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 based finite element method or DFEM. A range of numerical case studies and direct comparison to experimental data have shown that the reduced method is valid and may be even pushed into modelling deformation during constrained sintering18. To accommodate multi-cracking in the reduced model, this paper presents two different formats of its finite element implementation, i.e. the Arbitrary Lagrangian Eulerian (ALE) format and Eulerian format. The former has advantage to model shape change while the latter is more convenient to model multi-cracking. It is important to point out that both formats are not limited to the reduced finite element method. They 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. 2. THE REDUCED FINITE ELEMENT METHOD This section provides a brief overview of the reduced method so that the readers don't have to look for our previous publications ' . In a finite element analysis of sintering deformation the powder compact is treated as a viscous continuum solid, i.e. a material that deforms with time under a self existing stress (often refereed to as the sintering potential). At each time-step the velocity field of the sintering body is calculated at its current configuration and then the shape of the body is updated using the direct Euler scheme. Under the framework of continuum solid mechanics, the correct velocity field must satisfy four conditions: (a) compatibility, (b) equilibrium, (c) boundary conditions and (d) constitutive law. Therefore in a general stress analysis a full constitutive law must always be known. For example in an elastic stress analysis one has to know the Young's modulus and Poisson's ratio of the material. The conjecture of the reduced method is that in the special case of pressureless sintering, a solution that satisfies conditions (a), (b), (c) and partially (d) can provide a good approximation to the exact solution which satisfies all the four conditions. In a finite element formulation using the velocity field as its basic variable, the compatibility condition is guaranteed by representing the velocity field using appropriate shape functions and by calculating the strain rates from the velocity field using the relationship
£
1 du, ^ 2 ex¡
OUj_
dx¡
(1)
in which ¿0 is the strain rate tensor, ú¡ the velocity field and xt the Lagrange coordinate. The velocity boundary conditions are satisfied by setting the nodal velocities on the boundary to their prescribed values. The equilibrium condition is equivalent to the principle of virtual power, which states that \airSeljdV
= d,
(2)
V
in which a¡j is the stress tensor and Sé¡¡ the virtual variation of the strain rates which must satisfy the compatibility and the velocity boundary conditions. The integration is over the entire sintering body. Assuming a linear constitutive law:
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2η5
3ηΒ
3ηΒ
in which am is the mean stress, CTS the sintering potential, η5 the shear viscosity, ηΒ the bulk viscosity, S¡j the Kronecker delta function, and Sy the devitoric stress tensor which is defined as
In Eqn. 3 the first term represents the shear deformation, the second term represents the volume change due to the mean stress and the third term represents the volume change due to the sintering potential. A uniform compact of any shape shrinks according to the third term if it is unconstrained and not subject to any external force. Therefore this term as a whole can be determined from free sintering experiment using uniform samples according to that
έe p = --£- = - A *
3ηΒ
3D'
( 5)
( >
in which D represents the relative density and can be measured as a function of time in the experiment. Alternatively ¿exp can also be calculated from a master sintering curve19 using Eqn. 5 if such curve is available. The difficulty in measuring the constitutive law experimentally is to separate the sintering potential at from the bulk viscosity ηΒ. To avoid this difficulty, Kiani et alP assumed that <τ„=0 and therefore dropped the second term from Eqn. 3. The constitutive law then becomes
*'Ί£ + *-Α·
(6)
Using Eqn. 6 in Eqn. 2 gives ¡Isk-é^S^dV^O.
(7)
It is difficult to measure r¡s experimentally. Kiani eí al}1 further assumed that the shear viscosity is uniform within a powder compact so that it is eliminated from Eqn. (7). This is an empirical assumption and its validity for constrained sintering remains to be studied. The virtual power principle can then be written as
j(¿„-WS»X<^ = 0,
(8)
V
Eqn. 8 is the reduced formulation which requires only έ
as material input. It is based on two rather
crude assumptions. However, its validity is far beyond cases for which the two assumptions are strictly true as being shown in the numerical case studies in section 4. It is also possible to understand Eqn. (8) in a common sense argument. Eqn (8) tries to match the strain rates é¡¡ with the free sintering rate and
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satisfy the velocity boundary conditions at the same time. Using the standard finite element procedure20, the velocity field ú¡ is represented using a set of shape functions and the strain rates ét¡ are calculated using Eqn. (1). Writing the results in the matrix form gives
[4 = M4
(9)
in which e indicates that the matrixes are defined for the e element, [B\ is a matrix calculated from the shape functions, and [ú\ contains the velocities of all the nodes on the e"1 element. Substituting expression (9) into (8) leads to
I<WM.[4-M.}=o
(io)
[Kl=¡[Bj[B}lV
(11)
elements
in which
And
[H=jWk,p ¿„ ¿„ 0 0 <ψκ
(12)
yc
For Eqn. (10) to be true for arbitrary δ[ά], we must have
ΣΜ.[4=ΣΜ.
elements
elements
(i3)
Eqn. (13) is a set of linear simultaneous equations which can be solved using a standard solver to give the velocity field of the sintering deformation. It can be seen that the material data, ¿ exp , enters the force matrix (Eqn. (12)) while the usual material matrix in the viscosity matrix of Eqn. (11) is simply unity. Therefore the reduced analysis can be readily implemented using a commercial finite element package (which provides an option of linear viscous material with large deformation) by setting the material matrix as unity and calculating the force matrix using Eqn. (12). 3. THE ARBITRARY LAGRANGIAN EULERIAN AND EULERIAN FORMATS Eqn. (13) is established in the current configuration imbedded inside a fixed Eulerian coordinates, which is known as the Arbitrary Lagrangian Eulerian (ALE) format. The ALE format is a dominant format used in the finite element analysis. In this format the finite element mesh deforms with the object so the mesh itself represents the current configuration. This fact makes the ALE format an ideal candidate for modelling deformation. An alternative format, i.e. the Eulerian format is also available for implementing the reduced method. When a crack nucleates and propagates, the finite element mesh for the previous configuration must undergo topology change by either splitting connected elements or eliminating damaged elements. The ALE format becomes inconvenient. By contrast, in Eulerian format, the mesh is fixed at the Eulerian coordinates without any deformation. The current configuration is
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represented by the moving of representative material points which carry all the state information of material such as strain, relative density and damage. The Eulerian format is inferior to the ALE format in deformation modelling since the discrete points cannot exactly represent the shape of an object and its boundary condition. However, this format is superior to the ALE format when modelling multi-cracking due to its flexibility of representing cracked or damaged using discrete material points21. Figure (1) illustrates the difference between the two formats. A finite element mesh is generated in the initial configuration, B 0 , as shown in Fig. 1(a) for both formats. For the ALE format each node of the mesh is attached to a material point X E B , and the node moves with this material point keeping its material coordinates X fixed. The mesh itself deforms consistently to represent the current configuration, Bt. For the Eulerian format the representative material points are assigned to (located at 2x2 Gaussian points here) each element to represent the current configuration, Bt of the shrinking body.
(a)
(b)
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(c) Figure 1. The difference between the ALE format and the Eulerian format (a) initial configuration with mesh for both formats and representative material points for the Eulerian format, (b) current configuration and mesh for the ALE format, and (c) current configuration and representative material points for the Eulerian format. For both formats, the integrations in eqns. (11) and (12) are carried out in the entire mesh. We follow the idea of Kitsunezaki16 and remove damaged material points from the integrations if the strains at a material point meet the following damage criterion, max(e jf +f exp á' jf )n ( n y >£ c .
(14)
in which ei} is the Green strain at time t, eavStj is the isotropic Green strain of free sintering without pressure at the same time r, maxif^ +ε^δΛηιη] e
t
+E
afí¡j) > a n d £c ' s
me
represents the maximum eigenvalue of
critical strain. It is worth to point out that sc could have different values
at the compact-substrate interface and inside the powder compact14. For the ALE format, the integrations in eqns. (11) and (12) are straightforward because the mesh simply represents the integration domain. The finite element routine using the ALE format is listed in Table 1. Table 1: Numerical scheme for the ALE format Step 0: input initial data (initial configuration, relative density) Step 1: element level integration at time tn: compute the matrixes [K] and [F] by Gaussian integration. Step 2: global level assembly of element contribution to establish the DFEM eqn. (13). Solve the eqn. (13) to get the velocity field on the current configuration. Step 4: update the position of all nodes of the mesh by using current velocity field. A strain rate field έ is calculated by the velocity field. Rate of change of relative density D in each representative material point is calculated by the relation DID = -3έ„. This leads to the update of relative density. By using the updated configuration, the (Green) strain field is updated. Step 5: check for newly damaged elements by damage criterion. If number of broken elements is more than a certain number, e.g. 10, adopt a smaller time step and return to Step 1 for time r„. otherwise renew the mesh and go to next time r „ , .
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In the Eulerian format, the material points which represent the current configuration may move from one element to the other, and one element may contain different material points at different time. At any time t, if there is no material point inside the e* element, the integration simply vanishes in this element. If material points exist inside an element, they are divided into two catalogues as shown in Fig. 2,: the damaged ones and intact ones judged according to Eqn (14). o ■«
Intact material point
X "*
damaged material point
Figure 2. Intact and damaged material points in a fixed element The damaged material points make no contribution to the integrations. If there are nm material points inside the element, of which nd are damaged, the intact fraction of the element volume, / = (nm -nd)Inm
, is inserted in front of the integrations in both eqns. (11) and (12), i.e. to replace
\*dV by / \*dV, to represent the effect of damage. The numerical scheme using the Eulerain format is listed in Table 2. Table 2: Numerical scheme for the Eulerian format Step 0: input initial data (initial configuration, relative density) Step 1: element level integration at time tn : detect the existence of intact and damaged representative material points, calculate volume fraction / compute the έ at computational Gaussian points by interpretation over intact material points, implement Gaussian integration to compute matrixes [K] and [F] . Step 2: global level assembly of element contribution to establish the DFEM eqn. (13). Solve the eqn. (13) to get the velocity field on the whole FE mesh. Step 4: update the position of all representative material points by using current velocity field. A strain rate field έ is calculated by the velocity field. Rate of change of relative density D in each representative material point is calculated by the relation D/D = - 3 ¿ a . This leads to the update of relative density. By using the velocity field, the (Green) strain in representative material points are updated as well. Step 5: check for newly damaged material points by damage criterion. If number of broken points is more than a certain number, e.g. 10, adopt a smaller time step and return to Step 1 for time tn. otherwise go to next time tnt¡.
4. NUMERICAL CASE STUDIES When a full constitutive law and all its parameters are available, the free shrinking rate ¿
can
be calculated from the constitutive law using Eqn. (5). We consider the constitutive law developed by Du and Cocks22 for alumina powder compacts which sinter in the solid state:
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■j(í)(?W*+3/«*'.-*.*
(15)
in which d0 and d represent the initial and current grain size respectively, ¿0 is the strain rate of the fully dense material of grain size d0 at a constant uniaxial stress σ 0 , and the two functions c a n d / are dependent on the initial and current relative densities, D0 and D : 0.54(1 -D0f f(D)-
c(D)-
D(D
D0f
(16)
3.2(1-Do)"2 D
D > 0.95
1.08(1-Z?0)2 D(D-D0)2 1
D < 0.95 1,
1 - 2.5(1 -D)
(17)
D > 0.95
The free shrinking rate ¿rap for the reduced analysis can be calculated from the Du and Cocks model as (18) "old ) Du and Cocks used the nominal data of σ 0 = 3.33ΜΡα, έ0 = 4.53xlO~V\ d0 =7.48x10 °ms and as = XMPa, which are also used in this study. In our analysis, a random distribution of the initial relative density is assumed which follows the following format: ο 0 = 5 0 ( 1 + ΛΤ(0,σ2)).
(19) 2
in which D0 =0.64 is the average initial relative density, and JV(0,a )is the normal distribution with mean value of 0 and variance of σ2. We have set the critical strain cc =0.13 for the compact substrate interface and ec =0.1 for inside the compact respectively. These values are for numerical demonstration only. Experimental determinations of the critical strains are undergoing. CASE 1: CRACKING OF A 2-D FILM DURING CONSTRAINED SINTERING L=10h
Figure 3. A single layer constrainedfilm(2-D plane strain model) We consider a single porous layer perfectly attached to a rigid substrate as shown in Fig.3. In the
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finite element model a total number of 1000 8-noded elements are used for the film and plan strain condition is assumed. The deformation of this structure was studied in our previous work18. In the present work the Eulerian format of the reduced finite element method is used to model cracking during the constrained sintering. The value of σ 2 is set as 0.01 to give an initial random density distribution. The crack evolution in the layer is presented in Fig. 4 by showing the intact material points only. There is some deterministic behaviour in the cracking pattern. The first transversal crack nucleates on the symmetrical axis of the layer at the middle point of film-substrate interface and then propagates vertically toward the top surface of the film. The subsequent minor cracks nucleate in a more disordered style after the very deterministic first crack. These results agree well with the work reported in a similar study for multi-cracking during drying16.
Figure 4. Temporal evolution of cracks in a constrained film during sintering. The corresponding relative densities of an uncracked film are 0.78, 0.79 and 0.82 respectively. CASE 2: CRACKING OF A 3-D FILM DURING CONSTRAINED SINTERING Next the porous layer attached to a rigid substrate is studied using a 3-D finite element model as shown in Fig. 5. Two different views of the crack pattern are also illustrated in the figure. The thickness to length ratio (h/b) is set as 1/12.5, and the ratio of b/a is set as 5/3. A total number of 2700 (30x18x5) 20-noded elements are used to model the film. The value of σ2 is set as 0.01 again. Fig 6
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shows the crack pattern at the film-substrate interface (Fig 6(a)) and viewed from the top surface of the film at t = 33J. Again a deterministic cracking behaviour is observed such that the first crack nucleates from the middle of film-substrate interface and propagates upward to the film surface. Significant peeling is observed at the film-substrate interface.
Figure 5. A patch of constrained porous film. Two different views of the crack pattern are illustrated: crack viewed on the top surface and peeling at the film-substrate interface.
Figure 6. Crack patterns in the porous film as it shrinks (a) at thefilm-substrateinterface and (b) viewed from the top surface of thefilm.The corresponding relative density of uncracked film is 0.8.
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CASE 3: DISORDER IN THE CRACK PATTERN In Cases 1 and 2 we have observed relative deterministic cracking behaviour. From our numerical study it is found that decreasing the thickness/length ratio of the film or increasing σ2 can lead to a more random cracking behaviour. Fig. 7 shows the crack patterns viewed from the top surface of the film for a square patch of film (a/b=l) with the thickness/length ratio of h/b=0.1. The ratio of h/b is set as the same as that in case 1, but a much larger standard variance, σ 2 =0.1, is used. A total number of 4225( 65x65x1) 20-noded elements are used in the finite element model. It can be observed from the figure that although the cracks are still clustered around the symmetry lines, a more random pattern is developed. Further increasing the standard variance of the initial density distribution can lead to a complete random cracking pattern.
t = 190s
Figure 7. Cracking pattern viewed from the top surface of the film for a case with a larger standard variance of the initial density distribution than the case shown in Fig 6. 5. CONCLUSION This paper shows that the reduced method can be implemented in two different formats, the ALE and Eulerian formats. The ALE format has been used in modelling deformation for a sintering body while the Eulerian format has an advantage when modelling the nucleation and propagation of cracks during sintering. It is important to point out that the case studies shown in this paper simply serve as a demonstration of the capacity of the numerical scheme, not as a validation of the underlying physics in the model. It remains to be studied that whether the reduced formulation and the strength based cracking criterion can give the correct prediction for cracking during constrained sintering. There is always the fallback position of using the full constitutive laws in the finite element analysis if the reduced formulation is invalid. However the reduced formulation offers such an advantage over the full constitutive laws that it is worthwhile to push it to the limit of constrained sintering.
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ACKNOWLEDGEMENTS This work is supported by an EPSRC research grant S97996 which is gratefully acknowledged. REFERENCES 1 A.C.F. Cocks, The structure of constitutive laws for the sintering of fine grained materials, Acta Metall., 42, 2191-2210 (1994). 2 E.A. Olevsky, Theory of sintering: from discrete to continuum, Material Science and Engineering R23,41-100 (1998). 3 J. Pan, Modeling sintering at different length scales, International Materials Reviews, 48, 69-85(2003). 4 R.M. McMeeking and L. T. Kuhn, Diffusional creep law for powder compacts, Acta metal. Mater., 40,961-969(1992). 5 J. Pan and A.C.F Cocks, Constitutive model for stage 2 sintering of fine grained materials-1 grain-boundaries act as perfect sources and sinks for vacancies, Acta Materialia 42, 1215-1222(1994). 6 T. Kraft and H. Riedel, Numerical simulation of solid state sintering; model and application, Journal of the European Ceramic Society, 24, 345-361(2004). 7 J. Svoboda, H. Riedel and R. Gaebel, Model for liquid phase sintering, Acta mater, 44, 3215-3226(1996). 8 P. E. McHugh and H. Riedel, Liquid phase sintering model: Application to SÍ3N4 and WC-Co, Acta mater, 45, 2995-3003(1997). 9 Gillia, PhD theses, INPG, France, (2000). 10 Gillia, C. Josserond and D. Bouvard, Viscosity of WC-Co compacts during sintering, Acta mater, 49, 1413-1420(2001). 11 H.G. Kim, O. Gillia, P. Doremus and D. Bouvard, Near net shape processing of a sintered alumina component: Adjustment of pressing parameters through finite element simulation, International Journal of Mechanical Sciences, 44, 2523-2539(2002). 12 H. G. Kim, O. Gillia and D. Bouvard, A phenomenological constitutive model for the sintering of alumina powder,/. Euro. Ceram. Soc, 23, 1675-1685(2003). 13 J. Liang, R. Huang, J.H. Prevost, and Z. Suo, Evolving crack patterns in thin films with the extended finite element method. International Journal of Solids and Structures, 40, 2343-2354(2003). 14 P. Federl, Modeling Fracture Formation on Growing Surfaces. PhD thesis, University of Calgary, 2002. 15 E.A. Jagla, Maturation of crack patterns. Physical Review E, 69, 056212(2004). 16 S. Kitsunezaki, Fracture patterns induced by desiccation in a thin layer, Physical Review E, 60, 6449-6464(1999). 17 S. Kiani, J. Pan, J.A. Yeomans, M. Barriere and R Blanchart, Finite element analysis of sintering deformation using densification data instead of a constitutive law, J. of the Euro. Ceram. Soc, 27, 2377-2383(2007). 18 R. Huang and J. Pan, A further report on finite element analysis of sintering deformation using densification data-Error estimation and constrained sintering, J. of the Euro. Ceram. Soc, 28, 1931-1939(2008). 19 S. Kiani, J. Pan and J. A. Yeomans, A new scheme of finding the master sintering curve, Journal of American Ceramics Society, 89, 3393-3396(2006). 20 O.C. Zienkiewicz and R.L. Taylor, The Finite Element Method (McGRAW-Hill Book Company 1989).
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D. Sulsky, S.-J. Zhou, H.L. Schreyer, 1995. Application of a particle-in-cell method to solid mechanics, Comput. Phys. Commun. 87 236-252. Z.-Z. Du and A. C. F. Cocks, Constitutive models for the sintering of ceramic components-I. Material models, Acta metal., 40, 1969-1972(1992).
