is controlled by the resistance of the grain boundary; – if L>2Ld, the conductivity is controlled by the resistance of the neck between two grains; – if L<2Ld, all the grains display a depletion area. The grains become the most resistant elements: the conductivity is controlled by the resistance of the grains. In each of these cases, the gases will have a special role to play, either at the grain boundaries or at the material level. An almost identical electric conduction model is proposed by W. Göpel.5 The electric diagrams equivalent to such models are displayed in Figure 7.3; they show the presence of a capacitive process at the depletion area. This effect was discovered using complex impedance spectrometry.
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219
Figure 7.3. Electric diagrams equivalents, depending on the size of the grains, suggested by W. Göpel4
7.2.2. Reactive evaporation5 Reactive evaporation is a process defined by the evaporation of a metal under slight pressure from an oxidizing gas, like oxygen or steam, and its subsequent condensation on an adapted stand. This process allows us to obtain oxide films directly. Because of their porous character, the films obtained do not necessarily belong to the class of film considered compact. The choice of such a reactive process stems from the fact that direct evaporation or sublimation emerges as an important technological problem. This material is very oxidizing at high temperatures. It turns out to be extremely aggressive towards the crucible, which is generally made using metallic filaments. An intermediate solution consists of evaporating the tin and then oxidizing the obtained metallic film. In fact, after oxidizing, this process yields irregular films with very poor adhesion to the support. 7.2.2.1. Experimental device The device used is an evaporator. This evaporator was initially designed to carry out plating by evaporation under vacuum.
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Physical Chemistry of Solid-Gas Interfaces
Minor modifications allow us to use it for reactive evaporation. This device is composed of a glass bell jar, in which a primary vacuum can be achieved using a paddle pump and, if necessary, a diffusion pump. This jar contains a crucible composed of a filament of refractory metal, generally tungsten. This filament, whose diameter is 0.05 mm, is shaped to form a cone made of an unjointed turn of coil. Such a source emits in every direction, but not in an isotropic way. Variations have been measured under vacuum using a quartz microbalance. The maximum of these variations depends on the emission angle and can reach 35%. In fact, the films will always be deposited at the same place under the source. Integrating the curve in Figure 7.5, we can calculate that a film placed under the filament (ș = 180°) will receive a mass equal to 96% of the mass that would be received if the evaporation was isotropic. The filament is heated using the Joule effect. The electrical power is supplied by a variable auto-transformer, connected in series with a transformer decreasing the voltage. At a temperature of 1,200°C, the necessary power is 25 W. The current flowing through the filament is then 25 amperes. A micro leak allows us to regulate the amount of gas flowing in the jar. Consequently, the micro leak regulates the total pressure as long as the gas is continuously pumped into the bell jar. Metallic sheets made of tin (Merck high purity) are shaped into a ball, and then placed into the crucible.
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221
Figure 7.4. Device description
Figure 7.5. Influence of the anisotropic source on the thickness of the deposit as a function of the depositing angle
The chosen substrates are either oxidized silicon or glass. In fact, it seems that the substrate nature has little influence on the sensitivity of the film. Thus, samples have been successfully made with unpolished alumina plaques as substrate.
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Physical Chemistry of Solid-Gas Interfaces
7.2.2.2. Measure of the source temperature The source temperature is very high and thus involves technological problems: it is hard to measure and regulate. The measure of the empty crucible’s electric resistance has turned out to be the most accurate way to determine the source temperature. Indeed, the resistance of a tungsten filament rises with the temperature, according to the law: R
U I
T
R0 [ 1 Į(T T0 )] with Į
T0
7.8 x10 -3 qC 1 or
1 U ( R0 ) ĮR0 I
where R0 is the resistance at the temperature T0, U is the voltage at the filament’s extremities and I is the current that flows through the filament. It seems that the temperature is homogenous on the filament between the poles; it implies that the temperature calculated with the measure of the resistance R is the correct temperature. The measure of the current and the voltage allows us to calculate the electric power P supplied to the filament, and thus the characteristic P=f (T) of an empty crucible. The measure of the voltage has to be made with a connection very close to the useful part of the filament. When the crucible contains melted tin, its resistance is changed and the calculation of temperature using this method becomes impossible. However, we can assume by primary approximation that the characteristic P=f (T) does not vary much. Indeed, at the pressure present, the heat is mainly dissipated by radiance and the emitting area is about the same size whether the tin is inside the crucible or not. At a constant electric power, we hope to keep a constant temperature (± 25°C). 7.2.2.3. Thickness measure With a quartz microbalance, it is easy to measure the thickness of a compact film, but it turns out to be impossible if the film is porous. Indeed, the quartz cannot take in any of this information: the likely cause is the lack of elastic properties of quartz and films.
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223
Nevertheless, using the measure of the total tin mass evaporated, we can calculate the total mass of tin dioxide mSnO2 deposited, which supposes that the oxidation is complete. We can then deduct the mass per unit area of a film deposited at a distance d of the source. The plane of the substrate is normal to the deposit: mSnO2
mSn
M SnO2 M Sn
1,27 mSn
This relation supposes that the oxidation is complete. We can then deduct the mass per unit area m d of a film deposited at a distance d of the source. The plane of the substrate is normal to the deposit: md ( g / cm2 )
a mSnO / 4Sd 2 2
The factor “a” is a corrective factor linked to the emission anisotropy of the filament. We determined that a = 0.96 underneath the source. At high enough pressures, that is to say in most cases, “a” is considered equal to 1 because we can assume that anisotropy is negligible due to the gas diffusion. If a slot is present on the film, the thickness e of the film can be measured. The point of this slot, made using a sharp tool, is to lay bare the substrate. Using a scanning electron microscope, the thickness is calculated by scanning samples inclined at 45 degrees. For thicknesses of several μm, the microscope is more effective. Two focus adjustments are needed: one on the substrate, and the other on the surface of the film. The device used (Zeiss “Axioskop”) then enables us to read the thickness with an accuracy of 0.5 μm. Subsequently, the relative density dR of the film will be defined by the quotient: dR
density of the film theoretical density of SnO2
md / e d SnO2
with d SnO2
6.9
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Physical Chemistry of Solid-Gas Interfaces
7.2.2.4. Experimental process Once the substrate and the tin are set up, an initial pumping is performed until the pressure reaches about 2 Pa. The tin is then melted and heated at a temperature of 800°C for several seconds, in order to allow a possible outgasing. The gas is then introduced for the first time under a pressure of several thousand Pa. A second pumping is then performed until the pressure reaches 2 Pa. This ensures the device is completely rid of the air which was present at first. Once this operation is done, the gas is reintroduced at the desired pressure, which is regulated by the micro leak. After the stabilization of this pressure, the filament is heated at the desired temperature. To do so, we have to fix the electric power using a wattmeter (generally 25 W if T = 1,200°C). At 1,200°C, the saturated vapor pressure magnitude of the metal is 10-4 Pa. While the tin is deposited (it generally lasts several minutes), the pressure and the electric power have to be “deregulated”, until the tin vanishes completely between the turns of coil. The heating, the gas circulation and lastly the pumping are then stopped. The pressure of the bell jar is decreased until it reaches atmospheric pressure. Golden electrodes can then be made by evaporation under vacuum on the samples designed to be electrically tested. The samples are then heated again in a furnace, in ambient air (generally, the samples used are substrate oxidized for 15 hours at 600°C). 7.2.2.5. Structure and properties of the films In this section, we will see that the structure and physical properties of the films deposited using the method described previously depends upon certain parameters. Indeed, the way the film is deposited influences its properties, especially the pressure in the bell jar. – Influence of the pressure The films are heated in ambient air again after the deposit at a temperature of about 600°C. For low pressures of oxygen (P< 2 Pa), we obtain films whose characteristics are close to those obtained using non-reactive evaporation. Consequently, these films are not usable for the designed application.
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225
In these conditions, the films are compact and irregular (see Figure 7.6a). The thinness of the X-ray diffraction rays shows that the size of the grain is greater than 250 Å. Thus, the studied films will all be deposited in an oxygen pressure greater than 2 Pa (T#1,200°C) so that the films will be non-metallic. – Texture The photographs of electron microscope of films deposited in oxygen (Figure 7.6) confirm the influence of pressure on the texture: – if the pressure is contained between P0 and a few Pascals, the texture is compact (see Figure 7.6b); – if the pressure is contained between a few Pascals and about 100 Pa, the texture is of columnar type (see Figure 7.6c); – if the pressure is greater than 100 Pa, the texture is spongy (see Figure 7.6d). The oxide films deposited at low pressure (P0< P < 10 Pa) tend to crackle during the firing which takes place after the deposit (see Figure 7.6b), especially the thick films. These films, which are relatively dense, withstand the thermal conditions of the annealing with more difficulty than the more porous films. – Density The relative density of the films decreases spectacularly when the deposit pressure increases (see Figure 7.7); this density is equal to 1 for a compact film, and reaches 10-2 for spongy films. – Influence of the oxygen proportion In general, the speed of the deposit is proportional to the oxygen pressure or, more accurately, the total gas pressure in the reactor. Indeed, we observe that the films deposited under the same total pressure composed of oxygen or air (O2 20% + N2 80%) are deposited at the same speed, and that their morphology are about the same.
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Figure 7.6. Photographs of scanning electron microscope and diffraction spectra of the films after annealing
Material Elaboration
227
spongy
Figure 7.7. Relative density according to the pressure
Nevertheless, the oxygen partial pressure has to be higher than 2 Pa in order to have a sufficient oxidizing speed. It is also important to note that too great an oxygen partial pressure can cause oxidation of the tungsten filament (>60 Pa), which is then quickly out of use. The films containing tungsten oxide have different electric properties, and cannot be used to detect gases. For some applications, it is important that we can explore films under high pressure. Thus, to solve the oxidation, we have to use a mix of oxygen + nitrogen at the desired pressure, so that the oxygen pressure is less than 50 Pa. Generally, we use oxygen until the pressure reaches 35 Pa and air until it reaches 160 Pa. We then note that the average reaction speed is the same under a pressure of 35 Pa of oxygen and under a pressure of 175 Pa of air, which corresponds to an oxygen partial pressure of 35 Pa. It is possible to mix the oxygen with another inert gas. We then note that the molar mass of this gas has a great influence on the texture and the density: thus, with the same total pressure, an increase of the molar mass implies a decrease of the film density (Table 7.2).
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Physical Chemistry of Solid-Gas Interfaces
66 Pa O2 M = 32 g
66 Pa O2
66 Pa O2
+ 200 Pa H2
+ 200 Pa A2
(M = 4 g)
(M = 40 g)
0.022
0.0125
266 Pa O2 or air
Relative density d/dSnO
2
0.0266
0.0167
at 2.5 cm Table 7.2. Relative density variation
It is then normal to note that the films deposited in the same oxygen or air pressure are identical, because the molar masses of oxygen and nitrogen are close (32 and 28 respectively). Thus, at a constant total pressure, the oxygen pressure acts only on the deposit speed. – Size and composition of the grains The X-ray diffraction pictures on the annealed samples do not show the rays typical of SnO2 (Figure 7.6). Nevertheless, the films deposited under a pressure close to 2 Pa, and therefore composed before firing of a mixture of metal and oxide, after firing contain different tin oxides, as well as a low quantity of metal. The measure of the width of the diffraction rays shows that the size of the grains is about 50 or 60 Å after annealing, and does not depend much upon the deposit pressure. – Surface analysis (Figure 7.8) The results obtained using the Auger spectroscopy show that the oxygen concentration at the surface of the films increases with the pressure. Remember that this method allows an analysis not far below the surface, that is to say below 10 Å. We can also detect impurity (sulfur and carbon), especially on the most compact films. After evaporation, tungsten traces can be observed on the films in an oxygen partial pressure greater than 60 Pa. As was explained before, these traces come from the filament oxidization and confirm the necessity to limit the oxygen partial pressure during the deposit. A great part of the impurities on the compact films disappear thanks to ionic abrasion. So, it seems that the impurities are concentrated on the surface of such films.
Material Elaboration
229
Figure 7.8. Influence of the oxygen pressure on the AUGER spectrum, E =3 keV
– Electric conductivity measure The electric conductivity measures mentioned here are made using the four points method, at a temperature of 500°C in dry air. This conductivity, which is defined by the quotient of surface conductivity compared to the thickness of the film, is the average conductivity of the film. It is necessary to divide this value by relative density in order to know the conductivity of a grain or the conductivity of the compact material composing the film. The conductivity V (S/cm) greatly decreases when the depositing pressure increases (Figure 7.9).
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Physical Chemistry of Solid-Gas Interfaces
Figure 7.9. Conductivity at 500°C in dry air according to the deposit pressures
The peculiar values observed between 2 and 10 Pa correspond to the crackled films already mentioned. The conductivity of these films greatly drops, and it is sometimes impossible to measure. Furthermore, the density of the films decreases when the pressure increases: this can partially explain the part of the curve where the conductivity Vdecreases. If, as in Figure 7.10, we plot V as a function of the density d, we obtain a curve which can be modeled by the following expression:
V
kd a
with 3 < a < 3.3. Thanks to the percolation theory, we know the laws which rule the electric conductivity of a mixture of insulating and conducting powders. Thus, if n is the conducting powder proportion, the conductivity V of the mixture is calculated using the following expression:
V
( n nS ) a
nS is called the percolation threshold and represents the value of n under which the mixture is no longer conductive.
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231
Figure 7.10. Conductivity at 500°C in air as a function of the relative density
This theory can be applied to the porous conductors, if we imagine that the pores and the grains of the material are the two constituents of the mixture. In this peculiar case, the percolation threshold necessarily tends towards zero, because there will always be an electric charge transfer in the material. This case has been studied by Deptuck et al.,6 using sintered submicronic silver powder. This powder is prepared using silver evaporation in inert gas. They then find the value of the exponent: a = 2.15 ± 0.25. This value is smaller than the one we found, which seems to indicate the film’s porosity is not the factor responsible for the decrease of V with the pressure. Another factor could be the increase of the oxygen concentration noted on the grain’s surface during the Auger analysis. The intrinsic conductivity of each grain is in effect controlled by the oxygen stoichiometry deviation. In this case, the phenomenon can be limited to the surface of grains, but given their tiny dimensions (50 to 60 Å), we can expect determining effects on the film conductivity. – Reproducibility of the electric measures Often, the reproducibility of the electric measures is weak; for two distinct films deposited using the same method and conditions, there can exist a factor 5 between the measured values. This particularly concerns films deposited under low pressure and thin films.
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Physical Chemistry of Solid-Gas Interfaces
Nevertheless, this error level does not matter much compared with the variations of V according to the studied parameters. Indeed, we have seen that there exists a ratio of 107 between the extreme values measured. This lack of reproducibility seems to be mainly due to an uncertainty concerning the value of the pressure, which is difficult to regulate during the deposit. Indeed, a small variation of the pressure can have an important effect on ı. This value is multiplied by 104 when P increases from 10 to 100 Pa. The variation of ı with the pressure is not as important when the pressure reaches high values (P > 100 Pa). Thus, it will be better to deposit under high pressure if we seek a good reproducibility, although this implies obtaining films whose conductivities will be lower. – Influence of the distance between the source and the substrate For an initial mass m0 of tin in the crucible, we obtain a film whose mass per unit area depends on the evaporation distance. If we want to study, at a constant mass per unit area, the influence of the distance between source and substrate, then we are obliged to vary m0 as a function of the chosen distance. In these conditions, the distance source/substrate seems to have the same influence as the total pressure, be it at the texture level (compact, columnar or spongy), at the density level (see Figure 7.11) or, consequently, at the electric conductivity level (see Figure 7.12). It then appears interesting to draw the iso-density curves (see Figure 7.13) which enable us to characterize the deposit conditions for a given density value and, consequently, for a given conductivity value.
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233
Figure 7.11. Influence of the distance between source and substrate on the relative density
Figure 7.12. Influence of the distance between source and substrate on the conductivity (P = 66 Pa)
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Figure 7.13. Iso-density curves
– Influence of the mass unit area at constant distance To study this influence, we vary the tin mass m0 initially present in the source. The mass unit area and, consequently, the thickness seem to have no observable influence at the texture level, at the density level or at the conductivity level. The thicker films have the advantage of a conductance which is proportional to the thickness and, consequently, greater. Nevertheless, they will be mechanically more fragile. – Influence of the annealing The annealing is performed at a temperature contained between 500 and 650°C, in ambient air for 15 hours. We observe, comparing the different X-ray diffraction spectra, that the annealing increases the size of the grain from 25-35 Å to 50-60 Å. Indeed, we will see in section 7.2.3.3 that there is a relationship between the diffraction ray width halfway up and the size of the grain. The influence of the length and temperature of the annealing have been succinctly studied using the X-ray spectra (Figure 7.14): a) at 500°C, four hours of annealing are necessary to obtain a product, of an apparently structure stable; b) for an annealing of 15 hours, a temperature greater than 450°C is then necessary. Nevertheless, it is advisable to increase these values in order to be certain that the final product will be adequately stabilized (in practice: 600°C during 10 hours).
Material Elaboration
Figure 7.14. Influence of the annealing on the X-ray diffraction spectra
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7.2.3. Chemical vapor deposition: deposit contained between 50 and 300 Å
7.2.3.1. General points The chemical vapor deposition consists of bringing a volatile compound of the material to be deposited into contact with either another gas in the neighborhood of the concerned surface or with the concerned surface directly in order to provoke a chemical reaction which produces the sought solid. This method, commonly called CVD (chemical vapor deposition), allows the development of a great many materials, including pure elements, solid solutions and composite materials of different substrates. The chemical vapor deposition, though widely used in the industry, proves to be a complex technology, which demands an extensive knowledge of: hydrodynamics of fluids, thermodynamics, kinetics, adsorption and chemistry. The complexity of the involved mechanisms also comes from the great number of interdependent parameters like pressure, temperature, the gaseous phase composition, the gaseous flow and the kind of reactor used. Among the different reactors, we distinguish reactors with a hot inner surface from reactors with a cold inner surface. In a hot inner surface reactor, the whole device is kept at working temperature. This method, which implies a homogenous temperature in the reactor, has the drawback of depositing the material sought on the whole device. In a cold inner surface reactor, the material is deposited on the specified surface, though it is done to the detriment of the temperature homogenity on the surface to cover and in its gaseous neighborhood. For technical reasons linked to conceptual problems and the size of the devices, the device shown in this book is a cold inner surface reactor; indeed, hot inner surface reactors are more specifically used for industrial applications. In general, and especially for this kind of reactor, the process can be split into five main stages: 1) the diffusion of the gaseous phase reagent, through the diffusion-limiting layer, towards the substrate surface. Indeed, there exists, in the neighborhood of the substrate, a film containing some gaseous products stemming from the reaction, and inside which exists a gradient of the reagent concentration; 2) the adsorption of the reagents on the substrate surface;
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3) the diffusion of chemical species on the surface of the substrate; 4) the germination-growth process of the film; 5) the diffusion of products stemming from the reaction through the diffusionlimiting layer, towards the gaseous phase. The whole of this process is illustrated in Figure 7.15. On the kinetic level, it is obviously the slower part which imposes its speed on the process. We distinguish two growth modes, depending on whether the limiting stage is the mass transfer in vapor phase (diffusion process) or the surface reactions (kinetic process).
Figure 7.15. Process diagram
In general, the phenomena in the vapor phase are furthered by a pressure increase, surface phenomena by a temperature increase.
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7.2.3.2. Device description 1) Choice of the precursor The tin precursor, chosen to deposit SnO2, is an organometallic compound: tin dibutyldiacetate. In ambient air it is a colorless and viscous liquid compound and does not react with air. It is used because of its physical properties: it has a saturated vapor pressure of about 100 Pa at 100°C, which makes it easily transportable through the use of an inert gas. Furthermore, it is one of the few organostannic compounds that are common. Because of its toxicity, this product has to be handled with care. 2) The CVD device – The CVD reactor The choice of the reactor is very important because it influences the way the reaction happens and can alter the deposit’s nature. We use a reactor with a cold inner surface, cylindrical and vertical. The gas inlet is at the top with a heating device in the middle, and the outflow of the gas at the bottom. This symmetric axial configuration, associated with the regulation of the total pressure in the reactor, is intended to ensure hydrodynamic conditions favorable to realizing a homogenous deposit (the flow of gas is laminar because of the low pressure and the high pumping speed (see Figure 7.16)). The device is composed of a component generating the reagents in the vapor phase, a reactor equipped with a heating system, a pressure regulation system and a gas draining system.
Material Elaboration
Figure 7.16. Laminar flow of gases in the reactor. Experimental device
Figure 7.17. Device description
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3) Experiment conditions In order to get rid of the problem of stoichiometry and reaction efficiency, we use more oxygen than DBTB so that the stannic precursor is completely consumed. Liquid tin dibutyldiacetate is then put into a jacketed Pyrex balloon at a temperature of 100°C. At this temperature, the saturated vapor pressure is 100 Pa. It is transported by nitrogen current. This is carried out at atmospheric pressure, so that, in conditions of thermodynamic balance between the liquid and gas phases, the DBTD concentration in the gas phase depends on its saturated vapor pressure at the temperature of the liquid. At 100°C, the molar proportion of the DBTD in the nitrogen is about 0.1%. The DBTD is then put into contact with oxygen through the use of a mixer in order to elaborate the reagent. The design of the gas mixer ensures the best homogenization possible. It is made of Pyrex: two independent tanks are linked by a tube. In the first tank, the two gas inlets are facing each other: it creates turbulences and an efficient mix. Then the gases enter the second tank before entering the reactor. Another inlet of nitrogen makes it possible either to dilute the mixture, or to purge the whole gas circuit (see Figure 7.18).
Figure 7.18. Gas mixer description
The gas flows are regulated by flowmeter. The pressure at which the gas flows is the atmospheric pressure, and when there is no deposit, the gas is directed towards a column before being evacuated. We thus recover the DTBD which has not reacted. The introduction of the gases in the reactor is carried out through the use of two electromagnetic valves. The first is a three-way electromagnetic valve which allows us to let in either the reagent mixture (N2 + DBTD + O2) or a nitrogen purge. The second is a two-way electromagnetic valve placed just before the gas entry to the reactor: it is this valve that lets the gases into the reactor.
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Between these two valves, there is another valve that allows accurate regulation, of very low conductance, which allows us to introduce the gases under a low total pressure. The pressure before the valve is the atmospheric pressure. After the valve, the gases are at the reactor’s pressure (10 to 1,000 Pa). The reduction in pressure, which happens at this valve’s level, implies a great decrease of the gases’ temperature, and a condensation of the tin dibutyldiacetate, which tends to block this valve. In order to solve this problem, a steam-drying at 200°C is performed. – The reactor As stated above, the reactor is a vertical cylinder made of stainless steel. Its inner diameter is 216 mm and its height is 224 mm: thus, the reactor’s volume is 8.2 liters. The reactor is equipped with a circular porthole (Ø 100 mm) on its top part. Thanks to this porthole, we can oversee the depositing process and control the deposit’s thickness and subsequently the depositing speed, using, especially for SnO2, the color of the thin films deposited on the silicon substrate. Two symmetric openings are placed at 4.2 cm of the top; their diameter is 16 mm. The first is used for the gases introduction and the other is used to measure the pressure. On the reactor inner surface, a circular opening is linked to the pumping system. This opening is centered and it must have a sufficient size (here, its diameter is 45 mm). Four openings are placed at the reactor’s bottom and are used for the measure of the temperature and the supply of the heating system in electricity. A copper tube, inside which circulates a fluid, surrounds the reactor outer surface. This tube allows us to better control the temperature of the gaseous phase inside the reactor. Indeed, it is possible to use cold water as the fluid in order to cool down the reactor or, on the contrary, steam-drying to prevent variations of the temperature: thus, this cold inner surface reactor becomes a hot inner surface reactor. In this case, the tube is only used with cold water at the end of the deposit, in order to forcefully stop the reaction by condensing the DBTD molecules on the cooled down surface and also to speed up the cooling of the whole reactor, which has a great thermal inertia. – The furnace This is one of the main parts of the device. Indeed, the CVD reaction is thermally activated and the temperature has a great influence on the speed and the growth method, as well as the deposit texture. The furnace is composed of a brass block which has the shape of a parallelepiped measuring 8 x 8 x 1.6 cm; it is placed at the
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center of the reactor. It is supported by a vertical axis made of alumina which insulates it from the inside of the reactor (made of stainless steel). The heating of the furnace is accomplished using 4 cylindrical resistances wired up in parallel, so that the total resistance is 35 ȍ. These four resistances are placed inside the stainless steel block. A thermoelectric couple is placed just below the furnace surface. The regulation of the temperature is ensured by a temperature regulator-programmer. The size of the furnace is large enough to have a significant depositing surface (6 x 6 cm) with a homogenous temperature, at least in the depositing zone. Nevertheless, there are also a few drawbacks. Indeed, the necessary power to heat the furnace at the average working temperature (450°C) is large (about 100 W) even at low pressures, that is to say under conditions which do not favor the thermal conduction phenomena. Indeed, it seems that only radiant heating is able to increase the temperature in the whole reactor. – Pressure regulation There are several methods to regulate the pressure in a tank, depending on the inflows of gases and the pumping speed. It is theoretically possible to work in nearstatic conditions if we let in the quantity of gas necessary to attain the desired pressure. To compensate for the decrease of the pressure during the reaction gassolid, we introduce gases in the reactor to maintain the pressure. As these conditions are difficult to implement, we prefer to work in dynamic conditions with a constant pumping speed. The pumping capacities (38 m3/hr) have to be large because of reactor’s volume. These operations are carried out using a micro leak. Depending on the characteristics of the device (reactor volume, conductance, pumping speed), we experimentally determine the flow-pressure curves when the valve is open and closed. 7.2.3.3. Structural characterization of the material – Characterization means The thin films obtained using CVD are characterized by: – the size of the grains which compose the film; – the thickness of the film; – the crystallization state; – the texture.
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All of these parameters can influence the electric properties of the films. – Size of the grains The size of the grains can be measured in two ways. The first method consists of using an X-ray diffraction peak of the material7. In effect, this peak is representative of the crystallographic field of a SnO2 grain. The size L of the coherent fields can be calculated from the diffraction peak width halfway up, using the Scherrer formula: L
0.9O / ' cos T
In practice, L is calculated for the most intense diffraction rays, and the calculated value is an average. In the case of thin films whose thickness is not greater than 300 ǖ, it is difficult to obtain the X-ray diffraction spectra. In a usual assembly to detect X-ray diffraction, the source is fixed and the sample and the detector rotate at angular speeds of T / t and 2T / t respectively: this method is called: T 2T . Given the large angle of incidence for the beam in the sample and its thinness, the obtained information is representative of the sample’s support and not the sample itself. In order to overcome this drawback, we use a device able to work with a small angle of incidence. In this case, the source and the sample are fixed, and only the detector moves at the speed of 2T / t . The angle of incidence is Į. The advantage of such a method is shown in Figure 7.19.
