Advances in Sintering Science and Technology Ceramic Transactions, Volume 209 A Collection of Papers Presented at the International Conference on Sintering November 16-20, 2009 La Mia, California Edited by
Rajendra K. Bordia Eugene A. Olevsky
)WILEY A John Wiley & Sons, Inc., Publication
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Advances in Sintering Science and Technology
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Advances in Sintering Science and Technology Ceramic Transactions, Volume 209 A Collection of Papers Presented at the International Conference on Sintering November 16-20, 2009 La Mia, California Edited by
Rajendra K. Bordia Eugene A. Olevsky
)WILEY A John Wiley & Sons, Inc., Publication
Copyright © 2010 by The American Ceramic Society. All rights reserved. Published by John Wiley & Sons, Inc., Hoboken, New Jersey. Published simultaneously in Canada. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107orl08ofthel976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 750-4470, or on the web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008, or online at http://www.wiley.com/go/permission. Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages. For general information on our other products and services or for technical support, please contact our Customer Care Department within the United States at (800) 762-2974, outside the United States at (317) 572-3993 or fax (317) 572-4002. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic format. For information about Wiley products, visit our web site at www.wiley.com. Library of Congress Cataloging-in-Publication Data is available. ISBN 978-0-470-40849-0 Printed in the United States of America. 10 9 8 7 6 5 4 3 2 1
Contents
Preface Acknowledgements
xi xiii
APPLICATION OF SINTERING IN EMERGING ENERGY APPLICATIONS: FUEL CELLS, SOLAR CELLS, HYDROGEN STORAGE Sintering Behavior of Ce0 9 Gd 0 -,0-, 95.8 in Reducing Atmosphere
3
Hydrogen Sorption Properties of Ti-Oxide/Chloride Catalyzed Na2LiAIH6
13
High Density Green Pellets of ZrN Fabricated by Particle Processing
21
A. Kaiser, J. W. Phair, S. Foghmoes, S. Ramousse, Z. He
Enrique Martinez-Franco, Thomas Klassen, Martin Dornheim, Ruediger Bormann, and David Jaramillo-Vigueras
Thomas T. Meek, K. Gwathney, Chaitanya K. Narula, and L.R. Walker
EVOLUTION AND CONTROL OF MICROSTRUCTURE DURING SINTERING PROCESSES The Effect of Carbon Source on the Microstructure and the Mechanical Properties of Reaction Bonded Boron Carbide
29
S. Hayun, H. Dilman, M. P. Dariel, N. Frage, and S. Dub
Modification of Mass Transport during Sintering Induced by Thermal Gradient Sébastien Saunier and Frangois Valdivieso
41
FUNDAMENTAL ASPECTS OF SINTERING Effects of Crystallization and Vitrification on Sintering Properties of Bentonite Clay
53
H. Camacho, CA. Martínez, P.E. García, H J . Ochoa, J.T. Elizalde, A. García, A. Aguilar, M. Bocanegra, and C. Domínguez
Dissolution of Alumina in Silicate Glasses and the Glass Formation Boundary
61
The Effect of Volume Fraction on Grain Growth during Liquid Phase Sintering of Tungsten Heavy Alloys
71
Keith J. DeCarlo, Thomas F. Lam, and William M. Carty
John L. Johnson, Louis G. Campbell, Seong Jin Park, and Randall M. German
IN-SITU MEASUREMENTS IN SINTERING In-Situ Investigation of the Cooperative Material Transport during the Early Stage of Sintering by Synchrotron X-Ray Computed Tomography
85
R. Grupp, M. Nöthe, B. Kieback, and J. Banhart
Geopolymers Sintering by Optical Dilatometry
91
Elie Kamseu, Cristina Leonelli, and Dan S. Perera
MODELING OF SINTERING AT MULTIPLE SCALES Meso-Scale Monte Carlo Sintering Simulation with Anisotropie Grain Growth
103
Numerical Simulation of Densification and Shape Distortion of Porous Bodies in a Granular-Transmitting Medium
113
Gordon Brown, Richard Levine, Veena Tikare, and Eugene Olevsky
Junkun Ma and Eugene A. Olevsky
The Effect of a Substrate on the Microstructure of Particulate Films
125
C.L. Martin and R. K. Bordia
Modelling Constrained Sintering and Cracking
135
Atomistic Scale Study on Effect of Crystalline Misalignment on Densification during Sintering Nano Scale Tungsten Powder
149
Variations in Sintering Stress and Viscosity with Mixing Ratio of Metal/Ceramic Powders
161
Ruoyu Huang and Jingzhe Pan
Amitava Moitra, Sungho Kim, Seong-Gon Kim, Seong Jin Park, Randall German, and Mark F. Horstemeyer
Kazunari Shinagawa
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NOVEL SINTERING PROCESSES: FIELD-ASSISTED SINTERING TECHNIQUES Finite Element Modelling of Microwave Sintering
173
Direct and Hybrid Microwave Sintering of Yttria-Doped Zirconia in a Single-Mode Cavity
181
The Influence of Minor Additives on Densification and Microstructure of Submicrometer Alumina Ceramics Prepared by SPS and HIP
193
D. Bouvard, S. Charmond, and C.P. Carry
S. Charmond, C. P. Carry, and D. Bouvard
Jaroslav Sedlácek, Monika Michálková, Deniz Karaman, Dusan Galusek, and Michael Hoffmann
The Electro-Discharge Compaction of Powder Tungsten Carbide-Cobalt-Diamond Composite Material
205
Microwave Sintering Explored by X-Ray Microtomography
211
Evgeny G. Grigoryev and Alexander V. Rosliakov
Kotaro Ishizakl, Manjusha Battabyal, Yoko Yamada Pittini, Radu Nicula, and Sebastien Vaucher
Pulse Plasma Sintering and Applications
219
Influence of Electric Fields during the Field Assisted Sintering Technique (FAST)
227
Sintering of Combustion Synthesized TiB 2 -Zr0 2 Composite Powders in Conventional and Microwave Furnaces
237
Andrzej Michalski and Marcin Rosinski
Michaela Müller and Rolf Ciasen
Hayk Khachatryan, Alok Vats, Zachary Doorenbos, Suren Kharatyan, and Jan A. Puszynski
Production and Characterization of WC-Co Cemented Carbides by Field Assisted Sintering
249
Rafet Emre Özüdogru, Filiz Cinar Sahin, and Onuralp Yucel
Microwave Rapid Debinding and Sintering of MIM/CIM Parts
259
P. Veronesi, C.Leonelli, G. Poli, L. Denti, and A. Gatto
SINTERING OF BIOMATERIALS Analysis of Sintering of Titanium Porous Material Processed by the Space Holder Method
273
L. Reig, V. Amigó, D. Busquéis, M.D. Salvador and J.A. Calero
Advances in Sintering Science and Technology
· vii
Effect of Sintering Temperature and Time on Microstructure and Properties of Zirconla Toughened Alumina (ZTA)
283
Sintering Zirconia for Dental CAD/CAM Technology
291
M. M. Hasan and F. Islam
Kuljira Sujirote, Sukunthakan Ngernbamrung, Kannigar Dateraksa, Tossapol Chunkiri, Marut Wongcumchang, and Kriskrai Sitthiseripratip
SINTERING OF MULTI-MATERIAL AND MULTI-LAYERED SYSTEMS Co-Sintering Behaviors of Oxide Based Bl-Materials
307
Coupling between Sintering and Liquid Migration to Process Tungsten-Copper Functionally Graded Materials
321
Laser Sintering of Nanosized Alumina Powder for Scratch Resistant Transparent Coatings
333
Optimization of Density, Microstructure and Interface Region in a Co-Sintered (Steel/Cemented Carbide) Bi-Layered Material
343
Claude Carry, Emre Yalamag, and Sedat Akkurt
J.-J. Raharijaona, J.-M. Missiaen, and R. Mitteau
Christoph Rivinius and Rolf Ciasen
A. Thomazlc, C. Pascal, J.M. Chaix
SINTERING OF NANOSTRUCTURED MATERIALS MoSi2 Formation Mechanisms during a Spark Plasma Synthesis from Mechanically Activated Powder Mixture
357
Spark Plasma Sintering of Nanocrystalline WC-12Co Cermets
367
Si3N4/SiC Materials Based on Preceramic Polymers and Ceramic Powder
379
Grain Growth during Sintering of Nanosized Particles
389
F. Bernard, G. Cabouro, S. Le Gallet, S. Chevalier, E. Gaffet, and Yu Grin
Victoria Bonache, Maria Dolores Salvador, Vicente Amigo, David Busquéis, and Alicia Castro
U. Degenhardt, G. Motz, W. Krenkel, F. Stegner, K. Berroth, W. Harrer, and R. Danzer
Z. Zak Fang, Hongtao Wang, Xu Wang, and Vineet Kumar
Atomic Investigation of Thermal Stability of Nanosized Ceria Particles on Metal Oxide Surfaces
401
Two-Step Sintering of Molybdenum Nanopowder
415
W. Jiang, M. Wong, A.R. Rammohan, Y. Jiang, and J.L. Williams
Min Suh Park, Tae Sun Jo, Se Hoon Kim, Dae-Gun Kim, and Young Do Kim
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Standard and Two-Stage Sintering of a Submicrometer Alumina Powder: The Influence on the Sintering Trajectory
421
SAXS Investigation of the Sintered Niobium Powder: Method of Stabilizing Porosity and Fractal Properties
429
M. Michálková, K. Ghillányová, and D. Galusek
Leonid Skatkov
Author Index
437
Advances in Sintering Science and Technology
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Preface
This issue of the Ceramic Transactions compiles a number of papers presented at the International Conference Sintering 2008, which was held in San Diego, USA on November 16-20, 2008. The meeting was chaired by Professors Rajendra Bordia and Eugene Olevsky and was organized under the auspices of The American Ceramic Society. This was the fifth meeting in a series that started in 1995 as a continuation of a famous cycle of conferences on Sintering and Related Phenomena organized by G. Kuczynski in the period from 1967 till 1983. The first three meetings in the newly re-established series of conferences have been held at Pennsylvania State University in 1995, 1999, 2003, and the fourth has been held in Grenoble, France in 2005. In parallel to the US-based cycle of conferences on sintering, from 1969 till 2002 another important series of conferences named Round Tables on Sintering have been held in Eastern Europe and have been attended by many sintering professionals from that geographical area as well as by scientists from Western Europe and Asia. In general, over the past 50 years, there has been a series of important conferences aimed at documenting the status of sintering theory and practice. Previous meetings were also organized by the Tokyo Institute of Technology, University of Notre Dame, and the University of British Columbia. Sintering 2008 became the -largest specialized sintering forum in history by bringing together more than 200 registered participants of various research communities, which fostered the high level of scientific interaction and created atmosphere of broader international collaboration. The meeting included participants from North and Central America, Europe (both Eastern and Western), Asia, Australia and Africa. The technical program at this meeting included 203 presentations from 30 countries, which addressed the latest advances achieved in the sintering processes for the fabrication of powder-based materials in terms of fundamental understanding, technological issues and industrial applications. The conference has demonstrated a significant progress that has been made in multi-scale modeling of densification and microstructure development, better understanding of the processing of complex systems (multi-layered, composites and reactive systems). In sintering technology, innovative approaches like Field Assisted Sintering (also known as Spark Plasma Sintering) gain more attention of the materials processing community. Another very XI
timely and well represented topic was sintering and microstructure development in nanostructured materials. Papers were also presented on the sintering of bio- and energy applications-related materials. To augment the traditional technical presentations, a Plenary Round Table Discussion on the "Challenges and Opportunities in Sintering Science and Technology" identified critical avenues for research and development as well as the most exciting developments in the science and technology of sintering. This volume contains 43 papers covering a rich diversity of the sintering science and technology topics. Another 19 papers were published in a special issue of the Journal of the American Ceramic Society (July 2009). Together, a third of the papers presented during the conference were published in these two publications, Thanks go to both the conference participants and organizers who had to meet numerous deadlines to enable the timely publication of this volume and of the special issue of the Journal. We hope you will enjoy the papers assembled here and we are looking forward to see you in 2011 in Jeju Island, Korea at the International Conference on Sintering 2011. Rajendra K. Bordia University of Washington Eugene A. Olevsky San Diego State University
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· Advances in Sintering Science and Technology
Acknowledgements
The Co-chairs of Sintering 2008 gratefully acknowledge the advice and help given to us in organizing this meeting by colleagues on the Organizing and International Advisory Committees listed below. We also appreciate the support from the conference sponsors listed below. Support from the staff at The American Ceramic Society is gratefully acknowledged. Finally, RKB acknowledges the opportunity to work at the Whiteley Center of the University of Washington during two critical periods of editing this proceedings. Organizing Committee Iver Anderson, AMES National Laboratory Gary Messing, Pennsylvania State University Randall German, Mississippi State University Khaled Morsi, San Diego State University Ian Nettleship, University of Pittsburgh Veena Tikare, Sandia National Laboratory International Advisory Committee Debby Blaine, Stellenboch University, South Africa Aldo Boccaccini, Imperial College - London, UK Didier Bouvard, INP Grenoble, France W. Roger Cannon, Rutgers University, USA Alan Cocks, Oxford University, UK Lutgard C. DeJonghe, University of California, Berkeley, USA Terry Garino, Sandia National Laboratory, USA Joanna Groza, University of California, Davis, USA Vikaram Jayaram, Bangalore India Institute of Science, India John Johnson, Alldyne, USA Suk-Joong L. Kang of KAIST, Korea Torsten Kraft, Fraunhoffer Institute, Germany Robert McMeeking, University of California, Santa Barbara, USA
XIII
Sung-Tag Oh, Seoul National University of Technology, Korea Jingzhe Pan, Leicester University, UK Irene Peterson, Corning Inc., USA MohamedN. Rahaman, Missouri University of Science and Technology, USA Jürgen Rodel, Universität of Darmstadt, Germany Lucio Salgado, IPEN/CNEN, Brazil Graham Schaffer, Queensland University, Australia Aziz Shaikh, Ferro Corporation, USA Valery Skorohod, National Academy of Sciences, Ukraine Mark Thompson, General Electric Co., USA Francois Valdivesco, Ecole des Mines de Saint-Etienne, France Fumihiro Wakai, Tokyo Institute of Technology, Japan Antonios Zavaliangos, Drexel University, USA Conference Sponsors Sandia National Laboratories Netzsch Thermal Technology LLC Metal Processing Systems, Inc. American Elements
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Application of Sintering in Emerging Energy Applications: Fuel Cells, Solar Cells, Hydrogen Storage
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SINTERING BEHAVIOR OF Ce 0 . 9 Gd 0 .,O 1 . 95 . s IN REDUCING ATMOSPHERE A. Kaiser, J. W. Phair, S. Foghmoes, S. Ramousse, Z. He Rise National Laboratory, Fuel Cells and Solid State Chemistry Department 4000 Roskilde, Denmark ABSTRACT At low oxygen partial pressures and high temperatures Gd-doped ceria can be reduced and the material becomes electronic conducting (e.g. 0.08 Scm"1 at 800°C at a ρθ2 of 10"16 arm for Ceo.9Gdo.i 01.95.5 CGO 10). These properties make CGO attractive for use in oxygen membranes above 600°C. The sintering temperature of CGO ceramics might be significantly reduced, if a sintering atmosphere with very low oxygen partial pressure is applied (for example a p02 of 10"15 arm or below). In the present work, the densification behaviour of CGO 10 was investigated in reducing atmosphere and in air. Samples were prepared by tape casting and lamination of the single layers into multi-layers and by die pressing. A dilatometer was used to measure the sample shrinkages from room temperature to 1773 K with different constant heating rates. Based on the sintering results of pressed samples the activation energy for densification was determined. The activation energy for densification of CGO 10 can be reduced significantly from 770±40 to 300±40 KJ/mol by switching atmosphere from air (pO2=0.21 arm) to highly reducing conditions (pU2 down to 10" arm), which indicated enhanced densification behaviour of CGO 10 in reducing atmosphere during early stage sintering. INTRODUCTION Ceria based solid solutions have been investigated intensively as promising electrolyte materials for intermediate temperature solid oxide fuel cells (IT-SOFC), as cathode barrier layers in SOFC1 and as membrane material for oxygen separation membranes2. The doping with gadolinium leads to one of the highest ionic conductivities in ceria among different other dopants at intermediate temperatures3 (500-600 °C). Cerium Gadolinium Oxide (CGO) has therefore been proposed as electrolyte material for stainless steel supported fuel cells4. The sintering of ceria to full density requires relatively high sintering temperatures, as high as 1300°C tol600°C, depending on raw powders and processing. For many processes, such as the manufacturing of solid oxide fuel cells or membranes, it would be beneficial, if the sintering temperature to achieve dense CGO ceramics could be reduced significantly. Several studies have been under-taken on the addition of dopants to lower the sintering temperature of CGO ceramics in air5'6,7,8·9'10. The sintering behaviour of CGO is expected to be quite different in reducing atmosphere due to the reduction of Ce4+ to Ce3+ and the related change in oxygen vacancy concentration, which is expected to have a significant influence on the sintering kinetics. The influence of sintering atmosphere has so far only rarely been investigated. J.-G. Li et al." have reported an increase in density and grain growth of nano crystalline yttria doped ceria ceramics, if the atmosphere was switched to more reducing atmosphere, e.g. from oxygen to air. Grain growth and enhanced densification in CGO compared to un-doped ceria was explained by reduction of some Ce4+ to Ce3+ and a correlated formation of oxygen vacancies, which should cause rapid grain boundary migration due to changed grain boundary energies12,13. It is well known, that the CGO lattice shows a volume expansion upon reduction and volume reduction during re-oxidation13'14. This paper investigates the densification kinetics of Ceo.9Gdo.1O1.95-6 at relatively low oxygen partial pressures (ρθ2 = <10"16 arm) and compares the results to sintering in air for pressed and tape casted structures. Using a dilatometer, we sintered the CGO10 with 4 different constant heating rates and we
3
Sintering Behavior of Ce0 9 Gd 0 -,Ο-, 95_δ in Reducing Atmosphere
investigated the microstructure of the CGOIO samples by scanning electron microscopy (SEM) after complete re-oxidation. EXPERIMENTAL A commercial nano-sized Ceo.9Gdo.1O1.95 powder from Rhodia was used as raw material (CGOIO, primary particle size less than 50 nm, α5ο=0.45μιη after dispersion in ethanol and BET measured specific surface area 35 m2/g). For preparing the pressed compacts, polyvinyl butyral (PVB) binder and ethanol were added and mixed with the powders in a mortar. Hard agglomerates were removed by sieving. CGOIO pellets were made using a hydraulic pressing machine at a uniaxial pressure of 200 MPa. The samples had a diameter of 5.5 mm and a length of 5.3 to 5.6 mm after pressing. The samples were pre-sintered at 1173 K to remove the binder and give the samples sufficient strength for measurement in the dilatometer. To compare the smtering behaviour of pressed samples with laminated samples, CGO multi-layered tapes were laminated from CGOIO single-layered tapes. The CGOIO powders were first ball milled in an ethanol based slurry with polyvinyl pyrolidine (PVP) as dispersant and polyvinyl butyral as binder. Thereafter the slurry was tape cast into a 100 μιη thick film. The film was finally laminated several times to a thickness of 2.5 mm and was then stamped out into rounds with a diameter of about 4 mm. Uniaxial pushrod dilatometry was conducted at heating rates of 1, 3, 5 and 10 K/min in air and in reducing atmosphere (mixture of 9 vol.% of hydrogen and 91 vol.% of dry nitrogen) up to a maximum temperature of 1773 K using a Netzsch differential dilatometer CD402. The ρθ2 for the measurements in reducing atmosphere was recorded by a downstream p02-monitor on the dilatometer. The recorded voltages for all measurements were about 1.075 ± 0.025 V at sintering temperatures from 1173 K to 1773 K. These voltages correlate to ρθ2 values as low as 10"12 to 10"2 arm. The microstructure of the sintered samples was observed using a Hitachi TM 1000 SEM.
RESULTS AND DISCUSSION The shrinkages of laminated CGO10 samples are plotted in Figure 1 against sintering temperature. For the tape cast and laminated samples a decrease in sintering temperature and a fast densification of CGO10 under reducing atmosphere was observed compared to sintering in air. In the case of laminated CGO10 samples a significant deformation of sample shape was observed during binder removal in the temperatures range 293 K to 873 K. Even if the laminates were pre-sintered before starting the dilatometry, these samples deformed considerably and signs of delamination were observed after sintering. For this reason exact calculations of the sintering kinetics were not performed on laminated samples, but further investigation on the sintering kinetics of CGOIO in air and in H2-N2 atmosphere were performed on pressed samples only.
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Sintering Behavior of Οβ09ΘοΌ-ιθ-, 95.s in Reducing Atmosphere
-5 CD CJ)
CO ¿¿
c
'l_
J= ¡Λ L_
CO
c
-10 -15 -20 -25 -30 -35
600
800
1000
1200
1400
1600
1800
2000
Temperature [K] Figure 1: Shrinkages of tape cast and laminated CGO10 samples in air (blue line) and in H2-N2 (pink line). The heating rate was 3 K/min in this experiment. Figure 2 shows the variations of shrinkage with temperature of the pressed CGO10 compacts sintered in air and in reducmg atmosphere with the constant heating rates of 1 and 10 K/min, respectively. The onset temperature for densification of CGO10 in reducmg atmosphere is 150 K lower than the onset temperature for sintering in air. This indicates that densification of CGO10 in reducing atmosphere was significantly enhanced at low temperature. It is also noted that, for a fixed sintering atmosphere, either air or H2-N2, the compact with slower heating rate (1 K/min) achieved the same shrinkage at lower sintering temperature compared to that with higher heating rate (10 K/min). Similar effect of heating rate on densification was reported by Ewsuk et al15 when they investigated the sintering behaviour of ZnO. This fact was explained as the increased diffusion time for densification at a certain temperature resulted from the lower heating rate16. The variations of shrinkage rate with temperature of the pressed CGO10 compacts sintered in air and in reducing atmosphere with the constant heating rates of 1 and 10 K/min, respectively, are presented in Figure 3. Compared to that of sintered in air, the shrinkage rate maximum (absolute value considered in this work) of the compact sintered in reducing atmosphere is larger and also occurred at lower sintering temperature, which corresponds to a high densification rate in early stage sintering for reducing sintered CGO10. On the other hand, the shrinkage rate maximum with the heating rate of 10 K/min is larger than that of with 1 K/min for the compacts sintered both in air and in H2-N2. This is mainly attributed to the temperature effect17, as it could be seen that the temperature for reaching maximal shrinkage rate of the compact with higher heating rate is higher than that of with lower heating rate.
Advances in Sintering Science and Technology
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Sintering Behavior of Ce0 9 Gd 0 -¡0-¡ 95_s in Reducing Atmosphere
With respect to Figures 2 and 3, it is noted that the early-staged densification of CGOIO in H2-N2 was significantly enhanced compared to that sintered in air. To understand the densification difference caused by different sintering atmospheres more clearly, the activation energies for densification of the compacts sintered in both air and H2-N2 are evaluated from the densification law and the experimental results. Δ/ From the densification law , the shrinkage rate d\ — \/dt is correlated to the activation energy Q for densification as (1)
dt
RT
exp
RT
'<·«
where A is a material constant independent of temperature T, R is the gas constant, and fi — , L) is a '0
function of shrinkage — and grain size L. Rearranging and taking the logarithm of both sides of Equation 1, gives
'0
(2) In
*τ dt
iHiW'f· 1 »
For pressure less sintering, the grain size is only the function of shrinkage, that is, independent of the sintering conditions, for example, the heating rate18. Therefore, the activation energy could be Δ/ evaluated from the slope of the plot of In
dt
versus 1/T at a given shrinkage. In the present
work, the data of shrinkage rate and temperature at three different shrinkages (-0.025, -0.050, -0.075) obtained from four different constant heat rates (1, 3, 5,10 K/min) were used, and the corresponding plot is shown in Figure 4. The activation energy for densification of CGO10 in early stage air sintering is 770± 40 KJ/mol, which is close to that of Ceo.8Gdo.2O19 reported by Jud et al16. The activation energy for densification of CGO10 in early stage reducing sintering is 300±40 KJ/mol, which is much lower.
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· Advances in Sintering Science and Technology
Sintering Behavior of-CeogGdo,ΟΊ
-95-δ in Reducing Atmosphere
0,02 0,00 -0,02 -0,04 §
-0,06 -0,08 -0,10 -0,12 -0,14
800
1000
1200
T(K)
1400
1600
1800
Figure 2: Variation of shrinkage with temperature of pressed CGO10 compacts sintered in air and in a mixture of 9%H2-91%N2 at different heating rates of 1 and 10 K/min.
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Sintering Behavior of Ce 09 Gd 0 ,Ο^ 95_δ in Reducing Atmosphere
0,001
0 -0,001 ¿ -0,002
I ^
-0,003
"5"
-0,004
-0,005 -0,006 800
1000
1200
T(K)
1400
1600
1800
Figure 3: Variation of shrinkage rate with temperature of pressed CGO10 compacts sintered in air and in a mixture of 9%H2-91%N2 at different heating rates of 1 and 10 K/min.
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■ Advances in Sintering Science and Technology
Sintering Behavior of Ce 09 Gd 0 -,Ο-, 95_δ in Reducing Atmosphere
c
Έ 2 3
T3
■E 0
-1 0,6
0,7
0,8
0,9
1
1000/T(K" )
Figure 4: Variation of In
dt
with reciprocal temperature of pressed CGO10 compacts
sintered in air and in a mixture of 9%H2-91%N2 at different heating rates of 1, 3, 5 and 10 K/min (best fitting straight lines are shown). The present dilatometry experiment shows quite different densification behaviour of CGO10 sintered in air and in reducing atmosphere, especially, the fast densification of CGO10 in H2-N2 in early stage sintering. In addition, the appearance and the microstructure of the investigated reducing sintered compacts also showed some difference. Figure 5 shows a pressed CGO10 compact before and after sintering in the dilatometer in reducing atmosphere. The CGO10 is black after sintering at reducing atmosphere due to the occurrence of the reduction of ceria from Ce4+ to Ce3+. After the CGO10 ceramic was removed from the dilatometer and had contact with air, the sample changed back to white/yellow colour after a couple of minutes. During colour change the sample heated up and gained weight due to re-oxidation (take up of oxygen).
Advances in Sintering Science and Technology
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Sintering Behavior of Ce0 9 Gd 0 -,Ο-, 95_δ in Reducing Atmosphere
Figure 5: Pressed samples of CGOIO before (right side, white colour) and directly after sintering in reducing atmosphere (black colour) The effect of sintering atmosphere on the microstructure of the CGOIO ceramics after sintering at 1773 K is shown in Figure 6. The sample sintered in air resulted in relative small grains, with grain size of about 2 μιη (figure 6, left side), whereas the one sintered under strongly reducing atmosphere led to excessive grain growth with grain sizes of 10 um and above. Furthermore the CGOIO ceramic fabricated under reducing atmosphere shows cracks along the CGOIO grain boundaries (figure 6, right side). This phenomenon needs further investigations, but is most likely caused by stresses in the ceramic that occur during re-oxidation and the accompanied volume reduction of the CGOIO lattice.
Figure 6: Excessive grain growth of CGOIO during sintering under reducing atmosphere. SEM pictures of CGOIO ceramic after sintering to 1773 K in air (on the left side) and in 9%hydrogn-91%nitrogen atmosphere (on the right side). CONCLUSIONS Fast densification for CGOIO during early stage sintering in reducing atmosphere is shown. The activation energy for densification can be reduced significantly from 770±40 to 300±40 KJ/mol by switching atmosphere from air (pO2=0.21 atm) to highly reducing conditions (p02 down to 10"20 arm).
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Sintering Behavior of Ce 09 Gd 0/l 0 1 95_6 in Reducing Atmosphere
It is of fiirther interest to find out more details about the mechanism of sintering of CGO10 under reducing atmosphere. Principally it sounds reasonable, that the reduction of ceria and creation of oxygen vacancies accelerates the sintering. In a future paper, further investigations on the grain growth and vacancy formation of CGO10 during sintering under different atmospheres will be reported. For practical application in multilayer structures the influence of the volume change of CGO10 on the microstructure during sintering in reducing atmosphere and during subsequent exposure to air needs further attention. LITERATURE Ά . Mai, V.A.C. Haanappel, F. Tietz, D. Stöver, Solid State Ionics 177, 2103-2107 (2006). 2 J.M. Serra, O. Büchler, V.B. Vert, W.A. Meulenberg, H.P. Buchkremer, Chem. Mater. 20,3867-3875 (2008). 3 S. M. Haile, Acta Materialia 51,5981 (2003). *N. P. Brandon, D. Corcoran, D. Cummins, A. Duckett, K. El-Khoury, D. Haigh, R. Leah, G. Lewis, N. Maynard, T. McColm, R. Trexona, A. Selcuk, M. Schmidt, Journal of Materials Engineering and Performance 13 (3), 253 (2004). 5 C. Kleinogel and L.J. Gauckler, Solid State Ionics, 135, 567 (2000). 6 C. Kleinogel and L.J. Gauckler, in Solid Oxide Fuel Cells VI, S. C. Singhal and M. Dokiya, Editors, PV 99-19, p. 225, The Electrochemical Society Proceedings Series, Pennington, NJ (1999). 7 T. S. Zhang, L. B. Kong, Z. Q. Zeng, H. T. Huang, P. Hing, Z. T. Xia, and J. A. Kilner, J. Solid State Chemistry, 7, 348 (2003). 8 T. S. Zhang, P. Hing, H. T. Huang, J.A. Kilner, J. Mater. Sei, 37, 997 9 J. D. Nicholas and L.C. De Jonghe, Solid State Ionics 178, 1187-1194 (2007). ,0 T.S. Zhang, J. Ma, Y.J. Leng, Z.M. He, Journal of crystal growth 274,603-611 (2005). "j.-G. Li, Y. Wang. T. Ikegami, T. Ishigaki, Solid State Ionics 179, 951-954 (2008). 12 H. Inaba, T. Nakajima, H. Tagawa, Solid State Ionics 106,263-268 (1998). 13 J.-G. Li, T. Ikegami, T. Mori, J. Solid State Chemistry 168, 52 (2002). 14 Y. Zhou, M.N. Rahaman, Acta Mater. 45, 3635 (1997). 15 K.G. Ewsuk, D.T. Ellerby, C.B. DiAntonio, J. Am. Ceram. Soc. 89, 2003-2009 (2006). 16 E. Jud, C.B. Huwiler, L.J. Gauckler, J. Am. Ceram. Soc. 88, 3013-3019 (2005). I7 Z. He, J. Ma, Philosophical Magazine 83, 1889-1916 (2003). 18 Z. He, J. Ma, C. Wang, Biomaterials, 26, 1613-1621 (2005).