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ATOMISTIC SCALE STUDY ON EFFECT OF CRYSTALLINE MISALIGNMENT ON DENSIFICATION DURING SINTERING NANO SCALE TUNGSTEN POWDER Amitava Moitra1, Sungho Kim1, Seong-Gon Kim1, Seong Jin Park1, Randall German2, and Mark F. Horstemeyer1 Center for Advanced Vehicular Systems, Mississippi State University 200 Research Blvd., MS 39759, USA 2 College of Engineering, San Diego State University 5500 Campanile Drive, San Diego, CA 92182-1326, USA ABSTRACT An atomistic simulation is used in this research to probe the sintering process of crystalline tungsten and tungsten alloys at the sub-microscopic level. We have performed an atomistic simulation with nanoscale tungsten particles. Of primary interest is the application and development of classical and quantum mechanical methodologies to gain insight into the fundamental characteristics of atomic movement during sintering and how various additives influence the sintering processing. Since both neck growth and shrinkage result, it is possible to extend these calculations to the physical properties of the material. Also, this paper focuses on densification and grain growth during sintering as a function of the crystalline misalignment between particles. These findings can provide a foundation for a new virtual approach to nanoscale processing and material design. INTRODUCTION Tungsten, along with its alloys and compounds, occupies a unique position in materials science. The material properties that make tungsten attractive to the metals industry are high density, hardness, melting temperature, elastic modulus, and conductivity in conjunction with low thermal expansion. The combination of these unique properties explains the diverse applications of tungsten ranging from home lighting to thermonuclear fusion firstwall protection [1-2]. Tungsten is the logical first choice for a full model of nanoscale powder processing. Refined sintered microstructures off a means to improve properties, especially in electrical, mechanical, and wear components. With nanoscale tungsten powders available at reasonable costs, it is clear a new thinking is required on how to balance the size-dependent advantages against the temperaturedependent limitations. The Hall-Petch effect—the hardness increases in proportional to the inverse square-root of grain size [3-4]—suggests that significant opportunities exist if nanoscale powders could be consolidated to full densities with minimized coarsening. Therefore, it is of great importance to understand the sintering behavior of tungsten nanoparticles for their advancement of present engineering and technological growth. Nanoscale tungsten powders have some processing attributes that scale with particle size, while others are only temperature-dependent. Accordingly, novel consolidation cycles need to be created to adapt to the differing sensitivities. For example, 20 nm tungsten sinters to near full density at temperatures below 830°C [5], but oxide reduction that is a part of sintering in hydrogen is delayed to higher temperatures [6]. Thus, nanoscale tungsten materials need to be reassessed for a balance between thermodynamics and processing. It is the contention here that modeling provides a means to identify processing cycle options customized to nanoscale tungsten-based materials. Data on powder characteristics, sintering response, and product properties exist for tungsten powders [1-2, 4, 6-8]. Likewise, processing models are known with regard to compaction and sintering [9-10]. Recent research has assembled the processing models into a model customized for the consolidation of
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nanoscale tungsten powders, pinned using existing data. Accordingly, predictions can now be made for product properties as functions of the starting powder and processing conditions. This procedure allows examination of opportunities as a guideline to future research. Molecular dynamics (MD) simulations offer an effective tool to study the melting and coalescence of nanoparticles [11-13]. These atomistic simulations require accurate atomic interaction potentials to compute the total energy of the system. First-principles calculations can provide the most reliable interatomic potentials. However, realistic simulations of the melting of nanoparticles often require a number of atoms that renders these methods impractical: they either require too much computer memory or take too long to be completed in a reasonable amount of time. One alternative is to use empirical or semiempirical interaction potentials that can be evaluated efficiently. In this study, we use the modified embedded atom method (MEAM) originally proposed by Baskes et al. [14-15]. MEAM was the first semi-empirical atomic potential using a single formalism for fee, bec, hep, diamond-structured materials and even gaseous elements, in good agreement with experiments or first principles calculations [15-16]. The MEAM is an extension of the embedded-atom method (EAM) [1718] to include angular forces. Cherne et al. made a careful comparison of MEAM and EAM calculations in a liquid nickel system [19]. Atomistic simulations of a wide range of elements and alloys have been performed using the MEAM potentials. A realistic shear behavior for silicon was first obtained using the MEAM by Baskes et al. [14]. The MEAM was also applied to various single elements [15] and to silicon-nickel alloys and interfaces [20]. Gall et al. [21] used the MEAM to model the tensile debonding of an aluminumsilicon interface. Lee and Baskes [22] extended the MEAM to include the second nearest-neighbor interactions. A new analytic modified embedded-atom method (AMEAM) many-body potential was also proposed and applied to several hep metals, including Mg [23-24]. For the Mg-Al alloy system, a set of EAM potentials has been developed using the "force matching" method by Liu et al. [25]. Recently, a new set of MEAM potentials for Mg-Al alloy system was developed by Jelinek et al. [26], These new potentials show a significant improvement over the previously published potentials, especially for the surface formation, stacking faults, and point defect formation energies. In this paper, we developed an atomistic sintering simulation with crystalline tungsten materials at the sub-microscopic level based on the MEAM. We considered temperatures and misorientation between particles as variables for investigating sintering mechanism of crystalline tungsten nanoparticles. THEORY AND SIMULATION Modified Embedded Atom Method (MEAM) The total energy E of a system of atoms in the MEAM [20] is approximated as the sum of the atomic energies E¡ I
The energy of atom / consists of the embedding energy and the pair potential terms:
F¡ (p¡) is the embedding energy, p¡ is the background electron density at the site of atom i, and φι/τ%) is the pair potential between atoms i and/ separated by a distance r¡j. The embedding energy F¡ (p¡)
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represents the energy cost to insert atom i at a site where the background electron density is p¡. The embedding energy F¡(pi) is given in the form ^.(ρ,.)=4£, 0 Λΐηρ,..
(3)
where the sublimation energy Ef and parameter A¡ depend on the element type of atom i. The background electron density ~pi is given by PT ■σ(Γ,) Pi
Pi where
(4)
G(r)=VT+TT
(5)
and '■
(6)
L·1' (0) k=l V Pi
In the above equations, p\k) is the &-th order density of ¿-th atom given in equation (9) and f/*' is the corresponding average weighting factor given by equation (11). The composition-dependent electron density scaling pf is given by
pf = piaZi0G(rrf)
(7)
where p,o is an element-dependent density scaling, Z¡o is the first nearest-neighbor coordination of the reference system, and T"f is given by i
Π
(8)
/2 ' ¡ 0 k=\
where sf is the shape factor that depends on the reference structure for atom i. Shape factors for various structures are specified in the work of Baskes [15]. The partial electron densities are given by (9a) (9b)
(2)\
w
= ΣΣΡ?\
m - Σ ΣΡ' *ι α,β,ϊ J*>
\rijarijß
Γ9μύ£»5ι ¡i
Σ/ΛΚ
(9c)
ΣΡΠΊ^
(9d)
where r¡¡a is the a component of the displacement vector from atom i to atomy. S¡¡ is the screening function between atoms / and/ and is defined in equations (16a)-(16e). The atomic electron densities are computed as ,<■(*)
- m\-X
■ pi0 exp P
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where r¡ is the nearest-neighbor distance in the single-element reference structure and ß\ ' is element-dependent parameter. Finally, the average weighting factors are given by ?(*) .
P^J
ΣΟ>;(0)(^
(11)
where í¿ ' is an element-dependent parameter. The pair potential is given by (12)
2^b
^y
-FÁfP"(%)
■F\^-pr{rv
(13)
-^(i+4('i/))exPÍ-4('íf)J
(14)
ί ,
(15)
-1
where a¡j is an element-dependent parameter. The sublimation energy Eg, the equilibrium nearestneighbor distance r^, and the number of nearest-neighbor Z¡¡ are obtained from the reference structure. The background densities /?,(/;■,) in Eq. (13) are the densities for the reference structure computed with inter- atomic spacing r¡¡. The screening function S¡¡ is designed so that S¡¡ = 1 if atoms i and y' are unscreened and within the cutoff radius rc, and S¡j = O if they are completely screened or outside the cutoff radius. It varies smoothly between 0 and 1 for partial screening. The total screening function is the product of a radial cutoff function and three body terms involving all other atoms in the system:
S =S f
°6a)
" » {^j
(16b) (16c) (16d)
(16e) Note that Cmi,, and Cm,* can be defined separately for each i-j-k triplet, based on their element types. The parameter Ar controls the distance over which the radial cutoff is smoothed from 1 to 0 near r = rc.
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Atomic Potential for Molecular Dynamic Simulation We use the MEAM potential parameters for tungsten (W) proposed by Baskes [15]. The potential parameters that are used for our simulation of W nanoparticles are listed in Table I. These parameters are obtained by fitting the room temperature elastic properties using bcc as the reference structure. CmaX and C^ are chosen to include only the first nearest-neighbor interactions [27]. Table I. The MEAM potential parameters for W from ref. [27]. £° is the sublimation energy, r° is the equilibrium nearest neighbor distance, A is the scaling factor for the embedding energy, a is the exponential decay factor for the universal energy function, //°~ 3) are the exponential decay factors for the atomic densities, r ' are the weighting factors for the atomic densities, C^a and Cmm are the screening parameters. A £°[eV] a fP 3.98 1.00 0.98 8.66 2.74 5.63 1.00 i<6> tih i* /" t-rriax t^min ^ 1.00 1.00 3.16 8.25 -2.70 2.80 2.00
Ml
0*
p
The physical properties of W computed using the present MEAM parameters are compared with those of DFT calculations as shown in Table II. All first-principles calculations have been performed using DFT as implemented in VASP code [28]. Energy calculations and geometry optimizations of various structures were performed using Blöchl's all-electron projector augmented wave (PAW) method [29] as implemented by Kresse and Joubert [28]. For the treatment of electron exchange and correlation, we used the generalized gradient approximation (GGA) using Perdew-Burke-Ernzerhof scheme [30]. The plane-wave cutoff energy was set to 300 eV in all calculations and the Brillouin zone was sampled using Monkhorst-Pack scheme [31]. Table II shows that the results of DFT calculations and experimental values are reproduced satisfactorily by the present MEAM parameters for W. In particular, we note that the elastic constants are well matched with the experimental values, although the present MEAM parameters show a tendency to underestimate the bulk modulus and the surface energies.. As we discuss it further in [13], this shortcoming causes W nanoparticles to melt at lower temperatures due to premature premelting of surface layers. Table II. Calculated physical properties of W using the present MEAM parameters in comparison with DFT calculations. Bo is the bulk modulus (GPa); Cu, Cu, CM are the elastic constants (GPa); £(ioo), £(iio), £(ΐιΐ) are surface energies of corresponding surfaces (mj/m2); A£"s are the structural energy differences (eV/atom). parameter DFT Expt. (Ref. 32) MEAM 314 330 270 Bo (C,,-C 1 2 )/2 163 190 160 C44 280 163 160 7810 5980 £(100) 6390 5660 £(110) 7190 5030 £(111) 0.494 0.325 Δ£. bcc—»fee 0.397 2.168 —*hCD
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Simulation Procec Particle M ;: We performed detailed MD simulations of the melting and sintering of unsupported sphencal ußC W nanoparticles. The surface boundary condition was free and no external pressure was applied. Each nanoparticle was constructed by cutting out atoms within a specified radius from the tungsten bulk in the bcc structure that is the stable phase of W at standard temperature and pressure (STP). In Figure 1, we calculated the total energy of system as we change lattice constant of tungsten crystal unit cell. The unit cell is cubic and contains BCC structure of tungsten atoms at standard temperature and pressure (STP). Optimum lattice constant of BCC tungsten crystal is determined from Figure 1(a). The calculated lattice constant is 3.165 A which is same with experimental lattice constant (0.3165 Á) because it is one of MEAM potential fitting parameters. Figure 1(b) show one nano-size tungsten particle in power which is build using 6 the optimum lattice constant. The radius of the particle is 10 run. Total number of atoms is 33,700. The total number of atoms in this unit cell is big enough to simulate thermal effect as shown in Figure 2. We also note that the present MEAM parameters predict the bcc phase to be the most stable structure in these conditions as shown in Table III. Ten different initial configurations for each size of nanoparticles are then obtained by performing MD simulations at the room temperature for 30,000 time steps and saving the atomic configurations at every 3,000 time step. We complete the preparation of initial configurations by randomizing the atomic velocities of the nanoparticles according to the Maxwell-Boltzmann distribution at the initial temperature T¡ = 500 K. The equations of motion were integrated using time steps ΔΓ = 4 * 10" 15 s.
(a) Lattice constant (b) model for single tungsten particle Figure 1. Particle preparation for atomistic simulation of nano tungsten powder sintering; (a) lattice constant and (b) model for single tungsten particle (BCC, 10 nm, 33,700 atoms).
Figure 2. Temperature control with time step of 0.01 ps in atomistic simulation for tungsten nanoparticle sintering. Temperature Control: We increase the temperature of the heat bath in steps of ΔΓ= 100 K from the initial temperature T¡ = 500 K to the final temperature up to T/= 4500 K as shown in Figure 2. We run the MD simulations for 50,000 time steps at each temperature. Statistical (time-averaged) data for the energetics are collected after the system has adjusted to the new temperature, which is typically after 25,000 time steps following a temperature increase. For the particles of diameters less than 8 nm, 20,000 time steps were used to adjust the particles to each new temperature. The isothermal condition
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was maintained by using Nosé-Hoover thermostat [33-34]. Final results are obtained by taking the ensemble average among the ten different samples for each size. We discussed amply about melting response of crystal and various sizes of nanoparticles from atomistic molecular dynamic simulations in reference [13].
Figure 3. Schematic diagram of two-particle sintering. Sinterine Simulation: We simulated sintering of tungsten nanoparticles with nonisothermal and isothermal sintering conditions from 2000 to 3500 K. Initial distance between tungsten nanoparticles is one atomic distance. In isothermal sintering simulation, we stabilized tungsten nanoparticles first at target temperature before simulation for elimination of thermal expansion effect. For the misalignment simulation, we rotated one of the two nanoparticles, around the shorter distance (perpendicular to plane in Figure 4). We defined the angle of misalignment as the angle of rotation of the second nanoparticle. Based on the atomistic sintering simulation, we obtained several geometric dimensions as such D\, D2, X, and Θ, as shown in Figure 3, for investigating sintering mechanism. RESULTS AND DISCUSSION Sintering Simulation Nonisothermal Sinterine (Case 1): We constructed two particles separated by the distance of one lattice. We simulated non-isothermal simulations with a thermal cycle from 500 K to 3500 K with increment of 500 K at every 10 ps interval. Figure 4 shows dimensional changes including neck growth and shrinkage with temperature increment in 500 K. As temperature increases, the neck size between the two particles increases and finally two particles merge into one particle.
500 K (initial temperature), 0 s 2000 K, 30 ps 3000 K, 50 ps Figure 4. Sintering response of tungsten nanoparticle based on atomistic simulation. Isothermal Sinterine (Case 2): We performed isothermal sintering simulations at 1500-3500 K for 200 ps to investigate sintering mechanism. Figure 5 shows displacement vector of each atom due to thermally activated movement between two times in isothermal sintering simulation at 2000 K. The premelting layer can be observed very clearly and the thickness of the premelting layer increases as sintering time increases. The atoms at interface between particles are the most active, then the atoms at surface at single particle are active, and then atoms inside of particle are least active.
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Figure 5. Vector plot for displacement of tungsten atoms during isothermal sintering simulation at 2000 K. Dimensional Chames and Densification Behavior. We measured two dimensions D\ and D2 from simulation results to calculate neck size X using simple geometric relation. Figure 6 shows dimensional changes including neck growth at 3000 K. • Diameter of each particle D¡ is the average value of four measurement; diameter in two perpendicular directions in two particles, which shows almost constant during the whole sintering process at the value of about 12 nm after thermal expansion stabilization treatment at 3000 K. More precisely D\ increases slightly due to premetling of surface. • The longest distance between two particles D2 reduces as the time goes during the sintering. The neck size X is calculated by geometrical relation from £>i and Di. • The initial neck formation occurs very abruptly at 25 ps, and then the neck grows very fast for 10 ps, and then the neck grows linearly with time. Based on the simulation results of Case 2, Figure 7 shows dimensional changes such as X, Θ, shrinkage and densification during isothermal sintering process.
Figure 6. Dimensional change during isothermal sintering simulation at 3000 K.
(c) shrinkage (d) densification Figure 7. Isothermal sintering at different temperatures.
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Sintering Mechanism Two-Particle Sintering Model: Bulk transport process changes the compact density by removing mass from the compact between particles and redepositing that mass to form the neck. The result is powder compact shrinkage. Early in sintering, the approach of particles can be related to the neck size as follow [35]: (23) A> 40, where the shrinkage S is the compact length change ΔΖ, divided by the initial length LQ. Because of shrinkage, the compact densifies from the fractional initial density pt, to the fractional sintered density p according to the relation [35],
P.-—Í
(24)
(1-Sf
Initial stage sintering models generally trace their origin to the calculations of Frenkel for viscous flow sintering of two equal sized spheres. The Frenkel model suggested a relation between time and the size of the sinter bond. It was followed by the Kuczynski model and many similar treatments of this core problem. Although most solutions are based on several approximations, still there is a consistent finding that the neck-size ratio XID as a function of a kinetic term B, isothermal time r, and particle size D is as follows [36]: '* ! " = * - . (25) D) Dm The exponent n depends on the sintering mechanism and typical values are tabulated below. The particle size exponent m is known as the Herring scaling law exponent. The neck size is given by the diameter X of the neck bonding the particles together, D is the sphere diameter, r is the isothermal sintering time, B is the kinetic term treated below where temperature T enters in an exponential form as associated with the mass transport process delivering neck growth,
S = S eXP
° (~Ä)·
(26)
Typically B0 is a collection of material, crystal structure, and geometric constants, R is the gas constant, T is the absolute temperature, and Q is an activation energy associated with the atomic transport process. The activation energy varies with each of the mechanisms. The values of n, m, and if also depend on the mechanism of mass transport as described Table III. In the Table III, js^is the solidvapor surface energy, η is the viscosity, Dv is the volume diffusivity, b is the Burger's vector, Ω is the molar (atomic) volume, P is the vapor pressure, pr is the theoretical density, M is the molecular weight, ¿is the diffusion layer width or thickness, D\, is the grain-boundary diffusivity, and Ds is the surface diffusivity. Table III. Initial-stage sintering model mechanism viscous flow plastic flow evaporation-condensation lattice (volume) diffusion grain-boundary diffusion surface diffusion
n 2 2 3 5 6 7
m 1 1 2 3 4 4
B0 3χςν/(2η) 94rsMb2)(n/RT) (n/2Y,2QPrsy!pT)(M/RT)2'2 %0DvrSiai(RT) 2ombrSiM(RT) 56SDsrsrCl/(RT)
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Apparent Activation Enerev: We obtained the apparent activation energy based on equations (25) and (26) of the two-particle neck growth model from isothermal sintering simulation as follows: 1. Firstly, obtain the slope B at each isothermal temperature using the following equation. X" Q_ (27) -Bt- Ä0exp RT 2. From the B value obtained by Step 1, obtain the slop Q using the following equation. (28) Figure 8 shows the plots corresponding to equations (27) and (28). The mechanism with higher n occurs the later.