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Figure 7.19. X-ray diffractograms with low angle of incidence, using ș-2ș with Į = 0.7°
The second method consists of observing the samples using a scanning electron microscope. This method gives a microscopic representation of the grains. Besides information concerning the grains, it is possible to obtain information on the grain shape, the distribution of the grain size and the shape of the links between the grains. In dark field, we obtain a diffraction diagram which informs us about the crystallization state of the film. This technique entails using very thin samples, which prevent the use of substrates. We can then either deposit the material directly on the grid holder samples, when we deal with very thin films (100 to 300 Å), or retrieve the thicker films (700 Å) using the reaction of the hydrofluoric acid on the silicon substrate. The thickness can be measured by an optical process: – the X reflectometry for thin films (100 to 700 Å); – the optical characterization for intermediate films (500 to 100,000 Å); – the scanning electron microscope for thick films (Figure 7.29).
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7.2.3.4. Influence of the experimental parameters on the physico-chemical properties of the films 7.2.3.4.1. Influence of the temperature and the pressure on the depositing speed In general, the depositing speed depends on the total pressure in the reactor and the substrate temperature. Figures 7.20 and 7.21 confirm these observations, and it is important to note that it is the total pressure in the reactor which influences the speed. Specifically, as in the case of reactive evaporation, this will allow us, thanks to gases like nitrogen, to control, at the same time, the total pressure to solve kinetic problems and the oxygen pressure to solve chemical problems.
Figure 7.20. Influence of the total pressure on the depositing speed at a temperature of 450°C
Figure 7.21. Influence of the temperature on the depositing speed
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The duration of the depositing implies a regular increase of the thickness of the film (see Figure 7.22).
Figure 7.22. Influence of the deposit duration on the thickness at 350 and 550°C
7.2.3.4.2. Influence of the depositing temperature on the thickness of the film and the size of the grains To study the size of the grains of the films, X-ray diffraction spectra are used. A great increase in their size is noticed when the depositing temperature increases (see Figure 7.23 and Table 7.3). The results obtained using the scanning electron microscope confirm this fact. Furthermore, they show that the films obtained at high temperature are better crystallized.
Figure 7.23. Influence of the depositing temperature on the grain size (e = 720 Å, non-annealed sample)
Material Elaboration Depositing temperature (ºC)
Depositing duration (mn)
Layer thickness (Å)
Average size of the grains (Å)
425
22.5
720
125
425
205
6500
230
525
21.5
720
155
525
180
7000
280
550
19
720
200
550
990
35,000
| 600
247
Table 7.3. Influence of the temperature and the duration of the depositing on the morphological parameters of the film
Figure 7.24. TEM (transmission electronic microscope) micrographs: evolution of the crystallization state depending of the depositing temperature (magnification = x 200,000)
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7.2.3.4.3. Influence of the annealing on the crystallization state and the size of the grains Figure 7.25 perfectly shows the influence of annealing on the crystallization state of a film deposited at low temperature, and which was amorphous before the annealing. Furthermore, we note that the size of the grain is a bit altered by the annealing temperature (the diffraction rays become thinner: Figure 7.26). The intensity of these effects also depends on the depositing temperature, as is shown in Figures 7.27 and 7.28.
Figure 7.25. Diffractograms of SnO2 thin films during successive annealings. Depositing temperature = 350°C/e = 720 Å
Figure 7.26. Influence of the annealing temperature on the grain size
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Figure 7.27. Diffractogram of SnO2 thin films deposited at different temperatures on a non-annealed sample (e = 720 Å)
Figure 7.28. Diffractogram of SnO2 thin films deposited at different temperatures, annealed 17 hrs at 600°C, then 13 hrs at 800°C (e = 720 Å)
7.2.3.4.4. Influence of the depositing temperature on the texture of compact films Here we address the macroscopic texture of thick films deposited at different temperatures. The information, obtained using a scanning electron microscope, allows us to observe an important evolution of the texture, whereby an increase in the temperature changes the film’s structure. From an amorphous structure (Figure 7.29a), it changes into a columnar structure from 450°C on. For temperatures greater than 400°C (see Figures 7.29c and 7.29d), the deposit surface becomes increasingly
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granular. At 500°C, we assume that the density of the columnar elements is smaller, thus favoring a greater porosity of the material and, subsequently, a better interaction between gas and solid.
Figure 7.29. Evolution of compact film texture according to the temperature
7.2.3.5. Influence of the structure parameters on the electric properties of the films The electric properties of the materials are generally studied using the values of the electric conductance. The conductance is measured under a controlled gaseous atmosphere, and using two metallic electrodes placed at the material surface. 7.2.3.5.1. Influence of the thickness on the electric conductance These results (Figure 7.30) show that the electric conductance is not proportional to the thickness, though the geometric parameters have an influence on the conductance. Furthermore, we observe huge variations in the conductance, which increases from 3 10-9 to 10-5 ȍ-1 when the temperature increases from 80 to 800 Å.
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Figure 7.30. Influence of the thickness on the conductance in air at 500°C; TD = 450°C, annealed at 600°C
Figure 7.31. Influence of the thickness on the conductance under air for different depositing temperatures
This influence has been studied for different depositing temperatures (see Figure 7.31).
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7.2.3.5.2. Influence of the annealing on the electric conductance The influence of the annealing has been studied on films of intermediate thickness deposited at high and low temperatures. An increase of the annealing length or the temperature results in a quite significant decrease of the measured conductance (in air). The effect of the annealing is even more important than its temperature and is high compared to the depositing temperature. These results shows that the annealing is interesting in order to obtain stable films to be used as material sensitive to the effect of the gases. Indeed, the working temperature of the detection devices is contained between 400 and 500°C. 7.2.4. Elaboration of thick films using serigraphy
7.2.4.1. Method description This method (see Figure 7.32) consists of depositing the sensitive material to form a thick film, using a paste (also called ink). The paste, supported by a screen, including a window that has a thin mesh, is deposited using a scraper on an alphaalumina substrate.
Figure 7.32. Diagram of serigraphy depositing process
First, the substrate being located under the screen, we deposit ink on the screen. The metallic mesh allows the ink to pass through when the ink is under the scraper’s pressure. The structure of deposits is controlled by the presence of a polymeric film covered by a mesh at the places where the paste is not to be deposited.
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This technology, commonly used in the industry, is particularly well adapted to mass production. The quality of the deposited film mostly depends on the physicochemical properties of the paste used. 7.2.4.2. Ink elaboration The paste, of which the ink is made, must possess rheological properties peculiar to the depositing technology. Specifically, it must be sufficiently fluid to cross the mesh under pressure from the scraper, and, after that, regain a sufficient viscosity to stick to the substrate. To make this paste, you have to mix the following ingredients: – the ceramic powder that we want to deposit; – an organic binder; – an organic solvent; – if necessary, a permanent binder. The organic binder allows us to regulate the paste’s viscosity, whereas the solvent helps to homogenize the ink’s constituents. After the elimination of the organic compounds by thermal treatment, the deposit still has to have a good adhesion to the substrate. If that is not the case, we add a permanent binder to the paste which, after fusion, will ensure a good adhesion of the deposit on the substrate. As far as tin dioxide is concerned, however, it seems no commercial ink exists. This has led our laboratory to produce a new paste. The mineral binder is produced using an organic precursor: tin alkoxide. Its thermal decomposition produces tin dioxide. Tin alkoxide allows us to chemically bind the substrate and the initial silicon powder. In practice, the paste is composed of tin dioxide grains (average size 0.5 μm), tin alkoxide and an organic solvent (liquid). The proportions are given in Table 7.4. Component
Quantity
SnO2 (Prolabo)
4g
organic binder
1.7 g
organic solvent
20 Drops
Table 7.4. Ink composition for tin dioxide
The films obtained are steam-dried, after depositing for ten minutes at 100°C, in order to eliminate the solvent; they are then thermally treated at 800°C for 15 hours.
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This method, which prevents the use of a mineral binder different from the deposited compound, also allows us to keep a homogenous electric conductivity in the film. Thick films are generally deposited on two types of substrate: alpha-alumina alone and alpha-alumina with titanium oxide. One deposit has a thickness of 10 μm. This thickness can be controlled by a profilograph. Multiple deposits with thicker films can be made by adding a steamdrying process between the deposits. In this case, the thicknesses are contained between 10 and 80 μm. 7.2.4.3. Structural characterization of thick films made with tin dioxide The specific area of the powder measured by BET is about 7m²/g. The thick films obtained show a comparable area.
Figure 7.33. MEB photograph of a SnO2 serigraphed film of 20 μm, deposited on alpha alumina: a) cross-section (x 500), b) top view (x 5,000)
The MEB pictures shown in Figure 7.33 show that on an alpha-alumina substrate, the films of 20 μm adhere perfectly to the substrate, and that on the whole, these films are not fissured. The greatest magnification shows that the film is porous.
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7.3. Beta-alumina 7.3.1. General properties
For research into the manufacture of gas sensors of a potentiometric type, we have tested different solid electrolytes. The unique property of these sensors is that the two different metallic electrodes are located in the same gaseous phase. This property has prompted us to study particularly the beta-alumina and calcium sulfate. Sodium sulfate, which possesses good electrolytic properties and a good chemical stability towards gases, appeared a good choice for such an application. Unfortunately, this material cannot be used under a ceramic shape because it does not withstand the temperature variations. Indeed, at about 300°C, there is an allotropic change, that is, in the useful field of the sensor: the mechanical tensions this transformation implies favoring the crackling of the sintered material. Beta-alumina, rich in sodium, possesses a good adhesion on the support and a good ionic conduction. Its weak point is linked to its reactions with some gaseous compounds. To overcome these different drawbacks, and to use every advantage provided by these materials, we have chosen to chemically treat sintered beta-alumina: we make beta-alumina react with sulfur dioxide to form sodium sulfate film on the surface of the material. This process takes place at 600°C in 10,000 ppm of sulfur dioxide in the air and it lasts 90 minutes. Thus, we can elaborate a material composed of a superficial film of sodium sulfate which is perfectly stable mechanically (it does not fissure when the temperature varies) and chemically (it does not react with gases). Obtaining and characterizing beta-alumina remains one of the necessary points to produce the sensitive material. The poly-aluminates (formula nAl2O3-mR2O with: R = Na, K, Li or Ag) are called E-alumina. At high temperature (>1,000°C), these compounds crystallize into two forms: E-alumina and E''-alumina whose formulas are 11Al2O3-R2O and 5Al2O3-R2O respectively. Their crystalline structure is constituted of spinel blocks containing aluminum ions and oxide ions separated by symmetric plans composed of oxide ions and R+ ions. E-alumina contains two spinel blocks and a symmetric plan, and E''-alumina contains three spinel blocks and two symmetric plans. Figures 7.34a and 7.34b show the structure of E-alumina mesh and E''-alumina mesh respectively.
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Figure 7.34. (a) Structure of Al2O3-ȕ; (b) structure of Al2O3-ȕ’’
E-alumina belongs to the ionic supra-conductors family, which means that this material displays a structure that, in a certain temperature range, has a good ionic conduction.
In the case of E-alumina, we observe at high temperature a stable compound stemming from this conduction. This property, caused by the cationic site occupation in the mirror plans (also called conduction plans), allows a great mobility of the R+ ions in a direction perpendicular to the c axis. The value of conductivity measured is of a magnitude of 10-1 S.cm-1 at 300°C (see Figure 7.35), for a poly-crystalline sample of E-alumina, though E''-alumina is slightly more conductive.
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Figure 7.35. Conductivity of monocrystalline and polycrystalline sample o f ȕ and ȕ’’ alumina
7.3.2. Material elaboration
Given the complexity of such a material and its reactivity with a gaseous environment, it is necessary to perfectly elaborate it as well as to ensure an exact reproducibility of the product. These difficulties are mostly linked to the composition and control of the obtained product’s micro-structure (sodium oxide evaporation) and the segregation of sodium carbonate. The elaboration process adopted is the sol-gel process pioneered by L. Montanaro and A. Negro (Department of Materials Science and Chemical Engineering, Politecnico of Turin). The organization chart shown in Figure 7.36 depicts the main stages of this process. To an aqueous solution of an organic salt of sodium (sodium acetate or oxalate), easily decomposable, we add, maintaining a constant agitation, aluminum isopropylate.
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The chosen mass proportions are: 7% of sodium oxide (Na2O) and 93% of aluminum oxide (Al2O3), which implies 1 mole of Na2O for 9 moles of Al2O3. At 25°C, the polymerization and condensation reactions lead to the elaboration of a “sol”. At 80°C, the polycondensation can happen, and we then obtain a “gel”. In order to eliminate the water, two solutions are possible: either the gel is placed in a drying oven at 105°C for 24 hours and the product obtained is then ground is an agate mortar, or the gel is dried by hot air pulverization (a method commonly called spray-drying). In order to crystallize the beta-alumina or the beta”-alumina, the amorphous powder, located in an alumina container resistant to high temperatures, is heated at 5°C/mn until the temperature reaches 1,200°C in ambient atmosphere. We maintain these conditions for two hours, then the powder is slowly cooled down until its temperature reaches 1,000°C. Finally, the powder is quenched at ambient temperature. Whether the powder is obtained using sodium oxalate or acetate, the X-rays diffraction spectra shows the presence of the beta-alumina and beta”-alumina stages. In the case of sodium oxalate, the ratio of the beta-alumina/beta’’-alumina stages is calculated using d = 1.976 Å (beta”-alumina stage) and d = 2.690 Å (beta-alumina stage). The value of this ratio is about 0.75.
Material Elaboration
Figure 7.36. The different stages to obtain E-alumina using a sol-gel process
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Figure 7.37. X-ray diffraction spectra of the powder obtained using sodium acetate or oxalate
These measures, performed using laser granulometry, show that the spray-drying method allows us to obtain a thinner and more homogenous powder than the powder obtained using an agate mortar.
Figure 7.38. Granulometric distribution of the powder obtained using sodium oxalate after steam-drying
Using the BET method, the specific surface area measured is about 1 m2/g after calcination at 1,200°C and will thus be whatever the other conditions are.
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Electric conductivity measures, with an alternating current, allow us to assess ion mobility, and subsequently, the response time of the solid electrolyte. Furthermore, these measures test the reproducibility of the samples using different powders. As is shown Figure 7.39, at 500°C and in air, the conductivity of the product obtained with sodium oxalate is ten times that obtained with sodium acetate.
Figure 7.39. Conductance measure in air according to the temperature
For these reasons, we have decided to use powder prepared using the sol-gel method and to use sodium oxalate. The steam-drying of the product is performed at a temperature of 105°C for 24 hours. The powder is ground in an agate mortar and sifted in order to keep only the grains whose diameter is less than 80 μm. Then the amorphous powder is placed in a heatproof container (made of alumina) and heated at a temperature of 1,200°C under the previously described conditions. 7.3.3. Material shaping
The beta-alumina powder has been conditioned by two different methods: monoaxial compression and serigraphic depositing. 7.3.3.1. Mono-axial compression This method is similar to the one described in the case of tin dioxide, with the elaboration of the material performed using mono-axial cold-compression. With the aid of preliminary samples, we have been able to fix the operating conditions. 500 mg of powder compressed at 450 MPa for 30 seconds. The pellets obtained have a diameter of 13 mm and a thickness of 1.5 mm.
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The temperature for annealing the samples is generally 1,050°C, lasts 1 hour and is realized in air. This temperature enables us to obtain mechanically stable pellets and prevents any phase changes. Furthermore, sodium oxide evaporates. The samples are generally stored in ambient air. Their ageing depends on the time separating the analysis from the heating. 7.3.3.2. Serigraphic process The principle of this depositing method has already been displayed in section 7.2.4: only the compound’s nature changes. – Ink elaboration As for the pulverulent material, the serigraphic ink has been elaborated by L. Montanaro and A. Negro (Department of Materials Science and Chemical Engineering, Politecnico of Turin). The binder used to link the material to the support is a glass material (its fusion temperature is low, about 800°C). In order not to exorbitantly increase the deposit resistivity, we have chosen a sodic glass material (mass proportions: 26.1% Na2O, 12.3% Al2O3, 61.6% SiO2). The glass and the beta-alumina are mixed by grinding in a planarian grinder in a liquid, until the granulometry is less than about 10 μm (which is necessary for depositing). The powder is then mixed for several hours with an organic binder and a dispersion liquid (composition: 10 g of the mix glass/beta-alumina, 0.5 g of PVB and 5 cc of dispersant) – Thermal treatment of the films After the serigraphic depositing of the thick film, the first stage of the drying is enacted at a temperature close to the ambient temperature for 12 hours, in order to evaporate the dispersant liquid without cracking the film. The deposit is then heated in order to thermally decompose the organic binder and to then melt the glass material. When the temperature rises above the fusion temperature of the glass material, the glass material links the film to the substrate, and also links the particles of material between them. In this case, the chosen glass is an ionic conductor which allows us to maintain the conductivity properties necessary for it to act like a solid electrolyte.
Material Elaboration
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Table 7.5. Heating program
The curve displaying the temperature as a function of time is shown in Table 7.5. Finally, it is important to note that the temperature of the plateau is going to be adapted to the composition ratio E-alumina/glass. – SO2 treatment The chemical treatment of the sintered pellets or the thick films occurs in the presence of sulfur dioxide diluted at 1% in dry air, for 90 minutes at 600°C. Such a treatment is enough to begin the elaboration of sodium sulfate using beta-alumina. 7.3.4. Characterization of materials7, 8
7.3.4.1. Physico-chemical characterization of the sintered materials The characterization of these materials is mostly linked to the effect of the sulfur dioxide treatment. Figures 7.40a and 7.40b make it possible to compare the different analysis, using X-ray diffraction, of a sample of beta-alumina crystallized at high temperature, pellet-shaped and sintered using the previously described process, before and after the SO2 treatment The first is the diffractogram of a sample of beta-alumina not treated with SO2. The characteristic peaks of the beta-alumina can be recognized. If we compare this diffractogram with that of the SO2-treated sample, we can distinguish three peaks, located at 22.6°, 23.6° and 25.5° characteristic of the sodium sulfate (formula Na2SO4).
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Figure 7.40. a) Diffractogram of a beta-alumina pellet not treated with SO2; b) diffractogram of a beta-alumina pellet treated with SO2
A scanning electron microscope allows us to observe the evolution of the betaalumina before and after sulfatation. The photograph (Figure 7.41) shows at great magnification (x 3,500), the sample surface before the SO2 treatment. We note the presence of needle-shaped peaks or inflorescence whose structure is similar to the structure of hydrated sodium carbonate. This compound confirms the reactivity of the beta-alumina even at ambient temperature.
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To prevent the presence of such a phase on the samples, we proceed to the SO2treatment just after the sintering stage in order to prevent a weak homogenity for the sodium sulfate.
Figure 7.41. Photograph of a beta-alumina pellet not treated with sulfur dioxide
Figure 7.42. Photograph of a beta-alumina pellet treated with sulfur dioxide
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Figure 7.43. Photograph of a sodium sulfate pellet after several temperature cycles
If we observe a sample after SO2-treatment (see Figure 7.42), we can see the influence of such a treatment. Indeed, the surface shows a multitude of crystals, anchored in what resembles the formation of a compact and homogenous film, composed of a compound difficult to identify with mere photography. Nevertheless, this evolution of the surface texture has been observed in every SO2-treated sample. In Figure 7.43, showing the sodium sulfate sample, we can observe deep cracks after several temperature cycles. 7.3.4.2. Physico-chemical treatment of the thick films We seek here to characterize different films distinguished by their composition, their sintering temperature or the absence of sulfur dioxide treatment. These films are characterized, on a crystallographic level and on a structural plan, by the X-ray spectrometry and the scanning electron microscope respectively. – Influence of the composition ratio beta-alumina glass Three different compositions have been tested: – 60% of glass and 40% of beta-alumina; – 50% of glass and 50% of beta-alumina; – 40% of glass and 60% of beta-alumina.
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The photographs in Figures 7.44, 7.45 and 7.46 – produced at low magnification (x 55) – show the influence of the composition on the morphology of the films treated at 900°C. In the case of the 50/50 ratio the link to the support is the worst of the three: this is due to the fact that the two materials (glass and beta-alumina) have very different thermal coefficients. We observe on these photographs the trace left by the serigraphy screen; this trace appears because of viscosity phenomena which are a function of the composition. The photographs in Figures 7.47, and 7.48 – obtained with a greater magnification (x 1,600) and realized in the middle of the thick film – show a difference between the depositing made with 40% and 60% of beta-alumina. These films are treated at 1,000°C, but the distinction is valid whatever the heating temperature. The film made with 40% of beta-alumina possesses the properties of wettability which allow the beta-alumina to form an amorphous matrix. Nevertheless, the structure shows cracks and cavities.
Figure 7.44. Photograph of the surface of thick films containing 40% of beta-alumina
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Figure 7.45. Photograph of the surface of thick films containing 50% of beta-alumina
Figure 7.46. Photograph of the surface of thick films containing 60% of beta-alumina
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Figure 7.47. Photograph of a thick film containing 40% of beta-alumina not treated with sulfur dioxide (1,000°C/2 hours, x 1600)
Figure 7.48. Photograph of a thick film containing 60% of beta-alumina not treated with sulfur dioxide (1,000°C/2 hrs, x 1600)
Yet, in the film containing 60% of beta-alumina, the structure shows jointed grains. Furthermore, the beta-alumina particles are not necessarily wrapped up in the glass. As in the case of sintered material, these films react in the presence of CO2 and water vapor. This causes the apparition of inflorescences: we can thus assume the formation of sodium carbonate.
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No fundamental change has been observed in the structure when we modify the adhesion temperature of the glass. – Influence of the thermal treatment on the films The presence of glass mixed with beta-alumina, rich in sodium, can provoke, at high temperatures, a certain number of chemical reactions (especially the formation of nepheline). This compound (formula: NaAl(SiO4)) crystallizes into a hexagonal shape characteristic of the Na2O-SiO2-Al2O3 system phase diagram (see Figure 7.49).
Figure 7.49. Na2O-SiO2-Al2O3 system phase diagram
The diffractogram in Figure 7.50 displays the diffraction rays of a thick film containing about 60% of beta-alumina treated at 900°C. Į and ȕ characterize the rays of alpha-alumina and those of beta-alumina respectively, used as substrate for this application. In this figure, we can also distinguish the rays characterizing the
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nepheline. The nepheline can be very clearly identified. The diagram shows five characteristic rays contained between 20° and 30°. The intensity of these rays indicates a great number are present. Diffractograms for different thermal treatments show that the nepheline formation is accompanied by an increase in the annealing temperature, at least for films containing 40% of beta-alumina and a large quantity of glass.
Figure 7.50. Diffractogram of a thick film containing 60% of beta-alumina
– Influence of the sulfur dioxide treatment The photographs in Figures 7.51 and 7.52 show the films obtained after treatment. The films displayed are those that were captured by the photographs in Figures 7.47 and 7.48. In the first, we can clearly observe the influence of this treatment, which turns the amorphous glass matrix on the surface and lets a great number of crystals appear, produced by the reaction of the sulfur dioxide producing sodium sulfate. The film which contains more beta-alumina does not show a great modification of its structure, although we can observe small crystals stemming from compact blocks; this tends to prove that sodium sulfate is formed. These observations show that the material cracking is more noticeable with films containing 40% of beta-alumina.
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Figure 7.51. Photograph of a thick film containing 40% of beta-alumina treated with sulfur dioxide (1,000°C/2 hrs, x 1600)
Figure 7.52. Photograph of a thick film containing 60% of beta-alumina treated with sulfur dioxide (1,000°C/2 hrs, x 1600)
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The influence of the treatment temperature is the same as in previous results. Nevertheless, in the case of films containing 60% of beta-alumina, the cracks become larger and more numerous when the heating temperature increases. In the case of the films containing 40% of beta-alumina, the influence of the SO2-treatment is more difficult to detect, and it becomes more and more difficult when the heating temperature increases. It is not possible to simply observe the adhesion of the sodium sulfate to the support because of the thermal cycle. Only electric tests allow us to check this property. 7.3.5. Electric characterization
Figure 7.53 compares the value of resistance obtained for the sintered material and the 6 thick film samples elaborated at different temperatures and containing different quantities of glass – all of these samples have been treated with sulfur dioxide. These results confirm the great difference between the two elaboration processes, with measured values 2 to 3 times higher for thick films than for sintered beta-alumina. This impedance varies according to the thermal treatment and percentage of glass in the film.
Figure 7.53. Variation of the electric resistance of the sintered material and the thick films according to the temperature
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At 600°C, these results are more clearly depicted in Figure 7.54, which compares the resistance value of the different materials studied and their main components. On the abscissa, there is the percentage of beta-alumina in the mixing beta-alumina + glass. At 0%, the resistance value of a thick film composed solely of glass is displayed and at 100%, those of a sintered pullet composed of beta-alumina only, of sintered pullet of sodium sulfate and a sintered pullet of nepheline, prepared for this study.
Figure 7.54. Comparison of the electric resistance value between the compounds and the different thick films (values obtained at 600°C)
It is important to note that these different compounds have intrinsic resistance (magnitude: kOhm) though the thick films have larger resistance values, even very high sometimes. The greatest values are observed for the films containing 50% of beta-alumina (magnitude MOhm). These films display a lot of cracks which are visible to the naked eye. The deposits containing 60% and 40% of beta-alumina, though, seem to possess a superior conductivity. For the film containing 40% of beta-alumina, this value is independent of the thermal treatment. However, at 60% it decreases when the thermal treatment temperature decreases.
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We can conclude, using these results, that the resistance value of the sensitive material depends largely on the development parameters, and that this resistance value can be used as a quality control in the elaboration process level. 7.4. Bibliography 1. N. YAMAZOE, N. MIURA, “Some basic aspects of semiconductor gas sensors”, Chemical Sensor Technology, vol. 4, Elsevier, 1988. 2. N. MURUKAMI, K. TANAKA, K. SASAKI, K. IHOKURA, “The influence of sintering temperature on the characteristics of SnO2 combustion monitor sensors”, Analyt. Chem. Symp. Ser., vol. 17, 165-170, 1983. 3. S. VINCENT, Influence du traitement thermique sur les propriétés électriques du dioxyde d’étain polycristallin. Application à la détection du méthane, Thesis, INPG-ENSMSE, Saint Etienne, 1992. 4. W. GÖPEL, K. SHIERBAUM, “SnO2 sensors: current status and future prospects”, Sensors and Actuators, B 26-27, 1-12, 1995. 5. P. BREUIL, Elaboration et caractérisation de couches minces de dioxyde d’étain sensibles à l’action des gaz, Thesis, INPG-ENSMSE, Saint Etienne, 1989. 6. D. DEPTUCK, J.P. HARRISON, P. ZAWADZKI, “Measurement of elasticity and conductivity of three dimensional percolation system”, Physical Review Letters, 54, 9, 1985. 7. E. FASCETTA, Etude d’un capteur potentiométrique élaboré à partir d’alumine bêta, Interprétation des phénomènes électrochimiques observés en présence de dioxyde de soufre et de monoxyde de carbone, Thesis, INPG-ENSMSE, Saint Etienne, 1993. 8. C. PUPIER, Etude d’un capteur de gaz sensible au monoxyde de carbone et aux oxydes d’nitrogen élaboré à base d’alumine bêta, Thesis, INPG-ENSMSE, Saint Etienne, 1999.