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HYDROGEN SORPTION PROPERTIES OF Ti- OXIDE/CHLORIDE CATALYZED Na,LiA!H6 Enrique Martinez-Franco CIITEC-IPN Mexico City, Mexico Materials Institute, GKSS-Research Center Geesthacht, Germany Thomas Klassen and Martin Dornheim Materials Institute, GKSS-Research Center Geesthacht, Germany Ruediger Bormann Materials Science and Technology, Technical University Hamburg-Harburg Hamburg-Harburg, Germany Materials Institute, GKSS-Research Center Geesthacht, Germany David JaramiHo-Vigueras CIITEC-IPN Mexico City, Mexico
ABSTRACT Mechano-synthesis through mechanical alloying (MA) has been employed to obtain a nanocrystalline complex sodium lithium alanate, namely, Na2LiAlH6 from starting materials NaH and LiAlH4. Different Ti-based additives were milled together with starting materials in order to achieve improved hydrogen absorption kinetics. Hydrogen titration experiments showed that the material processed with 5 mol% TiCl, has the fastest ab- and desorption kinetics, but at the sacrifice of hydrogen capacity. This could be correlated to the formation of NaCl during milling and after absorption. Differentia! scanning calorimetry (DSC) results demonstrate that the endothermic peak of TiCl, doped material shifted 53 °C to lower temperatures. INTRODUCTION Light metal-hydrides exhibit a great potential in safe and reliable hydrogen storage and have the highest storage capacity by volume. Alkali alanates have a high hydrogen capacity e.g. NaAlH4 and LiAlH4 have a hydrogen capacity of 7.4 and 10.5 wt.%, respectively. Decomposition of these materials is obtained in several steps and are not reversible at moderate conditions of hydrogen pressure, for NaAlH4: 3NaAlH4 ->· Na,AlH„ + 2A1 + 3H, T
(1)
Na,AlH„ ->■ 3NaH + Al + 3/2 H, t
(2)
NaH -> Na + 1/2H, t (3) Nevertheless, irreversibility of these materials is the drawbacks to use them as hydrogen storage materials. Although there are more than one dissociation step of alkali alanates and irreversibility, these new class of materials are considered because of their low absorption temperature as well as high hydrogen content. One of the pioneers of the synthesis of different alanates using chemical methods
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Hydrogen Sorption Properties of Ti-Oxide/Chloride Catalyzed Na2LiAIH6
was Bogdanovic and co-workers''. However, chemical methods requires high hydrogen pressures and relative high temperatures, for example Na2LiAlH6 has been prepared from NaH+LiAlH4 in toluene under 300 bar H, at 433 K or by the reaction of NaAlH4+LiH+NaH in heptane under hydrogen pressure. Furthermore, producing sodium lithium alanate (Na2LiAlHt) results in a change of equilibrium pressure to lower value". An alternative technique such as mechanical alloying (MA) has been employed to produce nanocrystalline alanates by Zaluska and Huot". On the other hand, Ti0 2 has been successfully used5" as catalyst in Mg-based hydrogen storage materials. For sodium alanate (NaAlHJ, TiCl, was found to be one of the most effective catalysts up to now1'''8. Due to the high reactivity of Na with Cl, the general solid state reaction proposed by Sandrock8 after milling is: (1 -x)NaAlH4 + xTiCl, -> (I -4x)NaAlH4 + 3xNaCl + xTi + 3xAl + 6xH,
(4)
where x is the mole fraction of TiCl, added to the initial material. Sandrock suggested that TiCl, act just as precursor and the real catalyst could be, according to the reaction, the zero-valent Ti. In addition, the real catalyst could also be TiHx, Ti-alloy or some intermetallic compounds formed during milling. Sun et al.' used titanium n-butoxide (Ti(OBu")4) and zircon n-propoxide (Zr(Opr")4) as catalysts on NaAlH4 and supposed that Ti and Zr doping results in lattice substitution of Na-cations. In this paper, we describe the preparation of nanocrystalline Na,LiAlH6 by simple method of ball milling with TiO, and TiCl, addition in order to find out the catalytic effect of the additions on the hydrogen sorption kinetics in Na2LiAlH6.
EXPERIMENTAL The powders used were NaH (95% purity, Aldrich Germany), LiAlH4 (98% purity, Alfa Aesar Germany), TiO ; (99.5% purity, Alfa Aesar Germany) and TiCl, (99.999% purity, Aldrich Germany). The milling was carried out in a Fritsch P5 planetary ball mill using an initial ball-to-powder mass ratio of 10:1. All handling of the powders, including milling and weighting, was performed inside a glove box under continuously purified argon atmosphere (oxygen and moisture content <20ppm). A small amount of powders were removed at regular time intervals to monitor the structural changes during the milling. X-ray diffraction (XRD) experiments were conducted in a Bruker Axs-D8 Advance using Cu Ka radiation. Alkali metals are very sensitive to exposure to air (and much more after milling) and any contact results in their hydration. To avoid exposure to air during XRD measurements, the powders were covered with a thin plastic foil, which had a negligible or easily deductible contribution to the diffraction pattern. For the sorption measurements, sample holders were sealed inside the glove box and attached to a hydrogen titration apparatus'". Kinetic measurements were performed in a temperature range 180 to 230 °C. DSC experiments were carried out in a Netzsch 404 apparatus with a heating rate of 5 K/min. this apparatus is located into a glove box under continuously argon flow.
RESULTS AND DISCUSSION Milling process Figure 1 shows the X-ray diffraction patterns of powders milled at 100 h without and with catalysts. Formation of NajLiAlH^ after milling without catalyst was successfully obtained". By adding TiO„ traces of LiAlH4 and NaH still remain. However, by adding TiCl,, the reaction is more complex because some Na,LiAlH6 was decomposed to LiH and Al and additionally NaCl phase is formed. Similar reaction was observed in using TiCl, in NaAlH, during mechanical alloying'8. Although the results are not included in this paper, NaCl is already formed after 2 hours milling, which confirms the
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Hydrogen Sorption Properties of Ti-Oxide/Chloride Catalyzed ^ L i A I H ,
strong effect on Na,LiAlHri. Because of the low content of catalysts, any Ti and Ti-based alloys were not detected in the XRD-patterns.
Figure 1. XRD-patterns of INaH+LiAlH^ + Ti-based catalysts after 100h milling. Sorption measurements In our previously work" we obtained the equilibrium pressures of Na,LiAlH6 at different temperatures. At 230 °C the absorption and desorption plateaus are 21 and 10 bar, respectively. In order to compare the sorption kinetics using different catalysts we carried out experiments at 230 °C/43 bar. Figure 2 shows absorption kinetic curves at 230 °C and 43 bar of hydrogen pressure for Na,LiAlH„ without and with the both catalysts. By adding Ti0 2 catalytic effect is not evident and 2.2 wt.% hydrogen was absorbed after 60 minutes. Faster kinetics is observed by using TiCl, and 1.5 wt.% is absorbed in 10 minutes; however, hydrogen capacity is lowered, i.e. 1.7 wt.% is absorbed in 60 minutes. The reduction of the capacity can be explained due the formation of NaCl after milling. Absorption rates using the 20 and 80 % of the maximum capacity absorbed at 230°C/43 bar are shown in Table 1. The most effective catalyst is TiCl,, and according to our results reaction to form NaCl phase during milling arises the assessment of Sun' that Ti* should to occupy the places that Na* leaves, when react with Cl. We conclude this a possible mechanism, because in the case of adding TiO, we do not observe the formation of NaCl and furthermore the absorption kinetics of Na,LiAlHe are not improved after TiO, addition.
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Hydrogen Sorption Properties of Ti-Oxide/Chloride Catalyzed Na2LiAIH|
Figure 2. Absorption kinetics of Na,LiAlH6 without and with Ti-based catalysts at 230 °C/43 bar. Some efforts have been made to elucidate the influence of Ti-based alloys on sorption kinetic in NaAlH4. Sun et al.' concluded that Ti and Zr doping in NaAlH4 results in lattice substitution of Nacations by either Ti or Zr. Taking this point of view, and two different Ti-based catalyst as TiO, and TiCl,, faster absorption kinetic obtained by using TiCl, is in very good agreement with our results. Other suggestions about possible mechanisms include Ti-Al phases could to have also a positive effect on the sorption process12, which is attributed to the formation of TixAl phases after milling and is believed these compounds act as catalysts. In our previously results" the following reactions were obtained without using catalyst: 2NaH + LiAlH, -> Na,LiAlH, Na2LiAlH„ -» 2NaH + LiH + Al + 3/2 H,
(after milling)
(5)
(after desorption)
(6)
by adding Ti-based catalyst, Ti and Al have the possibility to form an intermetallic phase. However, due to the low content of catalyst used, we could not detect after milling any peaks for an Al-Ti alloy phase by XRD powder diffraction. Table 1 Reaction rates calculated between 20 and 80 % of maximum capacity Material Desorption Absorption Wt.%/s Wt.%/s Without catalyst 0.0017 0.0013 +5mol% TiO, 0.0021 0.0032 +5mol% TiCl, 0.0061 0.0081 Figure 3 shows desorption kinetics of Na,LiAlH6 without and with Ti-catalysts. Faster kinetics were observed for materials in which Ti catalysts were used, compared to the material without those additives. The time for full desorption was 7, 18 and 50 minutes for samples with TiCl,, TiO, and without catalyst addition, respectively. Desorption rates calculated, in a range of linear region of the curves (between 20 and 80 wt.% of maximum capacity), are shown in Table 1.
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Hydrogen Sorption Properties of Ti-Oxide/Chloride Catalyzed Na2LiAIH6
Figure 3. Desorption kinetics of Na,LiAIH6 without and with Ti-based catalysts at 230 °C under vacuum (10"' bar) conditions. In order to analyze the phase transformations after absorption, one sample of powder without and with Ti-catalyst was charged with hydrogen at 230 °C/43 bar for 60 minutes, then the valve of sample holder was closed and cooled to room temperature. The sample holder was opened in the glove box and powders were prepared for XRD measurement. Figure 4 shows the corresponding XRD-results. The indexed patterns show that NaH and Al phases remain after absorption. For the sample with TiCl, catalyst, the presence of NaCl was detected. These results show that reaction (3) is not thoroughly reversible under these operation conditions even by catalysts additions. In the material without catalyst the proposed reversible reaction according to XRD results (Figure 4) after absorption is: 3NaH + LiH + 2A1 + 3/2 H, o · Na,LiAlHs + NaH + Al
(7)
Calculation of hydrogen content of the reaction (4) is 2.75 wt. %. From the absorption curves showed in the Figure 2, hydrogen content absorbed by the material without and with TiO, catalyst was 2.4 wt.%, which is close to the calculated. By using TiCl, the hydrogen capacity is 1.8 wt.%.
2 0, degrees
Figure 4. XRD-patterns of Na,LiAlH6 after absorption at 230 °C/43 bar.
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Hydrogen Sorption Properties of Ti-Oxide/Chloride Catalyzed Na2LiAIH,
Figure 5 shows the absorption properties of Na,LiAlH6 catalyzed with TiCl, at 60 bar and different temperatures. Absorption kinetics is faster with increasing temperature. Differences in kinetics at 230 and 200 °C are small and hydrogen content of 1.8 and 1.6 wt.% is obtained after 60 minutes, respectively.
Time [min]
Figure 5. Absorption kinetics ot Na,LiAIH6 catalyzed with 5 mol% 1 rCl, under 60 bar at different temperatures. Figure 6 shows desorption curves of Na,LiAlHs catalyzed with TiCl, at different temperatures. The fastest kinetics are obtained at 230 °C and complete desorption takes about 6 minutes. The slowest kinetics measured is at 180 °C and takes about 60 minutes.
Time [mini
Figure 6. Desorption kinetics of Na,LiAIHe catalyzed with 5mol% TiCl, under vacuum (10"' bar) conditions at different temperatures. DSC-measurements Figure 7 shows DSC measurements of as milled powders after milling lOOhrs. A decomposition peak of un-catalyzed Na,LiAlH,, at a temperature range of 222 - 292 °C is in a good agreement with the results of other research groups"4. The influence of catalyst is remarkable by using TiCl,: overlapping peaks in the temperature range of 140 - 282 °C are observed. The single DSC peak for Na,LiAlH6 did not shift significantly after addition of TiO„ but shifted by 53 °C to lower temperatures after addition of TiCl,. Unknown peak is observed at 267.5 9C in the sample with addition of TiCl3. Enthalpies recorded are 54.7, 49.7 and 32 kJ/mol for materials without catalyst, with TiO, and TiCl,, respectively. A decrease of enthalpy and temperature confirm the instability of the system and eases the
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Hydrogen Sorption Properties of Ti-Oxide/Chloride Catalyzed is^LiAIH,
decomposition and are in a good agreement with the desorption results obtained (Figure 3). Onset temperatures calculated by the program are 235, 234 and 172 °C for materials without catalyst, TiO, and TiCl,, respectively. These results confirm that TiCl, has strong influence on the decomposition, which enhances the sorption kinetics.
Figure 7. DSC measurements of as-milled at 100h of Na,LiAlHt without and with Ti-based catalysts.
CONCLUSIONS AND OUTLOOK Ti-based catalysed NaXiAlH,, was successfully synthesised by high-energy milling. Catalytic effect of TiCl, shows better absorption-desorption kinetics than TiOz, however hydrogen capacity is lowered due to NaCl formed during milling. DSC measurements confirm the strong influence on the thermal stability of Na,LiAlH„ in the presence of TiCl, catalyst by shifting the peak temperature for decomposition to about 50 °C lower value. Possible mechanisms for the catalytic effect of TiCl, were discussed by other research groups12'1 but still unclear. According to our results, elemental Ti (from TiO,) seems not have great influence on the sorption kinetics. In the case of TiCl, catalyst addition, the Na* is replaced in the Na,LiAlH6 structure by Ti/, which makes the incorporation of hydrogen into the structure easier, thereby improving the absorption and desorption kinetics. In order to overcome the capacity loss due the product of catalyst decomposition, NaCl, more efforts should to be made in the milling process and doping method. As results shown, high reactivity of Na* with Cl' is expected that different Ti-halides (F, Br, I) precursors could act as good catalyst for sodium alanate compounds. Therefore, different Ti-halides catalyst precursor such as TiCl4. TiF„ TiF4 and TiBr4 are going to be tested and will be reported ¡n a forthcoming paper. ACKNOWLEDGMENTS Authors acknowledge financial support for projects SIP-IPN 20080169 and IPN-SIP-ICYTDF 059. E. Martinez-Franco is gratefully for receiving a fellowship for Ph.D. research work by CONACyTMexico, DAAD-Germany and GKSS-Forschungszentrum.
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Hydrogen Sorption Properties of Ti-Oxide/Chloride Catalyzed Na2LiAIH,
REFERENCES 'Borislav Bogdanovic, Richard A. Brandt, Ankica Marjanovic, Manfred Schwickardi and Joachim Tolle: Journal of Alloy and Compounds 302 (2000) 36-58. 2 Borislav Bogdanovic and Manfred Schwickardi: Journal of Alloy and Compounds 253-254 (1997) 1-9. 'Zaluski, L. Zaluska, J.O. Ström-Olsen: Journal of Alloy and Compounds 290 (1999) 71-78. 4 J. Hout, S. Boily, V. Güther, R. Schulz: Journal of Alloy and Compounds 283 (1999) 304-306. 'Mat. Res. Bull. Vol. 22 pp. 405-412, 1987. "W. Oelerich, Ph. D. Thesis, Technische Univertität Hamburg-Harburg, 2000. 'K.J. Gross, G.J. Thomas, CM. Jensen: Journal of Alloy and Compounds 330-332 (2002) 683-690. S G. Sandrock, K. Gross, G. Thomas: Journal of Alloy and Compounds 339 (2002) 299-308. "D Sun, T. Kiyobayashi, H.T. Takeshita, N. Kuriyama, CM. Jensen: Journal of Alloy and Compounds 337 (2002) L8-L11. "'Bogdanovic, German patent 19526434, (1995). "E. Martinez-Franco: Ph. D. Thesis, ESIQIE-IPN, Mexico City, 2006. I! K.J. Gross, E.H. Majzoub, S.W. Spangler: Journal of Alloy and Compounds 356-357 (2003) 423-428. "P.S. Rudman: Journal of Less-Common Metals, 89 (1983) 93-110. "P. Claudy, B. Bonnetot, J.-P. Bastide, J.-M. Letoffe: Mater. Res. Bull. 17 (1982) 1499.
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HIGH DENSITY GREEN PELLETS OF ZRN FABRICATED BY PARTICLE PROCESSING Thomas T. Meek1, K. Gwathney2, Chaitanya K. Narula3, L.R. Walker4 ''2The University of Tennessee; 434 Dougherty Engineering Bid.; Knoxville, TN 37996-2200 34
' 0ak Ridge National Laboratory; MST Division, Oak Ridge, TN 37831-6115 3
Adjunct Professor, MSE Department, The University of Tennessee 434 Dougherty Engineering Bldg.; Knoxville, TN 37996-2200 ABSTRACT Fabrication of nitride nuclear fuels has generally been not successful due to instability of nitrides loss of americium nitride during the high temperature sintering process, (private communication with K. McClellan of Los Alamos National Laboratory) under hot pressing or conventional 1 arm sintering conditions to make net shapes. A low temperature-processing route that enables near net shapes in almost theoretical density is highly desirable. In order to carry out low-temperature pressing, it is necessary to synthesize nitride materials with controlled particle size. A compact made of the right mix of particles can be pressed at room-temperature to near theoretical density. In order to achieve controlled nitride powder synthesis, we are developing ceramic precursor processing that has been shown to offer unique advantages over conventional synthesis of advanced materials. In general, the precursors for metal nitrides already contain M-N bonds that are terminated into organic groups. A majority of these precursors are soluble in organic solvents enabling synthesis of powders. A major benefit of ceramic precursor processing is that the nano-particles of metal nitrides can be easily synthesized. These nano-particles can then be converted to particles of various sizes under carefully controlled thermal conditions. These powders have been blended to form bimodal distribution. Trimodal and continuous distributions are also under study. We should then be able to use these blends to isostatically press or uniaxial press samples to the desired fractional density (85%) at room temperature INTRODUCTION Metal-actinide nitride nuclear fuel is attractive because it can be used at higher operating temperatures than oxide fuels. The composite nitride fuel also has a higher thermal conductivity than does the oxide fuel. A serious drawback for the nitride fuel; however, is the loss of americium nitride during the conventional high temperature sintering cycle due to its high vapor pressure. Various conventional sintering approaches have been employed to sinter composite nitride fuel pellets. However, no conventional approach has solved the loss of americium problem. This paper investigates routes for the fabrication of high-density (>85% of theoretical) pellets of surrogate materials (eg. ZrN for UN and DyN for AmN) by using commercially available ZrN powders and by using the chemical precursor approach to synthesize the starting powders and then using either bimodal, trimodal or continuous powder distributions to process the powder into pellets using either cold isostatic pressing or uniaxial pressing at room temperature.
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High Density Green Pellets of ZrN Fabricated by Particle Processing
There are several traditional methods for the synthesis of zirconium nitride. Generally, a source of zirconium and a source of nitrogen are heated together at very high temperatures to obtain crystalline zirconium nitride. For example, heating of zirconium oxide and carbon in the presence of nitrogen, zirconium chloride and ammonia, zirconium chloride and sodium in the presence of nitrogen are some of the traditional methods [1-4]. Ceramic precursor technology has not been extensively developed for zirconium and dysprosium nitride materials [5]. The first ceramic precursor was reported by Brown and Maya in 1988 [6] from the reaction of [ ( C F ^ N ^ Z r with ammonia to obtain white powders. These powders, upon pyrolysis at 800°C, furnished carbon-contaminated zirconium nitride. The carbon content could be reduced by further pyrolysis in a hydrogen atmosphere. We have previously shown that ceramic precursors for zirconium nitride can be synthesized by simple reaction of hexamethyldisilazane, [(Me3Si)2NH], with zirconium tetrachloride [7]. The resulting compound is a free-flowing solid powder and can be recrystallized from dichloromethane. During pyrolysis of this compound trimethylsily chloride and hydrogen chloride are eliminated and elimination is complete by 600°C.
Figure 1: Size distribution of ZrN particles/agglomerates that formed during treatment at 1130'C for 45 minutes in vacuum.
Particles of ZrN in the 30nm - 15μηι range (Figure 1) form when sintered at 1075°c in vacuum The lattice parameter, a, for ZrN calculated from (111) and (200) is 4.567±0.0008 Á which is close to that for stoichiometric zirconium nitride (0.457756 nm from JCPDS 35-0753). This is a general approach and can be extended to synthesis of other nitrides. EDS spectra of the particles does not show Si or Cl impurities and particles are stable to oxidation under ambient conditions. There are no known ceramic precursors for Dysprosium Nitride, DyN. It is prepared from traditional methods by heating a source of Dy and a source of nitrogen at very high temperatures.
DISCUSSION During the fabrication of nitride composite nuclear fuel pellets when the green pellet is sintered conventionally at 1600°C for many hours there is observed a significant loss of americium due to its high vapor pressure. This is unacceptable and may be addressed by the fabrication of pellets using bimodal, trimodal or continuous powder distributions which when cold pressed yield densities of greater than 85%. For simulant pellets made using bimodal mixing, monosized particles of ZrN and DyN will be synthesized using the precursor technique described above. Particles of ZrN will be produced in the size ratios of 1:5 or greater (eg. 100 Á in diameter and 800 Á in diameter). DyN particles will also be synthesized in similar sizes. Figure 2 shows the effect of particle size ratio on the maximum fractional density for bimodal mixtures [8]. Note that when the size ratio is 1:1, the
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High Density Green Pellets of ZrN Fabricated by Particle Processing
fractional density is 63% while a ratio of 1:8 yields a fractional density greater than 80% when considering weight fractions of small versus large particles (eg. 73% large and 27% small particles in the ratio of 1:8) the optimum bimodal fractional packing density of 86% is achieved. Since packing density will increase as a function of the homogeneity of the mixture, care will be taken in how the bimodal mixture is blended.
Figure 2: The experimental results of MaGeary [ 10] showing the effect of the particle size ratio on the maximum fractional density for bimodal powder mixtures.
Figure 3: Percent of theoretical for mixtures of 10 μ ZrN powder and 44 μ ZrN powder,
Figure 3 shows bimodal mixing of two powder distributions of ZrN. One of 44μπι and one of ΙΟμιη were blended in different proportions as shown in Table 1. Maximum density achieved through dry mixing in a ball mill using 2mm zirconia media after isostatic pressing at 32.5 Ksi was 75% fractional density. Pellets of right circular cylinder geometry of OD 1.27 cm and height 1.27 cm with this density could then be sintered to 85% fractional density in a reduced time, thus resulting in less Am loss through volatilization. Table 1. ZrN Pellet Density for Bimodal Distributions Sample
Wt %44μ (G)
Wt°/c, 10μ (g)
1 9 1 2 8 2 7 3 3 4 6 4 5 5 5 *Samples 1 and 2 were broken prior to
p(g/cc) uniaxial pressed 71 70 71 69 68 isopressing.
p(g/cc) isostatic pressed
-
73 75 73
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High Density Green Pellets of ZrN Fabricated by Particle Processing
This work will also explore trimodal mixing of powders. Using data shown in Table 2 [11], a trimodal ratio 1:7:49 should yield factional densities of 87.8% to 95% depending on the volume fraction of small, medium and large particles used. Table 2 Some Optimized Trimodal Packings of Spheres [11] Relative volume % small % medium % large fractional density Size ratio 9.2 21.6 1:5:25 0.850 69.2 6.1 20.7 13.2 1:7:49 0.878 14.0 11.0 0.950 75.0 1:7:49 23.0 10.0 1:7:77 0.900 67.0 11.2 0.892 22.5 1:10:100 66.3 23.4 10.0 1:100:10000 0.916 66.6 Lastly, continuous distributions will be considered for the fabrication of simulant pellets. Using a wide distribution of particles, fractional packing densities have been reported as high as 0.95 [9, 11, 12, 13, 14, 15, 16] for powder distributions reported in the literature. Once the specified powder distributions are produced, various blends will be made by dry ball milling or wet milling in hexane for at least four hours or blended in a spex mill for a few minutes in hexane. The resultant powder will then be uniaxially pressed and cold isostatically pressed into pellets with an aspect ratio of approximately 1.0. CONCLUSION ZrN pellets of 75% fractional density have been made by blending 44μπι ZrN powder with ΙΟμπι ZrN powder in a bimodal distribution and then isostatically pressing at 37.5 Ksi. Initial attempts at trimodal distributions have not resulted in optimum density pellets (85% fractional density) because of hard aggolermates in the powders. These aggolermates have also affected the densities achieved in the bimodal distributions. ACKNOWLEDGEMENT The authors would like to acknowledge the support provided for this work from DOE (DE-FC07-06-ID14731). REFERENCES 1. Y. Kaeda, T. Oei, Jajn Kokai, 89-76,905 (1989) CA 111 (1989) 156958. 2. K. Hirano, Y. Miyamoto, M. Koizumi, Yogyo Kyokaishi, 95 (1987) 906, CA 107 (1987) 159987. 3. S. Somiya, K. Suzuki, M. Yoshimura, Adv. Ceram., 21 (1987), 279. 4. T. Ilda, T. Mitamura, Kagaku Kogyo, 37 (1986), 720.
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5. C.K. Narula Ceramic Precursor Technology and Its Applications (New York, NY:Marcel Dekker, 1995). 6. G.M. Brown and L. Maya, J. Am. Ceram. Soc, 71 (1988), 78. 7. C.K. Narula and L. F. Allard, J. Mater. Chem., 8 (8) (1998), 1881-1884. 8. G.M. Brown and L. Maya, J. Am. Ceram. Soc, 71 (1988), 78. 9. R.K. McGeary, "Mechanical Packing of Spherical Particles," Journal of the American Ceramic Society, 44 (1961), 513-522. 10. C.C. Furnas, "Grading Aggregates I - Mathematical Relations for Beds of Broken Solids of Maximum Density," Industrial and Engineering Chemistry, 23 (1931), 1052-1058. 11. R.F. Fedors and R. F. Landel, "An Empirical Method of Estimating the Void Fraction in Mixtures of Uniform Particles of Different Size," Powder Technology, 23 (1979), 225-231. 12. J.V. Milewski, "Packing Concepts in the Utilization of Filler and Reinforcement Combinations," Handbook of Fillers and Reinforcements for Plastics, ed. H.S. Katz and J.V. Milewski, (New York, NY: VanNostrand Reinhold, 1978), 66-78. 13. W. B. Fuller and S. E. Thompson, " The Laws of Proportioning Concrete," American Society of Civil Engineers Transactions, 59 (1907), 67-143. 14. F.O. Anderegg, "Grading Aggregates II - The Application of Mathematical Formulas to Mortars," Industrial and Engineering Chemistry, 23 (1931), 1058-1064. 15. A.H.M. Andreasen, "Ueber die Beziehung Zwischen Kornabstufung und Zwischenraum in Produkten aus losen Kornern (mit einigen Experimenten), Kolloid Zeitschrift, 50 (1930), 217-228. 16. N. Peronium and T.J. Sweeting, "On the Correlation of Minimum Porosity with Particle Size Distribution," Powder Technology, 42 (1985), 113-121.