Figure 8. Plots for obtaining apparent activation energy from isothermal sintering at different temperatures based on viscous or plastic flow (R2 = 9423). Table IV. Activation energy with various misalignments activation energy (kJ/mol) Sintering mechanism 0° 15° 30° viscous or plastic flow 49 110 110 evaporation-condensation 72 136 139 lattice (volume) diffusion 115 192 202 grain-boundary diffusion 142 224 237 surface diffusion 158 253 269
reference [9, 35] value (kJ/mol) >585 824 520 385 293
From the isothermal sintering simulation results at 2000,2500, 3000, and 3500 K, we calculate the sintering activation energies based on the above model, as listed in Table IV. The values of activation energies are very low compared with reference values [9, 35]. This probably results from several factors, the largest being the presumed bulk grain boundary behavior. Our early simulations assume no grain boundary or perfect alignment of the crystalline structures between two contacting particles. Accordingly, the absence of a grain boundary gives an uncertain fit with grain boundary diffusion. Surface diffusion is overall the best fit to the bulk diffusion data, but most probably the amorphous or premelted surface layer contributes to very active mass flow in a nontraditional manner specifically unique to nanoscale powders. Misalignment Effect We simulated isothermal simulations with various misalignments at 15° and 30°. Figure 10 shows neck growth and densification with various temperatures and misalignments. Misalignment reduces neck growth and densification.
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(a) various temperature at misalignments of 30° Figure 10. Sintering behavior during sintering; (a) various misalignments at 2000 K and (b) various temperature at misalignments of 30°. CONCLUSIONS We have created an atomistic level of simulation using the molecular dynamic method and modified embedded atom method to simulate the powder sintering process for nanoscale crystalline tungsten particles. With this approach, we calculated the shrinkage of tungsten during isothermal sintering as a function of time, as well as determine the necking shape. For two particles, we calculated the densification behavior with respect to sintering time for isothermal sintering. A sphericity concept is used to describe the sintering process in terms of densification. Further, we compared two-particle simulation and full three-dimensional simulation with a coordination number of six. One case of crystallographic misorientation is included in the study. Small-sized power enables sintering at low temperatures so that the cost of powder sintering goes down significantly. We found the pre-melting layer enhanced the mechanism of viscous flow during sintering. REFERENCES 1. S.W.H. Yih and C.T. Wang, Tungsten: Sources, Metallurgy, Properties, and Applications, Plenum Press, New York, NY (1979). 2. E. Lassner and W.D. Schubert, Tungsten: Properties, Chemistry, Technology of the Element, Alloys and Chemical Compounds, Kluwer Academic / Plenum Publishers, New York, NY (1999). 3. B. Roebuck, M.G. Gee, and R. Morrell, Hardmetals - Microstructural Design, Testing and Property Maps," Proc. Fifteenth International Plansee Seminar, 4, 245-266 (2001). 4. L. Bartha, P. Atato, A.L. Toth, R. Porat, S. Berger, and A. Rosen, Investigation of HIP Sintering of Nanocrystalline WC-Co Powder, J Advanced Mater., 32, 23-26 (2000). 5. L.P. Dorfman, D.L. Houck, and M.J. Scheithauer, Consolidation of tungsten-coated copper composite powder, unpublished manuscript, Osram Sylvania, Towanda, PA (2002). 6. G.K. Schwenke, Thermodynamics of the Hydrogen-Carbon-Tungsten System, As Applied to the Manufacture of Tungsten and Tungsten Carbide, Proc. Fifteenth International Plansee Seminar, 2, 647-661 (2001). 7. D.G. Kim, E.P. Kim, Y.D. Kim, and I.H. Moon, Interfacial Characteristic of W-Ni-Fe Heavy Alloy Using Ni-Coated Powder, Proc. the 2000 Powder Metallurgy World Congress, 1, 721-724 (2000).
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8. N.C. Kothari, Effects of Particle Size on the Sintering Kinetics in Tungsten Powder, Powder Metall, 7,251-260 (1964). 9. R.M. German, Sintering Theory and Practice, John Wiley and Sons, New York, NY (1996). 10. R.M. German, Powder Metallurgy Science, second edition, Metal Powder Industries Federation, Princeton, NJ (1994). U . S . J.-H., L. B.-J., and C. Y.W., Surface Science 512, 262 (2002). 12. S.-G. Kim and D. Tom'anek, Phys. Rev. Lett. 72, 2418 (1994). 13. A. Moitra, S. Kim, J. Houze, B. Jelinek, S. G. Kim, S. J. Park, and R. M. German, Melting Tungsten Nanoparticles: a Molecular Dynamics Study, J. Phys. D: Appl. Phys., 41, 185406 (2008). 14. M. I. Baskes, J. S. Nelson, and A. F. Wright, Phys. Rev. B 40, 6085 (1989). 15. M. I. Baskes, Phys. Rev. B 46, 2727 (1992). 16. M. I. Baskes and R. A. Johnson, Modell. Simul. Mater. Sei. Eng. 2, 147 (1994). 17. M. S. Daw, Phys. Rev. B 39, 7441 (1989). 18. M. S. Daw and M. I. Baskes, Phys. Rev. B 29, 6443 (1984). 19. F. J. Cherne, M. I. Baskes, and P. A. Deymier, Phys. Rev. B 65, 024209 (2001). 20. M. I. Baskes, J. E. Angelo, and C. L. Bisson, Modell. Simul. Mater. Sei. Eng. 2, 505 (1994). 21. K. Gall, M. Van Schilfgaarde, and M. Baskes, J. Mech. Phys.Solids 48, 2183 (2000). 22. B.-J. Lee and M. I. Baskes, Phys. Rev. B 62, 8564 (2000). 23. W. Hu, B. Zhang, B. Huang, F. Gao, and D. J. Bacon, J. Phys.: Condens. Matter 13, 1193 (2001). 24. W. Hu, H. Deng, X. Yuan, and M. Fukumoto, Eur. Phys. J. B 34,429 (2003). 25. X.-Y. Liu, P. Ohotnicky, J. Adams, C. Rohrer, and R. Hyland, Surface Science 373,357 (1997). 26. B. Jelinek, J. Houze, S. Kim, M. I. Baskes, and S.-G. Kim, Phys. Rev. B 75, 054106 (2007). 27. M. I. Baskes, Mater. Chem. Phys. 50 (1997). 28. P. E. Bl'ochl,Phys. Rev. B 50, 17953 (1994). 29. H. J. Monkhorst and J. D. Pack, Phys. Rev. B 13, 5188 (1976) 30. G. Kresse and D. Joubert, Phys. Rev. B 59, 1758 (1999). 31. G. Sun, J. Kurti, P. Rajczy, M. Kertesz, J. Hafher, and G. Kresse, J. Mol. Structure, 624, 37 (2003) 32. G. B. Gille and G. Leitner, Inter. J. Refract. Met. Hard Mater. 20, 3 (2002). 33. J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 11, 3865 (1996). 34. W. G. Hoover, Phys. Rev. A 31, 1695 (1985). 35. R. M. German, Powder Metallurgy & Particulate Material Processing, Metal Powder Industries Federation, Princeton, NJ (2005). 36. R. M. German and S. J. Park, Handbook of Mathematical Relations in Particulate material Processing, John Wiley & Sons, New York, NY (2008).
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VARIATIONS IN SINTERING METAL/CERAMIC POWDERS
STRESS
AND
VISCOSITY
WITH
MIXING
RATIO
OF
Kazunari SMNAGAWA Faculty of Engineering, Kagawa University Takamatsu, Kagawa, JAPAN ABSTRACT Distortions or cracking in metal/ceramic graded powder compacts during sintering may be caused by the variation in densification behavior of the layers with different mixing ratios. To clarify the constitutive response of the heterogeneous powder compacts, a micromechanics model for sintering is proposed. The sintering stress as well as the viscosity of the powder mixtures is expressed by using Eshelby's equivalent inclusion method and Mori-Tanaka's mean-field theory. The variation in sintering behavior with metal/ceramic mixing ratio computed by the proposed model is compared with the experimental data for N1/AI2O3 system. The present model can reproduce the decrease in sintering rate of the powder mixtures, which remarkably appears in the NÍ/AI2O3 powder compacts with small amount ofAI2O3. INTRODUCTION In metal/ceramic graded powder compacts during sintering, the difference in shrinkage among the layers often causes distortions or cracking1. To avoid the sintering defects, estimation of the internal stress generated in layered structures during sintering may be important2"5. In general, the sinterability of metal/ceramic powder mixtures is lower than those of each single powder compact. The sintering behavior has been examined for several metal/ceramic systems, for example, N1/AI2O3 mixtures , but only from the view point of the sintering shrinkage. As for the stress analysis, the sintering behavior should be characterized by the driving force and the viscous resistance. It seems that a few attempts have been done to clarify the sintering stress as well as the viscosity for some composite materials10"14. In those studies, however, the composition is limited to a certain range, and the influence of the mixing ratio of ceramic to metal on the sintering properties is not revealed. To establish the computer aided design for the functionally grade materials, fabricated by the sintering process, the database of sintering properties is necessary". As the first step toward making a prototype of the database, the author has examined the sintering stress and the viscosity of N1/AI2O3, as a model system, by using sinter-compression tests16. However, modeling of the sintering properties is needed to prove the validity of the experimental results and also to provide the expressions available for the analysis. Continuum models have been widely applied to various problems for properties of composites. For the powder processing of composites, sintering with rigid inclusions has been analyzed by using the continuum models17"21. In the preset study, micromechanics modeling is performed against the powder mixtures where every powder region shrinks during sintering. A continuum model to estimate the sintering stress as well as the viscosity of the powder mixtures with metal/ceramic ratio ranging from 0/100 to 100/0 is proposed. The calculated results are compared with the experimental data. MODELING Micromechanics Eshelby's equivalent inclusion method22 and Mori-Tanaka's mean-field theory23 are applied to the sintering of heterogeneous powder inclusion in powder matrix. The relationships between the free sintering strain rate and the sintering stress for the matrix and the inclusions are given by
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Variations in Sintering Stress and Viscosity with Mixing Ratio of Metal/Ceramic Powders
«:=*/'»:
(i)
έ°=Ε:λσΙ
(2)
where ¿land s¡ are the sintering strain vector,^ and E,are the viscosity tensors, σ^, and o¡ are the sintering stress vector, of the matrix and the inclusions, respectively. The difference in the sintering strain rate between the matrix and the inclusions is Δέ·=έ;-έ'„
O)
The above equations are for the compacts which are sintering independently, with no interaction. When the single inclusion is put into the matrix, the internal stress σ' and the internal strain rate ¿^ are produced by the interaction. If the many inclusions exist in the matrix, the interaction between them is added. The average stress and the average strain rate duetothe interaction are assumed to be given by σ and έ , respectively. When the external stressCTÍSapplied to the mixed powder compact, the stress of the matrix can be expressed by σ + σ = ΕΜ{έ'+έ-έ'Μ)
(4)
and the stress of the inclusions is given by σ + σ + σ* = Ε\έ' + ¿ +έτ -é¡) = Ε,(έ' +έ+έ"
-έ'„ -Δέ')
(5)
where έ' is the total strain rate of the matrix powder compact with no inclusion, produced by the external and the sintering stress as follows; έ·=Ε.-ι{σ
+ σ·.)
(6)
Consider the equivalent inclusions of which viscosity is the same as the matrix σ + σ + σ' = Em(s' +έ+έ"
-έ'Μ-έ')
(7)
where έ' is the eigen strain rate, which is necessary to give the same stress as Eq (5) in the scheme of Eshelby's equivalent inclusion method. The strain rate έ' and the stress σ * produced by the interaction can be expressed by έ' as follows; έ°=S¿*
(8)
σ*=Ε.(έ'-έ') = E.{S-I)é'
(9)
where 5 is Eshelby's tensor and / is the unit matrix. Taking/to be the volume fraction of the inclusions gives the stress as well as the strain of the mixed powder compacts as follows; σ = (\-/Χσ + σ) + /(σ + σ + σή é = (\-fÍé'+é)+f{s'+é+é*) Rearranging Eq. (10) with Eq. (9) gives
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(10) (11)
Variations in Sintering Stress and Viscosity with Mixing Ratio of Metal/Ceramic Powders
S = -fa*=-fEjS-l)é'
(12)
έ=Ε„'σ'
(13)
=-f(S-iy
By equating Eqs. (5) and (7) with substituting Eq. (8) and (13), ¿' is solved as follows; έ' = -D■'{(£,. - E u té1 -rm)-Ε,Δέ') D = (1 -f){(E,
-Em)S+
(14)
£.} + &,
Substituting Eqs. (8) and (13) into Eq. (11) gives έ = έ' + fe'
(15)
Equation (15) is rearranged after substituting Eqs. (6) and (14) with Eqs. (1H3) as follows; έ = {/-β>>(Ε,-E„)}£„-'(
(16)
Since the strain rate of the mixed powder compacts can be simply expressed by έ = Ει(σ
+ σή
(17)
comparing Eq. (16) with Eq. (17) gives E = Em{l-fiD-\E,-Emf
(18)
σ' = σΐ + fED ' (σ* - σ*)
(19)
Although Eq. (18) is analogous to that of the elasticity of composites24, the driving force for sintering of the mixed powder compacts is newly obtained as Eq. (19). The strain rates of the matrix and the inclusions are given by έ„=έ'+έ=έ-βε έ, =έ'+έ+έ"
(20) =é + {l-f)Sé'
(21)
Since the change in density is obtained from the strain rate, the evolution of the properties due to the densification can be taken into consideration for the individual region in the stepwise calculation. Conditions of Calculation Assuming the inclusions to be spherical in the present calculation, the following S is used. - S222Z- & 3 3 -
7-5v 15(1-v)'
J I I 2 2 - 02233- ¿3311-01133- J 2 2 U - 03322-
l-5v 15(1- v
4-5v Ñ 15(1-v)
οΊ212 = 52323 = 5 3 1 3 1 = — T
(22)
where v is the viscous Poisson's ratio and set to be 0.3 for both matrix and inclusions. Although .Eand é are generally expressed as functions of relative density, temperature, and so on, the
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Variations in Sintering Stress and Viscosity with Mixing Ratio of Metal/Ceramic Powders
sintering behavior of powder mixtures at a certain moment is discussed in the present study. Thus Eaad d as well as vare treated to be constant for an ideal numerical experiment to show the quality of the model. Table I shows the conditions of calculation, where E is the longitudinal viscosity £N?iin=£'2222==£3333 and the sintering stress is assumed to be purely hydrostatic; σ
σ
ίΐ = σ22 = σ33 = °' >
\2 = σ23 = σ 31 =
σ
(23)
« = σ55 = σ66 = °
In the powder mixtures of Table I, Ihe viscosity of ceramic is set to be always larger than that of metal. Each sintering strain rate calculated by ¿s = (l - ν)σ'/Ε is also listed in Table 1. Mixture ii) has the metal and the ceramic regions of which sintering strain rate is the same. In Mixture i), the sintering strain rate of the metal region is large compared with the ceramicregion,while it is set to bereversedin Mixture iii).
Table I. Sintering Properties of Metal and Ceramic Powder Compacts Used in Calculation Ceramic Metal Mixture E E σ" σ' έ' i) ii) iii)
1.2 1.0 0.88
0.18 0.20 0.22
45 30 25
0.06 0.08 0.10
8π
X
1
1
έ' 0.04 0.08 0.12
4.5 6.0 7.5
1
1
1
1
1
1
1
r
X
(a) (b) Figure 1. Variations in viscosity (a) and sintering stress (b) with volume fraction of ceramic calculated for powder mixtures in Table I.
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For comparison with the typical rules of mixture, calculations by using the Voigt and the Ruess models are also conducted as follows, respectively; A = {l-f)Am+fAt
(24)
A = ~,
(25)
^4=
where A is the quantity to be mixed, that is, d as well as £ in the present case. Calculated Results Figures 1 shows the variations in £and d of the powder mixtures with the volume fraction of ceramic X, calculated by the models. For the viscosity, the upper and the lower bounds, simply estimated by the Voigt and the Ruess models, respectively, become closer each other by using the micromechanics model, as well known. The estimated range of the sintering stress is also narrowed by the proposed micromechanics model for every mixture listed in Table I. The sintering strain rate calculated by the models is demonstrated in Fig. 2. The calculation of the micromechanics model for ceramic matrix results in theretardationof the sintering strain rate in the range of small amounts of ceramic for the all conditions, which cannot be expressed by the Voigt and the Ruess models. Note that the degree of the drop in sintering strain rate is affected by the value of v, which is related to the interaction between the matrix and the inclusions. This means that it is difficult to shrink for the metallic region under the constraint by the ceramic matrix with larger viscosity. The more v increases, the more deeply the sintering strainrateof the powder mixtures drops.
0.2 Π
nü
0
1
1
1
i
i
1
1
i
i
Micromechanics model Ceramic matrix Metal matrix Voigt bound Reuss bound
i
0.2
0.4
X
1
1
i
i
0.6
1
1
i
i
0.8
Γ
i
1
Figure 2. Variation in sintering strain rate with volume fraction of ceramic calculated for powder mixtures in Table I.
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Variations in Sintering Stress and Viscosity with Mixing Ratio of Metal/Ceramic Powders
0.9 h
Γ S> 0 . 7
Si 0.6 0.5 "'"0
- O - 1579K, 1.8ks ■ 1473K, l.gks - 1356K, 1.8ks ■1073K, Oks 0.2
0.4
X
0.6
0.8
1
Figure 3. Relative density of specimens. COMPARISON WITH EXPERIMANTAL DATA Specimens and Sinter-Compression Tests Ni powder (4SP-400, NOVAMET, mean size of 12.5um) and A1203 powder (AKP53, Sumitomo Chemical Co., Ltd., mean size of 0.3μιη) were individually granulated first The pure granules of Ni and AI2O3 were mixed with the ratio oiX, which was varied from 0 to 1 in increments of 0.2. Cylindrical mixed powder compacts for the sinter-compression tests were prepared by uniaxial pressing and the subsequent CIPing (cold isostatic pressing). Since the mixed powder compacts consist of Ni and AI2O3 agglomerates, they can be almost regarded as the composites of each single powder compact25. The relative density of the specimens is represented in Fig. 3. If Ni and AI2O3 regions are completely separated in the mixtures and have exactly the same state throughout the series of specimens, the packing density varies linearly with X, which may be an ideal condition for comparison with the model. There is, however, a certain discrepancy from the linearrelationbetween the initial relative density (1073K, Oks) and X. Therefore the comparison is to be made with the fundamental errors originated from the preparation of the specimens. The sinter-compression tests, at elevated constant temperatures (1356K, 1473K, 1579K), were performed by using a thermomechanical analyzer16. The specimens were heated up at a rate of 20K/min, and the initial applied stress of 0.006MPa was held or changed to σζ «0.006 - 0.3MPa at a time r = 0, which was 5min after reaching each prescribed temperature. The change in height of the specimens was measured for 30min. The strain rate ¿2 obtained from the reduction in height of the specimens is expressed by έ,=σ·+Σ'
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(26)
Variations in Sintering Stress and Viscosity with Mixing Ratio of Metal/Ceramic Powders
J
l n
,
1
,
1579K ■
-
4 1 0* ^-mS~Z.?
0
9
[X10 ] 14 12 10
i
1
0.2
i
1
0.4
,
X
s
1
i
1
■ -
1579K
Exp.
\^Λ
/ ^-
-
0.Í
,
1
T ~r Mkromechanics model A1203 matrix Ni matrix
•
|
/ i
1
0.6
i
OH
-
— 9 — — — —— —
|
•
^^-*·**/
_—-tf*"^ ,——-""^ β
i
- Micromechanics model A1203 matrix Ni matrix
~ -
e^ 6 L*a
10
1
Micromechanics model 12 " A1203 matrix Ni matrix 10 • Exp.
1
,
0.2 1
1
0.4
'
,
'
- Micromechanics model A1203 matrix 8 Ni matrix
Exp.
•
6
1
t
1
0.6
X
1
/\ A /
0.8 1
1
1473K - -
-
Exp.