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Chapter 8
Influence of the Metallic Components on the Electrical Response of the Sensors
8.1. Introduction To detect gases, the presence of a metal at the surface of the sensitive part of the sensor is necessary for electrical contacts. Sometimes, the metal is present in order to favor chemical reactions at the surface of the sensitive material. Sensors are always used at temperatures higher than 300°C, so we will use in the two cases the same metal, either gold or platinum or palladium, in both cases: that is, noble metals. The depositing of the metal on the sensitive material is rather difficult. These difficulties are related to the temperature at which the sensor is used and to the adhesion of the metal to the sensitive material (which is often a metallic oxide). The mechanic stability of the device is ensured by a good adhesion of the metal to the surface. The adhesion also influences the electric properties. The properties of the junction between metal and oxide are linked to the structure and as a consequence to electric conductance. Furthermore, such an interface can act as a catalyst to the phenomenon of oxidation or reduction concerned.
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The synergy between the two materials can indeed generate new catalytic effects or amplify catalytic effects which can alter the sensor’s response. The gas-metaloxide system is located at the metal-oxide interface; this zone is called the three boundary point. 8.2. General points 8.2.1. Methods to deposit the metallic parts on the sensitive element We will distinguish the following. – The methods which consist of depositing metallic wire These methods, used with sintered pellets, are especially designed to solve electrode problems. In this case, a part of these wires (diameter 0.1 mm) can be inserted directly into the powder contained in the matrix before the compression. The remaining wires are placed at the surface of the powder. After the compression of the powder, we are able to use the emerging part of the wires. We can also use metallic pastes, which, thanks to the presence of a glue, enable the wire to stick to the substrate. It is generally necessary to steam at 100°C to ensure the evaporation of the solvent, then to anneal the product at about 800°C. These methods are not easily implemented and reproducible, though they have the advantage of combining electrical contacts and wire connections in the same process. – Method of cathodic pulverization or thermal evaporation In this case, the metal is directly deposited as a thin film on the sensitive element. Perfectly controlled, and allowing for a good reproducibility, this process can be used to implant electrodes or for the realization of a catalytic filter. To exploit such technology to its maximum, at least for the sensitive elements deposited as thick or thin films, and to avoid the use of a glue, we can extend the metallic deposit on the substrate by tracks reaching zones exterior to the heating zones of the sensor. The temperature of these zones allows us to solder with tin.
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These devices will be described in detail in Chapter 9, which is devoted to applications. – Method of mixing or impregnation Solely exploited for catalytic property designs, these methods favor the dispersion of the metallic element in the sensitive element or at its surface. For the mixing with sintered pellets, we have only to prepare a mixture of the two powders before the compression operations. This method does not necessarily favor the presence of the metal at the surface of the sample. To achieve this, we employ the impregnation method. The sensitive element is immersed in a liquid precursor of the metallic element to be deposited. An adapted thermal treatment then makes it possible to obtain metallic clusters evenly distributed at the surface of the sensitive element. The metal plays a major role in the device because of its catalytic properties and because of the importance of the heterogenous interfaces generated at the surface of the sensitive element. Consequently, researchers have tried to understand the role played by electrodes in the response of chemical sensors to gas. The results of this research allow us to propose conduction mechanisms that fit these devices and/or systems. 8.2.2. Role of the metallic elements on the sensors’ response We will offer some familiar examples. Studies undertaken in 1986 by C. Pijolat1 demonstrate the influence of the electrode’s nature on the response of a sintered SnO2 sensor to benzene effect. These results (Figure 8.1) show the difference between gold and platinum as the metallic elements used to facilitate the electric contacts by inlaid wires. The effects of the metal are explained by a significant difference in temperature on the response curve. This difference in the sensitivity of the sensors can be attributed to phenomena activated by the temperature, among which electric potential barriers created at the oxide/metal interface.
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Figure 8.1. Electrical conductance of sintered SnO2 as a function of the temperature and according to the nature of electrodes
U. Hoefer,2 working with thin films of SnO2, exploits the results obtained using several electrodes of platinum but separated by different distances. This variation of a geometric parameter allows us to measure different electric resistance. Thus, it is observed that only the zones located near the electrodes are sensitive to gas effect. Furthermore, U. Weimar3 has shown, by complex impedance spectrometry, that in certain conditions, most of the electric phenomena are located near the electrodes. Weimar highlights the importance of the three boundary point: semiconductor/metal (electrode)/gas in the detection of phenomena and speaks of a space-charge area linked to this three boundary point. The extraction of an electron from this depletion zone located near the electrode has an electric effect larger than an extraction initiated far from the electrodes and, subsequently, less depleted.
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Finally, another model has been proposed by K. Varghese.4 According to this model, the material has a capacitive effect because of the accumulation of oxygen compounds in the zone where the SnO2 and the electrodes are in contact. The diagram proposed (Figure 8.2) shows the polarization of electrodes and indicates the presence of a large depletion zone that spreads from the electrode. From these works, we will remember that significant electric phenomena are located on the three boundary point oxide-metal-gas. Maybe this is one of the reasons why most of the commercial devices use interdigitating electrodes, which allows us to multiply the zones which behave like a three boundary point.
Figure 8.2. Model for electrode influence as proposed by K. Varghese
All of these examples are relative to tin dioxide, and subsequently relative to a semiconductor material. Nevertheless, there are comparable studies on solid electrolytes, more specifically beta-alumina. In 1982, D.E. Williams5 proposed a potentiometric sensor, elaborated using betaalumina and two metallic electrodes located in the same gaseous phase. Furthermore, these two electrodes were of different natures and sizes.
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We must remember that a classic potentiometric device works using two identical electrodes located in different compartments. The partial pressure in oxidizing gas or reducing gas, which is different in the two compartments influences the electrochemical potential on each electrode, and subsequently the electric potential between them. The originality of D.E. Williams’ device is the fact that the dissymmetry of the device is no longer linked to a difference in the (oxidizing or reducing) gas partial pressure on each electrode, but to the nature and/or geometry of the electrodes. Again, the role of the metal is not linked to a mere connection problem. 8.2.3. Role of the metal: catalytic aspects In general, we know that the presence of certain metals increases the oxidizing or reducing rate of a gas, and can even lead to selective reactions. Yet, in the case of a sensor, the presence of these catalysts is not limited to a mere reaction between gas and metal, and the electric effects observed seem to indicate that the whole process uses an oxide-metal-gas system. The problem is then to understand the synergy which exists between the catalyst and the sensitive element. As was shown by S. Morrison6 (see Figure 8.3), a simple catalyzing phenomenon with a metal located at the surface of SnO2 would not lead to an evolution of the electric performances of the material
Figure 8.3. Catalyzing mechanism at SnO2 surface according to S. Morrison
To describe this synergy between metal and tin dioxide, different mechanisms have been proposed.
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8.2.3.1. Spill-over mechanism The spill-over is a well-known process in the field of heterogenous catalysis. It has been particularly studied in the case of platinum and palladium. This process is illustrated in Figure 8.4.
Figure 8.4. Spill-over mechanism according to S. Morrison
On contact with the metallic catalyst, the oxygen molecule dissociates. The atoms migrate towards the surface of the oxide support. Then, by reacting with an electron of the oxide, ionization occurs. This consumption amounts to a modification of the oxide space-charge layer. O2 ( gas ) 2 sM 2(O sM )
O sM eOx s (O s ) sM
sM indicates an adsorption site on the metal, and s, an adsorption site on the oxide. Regarding kinetics, the presence of the catalyst makes the regeneration of the O—s compound easier at the surface. As for as the response to H2 action, the proposed model implies a dissociation of H2 on the metal and a reaction with the absorbed oxygen. H 2 ( gas ) 2 sM 2( H sM ) ( H sM ) s ( H s ) sM 2( H s ) (O s ) H 2O ( gas ) eOx 3s
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In this case, it is the consumption of the absorbed oxygen which leads to an evolution of the electric properties of SnO2. We observe that for oxygen dissociation in the first mechanism, the oxidation of the gas does not happen at the surface of the catalyst. The catalyst only increases the dissociation rate of the concerned gases. We also speak of “chemical sensitization”. A good dispersion of the catalyst is necessary to obtain a large effect. 8.2.3.2. Reverse spill-over mechanism The obverse of the spill-over mechanism, the reverse spill-over mechanism, mentioned by K. Grass,7 consists of an adsorption of the oxygen on tin dioxide, followed by a migration of the adsorbed species towards the metal, as is shown in Figure 8.5. The reaction between the gas and carbon monoxide takes place at the point where metal and oxide are in contact.
Figure 8.5. Reverse spill-over mechanism concerning oxygen, proposed by K. Grass and H. Lintz
Few authors mention such a mechanism and, to our knowledge, no publication gives information on the electric consequences of such a phenomenon on tin dioxide. 8.2.3.3. Electronic effect mechanism A third concept based on an electronic exchange between the metal and the semiconductor is behind two more mechanisms.
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The first, proposed by S. Morrison,6 describes an adsorption of oxygen at the metal’s surface accompanied by electronic transfer. The second, proposed by N. Yamazoe8, 9 takes into consideration the formation of an oxide film at the surface of the metal. – Case proposed by S. Morrison The chemisorption of the oxygen is illustrated in Figure 8.6.
Figure 8.6. Electronic effect mechanism, according to S. Morrison
In this case the oxygen takes the electron to the metal according to the equation: O2 ( gas ) 2 sM 2eM 2(O sM )
eM and sM respectively indicate an electron stemming from the metal and an adsorption site on the metal. The oxygen remains adsorbed on the metal. This negatively charged adsorbed phase is the cause of an electric perturbation at the SnO2-metal interface. This perturbation amounts to an electron exchange between the two materials. Again, this loss of an electron implies a modification in the space-charge layer. In the presence of a reducing gas RH2, we witness its oxidation at the surface of the catalyst according to the equation: RH 2 ( gas ) 2(O sM ) RO ( gas ) H 2O ( gas ) 2eM
Subsequently, an electron is given back to the oxide according to the equation: eOx eM
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Although this model clearly indicates the presence of a space-charge layer in the semiconductor, its exact location with regards to the metal and the oxide is not accurately determined. – Case proposed by N. Yamazoe In this case, we witness a chemical reaction between the metal and the oxygen. This reaction leads to the formation of oxide. We will note that such a reaction does not imply any modification of the electric properties of SnO2.
Figure 8.7. Schematization of the electronic effect mechanism with oxide formation
The presence of an oxide film at the surface of the metal implies a perturbation at the metallic oxide-SnO2 interface. Yamazoe positions the space-charge layer on top of the metal, as indicated in Figure 8.7. In these two propositions dealing with the electronic effect mechanism, the apparition of a new phase at the surface of metal (an adsorbed phase or metallic oxide) is the cause of an electron transfer from the semiconductor towards the metal. Given the thinness of the space-charge layer, which is about several angstroms at most at the gas-metal interface, it is difficult to imagine that such a perturbation could create new equilibriums at the SnO2-metal interface, which could themselves induce a space-charge layer located on top of the metal. Therefore, Yamazoe’s proposition is called into question. Morrison’s proposition seems more likely and will be used as a working hypothesis for the case of a physico-chemical model in Chapter 10, in which a localization of the space-charge layer will be proposed. 8.2.3.4. Influence of the metal nature on the involved mechanism We are going to see how the authors have tried to predict the kind of mechanism (spill-over or electronic effect) as a function of the added metal nature. The main studies focus on the three most used metals, that is, silver, platinum and palladium.
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Knowing the oxidation stages of the metallic aggregates is the first step that we must take in order to clearly understand the reaction process. In the case of palladium and silver, it is generally admitted that these elements form stable oxides (Ag2O and PdO) at the functioning temperatures of the sensors, whereas the platinum is less oxidizable. Initially, we considered that Pd and Ag would suit sensitization by electronic effect, while platinum would favor spill-over. These observations have only been partially confirmed by investigations performed using a XPS9, 10 method. This technology allows us to measure the energy of a Sn-O bond and oxidation degree of the metal simultaneously. If a correlation exists between these values, we conclude that the mechanism is an electronic effect. Such studies have been performed under different oxidizing (O2) or reducing (H2) atmospheres. Thus, Yamazoe notes an energy variation in the bond between metal and oxygen for SnO2 doped with silver. There is also a variation of the oxidation degree of the metal during the oxidation of Ag in a Ag2O compound. Though we also observe a variation of this degree with palladium and platinum, there is no variation of the bonding energy with these metals. This initial study proposes an electronic effect for Ag, whereas the spill-over mechanism dominates for Pt and Pd. Using the same kind of study Matsuhima shows the energy of the Sn-O bond is sensitive to the palladium concentration dispersed in SnO2. For low concentrations of palladium (<3% of the whole mass), he has demonstrated that the mechanism involved with Pd can be electronic effect. A different study realized with thin films of tin dioxide doped with platinum has been proposed by M. Gaidi.11 Gaidi assesses the oxidation degree of the platinum particles (using X-rays absorption spectroscopy), and links it to the electric measures performed in the presence of CO. These works, which describe islets of oxidized platinum (PtOx) at the surface of the metallic particles, clearly show the existence of a direct relation between the oxidation degree of the metallic particles and the electric response of the device, according to the following kind of reactions: PtO2 2CO ( gas ) 2CO ( gas ) Pt
Guidi concludes that an electronic sensitization exists for the platinum. Furthermore, the results indicate the existence of an optimal size for the metallic particles, which gives the maximum sensitivity to the tested films. With other metals, the mechanisms involved are not well known and are rarely studied. Nevertheless, we can quote the original study of Y. Shimizu,12 who
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witnessed a sensitizing effect for gold on sensors designed to detect hydrogen. The author attributes this effect to a chemical sensitization (spill-over). In short, aside from silver, where the electronic effect is often mentioned, the correlation between a mechanism and a metal is not automatic, and no general law can be applied. The type of mechanism depends not only on the metal and its oxygen affinity, but also on its environment inside the oxide (concentration, size of the particles). Furthermore, the coexistence of the two mechanisms seems to be possible. On the basis of these considerations, new experiments have been carried out with tin dioxide and beta-alumina. In both cases, our concern, essentially, is with the relatively uncharted aspects of the role played by metallic elements in behavior associated with gas sensors. 8.3. Case study: tin dioxide To begin this study, it is necessary to obviate the phenomena linked to the electrodes. Thus, for the purpose of being able to separate and analyze the different contributions of the metal on the interactions between gas and solid, a reactor has been specially designed. This reactor must be able to by turns isolate and bring into contact particular zones of the sample. These zones are pinpointed by the presence or absence of electrodes. The samples have to be elaborated and conditioned in a specific way.13, 14 8.3.1. Choice of the samples The two types of samples tested are displayed in Figure 8.8. They are composed of a tin dioxide bar (length: 10mm; width: 4mm; thickness: 1 mm). The bars are carved in a tin dioxide block. To obtain this block, an isostatic compression at 4.108 Pa is applied to a tin dioxide powder, it is then sintered at 800°C. The golden metallic films associated with these samples, are elaborated using cathodic pulverization, and have a thickness of 450 nm.
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Figure 8.8. Configuration for metallic zones
On each sample, we can distinguish three different sections. For the first kind of sample, the metallic deposits are realized at the two tips constituting the first and third section. The second section is composed of tin dioxide only. In the second kind of sample, the second section will be associated with a new metallic film. In both cases, the metallic deposits located in sections 1 and 3 are used as the measuring electrodes. 8.3.2. Description of the reactor The goal is to conceive a reactor which allows us to measure the electric conductance of the devices studied and enable us to independently vary the gaseous atmospheres of the different sections. In fact, because of the symmetry of the device, two zones will have to be taken into consideration: an external zone (sections 1 and 3) and an internal zone (section 2). Such a device has been built by J.C. Marchand13 and is displayed in Figure 8.9. It is jacketed to enable the imposition of different atmospheric conditions in internal and external compartments. The internal tube (diameter 10 mm) includes two rectangular windows diametrically opposite. Those windows are 2 mm wide and 5 mm long. Thus, its dimensions are very close to the dimensions of the bar. The air tightness of the sensitive element level is ensured by quartz wool, which is inserted between the bar and the tube at the level of the two windows. The external tube has a diameter of 25 mm. This device is placed in a vertical furnace provided with a regulation system.
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In order to minimize the possible gas leakage, the same gas linear flow rate Vl is applied in the two compartments (internal and external); this implies a relation between the gas flow rate D and the diameters d of the tubes.
Figure 8.9. Device description with internal and external compartments
Influence of the Metallic Components 2
DE d E
291
2
DI d I
Given: DE
6, 25 DI
The internal flow rate is adjusted at 21 l/hr, and the external flow rate at 12.5 l/hr. Air tightness is controlled by an infrared analyzer. It is possible to independently vary the nature of the gaseous atmosphere in the two compartments and subsequently, on the different sections of the sample. To make the introduction of the samples easier, the electric contacts are elaborated by the mechanic pressure of metallic elements using a system of feeders. The experiments are carried out at 450°C. 8.3.3. Experimental results 8.3.3.1. Influence of the oxygen pressure on the electric conductivity Firstly, we have tried to assess the effects of a variation in oxygen partial pressure on the two zones of the sensor, that is, the internal zone (marked I) and the external zone (marked E). In practice, we have chosen to study two kinds of atmosphere: an atmosphere with 1% oxygen and an atmosphere with 20% oxygen. In both cases the oxygen is diluted in nitrogen. 8.3.3.1.1. Sample with two metallic zones The results relative to the first kind of sample are displayed in Figure 8.10. As expected, a decrease in oxygen (from 20% to 1%) in E and in I entails an increase in the conductance (field B). These effects are entirely reversible, as indicated by the results reported in field C. These results were expected, given the nature of this oxide: the conductivity decreases when the quantity of chemisorbed oxygen increases.
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This is because the concentration of the ionized vacancies and, subsequently, of the free electrons stemming from the ionization of these vacancies decrease with the oxygen pressure.
Figure 8.10. Evolution of the conductance of sensors disposing of two metallic zones submitted to different atmospheres at 450°C
This phenomenon, which causes the formation of a depletion layer at the surface of the oxide, can involve the whole surface of the material or be limited to several zones neighboring the zone occupied by electrodes. Furthermore, we note that similar tests previously conducted with platinum have led to the same results. To solve this kind of problem, a new cycle of experiments has been carried out. During its first stage, the external zones were submitted to an atmosphere low in oxygen (1%); conversely, a high concentration is imposed in the internal zone. These results are displayed in zone D of Figure 8.10; according to this, the device in only partially blocked by an increase in oxygen concentration in the internal compartment, which is emptied of metallic elements. Thus, tin dioxide is very slightly perturbed by an increase of the oxygen pressure. The amplitude of this phenomenon is limited by the difference between the signal found in fields B and D. If the oxygen was active on tin dioxide alone, we
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would have recorded a conductance close to value G°, which represents field A in Figure 8.10. Conversely, if we impose a high concentration of oxygen on the external zones of the sample, while the internal remains under a low concentration, we obtain the results displayed in field F in Figure 8.11. These results confirm the fact that the disruptive effect of the oxygen is much more significant when the tin dioxide is associated with the metallic electrode. The slight effect observed in field F has an intensity close to the difference observed between fields B and D. This difference can be attributed to the effect of oxygen on tin dioxide alone. If we neglect the contribution of oxygen alone (zone 2), we obtain a system with two switches connected in series (zones 1 and 3) so that they are on under a low concentration of oxygen, and off under a greater concentration. The large effect of electric locking by the oxygen is supposedly linked to the presence of metallic electrodes set at each tip of the semiconductor. However, with such a setup the electric currents are channeled through the surface of the electrodes, the blocking effect could be attributed to a junction effect between the metal and the oxide, which is represented by a Schottky barrier adjusted by oxygen pressure. To confirm or invalidate such a hypothesis, a new series of experiments must be carried out on the second kind of sample, which has a metallic zone deposited at the surface of the internal zone. This metallic zone, without any connection to the system of electric measurement, is a mere element of the oxide-metal-gas system. 8.3.3.1.2. Samples disposing of three metallic zones To be able to compare the two samples, we have displayed both results in the same diagram (see Figure 8.11). Firstly, as indicated by fields A and B in Figure 8.11, we note that with the same gaseous concentrations, the conductance of the sample with three metallic zones is slightly lower than the conductance of the sample with two metallic zones. This indicates that adding a metal in the internal zone entails another effect of electric blocking. In any case, the effects are perfectly reversible, as indicated in field C, in which the oxygen concentration is 20%. The situation described in field E is associated with a concentration of 1% at the level of the electrodes and a concentration of 20% in the internal zone. The results are significant: we observe an electric blocking effect much larger for the sample disposing of three metallic zones than with the sample disposing of two metallic zones.
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Figure 8.11. Evolution of the conductance of sensors with three metallic zones submitted to different atmospheres at 450°C
This last experiment shows that the action of electric locking by oxygen on tin dioxide in the internal zone is accentuated if a metal is present. Finally, in the reverse case, where the external compartment has an oxygen concentration of 20% and the internal compartment a concentration of 1%, the sample with three metallic zones shows an electric blocking slightly larger than the one observed in the case of the device possessing two metallic zones. Thus, in all the cases, the presence of a third metallic zone amplifies the effect of electric locking by oxygen on tin dioxide. The device with three metallic zones is comparable to a system possessing three switches connected in series. The same results have been obtained with three platinum zones. As far as the action of the metal is concerned, at least in the internal zone, we can imagine that it generates a new space-charge layer in the oxide and that the thickness of the zone is controlled by the oxygen concentration. This situation is perfectly compatible with the notion of the three boundary point. This aspect will be specifically developed in Chapter 10, relative to the models of the phenomena.
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8.3.3.2. Influence of the reducing gas on the electric conductions In a third series of experiments, we have tried to assess the effect of a reducing gas on the external and internal zones of a sensor possessing of two metallic zones, which are located in the external parts of the sensor. In practice, the tests are carried out using a bottle of different gases diluted in air. We worked with carbon monoxide (500 ppm), methane (1,000 ppm) and alcohol (200 ppm).
Figure 8.12. Evolution of the conductance of sensors with two metallic zones submitted to different atmospheres at 450°C
The results obtained for a device with two gold electrodes are displayed in Figure 8.12. As expected, and as indicated by the results reported in fields B and C, all the reducing gases provoke a reversible increase of the conductance in the two compartments. Unlike oxygen, the reducing gases possess an electric unlocking action. This is due to the fact that these gases react with chemisorbed oxygen, which decreases the concentration of this species.
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As with oxygen, we still have to determine whether this unlocking effect is relative to the electrodes, tin dioxide or a combination of the two. To do this, we have “unblocked” the external zones using the presence of a reducing gas, while locking the internal zone using air. The results displayed (field D) lead to the supposition that gas does not cause any electric effect on tin dioxide alone. This effect is indeed limited to the difference between fields B and D. Conversely, if we only “lock” the external zone (we impose the presence of air), while the internal zone is maintained under the presence of a reducing gas, we observe that the slight effect produced (field F) has an intensity close to the intensity observed in fields B and D. Thus, this effect is relative to the effect of the reducing gas on tin dioxide alone. These results demonstrate that the electric effect due to the presence of the gas is much greater when the tin dioxide is associated with the metal. This behavior confirms the results previously obtained with oxygen, if we admit that the reducing gases consume the chemisorbed oxygen. As for the detection, we note that the electric effect, associated with the presence of a reducing gas, is amplified by the presence of a metal. This conclusion only justifies the many attempts by researchers to increase the sensitivity of the sensors by adding metallic elements in the sensitive element. 8.4. Case study: beta-alumina We have seen in section 8.2.2 that the functioning of the potentiometric sensor elaborated with beta-alumina was wholly associated with the different nature of the electrodes deposited at its surface. The research carried out on this kind of device has until now been limited to sensors functioning because of a dissymmetry linked to the gold-platinum system constituting the electrodes. Consequently, it is interesting to study other dissymmetric systems involving either metallic couples different from gold/platinum or using electrodes of identical nature but different size.
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As far as the choice of metals is concerned, a bibliographic study allowed us to review several metals well known for their catalyst properties and which could be interesting to use in such an application. Among those metals, we have chosen rhodium which, like platinum, has good catalytic properties in oxidation, palladium, which is a good catalyst of hydrogenation, very efficient with hydrocarbons, and copper, which is a good catalyst to reduce the nitrogen oxides. 8.4.1. Device and experimental process During this study, we have used a test bed which allows us to record the electrical responses of four sensors simultaneously. This approach enables us to record information on different kinds of sensors with the same experimental conditions. The four samples are located on the same sample holder made of stainless steel. This sample holder is located on a quartz tube heated by a tubular and vertical furnace. The electric contacts at the surface of the serigraphed electrodes are elaborated by mechanic compression of gold, which is connected to platinum wires. The regulation of the gaseous atmosphere is ensured by several valves (micro leaks). Two of them are linked to the gaseous circuit, and allow us to independently inject two gases in the reactor. The device is described in Figure 8.13.
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Figure 8.13. Experimental device description
The gas pressures are regulated with two pressure gauges: a Varian capacitive gauge (0-105 Pa), and a Leybold Heraus ionization gauge (0.133–1,333 Pa). For the oxygen, all the experiments have been carried out under static conditions, with pressures contained between 10 and 104 Pa, and for temperatures contained between 250 and 600°C. To ensure a perfect stability of the system, the samples are initially conditioned under 10 Pa of oxygen for two hours. After each introduction of oxygen, it takes about 10 minutes for the system to reach equilibrium. In order to ensure a good reversibility at the level of the sensors’ electric response, these experiments are carried out again, with oxygen pressure decreased from 104 Pa to 10 Pa. 8.4.2. Influence of the nature of the electrodes on the measured voltage15 We have compared the electric response of several devices, while favoring gold and platinum. We have studied the platinum/gold, platinum/rhodium, platinum/copper, rhodium/gold and copper/gold couples. It is important to note that the first metal of each couple is the positive electrode of the device.
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8.4.2.1. Study of the different couples of metallic electrodes Preliminary experiments rapidly demonstrated the instability of the copper and palladium electrodes. Only gold, platinum and rhodium have allowed us to obtain reproducible results. In these conditions, we have essentially compared the performances of the reference couple Pt/Au to the performance of the Rh/Au and Pt/Rh couples.
Figure 8.14. Electric response of the sensors with different kinds of electrodes according to the oxygen pressure at 400°C (1 mbar = 102 Pa)
The electric responses, displayed in Figure 8.14, are relative to the evolution of the electromotive force recorded, according to the oxygen pressure at a temperature of 400°C. These results are representative of those registered in the whole temperature field. We observe that the rhodium/gold couple has a behavior similar to the one of the reference platinum/gold couple. The amplitude of the response is slightly lower in the case of rhodium.