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Evolution and Control of Microstructure during Sintering Processes
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THE EFFECT OF CARBON SOURCE ON THE MICROSTRUCTURE AND THE MECHANICAL PROPERTIES OF REACTION BONDED BORON CARBIDE S. Hayun, H. Dilman, M. P. Dariel, N. Frage Department of Materials Engineering, Ben-Gurion University of the Negev, P. 0. Box 653, BeerSheva 84105, Israel S. Dub Institute for Superhard Materials of the National Academy of Science of Ukraine Avtozavodskaya str. 2 Kiev 04074 Ukraine ABSTRACT The present communication is concerned with the effect of the carbon source on the microstructure and mechanical properties of reaction bonded boron carbide composites. The composites were fabricated by molten Si-infiltration of partially sintered boron carbide preforms with 20, 30, or 40 vol.% porosity with and without free carbon addition. The infiltrated composites consist of four phases namely the original boron carbide particles, the ternary Bi2(B,C,Si)3 compound, formed in the course of the infiltration process, ß-SiC and residual silicon. In the absence of initial free carbon, the ß-SiC phase appears as plate-like particles. In the presence of initial free carbon, the ß-SiC phase particles display an irregular polygonal form. The plate like morphology of the SiC phase improves significantly the strength, the fracture toughness and reliability of the infiltrated composites. For an equal volume of SiC, the high aspect ratio of the plate-like particles increases their number per unit volume and thereby, the number of boundaries that a propagating crack has to cross. Moreover, crack deflection on SiC plates was also observed. INTRODUCTION Light ceramics are particularly attractive for personal, land and airborne vehicle armor. High values of hardness are by common consensus of crucial importance for good ballistic resistance. Thus, it is not surprising that boron carbide , the hardness of which is third after that of diamond and cubic boron nitride (CBN), and which has one of the lowest mass per volume ratio, has long been considered as a choice armor material candidate. However, difficulties and costs of fabrication, mainly by hot pressing, are factors of paramount importance in determining whether a particular material is considered for armor applications and limit the extended use of boron carbide based armor. An alternative way for the fabrication of a fully dense boron carbide composite is the socalled "reaction bonding" process2"4. According to mis method, a green body of boron carbide with or without free carbon is infiltrated with molten silicon. The reaction of molten silicon with the boron carbide particles or with free carbon leads to the formation of silicon carbide. The final composite consists mostly of the initial boron carbide grains, a newly formed Bi2(B,C,Si)3 phase, which surrounds the initial boron carbide particles, ß-SiC and some unreacted residual silicon. In order to improve mechanical properties of the composites the amount of the residual silicon has to be reduced. One approach for achieving this goal is to reduce a porosity of the boron carbide preform by its pre-sintering before infiltration with molten Si. This approach was described in our previous communication5 and allows fabricating composites with and without free carbon additions. It was established that the morphology of the new formed SiC phase depends on the
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Effect of Carbon Source on Microstructure and Mechanical Properties of Boron Carbide
carbon source5. In composites fabricated without free carbon addition the ß-SiC phase appears with a plate-like morphology, while free carbon addition to boron carbide leads to the formation of SiC particles with a polygonal shape. In addition, boron carbide particles display a core-rim structure and the rim regions, the composition of which corresponds to the ternary B]2(B,C,Si)3 carbide, interconnect to a large extent the boron carbide particles. The mechanism of the rimcore structure formation has been discussed previously5 and was attributed to the dissolutionprecipitation process in the boron carbide - silicon system. The issue of free carbon addition in the reaction-bonding process is of current interest both from fundamental and processing standpoints. The present work was performed in order to further our understanding and to evaluate the effect of the resulting microstructural features on the mechanical properties of the reaction bonded composites, fabricated with and without free carbon additions. EXPERIMENTAL PROCEDURE. Sample fabrication. Boron carbide (average size of about 5μπι, "Mudan Jiang" Chinese company) powder were uniaxially compacted at 10 MPa and then partially sintered in the 1900-2100°C temperature range for 30 min in order to obtain preforms with 20, 30 or 40 vol.% porosity. Free carbon was added to some of the preforms using a water-sugar solution (50:50). The preforms were infiltrated with this solution, dried, and heat-treated at 500°C in inert atmosphere (Ar 99.999%). Under these conditions, complete pyrolysis of the sugar takes place. The preforms with and without carbon addition were subsequently infiltrated with liquid silicon (Alfa-Aesar 98.4%) in a vacuum furnace (10~5 torr) at 1480°C for 20 min. The infiltration was carried out by placing an appropriate silicon lump on the top of the porous preform. The composites fabricated without carbon addition are denoted as (type-A) and the composites fabricated with the free carbon addition are denoted as (type-B). Microstructural investigation. The microstructure of the samples was studied by optical microscopy (OM, Zeiss Axiovert 25), scanning electron microscopy (SEM, JEOL-35) in conjunction with an energydispersive spectrometer (EDS) and a wavelength-dispersive spectrometer (WDS). The samples for the OM and SEM characterization were prepared using a standard metallographic procedure that included a last stage of polishing by 1 μηι diamond paste. Image analysis was performed using the Thixomet software in order to determine the amount of residual silicon in the composites. In order to emphasize the difference between the rim and core regions and the SiC morphology an electro-chemically etching in KOH solution and chemical etching (HF-NHO,) were used respectively. The phase composition and the structure of the samples was analyzed by X-Ray diffraction (XRD), using a Rigaku RINT 2100 diffractometer with Cu Ka radiation. Mechanical Properties Mechanical properties (hardness and Young's modulus) of the core and rim regions of boron carbide particles, were determined by the nanoindintation technique preformed using a Nano Indenter-II, MTS Systems Corporation, Oak Ridge, TN, USA. The Young's modulus of the composites was determined by the pulse-echo technique using a 5 MHz probe. The Young (E) and shear (G) moduli, were derived from the longitudinal Q and shear Cs speeds of sound and using the density values, determined by the Archimedes method. Vickers hardness of the
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composites was measured under 20N load in a Buehler-Micromet 2100 hardness tester. The fiexural strength was determined on the basis of three-point bending tests on 3x4x20 mm bars in an LRX Plus LLOYD instrument (Lloyd Instruments, Fareham Hants, U.K.). The fracture toughness of the composites was measured by a single-edge notched beam (SENB) method. The notch on a specimen was machined by an electrical discharge machining (EDM) with a 0.1 mm thick Cu wire. The notch depth was measured by an optical microscope and was close to one quarter of the specimen width W (see Fig 1). The specimens were fractured in the three-point bending mode. The fracture toughness value was calculated using equations:6
Kxc=g{alw\^]
3[a/Wfs 2[l - a/W]
(1)
g(a/^) = 1.9109-5.1552(a/FF)+12.6880(a/fr)2 19.5736(a/Pf )3 +15.9377(a/ff)4 -5.U54(a/Wf where Pmax is the maximum load, W is the specimen thickness (4±0.lmm), b is the specimen width (3 ± 0. lmm), L is the span length between supports ( 20mm), a is the notch depth, and g(a/w) is the stress intensity shape factor. p
Figure 1. Single- edge notched beam test
RESULTS AND DISCUSSION Microstructure of the infiltrated composites The XRD spectra of type-A and type-B samples are shown in Fig.2. The diiffractograms are quasi identical and show that four phases, namely, the original boron carbide particles, the ternary Bi2(B,C,Si)3 compound, ß-SiC and residual silicon are present in both types of infiltrated composites.
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Effect of Carbon Source on Microstructure and Mechanical Properties of Boron Carbide
- -r~
20
~T
|
25
i
1
30
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1
35
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45
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Figure 2. XRD pattern of type-A and type-B composites. In type-A samples, SiC is formed as the outcome of the reaction between molten silicon and carbon that originates in the boron carbide phase. In type-B samples, the SiC phase is mostly formed by the reaction between free carbon and molten silicon. A typical microstructure of the composites is presented in Fig. 3. In the type-A composite the ß-SiC phase appears as white plate-like particles (Fig. 3b), while in the type-B composite the ß-SiC phase appears in an irregular polygonal form (Fig. 3a) and only a small fraction of the particles display the plate-like form. The light-gray regions correspond to residual silicon and the dark gray areas correspond to the partially sintered boron carbide skeleton. The microstructure after etching and removal of the residual silicon clearly puts in relief the morphology differences of the SiC phase (Fig. 4).
Figure 3. The microstructure (SEM images) of type-A (a) and type-B (b) composites. The initial open porosity of the preforms was about 20 vol.%.
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Effect of Carbon Source on Microstructure and Mechanical Properties of Boron Carbide
Figure 4. SEM image of the chemical etched (HF-NH03) sample of type-A (a) and type-B (b) composites. The morphology of the SiC phase is clearly apparent. The mechanism of the reactions during the infiltration of the composites, which leads to the morphology differences in the composite have been, described previously5. In addition, the interaction between silicon and boron carbide leads to the formation of the "core-rim" structure (Fig. 5), consisting of an inner boron carbide core surrounded by a ternary boron carbide (B12(B,C,Si)3) rim.
Fig. 5. SEM image (backscatter electrons) of an electro-chemically etched (KOH solution) sample where the "core-rim" structure is put in evidence. Initial boron carbide particles (black core region) surrounded by a 3-7 μηι thick envelope (lighter black rim region).
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Effect of Carbon Source on Microstructure and Mechanical Properties of Boron Carbide
According to the image analysis7 of the microstructure (Table I), the amount of the SiC phase increases from 10 to 16 vol% with increase initial porosity of the perform from 20 to 40 vol%. It is noteworthy that the relative amount of the SiC phase depends essentially on the initial porosity of the preforms and only to a slight extent on the source of carbon. Table I - Phase composition (average values) of the composites. Boron Initial Carbon Silicon Materials porosity, addition, Carbide, vol. % vol. % Vol. % vol. % 20±3 0 80±3 10±3 type-A 70±3 30±3 0 16±3 40±3 0 60±3 24±3 20±3 3±0.5 80±3 10±3 type-B 30±3 4±0.5 70±3 15±3 40±3 6±0.5 60±3 25±3
Silicon Carbide, vol. % 10±3 14±3 16±3 10±3 15±3 15±3
MECHANICAL PROPERTIES. Mechanical properties of core (initial boron carbide particles) and the rim regions. The mechanical properties of the silicon containing boron carbide compound (Bi2(B,C,Si)3) were studied by nano-indentation. Typical force-displacement curves for B4C (core) and for Bi2(B,C,Si)3 (rim) are presented in (Fig. 6). The raw data were treated according to Oliver and Pharr8. The hardness and the Young's modulus values of the Bi2(B,C,Si)3 phase are slightly higher then those for the initial boron carbide phase (Table II). The inspection of a crack propagation path indicates that the boundary between the core and the rim regions is a relatively strong one and that no crack deflection takes place (Fig. 7). These observations are in a good agreement with the TEM analysis of the boundary between the core and the rim, which is apparently a semi coherent boundary5.
Table II. The values of Young modulus and hardness for Bi2(B,C,Si)3 and B4C Young Contact Load Hardness Displáceme diameter modulus nt ,nm ,mN ,GPa ,nm ,GPa 63.8+4.1 474+34 46.1+4.2 103.2+4.3 10+0 B12(B,C,Si)3 B4C 106.3+2.7 10+0 67.9+37.9 460+23 42.0+3.3
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40
60 Displacement, n m
Figure 6. Force vs. displacement plot for core (B4C) and rim (B12(B,C,Si)3) regions.
Figure 7. The crack propagation path in the composite material underlines the strength of the boundary between the core of the boron carbide particles and the adjacent rim.
Mechanical properties of type-A and type-B composites The Young's modulus and the hardness values of the composites decrease with increasing the amount of residual silicon (Fig 8 and 9). It is important to stress that the hardness values refer to the average hardness of the composite and reflect the contribution of the different phases with widely varying individual hardness values4.
Figure 8. Elastic modulus of the composites as a function of the residual silicon
Figure 9. Vickers hardness of the composites as a function of the residual silicon
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Effect of Carbon Source on Microstructure and Mechanical Properties of Boron Carbide
The experimental results for the flexural strength exhibit a different behavior (Fig. 10). The amount of the residual silicon exerts only a minor effect on the flexural strength, while the effect of the carbon source is significant. The flexural strength of the composites with carbon addition (type-B) is significantly lower then those of type-A composites. A similar tendency was observed for the fracture toughness of the composites. The values of the fracture toughness, which were obtained for the composites, fabricated by infiltration of the preforms with about 30 vol. % porosity, are 3.62 ± 0.16 MPa4m and 2.57 + 0.36 MPa4m for type-A and type-B composites, respectively.
O ■
type-A type-B
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1
10
,
1
,
15
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,
20
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25
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residual silicon, % vol.
Figure 10. Flexural strength of the composites as a function of the amount of residual silicon These results may be attributed to the specific plate-like morphology of the SiC phase in the type-A composites. A similar strengthening effect of plate-like SiC particles on ceramic composites was reported in9"11.The presence of the SiC particles with the plate-like morphology affects the crack propagation through the composites (Fig. 11). As was noted above, the volume fraction of SiC particles in the composites, fabricated from the preforms with a given porosity, doesn't depend on the carbon source. Moreover, the polygonal SiC particles are significantly coarser than the plate-like particles. These features stand behind the larger number of the particles with the plate-like morphology per unit volume and thus the larger number of boundaries, which are crossed by a crack (Fig. 11 a,b) resulting in larger crack energy losses. It is also noteworthy that crack deflection takes place on the interaction with the SiC plates (Fig. 11 c,d).
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Effect of Carbon Source on Microstructure and Mechanical Properties of Boron Carbide
Figure 11. SEM images of crack propagation paths in the composites fabricated with and without carbon additions. The scatter of mechanical properties of the reaction bonded boron carbide composites is of relevance. The WeibuU modulus12 of the composites with 15-16 vol.% of residual silicon, as determined on two groups of 16 samples, is equal to 5.84 and 3.67 for type-A and for type-B composites, respectively (Fig. 12).
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Effect of Carbon Source on Microstructure and Mechanical Properties of Boron Carbide
1.5-, 1.0-
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4.8 5.0 5.2 5.4 5.6 5.8 6.0 6.2 1η(σ)
Figure 12. Weibull plots of flexural strength of the type-A and type-B composites. SUMMARY AND CONCLUSIONS Reaction bonded boron carbide composites, fabricated with and without free carbon additions, consist of four phases: the original boron carbide particles, the ternary Bi2(B,C,Si)3 compound, ß-SiC and residual silicon. With no free carbon added, the ß-SiC phase appears as plate-like particles. With an initial free carbon addition, the ß-SiC phase displays mostly an irregular polygonal form. The plate like morphology of the SiC phase enhances significantly the strength and the fracture toughness of the infiltrated composites. It does not affect the hardness and the stiffness of the composites. This specific morphology of SiC provides a larger number of the particles with a high aspect ratio per unit volume and thus a higher number of boundaries to be crossed by a propagating crack REFERENCES 'F. Thévenot, Boron carbide - a comprehensive review, J. Eur. Cer. Soc. , 6 205-225 (1990). 2 M. K. Aghajanian, B. N. Morgan, J. R. Singh, J. Mears and R. A. Wolffe, A New Family of Reaction Bonded Ceramics for Armor Applications, in "Ceramic Armor Material by Design" Eds. J. W. McCauley et. al. Ceramic Transactions, Vol. 134, American Ceramic Society 2001, pp. 527-539 K.M. Taylor and R.J. Palicke, Dense Carbide Composite for Armor and Abrasives, U.S. Pat. No. 3 765 300, Oct. 16 1973 4 S. Hayun, A. Weizmann, M. P. Dariel and N. Frage, The Effect of Particle Size Distribution on the Microstructure and the Mechanical Properties of Boron Carbide-Based Reaction-Bonded Composites, Int. J. Appl. Ceram. Tech., DOI: 10.1111/J.1744-7402.2008.02290.X (2008) 5 S. Hayun, N. Frage, M. P. Dariel, The morphology of ceramic phases in BxC-SiC-Si infiltrated composites, J. Sol. St. Chem., 179( 9), 2875-79 (2006) 6 ASTM E399-74. American Society for Testing Materials Standard Test method for plan Strain Fracture Toughness of Metallic Materials PP. 923-36 ASTM Philadelphia PA (1983). 'Underwood, E. E.„ Weibel. E. R. and Exner, H. E., and H. P. Hougardy, in Physical Metallurgy, edited by Robert. W. Cahn and Peter Haasen (North-Holland, Amsterdam, 1996), pp. 1000-1007.
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W.C. Oliver and G.M. Pharr, An Improved Technique for Determining Hardness and Elastic Modulus Using Load And Displacement Sensing Indentation Experiments, J. Mater. Res, 7(6), 1564-83 (1992). K. Lee, Y.C. Kim and C.H. Kim, Microstructural development and mechanical properties of pressureless-sintered SiC with plate-like grains using AI2O3-Y2O3 additives. J. Mater. Sei., 29, 5321-26, (1994). 10 W. J. Moberlychan, J. J. Cao and L.C. DE Jonghe, In Situ Toughened Silicon Carbide with AlB-C Additions, Acta Mater., 6(5), 1625-35, (1998). "S. Hayun, D. Rittel, N. Frage and M.P. Dariel, Static and Dynamic Mechanical Properties of Infiltrated B4C-S1 Composites, Mat. Sei. Eng. A, 487(1-2), 405-409, (2008). I2 W. Weibull, "A Statistical Distribution Function of Wide Applicability. J. Appl. Mech., 18 293297(1951).
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MODIFICATION OF MASS TRANSPORT DURING SINTERING INDUCED BY THERMAL GRADIENT Sébastien SAUNIER, Francois VALDIVIESO Departement MPE, Centre SMS, UMR CNRS 5146, Ecole Nationale Supérieure des Mines de Saint-Etienne 158 cours Fauriel, 42023 Saint-Etienne cedex 2, France ABSTRACT Due to the developments of the new sintering processes, the thermal cycles duration has been considerably reduced. But it turns out that this cycle time decrease can also conduct to thermal gradients in the sample. Up to day, the effects of such gradients are not well known. That's why the aim of this study is to contribute to understand phenomena induced by thermal gradients applied during the initial stage of sintering. We will observe the consequences on this stage but also on the further densification. Two important results are brought out: - For pure alpha-alumina : the comparison between conventional treatments and treatments under thermal gradients has shown that a gradient modifies the specific surface area drop and then accelerates the further densification. - For alpha-alumina containing impurities : The experiments have revealed that a gradient can modify the impurities' dissolution and change the mass transport. Finally grain growth can be favoured at the expense of densification. INTRODUCTION Compared to conventional sintering, sintering under microwaves leads to a better homogeneity and to an improvement of the microstructure with a reduction of porosity and grain size1' . Moreover, experimental data on spark plasma sintering showed a higher sintering activity3'4. In addition to these advantages, both new processes are based on very fast heating rate. In such processes, the high heating rate inevitably leads to a complex temperature distribution, and possibly to the appearance of temperature gradient in the piece. The presence of density gradients in samples sintered by field activated sintering processes is mentioned in the literature5'6. This constitutes an indirect evidence of the development of temperature gradient during this sintering process. Moreover, Zavaliangos et al.7'8 have recently studied the temperature distribution in the FAST device using the finite elements methods simulation. They have showed the development of temperature gradient in this device. Although thermal gradients are present in a lot of sintering processes, few experimental studies treat about the consequences induced by thermal gradients 9 ' 011 . This can be explained by the difficulty to dissociate the effect induced by heating rate and the effect induced by the thermal gradient. Then the consequences of a thermal gradient are not well known. Nevertheless, it seems that a thermal gradient can enhance the densification. Other studies have mentioned that a thermal gradient can induce mass transport which lead to a demixing in multi-component oxides12'13. The present study deals with the quantification of the effect induced by the existence of a thermal gradient applied during the initial stage of sintering on submicronics aluminas with different purities. 41
Modification of Mass Transport during Sintering Induced by Thermal Gradient
MATERIALS STUDIED AND EXPERIMENTAL METHODS Powder formulation and processing The powder used in this study is a submicronic a-alumina powder (named UF powder) generated by ex-alun process. This alumina contains initially 210 ppm of impurities. The main impurities are: Na, K, Si and Ca. To carry out a slurry of 60 wt.% powders, alumina is dispersed in a pH 10 deionised water using polyacrylic acid (Acros Organics, USA) of molecular weight 2000. After 24 hours in a mixer with rollers, attrition using zirconia balls doped with CaO, MgO and S1O2 has been carried out (830 rpm for 1 h). In these conditions, the contamination in zirconia due to the attrition is quantified at 0.79 weight % (measured by X-ray fluorescence). Then 2.25 wt.% of polyvinyl alcohol 4/125 (Prolabo, France) and 0.75 wt.% of plasticizer polyethylene glycol 4000 (Merck-Schuchardt, Germany) are added. After attrition milling the powders are atomized. Cylindrical samples of 6 cm lengths are obtained by uniaxially compaction at 40 MPa in a steel die of 8 mm diameter and cold isostatically compacted at 400 MPa. Finally, in order to remove the organic phases, green samples are treated during 1 hour at 600°C. The theoretical density of the material takes into account the zirconia contamination coming from attrition milling (measured by X-ray fluorescence). After debinding, the density homogeneity of the green sample is verified (equal to 53.1 % ± 1% TD). Furnace with heat gradient To carry out thermal gradients, a muffle furnace has been used (figure 1). Inside this furnace, different systems of porous refractory masks are introduced to make a thermal barrier. By the modification of the thickness of the masks, thermal gradients can be reached. To study the thermal gradient in the initial stage of sintering, the samples stay under the mask. The temperature regulation of the furnace allows to obtain a temperature difference of 100°C on the 6 cm length sample. The temperature applied on the sample is reported in figure 2. After this pre-treatment the samples are cut in sections of one centimetre length and then undergo various analyses (analyses of specific surface areas, sinterability,...). In these operating conditions, each section do not have the same thermal history. To quantify thermal gradient effects, reference samples (1 cm length) are sintered with a same thermal schedule of each section but without thermal gradient.
Figure 1. Representation of the thermal furnace.
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Figure 2. Temperature profile in the thermal furnace Experimental analysis Relative densities and porosities are measured by using the water immersion method. The error of measurement on the density is estimated at 0,1 % in the case of the double weighing. This error can reach 0.5 % in the case of triple weighed. To study the influence of the thermal gradient in the initial stage of sintering, the specific surface area of the specimens is evaluated by the Brunauer-Emmet-Teller (BET) method. Microstructural observations are carried out via scanning electron microscopy (model 6500 F, JEOL, Japan). RESULTS Influence of a thermal gradient applied in the initial stage of sintering Analyses of specific surface area measured by the BET method are done on presintered samples (UF alumina) under thermal gradient and without thermal gradient. The specific surface area is measured at both extremities (average temperatures of 880°C and 980°C) of the samples treated under thermal gradient and compared with those obtained in conventional treatment (Table 1). It appears a more important specific surface area decrease for conventional heating than for heating under thermal gradient. This result is valid for an average temperature of 880°C and 980°C. However, this difference is less significant when the temperature increases. These results obtained suggest that a thermal gradient applied in initial stage of sintering leads to neck formation delay. Table 1 . Specific surface area of UF alumina Green samples Conventional pre-treatment at 880°C Pre-treatment under gradient at 880°C Conventional pre-treatment at 980°C Pre-treatment under gradient at 980°C
Specific surface area (m2/g) 17.3 ±0,1 AS/So (%) 14.2 ±0,1 -17.9 -12.7 15.1 ±0,1 12.8 ±0,1 -26.0 13.4 ±0,1 -22.5
To see the consequences of a thermal gradient applied in the initial stage of sintering on the future densification of the material, a dilatometric study is realised for each section. A relatively low temperature of sintering is chosen (1450°C) in order not to be nearby to the theoretical density and then to mask the effects of gradient. Besides, the heating rate used is fast (20cC/min), in order to avoid the screening of the initial treatment effects. The dilatometric results (Figure 3) show a densification gain (compared to conventional sintering) when the sample is first pre-treated under thermal gradient. This gain is more important for a pre-treatment at lower temperature.
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Modification of Mass Transport during Sintering Induced by Thermal Gradient
Figure 3. Dilatometric behaviour of UF alumina after different pre-treatment. Effect thermal gradient and impurities on sintering To enhance the level of impurities present in the alumina powder, the attrition time has been increased. Thus the contamination in zirconia measured by X-ray fluorescence in this new powder (noticed UF*) is 1,81 weight %. A same pre-treatment under thermal gradient is applied on the UF* alumina. After cutting up the pre-treated samples, measures of specific surface areas have been carried out (Table 2). For a same pre-treatment under gradient, it appears a strongest specific surface area decrease for UF * samples (i.e. sample with more impurities) than for UF samples. Table 2. Specific surface area of UF and UF* alumina after pre-treatment under gradient. UF alumina SBET (m2/g)
Green samples Pre-treatment at 880°C Pre-treatment at 980°C
AS/SO
(%)
UF* alumina
Final density (1450°C) SBET(nrVg)
AS/So (%)
Final density (1450°C)
18.2 ±0,1
17.3 ±0,1 15.1
-12.7
90.1%TD
15.0
-17.6
77.1%TD
13.4
-22.5
90.9%TD
13.2
-27.4
84.8%TD
Nevertheless, after sintering cycle (20°C/min up to 1450°C), the densification rate of samples with impurities (UF*) are lower than those recorded for pure alumina UF (Table 2). This phenomenon is the more pronounced if the pre-treatment is realized at low temperatures.
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Sintering with high heating rate UF* sample (without pre-treatment) has been sintered at 1450°C with a heating rate of 20°C/min in a muffle furnace and in a dilatometer. The obtained densification is 87.3 + 0.3 %TD in the case of the muffle furnace. For the sintering in the dilatometer the final density is only 63.3 % ± 0.8 %. The microstructure obtain in this two cases are presented in figure 4. For sintering in the muffle furnace, the grain size is smaller in spite of a better densification.
Figure 4. Microstructural observations after sintering with a heating rate of 20°C/min in a dilatometer (a) and in a muffle furnace (b).
For an identical thermal cycle (heating rate and sintering temperature), the behaviour of UF* is totally different according to the furnace type (muffle and dilatometer). Nevertheless, the temperature field is more uniform in the muffle furnace than in the dilatometer. Thus, reactivity difference experimentally observed are linked with the existence of thermal gradient in the dilatometer. Besides, in the next part, we are going to study the effects of technological parameters of the dilatometer affecting the thermal gradient value. Various parameters can affect the thermal gradient value which can be developed in the dilatometer: - the gas flow; - the sample height; - the heating rate. The influences of these parameters on the alumina UF* sintering without presintering are summarised in table 3. Increasing the heating rate or the gas flow or the sample heights leads to a significant decrease in final densification. In addition, analysis of microstructure fracture show an increase of the grains size and a faceted aspect when the gas flow, the heating rate or the sample heights increase (Figure 5).
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Modification of Mass Transport during Sintering Induced by Thermal Gradient
Table 3. Effect of technological parameters on the final density. Heating Gas Sample Final rate flow height density (°C/min) (L/h) (mm) (% TD) 92,4 5 1,8 7 63,3 20 1,8 7 76,2 20 0 7 (a) 64,1 20 0,5 7 63,3 20 1,8 7 62,4 20 3 (b) 7 68,1 20 1,8 (c) 2 63,3 20 1,8 7 59,5 1,8 15 (Φ 20
Figure 5. Microstructure fracture of UF* sintered alumina according to conditions presented in table 3. Effect of intergranulares impurities At any time during sintering, it is possible to create a thermal gradient with dilatometer thanks to particular condition (fast heating rate and high gas flow). Thus we apply different thermal cycles, with high heating rate and high gas flow in the initial stage or all along sintering process. For UF* samples, the temperature gradient induced by the dilatometer is applied only in the initial stage of sintering (between 20°C and 980°C). Beyond 980°C, the heating rate is 5°C/min (minimization of thermal gradient). The dilatometric curve is reported in figure 6-(a). This sintering cycle leads to a densification of 73.7% TD.
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For comparison, the figure 6 also presents the dilatometric behaviour of UF* alumina sintered until 1450°C at two heating rate : 5°C/min (figure 6-(b)) and 20°C/min (figure 6-(c)).
Figu re 6. densification curves of UF* alumina, from dilatometric experiments, (a : 20°C 20°ami° »980°C 5°c/mi° »1450°C / b : ?Π°Γ 5°c/min >14Sn°r / c : 20°C 20°c/mip» 1450°C) Dilatometric studies reveal that a thermal gradient applied only in the initial stage of sintering (figure 6-(a)) leads to a densification which is far less advanced than when conventional heat treatment is applied over the cycle sintering (figure 6-(b)). The densification of UF* alumina is the less advanced when a thermal cycle is present in all the thermal cycle (figure 6-(c)). On this figure, the gap is more important between curves (a) and (b) than between curves (a ) and (c). In consequence, for UF* alumina, the existence of a thermal gradient in the initial stage sintering is the principal source of the densification delay. In the case of a powder (like UF*) containing impurities coming from attrition contamination (ZrC>2, S1O2, MgO, CaO), these impurities are initially located in intergranular position. The location of these impurities is therefore different from that of impurities initially present in the powder (dissolved in grains of alumina due to process ex-alun production). The aim of this part is to establish whether or not the impurities location before the gradient application affects the densification. A long conventional pre-treatment (72 hours at 920°C) is realized. After this pretreatment, sintering cycle in a dilatometer with a heating rate of 20°C/min up to 1450°C is applied. The density obtained in this case is 91.2%TD. Thus, in the case of UF* alumina (alumina containing initially intergranular impurities), a long thermal schedule (long dwell time) at low temperature drives to a dissolution of impurities before the sintering starts. This can finally increase the densification under thermal gradient. SUMMARY AND INTERPRETATION OF RESULTS The experimental study highlights the effects of a thermal gradient applied in the initial stage of sintering. This gradient must be benefit to the further densification in the case of pure alumina. By delaying the necks formation, a temperature gradient applied in the initial stage of sintering can keep a high sintering potential and therefore lead to a better densification. Advances in Sintering Science and Technology
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In other side, this gradient can also block the densification and increase the grain size. This phenomena has been observed in the case of alumina which contains intergranular impurities. Such grains growth without significant densification has previously been observed in different materials such as A120314, Zr0 2 15, Ti0 2 I6or ZnO ". The causes advanced by the authors to explain the existence of such porous structure are based on an amplification of evaporation-condensation or surface diffusion mechanisms. In the case of two particles in contact, it produces a rapid enlargement of the neck and then to a grain boundary moving towards the curvature centre, leading finally to a single particle of an important size. In addition, Petot and al.12'1 have demonstrated a modification in the distribution of magnesium impurities (phenomenon of segregation) which is induced by a temperature gradient. By analogy, it is possible to think that in our study, the temperature gradient change the transport mechanisms of matter by a modification of impurities distribution. Other studies show the influence of the impurities location on the materials sinterability. Gouvea18 has studied the densification of Sn0 2 added Mn0 2 . He has shown the effect of foreigners cations distribution before sintering. If the foreigners cations are distributed on the surface of the grains Sn0 2 (in the first surface layers of grains) sintering begins at a lower temperature than in cases of foreigners cations initially distributed outside the Sn0 2 grains. The authors have proved that in the latter case, the densification begins only when a critical concentration in foreign element is present on the surface grains of the matrix. Below this critical value, they have demonstrated that only the surface of grains is concerned by diffusion. Beyond this limit the material densifies. The authors have concluded a modification of mass transport mechanism depending on the concentration of foreign elements on the grain surface. It results a densification delay if the foreigners elements remained outside the grains. The results and observations from the present study suggest that the thermal gradient can change the surface diffusion of alumina grains according to impurities distribution within the alumina grains or in the periphery ofthat grain. For pure alumina, without intergranular impurities, a strong reactivity of the system is maintain to a higher temperature. So, that leads to a better densification. For contamined alumina powder, the present impurities modify the kinetics of matter transport. So, that can lead to grain growth at densification's expense. CONCLUSION By this analysis several points can be mentioned and emphasized : - Comparisons between thermal treatments carried out in the initial stage of sintering (with and without thermal gradient) show that the gradient induces delay of specific surface area drop. In this case, the further densification of the material is improved. The interpretation of these experimental results due to correlate delay of specific surface area drop to a delay in the necks formation. This delay helps to maintain a strong reactivity of the system to a higher temperature and thus a better densification. - Through complementary experiments, it has been demonstrated that a thermal gradient applied in the initial stage of sintering can affect the impurities dissolution. The mass transport is then modified : the grain growth is promoted at the expense of densification. Optimising the co-doping and a thermal gradient is an interesting way to obtain porous ceramic with stable and controlled microstructures. REFERENCES 1 Z. Xie, J. Yang, Y. Huang, Densification and grain growth of alumina by microwave processing, Mat. Letters, 37 (4-5), 215-220 (1998).