0.
>, ~ 4
-
<~1
^^
2 0*
^*r
0 [ Χ ΐ θ ' ] 14 12 10
Figure 4.
—' 1 ' 1 ' 1 Micromechanics model A1203 matrix Ni matrix
'
-r r 1356K
10
1
0.2
,
1
,
0.4
1
X
Micromechanics model A1203 matrix Ni matrix
0.6
s' ••^ W m 1
_--'
y*
js
y
-t
/'
i
-
1
0.Í
1356K
Comparisons of calculated viscosity (a) and sintering stress (b) with experimental data.
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Variations in Sintering Stress and Viscosity with Mixing Ratio of Metal/Ceramic Powders
■
0-03
Q Ü
0
i
I
0.2
i
I
0.4
i
X
I
0.6
i
I
0.8
i
i
i
I
I
1
Figure 5. Comparison of calculated sintering strain increment with experimental data for t = 0.9 ks; symbols are experimental data, solid and broken lines are for AI2O3 and Ni matrixes, respectively, by micromechanics model. where £Ό is the longitudinal viscosity for the time t=1 - 65, vc is the viscous Poison's ratio of the specimens, and io, q are constants common to all the specimens at the same test temperature. From the compression tests with different values of σζ, £Ό and Σ* were determined simultaneously with to and q by the method of least squares. The error was evaluated by the formula for standard deviation and error propagation. Since vc was not measured in the tests, Is is used instead of d for the comparison of calculation and experiment. With regard to the longitudinal viscosity for the comparison, £0 is used as a representative of variable E. The experimental data for the sintering strain increment for a short time of t = 0.9 ks is also compared with the calculation. Since to and q are common to Ni and AI2O3, the change in viscosity E with time can be considered outside the micromechanics model. Assuming constant £Ό and Σ' for a short time, the sintering strain increment can be calculated by Δε$ = ['έ'Λ = I " — β - — - d t = At—,
At = I",
*
dt
(27)
where At is the effective time. In the present study, the effective time was roughly determined to be At =14s by usingfo= 68 and #=0.7, which are the average values obtained by the experiment. Results and Discussion Figure 4 shows the experimental data of £Ό and Is. Both £b and Σ* of AI2O3 (AM) powder compacts are larger than those of Ni (A=0). Wide margin of error at X=\, compared with tiie others, implies that the sintering strain rates of AI2O3 varied widely, but the best estimates were determined through the least-squares fit to data. The calculated results for the mixed powder compacts using the data of the single powder compact of Ni and AI2O3, that is, £Ό and Is aiX= 0 and 1, are also plotted in Fig. 4. Although the assumption of the equal initial density for each region overXmay become unreasonable after sintering, the discrepancy from the
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Variations in Sintering Stress and Viscosity with Mixing Ratio of Metal/Ceramic Powders
linearity between the relative density and X does not seem to be enlarged much at the test temperatures, as can be seen in Fig. 3. Experimental data of the mixed powder compacts is within the range estimated by the present model for every test temperature, which may suggest a possibility of the use of the micromechanics model to express the sintering behavior of composites. Figure 5 represents the sintering strain increment of N1/AI2O3 powder compacts obtained in the experiment. The drop in the sinterability can be seen around X=02 for all test temperatures. The results calculated by the micromechanics model with v = 0.3 are superimposed in Fig. 5. The sintering strain increment of the powder mixtures calculated for the case of AI2O3 matrix is in good agreement with the experimental data, especially for 1356 and 1473K. The quantitative agreement with the experimental data cannot be confirmed essentially at present, because the actual microstructure of N1/AI2O3 powder compacts may be the intermediate state of Ni and AI2O3 matrix cases. At least, however, the retardation of the sintering in powder mixtures may be expressed by the present model. CONCLUSIONS A mean-field micromechanics model for the sintering of metal/ceramic powder mixtures was proposed. The sintering stress as well as the viscosity of composites during sintering was expressed as the function of those of the component powder compacts. The calculated results were verified through comparison with the experimental data for N1/AI2O3 system. Sintering strain rate was also calculated by the proposed model, and it was found that the model can explain the drop in sinterability of metal/ceramic powder mixtures. ACKNOWLEDGMENT This work was supported by JSPS.KAKENHI(19560733). REFERENCES 'R. Watanabe, Powder Processing of Functionally Gradient Materials, MRS Bulletin. 20-1,32-34 (1995). 2 H.Riedel and T. Kraft, Distortions and Cracking of Graded Components During Sintering, Mat. Sei. Forum, 308-311,1035-1040(1999). \ll. Gasik and B. Zang, Sintering of FGM Hardmetals in Different Conditions: Simulation and Experimental Results, Ceram. Trans. 114,341-347(2000). 4 A. Maximenko and O. V. D. Biest, Modeling of Sintering of WC-Co Functionally Graded Materials, inRecent Developments in Computer Modeling ofPowder Metallurgy Processes, Eds. by A. Zavaliagnos and A. Laptev, 105-111(2001), IOS Press. 'Κ. Shinagawa and Y. Hirashima, Stress Analysis of Powder Compacts with Graded Structures in Sintering Process, Mat. Sei. Forum 492-493,477-482 (2005). 6 A. N. Winter, B. A. Corff, I. E. Reimanis and B. H. Rabin, Fabrication of Graded N1-AI2O3 Composites with a Thermal Behavior Matching Process,./ Am. Ceram. Soc. 83-9,2147-2154 (2000). 7 A. Zavaliangos and Y. Li, Sintering of N1/AI2O3 Powder Compacts with Compositions Ranging from 0 to 100 v/o AI2O3, in Recent Developments in Computer Modeling of Powder Metallurgy Processes, Eds. by A. Zavaliagnos andA. Laptev, 112-121(2001), IOS Press. 8 M. L. Pines and H. A. Brück, Pressureless Sintering of Particle-Reinforced Metal-Ceramic Composites for Functionally Graded Materials: Part I. Porosity Reduction Models, Acta Materialia, 54,1457-1465 (2006). ' M . L. Pines and H. A. Brück, Pressureless Sintering of Particle-Reinforced Metal-Ceramic Composites for Functionally Graded Materials: Part Π. Sintering Model, Acta Materialia, 54,1467-1474 (2006). 10 R. K. Bordia & R. Raj, Sintering of T1O2-AI2O3 Composites: A Model Experimental Investigation, J. Am. Ceram. Soc. 71-4, 302-310 (1988). n P. Z. Cai, G L. Messing and D. L. Green, Determination of the Mechanical Response of Sintering Compacts by Cyclic Loading Dilatometry, J. Am. Ceram. Soc., 80-2,445-Í52 (1997).
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O. Gillia and D. Bourvard, Phenomenological Analysis of Densification Kinetics during Sintering: Application to WC-Co mixture, Mat. Sei. Eng. ΑΧΊ9,185-191(2000). 13 0. Gillia, C. Josserond and D. Bouvard, Viscosity of WC-Co Compacts during Sintering, Acta mater. 49, 1413-1420(2001). I4 A. Petersson and J. Agren, Constitutive Behavior of WC-Co Materials with Different Grain Size Sintered under Load, Acta Materialia 52,1847-1858 (2004). I5 K. Shinagawa, Computer Aided Design of Graded Powder Compacts, in Functionally Graded Materials in the 21st Century (Ed. by K. Ichikawa), 27-34 (2001), Kluwer Academic Publishers. 16 K. Shinagawa, Sintering Stress and Viscosity of NÍ/AI2O3 Powder Mixtures, in Multiscale and Functionally Graded Materials, Eds. by G H. Paulino etal., 22-27(2008), AIP. I7 C.-H. Hsueh, A. G Evans and R. M. McMeeking, Influence of Mutiple Heterogeneities on Sintering Rates, J. Am. Ceram. Soc, 69A, C-64-C-66(1986). 18 R. K, Bordia and G W. Scherer, On Constrained Sintering - ΙΠ. Rigid Inclusions, Acta metal, 36-9, 2411-16(1988). 19 G W. Scherer, Viscous Sintering of Particle-Filled Composites, Ceram. Bull., 70-6,1059-63(1991). 20 G W. Scherer, Sintering with Rigid Inclusions, J. Am. Ceram. Soc, 70-10,719-25(1987), 21 Z.-Z. Du and A. C. F. Cocks, Constitutive Models for the Sintering of Ceramic Components - II. Sintering of Inhomogeneous Bodies, Acta metal. Mater., 40-8,1981-94(1992). ^J. D. Eshelby, The Determination of the Elastic Field of an Ellipsoidal Inclusion, and Related Problems, Proc. Roy. Soc. Land., A241,376-96(1957). Ώ Τ. Mori and K. Tanaka, Average Stress in Matrix and Average Elastic Energy of Materials with Misfitting Inclusions, Acta Metall., 21,571-574(1973). M M. M. Gasik, Micromechanical Modelling of Functionally Graded materials, Computat. Mater. Sei. 13, 42-55(1998) ^Κ. Shinagawa, Effects of Inhomogenization on Sintering Behavior on N1/AI2O3 Powder Mixtures, Mat. Sei. Forum, 631-632,245-250(2010).
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FINITE ELEMENT MODELLING OF MICROWAVE SINTERING D. Bouvard, S. Charmond, C.P. Carry Laboratoire SIMAP, Grenoble INP / CNRS / UJF BP 46, 38402 Saint Martin d'Héres, France ABSTRACT Microwave sintering involves several phenomena strongly coupled to each other: electromagnetism, heat transfer and sintering. For a better understanding of this complex process the simulation of microwave sintering is carried out with COMSOL finite element code. At a given time a stationary calculation provides the electromagnetic field in the cavity and in the compact when an incident power is assumed. From the electric field in the compact the value of the generated heat is deduced. A transient thermal calculation is thus run with this value as a heat source and with radiative losses at the boundaries of the compact. The density of the compact is updated through a prescribed densification law. Dielectric permittivity and thermal parameters are supposed to depend on relative density or temperature. Finally temperature and density kinetics are obtained. The results of several simulations are presented to show the interest of such modeling. INTRODUCTION Microwave sintering is an emerging fast sintering technique that provides monolithic materials with fine microstructures1' . It could also be used for fabricating multicomponent, multifunctional structures, such as metal-ceramic or dense-porous layered structures3. Microwave heating of dielectric materials results from the absorption of part of the energy transported by an oscillating electric field by molecule polarization. As compared to conventional heating, it leads to higher heating rates and thus may slow down unwanted microstructural changes arising during sintering, such as grain growth in fine grain ceramics. Microwave sintering is however a complex process, which is much more difficult to control than conventional sintering. Even a basic issue as measuring the temperature of the sintering part is a problem4. Also, part insulation and positioning may be critical. Computer models representing the process as a whole would be of great help in this effort of understanding microwave sintering process and bringing it to an industrial scale. Microwave sintering is a complex process involving several phenomena that are strongly coupled to each other: electromagnetism, heat transfer and sintering. For example, electromagnetic energy absorption that controls heating and thus sintering depends on temperature-dependent material parameters and on the electromagnetic field, which changes as the sintering progresses. Taking into account such coupling effect is thus necessary for a realistic modeling of microwave sintering. Ideally, modeling should be conducted both at microstructural scale where particle interactions can be explicitly described and at macrostructural scale considering the sintering material as a continuum, with a two-way coupling between both scales. Achieving such a modeling frame will of course be a long and tricky task. Macroscopic scale simulations of microwave sintering coupling electromagnetism and heat transfer have been presented in the literature5'6. There are mainly based either on the finite element method or on the finite difference time domain techniques. Most of these studies do not introduce densification. Notable exceptions are the model by Birnboim and Carme7, who calculated density gradients in complex shape component, and the model by Riedel and Svoboda8, who found density and grain size distributions in a cylindrical compact surrounded by a susceptor inside an axisymmetric resonant cavity. We present in this paper the first results of a 3D finite element simulation of microwave sintering in a monomode cavity furnace. This simulation includes electromagnetism, heating transfer and densification. It takes into account part of the coupling effects between these phenomena. The
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simulation procedure is first described. Next, several examples of calculation of microwave sintering of a zirconia compact are shown to demonstrate the interest of modeling. Zirconia is a dielectric material that absorbs microwave energy moderately at room temperature but significantly at sintering temperature. Emphasis is put on the influence of the size of the compact and of the insulation condition on temperature and density fields. Also the question of hybrid heating is discussed. MODEL DESCRIPTION The model schematized the conditions met in a monode cavity microwave furnace as the one developed at Grenoble INP by Charmond et al. In this equipment, a rectangular wave-guide transports microwave radiation to a rectangular TEiop cavity of section 86.36 x 43.18 mm. This cavity is ended at one extremity by a movable short-circuiting piston (electric conductor) reflecting the radiation, what creates a standing wave, and at the other extremity (wave guide side) by a movable iris consisting of a copper sheet with a vertical slot. When the distance between the short-circuiting piston and the iris is adapted, the backward radiation is reflected by the iris and the stacking of forward and multiplereflected microwaves results in an increase of the electromagnetic energy in the cavity (resonance phenomenon). When the cavity is empty, the adapted distance is a multiple of half guided wave length. When it contains a dielectric sample, the wave is modified and this distance changes, more or less depending on material permittivity and sample dimensions. In this study we simply simulated a standing wave in the cavity with a value of electromagnetic energy adjusted so that the sample reaches a prescribed temperature in the steady state. The iterative simulation process is schematized in Figure 1. At a given time a stationary calculation provides the electro-magnetic field everywhere in the cavity, including in the compact, and the energy absorbed by the compact. This energy depends on the electric field within the compact and on the imaginary part of material permittivity. It is an internal source for the heating of the material. Also a heat flux goes out of the compact, according to the assumed boundary conditions. The resulting heterogeneous temperature variation is calculated for the next time increment. As a consequence of local temperature rise, the material density increase is deduced by integrating a prescribed densification equation. This increase obviously results in a deformation of the compact. However for simplicity's sake, in this preliminary study, we assume that the dimensions of the compact do not change during the process. It means that the relative density is a local parameter that describes the microstructure of the material but does not affect the geometry of the sintering compact. Also we do no calculate the stresses and strains resulting from heterogeneous density variation.
Í
Electromagnetic calculation (sta tionary) ^ Electric field E in the cavity and compact ■^ Dissipated power in the
I
Thermal transfer calculation (ti ansient) ■^ Local temperature changt :s during time increment Densification calculation (transí ient) -> Local density changes during time increment
Figure 1. Schematics of microwave sintering simulation
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Such calculation procedure has been achieved in 3D with COMSOL Multiphysics finite element code. Three "models" have been used: - Electromagnetics Waves (COMSOL model reference : "rfw") in harmonic propagation, - Heat Transfer by Conduction ("ht") in transient analysis, in the compact only, - Partial Differential Equations, General Form ("g") in transient analysis with the relative density as a variable. The complex permittivity in the compact, is supposed to be a function of the temperature, T. The thermal conductivity of the compact is supposed to be a function of the relative density, pr. The densification rate is expressed as a function of temperature and relative density; it is supposed to roughly describe the behavior of submicronic zirconia powder. PROCESS AND MATERIAL PARAMETERS The following parameters have been introduced in the simulation. Some of them have been taken in the literature, other ones have been intuited. It should be emphasized that dielectric parameters as permittivity are very poorly known. Figures with different orders of magnitude can be found in the literature. This is of course a serious issue for modeling, which should be considered in a further step, when a quantitative description of microwave sintering will be searched for.
-
-
Electromagnetic parameters: Relative permittivity of the air in the cavity: 1 Relative permittivity of the compact: εΓ = 10 — 0 . 1 e 0 0 0 1 7 ( T _ 2 9 3 ' i , i.e. the real part of εΓ is constant and its imaginary part increases from 0.1 to 1 when the temperature increases from room temperature to 1700 K. Input power in the cavity entry section : constant in every simulation, adjusted by trial and error to reach a prescribed temperature Cavity boundaries : perfectly conducting Heat transfer parameters: Heat source : microwave energy absorbed by the material, as provided by electromagnetic simulation Conductivity : k = 30.pr W/(m.K) Weight density : p = 6000.pr kg/m3 Heat capacity : Cp = 900 J/(kg.K) Initial temperature : To = 293 K Boundary conditions : radiative loss with a value of emissivity equal to 0.1 or 0.9 Densification parameters: ,
.
20000 f
,_
\2
-
Densification law : -^-—
-
densification around 1700 K, has been roughly adjusted from experimental data9. Initial density : ρ,ο = 0.65
dt pr
= 200 e
τ
——
U-0.64J
. This law, which describes significant
Only the cavity and the compact are modeled. Modeling also the parts supporting the compact will be of course possible but it will require much more meshing elements and then much longer computing time.
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RESULTS We first present in Figure 2 the calculation of the electric field distribution in the cavity with various configurations: empty cavity, cavity including a short compact (1 mm diameter, 1 mm height), cavity including a long compact (1 mm diameter, 43.18 mm height, i.e. exactly the height of the cavity). For these simulations a constant relative permittivity, εΓ = 10 - 0.3i, has been assumed. In every case the electric field is zero on the conducting vertical walls. In the empty cavity, it shows regular nodes and antinodes along the wave direction. In both other cases, the compact has been positioned at a peak so that it absorbed as much energy as possible. The short compact does not significantly change the position of nodes and antinodes but the electric field inside it is very low (about 15% of the field found in the empty cavity) and a strong gradient is observed in the air below and above it. It means that the absorbed energy will be much lower than expected. Thus a larger electric field, i.e. a higher electromagnetic power will be required in the cavity to heat the compact. Also the gradient may lead to detrimental phenomena as plasma formation. The electric field distribution is very different when the compact is long. The position of nodes and antinodes is modified. Although the electric field inside the compact is lower than it was in the empty cavity, it keeps a relatively high value (about 70% of the field in the empty cavity) and there is no gradient around it, which will be favorable for heating. Next we will show results of multiphysics simulations. We investigated the effect of compact insulation on temperature and density gradients. In the first case, the 1 mm height, 1 mm diameter cylindrical compact is insulated at every side (an emissivity of 0.1 is assumed) whereas in the second case it is insulated everywhere except on its upper surface (an emissivity of 0.9 is assumed). The second case schematizes experiments of Charmond et al.9, during which the temperature in the upper surface is measured by an infrared camera. The input power in every experiment is adjusted so that the average temperature after 30 min is about 1680 K. Figure 3 shows the temperature on the surface of the compact in both cases. With full insulation the compact exhibits a temperature higher by 16 K in the center than in the edges of upper and local surfaces. With partial insulation the temperature distribution is non symmetrical. The temperature is maximal in the lower part of the compact and minimal in the upper section. The maximum temperature difference is 57 K. This second case has been more deeply investigated. We plotted in Figure 4 the changes of temperature and and relative density during sintering in three points of the compact, the centre of the lower section (called "Bottom"), the centre of the compact ("Centre") and the centre of the upper section ("Top"). It can be observed that the heating rate is about 200 K/min and the temperature reaches a peak before a slight decrease. This variation results from the assumed constant input power. It could be tuned by adjusting this power throughout the simulation. We find that the bottom and centre temperatures, which are about equal, and the top temperature separate around 1300 K. This difference leads to a variation of about 1% in density. Finally we present the results of simulation with a cylindrical susceptor (height: 15 mm, external diameter: 30 mm, thickness: 5 mm, relative permittivity: 10 - i) surrounding the compact (Figure 5). Such a configuration has been frequently used in experimental works to preheat materials with a low permittivity at room temperature by radiation or to sinter materials that poorly couple with microwaves in sintering temperature range. A relevant question is whether the electric field in the compact is large enough to allow microwave heating when the material can couple with the electric field. Figure 6a shows that the electric field in the susceptor and in the compact are much lower than the maximal value in the cavity as in the case when only the compact is the cavity (Figure 2b). However, with an adapted scaling (Figure 6b), we found that the electric field has the same order of magnitude in the compact and in the susceptor. More precisely, it is about twice lower in the compact. This means that the susceptor does not completely shield the compact from the field. Thus the compact may be submitted to hybrid heating, i.e. radiation coming from the susceptor and coupling with the microwaves if the imaginary permittivity of the material is high enough, as it is for zirconia.