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For the platinum/rhodium couple though, the amplitude of the response is extremely low. This can be explained by the fact that, just like platinum, rhodium has good catalytic properties on oxidizing reactions. These results confirm the catalytic role played by the electrodes in the detecting process. We take from this study the fact that, among the noble metals, the choice of electrode will have to take into account their catalytic properties, at least for the reaction concerned and, subsequently, for the gas to be detected. From what we have just seen, rhodium, associated with gold, could be used as an electrode for this kind of sensor. The main problem with its use is its poor stability at high temperatures. Indeed, heated in the presence of oxygen, this metal oxidizes with rhodium oxide Rh2O3 all the more quickly as the temperature increases. The oxidation kinetics of the rhodium, displayed in Figure 8.15, illustrates this phenomenon perfectly.
Figure 8.15. Oxidation kinetics of the rhodium under air according to the temperature
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8.4.2.2. Electric response to polluting gases For several couples of sensitive electrodes to oxygen action, it seemed interesting to test them in the presence of other gases like carbon monoxide or nitrogen oxides. Rhodium is indeed considered a good catalyst for the reduction of nitrogen oxides. Thus, we wanted to compare the observed sensitivities in order to determine selectivity criteria, and subsequently to be able to detect these different gases. For this purpose, we have tested the platinum/gold, platinum/rhodium and rhodium/gold couples. Figure 8.16 depicts the response of these three kinds of sensor under air at 500°C, and in the presence of different gases and mixtures.
Figure 8.16. Electric response of the sensors with different kind of electrodes in the presence of synthetic air, of carbon monoxide (300 ppm/air) and nitrogen dioxide (100 ppm/air) at 500°C
The injection of 300 ppm of carbon monoxide in the air implies a positive response for all the sensors, a result characteristic of a reducing gas. The greatest response is given for the Pt/Au couple. This confirms that these two metals have a great difference in their catalytic activities as far as the oxidation of carbon monoxide is concerned. The lowest response is obtained for the Pt/Rh couple.
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We then proceeded to introduce nitrogen dioxide (100 ppm in the air). The response of the Pt/Au and Rh/Au sensors in the presence of the mixture CO + NO2 indicates a decrease in the signal, confirming the presence of oxidizing gas NO2. Nevertheless, given the response of the Pt/Rh sensor, it seems this couple is not particularly sensitive to nitrogen oxide. Such behavior leads to the supposition that the catlytic activity of the rhodium electrode towards the mixture CO/NO2 is about the same as that of the platinum, while the catalytic activity of platinum towards carbon monoxide remains higher than that of the rhodium. These results are confirmed if we inject the same concentration of nitrogen oxide in the air. If we look at Tables 8.1 and 8.2, which call up the catalytic performances of the materials and the difference in the catalytic activities of the different couples, we note that, in the present case, there is a good correlation between the catalytic activities of the sensors and the sensitivities of the device associated with the metals (Table 8.3). CO oxidation
NO2 reduction
platinum
+++
++
rhodium
++
++
gold
0
0
Table 8.1. Catalytic property assessment of the different metals used
Reactivity to CO
Reactivity to NO2
Pt-Au
+++
++
Pt-Rh
+
0
Rh-Au
++
++
Table 8.2. Assessment of the difference in catalytic properties for the different metal couples used
Influence of the Metallic Components Response to CO
Response to NO2
Pt-Au
+++
++
Pt-Rh
+
0
Rh-Au
++
++
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Table 8.3. Assessment of the sensor’s response using the values from Table 8.2
In the present case we lay out a sensor which selects nitrogen dioxide above other gases like carbon monoxide. The only restriction involves the temperature domain, because of the instability of rhodium at high temperatures. This example shows that it is possible to use several couples of electrodes to control the selectivity of the device. If the choice of the electrodes is restricted, it is conceivable to use materials which are electronic conductors and more stable, like some metallic oxides. 8.4.3. Influence of the electrode size Convinced that the functioning of a potentiometric sensor relies on the dissymmetry of the physico-chemical effect which occurs at the two electrodes, we have thought it appropriate to check whether a mere geometric dissymmetry could be the source of potentiometric effects. To this end, electrodes of the same nature but of different sizes have been used. 8.4.3.1. Description of the studied devices The samples studied use two electrodes of same nature: gold or platinum, and their thickness is 450 mm. The have been deposited by cathodic pulverization at the surface of samples of serigraphed beta-alumina. For these electrodes, three different surfaces Si have been chosen: S1 = 20, S2 = 10 and S3 = 2 mm2. The reference electrode will always be the one with the greater area: Sref = 20 mm2. Finally, the distance between the two electrodes is kept constant and is about 2 mm long.
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The samples are characterized by the ratio E < 1. They always refer to the reference electrode following the law:
E
S1 / S ref , with i = 1, 2 and 3.
For each metal, we set out three different samples: the first is composed of two identical electrodes of great size, with a ratio ȕ = 1; the second, which possesses an electrode of intermediate size, has a ratio ȕ = 0.5; the third has small electrodes, with a ratio ȕ = 0.1. 8.4.3.2. Study of the electric response according to the experimental conditions The electric response of such devices has been studied according to the oxygen pressure and the temperature. The results, displayed in Figure 8.17, show that the electric response of the sensors, whose ratio ȕ = 1, is quite large, especially if gold electrodes are used.
Figure 8.17. Electric responses of sensors composed of two electrodes of same nature with a ratio ȕ = 1/10 according to the oxygen pressure at 300°C (a); and according to the temperature for an oxygen pressure of 0.1 mbar (b)
Firstly, we can note that the electric response of the sensors is negative. This means that for the reference electrode, the potential of a large electrode is less than that of a small electrode.
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We also note that the potential difference is much greater with gold electrodes than with platinum electrodes. This potential difference, which is relatively large for low pressures and low temperatures, decreases when we increase the oxygen pressure or the temperature. In the same conditions, as can be observed in Figure 8.18, the electric response of the devices which possess identical electrodes (E = 1) remains small and does not vary with the oxygen pressure or temperature. The response of the sensors, whose ratio E = 0.5 (see Figure 8.19), appears as the intermediate case.
Figure 8.18. Electric responses of sensors composed of two electrodes of same nature (gold or platinum) with a ratio ȕ = 1/1 according to the oxygen pressure at 300°C (a) and according to the temperature for an oxygen pressure of 0.1 mbar (b)
Figure 8.19. Electric responses of sensors composed of two electrodes of same nature (gold or platinum) with a ratio ȕ = 1/2 according to the oxygen pressure at 300°C (a) and according to the temperature for an oxygen pressure of 0.1 mbar (b)
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Another notable point concerns the variation of the sensors’ response according to the temperature. The influence of this parameter seems much greater when the electrodes are made of gold. In the case of gold, the electric signal increases, in a quasi-linear way with the temperature, while with platinum, it increases abruptly between 250 and 300°C and then stabilizes. This is true for E = 0.5 and 0.1. Nevertheless, for E = 1, we note that the electric response is very low and quasi-constant according to the temperature. Results stemming from the same kind of studies have been issued from the IXL Laboratory of Bordeaux.16 These results have been obtained on a potentiometric sensor designed to detect CO2. 8.5. Conclusion These experiments on different kinds of electrodes have allowed us to study the role of the electrodes more accurately. The nature of the metals used to elaborate the electrodes is an essential factor in the resistant sensor response and in the potentiometric sensor response to the gas present in a gaseous environment. Using the catalytic properties of these electrodes, it is then possible to select, for potentiometric sensors, the metal couple that most enhances the selectivity of the sensors towards certain gases. Nevertheless, the second part of the study shows that devices using electrodes of the same nature but of different size are likely to provoke great tension between the electrodes. The results involving the size of the electrodes are relatively unexpected if we take into account the fact that the electric potential is an intensive variable. This implies that the metal plays a peculiar role here. This aspect will be studied and analyzed in Chapter 10.
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8.6. Bibliography 1. C. PIJOLAT, Etudes des propriétés physico-chimiques et des propriétés électriques du dioxyde d’étain en fonction de l’atmosphère gazeuse environnante, Application à la détection sélective des gaz, Thesis, Grenoble, 1986. 2. U. HOEFER, K. STEINER, E. WAGNER, “Contact and sheet resistance of SnO2 thin films from transmission-line model measurements”, Sensors and Actuators, B 26-27, 59-63, 1995. 3. U. WEIMAR, W. GÖPEL, “A.C. Measurements on tin oxide sensors to improve selectivities and sensitivities”, Sensors and Actuators, B 26-27, 13-18, 1995. 4. O.K. VARGHESE, L. MALHOTRA, “Electrode sample capacitance effect on ethanol sensitivity of nano-grained SnO2 thin films”, Sensors and Actuators, B 53, 19-23, 1998. 5. D.E. WILLIAMS, UK Patent application GB 2 119 933 A. 6. S. MORRISON, “Selectivity in semiconductor gas sensors”, Sensors and Actuators, 12, 425-440, 1987. 7. K. GRASS, H. LINTZ, “The kinetics of CO oxidation on SnO2 supported Pt catalysts”, Journal of Catalysis, 172, 446-452, 1997. 8. N. YAMAZOE, “New approaches for improving semiconductor gas sensors”, Sensors and Actuators, B 5, 7-19, 1991. 9. N. YAMAZOE, Y. KUROKAWA, T. SEIYAMA, “Effects of additives on semiconductor gas sensors”, Sensors and Actuators, 4, 283-286, 1983. 10. S. MATSUSHIMA, Y. TERAOKA, N. MIURA, N. YAMAZOE, “Electronic interaction between metal additives and tin dioxide in tin dioxide-based gas sensors”, Jpn. J. Appl. Phys., 27, 1798-1802, 1988. 11. M. GAIDI, Films minces de dioxyde d’étain dopés au platine et au palladium et utilisés pour la détection de gaz polluants: analyses in situ des corrélations entre la réponse électrique et le comportement des agrégats métalliques, INPG Thesis, Grenoble, 1999. 12. Y. SHIMIZU, E. KANAZAWA, Y. TAKAO, M. EGASHIRA, “Modification of H2 – sensitive breakdown of SnO2 varistors with noble metals”, Sensors and Actuators, B 52, 39-44, 1998. 13. P. MONTMEAT, J.C. MARCHAND, R. LALAUZE, J.P. VIRICELLE, G. TOURNIER, C. PIJOLAT, “Physico-chemical contribution of gold metallic particles to the action of oxygen on tin dioxide sensors”, Sensors and Actuators, B 95, 1-3, 83-89, 2003. 14. P. MONTMEAT, Rôle des éléments métalliques sur le mécanisme de détection d’un capteur à base de dioxyde d’étain, Application à l’amélioration de la sélectivité à l’aide d’une membrane de platine, Thesis, INPG-ENSMSE, Saint-Etienne, 2002. 15. N. GUILLET, R. LALAUZE, J.P. VIRICELLE, C. PIJOLAT, “The influence of the electrode size on the electrical response of a potentiometric gas sensor to the action of oxygen”, IEEE Sensors Journal, 2(4), 349-5, 2002.
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16. F. MENIL, B. OULD DADDAH, P. TARDY, H. DEBEDA, C. LUCAT, “Planar LISICON-based potentiometric CO2 sensors: influence of the working and reference electrodes relative size on the sensing properties”, Sensors and Actuators, B 107, 695707, 2005.
Chapter 9
Development and Use of Different Gas Sensors
9.1. General points on development and use In this chapter, we will focus on the development of different types of sensors and their performance. All of this will be linked to certain kinds of applications. The development of a gas sensor is necessarily associated with that of the sensitive element. Nevertheless, it implies other developments linked to the heating element’s conception, as well as the electrode’s conception and conditioning. In general, the sensor’s elaboration will have to take into account certain functional criteria (its autonomy, the nature of its environment while functioning) and economic criteria, often linked to the fabrication cost and, consequently, the elaboration process. As far as the autonomy is concerned, it mostly depends on the electric consumption, the majority of which is used to heat the sensitive element. As far as the environment is concerned, we have to consider the nature of the interfering gases, their aggressive character on the physico-chemical plan and the presence of dust in the environment studied.
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9.2. Examples of gas sensor development We will distinguish here two kinds of sensors: the sensors which use sensitive elements elaborated using sintered materials, and those that exploit thick films. 9.2.1. Sensors elaborated using sintered materials As discussed in Chapter 7, this kind of sensor will, in this book, always be elaborated using tin dioxide. Only the micro-bars obtained by carving in a block of sintered tin dioxide have been used. These bars, in the shape of a parallelepiped, whose dimensions are 0.5 x 0.5 x 2 mm, can be fixed on two kinds of supports. The first kind favor very low energy consumption as far as heating is concerned. Developed by the CORECI Company, this support is realized using an alphaalumina plaque (it is of square shape and its side measures 63 mm; see Figure 9.1). The originality of this structure consists of carving indentations in the plaque in order to reduce the thermal loss. The sensitive element support then appears hung from two arms, on which the electric connections are deposited using gold serigraphic depositing. The heating element is deposited using the same principle; the deposit composed of platinum is located on the central part of the support. The sensitive bar is directly fixed at the back of the heating element using a gold paste. The connections to the external circuits are elaborated using this very paste. This sensor, manufactured by the CORECI Company, is then enclosed in a box, which does not let the suspending particles in (see Figure 9.2). A new version (see Figure 9.3), much less fragile than the latter on the mechanical plan, allows us to dispose of the gold paste as far as the connections with the external circuit are concerned.
Figure 9.1. CORECI support
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Figure 9.2. Caped sensor
Serigraphed gold lines on the support allow, in effect, the relay of these connections in the distant zones of the heating element situated at the other end of the support. The temperature of the lines is then compatible with a process of soldering using tin.
Figure 9.3. Sensor, new version
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9.2.2. Sensors produced with serigraphed sensitive materials In this case, the sensitive element is already supported by a structure made of alpha-alumina. The shape and size of this support will be chosen according to the operation that we wish to perform. The general process of elaboration for such a sensor is displayed in Figure 9.4. It is composed of several steps, with the aim of favoring the serigraphic process for each one. The principle used is similar to that used for sensors made with tin dioxide or beta-alumina, the only differences being located at the level of the electrodes: two gold electrodes for the tin dioxide used as a resistant sensor, a gold electrode and a platinum electrode for beta-alumina, used as a potentiometric sensor.
Figure 9.4. Elaboration process of a thick film sensor
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The different steps of the elaboration process are: – the elaboration of the heating element (see Figure 9.5). To make this device perfectly self-contained, it is necessary to inlay a heating element which has the shape of platinum resistance. This resistance is deposited using serigraphic depositing on ceramic substrates of alpha-alumina (length: 38 mm; width: 5 mm). After steam-drying at 105°C for 10 minutes, the sample is placed in a furnace. There, a thermal treatment is applied to the samples at 980°C for 10 minutes;
Figure 9.5. Heating resistance deposited using serigraphy
– the depositing of the sensitive element (see Figure 9.6). The sensitivity element is deposited using serigraphic depositing on the face opposite the heating element in shape of a rectangular film (2 x 4 mm).
Figure 9.6. Film of beta-alumina deposited using serigraphy
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The sample is then steam-dried at 105°C for 10 minutes. Afterwards, it is annealed at 900°C during 2 hours following the curve displayed in Figure 9.7. This thermal treatment is particularly important to stabilize the film of betaalumina:
Figure 9.7. Treatment cycle of beta-alumina
– the depositing of the electric connections (see Figure 9.8). In order to ensure the electric connections with the heating element and the sensitive element on each side of the sample, gold lines are serigraphed on the two sides of the support. After a steam-drying at 105°C for 10 minutes, the sample is annealed again at 850°C for 20 minutes;
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Figure 9.8. Gold lines deposited using serigraphy
– the depositing of the electrodes (see Figure 9.9). The electrodes are always deposited by serigraphic depositing on beta-alumina and the inks used are made of gold or platinum. These deposits are 5 mm long and 2 mm wide. The distance between the electrodes is about 2 mm.
Figure 9.9. Serigraphed electrodes Au and Pt
As regards tin dioxide, the electrodes can be deposited by serigraphic depositing or by cathodic pulverization. This last method gives better results at the level of the selectivity;
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– the dielectric depositing (see Figure 9.10). The last step consists of depositing a dielectric film on the heating resistance by serigraphic depositing. The role of this film is to protect the platinum resistance in order to prevent any short-circuit and the interactions between gas and platinum. The annealing follows the same curve that was followed for the other lines.
Figure 9.10. Dielectric film deposited by serigraphy on the heating resistance
Once the elaboration of the sensor is performed, the wires are brazed on a plastic connector often used in electronics (see Figure 9.11).
Figure 9.11. Complete serigraphed sensor
9.3. Device designed for the laboratory assessment of sensitive elements and/or sensors to gas action Having perfectly self-contained sensors does not rule out several studies on the properties of the sensitive element. This is particularly true for sensors elaborated with sintered tin dioxide, for which the quality and/or the nature of the electric connections plays an important role at the response level. Furthermore, the reactors especially elaborated for this kind of assessment have a homogenous temperature on the whole material. It is from this point of view that we are first going to describe the reactors and test benches used for this study.
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9.3.1. Measure cell for sensitive materials (see Figure 9.12) This is a unit able to simultaneously produce, by mechanic compression, 4 electric contacts on a sample whose area is less than 1 cm2. All of this can be carried out at temperatures contained between 20 and 600°C, in a controlled, gaseous and potentially corrosive atmosphere. The heart of the container is a brass block (a) heated by cylindrical heating elements on which sample (b) is deposited. The electric measures are produced with stainless steel spikes (c) whose extremities are covered with platinum (d). Platinum wires ensure the electric conduction between the spikes and the low temperature zone. In order to have identical and sufficient pressures on the four contacts, we use adjustable counterweights (f), while the stainless steel spikes have elastic properties, though this is limited to the low temperatures. The whole device is placed in a container made of quartz and steel whose bulk is about 0.5 liters and which can be dismantled. A stainless steel lid (h) covered inside the container by an aluminum sheet can be placed on the hot part in order to improve the thermal isolation and to decrease the response time of the system to the gaseous variations by decreasing the gaseous volume around the sensor. The heating elements (k) and the thermocouple (i) are linked to a regulator. Figure 9.13 represents the gaseous circuit associated with the system previously described. The air used is ambient air compressed and then dried in a silica gel column. Its humidity relative to the atmospheric pressure is then less than 0.5 at 20°C. Its flow in the container remains contained between 3 and 30 l/hr. The gases added stem either from gas bottles containing mixtures like air + CO or CH4 or SO2, or vapors generated by permeation tubes. Their concentration can be measured by weighing the tube every few hours.
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The three mass flow meters c, d and e, as described in Figure 9.13, allow us to continuously vary the concentration of the species studied without either varying the total flow in the container or the air flow at the level of the permeation tube.
Figure 9.12. Photograph (a) and diagram (b) of the device measuring with spikes
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Figure 9.13. Diagram of the gaseous experimental device
9.3.2. Test bench for complete sensors The test bench, entirely automated as described in Figure 9.14, allows us to simultaneously test 4 sensors using electronic cards. These sensors are tested in the same conditions thanks to Labview software controlling the automatic opening and the closing of the electro-valves. The gas used is conditioned in bottles and then mixed with air. At the exit of the bottles, a series of automated mass flow meters allow us to regulate the gas flow, fixed at 4 l/hr for each unit. This device enables us to create dilutions and to work with different concentrations of gases. The temperature of each sensor can be regulated independently. 9.3.3. Measure of the signal 9.3.3.1. Measure of the electric conductance Obviously, this kind of measurement only involves electrical resistance sensors. The principle is to measure in direct current the electric resistance of the sensitive element, using two contacts. For this purpose, we use the electric circuit displayed in Figure 9.15.
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Figure 9.14. Test bench diagram
Figure 9.15. Electric circuit elaborated to measure R
The resistance R that we want to measure is connected in series with a resistance r whose value is known but negligible compared with the value of R. The volatge E is imposed in the circuit and can be expressed by: E
( R r )i
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yet: U
Ri o U
U
rGE if G
rE rE | Rr R
and: 1 R
The unit of G is the Siemens (Ƿ-1). In practice, the applied voltage is 1 volt, and the value of the resistance r is adjusted to allow us to measure the electric conductance in the field used, which is 9 1 2 1 contained between 10 ȍ and 10 ȍ . To be precise, the resistance that we want to measure is generally associated with two contact resistances whose values are added to that of R. In certain cases, and to get rid of such contact resistance (called r here), we use the four points method (see Figure 9.16). With this process, the measured current is brought to the material by two electrodes different from those used to measure the voltage. In these conditions, and if the resistance of the voltmeter is relatively high, no noticeable current flows through the R M circuit. Thus, the contribution of these two resistances to the circuit is zero. From this we obtain the following expression: U
RI
For thin films, whose thickness determines the electric conductance, we introduce the notion of square conductance. If we suppose that the shape of the sample is square (see Figure 9.17), we can effectively free ourselves from the dimensions of the cross-section and thus express a conductance noted by Gsquare which is directly proportional to the thickness of the studied film, according to the following expression: Gsquare1
V S1
V L1e
L1
L1
V e Gsquare 2
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Figure 9.16. Measurement principle for the four points method
Figure 9.17. Assessment method of a square conductance
9.3.3.2. Measure of the potential The most sophisticated systems include electronic cards. The signal stemming from these sensors is then collected with a data gathering system (DGS), whose input impedance is about 1 G:. The card is fed by a continuous current (the voltage is contained between 12.5 and 15 V). Furthermore, the signal is amplified by two. 9.4. Assessment of performance in the laboratory 9.4.1. Assessment of the performances of tin dioxide in the presence of gases The sensors elaborated with tin dioxide show sensitivity towards the action of many gases. In general, these sensitivities depend on the nature of the gas and the temperature of the sensor. These performances can evolve during the functioning of the device (ageing effect). Figures 9.18 and 9.19 illustrate such behavior perfectly. We deal here with a sensor elaborated with a serigraphed thick film. It possesses two gold electrodes, obtained by cathodic pulverization.
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Figure 9.18. Response of a sensor before ageing, at different temperatures and under different atmospheres, with dry air
These results were obtained continuously through a temperature cycle, and under a gas flow of 5 l/hr. The temperature cycle consists of stabilizing the sensor at 500°C, then decreasing (about a 100°C less per minute) its temperature until it reaches the ambient temperature. The gas or vapors tested are: carbon monoxide (300 ppm/air), methane (1,000 ppm/air) and alcohol (50 ppm/air). Figure 9.18 displays the results obtained for a sensor which has just begun to function. This sensor reacts to the action of three different gases, and we note that the maximum sensitivity is at 150°C for alcohol and at 410°C for methane. After 17 days of functioning (see Figure 9.19), we note an important evolution of the signal, at least as far as alcohol is concerned. After this time, we note that the different responses stabilize.
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Figure 9.19. Response of a sensor after 17 days of aging, at different temperatures and under different atmospheres, with dry air
We observe the same kind of behavior when the air has a large percentage of humidity (see Figures 9.20 and 9.21). Nevertheless the maximum conductances are shifted at higher temperatures; thus, for alcohol, the maximum which appears at 250°C will be located at 400°C after ageing. These results are obtained at 500°C in an argon/oxygen (5%) mixture and over long periods of time (25 hours in humid air and 90 hours in dry air).
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Figure 9.20. Response of a sensor before ageing, at different temperatures and under different atmospheres, with humid air (90% at 20°C)
Figure 9.21. Response of a sensor after 17 days of ageing, at different temperatures and under different atmospheres, with humid air (90% at 20°C)
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Figure 9.22. Response of a SnO2 sensor to the action of hydrogen at 500°C, under humid air
Figure 9.23. Response of a SnO2 sensor to the action of hydrogen at 500°C, under dry air
These results show the complexity of the SnO2 sensors sensitive to the action of numerous parameters like temperature, the functioning duration and the nature of gas. Once these parameters are known, we can exploit such devices for targeted applications.
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9.4.2. Assessment of beta-alumina in the presence of oxygen1 9.4.2.1. Device and experimental process During this study, we have used the test bench described in Chapter 8, which allows us to register the responses of four sensors simultaneously. Using this test bench allows us to ensure that several sensors are tested with the same experimental conditions. With oxygen, all the experiments are carried out in static conditions for pressures contained between 10 and 104 Pa, and for temperatures contained between 250 and 600°C. To ensure perfect stability in the system, the samples are initially submitted to 10 Pa of oxygen during 2 hours. After each introduction of oxygen, the system takes about 10 minutes to reach equilibrium. In order to ensure a good reversibility at the level of the electric response, these experiments have been carried out with pressure either rising or falling. 9.4.2.2. Electric response to the action of oxygen We notice that in Figure 9.34, the signal decreases when the oxygen pressure increases, whatever the temperature is. We note that the lower the temperature becomes, the higher the amplitude of the signal is. Only the results obtained at 250°C display a discontinuity for pressure lower than 1,000 Pa (10 mbar). We will see in Chapter 10 that the information obtained at 250°C is not an anomaly.
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Figure 9.24. Response curve of the sensor as a function of oxygen pressure and for different temperatures (1 mbar = 100 Pa)
Figure 9.25. Response curve of the sensor as a function of temperature and for different values of the oxygen pressure (1 mbar = 100 Pa)
Next, observing the signal as a function of temperature, the curves in Figure 9.25 show a maximum which is located at about 320°C for pressures contained between 10 and 100 mbar. At higher pressures, the maximum shifts towards lower temperatures, and no longer appears in the exploited field of temperature for pressures higher than 1,000 Pa. Furthermore, we note that the lower the temperature becomes, the more important it is that the signal is small.
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9.4.3. Assessment of the performances of beta-alumina in the presence of carbon monoxide 9.4.3.1. Measurement device Electric measurements were carried out on the test bench which was used to study the responses according to temperature and oxygen pressure. Nevertheless, some modifications have been made in order to have a circulation of gas: that is, to use it in a dynamic condition. This choice is explained by the following fact: to assess the behavior of the sensor, it is convenient to work in a stationary condition because unlike oxygen alone, carbon monoxide is consumed in this reaction. The device is as described in Chapter 8, Figure 8.13. Once the response of the sensor is stabilized at the chosen oxygen pressure, we adjust the carbon monoxide partial pressure. The field of study has been voluntarily limited to low concentrations of carbon monoxide, that is, below 200 ppm. We have then been able to check that, whatever the experimental conditions, the electric response of the sensor is stable and reversible. 9.4.3.2. Electric results For an improved clarity of results, we have represented the response R of the sensor as a function of carbon monoxide concentration. R is defined as the difference between the measured voltage V1, in the presence of a mixture of oxygen/carbon monoxide and V2, measured under the same pressure of oxygen and the same temperature, given: R V1 V2
Figures 9.26, 9.27 and 9.28 display results for the response of the sensor to the action of carbon monoxide as a function of temperature. It is interesting to note that these results depend on the value of the oxygen pressure, and we can even observe an inversion of the signal’s gradient. We can check that the response is always positive for an oxygen pressure of 1,000 Pa (see Figure 9.27) and that it is always negative for an oxygen pressure of 100 Pa (see Figure 9.28), and we can observe transitory effects which are dependent on the temperature. The electric responses observed appear particularly complex if we consider the sign change that occurs when the oxygen pressure increases (see Figure 9.29). As can be noted in Figure 9.28, the positive electric response has a maximum whose position varies according to the carbon monoxide concentration. At low concentrations (about 10 to 25 ppm), the maximum amplitude of the obtained response is about 400°C. At higher concentrations of carbon monoxide (100 to 200 ppm), the maximum is observed at about 500°C.