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2
J.H. Yang, K.W. Song, Y.W. Lee, J.H. Kim, K.W. Kang, K.S. Kim, Y.H. Jung, Microwave process for sintering of uranium dioxide, J. Nucl. Mat., 325 (2-3), 210-216 (2004). J.R. Groza, Consolidation of atomizaed NiAl powders by plasma activated sintering process, Scr. Mater., 30, 47-52 (1994). 4 Y. Zhou, K. Hirao, Y. Yamauchi and S. Kanzaki, Densification and grain growth in pulse electric current sintering of alumina, J Eur. Ceram. Soc, 24 (12), 3465-3470 (2004). 5 B. Klotz, K. Cho, RJ. Dowding and R.D. Jr. Sisson, Boron carbide consolidated by the plasma pressure compact (P2C) Method in air, CESP, 22, 4 (2001). K. Ozaki, K. Kobayashi, T. Nishio, A. Matsumoto and A. Suyiyama, Sintering phenomena on initial stage in pulsed current sintering, J. Jpn. Soc. Powder Powder Metall, 47, 293-297 (2000). 7 A. Zavaliangos, J. Zhang, M. Krammer and J. R. Groza, Temperature evolution during field activated sintering, Materials Science and Engineering A, 379 (1-2), 218-228, (2004). 8 B. Mc Williams, a. Zavaliangos, Temperature distribution and efficiency considerations for field activated sintering (FAST), presented at sintering'05, Grenoble, (2005). 9 P. Braudeau, Transport de matiére dans les oxydes - Influence d'un gradient thermique Approche du frittage rapide, These Université Paris VI, (1983). 10 A.W. Searcy, D. Beruto, Theory and experiments for isothermal and non isothermal sintering, Science of ceramics, 14, 1-13 (1987). n R. Botter, A.W. Searcy, Influence of Temperature Gradients on Sintering : Experimental Tests of a Theory, J. Am. Ceram. Soc, 72 (2), 232-235 (1989). 12 D. Monceau, C. Petot, G. Petot-Ervas, Kinetic demixing profile calculation under a temperature gradient in multi-component oxides, J. Eur. Ceram. Soc, 9, 193-204 (1992). 13 C. Petot, G. Petot-Ervas, M. Tebtoub, J.W. Fräser, MJ Graham, G.I. Sproule, Kinetic demixing in a-alumina during cooling : Influence of the powder reactivity, Solid State Ionics, 95 (1-2), 65-72 (1997). C. Greskovich, K.W. Lay, Grain growth in very porous AI2O3 compacts, J. Am. Ceram. Soc, 55 (3), 142-146(1972). 15 M.J. Readey, D.W. Readey, Sintering of ZrÜ2 in HC1 atmospheres, /. Am. Ceram. Soc, 69 (7), 580-582(1986). 16 M.J. Readey, D.W. Readey, Sintering T1O2 in HC1 atmospheres, J. Am. Ceram. Soc, 70 (12), 358-C361 (1987). 17 T. Quadir, D.W. Readey, Microstructure development of zinc oxide in hydrogen, J. Am. Ceram. Soc, 72 (2), 297-302 (1989). 18 D. Gouvea, A. Smith, J.P. Bonnet, J.A. Várela, Densification and coarsening of SnCVbased materials containing manganese oxide, J. Euro. Ceram. Soc, 18 (4), 345-351 (1998).
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EFFECTS OF CRYSTALLIZATION AND VITRIFICATION ON SINTERING PROPERTIES OF BENTONITE CLAY H. Camacho, C.A. Martinez, P.E. Garcia, H.J. Ochoa, and J.T. Elizalde Instituto de Ingeniería y Tecnología. Universidad Autónoma de Ciudad Juárez. Av. del Charro 610 norte, Ciudad Juárez, Chih., México 32310 A. García Interceramic Technological Center, Av. Carlos Pacheco No. 7200, Chihuahua, Chih., México 31060 A. Aguilar, M. Bocanegra, C. Domínguez Centro de Investigación en Materiales Avanzados, S.C. Miguel de Cervantes 120 Chihuahua, Chih., México 31109 ABSTRACT Bentonite clays are frequently used in the formulation of structural ceramics at low concentration in spite of its chemical composition which is similar to kaolinite, the most used clay for this purpose. During the study of the sintering properties of natural bentonite clay, we found that the studied bentonite can be used as main component to formulate structural ceramic products where control of dimension is fundamental. According to our study, with ceramic formulation based on bentonite clay, during thermal treatment a plateau where dimensional changes are minimal can be used to sinter the ceramic pieces. This process represents a significant advance related to the conventional process where CaC03 is used to promote the crystallization/vitrification process of several phases by reaction of amorphous silica and amorphous meta kaolinite with the CaO produced during the thermal decomposition of CaC03. INTRODUCTION Traditional ceramics generally concerns with the use of silicate-primary clay minerals and/or silicate glasses as raw material. Traditional ceramic industry have been spending great part of their efforts searching for proper clay minerals and due to requirements of production costs and exhausting of deposits under mining, this is still an issue.1"4 In ceramic industry, local minerals are usually the source for raw materials and they need to be studied before they can be incorporated to ceramic processes.5,6 Current models of ceramic sintering7 do not consider phase transformation during thermal treatment. For natural clay minerals, crystallization and vitrification is frequently a common process during ceramic processing to obtain ceramic materials.8"10 In the present work, the attention is focused on the study of sintering of a natural bentonite clay in order to characterize the processes of crystallization and vitrification during thermal treatment. This type of clay is known as SodiumCalcium Bentonite, it has a dimensional stability region between 950 - 1080 °C, the relation of this stability region with the chemical transformations is an issue of scientific interest. It has consequences for the traditional ceramic processing, because for some applications porous and light ceramic titles are of interest. In addition, this regional Bentonite clay offers an economic option. In this work, evolution of phase transformations is obtained mainly by XRD and SEM analysis. Two kind of dilatometric tests were made to study the sintering process, linear shrinkage and beam deflection. EXPERIMENTAL PROCEDURE Bentonite clay currently used to formulate ceramic bodies was taken from a mine located at 28° 57' 3 3 " lat N;105° 35'20" long W and 1269 m over sea level. Clay was milled in an alumina jar mill and then dried in order to eliminate free water. Elemental analysis was developed in a Bruker AXS S4-
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Pioneer Wavelength dispersive X-ray fluorescence spectrometer (WDXRF) and the samples preparation was made by the pressed pellets method, the elemental composition was obtained by means of standardless program. After drying the clay samples, alumina jar ball-mill and planetary equipment was used to wet mill the clay and drying to have the clay as a powder with particle size lower than 420 μπι. Next step was to humidify the clay in order to obtain standard conditions (6 % of water), and finally the wet powder was compacted by unidirectional pressing in steel mould in an automatic hydraulic press. For each experiment, clay discs of 5 cm of diameter and 0.6 mm of thickness were pressed in unidirectional way under 280 Kg cm" of load. Differential Thermal Analysis (DTA) and Thermo Gravimetric Analysis (TGA) were carried out to detect phase transformations in TA instrument DTA/TGA model Q 600 in static air atmosphere, heating rate 14 °/min from T=25 °C - 1180 °C, The calibration was made with STD of Indium, Zinc and Silver. These analyses were complemented using X-Ray Diffraction (XRD) with Copper radiation (λ = 1.540598Á) made to samples heated under different thermal treatments of 900, 950, 1000, 1050, 1100, 1150 and 1180 °C. XRD patterns were obtained in a PANanalytical X'Pert PRO Difractometer. As the main objective is to study sintering behavior, it is especially useful to quantify the crystal/amorphous ratio of phases generated during heating treatments. Hence, the Scanning Electron Microscope is used to characterize the amorphous and crystalline phases. Quantification of the amorphous phase is conducted by SEM image processing. SEM micrographs were obtained with a JEOL JSM-5800 LV. The TDA (Thermo dilatometric analysis), developed in a Misura-ODHT Model M3D1400/50, is applied to measure shrinkage. A green sample was prepared where the three dimensions were in the same order. Shrinkage, ha I a , is measured experimentally along the three axes to calculate the total relative volume shrinkage, Θ, which permits to follow the progress of sintering. Θ is given by 0=l-£ ^-[(l-^Kl-M/Ml-dc/q,)]
(1)
where Aa = ao - a; Ab and Ac are similarly defined. The parameters, Vo and V are the sample volume values at starting and at any time (t) corresponding to temperature T. Values are in the range 0< Θ < 1 and they correspond to shrinkage. If the mass remains constant, this shrinkage means densification. Finally, a beam was prepared to perform the bending creep test to measure the maximum deflection, δ. RESULTS AND DISCUSSION Table I shows the elemental analysis for the Bentonita herein studied showing that it may be call as a Sodium-Calcium Bentonite clay. Clay samples as obtained from mining were analyzed by DTA using a heating program from room temperature to 1180 C under heating rate of 14 C/min. Below 500 C a characteristic signal of endothermic process was observed, which can be associated with the evaporation of free and interlaminar water. Above 500 C a close sequence of endothermic and exothermic process suggest that several kinds of phase transformations are going on at the same time. One of these is the endothermic lost of chemically bonded water occurring between 650 C and 700 °C, which is typical for bentonitic clays. The typical pattern of crystallization as reported by Syam and Varma11 is not observed.
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Table I. Elemental Analysis for the Sodium Calcium Bentonite Clay in percent for each element
10
20
30
40
50
60
2Θ
Figure. 1. X-ray diffraction patterns for untreated and thermally treated clay:(a) Raw Clay, (o) 900°C, (Δ) 950 °C, (V)1000 °C, (0) 1050 °C, («)1100 °C, (·)1150 °C, (A) 1180 °C. Phase transformations may be observed as result of the thermal treatment.
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550·
Anorthite 21.97 500
■Ä
450
Π3 Φ Q.
400
> ω DT
350·
300
— i — ' — i — ■ — i — ' — i — ' — i — ' — i — ' — i —
900
950
1000
1050
1100
1150 1200
Temperature ( C) Figure. 2. Dependence of the intensity of Anorthite phase peak (2Θ= 21.97) on temperature of thermal treatment. Values were taken from Fig. 1 data. It can be inferred that for temperatures higher than 1100 C the volume fraction of Anorthite tends to decrease. Fig. 1 shows the X-ray diffraction patterns carried out for several temperatures from 950 C to 1180 C. Before any thermal treatment, besides montmorillonite, mainly detected phases are anorthite, albite, opal and quartz (CaAl 2 Si 2 0 8 , NaAlSi 3 0 8 , Si0 2 X H 2 0 and SiÓ2), being montmorillonite and quartz the main phases whose signals decrease significantly after thermal treatment. Albite or anhortite phase signal increased with the thermal treatment up to 1100 °C, above this temperature, rapidly tend to disappear, which clearly can be seen at figure 2. In the insert the sharpening of this peak is observed from 800 to 1150 °C, which indicates that crystals are growing. Above 1150 °C the dissolution of anorthite phase is indicated by the widening of peak and the lowering of intensity. Fig. 3 shows the SEM micrographs of several samples fired for 30 min at a fixed temperature from 900 °C to 1180 °C. For treatments of 900 °C to 1000 °C, the observed changes in microstructure are mainly related to sintering. For 1050 C the fraction of the amorphous phase starts to increase. For the sample treated at 1100 C, the amorphous phase becomes dominant and for higher temperatures, a lot of well defined crystals can be observed. According to XRD analyses (Fig. 1) anorthite, quartz and montmorillonte phases were dissolved to form vitreous phase. SEM image analysis is implemented to estimate the amorphous/crystal fraction. Fig. 4 shows the amorphous volume fraction as function of temperature. This fraction was calculated from Fig. 3a to 3g. At 800 C, sintering is activated and shrinkage is observed according to TDA curve (Fig. 4), which is probably due to the activation of the viscous flow in the amorphous matrix. For temperatures higher than 950 °C, the crystalline fraction tends to increase and shrinkage almost stops, thus the crystallization process increase the viscosity of the vitreous phase and as a result the sintering process is inhibited. The stabilization of volume can be qualified as unusual for most sintering materials and can be taken as an advantage, since this property can be manipulated for specific needs of the ceramic industry.
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Fig. 3. SEM micrographs (Magnification: 2200 Voltage: 15 KV) of the Sodium-Calcium Bentonite Morrión fired at (a) 900°C, (b) 950°C, (c) 1000°C, (d) 1050°C, (e) 1100°C, (f) 1150°C, and (g) 1180°C during 30 min. The maximum for the amorphous volume fraction is observed for 1100 C.
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For treatments at temperature higher than 1050 °C a tendency for the decrease of crystals phase can be observed and the sintering shrinkage is activated again. It is worthily to point out that, in this case, crystallization is related to sintering inhibition, this sintering mechanism is knowing as liquid reactive phase, since_diffusional sintering related to crystals structures occurs much slower than viscous sintering related to amorphous structures.'2'13 This sintering mechanism exhibits behavior differences in comparison to traditional mechanism of vitrification, which is well known for production of traditional ceramic bodies (wall, floor and porcelain tiles).14 The possibility to take control of shrinkage in an extended range of temperatures can be useful to produce ceramic bodies where minimum changes on dimensions are required, as in the porous ceramic body (wall tiles). At industry this kind of behavior is currently obtained using calcium carbonate for ceramic body formulations (silica, kaolin, ball clay, feldspar and calcium carbonate (CaCCh)) to promote the crystallization process of wollastonite, gehlenite and anorthite phases by reaction of amorphous silica and/or amorphous meta kaolinite with the CaO produced during the thermal decomposition of CaCCh giving thus a relatively gradual vitrification process. For the vitrification process promoted with CaCC>3, reaction is not fully achieved and many intermediary phases are presented at the end of the vitrification step, imparting some undesirables characteristics at the final product like water absorption expansion (time dependant products).14
Temperature ( C) Figure. 4. Dependence of the amorphous fraction (left axe) calculated from SEM images and relative shrinkage (right axe) on temperature for heating rate of 14 C/min determined by TDA. The connection between the amorphous volume fraction and the relative shrinkage may be observed.
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CD
-i—'—i—'—i—'—i—'—r 1000 1050 1100 1150 1200
Temperature ( C) Figure. 5. Relative volume shrinkage (left axe) and beam deflection (right axe) as a function of temperature. About 1100 °C, the average slope for beam deflection shows a remarkable change. At this temperature, the Anorthite volume fraction start to drops and the maximum volume fraction of the amorphous phase is reached. Figure 5 shows the evolution of the Relative volume shrinkage together with Beam deflection with the temperature increase at 7 °C / min. Relative volume shrinkage and density may be related by p = p„ /(l - θ). Then, the free sintering density evolution for amorphous materials15 exhibits somehow a similar tendency to that shown in Fig. 5. Then, the effect of phase transformations on volume shrinkage is low. Beam deflection is more sensitive to crystallization and vitrification. For low temperatures up to 950, the tendency for the deflection is to increase. This tendency is interrupted and it appears again for temperatures higher than 1000 °C. It can be noticed that this tendency is close related to the amorphous fraction with temperature shown in Fig. 4 and to Relative volume shrinkage (Fig. 5). A combination of density evolution and Beam deflection may lead to estimate uniaxial viscosity1 . Uniaxial viscosity and density evolution depends on the viscosity of the sintering material15. Phase transformations play a key role on the matrix viscosity and it is expected to affect all the parameters used to describe sintering. CONCLUSIONS • The phase transformation of Sodium-Calcium Bentonite clay as function of thermal treatment is reveled. For lower temperatures, anorthite, opal and quartz are the identified phases. As temperature increases, vitrification takes place. • For this clay sintering is favored between 800 °C and 950 °C and for temperatures higher than 1100 °C. Between 950 °C and 1100 °C the dimensional changes are inhibited due to crystallization and the sintering mechanism, known as liquid reactive phase. • Beam deflection slope change (macroscopic constrained sintering) can be observed as a clear evidence of crystallization phases from bentonite clay. • Bentonite clay offers the possibility to control the crystal/amorphous fraction in ways that are beneficial to specific application in the ceramic industry.
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ACKNOWLEDGEMENT This work was supported by CONACYT Chihuahua CHIH-2006-C02-58108. The support of the Interceramic Technological Center is also highly appreciated. REFERENCES 'C. Zhang, K. Komeya, J. Tatami, T. Meguro, and Y-B. Cheng, Synthesis of Mg-α SiAlON powders from talc and halloysite clay minerals. J. Eur. Ceram. Soc, 20, 1809 - 14 (2000). 2 A. J. Flynn, and Z. H. Stachurski, Microstructure and properties of stoneware clay bodies. Clay Minerals, 41, 775 - 89 (2006). 3 B. Bauluz, M. J. Mayayo, A. Yuste, C. Fernandez-Nieto, and J. M. Gonzalez-Lopez, TEM study of mineral transformations in fired carbonated clays: relevance to brick making. Clay Minerals, 39, 333 44 (2004). 4 K. Traoré, G.V. Ouédraogo, P. Blanchart, J.-P. Jernot, and M. Gomina, Influence of calcite on the microstructure and mechanical properties of pottery ceramics obtained from a kaolinite-rich clay from Burkina Faso. J. Eur. Ceram. Soc, 27, 1677-81 (2007). 5 S. Kacim, and M. Hajjaji, Firing transformations of a carbonatic clay from the High-Atlas, Morocco. Clay Minerals, 38, 3 6 1 - 6 5 (2003). 6 G. E. Christidis, P. Makri, and V. Perdikatsis, Influence of grinding on the structure and colour properties of talc, bentonite and calcite white fillers. Clay Minerals, 3 9 , 1 6 3 - 1 7 5 (2004). R. K. Bordia, and G. W. Scherer, On constrained Sintering-1. Constitutive Model for a sintering body. Acta Metall, 36,2393 - 2397 (1988). 8 M. Murat, and M. Driouche, Characterization of the crystallinity of silicates by dissolution conductimetry. J. Eur. Ceram. Soc, 6, 73 - 83 (1990). M. Roskosz, M. J. Toplis, and P. Richet, Kinetic vs. thermodynamic control of crystal nucleation and growth in molten silicates. J. Non-Crystal. Solids, 352, 180-84 (2006). °S. Chandrasekhar, and P. N. Pramada, Sintering behaviour of calcium exchanged low silica zeolites synthesized from kaolin. Ceram. Int., 27, 105 - 14 (2001). N. Syam Prasad, and K. B. R. Varma, Crystallization Kinetics of the LÍBO2-ND2O5 Glass Using Differential Thermal Analysis. J. Am. Ceram. Soc., 88, 357 - 61 (2005). 12 M. Reiterer, T. Kraft, and H. Riedel, Application of a microstructure-based model for sintering and creep. In Proc. 106th Annual Meeting of ACerS, ed. C. DiAntonio, Indianapolis, Ceram. Trans., 157, 49 - 58 (2004). 13 G.W. Scherer, and D.L. Bachman, Sintering of low-density glasses: II, Experimental study. J. Am. Ceram. Soc, 60, 239 - 43 (1977). '"Applied Ceramic Technology volume 1 SACMI, ISBN 88-88108-48-3, Edifice La Mandragora of Imola s.r.l, Chapter VIII, 245 - 54 (2002) 15 G. W. Scherer, Cell Models for Viscous Sintering. J. Am. Ceram. Soc, 74, 1523 - 31 (1991). 16 S-H. Lee, G.L. Messing, and D. J. Green, Bending creep test to measure the viscosity of porous materials during sintering. J. Am. Ceram. Soc, 86, 877 - 82 (2003).
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DISSOLUTION OF ALUMINA JN SILICATE GLASSES AND THE GLASS FORMATION BOUNDARY Keith J. DeCarlo, Thomas F. Lam, and William M. Carty Kazuo Inamori School of Engineering, Alfred University Alfred, New York, USA ABSTRACT Chemical impurities typically segregate to the grain boundary in oxide ceramics and it is proposed that the grain boundary chemistry is dictated by the glass formation boundary in the system. For this to be possible it is necessary that the matrix grains readily dissolve into the grain boundary during liquid-phase sintering. Alumina is a model material for this study because the impurities are typical alkali and alkaline earth oxides plus silica and the glass formation ability of alumino-silicates is well known. This study examined the dissolution of alumina into a silicate glass through the use of glass-alumina diffusion couples and chemical mapping via WDS. The diffusion couples were heat treated to different temperatures, held for various times, then quenched. Samples were sectioned and polished for WDS analysis. The data shows alumina dissolution rate is rapid and that resulting chemistry of the diffusion couple interface was consistent with the glass formation boundary in the system studied. INTRODUCTION Solid state sintering is typically proposed to occur at approximately at 0.8 of the melting temperature (K). Alumina, however, has been observed to sinter to high densities at temperatures significantly lower (0.67-0.72) than those required for solid-state sintering and without magnesia additions.1' Due to these observations, it is proposed that many oxide systems, and in particular, refractory oxides such as alumina, typically sinter via liquid-phase mechanisms. This can only be true if alumina dissolves into the grain boundary phase efficiently. The dissolution rates of refractory solid oxides in a melt depend on three phenomena: 1) the solubility of the oxide in the melt, 2) the mobility of the reacting species within the melt, and 3) the mobility of the dissolved ion in the melt.3 The solubility of the refractory oxide in the melt is directly proportional to the mobility of the dissolved species. The rate-limiting step of a heterogeneous dissolution process is cither the introduction of the reacting species to the melt ("reaction-rate controlled") or the removal of the dissolved products from the interfacial region ("dissolution controlled"). The process of dissolution of alumina into the grain boundary phase is hypothesized to be "diffusion-controlled". Diffusion is modeled via Fick's second law:5 ^ = DS-± (1) a ' Sx1 where D, is the diffusion coefficient of the component in question, c¡ is the concentration of the diffusing component, and x is the direction of material flow. Application of Fick's second law frequently involves the error function. In the case of diffusion couples, the error function cannot be applied because the interdiffusion coefficient (interdiffusivity) of the system is not constant with changing concentration. The interdiffusivity takes into account the diffusivities of each diffusing component, which is known as the Darken relationship:6 D = NJ)I+NI~D;
(2)
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Dissolution of Alumina in Silicate Glasses and the Glass Formation Boundary
where D is the interdiffusivity of component 1 and 2, /V,is the mole fraction of component /, and D, is the intrinsic diffusivity of component /. The interdiffusivity from experimental data may be determined from a graphical technique commonly referred to as the Boltzmann-Matano analysis:5' '8
^-¿(f)>
(3)
The Boltzmann-Matano solution can be applied to a diffusion couple to calculate the interdiffusivity of the components. From the interdiffusivity it is possible to calculate the activation energy, Q, of the diffusion process. The relationship between diffusivity and temperature can be understood by the subsequent empirical equation:
D = DaexV[-j^
(4)
D0 and Q vary with material composition but are independent of temperature. The values of these two variables are obtained graphically by plotting the natural logarithm of interdiffusivity versus inverse temperature, yielding: lnD = lnD - — ( - ]
" R{T)
(5)
the slope is -Q/R and the x-intercept is In D„ (and R is the gas constant). Dissolution of alumina into the grain boundary during sintering also accounts for different grain boundary chemistries observed with sintering temperature.9 In order for the grain boundary chemistry to change during sintering, alumina must dissolve into the grain boundary efficiently. The original grain boundary chemistry typically consists only of the impurities within the system. The differences in impurity ion size and charge limit impurity solubility in the alumina lattice (or refractory oxide). If the working hypothesis is correct, as the system is heated, eutectic melts form first at low temperatures in the grain boundaries. The composition of the eutectic melt formed at the grain boundaries is dependent on the initial impurity ions (R+, R2+, Si4+, etc.). Upon further heating, the impurities not melted due to compositional restrictions are incorporated into the liquid phase. At this stage of sintering, the alumina grains can either be further dissolved or some of the dissolved alumina within the grain boundary melt can be precipitated based on the reaction paths predicted by phase equilibria. Once the impurity phase is completely melted, it is hypothesized that alumina continues to dissolve into the liquid following the composition path toward increasing alumina concentration, as illustrated schematically in Figure 1. The dissolution process of the grain into the grain boundary dictates the chemistry of the grain boundaries but is ultimately controlled by the glass formation boundary (GFB). If the final composition of the grain boundary phase lies within the glass formation region, the grain boundaries will be amorphous. In contrast, if the final composition of the grain boundary is outside the glass formation region crystals will precipitate in the grain boundary. It is hypothesized that when the chemistry of the grain boundary lies outside the glass formation region, the liquid phase from which the crystals precipitate will always be at the saturation limit, with respect to the GFB. If a crystalline phase incorporating Al + precipitates in the grain boundary liquid, the crystals will serve as a "sink" and grain dissolution will continue.
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Figure 1. The proposed dissolution path with increasing temperature (arrow) of AI2O3 into a grain boundary that contains S1O2 and CaO at a ratio of 1.4:1.0 (Si02:CaO). EXPERIMENTAL Diffusion couples were fabricated using a coarse-grained fused-cast alumina substrate (Monofrax'' M, Monofrax, Falconer, NY) and a commercial soda-lime-silicate glass sphere (Industrial Tectonics Inc., Dexter, MI). The fused-cast refractory substrate nominally consisted of 40% 01-AI2O3 and 60% β-Α1203. The typical chemistries are shown in Table I. Table I. Chemical Make-up of Diffusion Couple Materials Constituent AI2O3 Na 2 0 S1O2 CaO MgO Other
Monofrax M (weight %) 94 4.0 1.0 N/A N/A <1.0
Monofrax' M (mole %) 91.83 6.47 1.69 N/A N/A N/A
Glass (weight %) 1.0 15 72 9.0 3.0 N/A
Glass (mole %) 0.57 13.96 69.12 9.25 7.10 N/A
The glass spheres were bonded to the polished alumina substrates using a cyanoacrylate ester. Each diffusion couple was heat treated in air in an alumina crucible over a range of temperatures (1273, 1473, 1673, 1773, and 1873K) for varying times (30, 60, 120, 240, 360, and 480 minutes). The heating rate for all the trials was lOK/min and the samples were quenched in air when the soak time was completed. To obtain the aluminum concentration across the alumina-glass junction, each specimen was sectioned perpendicular to the glass-alumina interface, polished, and then mapped using wavelength
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Dissolution of Alumina in Silicate Glasses and the Glass Formation Boundary
dispersive spectrometry (WDS). The WDS maps were calibrated using the glass and alumina substrate as endpoints. Diffusion plots of mole % alumina versus the distance from the final interface were generated by studying each WDS composition map, each pixel was set to a known size. The final interface was determined from the WDS map based on the composition of alumina. Samples heat treated at 1773K with for 240 minutes and 1873K for 240 and 480 minutes were chemically etched using HF (10% HF, 0°C, 15 seconds) then imaged with SEM. The 1873K (480 minutes) sample was also used to determine the mineralogy of the crystallizing species via x-ray diffraction (XRD) analysis. RESULTS AND DISCUSSION Effect of Temperature (1273-1773K) Although the glass did not flow significantly at 1273K, intimate contact was maintained between the glass and the alumina substrate. At 1473K and above, however, the glass had a low enough viscosity to flow and coat the surface of the alumina substrate. No visual evidence of crystallization was observed in any sample below 1873K. The adhered glass layer crazed (cracked on cooling) in all the samples heat treated at 1273 and 1473K. At higher temperatures the adhered glass layer was intact (i.e., not crazed), indicating that the coefficient of thermal expansion (C.T.E.) mismatch between the alumina and the glass had decreased to the point that the glass C.T.E. was equal to or lower than that of the alumina. This is also consistent with significant alumina dissolution into the glass. The WDS chemistry maps of alumina concentration are presented in Figure 2 and show that as soak time increases, the penetration of aluminum into the bulk glass increases and the glass chemistry eventually becomes homogeneous. As temperature increased, as illustrated in the samples soaked at 1773K, the effect of soak time is essentially nil. Also, increasing time did not increase the maximum concentration of alumina in the glass. The rapid decrease in alumina concentration at various times and with various temperatures at large distances is an artifact of the edge of the glass layer. Effect of Temperature (1873K) It is proposed that the incorporation of alumina pushed the glass composition outside of the glass formation boundary. That is, within the phase diagram, 1873K falls outside of the GFB. Under the working hypothesis, crystallization would be expected to occur in these glasses. Figure 3a indicates that there is no crystallization evident upon cooling in the sample heat treated to 1773K. This supports the hypothesis that the glass chemistry has not moved outside of the glass formation region. Crystal formation for the sample heat treated to 1873K is evident in Figure 3b. It was not optically evident in the samples soaked at 1873K for times less than 240 minutes that crystallization had occurred, however in the 240 minute sample, crystals were evident in the SEM images, as illustrated in Figure 3b. The samples soaked for 360 and 480 minutes were clearly crystallized and the glasses were matted and opaque. The occurrence of crystallization indicates that the liquid composition lies outside of the GFB, but the time dependence is unexpected since the samples at times less than 360 minutes appear to have a similar alumina saturation level in the glass at approximately 33 mole % even though the 240 minute contained crystals. This may indicate that the shorter soak times contained crystals that were too small to be readily detected and that the concentration of these crystals is likely small. What is observed is that once crystals are formed, or at least after crystallization is extensive, alumina dissolution appears to increase significantly. This is evident by the opacity of the 360 and 480 minute samples and the correspondingly high alumina levels in the glass. Crystallization of an Al 3 'containing species serves as a sink, allowing alumina dissolution to continue. XRD analysis (shown for 480 minute sample in Figure 4) indicates that corundum and ß-alumina are the crystallizing species.
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(b)
(a) 100 90 80 70
_
^ ¡
8
3*
_ f ¡
eo 50
40
8
<"
30 20 10 0 •40
-20
0
20
40
100 90 80 70 60 50
40
30 20 10 0 -40 -20
60
0
Normalized Distance (μΓη)
90 BO
„ ? ¡
70
ε
4ο
E
50
¿7
;f
20 10 0
-20
0
20
40
60
SO
60
80 100 120 140 160 180
(d)
(c)
60
40
Normalized Distance (Mm)
100
t
20
100
120
HO
160
160
200
Normalized Distance (μΓη)
100 90 80 70 60 50 40
30 20 10 0 -60-40-20
0 20 40 60 80 100 120 140 160 180 200 Normalized Distance (μπι)
(e)
_ Í 1
¿7
$
100 90 80 70 60 50
Figure 2. Alumina concentration versus normalized distance (where "0" indicates the alumina-glass interface after quenching). Negative distance values indicate the alumina substrate; positive distances denote the glass layer. Each temperature is represented: (a) 1273K, (b) 1473K, (c) 1673K, (d) 1773K, and (e) 1873K. The different soak times studied are also shown in each graph.