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Figure 2. Electric field distribution in the cavity without compact (a), with a short compact (b) or with a long compact (c).
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Figure 3. Temperature distribution in a vertical cutting of the compact after 30 min heating in two conditions, thermal insulation on every side (a) or thermal insulation on every side except the upper surface (b).
1800 1600 ,—,1400 1200 0) 1000 0) 800 E 600 ω ^
0.9 c 0) Ό
0.8
400
0.7
200 0
0
5
10
15 20 Time (min)
25
30
>
ω CC
0.6
Figure 4. Temperature and relative density changes during sintering of the partially insulated compact. The curves corresponding to Center and Bottom temperature and relative density are almost superimposed.
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Figure 5. Position of the susceptor in the cavity
Figure 6. Distribution of the electric field in a plan normal to the wave propagation direction in the whole cavity (a), in the compact and susceptor only (b)
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CONCLUSION The interest of finite element simulation for better understanding of microwave sintering in a monomode cavity has been demonstrated. We first calculated the distribution of electromagnetic field in the cavity and in compacts of various lengths and we found that it was easier to sinter a long compact. This effect has been confirmed by experiments. Next we showed the temperature and density gradients in a compact with complete or partial thermal insulation. Finally we investigated the electric field when a susceptor surrounded the compact and found that the compact undergoes hybrid heating. This simulation should be improved following two axes. First the dimensional changes of the compact resulting from densification should be taken into account as they certainly affect microwave propagation and heat transfer. The second requirement is more challenging and critical for a quantitative prediction of microwave sintering. It consists in finding reliable values of dielectric parameters as function of temperature and density. Both experimental and modeling approaches should be combined for this purpose. REFERENCES 1 J.D. Katz, Microwave sintering of ceramics, An. Rev. Mater. Sei., 22,153-70, (1992). 2 K.H. Brosnan, G.L. Messing, and D.K. Agrawal, Microwave sintering of alumina at 2.45 GHz, J. Am. Ceram. Soc, 86, 1307-12, (2003). 3 M.A. Willert-Porada, R. Borchet, Microwave sintering of metal-ceramic FGM, Proc. 4th Int. Symp. Functionally Graded Materials, Tsukuba, Japan, October 21-24, 1996, Elsevier, (1997). 4 J. Wang, J. Binner, B. Vaidhyanathan, N. Joomun, J. Kilner, G. Dimitrakis, Cross T.E., Evidence of the microwave effect during hybrid sintering, J. Am. Ceram. Soc., 89, 1977-1984, (2006). 5 Iskander M.D., Andrade A.O.N.M., FDTD simulation of microwave sintering of ceramics in multimode cavities, IEEE Trans. Microwave Heating and Techniques 42, 793-9, (1994). 6 J. Lasri, P.D. Ramesh, and L. Schächter, Energy conversion during microwave sintering of a multiphase ceramic surrounded by a susceptor, J. Am. Ceram. Soc, 83, 1465-68, (2000). 7 A. Birnboim, Y. Carmel, Simulation of microwave sintering of ceramic bodies with complex geometry,/ Am. Ceram. Soc., 82, 3024-30, (1999). 8 R. Riedel, and J. Svoboda, Simulation of microwave sintering with advances sintering models, Adv. in Microwave and Radio Frequency Processing, (2006). 9 S. Charmond, C.P. Carry, and D. Bouvard, Direct and hybrid microwave sintering of yttria-doped zirconia in a single-mode cavity, Ceram. Trans., this issue.
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DIRECT AND HYBRID MICROWAVE SINTERING OF YTTRIA-DOPED ZIRCONIA IN A SINGLE-MODE CAVITY S. Charmond, C. P. Carry, D. Bouvard Laboratoire SIMaP, Grenoble-INP / CNRS / UJF BP 75, 38 402 St-Martin d'Héres, France ABSTRACT The use of microwave energy to sinter ceramic materials is an emerging technology of wide interest for improving the microstructure and reducing the time of sintering process. The microstructural development of 2 mol% yttria-stabilized zirconia nanopowders during direct and hybrid microwave sintering was studied for a constant heating rate (25 °C/min). Microwave heating experiments were achieved in a 2.45 GHz single-mode cavity instrumented with a thermal imaging camera. Insulating materials around the specimen was used to limit radiative thermal losses and prevent specimen from too high temperature gradients leading to crack development. Moreover, a cylindrical SiC susceptor was used for hybrid sintering experiments. Constant-heating rate runs were controlled by adjusting the position of a removable reflector at constant microwave forward power. The microwave temperature-time profile and the microwave power dissipated in the cavity were recorded and discussed. Next, the final densities were measured and the microstructures were observed by SEM. These results were compared to those of the conventionally-sintered materials. Microwavesintered materials always presented higher final densities for a same maximum measured temperature and, especially for hybrid-microwave sintering, homogeneous and finer microstructures. But direct microwave heating runs led to heterogeneous microstructures due to thermal gradients, which makes difficult an analysis in terms of microwave effect. Anyway, in comparison to the classical "sluggish" grain growth of TZP materials, grain growth seemed to be accelerated during microwave heating above a density estimated to be about 96 %TD. We thus conclude that microwaves are beneficial under this density and detrimental above. INTRODUCTION Microwave processing is generally characterized by uniform heating on a macroscopic scale and rapid heating rates, as compared to conventional thermal processing. It has been shown that microwave-processed ceramics led to improved densification with lower temperature and shorter times than conventional sintering with the development of finer and more uniform grain microstructures '"5. These main characteristics were attributed to rapid heating rates because the heat is generated within the materials. For instance, microwave heating of dielectric materials results from the absorption of part of the energy transported by an oscillating electric field by ionic conduction and molecular vibration. The microwave sintering of yttria-doped zirconia has been ever largely studied in various kinds of microwave furnaces : multimode and single-mode cavities with more or less complex insulation and susceptor devices, with or without pre-sintering, with temperature measurements by thermocouple, optical and IR pyrometer, thermal imaging camera, with various shapes of green samples...4"17. All of these experimental procedures make difficult to determine the microwave heating behaviors and characteristics of zirconia ceramics under pure direct electric field. A rectangular single-mode cavity at 2.45 GHz instrumented with a thermal imaging camera was designed to study both direct and susceptor-assisted microwave sintering of various kinds of materials (ceramics and metals) under either electric or magnetic field. This microwave furnace is an ideal support for understanding microwave-materials interactions. The specificity and selectivity of the microwave heating appeared the most interesting characteristics for sintering multicomponents, multilayers and functionally gradient materials. In this study, we present the first results of the
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sintering experiments of ceramic material in our original microwave furnace. During the microwave process, constant heating rate sintering runs were achieved at a constant forward microwave power by positioning a movable reflector to yield to the desired temperature-time profile. The final densities and microstructures of microwave-sintered materials were compared to the conventionally-sintered ones. EXPERIMENTAL PROCEDURE Spray-dried 2 mol% yttria-doped zirconia powder manufactured by Tosoh was used. Its BET specific area is 16 m2/g and the primary crystallites mean size is 60 nm. The zirconia grains are agglomerated in spherical aggregates which are in the range 10-80 μπι in diameter, as observed by SEM. Green samples were prepared either by cold isostatic pressing (CIP) at 250 MPa or in two steps : first, uniaxial pressing (UP) at low pressure (50 MPa) and next, cold isostatic pressing at 250 MPa. The green density was around 2.9 g/cm (i.e. 48 % of theoretical density). Before sintering, the binder was burnt out under air in an electric furnace by heating at 5 °C/min up to 700 °C and soaking for 2 hours before cooling. The weight loss was about 0.5 %. Without debinding, we observed crack development during microwave heating due to heterogeneous temperature distribution, as mentioned by Janney 5 . Green samples were sintered by direct microwave heating, by susceptor-assisted hybrid microwave heating or by conventional heating in vertical dilatometers (SETARAM TMA92, France or LXNSEIS L75/1550, Germany). The reference thermal cycle includes heating at 25 °C/min up to the sintering temperature, without dwelling time, and fast coolmg (faster than 30 °C/min). Bulk density of the sintered samples was measured by ethanol immersion method (based on Archimede principle). Sintered samples were cut using a diamond saw in two half-cylinders. Polished sections were thermally etched in an electrical oven under air between 50 °C to 80 °C below their maximal sintering temperature during 40 min to reveal their microstructure. The average grain size was determined on SEM micrographs by a linear intercept method. EXPERIMENTAL SETUP As shown in Figure 1, the microwave furnace includes a high voltage power supply (microwave generator SAIREM GMP 20KSM, France) linked to a magnetron that delivers a variable forward power up to 2 kW at 2.45 GHz. A rectangular wave-guide (type WR340 - section 86.36 x 43.18 mm 2 ) allows the transport of the microwave radiation to a rectangular TEiop cavity. This cavity is ended on the magnetron side by a coupling iris (a vertical slot in a copper sheet) placed in the waveguide and at fixed position during experiments, and on the other side by a movable reflector, also called sliding short-circuit piston.
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Figure 1. Schematic of the microwave furnace Samples were set in our cavity on a quartz plate inside a 40 mm-diameter quartz tube and surrounded by insulating material (alumina fiberboard box), as shown in Figure 2. In case of susceptorassisted microwave heating (hybrid sintering), a cylindrical SiC susceptor (internal diameter : 20 mm, height : 15 mm, thickness wall : 5 mm) is placed around the compact (cf. Figure 3). The temperatures of the upper surface of the specimen and of the susceptor were measured by an IR camera (FLIR SYSTEMS, ThermoVision™ A40M, Sweden) during the process to yield to the desired temperaturetime profile. This IR camera is placed just behind a ZnSe window setting about 14 cm above the center of the cavity. As drawn in Figure 2 and Figure 3, a small hole in the cap of the insulating box is needed to measure temperature of the upper section of the sample. During a test we measure the input power delivered by the magnetron (forward power) and the output power leaving the cavity (reflected power). We defined the dissipated powder as the difference between the input and output powers. All the experiments and data recordings were conducted manually.
Figure 2. Direct microwave sintering Figure 3. Hybrid microwave sintering The forward electromagnetic wave is reflected against the conductive wall of the short-circuit piston, leading to a standing wave made of a single stacking of forward and reflected waves. In the empty cavity, the points where the magnetic and electric fields are respectively maximum and minimum (near to zero) are exactly distant from each other by a quarter of the guided wave-length (43 mm). When the iris-piston distance is equal to 4 or 5 times the half guided wave-length, the iris reflects almost entirely the wave in the cavity (TE104 or TE105 resonance mode). The resonance phenomenon consists in the stacking of multiple waves reflected against the piston and the iris, which results in an increase of the electromagnetic energy in the cavity. In our single-mode cavity, the TE104 and TE105 modes are used for materials interacting respectively with the magnetic field or the electric field. Since ceramic materials as yttria-doped zirconia interact with the electric field, our specimens should be located where the electric field is maximum, i.e. theoretically in the centre of the cavity in TE105 mode. However, when materials are placed in the cavity (specimen, quartz and alumina holders, insulating materials, susceptor, etc.) the electromagnetic pattern and thus the distances between the iris, the
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specimen and the piston for getting resonance and stronger material-wave interaction are modified. In our setup the iris and the specimen are fixed during an experiment and the piston can be moved. In the tests presented here, the iris-specimen distance was chosen to be about equal to the specimen-piston distance allowing the best coupling between the material and the electric field at the resonance mode. During the test, the position of the piston was continuously adjusted so that the temperature measured by the infrared camera followed the prescribed cycle. This means that we did not stick to the position that was optimal for specimen heating. We observed in preliminary runs that this optimal position often results in overheating and cracking of the specimen. RESULTS In the following, six sintering experiments will be presented and analyzed : 3 conventional sintering tests (C), 2 direct microwave sintering runs (MWd) and 1 hybrid microwave sintering run (MWh). Table I provides the compaction mode, the dimensions of the green compact, the forward microwave power (FP), the maximum sintering temperature and the final density for each test. Note that the compacts had different sizes, ranging between 7.4 and 10.0 mm in diameter, 7.2 and 11.9 mm in height, 1.0 and 2.1 g in weight. Name
Pressing (MPa)
Cl UP50/CIP250 C2 CIP250 C3 CIP250 MWd4 CIP 250 MWd5 UP50/CIP250 MWh6 UP50/CIP250
Diameter (mm)
Height (mm)
Mass (g)
FP (W)
7.4 8.5-9.1 9.0 10.0 7.4 7.4
7.7 11.9 9.4 7.2 7.7 7.8
0.98 2.13 1.79 1.64 0.97 0.98
-
Tmax (°C)
1320 1390 1500 600 1390 1000 plasma 1000 1340
Density (g/cm3)
Relative Density
5.56 5.76 5.98 5.88 5.99 5.80
91.9 95.1 98.8 97.3 98.9 95.8
(%)
Direct microwave sintering The temperature of the sample upper surface and the dissipated power recorded during the two direct microwave sintering tests are drawn in Figure 4 (MWd4) and Figure 5 (MWd5). The temperature variations are compared to the reference thermal cycle. During the first run (MWd4), the forward power and the iris-cavity distance were fixed respectively to 600 W and 135 mm. The compacts weighted about 1.6 g.
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Figure 4. Direct microwave sintering run (MWd4 - 1390°C - FP : 600W) The heating rate of 25 °C/min was controlled from room temperature to about 1400 °C by adjusting the position of the sliding short-circuit piston. At low temperature, the dissipated power increased slightly up to 50 W and remained constant up to 500 °C. Next, the dissipated power decreased to 40 W while the temperature of specimen upper surface continued to increase up to 1000 °C. Above this temperature, the dissipated power increased steadily up to 170 W when the temperature reached 1400 °C. Finally, the forward power was cut off for dropping in temperature.
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Figure 5. Direct microwave sintering run (MWd5 - 1350°C - FP : 1000W) In the second run (MWd5) with a smaller sample, the forward power was fixed to 1000 W. From room temperature to 500 °C, this run was similar to the previous one : the dissipated power increased slightly up to 60 W and was next constant. But above 500 °C, temperature instabilities occurred during the test. It was impossible to control the heating rate by changing the position of the piston. For this range of temperature, we believe that specific changes in dielectric properties of zirconia (sharp increasing of loss tangent above 400 °C 18) combined with the higher forward power (1000 W instead of 600 W previously) led to this unusual behavior. Therefore, during this second run it has been difficult to control the heating rate in the 500-900 °C range. Finally, the dissipated power increased up to 100 W at 1350 °C before forward power being promptly cut off because of plasma occurrence. This plasma appeared in the small hole drilled in the insulating cap. It burnt a part of insulating- materials and overheated the specimen. Hence, the maximum temperature in the specimen was unknown. Despite this overheating, the specimen was not cracked. It was characterized but the results could not be decently compared to those of the conventional experiments. Hybrid microwave sintering In the hybrid sintering run, the distance between the iris and the cavity was set to 122 mm (determined from "pre-runs") to keep a symmetrical pattern and the maximum of the electric field in the susceptor and specimen area at the resonant mode. The temperature-time profile of this specimen followed the prescribed heating rate (25 °C/min).
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Figure 6. Hybrid microwave sintering run (MWh66 - 1350°C - 1000W) From room temperature to 600 °C, the sample remained colder than the SiC susceptor because of its poorer dielectric properties (loss tangent) at low temperature. Therefore, zirconia was mainly heated by thermal radiance from the susceptor. However above 600 °C, zirconia got hotter than the susceptor : its temperature followed more or less the prescribed thermal cycle from 600 °C to 1000 °C whereas the temperature of susceptor remained constant around 650 °C. We deduce that the compact is heated by both radiance from the susceptor and coupling with the microwaves (hybrid heating). The dissipated power varied in the 150 W - 350 W range. Above 1000 °C, the dissipated power increased steadily but sharply up to 900 W and the temperature reached 1350 °C at the upper surface of the zirconia specimen and only 950 °C in the susceptor. Moreover, we note that the evolution of the susceptor temperature vs. time shows the same trend as the dissipated power. Also this power is much higher than the one measured during direct microwave sintering runs. This proves that the main part of microwave energy dissipated in the cavity is used to heat the SiC susceptor and balance the radiative losses, especially above 700 °C. Characterization of sintered materials
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Figure 7. Relative Density vs. Temperature for Direct Microwave (MWd), Hybrid Microwave (MWh) and Conventional (C) Sintering First of all, the density of the conventionally-sintered materials increases from 91.9 % at 1320 °C up to 98.8 % at 1500 °C. Next, the density of the direct microwave-sintered material heated to 1390 °C (upper surface temperature) is significantly higher than the conventionally sintered one (97.3 % compared to only 95.1 %), i.e. the porosity was reduced from 4.9 % to 2.7 %. At last, the density of the hybrid-microwave-sintered material heated to 1340 °C is 95.8 %TD. This hybrid microwave-sintered sample was then much denser than the one conventionally sintered at 1320 °C and even slightly denser than the conventionally-sintered one at 1390 °C. The microstructures (Cl, C2, MWd4, MWh6) were observed by scanning electron microscopy (SEM - Secondary Electrons detector) along the axis of the cylindrical samples on longitudinal sections.
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Figure 8. Conventional sintering (Cl) Figure 9. Conventional sintering (C2) 1320 °C - g.s. = 400 nm 1390 °C - g.s. = 435 nm The conventional-sintered specimens presents a homogeneous microstructure of equiaxe grains, as expected, with an average size of 400 nm at 1320 °C (cf. Figure 8) and 435 nm at 1390 °C (cf. Figure 9).
g.s. = 395 nm
g.s. = 490 nm
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g.s. = 540 run Figure 10. Direct-microwave-sintering (MWd4) Microstructures of the top, central and bottom zones of the specimen The microstructure is heterogeneous in the direct microwave-sintered material. The grains are smaller, i.e. less than 400 nm, in top zone, but they are larger, i.e. about 490 nm in the central zone and 540 nm in the bottom zone (cf. Figure 10). This microstructural gradient likely results from a thermal gradient.