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Figure 9.26. Response as a function of temperature, for different concentrations in CO and for Po2 = 1,000 Pa
Figure 9.27. Response as a function of temperature, for different concentrations in CO and for Po2 = 10 Pa
Nevertheless, for pressures close to 10 Pa (see Figure 9.28), the signal becomes negative with a minimum located at about 300°C.
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Figure 9.28. Response as a function of temperature, for different concentrations in CO and for Po2 = 100 Pa
Figure 9.29. Response as a function of the concentration in CO and for different oxygen partial pressures and at 400°C (1 mbar = 100 Pa)
Figures 9.29 and 9.30 are representative of the carbon monoxide partial pressure for different temperatures (see Figure 9.30) or different oxygen partial pressures. We obtain complex results, directly linked to the results obtained previously.
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At high temperatures and high oxygen pressure, the response of the sensor is positive. If we decrease the oxygen pressure of the temperature, the response produces zero value, and becomes negative at very low oxygen partial pressure and at low temperatures.
Figure 9.30. Response as a function of the concentration in CO for different temperatures and for Po2 = 100 Pa
Such behavior is quite innovative and shows the essential role of oxygen in the response of a sensor in the presence of carbon monoxide. These results are particularly important for the application of such a sensor. Indeed, applications using mixtures of oxygen and carbon monoxide could use such a device. In this case, knowing the influence of oxygen pressure is necessary to assess the influence of carbon monoxide. 9.5. Assessment of the sensor working for an industrial application In this last part, we will use several applications as examples to analyze the behavior and performance of the different sensors we have just described.
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9.5.1. Detection of hydrogen leaks on a cryogenic engine2 9.5.1.1. Context of the study This application consists of developing a device used to regulate the hydrogen leak in a cryogenic engine that relies on the combustion of the hydrogen/oxygen mixture. These engines are developed by SNECMA (Société Nationale d’Etudes et de Construction de Moteurs d’Avions) and are currently used as launchers for the European expendable launch system Ariane V. In order to prevent explosions, these engines are placed in a gaseous flux composed of inert gases such as nitrogen or helium. To ensure the reliability of such a security system and to especially ensure the absence of hydrogen and oxygen, it is important to have two different sensors for these two gases. As far as hydrogen is concerned, and among the different solutions existing, SNECMA has requested to assess, in collaboration with our laboratory, SnO2 type sensors. Initially, the goal of this study was to assess the behavior of such a sensor in an environment full of reducing gases able to act on tin dioxide. It is from this point of view that a series of experiments were carried out on a A 5001 type sensor and a “bottle” type version. By comparison with the initial version (see Figure 9.1), the A 5001 type has proved much more resistant to the mechanic effects of vibrations. 9.5.1.2. Study of performances in the presence of hydrogen The test bed used (see Figure 9.31) allows us to work on a large field of hydrogen (0.1-4%) and oxygen (0.1-6%) concentrations, in a flux of nitrogen. Each concentration is controlled by a mass flow meter. Different electro-valves allow us to perform several cycles of gas injections. Furthermore, this test bench allows us to test four sensors both simultaneously and separately. Oxygen and humidity sensors are also present in this device.
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Figure 9.31. Scheme of the test bench
Preliminary experiments (see Figure 9.32) have helped to ensure the sensor functions well at 400°C in presence of hydrogen and in an environment low in oxygen (several ppm). We observed a great sensitivity for the field studied, a perfect stability of the signal for concentrations less than 1.5 ppm, and an excellent stability of the signal over long periods of time (several hours). Because of these results, it appeared interesting to systematically study the role of the oxygen and the temperature on the response of the sensor. As far as temperature is concerned (see Figure 9.33), we note an exponential variation, at least for high concentrations of hydrogen. The temperature of 400°C appears as the optimal functioning temperature.
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Figure 9.32. Response of the sensor to hydrogen action
Figure 9.33. Influence of the temperature on the response of the sensor
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The influence of the oxygen concentration is described in Figure 9.34. These results confirm the high sensitivity of the sensor in the absence of oxygen, or at least for oxygen concentrations of 1 ppm. If we consider that the potential leaks of oxygen, assessed by SNECMA, can vary from 0.5 to 5.5%, we note that the sensor still shows a sufficient sensitivity for this field of oxygen concentrations, and that the response to the action of hydrogen is virtually independent of this concentration.
Figure 9.34. Influence of the presence of oxygen on the response of the sensor
The response time of the device is another performance criterion demanded by SNECMA. This parameter, which depends on intrinsic parameters of the sensor and also on its gaseous environment and the temperature, is not always easy to assess. To get rid of those problems, a special reactor with a small capacity has been developed. The measured response time is then 10 seconds, that is to say it takes 10 seconds for the signal to attain 90% of its maximum amplitude. For the application that interests us, it was also necessary to produce a network of several sensors capable of locating the potential leaks more accurately. To this end, an electronic device (see Figure 9.35) with a microcomputer has been developed, and each sensor is linked to this system through an interface card. This device can control at most 8 sensors that can be located as far as 300 meters.
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Figure 9.35. Picture of the electronic device
To ensure the reproducibility of the different sensitive elements, three sensors of the same series have been tested, using the interface card, in a laboratory. The results are displayed in Figure 9.36. 9.5.1.3. Test carried out in an industrial environment These tests have been carried out with three sensors located at the level of the turbo-pump which ensures the injection of the gaseous hydrogen (sensor 1), at the level of the turbo-pump which ensures the injection of the gaseous oxygen (sensor 2) and at the level of the inflows of the two gases (see Figure 9.37). These points are especially sensitive because it is at the level of the turbo-pump that the reagents vaporize. This reaction results in many variations of temperature which can further leakages from airtight joints. Figure 9.38 displays the photograph of the engine equipped with many sensors designed for different controls.
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Figure 9.36. Reproducibility tests
During the different tests carried out on a cryogenic Vulcain engine, we have been able to observe several situations where the airtight system has failed. These situations have allowed us to test the efficiency of the device designed to detect hydrogen leaks. To ensure the accuracy of the results obtained using SnO2 sensors, gaseous samples, taken at the level of the sensors, are simultaneously analyzed by a mass spectrometer set on the hydrogen molecular mass. The results displayed in Figure 9.39 have been obtained during the operation of the Vulcain engine and during an accidental leak. These results are significant to the performances of the sensor; indeed, the signal is very close to the sensitivity and the response time observed with the mass spectrometer. The interest in using several sensors is perfectly illustrated in Figure 9.40, where the different responses obtained using sensors 1, 2 and 3 are displayed. Only sensors 1 and 3 react during a test of the engine; sensor 2 does not respond. In this case, there is a leak located at the level of the inflow of hydrogen. This conclusion will be confirmed later by the observation of the airtight joint failing. For this kind of application, the SnO2 sensors appear perfectly usable.
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Figure 9.37. Scheme of the sensors’ disposition
Figure 9.38. Picture of the Vulcain engine
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Figure 9.39. Responses of the sensor in laboratory conditions
Figure 9.40. Responses of the sensor in laboratory conditions
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9.5.2. Application of the resistant sensor to atmospheric pollutants in an urban environment3 Given the new European laws concerning air pollution, it is important nowadays to model the effect of conveying and dispersing these atmospheric pollutants. To resolve these problems it is necessary to use many databases and, subsequently, many measuring points. The control stations already existing use selective analyzers, like infrared or ultraviolet spectrometers. These analyzers are particularly expensive and do not allow the multiplication of measurement points that would be desirable. To overcome this difficulty, solutions using “electrical resistance” sensors and exploiting the variation of the electric conductance are currently being studied for this kind of application, especially concerning the effects of carbon monoxide, nitrogen oxides and hydrocarbons. In general, these sensors display a low selectivity towards the action of these gases. Three solutions can be considered to this drawback: – the first solution consists of getting rid of the selective character, considering that the measure of the total pollution can be sufficient to solve many problems; – the second solution consists of exploiting the different sensitive materials whose responses towards the action of polluting gases are sufficiently different to be used as selectivity criteria. To detect CO and nitrogen oxides, there are multi-sensor devices using three kind of sensors, elaborated with SnO2, TiO2 and In2O3 respectively; – the third solution consists of increasing the selectivity of a sensor by discriminating certain interfering gases. This discrimination can be obtained by the adding of catalysts or by the presence of filters. The interfering gases are eliminated by catalytic reactions with gold, platinum or palladium. Firstly, we will limit our experiments to the measure of the total pollution. The catalytic filters and the multi-sensor system will be dealt with later. Thus, we will observe the performance of a A 5001 type sensor elaborated with a mere sintered bar of sintered tin dioxide.
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9.5.2.1. Measurement campaign conducted at Lyon in 1988 During a measurement campaign carried out on the Garibaldi road and CroixRousse tunnel in Lyon, we developed a portable suitcase equipped with two A 5001 sensors, an electronic card associated with each sensor and a pump for taking gas samples and circulating them in the device. This device, able to work with 220 volts of alternative current or 12 V of continuous current, can hold up to 12,000 measurements, that is, a measurement every quarter of an hour for a month (see Figure 9.41). These sensors are here connected in parallel with an infrared analyzer sensitive to carbon monoxide.
Figure 9.41. Left picture: caped sensor, anti-deflagrating head and electronic circuit associated with the sensor. Right picture: whole portable device
Though we want to measure the total pollution here which is not limited to carbon monoxide, preliminary tests (see Figure 9.42) show that there exists a satisfying similitude between the response given by the sensor and the response given by the analyzer. The information given by the sensor appears representative of the presence of carbon monoxide.
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Figure 9.42. Correlation between the response obtained with a SnO2 sensor and the CO concentration measured by an infrared analyzer
A series of tests obtained during a short period on the Garibaldi road and under the tunnel are displayed in Figure 9.43. They are representative of the degree of pollution at the two sites. Figure 9.44 displays the evolutions of the signal given by the sensor for a period of 20 days in the tunnel. We note a regular increase in the signal as a function of time. The laboratory analysis of these sensors by thermodesorption shows the presence of sulphated species at the surface of the sensors that have spent a long period of time in the tunnel. The presence of such species could stem from a reaction between tin dioxide and sulfur dioxide, which is present at a relatively high concentration in the tunnel. To confirm this hypothesis, new sensitive samples have been treated in a laboratory with sulfur dioxide. This operation was performed at 500°C under 0.5 ppm of sulfur dioxide. Tested under the tunnel, these sensors then show a satisfying stability (see Figure 9.45). This result, which seems to confirm the previously proposed hypothesis, is particularly satisfying for the application concerned.
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Figure 9.43. Response of a sintered SnO2 as a function of the concentration of CO on a road (•) and in a tunnel (*) over a long period of time
Figure 9.44. Evolution of the signal obtained by a SnO2 sintered sensor placed in a tunnel for 20 days
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Figure 9.45. Stable response of a SnO2 sintered sensor that has been treated with sulfur dioxide. Sensor placed in a tunnel for 1 month
9.5.2.2. Measurement campaign conducted at Saint Etienne in 1998 This campaign, conducted with the collaboration of the “atmospheric pollution control in the urban area of Saint Etienne and the department of Loire” association (AMPASEL), has allowed us to assess a new urban site with the same kind of sensors and to compare them with analyzers of CO, NO and NO2. The results displayed in Figure 9.46, show the simultaneous behavior of two sensors as a function of the time of day for two different dates, May 28, 1998 and June 5, 1998.
Figure 9.46. Reproducibility of the response of two sensors: sensors 1 and 2. Response recorded over 24 hours and on two different days: May 28 and June 5
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Figures 9.47 and 9.48 display the comparison of the results observed with the sensor and the different analyzers, on three consecutive days, and after a space of three months. It is interesting to note that the evolution of each of the gases measured, is about the same, and that the signal given by the sensor gives a good representation of pollution peaks.
Figure 9.47. Comparison of the results obtained by different analyzers and the studied sensors (CO, NO, NO2) during the period lasting May 26–28, 1998
Figure 9.48. Comparison of the results obtained by different analyzers and the studied sensors (CO, NO, NO2) during the period lasting May 26–28, 1998
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Furthermore, it is interesting to note that these sensors have not been treated with sulfur dioxide, and that no drift of the signal has been observed. This can be interpreted as meaning there is less pollution with sulfur dioxide, a result explained by the fact that industrial discharge is better taken care of. Thus, we have seen that these devices allow us to assess the total pollution in an urban environment and that the obtained results can be exploited in certain alert networks. For other kinds of applications, the non-selective aspect is incompatible with the fixed goal and/or the nature of the gaseous environment studied, and other systems have to be studied. 9.5.3. Application of the potentiometric sensor to the control of car exhaust gas The works displayed in this section are inscribed within the context of a European contract (Brite Euram III BRPR-CT97-0480Contract, project BE – 4028 Gas sensor and associated signal processing for automotive exhaust pipe: ECONOX 1 and 2), conducted with the collaboration of the Politecnico di Turin, Fiat, the Renault company, the Volvo company, the Microtel company, the Coreci company and Trinity College, Dublin. The main goal of this project was to develop a sensor designed to analyze the exhaust gases of an automobile. Here, we will display several results obtained by the automobile car manufacturers on potentiometric sensors, called ECONOX sensors. 9.5.3.1. Strategy implemented to control the emission of nitrogen oxides To satisfy new European regulations for the amount of NOX emissions, the car manufacturers used conversion systems on the diesel trucks. These systems are able to chemically transform gases into nitrogen. The process consists of injecting urea ahead of the catalyst, which is itself located before the exhaust pipe. The efficiency of such a device is linked to the quantity of urea injected, which depends on the quantity of NOX produced.
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Figure 9.49. Diagram of the converting device of the nitrogen electrodes
In fact, too much urea in comparison to the quantity of NOX to treat leads to the formation of NH3 at the exit of the catalyzer. Conversely, not all the NOX can be converted and a part of this gas is found in the exhaust gases. To solve this problem, several car manufacturers aim to control the concentration of NOX and NH3 at the exit of the catalyzer. Such a device naturally implies the simultaneous exploitation of an ammoniac sensor and a nitrogen oxide sensor.
a)
b)
Figure 9.50. Response of the sensor to NH3 action: a) as a function of time, b) as a function of the ammoniac concentration
Figure 9.50a displays the response of the sensor placed after the catalyzer of a diesel engine in function of the time. This signal can be compared with the one given by a laser device able to detect NH3. These results appear effective for the
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application concerned. Figure 9.50b indicates how the response of the sensor evolves as a function of the NH3 concentration. Finally, in Figure 9.51 the response times of the sensor and the validation system associated with short variations of the NH3 concentration are displayed; this time has been assessed as 1 second.
Figure 9.51. Assessment of the response time
9.5.3.2. Strategy implemented to control nitrogen oxide traps If the goals are once more associated with the European regulation, they target in this case the automobiles equipped with a petrol engine or diesel engine which use poor fuel mixtures. The applications concerned entail the study of nitrogen oxide traps and controlling the efficiency of the combustion catalyst. – Nitrogen oxide traps In order to decrease nitrogen oxide emissions, car manufacturers have designed a way to stock these gases in a tank full of a solid able to trap these polluting gases. To prevent saturation, this tank must be regularly purged of its gases. This operation consists of working temporarily, and over a brief period, with mixtures rich in oil, and able to destroy the nitrogen oxides. In order to optimize the fuel consumption of such a process, it is important to be informed of the saturation state of the tank, and only an oxide sensor located before the tank can enable such a control (see Figure 9.52).
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Figure 9.52. Scheme of the nitrogen trapping device
– Combustion catalysts Most diesel vehicles are nowadays equipped with an oxidation catalyst whose role is to limit the carbon monoxide and hydrocarbon emissions. To permanently ensure the good functioning of this device, it is important to use a sensor sensitive to hydrocarbons and carbon monoxide (see Figure 9.53).
Figure 9.53. Scheme of the device designed to catalytically oxidize the hydrocarbons
It is from this point of view that we have studied the behavior of the ECONOX sensor. 9.5.3.3. Results relative to the nitrogen oxides traps Figure 9.54 displays the results obtained using an ECONOX sensor and using a nitrogen oxide sensor, used here for reference. We must also remember that the response of the ECONOX sensor decreases in the presence of nitrogen oxides. The results are obtained over a period of time, using a mixture rich in oil. We observe that during the period of rich combustion there is no more NOX at the exit of the tank. In a weak condition, we observe a slow evolution of the NOX concentration because a part of these gases is not adsorbed, and this part increases with the saturation of the adsorber.
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It is interesting to note that the ECONOX sensor reacts more quickly than the analyzer, at least at the beginning of the storage. In fact, if we consider Figure 9.54b, which displays the response of the ECONOX sensor as a function of the NOX concentration, it appears that this response follows a homographic law, which implies a much greater sensitivity at low concentrations.
Figure 9.54. Response of the sensor to NOX action: response as a function of the time and as a function of the NOX concentration
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9.6. Amelioration of the selectivity properties 9.6.1. Amelioration of the selective detection properties of SnO2 sensors using metallic filters Researchers, being able to elaborate a material sensitive to the action of certain gases, instead alter the nature and/or the composition of the gaseous phase in contact with the sensitive element. In fact, such an evolution of the gaseous phase can be performed either mechanically or chemically. In the first case, we use a molecular sifter to let through the molecules whose size are fit for the applications and which are shaped like a pulverulent or sintered material for which the size of the pores is perfectly defined. In the second case, we use catalysts capable of rendering certain interfering gases inactive. The oxidation of carbon monoxide in carbon dioxide on a metal is a typical example. These catalytic elements could be directly mixed with the sensitive element or shaped as a porous film and deposited at the surface of the sensitive element. It is in this context that we are going to display several results concerning the amelioration of the selectivity on the SnO2 type sensors using catalytic filters. 9.6.1.1. Development of a sensor using a rhodium filter In accordance with the conduction mode proposed for tin dioxide, we know that the electric conductance of this material increases in the presence of reducing gases, like hydrocarbons or carbon monoxide, and decreases in the presence of oxidizing gases, like nitrogen oxides (see Figure 9.55). Given the relative concentrations in oxidizing and reducing gases, such a situation can mean the complete absence of information if the two signals of opposite signs have the same intensity.
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Figure 9.55. Comparison of the effects of CO and NO2 on the response of the sensor
This case is one we frequently encounter with diesel vehicles equipped with a catalytic exhaust pipe. The pollution emitted by these vehicles carries a high risk for the passengers. Indeed, the passenger cell of a vehicle is regularly ventilated, although the air inlets of the device necessarily collect the gases emitted by the other vehicles. To solve this problem, some car manufacturers use filters able to decrease the concentration of the polluting agent. This device, though efficient, has the drawback of saturating quite quickly if the system is permanently functioning. The solution consists of the device having servocontrol of the degree of pollution. This supplies information about the carbon monoxide concentration: the gas most widespread and dangerous for the concerned applications. Because of their conception and their price, SnO2 sensors can be a solution to the problem as long as there is no nitrogen oxide to be taken into account. To achieve this goal, we have launched a research program on the elaboration of filters directly deposited on the sensitive element. The results obtained with thin (10 nm) and porous rhodium films deposited by cathodic pulverization under argon, at the surface of a SnO2 thin film obtained by chemical vapor deposition (see Figure 9.56), appear efficient compared with those obtained with other metals like palladium, copper or molybdenum.
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Figure 9.56. Scheme for the elaboration of a sensor covered with a membrane
Figure 9.57 perfectly illustrates the amelioration brought to the sensor in the matter of carbon monoxide selective detection. The rhodium acts here as a catalytic agent furthering the decomposition of the nitrogen oxides.
Figure 9.57. Comparison of the results obtained with or without a catalytic filter made of rhodium
The main drawback of such solutions is the ageing of the catalysts. 9.6.1.2. Development of a sensor using a platinum filter6, 7 The second example concerns the possibility of obtaining information on the aliphatic compounds present in an urban environment. The problem then consists of removing the effects of the carbon monoxide and alcohol vapors, which constitute the most significant organic and volatile compounds interfering with the aliphatic compounds and especially with methane.
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Platinum is an oxidizing catalyst which can solve this kind of problem. Tests carried out in a laboratory, conducted in conditions close to those of the targeted applications, show the efficiency of such a material in the transformation of carbon monoxide and alcohol into carbon dioxide (see Figure 9.58), without degrading the methane. Tests carried out on a SnO2 sensor covered with a thin platinum film show that this material must be used in great quantities to be fully efficient on the catalytic plan. Beyond 10 nm, we notice noxious short-circuit effects at the level of the information capture. Below 10 nm, the catalytic performance ceases to be satisfying.
Figure 9.58. Catalytic activity of a platinum film (thickness 1 mm) as a function of temperature. Conversion of CO (300 ppm), of C2H5OH (100 ppm) and of CH4 (1,000 ppm)
This solution, applying the technology of thin films, proved inefficient. Thus, new tests have been carried out with thick films, at least as far as the sensitive element is concerned. In this case, short-circuits linked to the presence of the platinum film do not appear below 30 nm if the electrodes are placed under this film.
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9.6.2. Development of mechanical filters 9.6.2.1. Development of a sensor detecting hydrogen Certain practical applications, like the management of nuclear waste or the optimization of the functioning, for instance, of a combustible cell, suggest the use of hydrogen sensors, which do not take into account the presence of interfering gases. The use of SnO2 sensors covered with a porous membrane has been studied by many researchers. The function of a molecular sifter is most often obtained using thin or thick silicone films (SnO2), the very small size of the pores obtained with this kind of material favor the crossing of hydrogen. This is the process we used in our laboratory. It uses SnO2 sensors elaborated as thick films, on which a thin silicone film obtained by chemical vapor deposition is deposited. The precursor used is hexamethyldiosiloxane, the deposition temperature is 500 or 600°C, and the depositing duration is 6 hours. The tests realized on this kind of sensor (see Figure 9.59) show the selective character of the device towards hydrogen, at least in the presence of methane, carbon monoxide and alcohol in air. 9.6.2.2. Development of a protective film for potentiometric sensors For the automobile applications previously described, the use of potentiometric sensors has brought about a problem: the phenomenon of sooting up of the sensitive element linked to the period of functioning. To get rid of the soot, which prevents a good functioning of the sensor, we have considered depositing a filter able to block certain solid particles, like metallic particles and soot on the sensitive element. A new solution using an alpha-alumina filter deposited by serigraphic depositing has been developed for this application. In this case, the ink is prepared with a mixture of alpha-alumina and an aluminum hydroxyl gel. The gel is designed to replace the metallic binder generally used to stabilize the film.
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After sintering a mixture rich in alpha-alumina at 700°C, we obtain a porous and protective film (see Figure 9.60) compatible with the application concerned.5, 6
Figure 9.59. a) SnO2 sensor elaborated with a thick film, b) SnO2 sensor elaborated with a thick film after a HDMS treatment during 6 hours at 600°C
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Figure 9.60. Micrography of the protecting film
This new method has the advantage of using only one element for the elaboration and the reinforcement of the film, as the gel transforms into gamma-alumina after sintering at 700°C. The thick film then appears to consist of a skeleton made from the grains of gamma-alumina powder. These grains are welded together, and to the sensitive element, by the solid elements stemming from the decomposition of the gel. The tests conducted with this kind of sensor show the efficiency of the film protecting it from soot after 80 hours of functioning in an urban environment. Furthermore, this film seems to have a positive effect on the level of sensitivity towards nitrogen oxides (see Figure 9.61). This elaboration method, which appears to be extremely promising for this application, can be considered and even adopted for the elaboration of a great number of inks.
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Figure 9.61. Behavior of a sensor covered with a protective film as a function of time
9.7. Bibliography 1. N. GUILLET, Etude d’un capteur de gaz potentiométrique, influence et rôle des espèces oxygénées de surface sur la réponse électrique, Thesis, INPG-ENSMSE, Saint Etienne, 2002. 2. C. PIJOLAT, G. TOURNIER, P. BREUIL, D. MATARIN, P. NIVET, “Hydrogen detection on a cryogenic motor with a SnO2 sensors network”, Sensors and Actuators, B, 82 (2-3), 166-75, 2002. 3. C. PIJOLAT, B. RIVIERE, M. KAMIONKA, J.P. VIRICELLE, P. BREUIL, “Tin dioxide gas sensor as a tool for atmospheric pollution monitoring: problems and possibilities of improvements”, J. of Mat. and Surf. Sci., 38, p. 4333-4346, 2003. 4. E.M. LOGOTHETIS, M.D. HURLEY, W.J. KAISER, Y.C. YAO, “Selective methane sensor”, Proc. 2nd Int. Meet. Chemical Sensors, 175-178, Bordeaux, France, July 7-10, 1986. 5. F. MENIL, C. LUCAT, H. DEBEDA, “The thick-film route to selective gas sensors”, Sensors and Actuators, B, B 24-25, 415-420, 1995. 6. E. BILLI, L. MONTANARO, A. NEGRO, C. PIJOLAT, J.P. VIRICELLE, R. LALAUZE, Composition de revêtement et procédé de revêtement d’une surface d’un substrat, French patent no. 00.11403 of 07/09/2000, European patent no. 01402318.8 of 07/09/2001. 7. E. BILLI, J.P. VIRICELLE, L. MONTANARO, C. PIJOLAT, Development of a protected gas sensor for automotive applications, IEEE Sensors Journal, vol. 2, no. 4, p. 342-348, 2002.
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Chapter 10
Models and Interpretation of Experimental Results
10.1. Introduction Describing and understanding a phenomenon by establishing the relationships between the parameters involved is the basis of a scientific reasoning that leads to the modeling of a process. To obtain such a model, it is important to layout certain information relative to the process, using various experimental results. The results obtained, using several complementary experimental technologies, are the primary source of information. The nature of this information involves: – the chemical nature of the species involved in the process, their ionization state, their location; – the thermal and kinetic aspects; – the electric effects involved by the interaction between the different materials and the gaseous phase. Using this information, it becomes necessary to imagine one or more reaction processes which are defined by several basic steps. These reaction processes will enable us to express the equilibrium conditions and the rate which will be used to establish relations between the parameters concerned. The variation laws of these parameters are sometimes governed by mathematical laws simple enough to be used directly.