40
30 20 10 0 -40 -20 0
20 40 60 80 100 120 140 160 180 200 Normalized Distance (μηι)
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Dissolution of Alumina in Silicate Glasses and the Glass Formation Boundary
Figure 3. Scanning electron micrographs showing the glass-substrate interface for samples heat treated at 1773K and 1873K for 240 minutes. The top images are backscatter micrographs of aluminaglass interface after chemical etching. The bottom images are WDS aluminum elemental scans (from unetched specimens). The inset provides a key to interpreting the color map: red indicates high concentration; blue indicates low concentration.
Figure 4. XRD pattern obtained from the thin section of the sample with a soak temperature of 1873K and a soak time of 480 minutes. The XRD specimen was cut from the diffusion couple so that there was no substrate attached, i.e., the XRD sample consisted of glass with the precipitated crystals.
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Alumina Concentration in the Glass The alumina concentration in the glass increases with increasing temperature but is essentially independent of time (Figure 5). At short times the concentration of alumina at the substrate-glass interface is typically greater, particularly at the lower temperatures, but rapidly equilibrates across the glass layer with time. The saturation levels are listed in Table II. (The alumina content for 1873K does not include the alumina levels measured for 240, 360, and 480 minutes, as these values represent the alumina levels in both the glass and the precipitated crystals). ~ 40 35 30 J5 CD 25
*
20
1 1510
Í
1200 1300 1400 1500 1600 1700 1800 1900 2000 Temperature (K) 80
Φ
o
¿ m g (1) XT.
70 60 50 40
,E 30 20
s
CD _l
O
10
_^ II <
103
102 Time (Minutes)
101
Figure 5. Measured average alumina content in the glass as a function of (a) soak temperature, and (b) soak time. Table II.
Measured Saturation Limit of AUCh in the Glass Temperature (K.) Average Alumina content (mole %) Standard Deviation
1273 11.25 3.42
1473 18.10 1.67
1673 29.90 2.50
1773 30.60 2.56
1873 32.97 2.05
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Dissolution of Alumina in Silicate Glasses and the Glass Formation Boundary
Interdiffusivity and Activation Energy Calculations The interdiffusivity of aluminum ions into the glass was calculated for each sample as a function of distance from the interface using the Boltzmann-Matano analysis discussed previously. The diffusion curves were modeled using a spreadsheet macro (Solver, Excel 2003 Microsoft Corp., Redmond, WA). Several equations were generated and the equation for each data set exhibiting a R value closest to 1.0 was selected. At least five points were modeled at a time and the last point was overlapped in the modeling to assure a smooth transition. Using the equations of the curve for the range fitted, the midpoint of the data was determined through integration of the curves. The Matano Interface, mid-point of the graph, was found by solving for the limits of integration which cause the areas of each side of the composition-distance graph to be equal. The curve was translated so the Matano Interface was at the y-intercept and the modeled curves were then reevaluated. The interdiffusivity was then calculated at different nonnalized concentration values as a function of the distance from the Matano Interface by determining the slope of the line and the area under the curve at each specific concentration. The interdiffusivity values for the different heat treatments were averaged and plotted versus inverse temperature (Figure 6) to obtain an activation energy value (Q) of 333 kJ-mole'1 from the slope (-Q/R). The plot demonstrates that the interdiffusivity values for each sample had a nominal range of two orders of magnitude, demonstrating the effect that concentration has on the value. As discussed earlier, the interdiffusivity was observed to be independent of soak time. -16 r -18 -20 « -ÍÍ!
F £·
-22 -24 -
> rn -w
¡t= TD
r
-
-?R -HI) -32 -34 -Sfi L 50.0
55.0
60.0
65.0
70.0
75.0
80.0
Temperature (K"1x105)
Figure 6. The aluminum interdiffusivity in the glass versus inverse temperature as calculated by the application of the Boltzmann-Matano solution (Equation 5) to the data in Figure 2.
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CONCLUSION The amount of aluminum dissolved into the glass is temperature dependent while the diffusion distance of the aluminum in the glass is time dependent. The rate-controlling step governing alumina dissolution is the diffusion of aluminum ions through the glass, so the dissolution of alumina into glass is "diffusion-controlled" process rather than "reaction-rate controlled" process. This implies that the rate of dissolution will be independent of particle size and surface area. Therefore, neither grain size nor grain morphology determine the grain boundary chemistry during sintering. The composition of the grain boundary phase produced from liquid-phase sintering depends only on the impurities in the system and sintering temperature. There is however a dependence of diffusion on temperature; at higher temperatures diffusion will occur faster due to two reasons: (1) more alumina will be dissolved creating a larger concentration gradient of alumina throughout the glass and (2) diffusivity increases at higher temperatures, causing the glass chemistry to homogenize more quickly. The activation energy of aluminum diffusion into SLS glass was determined to be 333kJ mol"1. As temperature increases, the alumina level in the glass increases following a line to alumina on a ternary phase diagram. If the glass composition exceeds the glass fonnation boundary, the conditions are then favorable for crystal nucleation and potentially growth. Crystal growth favors a long soak time, as demonstrated in the 1873K samples at times of 360 and 480 minutes. When the composition (and temperature) lies within the glass formation boundary, the sample remains amorphous. It is hypothesized that the precipitate within a grain boundary is dictated by the phase field in which grain boundary lies when outside of the glass formation boundary. FOOTNOTES *It is understood that the WDS is scanning for Al, not AI2O3, but in these samples, aluminum is always found in the oxide form. It is acknowledged that it is Al 3 ' is the diffusing species. For purposes of clarity, AI2O3 or alumina will be used to denote the aluminum in the glass. REFERENCES iM.N. Rahaman, Ceramic Processing and Sintering; p. 875. Marcel Dekker, New York, NY, 2003. :W.M. Carty, "Processing of Ceramic Fibers from Particle Suspensions"; Ph.D. Thesis. University of Washington, Seattle, WA, 1992. r.G.V. McCauley, Glass and Refractory Symposium, Am. Ceram. Soc. Bull., 4, 605-10 (1925). 4G.A. Pecoraro, How the Properties of Glass Melts Influence the Dissolution of Refractory Materials, Ceram. Trans., 141, 179-91 (2004). 5J. Crank, The Mathematics of Diffusion, 2 ed.; p. 414. Oxford University Press, Oxford, UK, 1975. (,L.S. Darken, Diffusion, Mobility, and Their Interrelation through Free Energy in Binary Metallic Systems, Trans. Am. Inst. Min. Metall Eng., 15, 184-201 (1948). ?P.G. Shewmon, Diffusion in Solids, Vol. 2; p. 203. Minerals, Metals, & Materials Society, Warrendale, PA, 1963. «D.V. Ragone, Thermodynamics of Materials, Vol. II; p. 242. John Wiley & Sons, Hoboken, NJ, 1995. <>P. Svancarek, D. Galusek, F. Loughran, A. Brown, R. Brydson, A. Atkinson, and F. Riley, Microstructure-Stress Relationships in Liquid-Phase Sintered Alumina Modified by the Addition of 5 Wt.% of Calcia-Silica Additives, Ada Mater., 54, 4853-63 (2006).
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THE EFFECT OF VOLUME FRACTION ON GRAIN GROWTH DURING LIQUID PHASE SINTERING OF TUNGSTEN HEAVY ALLOYS John L. Johnson1, Louis G. Campbell2, Seong Jin Park3, and Randall M. German4 'ATI Alldyne, 7300 Highway 20 West, Huntsville, AL 2 Eaton Corporation, VI Technology, 200 Westinghouse Circle, Horseheads, NY 3 Center for Advanced Vehicular Systems, Mississippi State University, 200 Research Blvd., Starkville, MS 4 College of Engineering, San Diego State University, 5500 Campanile Drive, San Diego, CA ABSTRACT Grain size distributions are determined for tungsten heavy alloys with compositions ranging from 35 to 93 wt.% tungsten after liquid phase sintering at 1500°C under microgravity conditions for isothermal hold times ranging from 1 to 600 minutes. The dependence of the grain growth rate constant on the solid volume fraction over the range of 0.048 to 0.858 is compared to the predictions of several grain coarsening models. Three-dimensional grain size distributions from these models are transformed into grain size distributions for two-dimensional crosssections for comparison with the experimental data. Chi-squared tests show that a coalescence model for grain growth fits the experimental observations better than solution-reprecipitation models even for dilute tungsten heavy alloys. INTRODUCTION Grain growth during liquid phase sintering occurs primarily via Ostwald ripening1, in which small grains dissolve, diffuse through the liquid, and reprecipitate on larger grains. Higher solid volume fractions increase both the probability of grain coalescence and the rate of grain growth. For diffusion-controlled grain growth, the mean grain size Gm during liquid phase sintering obeys the following relationship : Gl-G¡=Kt
(1)
where Go is the initial grain size, t is the sintering time, and K is the grain growth rate constant. Many models have been proposed for the grain size distribution and grain growth rate constant. Early models for grain coarsening were extrapolations of classic Lifshitz-Slyozov-Wagner (LSW) theory3'4 developed for spherical, non-contacting grains at a solid volume fraction near zero. In this case, the grain growth rate constant is given by: K
LSW - -^
-^Γ
(2)
where <5 is the diffusivity, C is the solubility of the solid grain atoms in the matrix, Ω is the molar volume of grain atoms, γ is the grain-matrix surface energy, R is the gas constant, and T is the absolute temperature. The probability density function (PDF) of the grain size G predicted by LSW theory is given by:
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Effect of Volume Fraction on Grain Growth during Sintering of Tungsten Heavy Alloys
| G P{G) =
2
e x p ^
0 + iG)" 3 (l-fG)"' 3
(3)
Ardell was one of the first to modify the LSW model to take into account finite solid volume fractions. His more realistic assumption on the diffusion geometry resulted in an altered kinetic equation. The resulting predictions better described the broader grain size distributions seen in experimental systems, but also showed a greater sensitivity of the grain growth rate constant to the solid volume fraction than seen experimentally. Davies et al. included statistical probabilities of encounters or grain coalescence events to modify the continuity equation of LSW theory. The result was an even broader grain size distribution and a lower sensitivity of the rate constant to the solid volume fraction. Brailsford and Wynblatt7 excluded coalescence events, but modified the medium in which the grains were placed to derive yet another kinetic equation. Instead of modifying LSW theory, Voorhees and Glicksman8, Marsh and Glicksman9, and Enomoto et al.m developed algorithms to solve the multigrain diffusion problem, but for very low solid volume fractions the results still approached the LSW result. DeHoff " developed a coarsening theory based on geometric quantities that introduced the concept of communicating neighbors to treat the interaction between grains. In comparison to LSW theory and its variations in which the diffusion length scale is related to the size of the grain, the communicating neighbor concept considered more realistic separation distances; however, the predicted grain size distribution was identical to Ardell's model for a solid volume fraction of 1.0. Takajo et al.12 developed a model for coarsening exclusively by coalescence, giving a broad grain size distribution, but did not derive a grain growth rate constant. More recently, German and Olevsky13 assumed a Rayleigh distribution for the grain size distribution and derived an analytical relationship for the grain growth rate constant using the contiguity to calculate the relative solid-state and liquid-phase contributions to coarsening. Testing of the model predictions with experimental results presents several difficulties. First, the PDFs in the original publications are normalized to different grain sizes (mean, median, critical, or LSW). Secondly, the PDFs describe three-dimensional (3-D) grain size distributions so they cannot be directly compared with the experimental data measured from two-dimensional (2-D) cross-sections. Thirdly, experimental observations of grain growth at low and medium solid volume fractions are limited due to density differences between the solid and liquid that result in gravity-induced grain segregation in most systems. Fourthly, large numbers of grains need to be measured to get good statistical comparisons, especially at the tail ends of the distributions. In this paper, we transform the 3-D grain size distributions from several models into distributions of 2-D cross-sections using the method of Takahashi and Suito14'15. We then renormalize the 2-D distributions to the median grain size. These model predictions are then compared with experimental data obtained from sintering dilute tungsten heavy alloys under microgravity conditions. THEORETICAL GRAIN SIZE DISTRIBUTIONS The function for transforming the PDF of the 3-D grain size distribution into that of 2-D cross-sections is14:
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p{d)--±)-jm=dD
(4)
where p(d) is the PDF of 2-D cross-sections, d is the cross-sectional grain size, Da is the average 3-D grain size, P(D) is the 3-D PDF, and D is the 3-D grain size. The cumulative distribution function (CDF) of 2-D cross-sections, c(d), is given by the following transformation function14: \4θΎ~άϊ
■ P(D)dD
dd) = \-±
(5) a
To normalize all grain size distributions to the median grain size din, it was first calculated from the 2-D CDF using Equation 5. The PDF of 2-D cross-sections was calculated using Equation 4 and normalized to d¡n by the relation: PÁ8) = dMp(d)
(6)
where p„(g) is the normalized 2-D PDF and g = d/du is the normalized grain size. The transformed PDFs for 2-D cross-sections from several models are plotted in Figure 1. For negligibly small solid volume fractions, Ardell's PDF5 and the Brailsford and Wynnblatt (B&W) PDF'' are identical to the LSW PDF3'4, which is the narrowest distribution. As the solid volume fraction increases to 1.0, Ardell's PDF becomes identical to DeHoff s PDF11. B&W PDFs are plotted for solid volume fractions of 0.2, 0.5, and 0.8. The solutions for the PDFs of Davies et al.6, Voorhees-Glicksman8, Marsh-Glicksman9, and Enomoto10 are numerical. Although not plotted, they follow a similar pattern with solid volume fraction as Ardell's PDFs and the B&W PDFs. In general, the models predict that as the solid volume fraction increases, the probability density function widens. The coalescence model of Takajo et al.12 gives the broadest theoretical distribution, but it is not as wide as the empirically fit Rayleigh distribution. EXPERIMENTAL PROCEDURES Tungsten heavy alloys with W contents ranging from 35 to 93 wt.% and Ni:Fe ratios of 7:3 were liquid phase sintered under microgravity conditions during three missions of the Space Shuttle Columbia: the Second International Microgravity Laboratory (STS-65, July 1994), the first flight of the First Microgravity Science Laboratory (STS-83, April 1997), and its reflight (STS-94, July 1997). The samples were heated at a rate of 18°C/minute. A peak sintering temperature of 1507±5°C was maintained for 1 to 600 minutes. The samples were cooled at a controlled rate of 3°C/minute to a temperature of 1400°C, well below the matrix solidification temperature of 1465CC, and then freely cooled to ambient temperature. Identically prepared samples were also sintered in ground-based experiments for comparison of the effects of gravity. After completion of the sintering experiments and return of the cartridges to Earth, the samples were removed and cross-sectioned from the top to bottom plane (the top orientation was defined by the parallel ground-based experiment). The sections were mounted, polished, and sputter coated with platinum oxide to enhance contrast16. Image analysis was performed by
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Effect of Volume Fraction on Grain Growth during Sintering of Tungsten Heavy Alloys
Clemex (Longueuil, Canada) Vision PE 3.5 software. The W grain size was determined by measuring the area of each grain and calculating the average circular diameter. A prior publication17 describes the procedure in more detail.
Figure 1. Model predictions for 2-D grain size distributions normalized to the median crosssectional grain size. EXPERIMENTAL RESULTS Mosaics of the microstructures of 35, 78, and 93 wt.% W are given in Figure 2 for both microgravity sintered and ground-based samples. The W grains settled in the ground-based 35W and 78W samples, while microgravity conditions permitted the processing of samples with uniform solid volume fractions for these compositions. The grains are generally well dispersed, although the grains in the 35W sample still tend to cluster and form chain-like structures due to agglomeration forces. No difference is seen between the two 93W samples. The measured microstructural parameters are summarized in Table I. The W volume fraction of the 78W samples stays relatively constant with sintering time, except for the 45 minute sample, which contained excess porosity. The grain size increases with W content. The grain size of the 35W sample sintered for 180 minutes was near that of the 78W sample sintered for 120 minutes, while the 93W sample sintered for 120 minutes was substantially coarser than either of these two samples.
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Figure 2. Mosaics of micrographs of (a) ground-based 35W sintered for 180 minutes, (b) 35W sintered in microgravity for 180 minutes, (c) ground-based 78W sintered for 120 minutes, (d) 78W sintered in microgravity for 120 minutes (e) ground-based 93W sintered for 120 minutes, and (f) 93W sintered in microgravity for 120 minutes
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Table I. Measured microstructural parameters for the microgravity sintered samples Median Max. Sintering #of Solid Liquid grain Maximum grain /median wt.% time measured volume volume size size grain size (min) grains W fraction fraction Porosity (μιη) (μηι) 35W 180 795 0.001 0.951 56.3 2.03 0.048 27.6 5382 0.000 78W 1 0.569 10.6 0.430 34.0 3.17 6167 0.012 0.421 2.81 78W 15 0.568 16.9 45.9 6374 2.42 78W 45 0.460 0.169 18.8 0.370 46.8 6377 0.441 2.52 78W 120 0.551 0.009 26.7 68.1 6674 2.64 0.020 0.463 79.5 78W 180 0.515 30.1 8419 0.562 0.007 45.3 0.433 101.3 2.27 78W 600 0.144 85.4 93W 120 7308 0.858 0.001 32.7 2.53 DISCUSSION Grain Growth Rate Constant The experimental data presented in the previous section enable analysis of grain growth for compositions that cannot be sintered in standard gravity due to grain settling. The cube of the grain size as a function of sintering time is plotted in Figure 3 for the microgravity sintered samples. For 78W, linear regression gives a grain growth rate constant of 2.42 μητνβ with an initial grain size of 11.11 μηι and a statistically significant correlation coefficient of 0.9996. The calculated initial grain size corresponds very closely to the measured average grain size (10.97 μπι) of the 78W sample sintered in microgravity for 1 minute. Using the same value for the initial grain size of 35W and 93W gives grain growth rate constants of 1.74 and 5.29 μπι'/β, respectively.
Figure 3. Grain growth of microgravity sintered 35W, 78W, and 93W follow a cubic relationship with time.
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The solid volume fraction of the 35W sample is only 0.048, its grains are nearly spherical, and grain growth is by a diffusion-controlled process. These conditions are close to those assumed by the LSW model, so its rate constant of 1.74 μηΛβ is expected to be near KLsw given in Equation 2. Using the relationship from the model of German and Olevsky : Κ = Κ^(\-ν.)-^
(7)
where Vs is the solid volume fraction, to extrapolate to a solid volume fraction of zero gives a value of 1.60 μπι3/8 for KLSW-
The solubility of W in Ni-Fe at 1500°C is estimated as 0.10 atomic fraction18, the W molar volume is 9.58· 10"6 m3, and the surface energy of W grains in liquid Ni-Fe is estimated as 0.8 J/m2 19. The greatest uncertainty is the diffusivity, which is often estimated from sintering studies and is typically given to the nearest order of magnitude. Using this value to back calculate the diffusivity in Equation 2 gives 4.3-10"9 m2/s, about twice that of the diffusivity of 2.4-10"9 m2/s determined by Leonard et al20 for W atoms in liquid Ni at 1500°C. The slight agglomeration of the grains for the 35W sample may have resulted in an increase in the rate constant due to locally higher volume fractions, but the extrapolated rate constant of 1.60 μπι3/8 is still a good approximate value for KLSWThe rate constants for the microgravity sintered samples are normalized to the extrapolated value for KLSW and compared with the predictions of the previously described models in Figure 4. The model of Davies et al.6 fits the data well for low solid volume fractions, but significant deviations occur at solid volume fractions above about 0.75. The DeHoff model exaggerates grain growth behavior at both low and high solid volume fractions. The data show that the German and Olevsky model relating the rate constant to the -2/3 power of the liquid volume fraction is valid for the entire range of solid volume fractions investigated.
Figure 4. Model predictions for the grain growth rate constant as a function of solid volume fraction. Data for microgravity sintered 35W, 78W, and 93W are given for comparison.
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Effect of Volume Fraction on Grain Growth during Sintering of Tungsten Heavy Alloys
Grain Size Distribution Histograms of the grain size data for 35W, 78W (sintered for 120 minutes), and 93W are plotted in comparison to the model predictions in Figures 5, 6, and 7. The Takajo model fits the upper tail of the 93W sample very well. For the 35W and 78W samples, the upper tails of the experimental distributions fall between the Ardell/DeHoff and Takajo models, but their peaks are shifted down and to the left of the experimental peaks. On the other hand, the B&W models show a better fit to the peaks, but the experimental distributions are much wider due to the upper tail. The B&W models fit the data better than the LSW model, but little improvement is seen with consideration of an increase in solid volume fraction from 0.2 to 0.8. The Rayleigh distribution does not fit the upper tail as well as the other models. Chi-squared (χ2) tests ' were used to determine the goodness-of-fit between the experimentally measured grain size distributions and the theoretical distributions. Bin widths were determined from the difference between the 75th percentile and 25th percentiles of the grain size data by population2 . Based on this calculation, all of the experimental distributions had a bin size of 0.06, except for the 78W sample sintered for 1 minute and the 35W sample, which had bin sizes of 0.09 and 0.15, respectively, due to variations in experimental grain counts. Since the χ2 test generally requires expected counts in all bins to be greater than or equal to five21, lowfrequency bins were added to the next largest bin size, summing both expected and observed counts at the larger bin size for calculation of the χ2 test statistic. Nearly all low-frequency expected bins were at the upper tail of the grain size distributions.
Figure 5. Histogram of the normalized grain size data for the 35W sample sintered for 180 minutes in microgravity compared to theoretical grain size distributions transformed into 2-D probability density functions.
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Figure 6. Histogram of the normalized grain size data for the 78W sample sintered for 120 minutes in microgravity compared to theoretical grain size distributions transformed into 2-D probability density functions.
Figure 7. Histogram of the normalized grain size data for the 93W sample sintered for 120 minutes in microgravity compared to theoretical grain size distributions transformed into 2-D probability density functions.
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The calculated χ2 test statistics are summarized in Table II. None of the models produced a statistically significantly fit for a significance level a of 0.05; however, ranking the χ2 test statistics gives some insight into the relative model fits. The best fits are achieved by the Ardell/DeHoff and Takajo models. With the exception of the sample sintered for 1 minute, the fits are relatively consistent for all of the 78W samples. For the 93W sample, the Takajo model gives a much better fit than the other models. Even at the dilute solid volume fraction of the 35W sample the coalescence model of Takajo gives a better fit than the LSW and B&W Ostwald ripening models. Table II. Summary of χ2 test statistics for the fit of the different theoretical distributions in comparison to the experimentally measured distributions. Sintering #of Compo- time grains sition (min) 1 5382 78W 15 6167 78W 45 6374 78W 120 6377 78W 180 6674 78W 600 8419 78W
35W 93W
180 120
795
7308
LSW
B&W
Vs=0.2 37893 2847 3166 2342 10317 7418 19486
49179 37415 45420 35049 45066 42384 78453 1390 403
B&W
B&W Ardell/ Vs=0.5 Vs=0.8 DeHoff 37544 15761 6775 387 2850 1245 256 3054 1190 1904 208 755 296 3683 1471 334 2338 1528 871 8051 3384 158
102
36
Takajo Rayleigh 1285 580 1005 229
119 213 159 305 84 54
839 978 856
1378
663 103
Linear combinations of the Takajo model with the LSW and B&W models were evaluated for a possible better fit to the 78W data. The coefficients were hypothesized to provide a measure of the relative contributions of coalescence and solution-reprecipitation to grain coarsening. The coefficients were optimized to give the lowest χ2 test statistics, but the fits are only slightly better than the Takajo model alone. The experimental grain size distributions are broader than predicted by Ostwald ripening models indicating a significant role of coalescence even at solid volume fractions as low as 0.048. The coalescence model of Takajo best fits the experimental distributions, but does not completely describe them. The experimental data give directions for developing new grain growth models. Both solution-reprecipitation and coalescence must be considered. Their relative contributions have been linked to the contiguity by German and Olevsky, but a more sophisticated relationship is needed. While the Rayleigh distribution function provides a convenient means of analyzing grain size distributions, more complicated functions are needed to accurately express them. Any new grain growth model should demonstrate a -2/3 power dependence of the grain growth rate constant on the liquid volume fraction. CONCLUSIONS Determination of grain growth rate constants for dilute tungsten heavy alloys confirms that they follow a -2/3 power dependence on the liquid volume fraction to solid volume fractions as low as 0.048. Extrapolation of grain growth rate constants to a solid volume fraction of zero gives a value near that predicted by LSW theory for Ostwald ripening. Transformation of theoretical three-dimensional grain size distributions to distributions of two-dimensional crosssections allows direct comparison to the experimental data. The coalescence model of Takajo et
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al. fits the experimentally measured grain size distributions better than models for solutionreprecipitation, indicating a significant coarsening contribution of coalescence even for dilute solid volume fractions, but none of the models completely describe grain growth. New grain coarsening models are needed that include both coalescence and solution-reprecipitation, and accurately predict the dependence of the grain growth rate constant on the solid volume fraction. ACKNOWLEDGMENTS This research was supported by the National Aeronautics and Space Administration under continuing grants from 1985 to 2006. REFERENCES 'P.W. Voorhees, Ostwald Ripening of Two-Phase Mixtures, Ann. Rev. Mater. Sei., 22, 197-215 (1992). 2 R.M. German, Sintering Theory and Practice, Wiley-Interscience, New York, NY (1996). 3 I.M. Lifshitz and V.V. Slyozov, The Kinetics of Precipitation from Supersaturated Solid Solutions,/. Phys. Chem. Solids, 19, 35-50 (1961). 4 C. Wagner, Theory of Precipitate Change by Redissolution, Z. Elektrochem., 65, 581-591 (1961). 5 A.J. Ardell, The Effect of Volume Fraction on Particle Coarsening: Theoretical Considerations, Acta Metall, 20, 61-71 (1972). 6 C.K.L. Davies, P. Nash, and R.N. Stevens, The Effect of Volume Fraction of Precipitate on Ostwald Ripening, Acta Metall, 28, 179-189 (1980). 7 A.D. Brailsford and P. Wynblatt, The Dependence of Ostwald Ripening Kinetics on Particle Volume Fraction, Acta Metall, 27, 489-497 (1979). 8 P.W. Voorhees and M.E. Glicksman, Ostwald Ripening during Liquid Phase Sintering - Effect of Volume Fraction on Coarsening Kinetics, Metall. Trans. A, 15A, 1081-1088 (1984). 9 S.P. Marsh and M.E. Glicksman, Kinetics of Phase Coarsening in Dense Systems, Acta Metall, 44, 3761-3671 (1996). 10 Y. Enomoto, K. Kawasaki, and M. Tokuyama, Computer Modeling of Ostwald Ripening, Acta Metall, 35, 907-913 (1987). n R.T. DeHoff, A Geometrically General Theory of Diffusion Controlled Coarsening, Acta Metall. Mater., 39, 2349-2360 (1991). 12 S. Takajo, W.A. Kaysser, and G. Petzow, Analysis of Particle Growth by Coalescence during Liquid Phase Sintering, Acta Metall, 32, 107-113 (1984). 13 R.M. German and E.A. Olevsky, Modeling Grain Growth Dependence on the Liquid Content in Liquid-Phase-Sintered Materials, Metall. Mater. Trans. A, 29A, 3057-3067 (1998). 14 J. Takahashi and H. Suito, Random Dispersion Model of Two-Dimensional Size Distribution of Second-Phase Particles, Acta Mater., 49, 711-719, 2355 (2001). 15 J. Takahashi and H. Suito, Evaluation Method of the Accuracy of the Three-Dimensional Size Distribution Estimated from the Schwartz-Saltykov Method, Metall. Mater. Trans. A, 34A, 171181 (2003). 16 A. Upadhyaya, B. Ozkal, and R.M. German, Application of Interference Layering for Metallography of Sintered Alloys, P/M Science & Technology Briefs, 1, 17-21 (1999).
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L.G. Campbell and R.M. German, Gravitational Effects on Microstructures in Liquid Phase Sintering, Advances in Powder Metallurgy & Paniculate Materials, J. Engquist and T.F. Murphy (eds.), Metal Powder Industries Federation, Princeton, NJ, 8.10-18.28 (2007). 18 P. Villars, A. Prince, and H. Okamoto, Handbook of Ternary Phase Diagrams, vol. 8, ASM International, Metals Park, OH (1995). 19 Smithells Metals Reference Book, 8th ed., W.F. Gale and T.C. Totenmeier (eds.), Elsevier and ASM International, New York, NY (1983). 20 J.P. Leonard, T.J. Renk, M.O. Thompson, and M.J. Aziz, Solute Diffusion in Liquid Nickel Measured by Pulsed Ion Beam Melting, Metall. Mater. Trans. A, 35A, 2803-2807 (2004). 2I R.M. Bethea, B.S. Duvan, and T.L. Boullion, Statistical Methods for Engineers and Scientists, Marcel Dekker, New York, NY (1985). 22 A.J. Izenman, Recent Developments in Nonparametric Density Estimation, J. Amer. Stat Assoc, 86, 205-224 (1991).