Figure 11. Hybrid microwave sintering (MWh6) 1340 ° C - g.s. = 370 nm The final microstructure of the hybrid microwave-sintered material heated at 1340 °C is the finest (cf. Figure 11), i.e. 370 nm instead of 400 nm for the conventionally-sintered one at 1320 °C (cf. Figure 9). Moreover, the microstructure can be considered as homogeneous (average grain size : 370 nm in the upper zone ; 378 nm in the center; 357 nm in the bottom zone). DISCUSSION The external surface of the conventionally-sintered compact is heated by radiation and convection and the heat is transferred by conduction from the surface to the core of the sample. Then the temperature should be higher in the surface of than in the core. But the effects of this gradient can be neglected because homogeneous microstructures are observed. Microwave processes involve a different heating behavior. During microwave sintering, the heat is produced in the bulk of the compact. Therefore, an inverse thermal gradient takes place in materials, with higher temperature in the core. That is why thermal insulation is necessary to reduce radiative thermal losses through external surfaces and, as consequence, decrease temperature gradients in the specimen. Besides, in our device the insulation of the upper part is incomplete because we need to keep a hole for temperature measurement. Thus it is expected that the temperature measured by the IR camera is inferior to the
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temperature in the core. During hybrid microwave sintering, heat is produced both in the bulk of the specimen and upon its surface by radiance from the susceptor. Thus it is expected that temperature gradients are less marked. As shown in Figure 7, for a given sintering temperature, both direct and hybrid microwavesintered materials reached higher final densities than the conventionally-sintered ones. As homogeneous microstructure was observed in the hybrid microwave-sintered specimen (MWh6), we can consider that the temperature measured on the specimen upper surface was representative of the bulk temperature. Therefore, the SiC susceptor acts as an efficient insulation system, which does not shield zirconia samples from microwaves. Besides, we noticed higher density (95.8 %) and finer microstructure (370 nm) than in conventional-sintered samples for comparable sintering temperature (respectively 93 % and 400 nm). Thus, we evidenced with this hybrid microwave heating experiment the existence of a favourable microwave effect on sintering behavior of zirconia, at least for relative density up to 96 %TD. In contrast with hybrid microwave sintering, the microstructural gradient observed in the direct microwave-sintered specimen (MWd4) is linked to thermal gradients. Higher grain size in the core of the specimen indicates higher temperature in the core than at the upper surface. Assuming no microwave effect for specimen MWd4, the temperature difference between the core and the upper surface could be estimated to be about 50 °C according to the density-temperature trend line of conventionally-sintered specimens (97.3 % at 1450 °C) in Figure 7. However, this temperature difference should be less if there is a positive microwave effect on densification as shown during hybrid microwave sintering. Concerning the microstructures, the average grain sizes measured in the upper zones of the direct microwave sintered specimens (395 nm) were always smaller than those observed in the conventionally-sintered ones (440 run), which is consistent with the hybrid sintering test. Nevertheless, the grain size in bottom (540 nm) and central (490 nm) zones is much higher than those observed in the conventionally-sintered ones (440 nm). In Figure 7, we noticed that the grain growth in conventional sintering is very slow, as already reported in the literature for such TZP materials in connection with the phase partitioning process ("sluggish" grain growth 19). As a consequence, the higher grain size in the core of MWd4 specimen may indicate that microwaves enhance the grain growth through the phase partitioning process. It is likely that such effect has not been observed in hybrid experiment due to lower density (95.8 % instead of 97.3 %). A hybrid microwave sintering experiment at higher temperature to reach higher density than 96 %TD should be achieved to validate that analysis. Also, as "sluggish" grain growth kinetics were not observed in 8 mol% yttria-doped zirconia materials, it will be interesting to sinter such materials with our setup and compare microwave effects with the effects evidenced in the present study. CONCLUSIONS Direct or hybrid microwave sintering experiments of 2 mol% yttria-doped zirconia were performed in a single-mode cavity instrumented with a thermal imaging camera measuring the temperature of the upper surface of the specimen. Hybrid microwave sintering experiments provided a homogeneous specimen with higher density and finer microstructure than the specimen conventionally-sintered at the same temperature. On the contrary direct microwave heating runs led to heterogeneous microstructures due to thermal gradients, which makes difficult an analysis in terms of microwave effect. Anyway, in comparison to the classical "sluggish" grain growth of TZP materials, grain growth seemed to be accelerated during microwave heating above a density estimated to be about 96 %TD. We thus conclude that microwaves are beneficial under this density and detrimental above. Further experiments will show (i) if there is enhanced grain growth during homogeneous microwave heating at densities higher than 96 %TD, (ii) if such effect is also observed during microwave sintering of 8 mol% yttria-doped zirconia.
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REFERENCES 1 W. H. Sutton, Microwave Processing of Ceramic Materials, Ceramic Bulletin, 68 [2], 376-386 (1989). 2 S. S. Park, T. T. Meek, Characterization of Ζ1Ό2-ΑΙ2Ο3 Composites Sintered in a 2.45 GHz Electromagnetic Field, Journal of Materials Science, 26, 6309-6313 (1991). 3 D.E. Clark, W.H. Sutton, Microwave Processing of Materials, Annu. Rev. Mater. Sei., 26, 299-331 (1996). 4 Y.-L. Tian, Pratices of Ultra-rapid Sintering of Ceramics using Single-mode Applicators, Ceramic Trans, American Ceramic Society, 21, 283-300 (1991). 5 M.A. Janney, C.L. Calhoun, H.D. Kimrey, Microwave Sintering of Oxide Fuel Cell Materials : I, Zirconia-8 mol% Yttria,y. Am. Ceram. Soc, 75 [2], 341-46 (1992). 6 C.E. Holcombe, T.T. Meek, N.L. Dykes, Unusual Properties of Microwave-Sintered Yttria-2 wt% Zirconia, Journal of Materials Science, 7, 881-884 (1988). 7 J. Wilson, S.M. Kunz, Microwave Sintering of Partially Stabilized Zirconia, /. Am. Ceram. Soc, 71 11], C-40-C-41 (1988). S.A. Nightingale, D.P. Dunne, H.K. Worner, Sintering and Grain Growth of 3 mol% Yttria Zirconia in a Microwave Field, Journal of Materials Science, 31, 5039-5043 (1996). 9 Z. Xie, J. Li, Y. Huang, X. Kong, Microwave Sintering Behaviour of ZrO2-Y203 with Agglomerate, Journal of Materials Science, 15, 1158-1160(1996). 10 S.A. Nightingale, H.K. Worner, D.P. Dunne, Microstructural Development during the Microwave Sintering of Yttria-Zirconia Ceramics,/. Am. Ceram. Soc, 80 [2], 394-400 (1997). 1 ' A. Goldstein, N. Travitzky, A. Singurindy, M. Kravchik, Direct Microwave Sintering of YttriaStabilized Zirconia at 2.45 GHz, Journal of the European Ceramic Society, 19, 2067-2072 (1999). 12 S. Fujitsu, M. Ikegami, T. Hayashi, Sintering of Partially Stabilized Zirconia by Microwave Heating Using ΖηΟ-Μηθ2-Αΐ2θ3 Plates in a Domestic Microwave Oven, J. Am. Ceram. Soc, 83 [8], 20852087 (2000). 13 C. Zhao, J. Vleugels, C. Groffils, P.J. Luypaert, O. Van Der Biest, Hybrid Sintering with a Tubular Susceptor in a Cylindrical Single-Mode Microwave Furnace, Acta mater., 48, 3795-3801 (2000). 14 D.D. Upadhyaya, A. Ghosh, K.R. Gurumurthy, R. Prasad, Microwave Sintering of Cubic Zirconia, Ceramics International, 27, 415-418 (2001). 15 J. Wang, J. Binner, B. Vaidhyanathan, N. Joomun, J. Kilner, G. Dimitrakis, T.E. Cross, Evidence for the Microwave Effect during Hybrid Sintering, J. Am. Ceram. Soc, 89 [6], 1977-1984 (2006). 16 J. Binner, K. Annapoorani, A. Paul, I. Santacruz, B. Vaidhyanathan, Dense Nanostructured Zirconia by Two Stage Conventional/Hybrid Microwave Sintering, Journal of European Ceramic Society, 28, 973-977 (2008). 17 M. Mazaheri, A.M. Zahedi, M.M. Hejazi, Processing of nanocrystalline 8 mol% yttria-stabilized zirconia by conventional, microwave-assisted and two-step sintering, Materials Science and Engineering, A492,261-267 (2008). 18 M. Willert-Porada, T. Gerdes, Metalorganic and Microwave Processing of Eutectic Ai203-Zr02 Ceramics, Mat. Res. Soc. Symp. Proc, Vol. 347, 563-569 (1994). 19 T. Stoto, M. Nauer, C. Carry, Influence of Residual Impurities on Phase partitioning and Grain Growth Processes of Y-TZP Materials, J. Am. Ceram. Soc, 74 [10], 2615-21 (1991).
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THE INFLUENCE OF MINOR ADDITIVES ON DENSIFICATION AND MICROSTUCTURE OF SUBMICROMETER ALUMINA CERAMICS PREPARED BY SPS AND HIP Jaroslav Sedlácek1,2, Monika Michálková1, Deniz Karaman2, Dusan Galusek1, Michael Hoffmann2 'Vitrum Laugaricio - Joint Glass Center of the Institute of Inorganic Chemistry, Slovak Academy of Sciences, Alexander Dubcek University of Trencin, and RONA, j.s.c, Trenöin, Slovakia 2
Institut fur Keramik im Maschinenbau, TU Karlsruhe, Karlsruhe, Germany
ABSTRACT Refinement of microstructure and complete elimination of residual porosity are prerequisite for improvement of mechanical properties and achievement of transparency for visible light in polycrystalline alumina (PCA). The two requirements are in obvious contradiction, as the elimination of porosity by conventional sintering requires high sintering temperatures and long dwell times, inevitably accompanied by grain growth in the final stage of densification. Spark plasma sintering (SPS) followed by hot isostatic pressing (HIP) were applied for preparation of fully dense PCA with submicrometre microstructure from high purity alumina powder Taimicron TM DAR with the initial particle size 150 nm. SPS resulted in some microstructure refinement in comparison to conventionally sintered samples. In the reference material A (pure PCA) temperatures > 1200 °C led to rapid grain coarsening without complete densification. Addition of 500 ppm of MgO, ΖΚ>2 and Y2O3 led both to microstructure refinement and deceleration of densification, and the temperatures by 50 - 100 °C higher in comparison to the reference A were required to achieve the same microstructure characteristics. The residual porosity was successfully eliminated by HIP at 1100 - 1250 °C. Fully dense reference material A with the mean grain size < 500 nm was prepared by HIP at 1150 °C. Higher HIP temperatures led to quick attainment of full density followed by rapid grain growth. The Y2O3 and Zr02-doped PCA required higher temperatures for complete densification, and fully dense materials with the mean grain size < 500 nm were prepared by HIP at 1250 °C.
INTRODUCTION Polycrystalline alumina with submicrometre grains (0.3 to 1 urn) was reported to exhibit high hardness, 1,2 good mechanical strength, 3 " 5 and improved wear resistance 6. Alumina also transmits infrared, and if sintered to high density (residual porosity < 0.01 %), also visible light with possible applications in high pressure envelopes of metal halide discharge lamps 7,8 , or transparent armours. Nevertheless, even if light scattering residual porosity is completely eliminated, polycrystalline ceramics are usually only translucent due to birefringence of alumina. The linear transmission of visible light is believed to be markedly increased by decrease of the grain size to less than the wavelength of visible light, i.e. to below ~ 300 nm . This goal is in obvious contradiction with the requirement of complete elimination of the residual porosity to less than 0.01 %, and cannot be attained by conventional sintering process, which for this purpose usually requires long soaking times at high temperatures in hydrogen atmosphere, accompanied by significant, and often abnormal, grain growth and inevitable deterioration of mechanical properties. During the standard sintering process grain growth is generally observed to take place at the final stage of sintering, or more specifically, when the last 3 % of porosity is eliminated 1 0 ' u . A number of works therefore describes the use of various, mostly pressure assisted, sintering techniques, e.g. spark plasma sintering12, hot isostatic pressing, or sinter-HIP techniques13 or their combinations with conventional sintering in order to eliminate residual porosity without excessive grain growth.
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Spark plasma sintering (or field assisted sintering technique FAST) attracted most attention in the last few years, with reported decrease of sintering temperature and shortening of required soaking times to a fraction of times usually applied in conventional sintering. Since about mid nineties a number of works dealt with spark plasma sintering of polycrystalline alumina 12,14 " 12. There seems to be general agreement that the method significantly accelerates the processes responsible for both the densification and grain growth, either by self heat generation by miroscopic discharge between particles, activation of particle surfaces 5 or by electric field accelerated grain boundary diffusion and grain boundary migration19. It is tempting to believe that grain boundary migration requires higher temperatures and pressures that densification, and that the SPS process might, under certain conditions, result in significant microstructure refinement during sintering of alumina. Indeed, some works report on refinement of the microstructure of SPS-PCA in comparison to traditional sintering, or retention of very fine grained microstructure of PCA prepared from submicrometre powders 14 ' 18 ' °. However, the densification rate and grain growth are influenced by the parameters of the SPS process, including heating rate17 " 19, applied pressure17' ", specimen thickness17, pulse sequence16, 9, and maximum temperature/time of isothermal dwell1 ' 19 and therefore no unambiguous conclusions can be drawn from the available data. In general, high pressure, high heating rate (> 50 "C.min"1) and low temperatures seem to be beneficial for retention of fine grained microstructure. Moreover, despite reported grain growth retarding action of MgO in SPS-PCA14·21, little attention has been paid to the influence of other additives/impurities, namely Z1O2 and Y2O3, whose influence on microstructure development during conventional sintering of alumina has been documented. The present work is aimed at the study of the SPS process of a submicrometre alumina powder, in particular the influence of minor, deliberately added dopants MgO, Z1O2 and Y2O3 on densification and grain growth during SPS, and post-SPS hot isostatic pressing. The results are compared to reference pure polycrystalline alumina densified by SPS and with the use of conventional pressureless sintering. EXPERIMENTAL Alumina powder (Taimicron TM-DAR, Taimei Chemicals Co., Japan) with the mean particle size 150 nm and the surface area 14.5 m2 g"1 was used as a starting material in all experiments. The reference aluminas were prepared both by pressureless sintering and by SPS. In the former green discs 12 mm in diameter and 6 mm thick, prepared by axial pressing in a steel die at 50 MPa followed by cold isostatic pressing at 500 MPa were sintered in an electrical furnace with M0SÍ2 heating elements in air at various temperatures ranging from 1000 to 1350 °C without isothermal dwell, heating rate 10 °C/min. In the latter 6 g of the alumina powder was filled into a graphite die with the diameter of 20 mm and spark plasma sintered in the temperature range between 1150 and 1250 °C, heating rate 400 °C/min, pressure 150 MPa, equilibration time at maximum temperature 1 min, and subsequent isothermal dwell between 1 and 6 minutes. The specimens are denoted as A in the following text. Doped powders were prepared by mixing 100 g of the alumina powder with respective amounts of suitable precursor: Mg(N03)2.6H20 (p.a., Lachema Brno, Czech republic), zirconium isopropoxide (p.a. Sigma Aldrich, and Y2O3 (99.9 % purity, Treibacher Industries AG, Austria) dissolved in nitric acid (p.a. Lachema Brno, Czech republic). The mixture was homogenised in a polyethylene jar in isopropanol (pure, Sigma Aldrich) with high purity alumina milling balls for 2 h. The water solution of ammonia was then added to precipitate respective hydroxides. The mixtures were then further homogenised for 2 h to complete the hydrolysis, and dried at continuous stirring under infrared lamp. The powders were gently crushed, sieved through a 100 um polyethylene sieve, calcined for 1 h at 800 °C in air, and again sieved to obtain a reasonably free flowing powder. The powders were filled into a graphite die with the diameter of 20 mm and spark plasma sintered at temperatures between 1150 and 1300 °C, under the same conditions as the reference A. The specimens containing the respective dopants MgO, Y2O3 and Z1O2 are denoted as AM, AY, and AZ.
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The density of sintered samples was measured by the Archimedes method in water. The microstructures were examined on fracture surfaces by scanning electron microscopy (Zeiss, model EVO 40HV, Carl Zeiss SMT AG, Germany). The mean grain size was determined using the linear intercept method on fracture surfaces 23. In order to eliminate possible error introduced by measurement of the grain size on fracture surface, an empirical correction factor was applied, calculated from the comparison of the grain sizes measured on the same specimen on both fracture surfaces and the polished and thermally etched cross sections. Minimum of 200 grains were measured in order to obtain statistically robust set of data. Selected specimens, which during SPS sintered to the stage of closed porosity (or near to it) were cut in four parts, and each part was hot isostatically pressed at a different temperature 1050, 1100, 1150 or 1250 °C, with 3 h isothermal dwell at the maximum pressure of 150 MPa with Ar as the pressure medium. The HIP-ed specimens were characterized in the same manner as described above. RESULTS AND DISCUSSION Spark Plasma Sintering The results of the SPS experiments are summarized in Fig. 1 - Fig. 5. The SEM micrographs of fracture surfaces of the pure PCA (material A) and PCAs with 500 ppm of the respective dopants (AM, AY, and AZ) subjected to the same SPS regime (1 min isothermal dwell at 1200 °C) are shown in the Fig. 1. Under these conditions the material A was already highly dense, with a characteristic microstructure consisting of angular microcrystals with the mean size of 230 nm. In the material AM both the densification and grain growth were slightly suppressed. This effect was even more pronounced in case of AY and AZ, where the alumina powder maintained its original round-shaped morphology, with only necks formed among individual particles. Grain growth was negligible (180, and 190 nm grain size in comparison to 150 nm in the starting powder), and the densification was almost entirely suppressed, the relative density achieving only 73.9 and 77.6 % in AY and AZ, respectively. The results demonstrate grain growth and densification retarding action of Y2O3 and Ζ1Ό2 additives. The influence of temperature and time of isothermal dwell on the microstructure development of PCA is illustrated in Fig. 2. In the reference A both the relative density and the mean grain size increased markedly with temperature and time of isothermal dwell. Heating of 6 minutes at 1250 °C resulted in microstructure with equiaxial alumina grains with the mean size 900 nm, which is 6 times the initial size of the powder particles. The powder AY sintered 6 minutes at 1300 °C achieved comparable relative density, with finer microstructure and the mean grain size of only 300 nm. Similar results were obtained also in AM and AZ, Y2O3 and Z1O2 being the most effective additives. The time dependencies of relative densities (/>,) of all materials sintered at various temperatures are summarized in Fig. 3. A marked influence of the temperature of isothermal dwell, but especially of the additives, is obvious. After 3 minutes of sintering at 1150 °C the reference A sintered to the stage of closed porosity (> 90 % relative density). The addition of MgO shifted the required temperature by about 50 °C to higher values, and the material AY required at least 1 minute isothermal dwell at 1300 °C to achieve the relative density exceeding 90 %. The situation is similar in the materials AZ. Quite clearly the addition of as little as 500 ppm of the respective oxides significantly influences the densification rate, most likely by segregation into grain boundaries and impairing the grain boundary diffusion in sintered compacts. Along with grain boundary diffusion, the grain boundary mobility is also affected (Fig. 4): while in the reference material A all temperatures > 1150 °C resulted in rapid grain coarsening, the additives suppressed the grain growth so that the grain size did not exceed 400 nm in the whole temperature and time interval studied.
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Fig. 1 SEM micrographs of fracture surfaces of SPS densified specimens after identical heat treatment 1 min at 1200 °C: a) A, pr = 93.6 %, MGS = 230 nm, b) AM, p, = 88.5 %, MGS = 210 um, c) AY, pr = 73.9 %, MGS = 190 nm, d) AZ, pr = 77.6 %, MGS = 180 nm. Bar = 200 nm. This effect is even more obvious if the data are plotted in the form of sintering trajectories (Fig. 5), i.e. the relations between the mean grain sizes and relative densities of sintered materials. The reference material A exhibits a typical sintering curve with exponential growth of the grain size in the final stage of sintering, albeit shifted to lower values in comparison to conventionally sintered alumina. The sintering curve of doped materials is quite flat, showing almost linear dependence between the grain size and relative density up to the p, < 98 % (99.6 % for AM). Apparent decrease of density and abnormal increase of grains size of the specimen AM after 3 min SPS at 1250 °C is believed to be accidental and caused most likely by improper packing of the powder in graphite die. However, these results cannot be taken as the unambiguous evidence that the grain growth is suppressed entirely: we did not succeed in preparation of fully dense material from any doped powder, except of AM, where the ρτ = 99.6 % was achieved. In all cases the content of residual porosity was > 2 %, and majority of grain growth is known to take place when the last 3 % of porosity is eliminated 10' ". One therefore cannot exclude that additional grain growth will take place at longer sintering times, or higher temperatures. In any case, highly dense doped materials with low fraction of closed residual porosity represented a promising starting position for complete densification by HIP.