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In the opposite case, we will use a computer to simulate them. This process will be made easier if we already know the values of certain constants relative to the studied system. Consequently, we will have to adjust these constants until the experimental results and the simulation reach a convenient accord. A good accord between the two kinds of result is a validity criterion of the proposed model. Otherwise, the proposed model will be rejected. We must note that several models can satisfy the validity criteria. In this case, certain pertinent supplementary experiments will help clarify the situation. Besides the scientific interest of such reasoning, it is also possible to use these results for a specific application: sensors, for instance. Thus, knowing the variation laws of the signal, given by the device as a function of the system’s parameters, will allow us to control its functioning and its regulation for a specific application. It is based on such reasoning that we propose here to interpret certain results obtained with nickel oxide, beta-alumina and tin dioxide. Results exploited for the development of a gas sensor. 10.2. Nickel oxide1 Nickel oxide is a non-stoichiometric material with cationic vacancies. The concentration of its vacancies is naturally associated with the oxygen pressure of its environment. An increase in the pressure results in the appearance of new chemisorbed oxygen species with an anionic character and, subsequently, a deficit of cationic elements. These cationic vacancies, which are initially located at the surface of the material, will gradually diffuse to the heart of the solid, because of the effect of the concentration gradient that exists between the surface and the bulk. The results obtained by the measurement of the electric conductivity and the calorimetry (Chapter 6) lead us to think that these different processes are slow, and that the duration of the steps observed with these two methods is representative of the time the system needs to reach equilibrium.
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363
Figure 10.1 perfectly illustrates the complexity of the phenomena observed during small injections of gas; we can observe that the time the system takes to reach equilibrium depends of the experimental conditions. Figure 10.2 particularly highlights the evolution of electric conductance. The material is submitted to different variations of the oxygen pressure. It takes several dozen hours under 40 Pa for the system to reach equilibrium.
Figure 10.1. Colorimetric response of nickel oxide to the action of oxygen 6.65
Such a hypothesis questions the fact that the electric signals characteristic of these steps represent a state of equilibrium – a hypothesis regularly proposed by scientists. Using this new approach, a kinetic model able to explain the shape of the curves has been developed. This model will allow us to note that the conductance is linked to the speed of the process.
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(a)
(b) Figure 10.2. Evolution of the electric conductance of nickel oxide as a function of time for different values of oxygen pressure: in Figure a, curve (a) P = 8 Pa, curve (b) P = 106 Pa; in Figure b, P= 40 Pa
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10.2.1. Kinetic model The creation of defects at the surface of the nickel oxide, through exposure to gaseous oxygen, is expressed by the reaction: 1 O2 O VNix O 2
VNix is the neutral defect, and we know it can ionize up to two times given: VNix l VNi' h
and: VNi' l VNi'' h
To simplify the mathematical symbols in the following calculus, we will suppose that all the vacancies are neutral. As for diffusion, it can be represented by the reaction: VNix surface Nibulk o VNix bulk Nisurface
and in general in the bulk
VNix bulk i Nibulk i 1 o VNix bulk i 1 NiBulk i : i is the crystallographic plan concerned, counted starting from the surface. Cs denotes the concentration of defects at the surface and Ci the concentration of the defects in the bulk. The two previous reactions, which are consecutive, produce intermediate species VNix surface whose variation of concentration Cs is dependent on the rate v1 of the first step and the rate v2 of the second step. We have: dCs dt
v1 v2
[10.1]
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If we suppose that these reactions are basic we can write the rate of the first step as: v1
G H k PO kCs 2
[10.2]
For the second step, which corresponds to a diffusion field, and if we study the reaction within the context of the Wagner approximation, that is, a gradient of linear concentration in the bulk (Chapter 4), we obtain: v2
D Cs Ci X
[10.3]
G H k , k , D and X refer to the kinetic constants of the first reaction, the diffusion coefficient of the defects and the half-width of the sample respectively. This halfwidth is measured at the heart of the material. We assimilate the sample to a plaque whose thickness 2X is negligible compared with the other dimensions. We will consider that only two faces (main and opposite) have a significant interaction with the gas (see Figure 10.3).
Figure 10.3. Evolution of vacancy concentration gradient within the Wagner hypothesis
Within the context of the Wagner approximation, Ci refers to the concentration of defects within the material. Given [10.2] and [10.3], equation [10.1] can be written: dCs dt
G H D k PO kCs Cs Ci 2 X
[10.4]
Because of the effect of the diffusion process, the defects will accumulate at the heart of the bulk and their concentration will vary according to the following law:
Models and Interpretation of Experimental Results
dCi dt
D Cs Ci X
367
[10.5]
The kinetic model comes down to a system of two differential equations [10.4] and [10.5]. By derivation and then by substitution, we obtain a new system of two second order differential equations: ªX « «D (I ) « « «X «D ¬
H d 2 Ci dCi H X k 2 kCi 2 dt D dt
G kPO1/ 2
H d 2 Cs dCs H X k 2 kCs 2 dt D dt
G kPO1/ 2
2
2
In the following calculus, we will set: HX k D
D
The two previous equations are identical from a mathematical point of view, and the solutions Cs = f (t) and Ci = g (t) will only differ because of their boundary conditions To solve system (I), it is necessary to know whether the equation: H X 2 r r D 2 k D
0
admits real or imaginary roots. Yet, the discriminant ǻ is positive: '
(D 2) 2 4D
D2 4
Therefore, we obtain two real roots r1 and r2: r1
D 2 D 2 4 X 2 D
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Physical Chemistry of Solid-Gas Interfaces
and: r2
D 2 D 2 4 X 2 D
We check that r1 and r2 are negative solutions. In these conditions, we obtain: Cs
O1 exp(r1t ) P1 exp(r2 t ) C1
Ci
O2 exp(r1t ) P1 exp(r2 t ) C2
and:
We determine C1 and C2 by reporting Cs and Ci in the equations of system (I), and we find: C1
C2
K
K k H k
KPO1/ 2 3
with:
Whatever the values of the constants O1 , P1 , O2 and P 2 , we note that the curves Cs = f(t) and Ci = g(t) do not display any maximum as a function of time. Such a property does not allow us to link the variations of the electric conductance to those of Ci and Cs . However, if we consider the expression relative to dCi dt
J
dCi
dt
, given:
D O1 O2 exp r1t μ1 μ2 exp r2t X
and if we take the boundary conditions into account, that is, at t = 0: Cs
Ci
C0
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369
a condition which implies that: (O1 O2 ) ( P1 P 2 )
0
we obtain: dCi dt
J
D O1 O2 exp r1t exp r2 t X
In this case, the expression of the diffusion flux in effect corresponds to the shape of the experimental curves which show a peak and return to the initial value. This result seems to confirm that at low oxygen pressures, the electric conductance of the oxide is linked to the diffusion flux of the defects, that is, to the concentration gradient of the defects and not their concentration. This model does not allow us to account for the shape of the curve obtained at high oxygen pressure, which displays a conductance plateau Gi. To better understand the physical meaning of this plateau, we can try to study the evolution of the experimental curves as a function of oxygen pressure. This evolution is schematized very roughly in Figure 10.4. Until a limiting pressure value P2, all the curves display a peak, the intensity of which increases with the pressure. From P2 onwards, we note a sudden discontinuity in the evolution of those curves displaying a peak and the appearance of a significant new phase of the process.
Figure 10.4. Evolution of the experimental curves as a function of the oxygen pressure
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Physical Chemistry of Solid-Gas Interfaces
To interpret such a modification of the kinetic process, we can reflect that the concentration of defects at the surface of the oxide creates an electric field whose intensity is a function of the oxygen pressure. This electric field will oppose the migration of the nickel vacancies in the bulk, and we observe a slowing down of this process. We can thus suppose that a stationary condition self-regulated by the resulting electric field will be established. To seek confirmation of these different hypotheses, we will simulate the kinetic models using electric circuits. 10.2.2. Simulation of a kinetic model using analog electric circuits 10.2.2.1. Simulation of the curves displaying a maximum – Case of an elementary reaction Let us consider the simple case of an elementary reaction: A ' B. It is possible to simulate the rate of such a reaction using an electric circuit. This circuit must comprise a capacity C and a resistance R connected in series (see Figure 10.5).
Figure 10.5. Scheme of the RC circuit
Indeed, we can determine the rate of the transformation A ' B and the charge dq / dt of the capacity C using the relations: d B dt
G H k A k B
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371
and: dq dt
V q R RC
V refers to the voltage applied to the poles of the circuit and q the charge of the capacity, which is linked to the intensity i of the current flowing in the circuit: dq dt
i
These two expressions are equivalent if we set: G k
1 R
H k
1 CR
and:
At the equilibrium B0
q0
CV
– Case of two consecutive elemental reactions A B BC
We know that: d B dt
G H G H k1 A k1 B k2 B k2 C
G H G H k1 , k1 , k2 , k2 refer to the rate constants of the reaction 1 and 2 respectively.
To simulate the variations of the concentration of B, it is necessary to create an electric circuit comprising two electric resistances connected in series and two capacities connected in parallel, following the scheme displayed in Figure 10.6.
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Physical Chemistry of Solid-Gas Interfaces
Figure 10.6. Scheme of the new RC circuit
If q1 and q2 refer to the charges of the capacities C1 and C2 respectively, we will obtain: ª dq1 « dt « ( II ) « « « dq2 «¬ dt
q dq V 1 2 R1 R1C1 dt
1 1 q1 q2 R2 C1 R2 C2
The current i flowing in R1 will follow the law: i
dq1 dq2 dt dt
If we follow the relations given in Table 10.1 we note that there is a perfect correspondence between the expression of d B / dt and that of d q1 / dt .
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373
Table 10.1. Table of the correspondences between kinetic and electric values
In the particular case of the kinetic model represented by equations [10.2] and [10.3], there is a perfect correspondence with system (II), if we set: C1
C2
C
Indeed, in this case: dq2 dt
1 q1 q2 R2 C
q1 - q2 refer to the difference in concentration between the surface and the bulk, and 1 / R2 C is analogous to D / X . We thus simulate diffusion within the Wagner approximation by choosing two capacities whose values are the same. From an electrical point of view, differential system (II) is expressed: ª dq1 « « dt « « « dq2 « ¬ dt
q V 1 1 q1 q2 R1 R1C R2 C 1 q1 q2 R2 C
By derivation, and then by substitution, we obtain: ª d 2 q2 dq2 R C « 2 dt 2 dt « « « « d 2 q1 dq1 R C « 2 dt dt 2 «¬
R2 1 2 q2 R1 R1C R2 1 2 q1 R1 R1C
V R1 V R1
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Physical Chemistry of Solid-Gas Interfaces
In practice, the electric circuit has been created with the following characteristics: C = 100 nF
R1 = 20 kȍ
R2 = 1 kȍ
The voltage applied is a continuous voltage, contained between 0 and 20 V. This voltage is delivered by an impulsion generator which thus allows the recording of the voltage U at the poles of R2 as a function of the time, using an oscilloscope. The curves obtained on the oscilloscope are photographed with a Polaroid camera. The voltage U at the poles of R2 equals R2 i2, that is, R2 dq2 / dt . Given the equivalences in Table 10.1, this value is representative of J and, consequently, of the nickel oxide electric conductance, if we admit that this conductance is linked to the migration of the vacancies. The resolution of the system allows us to write: dq2 dt
A exp r1t exp r2 t
with:
r1
2
1/ 2
2
1/ 2
§R · §R · ¨ 2 1¸ ¨ 2 ¸ 1 R © 1 ¹ © R1 ¹
2 R1C
and:
r2
§R · §R · ¨ 2 1¸ ¨ 2 ¸ 1 R © 1 ¹ © R1 ¹
2 R1C
Increasing the values of the applied voltage V, we obtain for the voltage at the poles of R2 the curves displayed in Figure 10.7. For curves stemming from a conductivity signal, a peak can be observed.
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375
Figure 10.7. Evolution of the curves displaying a peak as a function of the applied voltage
It is interesting to note that in this case: U
R2
dq2 dt
R2V t t exp exp 2 R1 R2 2 R1C R2 C
This expression is equivalent to that of the chemical diffusion and for kX / D 1 , we obtain: J
PO
H § D · exp 2k t exp ¨ t ¸ 1 X © X ¹ K k DK 2
H We can determine the kinetic constants k and D / X using the experimental curves. Given the interest that such analog circuits can provide in the interpretation of the kinetic mechanisms, it was interesting to prolong this study to the case of n consecutive basic reactions.
– Generalization in the case of n consecutive elementary reactions To treat such a generalization, we will adopt the model that uses n basic steps and n-1 intermediate species; this is a linear operation. A X1
(1)
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Physical Chemistry of Solid-Gas Interfaces
X1 X 2
(2)
--------------X i X i 1
(i+1)
--------------X n 1 B
(n)
From a kinetic point of view, this model will be written: ª d X1 « « dt « d Xi ( III ) « « dt « d X n 1 « «¬ dt
G H G H k1 A k1 X1 k2 X1 k2 X 2 G H G H ki X i 1 ki X i ki 1 X i ki 1 X i 1
where 2 < i < n-1
G H G H kn 1 X n 2 kn 1 X n 1 kn X n 1 kn B
Such a mathematical system can be simulated by an electric circuit comprising n resistances Ri connected in series, n capacities connected in parallel, and a voltage V0 applied at the end of the circuit, following the scheme displayed in Figure 10.8. The voltage V0 simulates the concentration of the B species.
Figure 10.8. Equivalent circuit with n basic steps
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377
In each junction of the circuit, for 1 < i < n, we can write: dqi dt
1 1 1 1 qi 1 qi qi qi 1 Ri Ci 1 Ri Ci Ri 1Ci Ri 1Ci 1
For the particular junctions N1 and Nn, this is: dq1 dt
1 1 1 1 V q1 q1 q2 R1 R1C1 R2 C1 R2 C2
dqn dt
1 1 qn 1 qn Rn Cn 1 Rn Cn
By way of comparison between systems (III) and (III’), we note the following analogies:
( III ')
ª X i { qi «G « ki { 1 « Ri Ci 1 «H «k { 1 « i Ri Ci « G « ki Ci «ki H { C ki i 1 « «A {V « « kG { 1 « 1 R ¬ 1
where 1 < i < n
Such an electric system allows us to simulate the different cases generally encountered in heterogenous kinetics. 10.2.2.2. Simulation of the curves displaying a plateau To explain the sudden slowing down of the kinetic process observed at high pressures, and as outlined in Figure 10.4, it is necessary to introduce new elements able to ensure a “blocking” effect into the electric circuit. The Zener diode appears to be the simplest element able to fulfill this task. The electric circuit displayed in Figure 10.9 has allowed us to obtain the curves in Figure 10.10.
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Physical Chemistry of Solid-Gas Interfaces
We note that for a critical voltage U1, a plateau appears, but its duration is not significant enough to represent a function of the applied voltage.
Figure 10.9. Equivalent circuit using a Zener diode
Figure 10.10. Evolution of the curves with plateau as a function of the applied voltage (circuit of Figure 10.9)
To better understand the kinetic aspect of a model based on a self-regulating process of the diffusion, it was necessary to choose an electronic component better adapted than the Zener diode to the simulation of the phenomenon.
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379
If we take into account the properties of the field-effect transistors, we can imagine that such a component would solve our problem. Indeed, the intensity I which flows though the transistor is regulated by the grid voltage; yet the circuit has been elaborated so that this voltage is proportional to I (see Figure 10.11).
Figure 10.11. Equivalent circuit using a field effect transistor
The results obtained, using the oscilloscope, by recording the voltage U at the poles of R2 are displayed in Figure 10.12. This represents increasing applied voltages. We then note the analogy between the experimental curves obtained by measuring the conductance of nickel oxide as a function of time. We have particularly observed that the duration of the plateau increases as the applied voltage increases.
Figure 10.12. Evolution of the curves possessing plateau according to the applied voltage (circuit of Figure 10.11)
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Physical Chemistry of Solid-Gas Interfaces
This study enables us to confirm that the shape of the experimental curves cannot be explained by variations in the concentrations of defects in the oxide, but by the diffusion of these defects in the bulk. Furthermore, it is necessary to account for a self-regulating phenomenon linked to the appearance of an electric field, whose intensity is a function of oxygen pressure. 10.2.3. Physical significance of the measured electric conductivity The previous kinetic model has allowed us to show that the electric effects observed on nickel oxide were linked to the migration of the nickel ions in the network. Such a phenomenon implies that these ions can temporarily be found in interstitial sites, favoring the creation of an activated complex electrically neutral and near the conduction band of the oxide; this proximity then favors an electron transfer, given: NiI o NiI2 2econduction
band
The electrons transferred by the conduction band have a short lifetime duration, at most the length of the complex life, and will thus ensure a permanent renewal of the material conductivity. In stationary condition, this effect will be permanent and keep a constant intensity. 10.3. Beta-alumina2, 3 The electric behavior of beta-alumina, both treated and not treated with sulfur dioxide, questions the interpretation of the phenomenon relative to the creation of a potential linked to the nature or the geometry of the electrodes, and linked to the nature of the gaseous atmosphere in which it is plunged. 10.3.1. Physico-chemical and physical aspects of a phenomenon taking place at the electrodes 10.3.1.1. Oxygen species present at the surface of the device The results stemming from calorimetric experiments and from the potential at the surface as they were presented in Chapter 6 are sufficiently clear to provide a certain amount of information concerning the presence of different oxygen species at the surface of the different materials involved. Firstly, we know, because of the calorimetric results, that there is an interaction between the gaseous oxygen and the solid electrolyte, and that this interaction is
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381
reversible and endothermic. Furthermore, this interaction can be assimilated to the adsorption of oxygen species not solidly linked to the oxide, which we will denote as [O]ȕ (see Figure 10.13). This species is not detected by the potential measures at the surface. Furthermore, we know that this species is electrically neutral.
Figure 10.13. Corrected thermograms obtained at 300°C with beta-alumina for different variations of the oxygen pressure (10 to104 Pa)
Figure 10.14. Evolution of the surface potential as a function of oxygen pressure for the beta-alumina/platinum structure (1 mbar = 100 Pa)
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Physical Chemistry of Solid-Gas Interfaces
Secondly, and in the presence of a metallic electrode, we can suppose that this mobile species can react at the level of an activated site to produce new species electrically charged so as to vary the potential at the surface (see Figure 10.14). This species, active from an electrical point of view, will be noted [O-]T. The fact that the metal alone does not generate any oxygen species at its surface, at least in the experimental conditions implemented here, leads to the supposition that the formation of [O-]T should happen in the zone where the solid electrolyte is in contact with the metal. This hypothesis subscribes to theories proposed to explain heterogenous catalysis4 where the metal-oxide interface of the supported catalysts is considered to be particularly reactive. This zone is also mentioned by contemporary electrochemists, who consider it as the place where most of the oxidation-reduction reactions take place, reactions from which stems the equilibrium between the oxygen and the oxygen vacancies, which are present in the solid electrolytes.5 We speak of a three boundary point which involves the inter phases associated with the gas, the metal and the solid electrolyte.6, 7 The phenomenon thus described is displayed in Figure 10.15. This scheme shows a phenomenon opposite to the classic spill-over phenomenon. According to the spill-over mechanism, the gas is dissociated at the surface of the metallic electrodes and the reactive species diffuse from the metal towards the material.7 This process resembles more closely a reverse spill-over phenomenon as proposed by Holstein and Boudart,8 and then confirmed by recent works that have revealed that chemical species diffuse between the support-material, which are apparently inactive, and the metallic phases, which are very reactive.9, 10 From a kinetic point of view, the comparison between the calorimetric signal relative to the adsorption of the oxygenated species and the response of the sensor (see Figure 10.16) indicates that the endothermic species take about as much time as the signal of the sensor to reach equilibrium. Because the electric signal is necessarily linked to a charged species of [O-]T type, we can conclude that the limiting step of the formation process of two species is the step in which the species [O-]T is formed, the chemisorptions step being rapid compared with the step in which the endothermic species is formed.
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383
Figure 10.15. Mechanism proposed for the interaction between oxygen and beta-alumina
Figure 10.16. Comparison between the calorimetric signal and the response of a sensor placed in the same conditions, and comparison with the gradient of the sensor response as a function of time
Besides the chemisorbed oxygenated oxygen species formed at the level of the three boundary point, it is not irrational to think that there may be other oxygen and charged species present on the metal. Several works indicate the existence of numerous oxygen species, more or less well bonded to the surface of the metals when they are supported by metallic oxides,11, 12 and even on gold.13 Therefore, we can imagine that the species [O-]T, created at the level of the three boundary point, can potentially be the origin of the formation of other charged species located at the surface of the metal, and that we will denote this by [O-]M. The latter would then be strongly linked to the metal and would therefore display catalytic properties much weaker than those of the intermediate species.14 Furthermore, these species can be in equilibrium with the gaseous phase.
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Physical Chemistry of Solid-Gas Interfaces
10.3.1.2. Origin of the electric potential The study of the electric device (Chapter 6) has revealed a large capacitive effect at the interface between the solid electrolyte and the metallic electrode. Such a capacitive effect necessarily results in the presence of charges Q at the level of the electrode, which could induce the appearance of a potential V, so that: V
Q C
In fact the formation of the chemisorbed species at the surface of the electrodes is not accompanied by a modification of the total charge of the system. The electrons involved in the chemisorptions phenomenon are extracted from the metal, and the system remains neutral. Such a system is not similar to a regular electrostatic system, which takes an external supply of charges stemming from the electrodes into account. If only the oxygen and charged species [O-]M located at the surface of the metallic electrodes are taken into account, we note that there is no direct relation between these charged species and the solid electrolytes. Because of the great quantity of charges in the metal, the charge per unit area induced by the presence of chemisorbed oxygen species is only compensated by a depletion layer, the thickness of which is extremely small in the metal15 (about several Å). These species present at the surface of the metal cannot provoke an accumulation of charges at the level of the metal/solid electrolyte interface. Only the charged species [O-]T, which are located at the level of the metal/solid electrolyte interface, are able to produce electrostatic interactions with the charges carriers of the solid electrolyte. Because the electrodes are ideally polarizable, that is, there is no charge or matter transfers between the electrode and the solid electrolyte, the presence of charged species at the level of the three boundary point can easily generate a local reorganization of the charges present in the material. In the conditions of this experiment, and as displayed in Figure 10.17, we can imagine that the creation of the charged species at the three boundary point will generate an electron transfer and a transfer of the charge carriers, that is, the ions Na+, from the solid electrolyte to the peripheral zone of the electrodes, that is, the three boundary point.
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385
Figure 10.17. Scheme explaining the electrostatic phenomena of which stem the equilibrium between the charges in the system
The charge –Q, which totalizes the charges [O-]T located at the three boundary point, will thus induct the appearance of a charge Q in the metal, and an accumulation of NA+ ions in the zone located near the electrodes. It causes a depletion of the ions Na+ under the electrode, which entails the appearance of a charge Q. The system can then be schematized, as in Figures 10.17 and 10.18, by four distinctly charged zones. As was previously seen, the space-charge layer is very thin in the metal; in the solid electrolyte, however, the number of charge carriers being much lower, the space-charge layer is much wider. The capacitive effect of this will be sufficiently large to produce the appearance of a significant potential. 10.3.2. Expression of the model 10.3.2.1. The electrode potential The new distribution of charges induced by the [O-]T species located at the level of the three boundary point causes the appearance of two capacitive effects: preponderant and parallel.
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Physical Chemistry of Solid-Gas Interfaces
The first Ce involves the zone located under the metallic electrode. The second, Cp is produced in the peripheral zone around the electrode. The width of this peripheral zone, symbolized by G in Figure 10.18, is representative of the zone of electrostatic influence of the oxygen species charged on the solid electrolyte.
Figure 10.18. Scheme displaying the location of each space-charge layer present in the system
By likening the electrode to a metallic disk of radius R deposited at the surface of the solid electrolyte, we can compare this peripheral zone to a crown defined by an internal radius equal to the radius of the electrode, and an external radius R+G, with G negligible compared to R. By admitting that these capacitive effects can be schematized by two planar capacitances connected in parallel, each capacity is then characterized by its surface “S” and the depth “e” of its space-charge layer in the material, given: C
HH 0 S e
The absolute value of the charge Q carried by the four concerned zones is identical. The charge produced in the material can be expressed as follows: Q
q[ Na ]Se
q is the basic charge of the electron and [Na+] is the concentration of the sodium ions, which are the charge carriers in the solid electrolyte.
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If we make Sp the surface of the peripheral zone of the electrodes, Se the surface of the electrode, and ep and ee the depth of the space-charge layer in the periphery of the electrodes and on the electrode, we will obtain: Q
q ª¬ Na º¼ Se ee
q ª¬ Na º¼ S p e p
[10.6]
Given the slight surface Sp of the peripheral zone of the electrodes, the depth ep of its space-charge layer will be much more important than the space-charge layer characterized by the surface Se of the electrode. We will thus obtain: Se !! S P and ee !! eP
and subsequently: Ce
HH 0 Se ee
!!
Cp
HH 0 S p ep
In these conditions, and given that the two capacities are connected in parallel, the total capacity of the device can be expressed by: C
Ce C p | Ce
The potential produced at the level of the electrode is then defined by: V
Q Q # C Ce
Qee HH 0 Se
We can then eliminate ee using expression [10.5] defining the space-charge layer: V
Q2 q [ N a ]HH 0 S e2
The charge Q created is necessarily proportional to the quantity of chemisorbed species at the level of the metal/solid electrolyte interface. If N0 is the number of sites available per unit area in the zone located at the periphery of the electrodes, and if T is the coverage degree of this surface by the chemisorbed species, we have:
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Physical Chemistry of Solid-Gas Interfaces
Q
qT N 0 S p
thus: V
V
Q
q 2 T 2 N 02 S
2
q [ N a ]H H 0 S e2
2 p
q [ N a ]H H 0 S e2
2 q N 02 T 2 S p [ N a ]H H 0 S e2
As: Sp
S [( R G ) 2 R2 ] 2S RG SG 2 | 2S RG
Se
S R2
and:
we obtain for V:
V
q N 02 T 2 ( 2 S R G ) ² [ N a ]H H 0 ( S R ) ²
V
D .T
2
§G · ¨ ¸ © R ¹
4 q N 02 T 2 § G · ¨ ¸ [ N a ]H H 0 © R ¹
2
2
This result indicates that the potential of the electrode is proportional to the square coverage degree of the electrode, which is covered by the oxygenated species located at the three boundary point. We will note that this expression is analogous to a Mott barrier. If we admit that the value of į is not a function of R, and that it keeps a relatively constant value, we note that the produced potential depends of the electrode’s radius, and consequently, its surface. Besides, because the ratio G / R has no dimension, the expression of the potential keeps its specificity: it is an intensive parameter.