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IN-SITU INVESTIGATION OF THE COOPERATIVE MATERIAL TRANSPORT DURING THE EARLY STAGE OF SINTERING BY SYNCHROTRON X-RAY COMPUTED TOMOGRAPHY R. Grupp*, M. Nöthe**, B. Kieback**, J. Banhart* * Helmholtz Centre Berlin for Materials and Energy, Berlin, Germany ** Technical University Dresden, Institute for Material Science, Dresden, Germany ABSTRACT A better fundamental understanding of the sintering process requires experimental data describing in 3D particle rearrangement processes, especially particle rotations. Therefore, synchrotron computed tomography (SCT) is used to investigate the particle rearrangements during sintering. The specimens consisting of spherical monocrystalline copper powder were measured in a special in-situ furnace. The data is analyzed by a custom image analyzing software based on photogrammetric methods to determine the coordination, the centre approach and rotation of each particle in a 3D specimen. The sintering of monocrystalline copper spheres analyzed using SCT is compared to literature data of different test arrangements and dimensions. INTRODUCTION Sintering is the most essential processing step of powder metallurgical production. Heat treatment of an assembly of loose or compacted particles results in the growth of interparticle bonds and shrinkage of the component. The driving force for the growth of sintering necks is the need to minimize the surface area and surface energy. The material transport takes place by diffusion of vacancies from the neck surface to the contact grain boundary or the particle surface. These mechanisms have been investigated since the 1940's and are now well understood. Extensive reviews have been written by J.E. Geguzin1, H.E. Exner2'3, W. Schatt and R.M. German5. Beside neck growth, cooperative material transport, e.g. by rotation, also contributes to the densification of sintered components. In the literature, asymmetric sinter necks4, tensions due to nonuniform neck growth6 or enhanced grain boundary energies due to the different crystallographic orientations of the contacting particles7 are discussed and thought to be the major driving forces for rotations. However, a fundamental understanding of these processes has not been achieved because of the inaccessibility of experimental data by conventional analysis. To investigate these rotations in three-dimensional samples, high-resolution synchrotron X-ray computed tomography (SCT) is the only adequate method. First investigations of the sintering process using SCT have been made by A. Vagnon et al.8 and O. Lame et al.9. Measurements of the cooperative material transport during sintering have been made by M. Nöthe et al.10. By combining synchrotron tomography with methods of photogrammetric image analysis it becomes possible to perform in-situ measurements and to obtain quantitative data of the particle rearrangement during sintering inside of three-dimensional specimens. EXPERIMENTAL Three-dimensional specimens for tomographic measurements have been produced from monocrystalline spherical copper particles. These particles were produced based on the Sauerwald process ' from polycrystalline copper powder provided by the company ECKA Granulate GmbH & Co. KG. Selection of the spherical particles was accomplished by rolling the particles down a tilted glass panel or mirror. Asymmetric particles rolled down in a curve caused by their geometry and could be rejected.
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In preparation for the tomography measurements the loose packing of particles with radii of approximately 30μπι were filled into a 1.3mm diameter silica capillary and fixed in a pre-sintering step at 600°C. After this step, the capillary was removed to achieve free sintering without any external influences during the following measurements. Preliminary measurements of samples in silica capillaries showed an approximately linear increase of rotation, density and centre approach as a result of the different thermal expansion coefficients of silica and copper. Thus measurements of free sintering samples are necessary. The synchrotron tomography measurements were conducted at the European Synchrotron Radiation Facility (ESRF) in Grenoble (France) at the beamline ID 15 A. The use of a white beam (polychromatic radiation) allows the measurement of 851 radiograms within a time of just 56 seconds which is sufficient to obtain one entire tomogram of high quality. A complete turn including the radiograms, 51 flatfield measurements, the turn back of the rotation stage and the readout of the CCDcamera required 3 minutes and 32 seconds. Due to the short measuring times it was possible to heat the specimens up continuously in a special in-situ furnace during the investigations. Two specimens were sintered with a heating rate of 1 OK/min. One of the samples was sintered with additional dwell times of one hour at 650°C, 750°C, 850°C, 950°C and 1050°C.
Figure 1: Tomography setup including the in-situ furnace. Here, the furnace has been lifted to change the sample. The sintering process took place in a reducing atmosphere consisting of 96% He and 4% H2. Since a rotation of the specimen was necessary a hole at the bottom of the furnace was required. Therefore an aluminium tube was installed from the manipulation stage close to the bottom of the furnace (Figure 1). By passing inert gas into the bottom of the aluminium tube it was possible to achieve a small overpressure in the tube and in the furnace chamber. This results in a gas flow out of the 3mm gap between tube and furnace and no oxygen could enter into the furnace chamber which enables a constant reducing atmosphere. The analysis of the measured data was performed by custom made image analysis software based on photogrammetric methods. This software allows detecting the centre positions of all copper spheres in a tomogram by searching for homogeneous spherical areas exceeding a given grey value12. The radii of these areas have to be slightly smaller than the radii of the measured spheres. The results are the approximate particle centres. In a next step, the precise positions of surface points are determined by interpreting virtual grey value lines from the detected centres to beyond the surface of the particles. Using these determined points the exact positions of the centres can be calculated.
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Furthermore the software is able to detect coordination partners and can track every single sphere across several sintering steps. Using the given data it is possible to investigate the rotations of the particles with respect to their coordination partners, the relative density, the centre approach and the shrinkage of the specimen. The contact partners are detected by analysing the grey value lines between a particle and its nearest neighborhood. The rotations are calculated by fitting each sphere and its coordination partners to their positions in another sintering step and evaluating the average change of the angle between the coordination partners. The error of the analysis is about 0.075 voxels. This corresponds to approximately 0.1°. The centre approach is calculated by the distance to the next coordination partner. Thus, new and broken contact partners during sintering are excluded from the analysis. RESULTS AND DISCUSSION Figure 2 shows the cumulative rotation in two specimens exposed to a heating rate of 10K/min. The figure displays almost no rotation up to 950°C. At this temperature the sample with dwell time shows first small rotations. Only above the dwell time at 1050°C a significant increase of cumulative rotation occurs. However, the value of the rotation of less than 0.7° after one hour dwell time is still very small compared to measurements on a plate-sphere-model13 or the one-dimensional measurements on a row of monocrystalline copper spheres by K.-P. Wieters. In both cases rotation values of up to 25° have been detected. Furthermore, these big rotations were measured between 600°C and 900°C14. In this range of temperature the sintering contact areas are still very small and the diffusion rates increase. Thus the rotations driven by misorientations of the contact partners increase as well. Caused by the high degree of freedom the driving force was sufficient to initiate some rearrangements. In this study, the particles possess between 6 and 7 contact partners on average (see Figure 4). Because of these high coordination values of the particles the driving forces counteract one another and, as a result, hamper particle rearrangements. Furthermore, the particle rearrangement shown in Figure 2 is correlated with the particle centre approach (see Figure 3). Thus, the contribution of the rotation shown in Figure 2 due to the misorientations in the contact areas is very small, but occurs by unequal centre approach during sintering at high temperatures. The rearrangement caused by misorientations can be negligible during solid state sintering in three-dimensional specimens.
temperature [°C] Figure 2: Differential and cumulative rotation vs. temperature. Monocrystalline spherical copper particles with radii of 30μιη. Heating rate: 10K/min. Dwell time 60min for each temperature.
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temperature [°C] Figure 3: Centre approach vs. temperature. Monocrystalline spherical copper particles with radii of 30μπι. Heating rate: 10K/min. Dwell time 60min for each temperature. Thermal expansion has already been subtracted from the curves in Figure 3. The small decrease up to 950°C can be explained by the small rotation values in the same temperature range (Figure 2). Above 950°C the centre approach starts and is stronger than the potential expansion induced by particle rearrangements. A steep increase follows at 1050°C. During heating up to 950°C no significant difference between the two specimens could be detected. The continuously heated sample shows a centre approach and rotation above 1000°C similar to the specimen heated with dwell times above 950°C. The reason for this behavior is the dwell time of 60min. In this additional time centre approach at lower temperatures and a simultaneous rotation takes place.
temperature [°C] Figure 4: Number of contact partners vs. temperature. Monocrystalline spherical copper particles with radii of 30μηι. Heating rate: 10K/min. Dwell time 60min each.
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The sample sintered with dwell times shows a decrease of coordination at the beginning of each heating period up to 950°C. This behavior is correlated with the negative centre approach in the mentioned temperature range. This demonstrates that even very small rotation values below 950°C influence the sintering process. The influence of the cooperative material transport during the heating periods exceeds the centre approach. In contrast, the centre approach during dwell periods is more intense than the dilatation of the specimen caused by cooperative material transport. CONCLUSION High resolution synchrotron tomography was found to be an adequate method to investigate the cooperative material transport in three-dimensions. Results obtained on one-dimensional samples cannot be transferred to 3D. The reason is the number of contact partners. One-dimensional specimens have fewer restrictions regarding their degrees of freedom, while a particle in a three-dimensional sample cannot rotate without moving its contact partners too. This is why the measured rotations are comparatively small. Further experiments showed a kind of intrinsic rotation of the particles during sintering around their own centre. This kind of rotation cannot be measured with the presented method. Therefore, in new specimens each sphere has been marked using a Focused Ion Beam. By tracking these markers the measurement of self rotations becomes possible. Results of these further measurements will be published soon. ACKNOWLEDGEMENTS The authors would like to thank the Helmholtz-Gemeinschaft for the financial support of the research in the project VI-PNAM (Virtual Institute - Photon and Neutron Research on Advanced Engineering Materials). We are grateful to ECKA Granulate GmbH & Co. KG for the supply of copper powder. Furthermore, thanks to M. Di Michiel for the support at ESRF. REFERENCES 1 J.E. Geguzin, Physik des Sinterns, VEB Deutscher Verlag für Grundstoffindustrie, Leipzig (1973). 2 H.E. Exner, Grundlagen von Sintervorgängen. Berlin/Stuttgart: Gebrüder Borntraeger (1978). 3 H.E. Exner, T. Kraft, Review on Computer Simulations of Sintering Processes. Proc. PM World Congress, Granada, 278-82 (1998). 4 W. Schart, Sintervorgänge, VDI-Verlag (1992). 5 R.M. German., Powder Metallurgy Science, Metal Powder Industries Federation, Princeton (1984). 6 P.C. Eloff, F.V. Lenel, The Effects of Mechanical Constrains upon the Early Stages of Sintering, Modern Developments in Powder Metallurgy, 4, 291-302 (1971). 7 A.P. Sutton, R.W. Balluffi, Interfaces in crystalline materials, Oxford University press (2003). 8 A. Vagnon, J.P. Riviere, J.M. Missiaen, D. Bellet, M. Di Michiel, C. Josserond, D. Bouvard, 3D statistical analysis of a copper powder sintering observed in situ by synchrotron microtomography, Acta Materialia, 58,1084-93 (2008). 9 O. Lame, D. Bellet, M. Di Michiel, D. Bouvard, Bulk observation of metal powder sintering by X-ray synchrotron microtomography; Acta Materialia, 52, 977-84 (2004). I M. Nöthe, M. Schulze, R. Grupp, B. Kieback, A. Haibel, Investigation of sintering of spherical copper powder by micro focus computed tomography (]iCT) and synchrotron tomography, Materials Science Forum, 539-543, 2657-62 (2007). II F. Sauerwald, L. Holub, Kristallisation zwischen möglichst weitgehend im Strukturgleichgewicht befindlichen Oberflächen; Zeitschrift ßir Elektrochemie und angewandte physikalische Chemie, 39, 750-53 (1933). 12 R. Grupp, Thesis, TU Dresden, in preparation.
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S.-W. Chan, R.W. Balluffi, Study of Energy vs. Misorientation for Grain Boundaries in Gold by Crystallite Rotation Method - 1 . [001] Twist Boundaries, Acta Metallurgica, 33, 1113-19 (1985) 14 K.P. Wieters, Korngrenzeneinfluß beim defektaktivierten Festphasensintem, Thesis, TU Dresden (1988).
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GEOPOLYMERS SINTERING BY OPTICAL DILATOMETRY Elie Kamseu*, Cristina Leonelli*, and Dan S. Perera" *Dept. of Materials & Environmental Engineering, University of Modena and Reggio Emilia, Modena, Italy. "Institute of Materials Engineering, ANSTO-Australian Nuclear Science and Technology Organisation, Sydney, NSW, Australia.
I. INTRODUCTION The extensive development of new technologies for the production of inorganic materials is balanced between property requirements and cost. For instance, inorganic materials with stable mechanical properties and thermo-physical properties are ideal requirement for many industrial applications. Geopolymer materials have been investigated for this purpose, as alternative low cost materials for thermal applications due to their low temperature production combined with low linear shrinkage, good mechanical properties with short term curing. Geopolymer materials are chains of alumino-silicates with alkali ions (Na+, K+, Cs+, ...) as charge balance for the negative charge of the AIO4. In the geopolymer structure, polysialates are homogeneously dispersed in the matrix where alkali ions take precise position for the chemical equilibrium of the structure and being part of the structure. In contrast, alkali ions are chemical elements with poor resistance to high temperatures. They are generally present in traditional alumino-silicates refractory materials and forming liquid phase at high temperatures. For example, the eutectic temperature of K2O-AI2O3-S1O2 system is 9850C'. Kaolin is one of the principal sources of alumino-silicates for geopolymer products. Reports regarding kaolinite-mullite reactions series show that the presence of mineralizors can reduce the temperature of mullite formation considerably2. The reaction mechanism of geopolymerisation involves the dissolution of Al and Si in the alkali medium, transportation of dissolved species, followed by polycondensation, forming a 3D network of alumino-silicate structure. Condensation occurs between alumino-silicate species or silicate species themselves, depending on the concentration of Si in the system. When Si/Al > 1, the silicate species formed as a result of hydrolysis of S1O2, tend to condense among themselves to form oligometric silicates which condense with Al(OH)4_ forming rigid 3D geopolymeric structures3'4'5. Typically, better strengths are obtained for mixtures with S1O2/AI2O3 molar ratios in the range of 1.65-2.10 with a Na20/Si02 ratio near 1. Higher amounts of hydroxyl ions facilitate the dissociation
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of different silicate and alumínate species, thus promoting further polymerization0. NaOH promtotes Na+ ions with strong pair formation (better dissolution) of silicate oligomers. KOH promotes K+ that favors the formation of larger silicate oligomers with which Al(OH)4" prefers to bind. Therefore in KOH solutions more geopolymer precursors exist resulting thus in better setting and stronger compressive strength since K+ would promote a high degree of condensation7. It was found that by combining NaOH and KOH, highly dissolved and cross linked samples of geopolymer materials can be obtained. The multiple alkali sources can act in a synergistic way to promote samples of optimal characteristics3'4. Geopolymer materials contain a considerable percentage of alkali ions, which should increase the sintering. Hence, use of geopolymer materials for high temperature applications is a challenge. Composition, effectiveness of geopolymerisation, physical and mechanical properties of matrixes developed are factors that should be considered when geopolymers are to be used for high temperature applications. In this work, we present some results of sintering behavior of two compositions of geopolymer materials using respectively sodium and potassium solutions (hydroxide and silicate). The aim of the work was to investigate on the relation of optimum dissolution and polycondensation and resistance at high temperature. Metakaolin was used as the principal source of alumino-silicate. The choice was based on the fact that it is the cheapest source of alumino-silicate that presents a higher degree of purity. Metakaolm improves mechanical strength and reduces the transport of water and salts in the final product8. It is important in the production of geopolymer materials for applications such as adhesives, coatings and hydroceramics . II. MATERIAL AND EXPERIMENTAL PROCEDURE High purity Kaolin from a commercial ceramic company in Italy was calcined at 700°C for 4 h to produce metakaolin. It was mixed with 8M sodium and potassium hydroxide together with sodium and potassium silicates with Si02/NaiO and Si02/Na20 molar ratio of ~3 (Table 1).
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Table I. Chemical composition (wt%) of the starting raw materials used to prepare geopolymers. Reactant
Si0 2
Na silicate
27.00
A1 2 0 3
Na 2 0
K20
Fe 2 0 3
Ti0 2
8.71
Supplier INGESSil Verona, Italy
K-silicate
INGESSil
14.07
26.89
Verona, Italy Standard kaolin
44.37
36.12
0.10
0.82
0.97
1.52
Ceramic
Co,
Italy
A mixture of sodium hydroxide and sodium silicate was prepared by volumetric mixing in the proportion 1:1. Similar mixture was made for potassium hydroxide and potassium silicate. The solution was then agitated for homogenization for 5 min and used to dissolve the metakaolin obtained from the calcination of kaolin at 700°C for 4h. These resultant pastes were ball milled for 10 min to apparent density of = 1.5 g/cm3 in a porcelain jar and poured into plastic moulds for 24 h curing at ambient temperature. Samples were named RGP-Na and RGP-K. They sample were dried at room temperature for a week before submitting to differential thermal analysis (DTA), thermo gravimetrical analysis (TGA ) and differential scanning calorimetry (DSC) and optical dilatometry. The DTA/TGA,DSC analyses was performed using a standard method (with a speed of 10°C/min) while the optical dilatometry were performed using MISURA HSM ODHT model 1600/80 with a speed of 10°C/min. The two samples were also heated from 200 to 1300°C. XRD analysis was used to study the phase evolution up to vitrification. III. RESULTS From the DTA/TGA (Figure la) and DSC (Figure lb) curves, it can be observed that geopolymer materials present peaks of dehydroxylation at 130°C. The peak is more important for RGP-Na compared to RGP-K. The TGA curve indicate a weight loss of 13% for RGP-Na and 9% for RGPK. From 200°C, these values remain constant up to 1300CC. The endothermic peaks correspond to the loss of water. After the water loss, the geopolymers are progressively densified with an exothermic peak which appear before 1000°C. This peak is identified as mullite. In the RGP-Na the peak is present at 942.8°C while in RGP-K it is present at 988.8°C. The 40°C difference can be explained by the fact that the Na20-Al203-Si02 eutectic is lower compared to K2O-AI2O3-S1O2.
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100 100
80
%
80
60
< h-
o
Q
40
70
20 60 0 0
200
400
600
800
1000
1200
1400
Temperature (°C)
Figure la: TGA (top) and DTA (bottom) curves of GP-Na and GP-K samples. 1.0 0.9 0.8 0.7
O S3 0.6 0.5 0.4 0.3
0.2 0
200
400
600
800
Temperature (°C)
1000
Figure lb: DSC curves of GP-Na and GP-K samples.
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After 900°C, the liquid phase becomes significant in the geopolymer matrix (Figure 2). The initial shrinkage during sintering of geopolymer samples is observed after 100CC should be linked to the capillary strain resulting from the dehydration. The shrinkage as observed in the Figure 2 is more important for GP-Na compared to GP-K; 2.5% of shrinkage is observed for GP-K up to 980CC while the shrinkage is > 5% for GP-Na after 200°C but remain constant as in the case of GP-K up to 940°C. The second and the large shrinkage is between 900°C and 1000°C and should be linked to the structural densification by viscous sintering.
o
-5
ε. -io
é W
-15
-20
-25
200
400
600 800 Temperature (°C)
1000
1200
1400
Figure 2: Dilatomtry curves of GP-Na and GP-K samples The XRD graphs (Figure 3) indicate that geopolymer materials are essentially amorphous. At 200°C there is no change in the phases present in different types of geopolymer. This is demonstrated by the fact apart from water loss (Figure 1), the structure of geopolymer is not affected by the temperature development up to 800°C. At 800°C the crystalline peaks already present increases in intensity for both types of geopolymers. Even at this temperature, it can be observed that potassium based geopolymer tend to develop more crystalline phases. The K form more complex crystalline phases as kaliophilite and leucite for K-geopolymer.
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40
50
60
70
2teta (degrees)
Figure 3a): Phase evolution in Na-geopolymer with temperature (25, 200 at 800°C)
Figure 3b): Phase evolution in K-geopolymer with temperature (25,200 at 800°C) As it can be observed in Figure 1, there is metakaolin in the matrixes that did not react and which will be transformed to mullite from 950CC. This is follow by formation of liquid phase responsible for the increase in mechanical properties, density and the reduction of porosity. For above reason geopolymer materials are indicated for thermal applications in the range of temperature under 950°C.
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Figure 4 a: SEM micrographs of geopolymer materials at 200°C (a: GP-Na, b: GPK) and 800°C (c: GP-Na, d: GP-K).
Figure 4 b: SEM micrographs of geopolymer material showing transformations at 1300°C due to the intensives liquid phase developed. In the Figure 4 it can be observed that geopolymers maintain their homogeneous and dense microstructure up 900°C but above this temperature as confirmed by dilatometry analysis, the geopolymer materials shrink considerably and surely can not maintain their high temperature properties. At 1100°C a vitrified phase was observed and at 1300°C only K-geopolymer maintain
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their structure even with vitrification (Figure 4). Na-geopolymer at this temperature shows fissures and cracks. CONCLUSION The sintering behavior of the geopolymer materials were studied using DTA/TGA, DSC and optical dilatometry. The different observations were correlated to XRD and SEM observations. Geopolymers are mostly influenced by the composition of the alkali activating solution. It can be observed from the results that the sintering behavior of the geopolymer materials is also influenced by the nature of alkali activator used. The K-geopolymers presented better resistance to shrinkage, vitrification and deformation compared to Na-geopolymers. Microstructural and mineralogical investigations showed that thermal shrinkage relates to the densification by reduction of porosity during dehydroxylation and sintering. The sintering of geopolymer can then be structured with sequences of dehydration, dehydroxylation, densification and deformation. ACKNOWLEDGMENT We are particularly grateful to dr. Braga Mirko, R.&D. Laboratory, INGESSIL S.r.l., (Verona, Italy) for providing with the potassium silicate solution. REFERENCES 1. E. M. Levin, C. R. Robbins, and H.F. McMurdie, Fig. No. 407 in phase Diagrams for ceramics, Vol. 1. Edited by M. K. Reser. American Ceramic Society, Columbus, OH, 1964. 2. S.M. Johnson, J.A. Pask, and J.S. Moya, Influence of impurities on High-Temperature Reactions of Kaolinite, J. Am. Ceram. Soc. 65[1]31-35(1982). 3. L. Weng, K. Sagoe-Crentsil, T. Brown, Speciation and hydrolysis kinetics of aluminates in inorganic polymer systems, presented to geopolymer, International Conference on geopolymers 2829 October, Melbourne, Austrialia (2002). 4. M.R. Anseau, J.P. Leung, N.Sahai, T.W. Swaddle, Interactions of silicate ions with Zinc(II) and Aluminium(III) in alkali aqueous solution, Inorg. Chem., 44(22) 8023-8032 (2005). 5. M.R. North, T.W. Swaddle, Kinetics of silicate exchange in alkaline alumino-silicate solutions, Inorg. Chem., 39(12) 2661-2665 (2000).
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6. J.S.J. Davidovits, Long term durability of hazardous toxic and nuclear waste disposals. In: Davidovits, J.S.J., Orlinski, J. (Eds.), Proceedings of the 1st International Conference on Geopolymers, Vol 1, Compiege, France, 1-3 June, PP. 125-134 (1988). 7. J. W. Phair, J.S.J.Van Deventer, Effect of the silicate activator pH on the microstructural characteristics of waste-based geopolymers. Intl. J. Min. Processing, 66 (1-4) 121-143 (2002). 8. J. A. Kostuch, G. V. Walters, T. R. Jones, High performance concrete containing metakaolin-A review. In: Dhir R.K., Jones M.R (Eds.), Proceedings of the Concrete 2000 International Conference on Economic and Durable Concrete through Excellence. University of Dundee, Scotland, UK, 7-9 September, 2, pp. 1799-1811 (2000). 9. P. Duxson, G.C. Lukey, J.S.J. Van Deventer, Physical evaluation of Na-geopolymer derived from metakaolin up to 1000°C, J. Matls Sei, 42 3044-3054 (2007).
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MESO-SCALE MONTE CARLO SINTERING SIMULATION WITH ANISOTROPIC GRAIN GROWTH Gordon Brown1 , Richard Levine1, Veena Tikare2, & Eugene Olevsky1; '-San Diego State University, 2-Sandia National Laboratory ABSTRACT Although Monte Carlo (MC) simulations are widely used for understanding the microstructural evolution of sintering bodies, the models currently in use do not accommodate materials with anisotropic properties. Anisotropy has a significant effect on grain growth rates, which impacts material properties. Computer simulation models are used to better understand phenomena associated with sintering. A two-dimensional algorithm to simulate the evolution of granular structure with anisotropic materials using a Potts MC model, which incorporates the sintering mechanisms of grain growth, pore migration and vacancy annihilation, is presented. Limitations of this algorithm imposed by the underlying lattice structure are identified and analyzed. Solutions to mitigate these artifacts are proposed and implemented. Results are discussed and evaluated. The ability to incorporate anisotropic grain growth in our meso-scale modeling allows the investigation of anisotropic granular development under several different situations to better understand some of the observed anisotropic phenomena like patterning in sintered materials. INTRODUCTION Monte Carlo (MC) models have been used by many researchers for the simulation of grain growth and sintering 122 . The most common is the Potts Model 23 , which is an extension of the Ising 24 Model . This model discretizes the initial grain structure onto a lattice, and assigns a state to each site on the lattice. This state is assumed to be constant and uniform on a cell surrounding the site. Contiguous sites with the same grain state are considered to be parts of the same grain. Grain boundaries are then implicitly defined as existing between neighboring sites with different grain states. This discrete representation of the grain structure is a reasonable approximation of the actual morphology provided that the size of the lattice spacing is small compared to the grain sizes. Later in our discussion, it will be important to keep in mind that these states of the lattice sites are just discrete approximations of the actual material structure. The dynamic evolution of this discrete grain structure is then simulated by using a Kinetic Monte Carlo (KMC) approach 25 with the Potts model. This approach assumes a quasi-equilibrium state where many molecular exchanges occur shifting back and forth without affecting the overall distribution of states on a time scale of the atomic vibrations. Then on a much longer time scale, an infrequent event occurs which shifts the state configuration to a new quasi-equilibrium state. It is these infrequent events which are simulated in this Potts model so that the dynamic evolution of the structure will be captured. This way we can track the changes that occur in the distributions of these quasi-equilibrium states. As we are only looking at one site changing state at a time, in order to simulate all sites changing simultaneously, one time step consists of a cycle through every site. This time unit is called a Monte Carlo Step (MCS) of the simulation process.
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THE POTTS MODEL The Potts model represents a sample of the material and thus it is a sampling from the distribution of configurations throughout the material. A fundamental result from statistical mechanics is that this distribution of configurations follows the Boltzmann distribution.
p(Q = ±e-E(c),k-T
Eq.(l)
where
/7(C) is the probability of configuration C of the state space, Z = ^ e ~ £ < c ) / * ' r i s the normalizing constant, c E(C) is the energy associated with configuration C, kB is the Boltzmann constant, and T is the temperature. The most widely used algorithm for sampling from this distribution is the Metropolis 26 algorithm . This algorithm first assumes that the energy associated with a particular site is only dependent on the state ofthat site and the states of the surrounding interacting "neighbor" sites. From this, the total energy of a configuration can then be computed as the sum of the energies associated with each site. The next assumption is that we can sample from the distribution of configurations by just looking at transitions associated with a single site and then do this repeatedly for all sites in the lattice. These conditions allow us to compute the probability that an existing configuration will transition into a new configuration. Under the Metropolis algorithm, the transition probability for such a change of state is P = {e-w,k*T if Δ£>0; 1 otherwise}
Eq. (2)
where AE is the change in energy from the existing state to the candidate state. There are various ways of calculating these energies, and the resulting microstructural evolution is determined by how these energies are calculated and the transitions under consideration. The simplest assumption for calculating these energies is to assume that the material is isotropic so that the energies associated with the states of neighboring sites are not affected by direction or orientation. Even with this assumption, there are considerations for variations in the boundary energies resulting from the anisotropy of the lattice. This was investigated by Holm et al.27 who found that using different boundary energies for first and second nearest neighbors of square or triangular lattices could result in lattice pinning and only using the first nearest neighbors also resulted in lattice pinning due to the larger anisotropy of the lattice. As a result, using the first and second nearest neighbors with the same boundary energies minimized the pinning effects of the lattice anisotropy. For this situation, the Hamiltonian for a transition associated with a site, /, is
//^/¿(l-^,,?,))
Eq.(3)
where H¡ is the Hamiltonian associated with lattice site /, J is the boundary energy with a boundary between any two neighboring sites q¡ is the state of site ¡,
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q¡ is the state of one of the neighboring sites on the lattice adjacent to site i, n is the number of neighboring sites considered, and S(q¡,q¡) is the standard Kroenecker delta function {1 if q¡=qf, 0 otherwise). The boundary conditions for this model are determined by the need to determine shrinkage and thus have a boundary for constant mass. This means that we will have a buffer of void sites surrounding the simulation cell. As vacancies are annihilated and pores sites migrate to this buffer, the change in density can be seen visually and easily measured. Using this expression for the Hamiltonian with constant boundary energies implies isothermal, isotropic materials. It is for this reason that although the Potts model has been widely used for simulating the dynamic evolution of the meso-scale morphology, most implementations assume isotropic materials. Unfortunately, many of the materials we are trying to simulate are anisotropic. In order to understand the impact of the material anisotropy on the evolution of the grain morphology, the anisotropy must be incorporated into our model. PREVIOUS ANISOTROPIC MODELS Several researchers have developed methods to incorporate anisotropy into the Potts model " ' 21, 27-31 j ^ e m o s t c o m m o n a p p r o a c ¿ ¡ s to incorporate the material anisotropy through various modifications of the energy calculations associated with the states of neighboring sites. For these models, the boundary energy can be different for each of the neighbors, so the Hamiltonian of equation (3) becomes
^ÉW1-«^..?,)))
Ε
ι·(4>
where Jtj is the boundary energy between sites i and_/. In 2000, Morhac and Morhacova " presented an algorithm where a percentage of the grains had anisotropy introduced through one of four directions in a square lattice. The boundary energies were at a fixed ratio for each of these four directions, and were randomly assigned to the anisotropic grains. The result is shown in figure (1).
Fig. 1: Results from Morhac & Morhacova ".
Several researchers including Holm et al. (2001) 28, Grest et al. (1985) 29, and Yu and Esche 30 (2002) have approached this issue by looking at boundary energy and mobilities. Boundary energy is calculated using Read-Shockley theory and the misorientation angles across the grain boundaries. Their results on a triangular lattice are shown in figure (2). The two images shown are for the isotropic case (a) and the anisotropic case with the anisotropy parameter set to 60% of the maximum
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value (b). Additionally, Upmanyu et al. 31 evaluated the relative impact of boundary energy and boundary mobility and found that the boundary energy was the dominant factor in anisotropic microstructural evolution.
Fig. 2: Results from Yu & Esche
with anisotropy parameter at 0 (a) and 60% (b).
A different approach was taken by Yang et al. in 1995 21 by using Wulff plots to capture the surface energy anisotropy. An example of the model results from this approach is shown in figure (3). The Wulff plots can take a variety of complex shapes, and can be modified for specific applications.