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Fig. 2 The microstructure development of SPS densified specimens A: a) 1150°C/lmin, p, = 86.6 %, MGS = 200 um, b) 1200°C/3min, pr = 97.3 %, MGS = 480 nm, c) 1250 °C/6min, pr = 98.9 %, MGS = 900 nm. Comparison with the AY material (d) densified 6 min at 1300 °C, pr = 98.0 %, MGS = 300 nm. Hot isostatic pressing The results of HIP experiments are summarized in Fig. 6 - Fig. 9. The conditions of HIP were selected as mild as possible to attain full densification, but if possible, to avoid grain growth. The SEM micrographs of fracture surfaces of the reference materials A spark plasma sintered for 3 minutes at 1150 °C (the mildest conditions facilitating to achieve the stage of closed porosity prerequisite for successful HIP) are shown in Fig. 6. Both the relative density and grain size increased markedly with the increasing temperature of isothermal heating. Although 1050 and 1100 °C was too low for complete densification, increase of density accompanied by only negligible grain growth could be observed. At 1150 °C the mean grain size 320 nm (18 % increase in comparison to the SPS material) corresponded to the relative density 98.9 % (7.3 % increase). Fully dense specimens could be prepared at temperatures > 1150 °C, but at these temperatures also rapid grain growth was observed, so that coarse grained microstructure (the mean grain size 2 um) resulted after HIP at 1250 °C. Similarly to SPS, refinement of the microstructure was achieved in doped specimens. The sample AY spark plasma sintered for 3 minutes at 1300 °C achieved full density by HIP at 1250 °C at the mean grain size of only 490 nm. Interestingly, the grain size is similar to the material A with the mean grain size of only 470 nm HIP-ed at 1150 °C, which was the lowest temperature facilitating complete elimination of residual porosity. The results indicate that both in doped and undoped PCA the grain boundary diffusion (densification) and grain boundary mobility (grain growth) are thermally activated processes, and a temperature interval can be found where densification is already activated, while grain growth is not. The dopants influence the temperatures where either process is activated, and shift them to higher values.
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Fig. 3 Time dependence of relative density of sintered specimens after SPS. 1000
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Pr/% Pr/% Fig. 5 Sintering trajectories of SPS densified aluminas. Fig. 7 summarizes the relative densitities of HIP-ed specimens as the function of the temperature of isothermal heating during HIP. Densification is fastest in the reference material A, where 1100 °C is sufficient to attain relative densities close to the theoretical value. Naturally, the initial density after SPS plays a significant role. Although the addition of MgO required by about 50 °C higher temperatures to attain the stage of closed porosity during the SPS in comparison to the reference A, no such effect was observed during HIP, and fully dense material AM could be prepared at 1100 °C. Materials AY and AZ behaved in a different way. The two curves shown in Fig. 7 for each composition represent the densification during HIP of materials with residual open porosity (SPS 1250 °C / 3 min) and those sintered to the stage of closed porosity (SPS 1300 °C / 3 min). The former could not be, quite obviously, sintered to full density due to the counter-pressure of Ar gas in gradually closing pores, the latter shows marked influence of applied hydrostatic pressure on densification. Complete elimination of residual porosity was achieved after 3 h HIP at 1300 °C. The grain size development with the temperature of HIP is summarized in Fig. 8. In the reference A and in MgO-doped material AM only limited growth of grains is observed at temperatures < 1100 °C. Above this temperature the grain growth is more pronounced, achieving the values 4 times higher than in the respective SPS samples and up to 1 0 - 1 2 times higher than the initial particle size of the alumina powder. Quite obviously the temperature 1250 °C is unnecessary high and results in excessive growth of alumina grains. The Y2O3 and ZrCh-doped specimens in turn exhibit nearly no grain growth, and even after 3 h at 1250 °C the mean grain size is at about the same level as in the respective SPS specimens. The data summarized in the previous two paragraphs are easier to understand if they are plotted in the form of sintering trajectories (Fig. 9). In the reference A full density can be achieved without significant grain growth (the points are marked by the rectangle in the Fig. 9). After that, if the temperature of HIP is unnecessarily high, grain growth is observed, which results in fully dense, but coarse grained microstructure. Fully dense specimens with the grain size less than 500 nm can be prepared under the following conditions:
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Fig. 6 Microstructure development of material A (spark plasma sintered 3 min at 1150 °C) with the temperature of HIP. a) 1050 °C, pr = 96.2 %, MGS = 270 nm, b) 1100 °C, pr = 98.9 %, MGS = 320 nm c) 1150 °C, pr = 100 %, MGS = 470 nm d) 1250 °C pr = 100 %, MGS = 2 μπι. A comparison with the material AY (SPS, 3 min at 1300 °C) e) 1050 °C, pr = 97.9 %, MGS = 380 nm f) 1250 °C, pr = 100 %, MGS = 490 nm.
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100.
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4 AM: Ά •■
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Fig. 9 Sintering trajectories of HIP-ed materials. (1) Closed porosity must be attained after the SPS, but the temperature of SPS must not exceed 1200 °C. Above this temperature the SPS itself results in undesirable microstructure coarsening. (2) The temperature of HIP must not exceed 1150 °C. Above this-temperature rapid grain growth takes place. Complete densification is quickly achieved, and after that the surface energy of polycrystalline material can be further reduced only by grain growth. (3) For the respective system the temperature interval between 1150 and 1200 °C seems to be the border where the mechanisms responsible for grain growth take the control over the mechanisms responsible for densification. The situation is similar in the MgO-doped system, with some suppression of the grain growth observed at 1250 °C in comparison to the A reference. In the Y2O3 and ZrCb-doped aluminas this temperature interval is shifted to higher values. For all temperatures applied during HIP only negligible grain growth is observed, and full density is attained at the mean grain size of about 500 nm. The dopants might possibly also extend the interval where alumina can be sintered without, or with only limited grain growth, but to verify this hypothesis further experiments are required. It is also quite possible that at higher HIP temperatures (e.g. 1400 °C) similar microstructure development will be observed as in the reference A, i.e. significant grain growth once full density is achieved. CONCLUSIONS Densification and microstructure development of reference pure polycrystalline alumina A and 500 ppm MgO, Ζ1Ό2 and Y203-doped aluminas AM, AZ and AY by spark plasma sintering, followed by hot isostatic pressing was studied in the present work. Although SPS resulted in some microstructure refinement in comparison to conventionally sintered samples, the temperatures above 1200 °C resulted in grain coarsening without complete densification in the reference material A.
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Addition of dopants led in all cases to some microstructure refinement, especially in case of Ζ1Ό2 and Y2O3, but this effect was accompanied by slower densification. In general, the dopants decelerated both the grain growth and densification, and the temperatures by about 50 - 100 °C higher in comparison to the reference A were required to achieve the same microstructure characteristics. Complete densification could not be achieved by SPS and in all cases the residual porosity > 2 % was present. The porosity was successfully eliminated by subsequent HIP in the temperature range 1100 - 1250 °C. Fully dense specimens with the mean grain size < 500 nm were prepared by HIP of the reference A at 1150 °C. The HIP temperatures > 1200 °C led to quick attainment of full density followed by rapid grain growth (the mean grain size up to 2 urn). The temperature interval between 1150 and 1200 °C seems to be the border where the mechanisms responsible for grain growth take the control over the mechanisms responsible for densification in the reference material A. In the Y2O3 and ZrCvdoped aluminas this temperature interval was shifted to higher values. Only negligible grain growth was observed, and full density was attained at the mean grain size of about 500 nm by HIP at 1250 °C in materials AY and AZ. ACKNOWLEDGEMENT The financial support of this work by the grant A P W 0485-06, the Slovak National Grant Agency VEGA, grant No 2/6181/26, the Alexander von Humboldt Foundation (D. Galusek), and by Maria Curie Research Fellowship Program (J. Sedlácek) is gratefully acknowledged. REFERENCES ' A. Krell, S. Schädlich, Nanoindentation hardness of submicrometer alumina ceramics, Mater. Sei. Eng., Α30Ί, 172-181 (2001). 2 A. Krell, P. Blank, Grain size dependence of hardness in dense submicrometer alumina, J.Am.Ceram.Soc, 78, 1118-1120 (1993). 3 K. Morinaga, T. Torikai, K. Nakagawa, S. Fujino, Fabrication of fine α-alumina powders by thermal decomposition of ammonium aluminum carbonate hydroxide (AACH), Acta Mater., 48, 4735-4741 (2000). 4 A. Krell, P. Blank, The influence of shaping method on the grain size dependence of strength in dense submicrometre alumina, J.Eur.Ceram.Soc, 16, 1189-1200(1996). 5 Y.T. O, J. Koo, K.J. Hong, J.S. Park, D.C. Shin, Effect of grain size on transmittance and mechanical strength of sintered alumina, Mater.Sci.&Eng., A374, 191-195 (2004). 6 A. Krell, D. Klaffke, Effects of grain size and humidity on fretting wear in fine grained alumina, AI2O3/T1C and zirconia,/.Λ/η. Ceram.Soc, 79, 1139-1146 (1996). 7 G.C. Wei, Transparent ceramic lamp envelope materials, J. Phys. D: Appl. Phys., 38, 3057-3065 (2005). 8 A. Krell, P. Blank, H. Ma, T. Hutzler, M.P.B. van Bruggen, R. Apetz, Transparent sintered corundum with high hardness and strength, J.Am.Ceram.Soc, 86, 12-18 (2003). 9 R. Apetz, M.P.B. van Bruggen, Transparent Alumina: A Light-Scattering Model, J.Am.Ceram.Soc, 86,480-486 (2003). 1 L.C. Lim, P.M. Wong, M.A. Jan, Microstructural evolution during sintering of near-monosized agglomerate-free submicron alumina powder compacts, Acta Mater., 48, 2263-2275 (2000). 1 ' C. Nivot, F. Valdivieso, P. Goeuriot, Nitrogen pressure effects on non-isothermal alumina sintering, J.Eur.Ceram.Soc, 26, 9-15 (2006). 12 Z. Shen, H. Peng, J. Liu, M. Nygren, Conversion from nano- to micron-sized structures: experimental observations, J.Eur. Ceram.Soc, 24, 3447-3452 (2004). 13 J. Echeberria, J. Tarazona, J.Y. He, T. Butler, F. Castro, Sinter-HIP of alpha-alumina powders with sub-micron grain sizes, J.Eur.Ceram.Soc, 22, 1801-1809 (2002).
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S. H. Risbud, C.-H. Shan, A.K. Mukherjee, M.J. Kim, J.S. Brow, R.A.Holl, Retention of nanostructure in aluminum oxide by very rapid sintering at 1150 °C, J.Mater.Res., 10 [2] 237-239 (1995) 15 L. Gao, J.S. Hong, H. Miamoto, S.DD.L. Torre, Bending strength and microstructure of AI2O3 ceramics densified by spark plasma sintering, J.Eur.Ceram.Soc, 20 2149-52 (2000) 16 R.S. Mishra, A.K. Mukherjee, Electric pulse assisted rapid consolidation of ultrafine grained alumina matrix composites, Mater.Sci. & Eng., A287 178-182 (2000) 17 S.W. Wang, L.D. Chen, T. Hirai, Densification of AI2O3 powder using spark plasma sintering, J.Mater.Res., 15 [4] 982-987 (2000) 18 L.A. Stanciu, V.Y. Kodash, J.R. Groza, Effects of heating rate on densification and grain growth during field-assisted sintering of (1-AI2O3 and M0SÍ2 powders, Metall & Mater. Trans. A, 32A 26332638 (2000) " Z. Shen, M. Johnsson, Z. Zhao, M. Nygren, Spark plasma sintering of alumina, J.Am.Ceram.Soc, 85 [8] 1921-27 (2002) 20 Y. Zhu, K. Hirao, Y. Yamauchi, S. Kanzaki, Densification and grain growth in pulse electric current sintering of alumina, J.Eur.Ceram.Soc, 24 3465-3470 (2004) 21 D.T. Jiang, D.M. Hulbert, U. Anselmi-Tamburini, T. Ng, D. Land, A.K. Mukherjee, J.Am.Ceram.Soc, 91 [1] 151-154(2008) 11 D. Chakravarty, S. Bysakh, K. Muraleedharan, T.N. Rao, R. Sundaresan, Spark plasma sintering of magnesia-doped alumina with high hardness and fracture toughness, J.Am.Ceram.Soc, 91 [1] 203208 (2008) 23 M.I. Mendelson, Average Grain Size in Polycrystalline Ceramics. J. Am. Ceram. Soc, 52, T39 -T42 (1969).
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THE ELECTRO-DISCHARGE COMPACTION OF POWDER TUNGSTEN CARBIDE - COBALT DIAMOND COMPOSITE MATERIAL Evgeny G. Grigoryev and Alexander V. Rosliakov The manufacturing of high strength structure of powder tungsten carbide - cobalt - diamond composite material is investigated and optimal operating parameters are defined. The structure of tungsten carbide - cobalt - diamond composite material reaches top strength at certain magnitudes of applied pressure and high voltage electrical discharge parameters. We studied densification process of powder material during electro-discharge compaction by means of high-velocity filming. Pulse current parameters were measured by Rogovsky coil. The temperature evolution during electro-discharge compaction process was measured by means of thermocouple method. We have installed that the powder densification process has wave nature in electro-discharge compaction. We defined wave front velocity of densification process and pressure amplitude in wave front subject to parameters of electro-discharge compaction. INTRODUCTION Tungsten carbide and diamond are well known for its exceptional hardness and wear/erosion resistance. Cemented carbides and diamond are used extensively in the industry involving high wear, abrasive applications. Apart from their exceptional hardness, WC has other unique properties such as high melting point, high wear resistance, good thermal shock resistance, thermal conductivity and good oxidation resistance [1,2]. WC with ductile metals such as cobalt as a binding medium, which is known to be helpful in cementing fine WC particles, is used in bulk sintered forms. Matrices of ductile metals, such as cobalt, greatly improve its toughness, hence elimination the possibility of brittle fracture during operation. WC-Co-diamond composites are extensively used to enhance the wear resistance of various engineering components, e.g. cutting tools and dies. There have been a large number of works performed on producing composite materials from powders by nonconventional powder consolidation methods in which densification is enhanced by the application of a pulsed electric current combined with resistance heating and pressure: plasma pressure compaction (P2C), spark plasma sintering (SPS), plasma activated sintering (PAS) [3, 4]. The interest in these methods was motivated by their ability to consolidate a large variety of powder materials to high densities within short periods of time and without having to increase grain sizes. In this paper, we focused on the consolidation of WC-Co and WC-Co-diamond powders into a solid bulk without increasing their crystallite sizes by electro-discharge compaction (EDC) [5, 6, and 7]. The principle of EDC is to discharge a high-voltage (up to 30 kV), high-density current (-100 kA/cm2) pulse (for less than 300 μβ) from a capacitor bank through the powders under external pressure. In this way, a full or near full densification may be achieved with minimal undesirable microstructural changes due to short consolidation time. Furthermore, WC-Co-diamond powders could be consolidated into solid bulks by electro-discharge compaction (EDC) with densities close to theoretical density. This method has demonstrated the possibility of consolidating difficult-to-sinter powders to provide distinct technological and economical benefits. EXPERIMENTAL PROCEDURES Dense WC-Co and WC-Co-diamond composites were fabricated by an EDC method. In this process, the WC-Co and WC-Co-diamond mixed powders were poured into an electrically non-conducting ceramic die. The ceramic die was plugged at two ends with molybdenum electrodes-punches and an external pressure up to 400 MPa was applied to the powder on air-operated press. A high voltage
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capacitor bank was discharged through the powder. The schematic of the Electro-Discharge Compaction (EDC) system is shown in Figure 1.
Figure 1. Schematic of the Electro-Discharge Compaction (EDC) system 1 — powder, 2 — die, and 3 — the upper and lower punches electrodes Electro-discharge compaction (EDC) apparatus for compacting the powders consists basically of a bank of capacitors; charging unit and trigatron switch to connect a powder column suddenly across the charged capacitor bank. The capacitor bank consists of thirty 200 μΡ capacitors that can store up to 6 kV. EDC uses the pulse current generated from the capacitor bank to quickly heat a powder column subjected to constant pressure. During electro-discharge compaction, we recorded, using the Rogowski coil, the parameters of the current pulse through the powder column. An oscillograph showing a typical output from the Rogowski coil is shown in Figure 2. The temperature evolution during electro discharge compaction process was measured by means of thermocouple method. We measured the temperature on the powder sample surface, using ChromelAlumel and tungsten-rhenium thermocouples. To study the powder consolidation kinetics, we used a high-speed SKS-1M camera, which makes it possible to record movies with a frequency up to 4* 103 frames s~K The high-speed consolidation kinetics of the WC-Co powder was experimentally investigated on samples with a diameter of 10 mm and a mass of 12.0 χ 10~3kg for different values of the current pulse parameters. The following commercial WC-Cc—diamond powder was used as starting material for electrodischarge compaction: WC - -80 wt.%, Co - 20 wt.%, free carbon 0.101 wt.%, total oxygen 0.13 wt.%, grain size WC < 5μπι, grain size of diamond < 40μιη. Powder column was a circular cross-section rod with a diameter of 10 mm and a length ranging from 10 to 15 mm. X-ray diffraction (XRD) was performed on the as-received powder using a DRON-3 diffractometer with a Cu target for 2Θ from 20° to 120° at a scan speed of 17min. XRD was repeated on the consolidated specimens, followed by density measurements. Density measurements were taken after EDC process using the Archimedes principle in distilled water.