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389
The consequence is that the difference of potential recorded at the poles of two electrodes 1 and 2 will depend of the coverage degree T1 and T2 respectively and of their radius R1 and R2, given:
'V
V1 V 2
ª§ T ·2 § T ·2 º D G «¨ 1 ¸ ¨ 2 ¸ » «¬ © R1 ¹ © R 2 ¹ »¼ 2
[10.7]
This expression will allow us to represent all of the results observed on such a device, that is, the influence of the nature and the geometry of the electrodes. The two cases considered during this study are the following: – In the first case, the two electrodes have the same size but different natures, which implies that R1 and R2 are equal, and that T1 and T2 are different, if we admit that the concentration of the adsorbed species is linked to the catalytic activity of each metal. The expression of 'V becomes:
'V V1 V2
DG 2
ª¬T12 T22 º¼ R
[10.8]
– In the second case, the two electrodes have the same nature but different sizes. Given that the coverage degrees are not a function of the area, we will have T1 = T2= T, with:
'V
V1 V 2
ª 1 1 º 2» 2 R2 ¼ ¬ R1
D G 2T 2 . «
[10.9]
According to the expression of 'V, only the coverage degree is a function of the experimental conditions (temperature and oxygen pressure). It is important to be able to express the relation between 'V and these parameters for each metal. 10.3.2.2. Expression of the coverage degree The previously proposed mechanism allows us to obtain a relatively simple expression of the difference in potential observed at the poles of the two electrodes. The only arguable point is the expression of the coverage degree. We will admit that the oxygen species adsorbed at the surface fulfill the hypothesis proposed in the Langmuir theory16:
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Physical Chemistry of Solid-Gas Interfaces
– The number of sites is constant, characteristic of the area, and is not a function of temperature and the coverage degree. – The chemical species adsorbed do not interact. – During the existence of adsorbed chemical species, the character and the solidity of the chemical bonds are not modified. To express the coverage degree T of the active zone, it is necessary to identify all the oxygen species present in the system, and to accurately express their fixation sites. Several solutions can be considered, and we will explain two of them below: 1) The three boundary point is a specific zone that has its own adsorption sites different from the sites of the solid electrolyte and of the metal. If we note by E the adsorption sites at the surface of the beta-alumina, s1 those present at the level of the three boundary point and s2 those of the metal, the different steps of the formation of the oxygen species present in the system can be expressed as follows: – formation of the endothermic species: O2 2 E 2(O E )
– chemisorption on a site of the three boundary point: (O E ) s1 e [O ]T E
– chemisorption on the metal: [O ]T s2 [O ]M s1
As has been demonstrated using the results of calorimetry (Chapter 6), the first species has a positive formation enthalpy whereas the other two chemisorbed species have a negative formation enthalpy. Figure 10.19 illustrates the energy diagram that these different species have to follow.
Models and Interpretation of Experimental Results
391
Figure 10.19. Energy diagram for oxygen species
If we note by TE the coverage degree of species O-E at the surface of the betaį alumina, T1 the coverage degree of the species ªO º T , which is the activated «¬ »¼ į species and T2 the coverage degree of the species ªO º M , on the metallic «¬ »¼ electrode, the thermodynamic equilibrium constants K1, K2, K3 of the different species formation reactions are expressed: K1
TE
1 T E
K2
Po2
T1 1 T E
T E 1 T1
and: K3
T 2 (1 T1 ) T1 (1 T 2 )
The expression of the coverage degree T1 of the considered responsible of the electric signal species will then be:
T1
K 2 K1 Po2 1 K 2 K1 Po2
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Physical Chemistry of Solid-Gas Interfaces
In fact, such an expression, already studied by C. Pupier17 in his thesis, cannot satisfy all of the experimental conditions. 2) The second solution consists of considering the two different species interacting with the metal and located on the same type of site s, which entails a three boundary point. The first species, noted by ªO º T , fixed at the metal/solid electrolyte interface «¬ »¼ will be considered in strong interaction with these two materials. This double interaction could imply polarization effects, noted by į , of the adsorbed oxygen. į
This polarization, favored by the presence of large quantities of electrons in the metal, will create inductive effects and, consequently, an accumulation of charges in the solid electrolyte. The second species, noted by ª¬ O- º¼ T , is supposed strongly bonded to the metal and has only a slight interaction with the solid electrolyte. The bound can here be considered like an ionic bound with exothermic character. į We will suppose in this case that only the species ª O º «¬ »¼ appearance of a potential at the electrode.
T
is responsible for the
Furthermore, we can suppose that the species [O-]M will be formed at the surface of the metal on D sites and will stem from the species ª¬ O- º¼ T . The reaction will then be written: O 2 2ȕ 2(O ȕ)
(O ȕ) s metal (O s)G - ȕ G -
(O s)
e (O s)
(O s) Į (O Į) s
with K1, K2, K3 and K4 the equilibrium constants relative to the previous equilibriums.
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393
If we note by TE the coverage degree of the species O-E, noted > O @ ȕ , at the į
surface of the beta-alumina, T1, the coverage degree of the species (O s) , noted ªO į º and T the coverage degree of the species (O s) , noted ªO - º at the 2, T ¬ ¼T ¬« ¼»
three boundary point, the equilibrium relations will be written: K1
TE
1 T E
K2
Po2
T1 1 T E
T E 1 T1 T 2
and: K3
T2 T1
The expression of the coverage degree T1 will then be:
T1
K 2 K1 Po2 1 K 2 K1 Po2 (1 K 3 )
[10.10]
Compared with the previous case, this expression relies on another equilibrium constant K3, which necessarily possesses an exothermic character. This expression allows us to express the coverage degree as a function of oxygen pressure and temperature. It should be noted that compared with the energy in Figure 10.19, it is the new į variety of species ªO º T which takes the place of the species ª¬O - º¼ . As far as the T ¬« ¼» species ª¬O - º¼ of the new model is concerned, it is located, because of a much T stronger bond than before, below the energy of the species O2. The influence of oxygen pressure is expressed by a homographic law.
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Physical Chemistry of Solid-Gas Interfaces
As for temperature, its influences depend of the expression of the different equilibrium constants, which are expressed by an expression of the following type: K
§ 'H f · K 0 exp ¨ ¸ © RT ¹
We then note that the formation enthalpy ǻHf of the different species considered will be a necessary factor to express the coverage degree of the species, which is responsible for the electric response. 10.3.2.3. Expression of the theoretical potential difference at the poles of the device We now have to express the theoretical potential obtained at the poles of two electrodes elaborated with two different metallic elements. To simplify the calculations, we will note: ª 'H f ([O ]E ) 'H f ([OG ]T ) º » K10 K 20 exp « RT «¬ »¼
KD
K1 K 2
Thus: ª 'H D ([OG ]T ) º KD0 exp « » RT ¬« ¼»
KD
with: G
G
'HD ([O ]T ) = 'H f ([O]E ) 'H f ([O ]T
We will note that the value of ǻH f >O @ ȕ must be considered as independent from the electrodes because it is caused by a mere interaction between the gas and the solid electrolyte; therefore:
T1
KD Po2 1 KD Po2 (1 K 3 )
Remembering that:
'V V1 V2
DG 2
ªT12 T22 º¼ J ª¬T12 T22 º¼ R ¬
[10.11]
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395
we can write: 'V
2 º¼ J ª¬ T Pt2 T Au
'V
2º 2 ª · § · » KDPt Po2 KDAu Po2 «¨§ ¸ ¨ ¸ » J« Pt Pt Au Au ¨ ¸ ¨ ¸ 1 K Po (1 K ) 1 K Po (1 K ) D D 2 2 «© 3 3 ¹ © ¹ » ¬ ¼
[10.12]
K Pt and K Au are equilibrium constants for platinum and gold respectively.
In order to validate such an expression, it is important to compare the experimental results to the shape of the theoretical curves obtained by varying ǻV as a function of temperature and pressure. In such a case, it is impossible to perform a simple mathematical analysis, which would not even allow us to determine the shape of the curves. We can then conduct a simulation using a spreadsheet, which will calculate the expression of ǻV for different values of the parameters concerned, and which will compare the calculated values to those obtained experimentally; these calculations are performed using the least squares method. 10.3.3. Simulation of the results obtained with oxygen
10.3.3.1. Behavior as a function of temperature and pressure In the present case, we have to take four different parameters for each metal, that is: 'H D , 'H f , K Į0 and K 3 . To avoid certain aberrant values peculiar to this device, and to shorten the calculations, we can impose these conditions: į
į
ǻH ĮAu ([O - ]T ) ! ǻH ĮPt ([O - ]T ) ! 0 (K Į0 )Au and (K Į0 )Pt ! 0 (K 3 )Au and (K 3 )Pt ! 0
The first two conditions stem from the fact that the positive pole of the device is gold, and we can admit that, in general, the species fixed at the three boundary point are more active and, subsequently, less bonded with gold than with platinum.
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Physical Chemistry of Solid-Gas Interfaces
The third condition is linked to the fact that here, 'H 3 is negative. The adopted calculation process allows us to reproduce, with accuracy, the complex behavior of the sensor as a function of temperature and pressure; the difficulty involves the simulation of a peak on the curves displaying the signal as a function of temperature and the simulation at the intersections of curves displaying the influence of the pressure on the signal. The best results obtained for the parameters’ value are displayed in Table 10.2.17, 18
Table 10.2. Values of the different parameters exploited for the simulation
The comparison between the simulation and the experimental results are displayed in Figure 10.20.
Figure 10.20. Results of simulations (dotted lines) as a function of temperature and oxygen pressure
Models and Interpretation of Experimental Results
397
The values given to the different parameters are not necessarily the only ones compatible with such a system; nevertheless we can assert that the magnitude of the values has to be respected to obtain satisfying results. Furthermore, the calculation process has convinced us that the formation enthalpy value ǻH Į
([O į ]T ) of the activated specie [O į ]T must be positive
on gold and on platinum. Conversely, the formation enthalpy ǻH Į ([O - ] T ) of the activated species [O - ] T must be negative on gold and on platinum. If not, it would be impossible to obtain a peak for the curves displaying the signal as a function of the temperature. It is also interesting to note that the mathematical solution imposes the existence of endothermic species. Using these results, we will see that it is possible to check certain electric behaviors peculiar to this device, with regards to the size of the electrodes and the information recorded by the surface potential method. 10.3.3.2. Behavior as a function of electrode size The previous simulation has allowed us to determine the variation of the coverage degree T at the level of the electrodes as a function of the experimental conditions and the nature of the metal. This simulation has been conducted with the results observed on the sensors whose electrodes are of the same size but different natures. As was seen in Chapter 8, the use of two electrodes which have the same nature but different sizes can cause a potential difference between these electrodes. This potential difference is expressed by:
'V
V1 V 2
ª 1 1 º 2» 2 R R 2 ¼ ¬ 1
D G 2T 2 «
Knowing T, at different temperatures and different pressures, then allows us to express the potential difference as a function of the radius of the two electrodes and to check the validity of the previous relation by comparing the corresponding experimental results. Before displaying the simulation results of such a phenomenon, we recall that the potential of each electrode is inversely proportional to its size: thus, the electrode which has the greatest size has the lowest potential. Connected to the positive pole of the measuring device, the response will be negative. Finally, the potential difference 'V between the electrodes will be all the greater if the difference in size is substantial.
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Physical Chemistry of Solid-Gas Interfaces
Knowing șAu and șPt, at different temperatures and different pressures, allows us to calculate ǻV for two identical electrodes, either in gold or platinum, and thus as a function of the ratio E R1 / R2 1 . ǻV is then proportional to ș2. The results, displayed in Figures 10.21 and 10.22 enable us to compare the experimental results and the results stemming from calculations. These results are the electric response of the sensors comprising two electrodes of the same size (the surface ratio is 1/10) and the results of the simulation. Results acquired at 300°C for different values of the oxygen pressure (see Figure 10.21) and results acquired under 10 Pa and different temperatures (see Figure 10.22). Given the shape of the curves obtained by the simulation we can consider that the behavior of the device, as a function of temperature and pressure is perfectly in accord with the previous expression, and that the adopted model is not put in check by this series of experiments.
Figure 10.21. Electric responses of sensors composed of two electrodes of the same nature (gold or platinum) with an area ratio equal to 1/10 (1 mbar = 100 Pa): a) experimental results; b) results of the simulation T = 300°C
Figure 10.22. Electric responses of sensors composed of two electrodes of same nature (gold or platinum) with an area ratio equal to 1/10 (1mbar = 100 Pa): a) experimental results; b) results of the simulation PO2 = 10 Pa
Models and Interpretation of Experimental Results
399
It appears these results all confirm the validity of the proposed model, and the values given to the different parameters as well. In order to confirm this, we are going to compare the results obtained by this model with the results obtained by measuring the surface potential. 10.3.3.3. Evolution of the surface potential The information recorded by the surface potential measurement (Chapter 6) naturally stems from the presence of charges located at the surface of the device. The previous model has allowed us to clarify their nature, their location and their concentration. The total charge: QTotal, which is proportional to the surface potential, can be expressed by an equation of the following type: Qtotal
q(n1T1 n2T 2 nM T M )
where q is the elemental charge of the electron, șM is the coverage degree on the metal and ni stems from the ionization degree of the species i considered. To simplify, we can consider that șM is negligible compared to ș1 and ș2. This hypothesis is justified by the fact this species, as noted before, is not detected by surface potential measurements conducted on the metal alone. For the other two species, we have admitted that the charge stemming from the į species ª O º T was of dipolar origin. To explain this difference, we have admitted «¬ »¼ į į that the species ª O º T has a greater charge effect than the species ª O º . Thus, ¬« ¼» ¬« ¼» T an arbitrary relation has been adopted: Qtotal
D q (T1 2T 2 )
If we note that the surface potential is proportional to QTotal, and if we remember that T2 = K3T1, it is possible to recalculate to the nearest factor this potential for different temperatures and different pressures. These results are displayed in Figures 10.23, 10.24, 10.25 and 10.26. Figures 10.23 and 10.24 deal with the results obtained with beta-alumina covered with gold; Figures 10.25 and 10.26 deal with the results obtained for beta-alumina covered with platinum. It is interesting to note that the simulation results obtained with gold are especially representative of the experimental results, both for the influence of the temperature as well as the influence of the pressure. With regards to the results
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Physical Chemistry of Solid-Gas Interfaces
obtained with platinum, they are as satisfactory, at least as far as the influence of the temperature is concerned.
Figure 10.23. Variation of the surface potential, observed on beta-alumina powder covered with gold as a function of the experimental conditions (oxygen pressure/temperature) (1 mbar = 100 Pa)
Figure 10.24. Evolution of the theoretical charge of the gold electrode as a function of the experimental conditions (oxygen pressure/temperature) (1 mbar = 100 Pa)
Figure 10.25. Evolution of the theoretical charge of the electrode covered with platinum as a function of the experimental conditions (oxygen pressure/temperature) (1 mbar = 100 Pa)
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401
Figure 10.26. Evolution of the theoretical charge of the golden electrode as a function of the experimental conditions (oxygen pressure/temperature) (1 mbar = 100 Pa)
Nevertheless, given the complex and peculiar shapes of the experimental curves, we can conclude there again that the proposed model is performing well even when many suppositions have been taken into account to simplify the problem. 10.3.4. Simulation of the phenomenon in the presence of CO
We have just seen that the previous model allows us to interpret with accuracy the results obtained with a sensor submitted to different conditions (temperature and pressure). Using such a tool, it is interesting to interpret and simulate the results obtained with the same device submitted to the action or carbon monoxide. 10.3.4.1. Description of the mechanisms considered After analysis of the experimental results concerning the action of carbon monoxide, it appears that oxygen has an essential role in the response of the sensor. Inspired by the model proposed in heterogenous catalysis, we have decided to suppose that the carbon monoxide reacts with the oxygen species present at the surface of the device to form carbon dioxide. This reaction will consume part of these oxygen species, and thus alter the electric response of the device. The potential difference produced will be all the greater if the catalytic activity of the two metals, constituting the electrodes, differs from the oxidation reaction of the carbon monoxide. For this application, platinum appears a better catalyst than gold.19, 20 The functioning principle of the sensor remains unaltered by the action of oxygen, whose concentration in adsorbed species is here controlled by the carbon monoxide concentration.
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Physical Chemistry of Solid-Gas Interfaces
The role of carbon monoxide is then limited to a mere consumption of the adsorbed oxygen species. Such consumption must be explained by a kinetic model in an open system. Before proposing such a model, we are going to try and determine which oxygen species is most concerned by this reaction, then study the different conceivable oxidation mechanisms. We have seen that there are at least four different oxygen species adsorbed at the surface of the device materials. Among these four species, only two are in relation with the three boundary point, but in the hypothesis of a supported catalyst, only the species fixed to the three boundary point characterize such a catalyst.4, 21, 22, 23 Finally, among the two different į species fixed to the three boundary point, only the species ªO º T displays an «¬ »¼ endothermic character and, subsequently, a weak bond. Thus, it is this species, the most reactive, which appears as the best applicant to interact with carbon monoxide. The kinetic model will therefore be developed on the basis of this hypothesis. 10.3.4.2. Oxidation mechanisms of carbon monoxide24, 25, 26, 27 Two kinds of oxidation mechanism for the carbon monoxide at the surface of the solids are frequently acknowledged by scientists. The first, proposed by Eley and Rideal ( Eley-Ridea lmodel) admits that the gaseous carbon monoxide directly reacts with the oxygen species adsorbed to form carbon dioxide, given: [CO] Oadsorbed [CO2 ]
The second, proposed by Langmuir and Hinshelwood (Langmuir-Hinshelwood model), relies on a much more complex reaction. In this reaction the carbon monoxide is in adsorbed form. The equation of the reaction is then written: [CO] COadsorbed COadsorbed Oadsorbed [CO2 ]
An oxidation mechanism of the carbon monoxide following the Eley-Rideal model is realistic if we consider the existence of a weakly bonded oxygen species and, subsequently, extremely reactive oxygen species. Nevertheless, it seems that
Models and Interpretation of Experimental Results
403
this model is valid only when the carbon monoxide partial pressure is low compared with oxygen partial pressure. The two mechanisms could both fit with our system, so both cases can be considered. To explain the electric results obtained, it is important to express the į concentration of the reactive species ªO º T , from which stem the potential of the ¬« ¼» electrodes, because they react with carbon monoxide; the hypothesis of a stationary state implies that the speed rate of the reaction is constant and, subsequently, a potentiometric signal that is not a function of time at a given carbon monoxide pressure. – Eley-Rideal model This model is represented by the following reactions: O2 2 ȕ 2[O] ȕ
[O] ȕ s metal [O į ] T ȕ į
[O ] T e [O - ] T CO [O
į
] T CO2 s
This model is treated as the hypothesis for a pure kinetic case or limiting step. This choice, which necessarily implies the hypothesis of a stationary state, allows us to deal with a simpler mathematical system. In fact, it is easy to demonstrate that whatever the chosen limiting step, this model appears incompatible with the experimental results. The expression of the coverage degree, from which stems the electric signal, is either independent of the oxygen pressure (case of the limiting reaction process 1 or 2), or independent of the carbon monoxide partial pressure (limiting reaction process 4), or even independent of the pressure of two gases (limiting reaction process 3). – Langmuir-Hinshelwood model In the case of the Langmuir-Hinshelwood model, the basic steps taken into account are the following: O2 2 ȕ 2[O] ȕ
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Physical Chemistry of Solid-Gas Interfaces
[O] ȕ s metal [O į ] T ȕ į
[O ] T e [O - ] T CO s CO s CO s [O
į
] T CO2
2s
We consider here that carbon monoxide can be directly adsorbed on site s of the three boundary point. If, firstly, we consider that the slowest step of the process is the adsorbed carbon į
monoxide oxidation reaction with the species [O ] T (step 5), we only have to express the fact that all the other steps have reached equilibrium, then we obtain the relation:
TE
T2 T CO
K1 Po2 1 K1 Po2 K 3T1 K 4 PCO >1 T1 (1 K 3 ) @ 1 K 4 PCO
and:
T E K 2 >1 T1 (1 K 3 ) T CO @ T1 (1 T E ) The resolution of this system comprising four equations and four unknown parameters allows us to express ș1 as follows:
T1
K 2 K1 Po2 1 K 2 K1 Po2 (1 K 3 ) K 4 Pco
This expression will allow us to express ǻV and to confirm that its variation as a function of temperature, the oxygen partial pressure, and of course the carbon monoxide partial pressure is compatible with the results obtained by the sensor.
Models and Interpretation of Experimental Results
405
For this, it is necessary to calculate the new potential difference that appears between two electrodes of different natures. If we note KD
K1 K 2 , the potential difference obtained between these two
electrodes of same size, which comprise one made of platinum and one made of gold, is expressed as follows: 'V
2 º¼ J ª¬ T Pt2 T Au
'V
2º 2 ª · § · » KDPt Po2 KDAu Po2 «¨§ ¸ ¨ ¸ J« Pt Pt ¨ 1 KDAu Po2 (1 K Au ) ¸ »» «¨© 1 KD Po2 (1 K 3 ) ¸¹ 3 © ¹ ¬ ¼
By comparison with the expression relative to oxygen alone, we still have to define two more constants K 40 and 'H4 to completely define this potential. 10.3.4.3. Results of the simulation The method used to determine the value of these constants is identical to the one used for the simulation of the experimental results obtained with oxygen. The comparison between the experimental results and those obtained by simulation are displayed in Figures 10.27 and 10.32. They allow to us check that, whatever the chosen evolution parameter, the model acts correctly. Figures 10.27, 10.28 and 10.29 display the influence of the carbon monoxide pressure on the potential difference recorded between the electrodes as a function of the oxygen pressure, and for different temperatures. We can note that whatever the oxygen pressure, the simulation, displayed as a dotted line, allows us to explain the complex variations observed, and especially the “toppling” of the response observed at high and low pressures. Figures 10.30, 10.31 and 10.32 concern the influence of the carbon monoxide pressure on the electric response at different oxygen pressures. Once more, and regardless of the temperature, the simulation is in accordance with the experimental results.
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Physical Chemistry of Solid-Gas Interfaces
We also confirm that there is a peak at 10 Pa, and a “toppling” of the response at low temperatures. The values of K 04 and ǻH4, which give the most satisfying results are displayed in Table 10.3.
Table 10.3. Values of the parameters used for the simulation
The value determined for platinum (-14.3 kJ/mole) can be compared with several values provided by publications. Thus, Li, Tan and Zeng28 have determined an adsorption enthalpy of -13.8 kJ/mole with CO on platinum supported by zirconium.
Figure 10.27. Comparison between experimental results (dotted lines) and simulation at different temperatures, PO2 = 1,000 Pa
Models and Interpretation of Experimental Results
Figure 10.28. Comparison between experimental results (dotted lines) and simulation at different temperatures, PO2 = 100 Pa
Figure 10.29. Comparison between experimental results (dotted lines) and simulation at different temperatures
407
408
Physical Chemistry of Solid-Gas Interfaces
Figure 10.30. Comparison between experimental results (dotted lines) and simulation for different partial oxygen pressures at 500°C (1 mbar = 10 Pa)
Figure 10.31. Comparison between experimental results (dotted lines) and simulation for different partial oxygen pressures at 400°C (1 mbar = 10 Pa)
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409
Figure 10.32. Comparison between experimental results (dotted lines) and simulation for different partial oxygen pressures at 250°C (1 mbar = 10 Pa)
Given the extreme complexity of the experimental results obtained, such an accordance appears to be an excellent argument in favor of this model. These results allow us to reinforce the thermodynamic model, which makes weakly bound oxygen species react, and furthermore to validate the kinetic model, at least as far as the consumption of these species by a reducing gas, like CO, is concerned. 10.4. Tin dioxide29, 30 10.4.1. Introduction
The results obtained on tin dioxide in interaction with different gases have allowed us to record information that is sufficiently significant and original to make us investigate the nature of the phenomena observed. To do this, we will recall two important results. The first is relative to the experiments described in Chapter 8 and which concerns the alteration of the electric effects observed when a metal is deposited at the surface of the sensitive material. The second is relative to the evolution of the sensitivity of the SnO2 thick films as a function of the thickness. The presence of a peak, whose location depends on the nature of the gas considered, generates interpretive problems that we will attempt to solve.
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Physical Chemistry of Solid-Gas Interfaces
To model such behaviors, we will, firstly, exploit the information obtained with the calorimetric, catalytic and electric tests As in the case of beta-alumina, this procedure will allow us to propose a physicochemical model relative to oxygen adsorption, with the consequences this entails on the depletion layers concerned by this phenomenon and on the electric response of the sensor. Secondly, this physico-chemical model, likened to a physical model of electric conduction in the material, will allow us to interpret the effects linked to the thickness of the sensitive film. 10.4.2. Proposition for a physico-chemical model
We have here to assess the physical and chemical behaviors of the three elements constituting the device, that is, the oxide, the metal and the oxide associated with the metal. In general, these three elements are active from a catalytic point of view, at least as far as the oxidation of carbon monoxide is concerned, the performance of platinum being superior to that of gold. This result led us to suppose the presence of oxygen species catalytically active at the surface of the different materials. The calorimetric tests which confirm the presence of adsorbed species on the oxide and on the oxide associated with the metal furthermore allow us to confirm that the bond between the oxygen and the material is greater with the oxide associated with the metal than with the oxide alone (see Figure 10.33).
Figure 10.33. Quantity of heat exchanged (-Q in mJ) with the different kind of sample during oxygen pressure variations contained between 10 and 5 x 103 Pa at 400°C
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411
Finally, these species are electrically charged, as is demonstrated by the electric conduction measurements realized in the cell especially set up to separate the effects linked to the oxide and the effects linked to the oxide/metal association (Chapter 8). Again, these results confirm that in the presence of oxygen, the oxide associated with the metal displays a much greater sensitivity than the oxide alone. Adsorbed oxygen has not been detected on the metal. Nevertheless, several works using the thermodesorption31 or the colorimetric titration32 confirm the presence of chemisorbed oxygen species at the surface of the gold or platinum. These results, displayed in Table 10.4, allow us to imagine the existence of three different species (see Figure 10.34).
Table 10.4. Assessment of the catalytic, electric and adsorption properties of the different parts of the sensor (the number of crosses reflect the intensity of the phenomenon observed)
– The species O1 In the current case, and conversely with the case of beta-alumina, this species fixed on an oxide with a semiconductor character will exchange one or more electrons with the tin dioxide following this kind of reaction: O2 ( gaseous ) 2neox 2 sD 2(O n sD ) with (O n sD )
O1
The surface of the tin dioxide is characterized by the sites sD . – The species O2 Chemisorbed on the element oxide/metal, for which the adsorption site is noted sJ , this species can be likened as in the case of beta-alumina to the three boundary point.20, 33
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Physical Chemistry of Solid-Gas Interfaces
Here again, it is important to explain the physico-chemical contribution of such a site, which can appear more reactive than a site owned by oxide alone. To explain the fact that this species is responsible for an important electric effect on the conductivity of SnO2, we have to imagine that its presence is able to induce an important depletion layer in the semiconductor. This can be explained by a greater degree of coverage for the species O2 than for the species O1 and/or by a greater degree of ionization for the species O2 than for the species O1. To explain a greater degree of ionization, we can imagine that O1 fixed on the oxide is analogous to a species O- - sD , and that the species O2 can be likened to a species of type O2- - sJ. The conversion of one species into another will then be favored by the presence of the metal. To explain the catalytic role of the metal, we will write: O sD eM sJ O 2 sJ sD eox eM
_____________________________ O sD eox sJ O 2 sJ sD
This reaction resembles that induced by S. Morrison34; nevertheless, it is here located at the three boundary point as in the case of certain potentiometric sensors.35 eM and eOX are the electrons present in the metal and the oxide respectively.