Fig. 3: Results from Yang et al ' on triangular lattice.
Although these models show anisotropic grain growth, none of them incorporate the mechanisms of pore migration and vacancy annihilation necessary to simulate sintering. Additionally, they are all limited to a small number of angles for the anisotropic grains. The Wulff plot approach will be used in this paper as the function for the plot can be evaluated at any angle and can be modified in the coded software to incorporate other mechanisms affecting the boundary energy in future work. THE ANISOTROPIC MODEL As the goal in this paper is to simulate the mesoscopic morphology of a sintered material, we will modify Yang's model to include porosity and add the mechanisms of pore migration and vacancy annihilation into the model as presented by Tikare, et al. . Additionally, the orientation angles will not be limited as in Yang's model. For simplicity, an ellipse will be used for the initial implementation of an anisotropic model, and the ratio of the axes (a/b) will be referred to as the "aspect ratio" of the ellipse. The magnitude of the surface energy in any direction will be the distance from the origin to the Wulff plot function in that direction as shown in figure (4).
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Fig. 4: Elliptical Wulff Plot
With this structure in place, the boundary energy (J¡¡) of equation (4) can be computed for any adjacent sites. Now for any two configurations, we can compute the change in energy (ΔΕ) and thus the probability of acceptance of the new candidate configuration using equation (2). As in other models, a grain growth step considers a single site and a transition of the state of that site from its current state to one of the states of a neighbor site. For a pore migration step, two neighboring sites are selected, where one is a pore and the other is a grain site. In this case, since there are two sites potentially changing state at the same time, all neighbor sites of both of these sites must be considered. Vacancy annihilation is incorporated into the model using the jump algorithm of Tikare et al. of 2003 32 and extended by Braginsky in 2005 33. All of these algorithms conserve the number of grain sites so by using a boundary around the structure the shrinkage of the simulated compact can be quantified. The initial configuration can be a bitmap transcribed from a micrograph, but for this research, a starting configuration is generated from random orientation assignments to all grain sites and then allowing the grain growth algorithm to proceed until a large enough average grain size is achieved. SIMULATION RESULTS To see the impact of the anisotropy in the Wulff plots, results are shown in figure (5) with all orientations aligned, time stopped at 40 MCS and the aspect ratio of the ellipse set to 1 (isotropic), 2, and 5. We can see that the increased anisotropy in the Wulff plots results in increased anisotropy in the grain growth and that with increased anisotropy, the average grain size is smaller. As all of these simulation results are for the same time (40 MCS) we may conclude that the grains are growing slower with increased anisotropy.
Fig. 5: Wulff Plot Anisotropy Ratios 1 (isotropic), 2, & 5
This result is consistent with the results of other models. To verify the impact of the orientation angle of aligned grains, results shown in figure (6) have the same time in MCS and the same aspect ratio for the Wulff plot ellipse, but the orientation angles are 0, 90, and 135 degrees in the CCW direction. The results are as expected for the angles.
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Fig. 6: Orientation Angles CCW 0 (vertical), 90, & 135 Degrees
Additionally, the diagonal directions appear to have more anisotropy. This is an artifact which results from the square lattice as the eight neighbors are all treated as equidistant, but in fact the diagonal neighbors are farther away than the vertical and horizontal neighbors. Now looking at the results with random orientations for various times (40, 100, and 200 MCS) it is apparent that even though the initial orientation angles are uniformly distributed, the grains only seem to grow in the directions of nearest neighbors.
Fig. 7: Random Orientations at MCS of 40, 100, & 200
This is an artifact induced by the lattice as there are no neighbors in the other directions. So how can this artifact be eliminated? A new novel approach is to rotate the lattice during the microstructural evolution so that there will be neighbors in other directions. LATTICE ROTATION There are several issues to overcome with rotating the lattice. First it is important to realize that any rotation other than multiples of 90 degrees will result in distortion as the original lattice sites will not coincide with the new lattice sites. Some distortion is acceptable as the states are just discrete approximations as we discussed earlier in this paper. Secondly, when the square lattice is rotated, some sites will no longer be in the domain of the lattice. This problem can be overcome by having a larger square lattice with only active sites in a circular region inscribed in the square. Then if we want to have a square specimen, it must be fully contained in the circular active region. With this in mind, the implementation in this paper will use a circular specimen to see the maximum use of the active region of the lattice. As the specimen is rotated, the distortion mentioned earlier will cause a shift of some neighbor sites so that they are no longer neighbors. As the diagonal neighbors are only contiguous at a corner point any amount of distortion can make them no longer neighbors. In fact, some shifting of neighbors is necessary to capture the other angles; we just wish to avoid excessive distortion. We want to
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maintain the number of grain sites and the grain size. To do this, the rotation algorithm must map the grain sites of each grain to the same number of sites after the rotation. This means that some of the sites of a grain which are neighbors before the rotation will not be neighbors after the rotation, but of course if the structure is rotated back to the original grid, the sites will be neighbors again. This means that the algorithm must have the same effect regardless of direction (CW or CCW). Additionally, this algorithm must be able to be extended to three dimensions. As the lattice geometry of a cubic lattice in the third dimension is topologically the same as the two dimensional square lattice, the algorithm is focused on the square lattice and is directly extendable to a third dimension by using two angles, azimuth and altitude. An algorithm to do this is to divide the lattice into concentric rings. To rotate the lattice, rotate the sites within these rings through the desired angle of rotation. The resulting distortion is of two types. One comes from the fact that the sites in the ring vary in radii within the ring. This distortion is reduced with smaller thicknesses of the rings. Of course as the thickness of the rings decreases, the density of sites in the rings decreases as well. This means that there will be more angular distortion. Nonetheless, this trade off is natural. As an illustration of this rotation algorithm, consider a circular specimen obtained from a sample micrograph with aligned grains so that the rotation angle is easier to visualize. Each lattice site is shown as a square, and the purpose of this figure is to demonstrate that the algorithm rotates the structure and that the grain and pore boundaries have some distortion as the structure rotates. Note that as the pores get smaller they approach the size of the square lattice site. Once they become the size of a single site, if on a grain boundary they are considered a vacancy and can be annihilated.
Fig. 8: Rotation of Grains with Circular boundary for angles of 0, 5, and 35 degrees.
The maximum distortion occurs at 45 degrees and is symmetric so that at 90 degree intervals there is no distortion at all as the ring sites line up exactly with similar sites in the rings. CONCLUSIONS The Potts model of Yang has been extended to include porosity and the mechanisms of pore migration and vacancy annihilation to simulate sintering. The lattice discretization causes directional artifacts. Rotation of the lattice is a novel approach to overcome these artifacts, but requires an algorithm for the rotation. Lattice rotation will result in some distortion. Some of distortion is necessary to remove the artifacts, but excessive distortion should be avoided. The proposed algorithm seems to meet the requirements for our concept and has a parameter (ring thickness) which can control the radial and angular distortion to find the best balance. This will be incorporated into the Potts model described above and results will be reported in a future paper. ACKNOWLEDGEMENTS The support of National Science Foundation Divisions of Materials Research (Grant DMR0705914) and of Civil and Mechanical Systems and Manufacturing Innovations (Grants DMI-0354857
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and CMMI-0758232) is gratefully appreciated. Sandia is a multi-program laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy National Nuclear Security Administration under the Contract DE-AC04-94AL-85000. REFERENCES 'Aldazabal, J., A. Martin-Meizoso, et al. "Simulation of liquid phase sintering using the Monte Carlo method." Materials Science and Engineering a-Structural Materials Properties Microstructure and Processing 365(1-2): 151-155. (2004). 2 Blikstein, P. "Monte Carlo Simulation of Grain G." Materials Research 2(3): 5. (1999). 3 Bordere, S. "The impact of fluctuations on the sintering kinetics of two particles demonstrated through Monte Carlo simulation." Scripte Materialia 55(10): 879-882. (2006). "Dudek, M. R., J. F. Gouyet, et al. "Q+l state Potts model of late stage sintering." Surface Science 401(2): 220-226. (1998). 5 Han, Y. S. and D. K. Kim "Monte Carlo simulation of anisotropic grain growth in liquid phase sintering." Journal of the Korean Physical Society 42: S1058-S1062. (2003). 'Hassold, G. N., I. W. Chen, et al. "MONTE-CARLO SIMULATION OF SINTERING." Journal of Metals 40(7): A44-A44. (1988). 'Huang, C. M., C. L. Joanne, et al. "Monte Carlo simulation of grain growth in polycrystalline materials." Applied Surface Science 252(11): 3997-4002. (2006). 8 Kim, Y. J., S. K. Hwang, et al. "Three-dimensional Monte-Carlo simulation of grain growth using triangular lattice." Materials Science and Engineering a-Structural Materials Properties Microstructure and Processing 408(1-2): 110-120. (2005). 'Li, H., G. H. Wang, et al. "Monte Carlo simulation of three-dimensional polycrystalline material." Materials Science and Engineering a-Structural Materials Properties Microstructure and Processing 357(1-2): 153-158. (2003). '"Luque, A., J. Aldazabal, et al. "Simulation of the microstructural evolution during liquid phase sintering using a geometrical Monte Carlo model." Modelling and Simulation in Materials Science and Engineering 13(7): 1057-1070. (2005). "Morhac, M. and E. Morhacova "Monte Carlo simulation algorithms of grain growth in polycrystalline materials." Crystal Research and Technology 35(1): 117-128. 12 01evsky, E. A., B. Kushnarev, et al. (2005). "Modelling of anisotropic sintering in crystalline ceramics." Philosophical Magazine 85(19): 2123-2146. (2000). "Potter, B. G., V. Tikare, et al. "Monte Carlo simulation of ferroelectric domain structure and applied field response in two dimensions." Journal of Applied Physics 87(9): 4415-4424. (2000). '"Radhakrishnan, B., G. B. Sarma, et al. "Modeling the kinetics and microstructural evolution during static recrystallization - Monte Carlo simulation of recrystallization." Acta Materialia 46(12): 44154433. (1998). ,5 Sault, A. G. and V. Tikare "A new Monte Carlo model for supported-catalyst sintering." Journal of Catalysis 211(1): 19-32. (2002). "Schmid, H. J., S. Tejwani, et al. "Monte Carlo simulation of aggregate morphology for simultaneous coagulation and sintering." Journal of Nanoparticle Research 6(6): 613-626. (2004). "Srolovitz, D. J., M. P. Anderson, et al. "MONTE-CARLO SIMULATION OF GRAIN-GROWTH." Journal of Metals 35(8): A60-A60. (1983). 'Teixeira, A. and R. Giudici "A Monte Carlo model for the sintering of NÍ/A1203 catalysts." Chemical Engineering Science 56(3): 789-798. (2001). "Tikare, V., M. A. Miodownik, et al. "Three-dimensional simulation of grain growth in the presence of mobile pores." Journal of the American Ceramic Society 84(6): 1379-1385. (2001). M Yamashita, T., T. Uehara, et al. "Multi-Layered Potts Model simulation of morphological changes of the neck during sintering in Cu-Ni system." Materials Transactions 46(1): 88-93. (2005).
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2I
Yang, W., L. Q. Chen, et al. "COMPUTER-SIMULATION OF ANISOTROPIC GRAINGROWTH." Materials Science and Engineering a-Structural Materials Properties Microstructure and Processing 195(1-2): 179-187. (1995). 22 Yu, Q. and S. K. Esche "Three-dimensional grain growth modeling with a Monte Carlo algorithm." Materials Letters 57(30): 4622-4626. (2003). "Potts, R. B. "SOME GENERALIZED ORDER-DISORDER TRANSFORMATIONS." Proceedings of the Cambridge Philosophical Society 48(1): 106-109.(1952). "Ising, E. "Beitrag zur Theorie des Ferromagnetismus"; Zeitschrift für Physik. 31, 253-258. (Engl. Translation: http://www.fhaugsburg.de/~harsch/anglica/Chronologv/20thC/Ising/isi fm00.html) (1925). 25 Voter, A. F. "Introduction to the Kinetic Monte Carlo Method". IPAM 2005, UCLA. (2005). 26 Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., and Teller, E. "Equation of state calculations by fast computing machines"; Journal of Chemical Physics 21;1087-1092. (1953). 27 Holm, E. A., Glazier, J. A., Srolovitz, D. J., Grest, G. S., "Effects of lattice anisotropy and temperature on domain growth in the two-dimensional Potts model", Physical Review A, 43(6): 26622668. (1991). 2, Tikare, V., Braginski, M. , et al. "Numerical Simulation of Anisotropie Shrinkage in a 2D Compact of Elongated Particles." Journal of the American Ceramic Society 88(1): 59-65. (2005). "Holm, E. A., G. N. Hassold, et al. "On Misorientation Distribution Evolution During Anisotropie Grain Growth" Acta Materiallia 49: 2981-2991. (2001) 2, Grest, G. S., D. J. Srolovitz, et al. "Computer simulation of grain growth. IV. Anisotropie grain boundary energies"; Acta Metallurgica. 33(3): 509-520. (1985). M Yu, Q., S. K. Esche "Modeling of grain growth kinetics with Read-Shockley grain boundary energy by a modified Monte Carlo algorithm"; Materials Letters, 56, (1): 47-52. (2002) 3 'Upmanyu, M., G.N. Hassold, et al. "Boundary Mobility and Energy Anisotropy Effects on Microstructural Evolution During Grain Growth"; Interface Science 10, (2-3): 201-216. (2002) 5! Tikare, V., M. Braginsky, et al. "Numerical Simulation of Solid-State Sintering: I. Sintering of Three Particles." Journal of the American Ceramic Society. 86, (1): 49-53. (2003). "Braginsky, M., V. Tikare, et al. "Numerical Simulation of Solid State Sintering." Intl Journal, of Solids and Structures 42: 621-636. (2005).
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NUMERICAL SIMULATION OF DENSIFICATION AND SHAPE DISTORTION OF POROUS BODIES IN A GRANULAR-TRANSMITTING MEDIUM Junkun Maa, Eugene A. 01evskyb "Southeastern Louisiana University, SLU 10847, Hammond, LA 70402, USA b San Diego State University, 5500 Campanile Drive, San Diego, CA 92182, USA ABSTRACT In an attempt to achieve maximum densification and minimum distortion for near-net-shaped manufacturing of powder-based components, the process of quasi-isostatic pressing (QIP) is studied. In QIP, the self-propagating high-temperature synthesis (SHS) and the subsequent consolidation are carried out in a rigid die where a powder body subjected to SHS is surrounded by a granular pressuretransmitting medium (PTM). Following the SHS, a uniaxial load is applied to the PTM, which builds up a quasi-isostatic stress in the die. The constitutive behaviors of both the post-SHS body and the PTM are determined based on theoretical and experimental studies. The densification and shape distortion of a post-SHS powder specimen are simulated using a finite element model and the results are compared to the experimental data with satisfactory agreement. To obtain the desired final shape, the optimized initial shape of the pre-QIP porous body is determined based on a special iterative simulation approach. INTRODUCTION Self-propagating High-temperature Synthesis (SHS) has been successfully used for the fabrication of numerous advanced industrial materials since the beginning of the large-scale systemic investigation of this process in 1960s1"7. Following the SHS reaction, the consolidation of a porous specimen by applying compressive mechanical stresses is an important processing step utilized for the fabrication of final products with high relative density. Obviously, during mechanical consolidation, both the volume and shape of a post-SHS porous specimen change. Ideally, Cold or Hot Isostatic Pressing (CIP/HIP) produces high density with least shape distortion. However, high cost of equipment and long processing time associated with these processes make other cost effective alternatives more attractive. Uniaxial pressing in a rigid die with rigid particulate materials working as a PressureTransmitting Medium (PTM), such as mixture of alumina and graphite powers, has been under extensive investigation and has been used in industries as such an alternative due to its simplicity and much lower cost8"12. As shown in Fig. 1, when a uniaxial compressive load is applied, the PTM redistributes the stresses and creates Quasi-isostatic Pressing (QIP) conditions for the powder specimen located inside PTM, which is contained itself in a rigid die. The analysis of how this quasiisostatic stress mode effects the densification and shape distortion of the post-SHS porous body during QIP is important for near-net-shaped manufacturing. For this purpose, the constitutive behaviors of both the post-SHS porous body and the PTM need to be investigated. This study focuses on the densification and shape distortion of the post-SHS porous body during QIP. The constitutive properties that relate the stress, strain rate and material properties of the post-SHS porous body and the PTM have been developed based on the theory of nonlinear-viscous deformation of porous bodies13, and experimental studies. These properties have been incorporated into a Finite Element Method (FEM) code. The density development and the shape distortion evolution of the post-SHS porous body during QIP are numerically calculated and agree well with the experimental results. An optimization procedure is also proposed for determining the optimized shape of the pre-SHS green body rendering the desired final shape of the powder specimen after QIP.
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Fig. 1 Schematic representation of Quasi-Isostatic Pressing CONSTITUTIVE MODELING The post-SHS porous body can be considered a nonlinear-viscous porous material. Based on the continuum theory of sintering 9, its constitutive behavior follows a rheological relationship, which relates stress tensor atj and strain rate tensor éy. In the general case, a power law is used to describe the hot deformation of a nonlinear crystalline material and the stress; strain rate relationship can be expressed as13: (Sintering stress is significantly smaller than the external mechanical stress and is therefore ignored.)
¡φγ +ye
rP
φ \éSu
(1)
where φ and ψ are the shear and bulk viscosity moduli, which depend on porosity Θ (for example, following Skorohod model 14 , φ = ρ2 , ψ = 2p3/3(l-p) ); δν is a Kronecker symbol ( < 5 s = l i f ;' = j and StJ = 0 if i Φ j ) ; é is the first invariant of the strain rate tensor, i.e. sum of tensor diagonal components: é = e,, + é22 + é33. The porosity Θ is defined as 1 - p/pT , where p and pT are relative and theoretical (corresponding to a fully-dense state) densities, respectively. Physically, é represents the volume change rate of a porous body. Parameter γ is the second invariant of the strain rate tensor deviator and represents, physically, the shape distortion rate of a porous body14:
3
"
1», 3
1/2
(2)
"
The strain rate sensitivity factor m varies in the range of 0 < m < 1. In one limiting case, when m = 1, the model describing the behavior of a porous body is reduced to linear-viscous law, and the corresponding constitutive equation can be obtained as :
K + l v-^
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(3)
Numerical Simulation of Densification and Shape Distortion of Porous Bodies
A-fp ¡φγ
+ψβ
ψ-^ψ\έδα
(4)
where A plays the role of the yield stress σ ν0 of a fully dense material. In our study, a cylindrical sample placed at the center of a rigid die with surrounding PTM, as shown in Fig. 1, is investigated. Based on the above-mentioned constitutive equations and the assumption that the stresses are uniform within both the PTM and the porous body, the densification and shape evolution of the porous body subjected to QIP can be analyzed. Since PTM is a porous mixture of solid particulates, it is also important to understand the mechanical behavior of the PTM itself under a compressive load (such as the porosity evolution of the PTM during QIP, effects of composition of the PTM). Based on the series of compressive tests conducted with a set of PTMs with different compositions of alumina and graphite in a rigid die (with no embedded post-SHS porous bodies), and the assumption that the PTM can be modeled as a porous rigid-plastic material, one can find that the normalized Young's modulus does not change substantially when the PTM's relative density is greater than 60% 3 . Therefore, the PTM's Young's modulus E(C, pp), which in general, is a function of the PTM's composition C and the PTM's relative density pp, can be represented as a product of two functions £ c (C)and E (p), where £ c ( C ) i s a function of the PTM's composition C (percentage of alumina), and Ep (/?)is a function of the PTM's relative density p: E{C,p) = Ec-EPr
(5)
By analyzing the data of the PTM compressive tests, the Young's modulus of the PTMs can be expressed as (details are explained in earlier work 13 ): £ ( C , p ) = 95.7854-(C + l)" 02728 ' (0.0118-^-0.1794)
(6)
With the understanding of the constitutive behaviors of the post-SHS porous body and of the PTM, one can assess the densification and the shape distortion of the post-SHS porous body during QIP. The only parameters that are missing are the two materials' constant A and m for porous viscous power law materials (see Eq. (1)). Following the experimental methods described in earlier work15, for the TiC-Ti cermets material system, the two parameters are determined to be A = \\0MPas02 and m-0.2. For the purpose of the generalization of the results, a normalized time τ = (Α/Ε0) " f is introduced, where E0 is the effective Young's modulus for a fully dense PTM material and t is the physical time of the QIP process. Utilizing the expressions for shear and bulk viscosity moduli φ-(ΐ-θ) and ψ=2(\-θ) ¡W 16~20 for the description of QIP behavior, one can obtain the evolution of the porosity of the post-SHS body during QIP based on equations (7), (8), (9) and (10) shown below. The details of the derivation of these equations and comparison to experimental results can be found in another publication13:
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άθ 143.( -(Ο + ΐ) ( _ 0 ' 2 7 2 8 1 ) (0.0118(ΐ-0,)-0.1794) _ = -(l-ö) dr
(7)
^ ( l - O ^ o / O - O J + OQ-O,) 2
(4-3g,) J 1-0, 1 ( 2 - 0 , ) 90,(1-0,) l , l - 0 , J ( 2 - 3 0 , ) ( l - f l ) '
0(4-30,)
H 2ΘΡ + (1-3ΘΡ)Θ άθ_ dt 3#„ θ(1-θ)(1-θ„)
d(H/Ht)= di
¿WS*)
R
dr
3Ä„
(8)
άθ_ dt
(1-θ)(1-
(9)
Based on the conservation of the mass of the PTM + SHS bodies system, one can also obtain
2 A«L^W ( 1 _ g ) + ÍAp( PpTM
d{ePjePa) dr
R,H0
dr
R°) S(A>
R» ) ^oV-^oJ
y
g g
/ o) ( 1 _ g ) ÍATA^
' [R,)
dr
+2£JL*MMJx) ^o-^o
dr
fl!-iU
{RQ
y
d
' UJ
H d
°*
H
W o) dr
(10)
R_) H_ H„
RQ)
H
n
The above four equations (7-10) can be used to solve for four unknowns of the QIP system as functions of the specific time r : (i) the post-SHS porous body's porosity Θ, (ii) specimen's height H, (iii) specimen's radius R, and (iv) the PTM's porosity θρ. A MATLAB code using the 4th order Runge-Kutta algorithm is developed to solve this set of four first order differential equations. As the result of this numerical solution, the optimal composition of the PTM, of 75%w.t. alumina and 25%w.t. graphite, rendering the maximum densification and minimum shape distortion, is obtained21. FEM SIMULATION To study the consolidation and the shape distortion of the post-SHS body during QIP, the boundary-value problem of the pressing of a cylindrical porous body in a rigid die filled with PTM is formulated for a numerical simulation. The processing schematics and the assumed boundary conditions are shown in Fig. 2. The critical porosity where the PTM becomes uncompressible is measured to be 25%. Therefore, the bulk and shear moduli of the PTM are expressed a s w = 0-25% and φ = (ΐ-θ) , respectively 22~25. The yield limit of the PTM during pressing in a rigid die is measured to be 180MPa. The post-SHS porous body is considered to be a power law creep-obeying
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porous material with parameters A-I lOMPa ■ S02 and m = 0.2 as aforementioned. The initial porosity of PTM is measured to be 50% and the initial porosity for the post-SHS porous body is 40%. The PTM has a composition of 75%wt alumina and 25%wt graphite (the optimal composition for most densification and least shape distortion); the cylindrical specimen has dimensions of D x H = 1 "x 1", and the PTM is filled up to approximately D x H = 6 "x 6" in a rigid die.
Fig. 2 FEM Schematics of the QIP following SHS The boundary conditions are represented by the material flow velocities: at the upper punch, the axial velocities coincide with the punch's velocity: Vz\ = Vpmdl, where h is the height of the PTM filling the die; At the bottom of the die, the axial velocities are equal to zero: V21 = 0. At the lateral walls of the die, the radial velocities are equal to zero: V\
= 0, where R
die. Friction of the PTM at the die and the punch surfaces is neglected. An FEM code is developed to conduct the numerical calculation and the Marc-Mentat commercial FEM package has been used for the post-processing of the calculation results. Due to axisymmetric character of the problem as shown in Fig. 2, only a quarter of the actual sample is modeled with a peak post-SHS load of 350MPa. The simulation results show that the powder samples are consolidated to a theoretical density of approximately 97% at this stress level and it is also obvious that the samples experienced both axial and radial deformations, as shown in Fig. 3. Assuming that PTM has similar properties to granulated materials, commercial FEM package ABAQUS has also been used to simulate the QIP process for comparison. In this case, the post-SHS porous body is modeled as a material following Gurson 26~31 porous metal plasticity. And the PTM is modeled as a soil 32 (granular flow) material following the Mohr-Coulomb 3 ~ and the DruckerPrager/Cap37_42 models respectively. The simulation results using the aforementioned FEM code, ABAQUS with Mohr-Coulomb model, and ABAQUS with Drucker-Prager/Cap model are shown in Fig. 4, Fig. 5 and Fig. 6 respectively. The background shown in these figures is a quarter of the axial cross-section of a consolidated sample and the white line is the simulated outer contour of the sample using different models. As it can be seen in these figures, the all the FEM simulation results using the three different models indicate an acceptable agreement with the experimental result. The normalized distortion
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aspect ratio (H/Ho)/(R/Ro) as a function of time (at various loading step and stress level) obtained using the three models and the experimental data is also shown in Fig. 7. All the three models show similar results and they agree with the experimental ones. For the models that are time independent, the time aspect ratio shown in Fig. 7 represents the moving velocity of the upper punch in the consolidation process. The simulated final shapes based on the time dependent models correspond to the full density.
Fig. 3 Results of FEM simulation for 350MPa Compressive Stress
Fig. 4 Comparison of simulation to experimental results using home-made code.
Fig. 5 Comparison of simulation to experimental results using ABAQUS with Mohr-Coulomb model.
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Fig. 6 Comparison of simulation to experimental results using ABAQUS with Drucker-Prager/Cap model.
Fig. 7 Comparison of measured and calculated distortion aspect ratio for experiments and different models (the top center location of the cermets sample) OPTIMIZATION OF INITIAL GREEN BODY SHAPE As shown above, the post-SHS porous bodies shrink non-uniformly throughout their volume during QIP process. The most deformed area is the center part of the cylindrical sample along the axial direction. To answer the question of what initial shape of a green pre-SHS sample should be prepared in order to obtain a final product of the required shape (for example, to obtain a perfect cylindrical final product), an FEM-based iteration procedure is proposed for the optimization of the initial green body shape. At the first iteration of the procedure (Fig. 8), the shape of the required final shape is chosen as the initial optimized shape. An arbitrary node A in the mesh representing the shape of the pre-SHS body is considered. The node A has a coordinate of (Zo, Ro) at the beginning of the iteration process. Upon the first step of iteration using the FEM code, node A moves to position (ZFO, RFO)· The difference between the displacement is used as a compensation factor for the initial location of point A,
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which moves from the initial position of (Zo, Ro) to (ZI=ZO+(ZO-ZFO), R I - RO+(RO-RFO))· The new optimized position of (Zi, Ri) at node A is a part of the optimized mesh representing the results of the first iteration. An optimized mesh can be reconstructed by applying such a transformation to all the nodes in the FEM model. Keeping all the material properties, boundary conditions and initial conditions the same, another simulation step of QIP is carried out based on the newly obtained mesh and then the nodes are updated again as (Z2=ZI+(ZO-ZFI), R2= RI+(RO-RFI))· The iteration keeps going until an acceptable result (convergence) is obtained. Fig. 8 shows the schematic representation of the iteration process. A cylindrical sample having a square diametric cross-section with a unit length edge of 2a is chosen as the desired target final shape after QIP. Following the iteration described above, it is found that the initial shape with the diametric cross-section shown in Fig. 9 will produce a very close to the required final cylindrical shape (after 3 steps of the above-mentioned iterations) as shown in Fig. 10.
Initial Optimizad Snap» • Final Required Shape
i
New Optimized Initial Shape
Direct QIP Simulation
Direct QIP Simulation
Deformed Shape Baaed On New Optimized Initial Shape
i
Update Initial Shape to Crean New Optimizad Initial Ship.
Satisfied^ NO
(
1
END
)
Check the Deformed Shape
Fig. 8 Schematic representation of the iteration process
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Fig. 9 Optimized initial shape
Fig. 10 Optimized Initial Shape after Three Iterations CONCLUSIONS 1. The constitutive behaviors of both the reacted SHS porous bodies and the PTM in a QIP powder consolidation process are analyzed. The densification and shape distortion of the porous bodies subjected to QIP are mathematically modeled. 2. An FEM code incorporating the constitutive behaviors of both the porous bodies and the PTM is developed to simulate the consolidation and the shape evolution of the porous bodies during
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QIP. The calculation results demonstrate an acceptable agreement with the experimental data on the sample shape distortion during QIP. 3. A comparison of the results using a granular flow model for PTM, Mohr-Coulomb and Drucker-Prager/Cap models for SHS porous bodies shows good agreement with the developed mathematical model. 4. An iteration algorithm for the optimization of a green body shape before SHS for the near-netshape fabrication is proposed. A simple unit square example indicates rapid convergence after only few steps of iterations.