– The species O3 The catalytic activity being bigger or smaller than for the metal alone, let us now suppose that at the surface of this material there are oxygen chemisorbed species. These locations are sites and the reaction can be written: O2 ( gaseous ) 2neM 2 sD 2(O n sD )
n is the number of electrons of the metal involved in this chemisorption and its value is a function of oxygen degree of oxidation.
Models and Interpretation of Experimental Results
413
The coverage degree and the thermodynamic constant associated with this equilibrium will be noted TE and KE respectively. In the case of gold, which possesses a catalytic activity lower than that of platinum, we can suppose that the coverage degree in chemisorbed TE will be lower than the coverage degree obtained with platinum.
Figure 10.34. Reaction scheme of the transformation of CO into CO2 on the surface of: (a) tin dioxide, (b) tin dioxide on which a metallic film has been deposited, (c) the metal
For the energy plan, we can propose a diagram like the one displayed in Figure 10.35.
Figure 10.35. Energetic diagram of the different oxygen species taken into account
414
Physical Chemistry of Solid-Gas Interfaces
Because the reaction involved in this model describes the formation of the species O3, we can simultaneously invoke the mechanisms of spill-over and reverse spill-over, mentioned in Chapter 8. Indeed, mechanism (A) is an approach of reverse spill-over type,36 insofar as certain “oxygen” species are initially adsorbed on the oxide, whereas the type (B) mechanism resembles the spill-over, if we consider that other “oxygen” species are initially adsorbed on the metal. Besides, our model allows a depletion layer to appear, linked to an electron transfer which, contrary to the electronic mechanism described by Yamazoe,37 is not located perpendicularly to the metal, but at the three boundary points. As in Figure 10.36, the intensity of the induced depletion is greater than the depletion provoked by the adsorption of oxygen on the oxide alone. Such a model is in perfect accord, firstly, with that of U. Weimar32 which indicates the presence of an important depletion layer at the three boundary point, and secondly with the model of K. Vargehse38 which explains the presence of an important depletion layer in the extension of a metallic electrode. These models were commented on in Chapter 8.
Figure 10.36. Mechanism proposed to explain the action of oxygen
We will retain from this physico-chemical model the fact that the synergy effects between the gas, the metal and the oxide are especially located at the inter-phase metal/oxide/gas, called the three boundary point, and that these effects are explained by a large space-charge layer, which is itself located in the oxide at the level of this very inter-phase. This configuration is compatible with the notion of the three boundary point, which involves, firstly, an electron transfer from the metal towards the gas and then
Models and Interpretation of Experimental Results
415
from the oxide towards the metal. Strictly speaking, the sensitive film elaborated with pulverulent oxide can display a natural and non-negligible porosity that enables metallic elements to diffuse. In these conditions, the inter-phase metal/oxide/gas and, subsequently, the space-charge layer, is localized in the zone of the oxide contaminated by the metal. We can thus imagine that in a real structure, there is a space-charge layer located perpendicularly to the surface of the metallic film. Such a configuration closely resembles the one proposed by K. Vargehse.38 The model, as displayed in Figure 10.36, appears as a limited and simplified case that we will be able to use in kinetic and mathematical plans. We imagine that in such a model, the vastness of the barrier effect must be considered caused by its amplitude compared to the thickness of the material. It remains to be seen whether the thickness of such a zone and, consequently, the value of its resistance is able to control the conductance of the whole device. It is based on these results, obtained on oxide alone as a function of the thickness of the deposited films, that we are going to develop a physical model of conduction able to justify the role of the space-charge layer generated by the presence of electrodes. 10.4.3. Phenomenon at the electrodes and role of the thickness of the sensitive film
The purpose of the present physical model is to demonstrate how the depletion layer at the level of the three boundary point, is able to modulate and control the electrical properties of the device according to the thickness of the material. This model is developed for thick film materials. The diagram of such a device, with two electrodes deposited on the outer surface of the material, is presented in Figure 10.37.
Figure 10.37. Space-charge layers present at the level of the electrodes for a thick film device
416
Physical Chemistry of Solid-Gas Interfaces
10.4.3.1. Calculation of the conductance G as a function of the thickness of the film – Geometric aspects In the present case, both electrodes are located on the same face of the material. The assessment of the global resistance is not easy because it needs the integration of many current lines whose paths are not linear between the two electrodes. To simplify the problem, our sample will be likened to a sensitive film shaped like a square parallelepiped, of length D (4 mm), of width L (2 mm) and of thickness e. The electrodes deposited at the surface of the sample are also of rectangular shape, of width d (1 mm) and of length L (2 cm). The space-charge layer, as indicated by Figure 10.38, can be decomposed into two zones: – D1, which corresponds to the action of oxygen on tin dioxide alone. This depletion layer can be likened to a square parallelepiped of length D-2d+h, of height y and of width L; – D2, relative to the action of oxygen at the three boundary point. This depletion layer can be represented by a square parallelepiped of height x, of width l and of length L, with x>> y.
Figure 10.38. Space-charge layers present at the level of the electrodes for a thick film device
Given the slight thickness supposed for y, we will consider that zone D1 is homogenous from an electric point of view, and that the resistivity US will have a constant value in all its thickness.
Models and Interpretation of Experimental Results
417
As far as D2 is concerned and given the greater value supposed for x, we will consider that this depletion layer is not necessarily homogenous from an electric point of view, and that there will be a linear resistivity gradient:
U ( x)
U S ax
The parameter “a”, which characterizes the amplitude of the gradient, will naturally be a function of the physico-chemical perturbation amplitude, that is, a function of the coverage degree at the three boundary point and of the nature of the reducing gases reacting with oxygen. Figure 10.39 displays the schematic representation of such a gradient. To respect the conditions relative to D1 and D2, we will indeed admit that for 0 < x
Figure 10.39. Distribution of the resistivity in the depletion layer linked to the three boundary point
Thus:
Ey since y << E.
US UM a
E |
US UM a
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Physical Chemistry of Solid-Gas Interfaces
If we wish that zone D2 regulates the thickness of the material, it is necessary to let certain current lines propagate between the two electrodes without perturbation from this controlling zone. This entails that the width of the depletion layer h must be less than the width of the electrode d. Otherwise, all the current lines would have had to cross this zone and the effect of the three boundary point would have been confused with the rectifier effect generally attributed to the junction oxide/electrodes. The electric diagram of such a structure is displayed in Figure 10.40. RS and RM are the resistance values of the depleted zone and the non-depleted zone respectively.
Figure 10.40. Electric scheme of the structure
– Calculation of the conductance G 1) Calculation of G under air If we work under air, there is a large coverage of oxygen and, subsequently, a large depletion layer; here we are in the most common case. The complete calculation of the conductance Gair is the sum of an element dG, of thickness dx on the whole thickness of film e. This element dG will be a function of the different zones, zones that are characterized by different values of U(x):
Models and Interpretation of Experimental Results
419
U ( x) U S for x y U ( x) US ax for y d x d E U ( x) U M for x ! E For the zone y < x < ȕ, an element dG(x), as it is represented in Figure 10.41, is relative to the association in series of two elements dGs(x) and dGM(x), with: dGS ( x)
L dx 2h U ( x )
dGM ( x)
L L dx | dx D u U M ( x) ( D 2 h) u U M ( x )
and:
We will also have: dG ( x)
dGS ( x ) u dGM ( x ) dGS ( x) dGM ( x)
that is to say: dG ( x )
L dx 2h U ( x ) D U M
The two other considered zones are homogenous and characterized by only one conductance value, which is the only function of the geometry of the system. The total conductance G air is obtained by integrating the different expressions of dG(x) for the thickness considered.
Figure 10.41. Conductance elements dG(x) for y < x < ȕ
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Physical Chemistry of Solid-Gas Interfaces
In the present case, we have three zones of thickness and, consequently, three integrating domains: – zone a: if e y: a ( e) Gair
eL
D 2d h U S (2d h) U M
|
eL
D 2 d U S 2d U M
The conductance is expressed: a Gair (e)
Ae
– zone b: if y < e ȕ: b Gair ( e)
x e
x y
x e
x 0
x 0
x y
b Gair ( e)
³ dG ( x)
³ dG ( x ) L ³
yL
D 2d U S 2d U M
1 dx 2h( U s ax) D U M
x e
ª 1 º L « ln 2h U S ax D U M » ah 2 ¬ ¼x
y
yL
b Gair ( e)
D 2d U S 2d U M ª L 2h U S ay D U M º « ln » ¬« 2ah 2h U S ae D U M ¼»
The conductance is expressed: b Gair ( e)
A B ln
C D Ee
– zone c: if ȕ < e: 2h U S ay D U M º ª L yL « ln » D 2 d 2 d 2 ah 2h U M D U M U U S M ¬ ¼ U UM · L § u e S ¸ D U M ¨© a ¹
c Gair ( e)
Models and Interpretation of Experimental Results
421
The conductance is expressed: c Gair ( e)
A Be
2) Calculation of G under a reducing gas As has been said, the action of a reducing gas on the sensitive material comes down to altering the coverage degree in oxygen and, subsequently, decreasing the bulk of the depletion layer. To geometrically explain the evolution of this zone, which is characterized by the two parameters ȕ and a, we have taken as boundary conditions that U(x) = US for x = 0, at least for the pressure field shown for the reducing gas. This implies that if ȕ varies, then a also varies. The gradient then takes the value Ja, with J > 1, as displayed in Figure 10.42. Here, ȕ (Ȗ), the deepness of the depletion layer, in the presence of a reducing gas has the value: E / a .
Figure 10.42. Distribution of the resistivity in the depletion layer linked to the three boundary point in the presence of a reducing gas or in presence of air (dotted line)
To express the conductance, we must determine the thickness of two zones: – zone a: if 0 < e ȕ (Ȗ): a (e ) Ggas
x e
³ dG ( x)
x 0
x e
1
x 0
2h( U s aJ x) D U M
L³
dx
422
Physical Chemistry of Solid-Gas Interfaces x e
G (e ) a gas
a Ggas (e )
ª º 1 ln 2h U S J ax D U M » L « ¬ 2aJ h ¼x ª L 2h U S D U M ln « «¬ 2J ah 2h U S J ae D U M
0
º » »¼
The conductance is expressed: a Ggas (e )
A 'ln
B' C ' D ' e
– zone b: if ȕ (Ȗ) < e: b Ggas (e )
ª L 2h U S D U M ln « 2 ah 2h U M D U M J ¬
º U UM · § L u¨e S » ¸ D U Ja ¹ © M ¼
The conductance is expressed: b Ggas ( e)
A ' B ' e
3) Expression of the sensitivity To express the sensitivity Sgas = Ggas/GAir, we have to deal with 4 thickness zones: e y y e E (J )
E (J ) e E E e The analytic study of the evolution of S as a function of e in the four thickness zones is not easy. Nevertheless, a mere digital simulation provides the varying sensitivities of these functions; these results are displayed in Table 10.5.
Models and Interpretation of Experimental Results
423
Table 10.5. Evolution of the conductance and the sensitivity as a function of the considered thickness zone
It is interesting to note that the variation laws of G under air and under gas can be different according to the thickness, and that this difference allows us to obtain sensitivity curves displaying a peak. 10.4.3.2. Mathematical simulation 1) Evaluation of the model’s parameters To conduct a true simulation of the phenomenon, it is necessary to use numeric values for the six variables involved: US, UM, E, h, y and J. For UM, which conveys the intrinsic behavior of the material, we have chosen values found in publications, values which concern the electric resistivity of tin dioxide under vacuum at 500°C. The proposed value is 1 :.m under an oxygen pressure of 100 Pa39. US must be sufficiently different from UM so that the space-charge layer at the three boundary point can ensure a limiting effect from a resistive point of view. The value of U S / U M is about 103. For E, the value is about the magnification of the film thickness, that is to say contained between 10 and 80 μm. As has already been mentioned in the geometric aspects of the section 10.4.3.1, h must be less than d = 10-3 m. We will finally note that y must be negligible compared to E.
424
Physical Chemistry of Solid-Gas Interfaces
2) Simulations of the sensitivity evolution of S as a function of the thickness This is based on similar data to that used when simulating the curve G under air and under gas and, subsequently, the curves S = GGas/GAir as a function of thickness. The first example deals with the action of CO. The comparison between the simulation and the experimental dots is displayed in Figure 10.43. We recall here that the three series of points displayed are relative to three different series of sensors. A satisfactory agreement has been obtained for the values: US = 9.3x104 :.m, UM = 5.7x10-1 :.m, E = 80x10-6 m, h = 0.5x10-6 m, y = 10-6 m and J = 9.
Figure 10.43. Comparison between the observed results and the simulated curves for the conductance under air, under CO and the sensitivity to CO. The parameters of the calculations are: ȡS = 9.3x104 ȍ.m, ȡM = 4.7x10-1 ȍ.m, h = 0.5x10-6 m, ȕ = 80x10-6 m, y = 2x10-6 m and Ȗ = 7
Models and Interpretation of Experimental Results
425
Using the same values for the parameters US, UM, h, E and y and by altering the value of Ȗ, we will see that it is possible to simulate the results obtained under alcohol and methane. Thus, with alcohol, by giving Jthe value 40 instead of 7 for the CO, we obtain the results displayed in Figure 10.44.
Figure 10.44. Comparison between the observed results and the simulated curves for conductance under air, under C2H5OH, and sensitivity to C2H5OH. The parameters are: ȡS = 9.3 x 104 ȍ.m, ȡM = 4.7 x 10-1 ȍ.m, h = 0.5 x 10-6 m, ȕ = 80 x 10-6 m, y = 2 x 10-6 m and Ȗ = 40
426
Physical Chemistry of Solid-Gas Interfaces
The fact that, for alcohol, the sensitivity peak moves towards the small thicknesses implies that the gradient Ja is greater with alcohol than with CO. This means that the quantity of chemisorbed oxygen consumed by alcohol is greater than the quantity consumed by CO. The simulation obtained for CH4 is displayed in Figure 10.45. The value of J giving the best agreement is 2.
Figure 10.45. Comparison between observed results and simulated curves for the conductance under air, under CH4 and the sensitivity to CH4. ȡS = 9.3 x 104 ȍ.m, ȡM = 4.7 x 10-1 ȍ.m, h = 0.5 x 10-6 m, ȕ = 80 x 10-6 m, y = 2 x 10-6 m and Ȗ = 2
Models and Interpretation of Experimental Results
427
In this case the slight value of J implies that the sensitivity maximum moves towards the greater thicknesses, which indicates that the quantity of oxygen consumed by methane is less than that consumed by carbon monoxide and ethanol. 3) Simulations of the sensitivity evolutions as a function of the distance separating the electrodes We have also studied the effect of the distance “D” between the electrodes on the sensitivity of the material. For instance, we have displayed in Figure 10.46 the results obtained by the simulation for a film of 30 μm thickness.
Figure 10.46. Simulation of the sensitivity. The distance between the electrodes varies (μm). The other parameters are fixed: ȡS = 9.3 x 104 ȍ.m, ȡM = 4.7 x 10-1 ȍ.m, h = 0.5 x 10-6 m, ȕ = 80 x 10-6 m, y = 9 and Ȗ = 2 x 10-6 m
We will note that the sensitivity decreases when D increases. These results only confirm the results obtained by U. Hoefer40, who reports a decrease in the sensitivity when the inter-electrode distance increases (for distances contained between 10 and 500 μm). 4) Limits of the model The more or less satisfying agreement that we have observed for the sensitivity curves could, given the nature of the reducing gas, be explained by a physicochemical action specific to each gas. Our simulation supposes that every gas acts the same: it alters the resistivity gradient.
428
Physical Chemistry of Solid-Gas Interfaces
Furthermore, this model is based on a simplified representation of the spacecharge layer, which can produce significant differences between the experimental results and the simulation. Finally, we can note that the value of the parameter y must not exceed 5x10-6 to be non-negligible compared to ȕ, ȕ(Ȗ). 10.5. Bibliography 1. J. MEUNIER, Mécanisme de l’interaction oxygène-oxyde de Nickel – Etude de la conduction électrique et des effets thermiques, Thesis, Grenoble, 1987. 2. N. GUILLET, Etude d’un capteur de gaz potentiométrique, influence et rôle des espèces oxygénées de surface sur la réponse électrique, Thesis, INPG-ENSMSE, Saint-Etienne, 2001. 3. N. GUILLET, R. LALAUZE, C. PIJOLAT, “Oxygen and carbon monoxide role on the electrical response of a non-Nernstian potentiometric sensor; proposition of a model, Sensors and Actuators B, 98(2-3), 10-9, 2004. 4. A. GABOR, Introduction to the Surface Chemistry and Catalysis, Interscience, 1994. 5. N.L. ROBERTSON, J.N. MICHAELS, “Oxygen exchange on platinum electrodes in zirconia cells: location of electrochemical reaction sites”, J. Electrochem. Soc., vol. 137, no. 1, p. 129-135, 1990. 6. M. KLEITZ, E. SIEBERT, “Electrode reactions in potentiometric gas sensors”, Chemical Sensors Technology, vol. 2, p.151-171, Elsevier, 1989. 7. W.J. FLEMING, “Physical principles governing non-ideal behavior of the zirconia oxygen sensor”, J. Electrochem. Soc., vol. 124, no. 1, p. 21-28, 1977. 8. W.L. HOLSTEIN, M. BOUDART, “Application of the De DONDER relation of the mechanism of catalytic reactions”, J. Phys. Chem., 101, 9991-9994, 1997. 9. M. BOWKER, L.J. BOWKER, R.A. BENNETT, P. STONE, A. RAMIREZ-CUESTA, “In consideration of precursor states, spill-over and Boudart’s ‘collection zone’ and of their role in catalytic processes”, J. of Molecular Catalysis A, Chemical, 163, p. 221-232, 2000. 10. A. NILGÜN AKIN, GÖZDEM KILAZ, A. INCI ISLI, Z. ILSEN ONSAN, “Development and characterization of Pt-SnO2/J-Al2O3 catalysts”, Chemical Engineering Science, 56, p. 881-888, 2001. 11. B.L. KUZIN, M.A. KOMAROV, “Adsorption of O2 at Pt and kinetics of the oxygen reaction at the porous Pt electrode in contact with a solid electrolyte”, Solid State Ionics, 39, p.163-172, 1990. 12. T.M. GUR, I.D. RAISTICK, R.A. HUGGINS, “AC admittance measurments on stabilized zirconia with porous platinum electrodes”, Solid State Ionics, 1, p.251-271, 1980.
Models and Interpretation of Experimental Results
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13. B.A. VAN HASSEL, B.A. BOUKAMP, A.J. BURGGRAAF, “Electrode polarization at the Au, O2(g)/yttria, Part I: Theoretical considerations of reaction model”, Solid State Ionics, 48, p. 139-154, 1991. 14. P.R. NORTON, K. GRIFFITHS, P.E. BINDNER, “Interaction of oxygen with Pt(1000) – II kinetics and energetics”, Surface Science, 138, p. 125-147, 1984. 15. G. BARBOTTIN et al., “Ideal and actual MOS structures”, Instabilities in Silicon Devices, vol. 1, p. 227. 1991. 16. T. WOLKENSTEIN, Physico-chimie de la surface des semi-conducteurs, Mir, Moscow, p. 56, 1977. 17. C. PUPIER, Etude d’un capteur de gaz sensible au monoxyde de carbone et aux oxydes d'azote élaborés à base d’alumine bêta, Thesis, INPG – ENSME, 1999. 18. C. PUPIER, C. PIJOLAT, J.C. MARCHAND, R. LALAUZE, “Oxygen role in the electrochemical response of a gas sensor using ideally polarizable electrodes, J. Electrochem. Soc., 146 (6), p. 2360-2364, 1999. 19. D.M. HAALAND, “Noncatalytic electrodes for solid-electrolyte oxygen sensors”, J. Electrochem. Soc., vol. 127, no. 4, p. 796-804, 1980. 20. B.A. VAN HAASEL, B.A. BOUKAMP, A.J. BURGGRAAF, “Electrode polarization at the Au, O2(g)/yttria stabilized zirconia interface. Part II: electrochemical measurements and analysis”, Solid State Ionics, 48, p. 155-171, 1991. 21. J.E. ANDERSON, Y.B. GRAVES, “Steady-state characteristics of oxygen concentration cell sensors subjected to non-equilibrium gas mixtures”, J. Electrochem. Soc., vol. 128, no. 2, p. 294-300, 1981. 22. M.J. VERKERK, M.W.J. HAMMINK. A.J. BURGGRAAF, “Oxygen transfer on substituted ZrO2, Bi2O3 and CeO2 electrolytes with platinium electrodes”, J. Electrochem. Soc., 130, 1, 1983. 23. F. RUMPF, H. POPPA, M. BOUDART, “Oxidation of carbon monoxide on palladium: role of the alumina support”, Langmuir, 4, p. 722-728, 1988. 24. H. OKAMOTO, H. OBAYASHI, T. KUDO, “Carbon monoxide gas sensor made of stabilized zirconia”, Solid State Ionics, 1, p. 319-326, 1980. 25. E.C. SU, W.G. ROTHSCHILD, H.C. YAO, “CO oxidation over pt/g-Al2O3 under high pressure”, Journal of Catalysis, 118, p. 111-124, 1989. 26. S. FUCHS, T. HAHN, H.G. LINTZ, “The oxidation of carbon monoxide by oxygen over platinum, palladium and rhodium catalysts from 10-10 to 1 bar”, Chemical Engineering and Processing, 33, p. 363-369, 1994. 27. R.H. VENDERBOSCH, W. PRINS, W.P.M. VAN SWAAJJ, “Platinum catalysed oxidation of carbon monoxide as a model reaction in mass transfer measurements”, Chemical Engineering Science, vol. 53, no. 19, p. 3355-3366, 1988. 28. N. LI, T.C. TAN, H.C. ZENG, “High temperature carbon monoxide potentiometric sensor”, J. Electrochem. Soc., 140, 4, 1068-1072, 1993.
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29. P. MONTMEAT, Rôle des éléments métalliques sur le mécanisme de détection d’un capteur à base de dioxyde d’étain. Application à l’amélioration de la sélectivité à l’aide d’une membrane de platine, Thesis, INPG-ENSMSE, Saint-Etienne, 2002. 30. P. MONTMEAT, R. LALAUZE, J.P. VIRICELLE, G. TOURNIER, C. PIJOLAT, “Model of the thickness effect of SnO2 thick film on the detection properties”, Sensors and Actuators, B 103, (1-2), p. 84-90, 2004. 31. B.L. KUZIN, M.A. KOMAROV, “Adsorption of O2 at Pt and kinetics of oxygen reaction at the porous platinium electrodes”, Solid State Ionics, 36, 1990. 32. U. WEIMAR, W. GÖPEL, “A.C. measurements on tin oxide sensors to improve selectivities and sensitivities”, Sensors and Actuators, B 26-27, 13-18, 1995. 33. U. HOEFER, K. STEINER, E. WAGNER, “Contact and sheet resistance of SnO2 thin films from transmission-line model measurements”, Sensors and Actuators, B 26-27, 59-63, 1995. 34. S. MORRISON, “Selectivity in semi conductor gas sensors”, Sensors and Actuators, 12, 425-440, 1987. 35. M. KLEITZ, E. SIEBERT, “Electrode reactions in potentimetric gas sensors”, Chemical Sensors Technology, vol. 2, Elsevier, 1989. 36. K. GRASS, H. LINTZ, “The Kinetics of CO oxidation on SnO2 supported catalysis”, Journal of Catalysis, 172, 446-452, 1997. 37. N. YAMAZOE, Y. KUROKAWA, T. SEIYAMA, “Effects of additives on semiconductor gas sensors”, Sensors and Actuators, 4, 283-286, 1983. 38. O.K. VARGHESE, L. MALHOTRA, “Electrode sample capacitance effect on ethanol sensitivity of nano-grained SnO2 thin films”, Sensors and Actuators, B 53, 1998. 39. M.S. DUTRAIVE, Etude des Propriétés électriques de SnO2, Nature des défauts et influence des modes d’élaboration, Thesis, INPG-EMSE, Saint-Etienne, 1996. 40. U. HOEFER, K. STEINER, E. WAGNER, “Contact and sheet resistance of SnO2 thin films from transmission-line model measurements”, Sensors and Actuators, B 26-27, 59-63, 1995.
Index
A–C
H–I
adsorption-reaction process, 120 alternating-current measurement, 191 atmospheric pollutants, 341 branched process, 125 calorimeters, 138–146 calibration, 142 capacitance modulation, 182 chemical vapor deposition, 236, 353, 356 chemisorption, 2, 8, 23, 24, 80, 82, 98, 108, 119, 127, 285, 382, 384, 390, 412 cryogenic engine, 333
Hill-Everett model, 10, 12 Hill model, 9 impedance spectroscopy, 191, 196–200, 211 interfacial phenomena, 70, 109 intrinsic semiconductors, 61 isotherms, adsorption, 4, 8, 13, 15 chemical adsorption, 23 multilayer adsorption, 18
E–G electrical conductivity, 40, 55, 56, 65, 66, 92, 94, 107, 149, 210 electrical interface, 187 electrode size, 303, 397 electron holes, 33, 35, 54, 56, 57, 59, 61, 64, 66, 71, 75, 98, 105, 210 transfers, 39, 64, 71, 73 electronic work function, 72, 73, 76, 77, 80, 173, 179 electrostatic potential, 74, 77, 102, 103, 173 extrinsic semiconductors, 62 Fermi level, 57–63, 72, 73, 77, 80, 101–103 gravimetric method, 2, 4, 8, 13
M–Q mixed potential, 133, 134 point defects, 33, 34, 64, 91, 92 structural, 36 potentiometric sensor, 23, 281, 296, 303, 306, 312, 347, 356, 412 powder compression, 216 process kinetics, 109, 116–118, 138 physical adsorption, 2, 4, 8, 13, 18, quantum mechanics, 40, 41, 53, 54
R–S reference electrode, 181, 182, 303, 304 Schrödinger equation, 42 selectivity properties, 352
432
Physical Chemistry of Solid-Gas Interfaces
semiconductor interfaces, 97, 98 serigraphy, 252, 267, 313, 315, 316 sintering, 206, 217, 265, 266, 357, 358 space-charge region (SCR), 73–75, 88, 98– 104, 107, 108, 132, 202 surface states, 71–73, 77, 78, 80, 82, 89, 163, 169, 172, 200
T–V thermodesorption, 156, 158, 161–171, 179, 200, 343, 411 thermogram, 144, 145, 150, 151, 153, 154, 156, 381 Van der Waals forces, 4 vibrating capacitor methods, 172 volumetric method, 3