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REFERENCES Ά . G. Merzhanov, Self-Propagating High-Temperature Synthesis: Twenty Years of Search and Findings, Chernogolovka: ISMAN (1989). 2 Anatoli A. Borisov, Luigi De Luca, and Alexander G. Merzhanov, Self-Propagating HighTemperature Synthesis of Materials, Combustion Science & Technology Book Series, Vol. 5 (2002). 3 J. J. Moore, and H. J. Feng, Combustion Synthesis of Advanced Materials: Part I. Reaction Parameters, Progress in Materials Science, 39, 243-73 (1995). 4 J. J. Moore, and H. J. Feng, Combustion Synthesis of Advanced Materials: Part II. Classification, Applications and Modeling, Progress in Materials Science, 39, 275-316 (1995). 5 Z.A. Munir, Synthesis of High Temperature Materials By Self-Propagating Combustion Methods, Am. Ceram. Soc. Bull, 67, 342-349 (1988). 6 H.C. Yi, and JJ. Moore, Self-Propagating High-Temperature (Combustion) Synthesis (SHS) of Powder-Compacted Materials, J. Mater. Sei., 25, 1159-68 (1990). 7 A.G. Merzhanov, and I.P. Borovinskaya, A New Class of Combustion Processes, Combust. Sei. Tech., 10, 195-201 (1975). 8 M. Ohyanagi, M. Fukushima, and M. Koizumi, TiC-TiAl composite fabricated SHS-dynamic pseudo isostatic compaction through sand medium, Proceedings of the International Conference on Hot Isostatic Pressing, Andover, MA, 289-94 (1996). 9 J. LaSalvia, D. Kim, and M. Meyers, Effect of Mo on microstructure and mechanical properties of TiC-Ni-based cermets produced by combustion synthesis-impact forging technique, Mat Sei Eng A, 206, 71-80 (1996). 10 R. German, Powder metallurgy science. 2nd ed. Princeton, NJ: Metal Powder Industries Federation; (1994). U R. Raman, M. Janney, and S. Sastri, An Innovative Processing Approach to Fabricating Fully Dense, Near-Net-Shape Advanced Material Parts, World congress on powder metallurgy. Washington, DC. Princeton, NJ: MPIF, 131-142 (1996). 12 Z. Fu, W. Wang, R. Yuan, and Z. Munir, Fabrication of cermets by SHS-QP method, Int. J. SHS, 2, 307-313 (1993). 13 E. Olevsky, J. Ma, J. LaSalvia, and M. Meyers, Densification of porous bodies in a granular pressuretransmitting medium, Acta Materialia, 55,1351-1366 (2007). 14 V. Skorohod, Rheological Basis of the Theory of Sintering, Naukova Dumka, Kiev, (1972). ,5 E. Olevsky, E. Strutt, and M. Meyers, Chracterization by Indentation of Combustion Synthesized Cermets, Scripta Mater., 44, 1139-46 (2001). 16 E. Olevsky, and R. German, Effect of gravity on dimensional change during sintering-I. Shrinkage anisotropy, Acta Mater, 48, 1153-1166 (2000). 17 E. Olevsky, and R. German, Effect of Gravity on Dimensional Change During Sintering-II. Shape Distortion, Acta Mater, 48, 1167-1180 (2000). I8 E. Olevsky, and A. Molinari, Instability of Sintering of Porous Bodies, Int. J. Plasticity, 16, 1-37 (2000). 19 E. Olevsky, Theory of Sintering: from Discrete to Continuum, Mater Sei Eng R Rev, 23, 41-100, (1998). 20 E. Olevsky, H. Dudek, and W. Kaysser, HIPing Conditions for Processing of Metal Matrix Composites using Continuum Theory for Sintering I. Theoretical Analysis, Acta Met Mater, 44, 70713 (1996). 21 J. Ma, Synthesis of Dense TiC-Ti Based Cermets via Self-Propagating High Temperature Synthesis and Quasi-Isostatic Pressing, Ph.D. Dissertation, 94, (2004). 22 E. Olevsky, Continuum Simulation of Consolidation in Porous Media, Proc. of World Congress on Powder Met. "PM'94", Paris, 2, 697- (1994).
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23
E. Olevsky, V. Skorohod, and M. Shtern, Continuum theory for sintering of the porous bodies: model and application, Int. J. Sei. Sinter., 23(2), 79- (1991). 24 E. Olevsky, A. Maximenko, and Y. Ivlev, Shape Distortion under Isostatic Pressing, Mater. Sei. Lett. 16, 1270-73 (1997). 25 E. Olevsky, G. Timmermans, M. Shtern, L. Froyen, and L. Delaey, The Permeable Element Method for Modeling of Deformation Processes in Porous and Powder Materials: Theoretical Basis and Checking by Experiments, Powd. Technol, 93(2), 127-41, (1997). 26 A. Gurson, Continuum Theory of Ductile Rupture by Void Nucleation and Growth: Part I, Yield Criteria and Flow Rules for Porous Ductile Media, J. Eng. Mater Technol. 99,2-15 (1977). "ABAQUS Theory Manual (Version 6.4), ABAQUSInc., Section 4.3.6 (2004). 28 ABAQUS Analysis User's Manual (Version 6.4), ABAQUS Inc., Section 11.2.9 (2004). 29 V. Tvergaard, Influence of Voids on Shear Band Instabilities under Plane Strain Condition, Int. J. of Fracture Mechanics, 17, 389-407 (1981). 3fl N. Aravas, On the Numerical Integration of a Class of Pressure-Dependent Plasticity Models, Int. J. for Numerical Methods in Engg., 24, 1395-416 (1987). 31 C. Chu, and A. Needleman, J. of Engg. Mat. and Tech., 102, 249-56 (1980). 32 A. Schofield, and C. Wroth, Critical State Soil Mechanics, McGraw-Hill, New York (1968). "ABAQUS Theory Manual (Version 6.4), ABAQUS Inc., Section 4.4.5 (2004). 34 ABAQUS Analysis User's Manual (Version 6.4), ABAQUS Inc., Section 11.3.3 (2004). 35 W. Chen, D. Han, Plasticity for Structural Engineers, Springer-Verlag, New York (1988). 36 Ph. Menétrey, and K. William, Triaxial Failure Criterion for Concrete and its Generalization, ACI StructuralJournal, 92, 311-18, (1995). "ABAQUS Theory Manual (Version 6.4), ABAQUS Inc., Section 4.4.4 (2004). D. Drucker, and W. Prager, Soil Mechanics and Plastic Analysis or Limit Design, Quarterly of Applied Mathematics, 10, 157-65 (1952). J. Rice, Constitutive Equations in Plasticity, Argon, A. S., Editor, MIT Press, Cambridge, Massachusetts (1975). 40 ABAQUS Theory Manual (Version 6.4), ABAQUS Inc., Section 4.4.2 (2004). "'ABAQUS Theory Manual (Version 6.4), ABAQUS Inc., Section 4.4.1 (2004). 42 ABAQUS Analysis User's Manual (Version 6.4), ABAQUS Inc., Section 11.3.2 (2004).
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THE EFFECT OF A SUBSTRATE ON THE MICROSTRUCTURE OF PARTICULATE FILMS C.L. Martin1, R. K. Bordia2 1: Laboratoire SIMAP - GPM2 Grenoble-INP, - UJF - CNRS 101, rue de la physique - BP46 38402 Saint Martin d'Héres cedex, France E-mail address:
[email protected] 2:Department of Materials Science and Engineering, University of Washington, Box 352120, Seattle, WA 98105, United States ABSTRACT Sintering on a dense substrate of paniculate films is an important process for a wide variety of applications including, for example, electronic packaging, sensors and actuators, and protective ceramic coatings. The presence of the substrate has significant consequence on the microstructure of the constrained sintered films. In particular, it has been observed that these films develop an anisotropic microstructure along the axis normal to the substrate. We use Discrete Element Method (DEM) simulations to study quantitatively such anisotropy. We model particles as spheres interacting through sintering forces both with other particles and with the substrate. Additionally, tangential viscous forces account for the drag that the substrate imposes on the particles. Our simulations show that indeed anisotropy develops along the thickness of the film. Using different film thicknesses, we show that the microstructure is more porous close to the substrate than far away from it. Also, pores that are close to the substrate are elongated, with their long axis preferentially oriented normal to the substrate. INTRODUCTION Following green state processing, the sintering of ceramic films leads to the final dimensions and microstructure of the component. Continuum mechanics models were first proposed in the 1980's to take into account the effect of the constraint [1-5]. These models use sintering stresses and sintering viscosities as the constitutive parameters [6-14]. Anisotropic continuum formulations were later shown to be more appropriate to model constrained sintering and sinter-forging due to the experimentally observed anisotropic microstructures [15, 16]. Because these continuum model work at a much larger length scale than the particle, they relate only indirectly to the microstructure. In parallel, Discrete Element Methods (DEM) have been developed to model sintering of metallic and ceramic powders. In DEM, the particles are modeled as spheres that interact with their neighbors through appropriate contact laws. DEM simulations of sintering allowed investigating the effect of particle rearrangements [17-20] and of local heterogeneities due to the presence of non-sintering particles [21, 22]. It was also shown that anisotropy of sintering kinetics due to prior pressing history [ 19] or to external stresses during sintering [23] could be tackled with DEM. It has been shown experimentally that anisotropy may also be induced during constrained sintering of ceramic films on a rigid substrate [16,24-26]. In that case, the microstructure development is influenced by a geometrical constraint due to the presence of the substrate. The detailed investigation of constrained sintering is well suited for DEM because anisotropy develops in DEM simply from writing the mechanical equilibrium of each particle. Microstructure anisotropy is the result of contact growth under preferential orientations in DEM [23]. Also, the constraint of the substrate may result in the appearance of new contacts and the loss of some others. Such phenomena can be naturally included in DEM simulations. The aim of this work is thus to use DEM simulations to improve our fundamental understanding of the basic mechanisms that govern microstructure development during the sintering of a particulate film on a substrate.
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MODEL DESCRIPTION The film is modeled as a 3D random assembly of spherical particles interacting mechanically through their contacts. The sum of contact forces is calculated to obtain the acceleration of particles at each time step. Details concerning the adopted methodology can be found in other works [19, 27, 28]. Sintering contact forces are given by Bouvard and McMeeking's model [29] for which grain boundary and surface diffusion are the main mechanisms of mass transport. For two spherical particles of identical radius R , having a contact radius as and indentation A (Fig. 1), the normal force Ns acting at the contact is given by : πα] áh 9 N=—KRV, * 8Δό di 8 ' where ys is the surface energy and Ab is a diffusio parameter : n with Db - Dob exp(-Qb/RT)
\ = ^ A
.. (1
(2
the diffusion coefficient for vacancy transport in the grain boundary with
thickness Sb and activation energy Qb; Ω is the atomic volume. A tangential contact force Ts opposes the tangential component of the relative velocity at the contact, du/dt [9, 30]: _ nalR1 du 7, = -η—where η is a viscous parameter with no dimension. viscous parameter is denoted as r\ for 8ΔThe di 6 particle-particle contact and η ^ for a particle-substrate contact. sub The contact radius grows according to Coble's model [31]:
f^Aü*
(4)
(5
di a, at which is in good accordance with numerical simulations on pairs of particles [29,32], As suggested by Parhami et al. [33], for two particles of radii n and r2, or for a particle in contact with the substrate (r2 —> oo ), we simply replace R by 2Ä*, where: (6 R-=r¡r2/(r]+r2l This is in good quantitative agreement with numerical simulations [32, 33] for moderate size ratios (r2lrt < 4) and for early and intermediate configurations. Table I. Material parameters leading to r = R,/Ab/1
=1.17 106 sec and used in the simulations and
typical for fine Al 2 O 3 particles. SbDab (m 3 /s) Q„ (kJ/mole) Ω (m 3 ) 1.3 10 os 475 8.47 10 3 0
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r
, (J/m 2 ) 2R (μνα) 1.1 0.2
The Effect of a Substrate on the Microstructure of Particulate Films
s-—
h
/
;
~~^
/&
,I
'"N,
X
■ - . .
:
"s
\°s K
TS
_ - ' ' '
; substrate '■
i
Figure 1. The two types of contacts taken into account in the DEM simulation: between a particle and a plane and between two particles. Material parameters chosen for the simulations are given in Table 1. However, lengths may easily be normalized by the mean radius of the particles R, while time can be normalized by z=R4/A¡,y¡. A total sintering time of 17 minutes at 1200°C was imposed. These conditions lead to a relative density in the film of the order of 0.80-0.85 for the initial relative density of the film that we have chosen (0.62). The initial packing, before sintering, was created by first generating a gas of randomly located particles in the simulation box with no contact. The gas of particles was then slowly densified following a procedure described in [34] up to 0.60 relative density. This packing was slightly densified further to attain 0.62 relative density and to obtain small contacts between particles (a/A=0.15). We have used the following values of η: 0.-0.001-0.01-0.1 and 1, in order to simulate a wide range of interfacial conditions between the film and the substrate. The bottom surface of the film can sinter with the substrate while all other surfaces are free. However, it is not possible to generate packings with enough particles to model a whole film. Instead, packings of 4,000 to 40,000 spherical particles are generated numerically to form micro-pillars of various heights (axis z defines the vertical axis of the pillar). Both cylindrical and rectangular pillar geometries were tested with height ranging from 10 to 25 particle diameter. EFFECT OF THE SUBSTRATE ON POROSITY GRADIENT Fig. 2 shows the typical evolution of a rectangular micro-pillar with initial height of approximately 20 particle diameters, and for which both the particle-particle and particle-substrate contacts are set to a large value (r\pan = η5„(, = 0.1). The initial rectangular shape of the sample is not homothetically preserved as sintering proceeds. Instead, the sample densities much less close to the substrate than away from it. This is due to the drag that the substrate exerts on the particles. We observed that the first 6 to 7 layers of particle exhibit large porosities that are preferentially oriented in the z direction. This result is in agreement with the observations of Guillon et al. on 20 μηι, 50 μπι and 150 μπι thick AI2O3 constrained films [24, 25], However, the dip coated films studied by Guillon et al. were much thicker in terms of particle number than those simulated here (particle mean size is 0.15 μπι). Similar observations were made on YSZ/AI2O3 coatings [26]. The gradient of porosities, which is qualitatively shown in Fig. 2, may be calculated as a function of the height of the micro-pillar. Figures 3 and 4 show the evolution of the relative density with position from the substrate z, for the various micro-pillars that have been simulated for a low r\su¡, (r\sub — 0.001, Fig. 3) and an intermediate r\sub (r|su¡,= 0.01).
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Figure2: Sections showing the microstructural evolution of a rectangular micro-pillar during sintering on a substrate with r\pan= r\su/,= 0.1. Initial height: 20 particle diameters; Total number of particles: 37,000.
Relative Density
Relative Density
Figure 3. Gradient of relative density along the z axis. The relative density is calculated in the brown cylinder. η ρ ο η = 0.1 and η^ί,= 0.001. The insert views in Fig. 3 and 4 give the final shape of the pillars. When the substrate viscous parameter increases (Fig. 4), the density gradient increases as compared to the small viscous parameter case (Fig. 3). The effect of the viscous parameter η5„/, at the particle-substrate interface is clear both on the final shape of the pillars and on the porosity gradient. The results for the value rjJU¡, = 0.1 may be found elsewhere together with more details on these simulations [28]. It is essentially identical to the one shown in Fig. 4. Thus it appears that above 0.01 the effect of η^ί, saturates.
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25
20
15
! 10
5 0 0.60
0.65
0.70
0.75
0.80
Relative Density
0.85
0.90
0.65
0.70
0.75
0.80
0.85
0.90
Relative Density
Figure 4. Same as .Fig. 3 with r\parl =0.1 and η™;, = 0.01. Symbols o and o indicate the average relative density along the whole height of the pillar. We did not observe a strong effect of the pillar geometry. However, we did observe that small chunks of particle clusters more often appear detached from the rectangular pillars than from the cylindrical ones. Also, we did not observe a strong correlation between the width to height ratio and the density gradient. We may thus infer that the present results should remain valid for films with larger width. We also measured the density gradient in the radial direction. Fig. 5 shows the typical gradient along the x and y directions (radial direction) for the pillar depicted in Fig. 2. From this figure, and from our observations on other pillars, it can be concluded that the substrate causes a gradient only along the z axis (apart from the very edge of the pillar). More interestingly, it shows that the free lateral surfaces play only a limited role in the microstructure development. This reinforces our belief that the results of the present simulations can be extended for much larger width that are typical of realistic films. Interestingly for applications, the height of the pillars influences the density gradient. Higher micro-pillars lead to larger porosity close to the substrate. The height effect is in qualitative agreement with the work of Guillon et al. who observed that, close to the substrate, 150 μηι ΑΙ2Ο3 thick films exhibit larger porosity than 50μιη AbOsthick films [24]. Fig. 4 shows that the top part of the highest pillars exhibit a relative density which is almost constant. Thus, it appears that above a height of approximately 10 particle diameters, the influence of the substrate fades. Note also that for the pillar heights studied here, the relative density averaged over the total height of the pillar does not depend on the pillar's height (as shown by the symbols in Fig. 4). EFFECT OF THE SUBSTRATE ON PARTICLE COORDINATION Additional microstructural information may be obtained from the coordination number of particles in the micro-pillar. Fig. 6 shows sections of a rectangular micro-pillar for r\sut, = 0.001 and f]mb = 0.1. The upper part of the micro-pillars shows approximately the same microstructure whatever the value of r\sub. Conversely, the particles close to the substrate have a lower coordination number especially for the η„;, = 0.1 case. More generally, observations on all tested samples have shown that the low coordination region is limited to 0.4 times the total initial height of the micro-pillar.
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Relative Density Figure 5. Radial gradient of density in the x and y (radial) directions for the pillar shown in Fig.2. ηΡ<„,= 0.1 and r\sub= 0.01.
Figure 6. Sections of a rectangular micro-pillar sintered on a substrate with two different values of η^ί,. The colors indicate the coordination number of particles. EFFECT OF THE INTERPARTICLE VISCOSITY PARAMETER So far, the simulations that we have discussed are limited to a single value of the viscosity parameter (r\pan = 0.1). This value is of the same order or larger than the typical values proposed in the literature [18, 20]. In any case, r\pan and r\sut, should be smaller than unity to ensure that the normal viscosity force term in eqn (1) is larger than the tangential force (eqn (4)). Figure 7 shows that the interparticle viscosity also has some influence on the density gradient and on the microstructure of the pillars. For the cylindrical pillars shown in Fig.7, a low value of r\pan (ηρο«=0.01) is associated with larger porosity close to the substrate followed by a steeper gradient in the upper region. Intermediate interparticle viscosity (r\pan=0.\) leads to the standard cases studied in the preceding section with large porosity close to the substrate followed by a gradual increase in relative density. Very large interparticle viscosity (r\parj=l.), is associated with a smaller porosity close to the interface. Interestingly, such a very large interparticle viscosity parameter does not impede densification as shown in Fig.7 (the microstructures are all compared at the same sintering time: 1000 sec). The sectioned pillars associated with each value of r\pa„ in Fig.7 help understanding the relative density gradient measured in these simulations. The lateral free surfaces associated with each value of
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r\par! shows that the pillar microstructure close to the substrate may be dictated by: • the substrate (ηρ„Λ=0.01, η„4=0.01); • both the substrate and the particles in the upper part of the pillar (r\parf=0.1, η™(,=0.01); • the particles in the upper part of the pillar (r\parp\., r\sui,=0.0l).
Relative Density
Figure 7: Gradient of the relative density along the z axis for three different values of ^„„.and η™;,=0.01. Colors in the cylindrical sectioned samples indicate the coordination number of particles. This section demonstrates that, on top of the drag with the substrate (characterized by r\sub), the interparticle viscosity also plays a role in the microstructure development in constrained sintering. However, it should be clear that the very large value r\parñl- is probably unrealistically large and provides only an upper bound to practical conditions. Also, we have observed that large interparticle viscosity may be associated with crack like defects as discussed in detail in a recent paper on the nucleation and growth of cracks during sintering [35]. CONCLUSIONS Microstructural information at the particle length scale was obtained for constrained sintering of particulate films using DEM simulations. The constraining effect of the substrate was characterized with the viscous parameter r\mb, which defines the drag between particles and the rigid substrate. In accord with experimental observations, we were able to reproduce that the film is more porous near the substrate, and that a gradient in porosity and in contact numbers arises along the thickness of the film. Since DEM operates at the particle length scale which is the pertinent length scale for the film microstructure, we believe that these simulations offer a powerful tool to improve our basic understanding of the microstructural evolution mechanisms of film constrained sintering. The main mechanism to explain the microstructure development of a constrained sintering film is the drag that the substrate imposes on contacting particles. Interfacial tangential forces resist the normal attractive sintering forces and cause loss of certain contacts. We also observed that the interparticle viscosity influences the microstructure development. The present simulations mainly yield qualitative results that help explain the mechanisms that lead to the anisotropic microstructure observed in constrained sintering. Quantitative comparisons will be possible in the future when simulations with a very large number of particles (at least one or two orders of magnitude larger than in the present simulations) will be available. This will be facilitated by heavy parallelization of the dp3D code. This improvement is currently under progress.
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ACKNOWLEDGEMENTS RKB would like to thank the Alexander von Humboldt-Stiftung for partial financial support for this work (Research Award for Senior Scientists to RKB). CLM acknowledges the financial support of CNRS during his sabbatical leave at the department of Materials Science and Engineering, University of Washington. REFERENCES [I] G. W. Scherer, Sintering inhomogeneous glasses: Application to optical waveguides, J. Non-Cryst. Solids 34, (1979) 239-256. [2] G. W. Scherer, T. Garino, Viscous Sintering on a Rigid Substrate, J. Am. Ceram. Soc. 68, (1985) 216-220. [3] R. K. Bordia, R. Raj, Sintering Behavior of Ceramic Films Constrained by a Rigid Substrate, J. Am. Ceram. Soc. 68 (1985) 287-292. [4] R. K. Bordia, G. W. Scherer, On constrained sintering . 1. Constitutive model for a sintering body, Acta Metall. 36 (1988) 2393-2397. [5] R. K. Bordia, G. W. Scherer, On constrained sintering .2. Comparison of constitutive models, Acta Metall. 36 (1988) 2399-2409. [6] A. Jagota, K.P. Z. Cai, G. L. Messing, D. J. Green, Determination of the Mechanical Response of Sintering Compacts by Cyclic Loading Dilatometry, J. Am. Ceram. Soc. 80 (1997) 445-452. [7] O. Gillia, C. Josserond, D. Bouvard, Viscosity of wc-co compacts during sintering 49 (2001) 1413-1420. [8] R. Mikeska and R. K. Bordia, "Isotropie Constitutive Models for Sintering Particle Packings", Journal of the American Ceramic Society, 73, [8], 2266-73 (1990). [9] A.C.F. Cocks, "The Structure of Constitutive Laws for the Sintering of Fine Grained Materials", Acta Metall. Mater., 42 [7] 2191-2210 (1994) Mohanram, S. H. Lee, G. L. Messing, D. J. Green, A novel use of constrained sintering to determine the viscous Poisson's ratio of densifying materials, Acta Mater. 53(2005)2413-2418. [10] P. Z. Cai, G. L. Messing, D. J. Green, Determination of the Mechanical Response of Sintering Compacts by Cyclic Loading Dilatometry, J. Am. Ceram. Soc. 80 (1997) 445^52. [II] E.A. Olevsky, "Theory of Sintering from Discrete to Continuum. Invited Review", Mater. Sei. Eng. R23 [2] 40-100 (1998) [12] O. Gillia, C. Josserond, D. Bouvard, Viscosity of wc-co compacts during sintering 49 (2001) 1413-1420. [13] R. Zuo, E. Aulbach, J. Rodel, Shrinkage-Free Sintering of Low-Temperature Cofired Ceramics by Loading Dilatometry, J. Am. Ceram. Soc. 87 (2004) 526-528. [14] A. Mohanram, S. H. Lee, G. L. Messing, D. J. Green, A novel use of constrained sintering to determine the viscous Poisson's ratio of densifying materials, Acta Mater. 53 (2005) 2413-2418. [15] R. K. Bordia, R. Zuo, O. Guillon, S. M. Salamone, J. Rodel, Anisotropie constitutive laws for sintering bodies, Acta Mater. 54 (2006) 111-118. [16] O. Guillon, E. Aubach, R. K. Bordia and J. Rodel, "Constrained Sintering of Alumina Thin Films: Comparison Between Experiments and Modeling", Journal of the American Ceramic Society, 90 [6] 1733-1737(2007) [17] W. J. Soppe, G. J. M. Janssen, B.C. Bonekamp, L. A. Correeia, H. J. Veringa, A computer-simulation method for sintering in 3-dimensional powder compacts, J. Mater. Sei. 29 (1994) 754-761. [18] F. Parhami, R. M. McMeeking, A network model for initial stage sintering, Mech. Mater. 27(1998)
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111-124. [19] C. L. Martin, L. C. R. Schneider, L. Olmos, D. Bouvard, Discrete element modeling of metallic powder sintering, Scripta Mater. 55 (2006) 425^28. [20] B. Henrich, A. Wonisch, T. Kraft, M. Moseler, H. Riedel, Simulations of the influence of rearrangement during sintering, Acta Mater. 55 (2007) 753-762. [21] A. Jagota, G. W. Scherer, Viscosities and sintering rates of composite packings of spheres, Journal of the American Ceramic Society 78 (1995) 521-528. [22] L. Olmos, C. L. Martin, D. Bouvard, Sintering of powder mixtures: experiments and simulations, Powder Technol. in Press. [23] W. Wonisch, O. Guillon, T. Kraft, M. Moseler, H. Riedel, J. Roedel, Stress-induced anisotropy of sintering alumina: Discrete element modelling and experiments, Acta Mater. 55 (2007) 5187-5199. [24] O. Guillon, S. Krauß, J. Rodel, Influence of thickness on the constrained sintering of alumina films, J. Eur. Ceram. Soc. 27 (2007) 2623-2627. [25] O. Guillon, L. Weiler, J. Rodel, Anisotropie Microstructural Development During the Constrained Sintering of Dip-Coated Alumina Thin Films, J. Am. Ceram. Soc. 90 (2007) 1394-1400. [26] X.-J. Lu, P. Xiao, Constrained sintering of YSZ/A1203 composite coatings on metal substrates produced from eletrophoretic deposition, J. Eur. Ceram. Soc. 27 (2007) 2613-2621. [27] C. L. Martin, D. Bouvard, S. Shima, Study of particle rearrangement during powder compaction by the discrete element method, J. Mech. Phys. Solids 51 (2003) 667-693. [28] C.L. Martin, R.K. Bordia. The effect of a substrate on the sintering of constrained films. Acta mater, in press (2008). [29] D. Bouvard, R. M. McMeeking, The deformation of interparticle necks by diffusion controlled creep, Journal of the American Ceramic Society 79 (3) (1996) 666-672. [30] R. Raj, M. F. Ashby, Grain boundary sliding and diffusional creep, Metall. Trans. 2 (4) (1971) 1113-1123. [31] R. L. Coble, Initial sintering of alumina and hematite, Journal of the American Ceramic Society 41 (1958) 55-62. [32] J. Pan, H. Le, S. Kucherenko, J. A. Yeomans, A model for the sintering of spherical particles of different sizes by solid state diffusion, Acta Mater. 46 (1998) 4671-4690. [33] F. Parhami, R. M. McMeeking, A. C. F. Cocks, Z. Suo, A model for the sintering and coarsening of rows of spherical particles, Mechanics of Materials 31 (1999) 43-61. [34] C. L Martin, R. K Bordia, Influence of adhesion and friction on the geometry of packings of spherical particles, Physical Rev. E 77 (2008) 031307. [35] C. L Martin, H. Camacho-Montes, L. Olmos, D. Bouvard, R. K Bordia, Evolution of defects during sintering - discrete element simulations. Submitted for publications to J. of American Ceramic Society, November 2008.
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MODELLING CONSTRAINED SINTERING AND CRACKING Ruoyu Huang and Jingzhe Pan* Department of Engineering, University of Leicester Leicester, UK ABSTRACT Predicting cracking during constrained sintering of ceramic powder compacts is an important issue to manufactures of ceramic components. In theory the finite element method can be used to predict the sintering deformation and cracking. In practice the method has not been used very often for a simple reason - the material data required in a finite element analysis is difficult to obtain. Furthermore simulating the nucleation and propagation of cracks is a very difficult task for the traditional finite element scheme. Consequently very few finite element models of multi-cracking during sintering have been reported. Pan and his co-workers developed a reduced finite element method (Kiani et. al. J. Eur. Ceram. Soc, 27, 2377-2383(2007); Huang and Pan, J. Eur. Ceram. Soc, 28, 1931-1939 (2008)) which does not require the viscosities. Instead the densification data (density as function of time) is used to predict sintering deformation. The present paper extends the reduced method to Eulerian format so that multi-cracking can be modelled conveniently. The Eulerian format is however not limited to the reduced finite element method. It can also be used with the full constitutive law taking into account of sintering anisotropy. Here the reduce method is pursued for its potential advantage of requiring much less material data. 1. INTRODUCTION To predict shape change and cracking of ceramic components during constrained sintering is a critical issue in sintering technology. The temporal evolution of shape and cracks of a component can be calculated using the finite element method. However, two essential difficulties in the finite element method limit its applications. Firstly, there is no generally valid constitutive law for sintering which is a key input in the finite element analysis describing the relationship between the strain rates and stresses'" . Two approaches can be used to establish a constitutive law. The first approach is to use micromechanical models in which a mechanism of matter redistribution is assumed2,4"8 and simplifications to the microstructure are made " . However the micromechanical models do not take substructures, such as particle agglomeration and large pores, in a powder compact into account because of the mathematical difficulty in obtaining an analytical solution for such a microstructure. Consequently the predictions of the material models differ from each other widely, each depending on its assumed microstructure and mechanism of matter redistribution9. It is often difficult to know which material model to choose in a finite element analysis. The second approach to establish a constitutive law is to fit the experimental data directly " . This is however an expensive and time consuming exercise. Secondly, when multi-cracking occurs, the simulations become difficult for the classical finite element method. In a fracture mechanics based model, the stress singularity has to be taken care of by introducing special shape functions or elements. Furthermore cracking alters the topological connection between the elements which have to be regenerated automatically13"16. The programming effort to deal with the topological change in computer coding is daunting. Recently Pan and his co-workers suggested a reduced finite element formulation to calculate sintering deformation which requires only the densification data (density as a function of time) as the material input17''8. The reduced formulation is valid as long as no external force is applied to the component during sintering. In the terminology of continuum solid mechanics, the reduced method satisfies ' Corresponding author. Tel.: +44 116 223 1092; fax: +44 116 252 2525. Email address:
[email protected] (J. Pan).
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exactly the conditions of equilibrium, compatibility and boundary constraints, but satisfies only partially the constitutive law. Because the sintering deformation is insensitive to the choice of constitutive law, the reduced solution can provide a good approximation to the full solution. If one uses the option of linear viscous material in a commercial finite element package, the reduced analysis can be implemented by inputing a unity material matrix and calculating force matrix from the densification data. In the following discussions the reduced method is referred to as the densification