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Figure 2 Typical pulse current traces from registration system (Rogowski coil) (Peak currents: 1 - 50 kA, 2 - 80 kA, 3 - 110 kA) EDC applies a high-voltage, high-density current pulse to the WC-Co-diamond powders under external pressure for a very short period of time. This method uses the passage of the pulse electric current to provide the resistive heating of the powder by the Joule effect. Joule heating occurs at the inter-particle contact to instantaneously weld WC-Co powder particles, resulting in densification. The achieved WC-Co-diamond composite density as a result of EDC process depends on applied external air-operated pressure, magnitude and waveform of pulse current that depends on RLC - parameters of the electrical discharge circuit. RESULTS AND DISCUSSION The measurements of the current pulse parameters with a Rogowski coil showed that the discharge current pulse width in all experiments did not exceed 300 μβ. This value determines the time of energy injection into the powder. Measurement of the time dependence of the surface temperature of the sample showed that the characteristic time of its cooling of about 2 s. Analysis of the problem parameters made it possible to reveal the hierarchy of the characteristic times of the processes occurring under electric-pulse pressing. The approximate general scheme is as follows. A current pulse passing through a powder and punches strongly heats only the powder material without significant punches heating, because the powder resistivity greatly exceeds that of the punches material. The intense heating of the powder significantly decreases its resistance to plastic deformation, and, under the action of an external mechanical pressure, it is consolidated with a characteristic rate, dependent on the pneumatic system type. Simultaneously, heat sink from the powder to punches and die occurs due to the thermal conduction. The time of energy injection to the powder is determined by the current pulse width: το < 10"3 s. The time of formation of a consolidated material from the powder, τι, depends on the loading system and lies in the range 2 x 10~3 < Xi < 2 x 10"2 s. The cooling time of the pressed material, τι, is determined by the thermal conductivity of the material and the characteristic size of the pressed sample: t2 = 2.5 s. In this case, the time scales of the processes obey the following relation: το < τ\ « Τ2. The most important factor which determines the success of the EDC process is the instantaneous current density in the powder column [7]. We studied influence of pulse current density and external
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pressure on kinetics of powder material densification at electro discharge compaction. Consolidation of powder material takes place at constant pressure P, created pressure system during all process of the electro discharge compaction. Time dependences of powder density during EDC process are resulted in Figure 3. P, % 100.0 92.5
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Figure 3 Variations of relative density as a function of time in EDC process at constant external pressure (external air-operated pressure 200 MPa) On a Figure 3 curves: 1 (75 kA/cm2), 2 (85 kA/cm2), 3 (97 kA/cm2), were got at constant pressure P = 200 MPa. Duration of process of powder material densification is range from 6 ms to 16 ms for all our experiments. The results of experiments show that motion of punches in the process of the electro discharge compaction takes place with steady speed. The value of speed depends on amplitude of pulse current and external pressure. The magnitude of external pressure determines initial specific resistance of powder column and, accordingly, amount of heat, selected in powder material. With the increase of pressure the specific resistance of powder column goes down sharply, that results in the less heating of powder material. The densification of the compacted material takes place due to an intensive plastic strain which depends on external pressure P and yield stress of powder matter - στ(Τ) (Τ temperature). Therefore speed of plastic flow of the compacted powder material and consequently speed of change of density of the compacted powder column is determined by the temperature at EDC process. The speed of densification depends on a dimensionless parameter β = στ(Τ)/Ρ. At constant amplitude of pulse current a densification speed is determined by temperature dependence of yield strength at different pressures, put to the powder column. The finishing density (Fig. 3) of a compacted material after EDC is defined by size of the external pressure and parameter β. Electro discharge compaction of a powder material represents steady state wave in the powder, created by a punch moving with constant speed. When the compaction wave reaches the second stationary punch, process of powder compaction is completed. It is shown on Fig. 3 by horizontal lines of density dependence vs the time. Duration of this compaction process is less than 20 milliseconds. Cooling of powder compact occurs during 2 second due to thermal conductivity of the punches and the die. The conventional powder consolidation processes (hot pressing, etc.) have no place because of short duration of EDC.
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The XRD results show that the main phases of WC-Co powder were WC and α-Co, but the main phases of WC-Co compact sample after EDC were WC and ß-Co. This is associated with a rapid cooling of WC-Co compact sample in the time of EDC process. CONCLUSIONS The response of WC-Co-diamond powder composites (loaded external pressure) to high energy electrical discharge was studied and has been described and understood in terms of peak current density and external pressure. It was found that the density of composite material reach its maximum values at certain magnitudes of applied pressure and high voltage electrical discharge parameters. It should be noted that kinetics of process of densification of powder material at EDC substantially differs from kinetics at P2C, PAS and SPS [4, 5]. It is related to distinction in speed of input energy and in the parameters of influence by external pressure on powder material. It is higher speed of input energy for EDC process and volume distribution of input energy dependence on external pressure. The lowest value of pressure provides the greatest allocation of energy and rise in temperature of compacted material because of the loose powder has the worsest metallic contact and with it the most sparking - local melting. Attempts to compact WC-Co-diamond powders by EDC method presage future fruitful results of development types of tools. REFERENCES [1] Erik Lassner and Wolf-Dieter Schubert: Tungsten-Properties, Chemistry, Technology of the Element, Alloys, and Chemical Compounds, 2000, Kluwer Academic/Plenum Publishers. [2] Tungsten and Tungsten Alloys-Recent Advances, Edited by Andrew Crowson and Edward S. Chen, 1991, Minerals, Metals and Materials Society. [3] V. Mamedov, "Spark Plasma Sintering as Advanced PM Sintering Method" Powder Metallurgy, 2002, vol. 45, no. 4, pp. 322-328. [4] Z. A. Munir, U. Anselmi-Tamburini, M. Ohyanagi, "The effect of electric field and pressure on the synthesis and consolidation of materials: A review of the spark plasma sintering method" J. Mater. Sei., 2006, vol.41, pp. 763-777. [5] J. R. Groza, A. Zavaliangos, "Nanostructured Bulk Solids by Field Activated Sintering", Rev. Adv. Mater. Sei., 2003, vol. 5, pp. 24-33. [6] M. Shakery, S. T. S. Al-Hassani, T. J. Davies, "Electrical Discharge Powder Compaction", Powder Met. Int., 1979, vol. 11, no. 3, pp. 120-124. [7] E. Grigoriev, A. Rosliakov, "Electro Discharge Compaction of WC-Co Composite Material Containing Particles of Diamond", Materials Science Forum, 2007, Vols. 534-536, p. 1181-1184.
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MICROWAVE SINTERING EXPLORED BY X-RAY MICROTOMOGRAPHY Kotaro Ishizaki, Manjusha Battabyal, Yoko Yamada Pittini, Radu Nicula and Sebastien Vaucher EMPA, Swiss Federal Laboratories for Materials Science and Technology, Laboratory for Materials Technology Feuerwerkerstrasse 39, Thun, CH-3602 Switzerland ABSTRACT Microwave energy is seen as offering potential energy and time savings for the processing of materials. For metal-diamond composite for example, selective heating of the metallic grain, could preserve the diamonds from allotropic conversion to graphite while the matrix could be brought to its sintering temperature. However, the interactions of microwave with random metal-dielectric mixtures are complex and not yet adequately described by any model, and the control of the process is difficult. Here we investigate the effect of microwave irradiation on a diamond-aluminium powder mixture. Using 3D X-ray microtomographic analysis, we show that for the same starting material, treated in similar conditions, very different microstructural changes inside of the powder beds can be found. The possibility to access extensively 3D microstructural information opens up new opportunities for the understanding and control of microwave processing of metal-dielectric systems. INTRODUCTION Due to its extremely high thermal conductivity and hardness properties, together with present availability and affordability of synthetic diamonds, the use of diamond is considered as first choice material in many industrial fields. Its low coefficient of thermal expansion (CTE) makes diamond the ideal filling material for metal matrix composites featuring high thermal conductivity and reasonably low CTE. Such composites are considered for use in heat sinks and heat spreaders. Recently also diamond metal composites have drawn attention due to their enhanced thermal conductivities, up to 670 W/mK, makes the composites attractive for demanding applications in microelectronics and semiconductors1. Metal diamond contacts are essential for almost any type of electromechanical sensors and electronic devices.1"3 The excellent thermophysical properties of diamond can only be exploited to the whole extent when an optimal interface between the diamond particles and the metal matrix is obtained. However, due to its high hardness property the bonding of diamond particles with metal is an extremely difficult task and has become an open and challenging area for researchers. Aluminum-diamond composites have been obtained by the metal infiltration method.1"3 According to our knowledge; the present work is the first attempt to produce aluminum-diamond composites using microwave irradiation. Microwave heating is fundamentally different from conventional sintering in that the energy is deposited volumetrically rather than relying in thermal conduction from the surface. Properly manipulated this may lead to a number of benefits, including improved product properties and reductions in manufacturing costs due to energy savings and shorter processing times.4 The reactivity and wettability of carbon with aluminum have been widely studied in the past decades since carbon fibers reinforced aluminum and aluminum alloys are an important group of metalmatrix composites. " When using diamonds however, cross sectioning becomes extremely difficult, and microtomography is of great help to visualize detailed morphological changes. 13,14 In the present study, synthesis of aluminum-diamond composites are prepared by microwave heating. The striking difference of morphology obtained for similar samples experimental conditions is analyzed using synchrotron- based X-ray tomographic microscopy.
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EXPERIMENTAL Diamond (synthetic uncoated diamond monocrystals, MBD8 grade, 140/170 mesh, Qming Superhard Material Co. Ltd) and Aluminum powder (65 μιη, GTV GmbH,) were placed in a 60:40 weight ratio for 64 hrs in a Turbula™ to obtain a homogenous distribution of powders. Two similar samples were prepared by filling 3 cm of a 012 mm quartz crucible embedded in a porous alumina thermal insulation (packing density 1.52-1.77 g/cm3). The crucibles were introduced in the center of a resonating TEioi microwave cavity and irradiated with a constant incident power of 600 W/2.45 GHz (Dipolar AB). The incident and reflected power was recorded using a high power impedance analyzer (S-TEAM STHT) .Resonant conditions were maintained using 3 stubs impedance matching as well as sliding short adjustments. The temperature was measured with an infrared pyrometer (Raytek 3.62-3.94 μπι) facing the top of the crucible. The schematic illustration of the microwave assembly is shown in figure 1.
Figure 1. Schematic illustration of the microwave chamber. After microwave irradiation, the samples were analyzed by synchrotron-based X-ray microtomography (X02DA-TOMCAT beamline, Swiss Light Source (SLS), Switzerland) with a radiograph resolution of 5.6 x 5.6 μιη2. After 3D-reconstruction, Amira™ was used for data visualization. RESULTS AND DISCUSSION The evolution of temperature and absorbed microwave power are shown in figures 2 and 3 for two similar samples (A and B) submitted to a constant incident power of 600W. Although the microwave power supplied to both samples is identical, the reaction of the two samples is largely different. For sample A the temperature rises in the first 150 seconds to reach 1450°C then falls to 1200°C (350 s). With a constant values in the interval 50-150 seconds and a regular decay until 350 seconds, the microwave absorption profile is consistent with the pyrometer signal. The variations are found smooth and continuous for both signals. The situation of sample B is completely different. The temperature and the absorption were unstable during all the heating period. During the initial 350 seconds the temperature do not exceeds 600°C while after 500 seconds, the averaged temperature finally reaches about 1100°C due to the development of plasma above the sample top.
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Figure 2. Time-temperature profile of sample A showing supplied and absorbed microwave powers.
Figure 3. Time-temperature profile of sample B showing supplied and absorbed microwave powers.
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Figure 4. Tomographie reconstruction of various cross sections obtained for aluminum-diamond composite sample A.
Figure 5. Tomographie reconstruction of various cross sections obtained for aluminum-diamond composite sample B.
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Tomography images of aluminum-diamond composites samples A and B are shown in figures 4 and 5, respectively. The figures include an over view of the sample after heating and the cross section views taken by X-ray microtomography. The over view image shows in which angle the cross section views were taken. Images a and b are vertical sections and c to g are horizontal sections. Black areas of these images represent porosities, dark gray, diamond and light gray aluminum. In the lower part of both samples (Fig 4 e-g and 5 e-g), localized aluminum coalescence often surrounding a closed pore suggests that melting of initial aluminum particles occurred all trough the samples. This change seems dominated by capillary forces leading to a dewetting of the diamond surface by the liquid metal. In the upper part of sample A (Fig 4a and 4b) a domain is present in the center within which diamond are completely wetted by aluminum. This localized densification has resulted in the creation of large porosities due to outwards mass transports from neighboring areas. Higher magnifications of this area (figure 6) underline the different microstructure of the composite in close vicinity. The 3D image I shows that the molten aluminum is not perfectly attached with the diamond. The small particles of aluminum were molten and assembled in a larger drop. During this agglomeration diamonds were expelled away, either due to the presence of alumina or to a too low temperature. In image II the distribution of diamonds inside of the molten aluminum is homogeneous and there are no gaps between both materials. Image III is similar as the image of initial situation of this composite. Aluminum particles are in the same size as at the beginning. The formation of dense aluminum-diamond composite is only produced in the top of sample A. The different response of sample A and B to the same incident microwave power lead to two different heating patterns and different microstructure. The stable microwave absorption in sample A, may be due to a higher and stable local electric field inside the sample. The instable behavior of sample B leading to a plasma outside of the sample is unpredictable.
Figure 6. 3D images of three different portions of sample A from figure 4 a.
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A possible explanation for the observed results may be that if the heating area is different inside of the sample, the size of molten aluminum is different. If the aluminum is melting slowly at low temperature the particle of aluminum will increase in size but without wetting the diamond because of the surface tension of molten aluminum is high; as it is the case in sample B. On the other hand, with a temperature profile like the one of sample A, the heating rate was fast and probably produced a large area of localized high temperature. If the temperature is high enough to reduce the surface tension of molten aluminum, it will make possible to wet the diamond surface by aluminum and a composite as the one obtained in portion II of sample A is possible to be produced. Once the diamond and aluminum are in contact, the interface AI4C3 is possible to be created at this temperature range. Another important factor is that diamond is transparent for microwave heating. To make this type of composite it will take long time by conventional heating. CONCLUSION For these two samples the composition is the same but localized geometry and distribution of local intern fields are not equal. This difference of local intern fields may induce a different way of absorption in the sample. Field distribution assumes continuum approximation, however; a mixture of non conductive diamond and metallic aluminum makes the discreet determination of the local field defiled and singular cases 3D X-ray microtomography is a powerful method to observed diamond composite materials. With this method we could find that in one portion of this composite; the diamond was completely wetted with aluminum and homogeneously distributed in the matrix. The findings open the possibility of optimizing the microwave processing conditions to obtain a desired kind of composite and homogeneous in the entire matrix. This heating can be used to heat volumetrically a metal-dielectric mixture. However, the control of local events remains to be solved to evolve a reproducible process. X-ray microtomography makes possible to reach this level of understanding which opens the possibility of optimizing the microwave sintering conditions to obtain a desired kind of composite. But the propagation and interaction of electro magnetic waves in a metal-dielectric mixture is not yet analyzed solved for random mixture or at high metallic volumetric fraction close and above percolation threshold. It would be desirable to develop a model of microwave interaction with random metal-dielectric mixtures. ACKNOWLEDGEMENT Kotaro Ishizaki would like to thank to COST (European Cooperation in the field of Scientific and Technical Research) for financial support to attend the international conference; Sintering 2008. The authors would like to thank Dr. Samuel McDonald for the technical support of TOMCAT at SLS. REFERENCES 1 P. W. Ruch, O. Beffort, S. Kleiner, L. weber, Selective Interfacial Bonding in Al(Si)-Diamond Composites and its Effect on Thermal Conductivity, Comp. Sei. Tech., 66, 2677-85 (2006). 2 0 . Beffort, F. A. Khalid, L. Weber, P. Ruch, U. E. Klotz, S. Meier, S. Kleiner, Interface Formation in. Infiltrated Al(Si)/Diamond Composites, Diamond and Related Mater., 15, 1250-60 (2006). 3 S. Kleiner, F. A. Khalid, P. W Ruch, S. Meier and O. Beffort, Effect of Diamond Crystallographic Orientation on Dissolution and Carbide Formation in Contact With Liquid Aluminium, Scripta Materialia, 55, 291-4 (2006). 4 J.G.P. Binner, B. Vaidhyanathan, Microwave Sintering of Ceramics: What does it offer?, Key Eng.
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Mater., 264-268, 725-30 (2004). 5 M. Yang, V.D. Scott, Carbide Formation in a Carbon Fibre Reinforced Aluminium Composite, Carbon, 29,877-9(1991). 6 M. Desanctis, S. Pelletier, Y. Bienvenu, M. Guigon, On the Formation of Interfacial Carbides in a Carbon Fibre-Reinforced Aluminium Composite, Carbon, 32, 925-30 (1994). 7 C.P. Ju, K.J. Chen, J.H.C. Lin, Process, Microstructure and Properties of Squeeze-Cast Short-CarbonFibre-Reinforced Aluminium-Matrix Composites, J. Mater. Sei., 29, 5127-34 (1994). 8 H.D. Steffens, B. Reznik, V. Kruzhanov, W. Dudzinski, Carbide Formation in Aluminium-Carbon Fibre-Reinforced Composites, J. Mater. Sei., 32, 5413-7 (1997). 9 M. Gu, G. Zhang, R. Wu, Interfacial Bondings in Gr(f)/Al Composites, Prog. Nat. Sei., 7, 600-6 (1997). 10 K. Landry, S. Kalogeropoulou, N. Eustathopoulos, Wettability of Carbon by Aluminum and Aluminum Alloys, Mater. Sei. Eng., A 254, 99-111(1998). 11 R. Asthana, Review Reinforced Cast Metals, J. Mater. Sei., 33, 1959-80 (1998). 12 E. Pippel, J. Woltersdorf, M. Doktor, J. Blücher, H.P. Degischer, Interlayer Structure of Carbon Fibre Reinforced Aluminium Wires, J. Mater. Sei., 35, 2279-89 (2000). 13 D. Bernard, 3D Quantification of Pore Scale Geometrical Changes Using Synchrotron Computed Microtomograghy, Oil Gas Sei. TechnoL, 60, 747-62 (2005). 14 S. Vaucher, P. Unifantowicz, C. Ricard, L Dubois, M. Kuball, J.-M. Catala-Civera, D. Bernard, M. Stampanoni and R. Nicula, On-line Tools for Microscopic and Macroscopic Monitoring of Microwave Processing, Physica B, 398, 191-5 (2007).
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PULSE PLASMA SINTERING AND APPLICATIONS Andrzej Michalski, Marcin Rosinski Warsaw University of Technology, Faculty of Materials Science and Engineering, Warsaw, Poland ABSTRACT The paper presents a new Pulse Plasma Sintering method (PPS), developed at WUT. Unlike other electric-field assisted sintering methods, the PPS method employs pulse high-current electric discharges for heating and activating the material to be sintered. The phenomena, taking place during the high-current pulses, which heat the powder during the PPS treatment and activate the sintering process, are similar to those occurring in other new techniques, but, in PPS, thanks to the much higher energy of the pulse discharge, these phenomena run much more intensively. The presentation will also contain some examples of application of PPS technique for producing sintered parts from a wide variety of materials. INTRODUCTION In modern sintering methods, such as PAS (Plasma Assisted Sintering) [1], SPS (Spark Plasma Sintering) [2, 3, 4] and FAST (Field Assisted Sintering) [5, 6], the sintering is carried out at lower temperatures and the process lasts for a shorter time than is the case in the conventional methods. A characteristic feature of these techniques is that the pulse current is used for heating powders to be sintered. During a current pulse, spark discharges are ignited in the pores. These discharges remove adsorbed gases and oxides from the powder particle surfaces, thereby facilitating the formation of active contacts between them. In effect, the process time can be shortened and the sintering temperature can be reduced. The paper gives some examples of producing sintered composite materials by the new PPS (Pulse Plasma Sintering) method. PULSE PLASMA SINTERING METHOD (PPS) The apparatus used for consolidating powders by the PPS method has been designed and constructed at the Faculty of Materials Science and Engineering, Warsaw University of Technology (Fig. 1). The PPS method utilizes pulsed high electric current discharges for heating the powder whilst it is being pressed. The current pulses are generated by discharging a 300 μΡ capacitor, charged to a voltage of maximum 10 kV.
Figure 1. Apparatus for PPS.
Figure 2. Schematic diagram of the PPS apparatus.
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The material to be sintered is placed in a graphite die in-between two graphite punches (Fig. 2). The pulses have amplitudes of tens of kilo-amperes and periods of several hundred microseconds (Fig. 3). It is worth noting that the PPS process has a very high thermal efficiency. Because of the short duration of the electric pulses (0.6 ms) compared to the interval between them (1 s) the temperature achieved during the current pulses is higher than the temperature measured during the sintering process. Fig. 4 shows schematically the temperature variation during the PPS process.
Figure 3. Examples of the electric current Figure 4. Temperature variations during the highand voltage waveforms during the PPS, current PPS. a) current, b) voltage. The high-current pulses, which heat the powder during sintering by the PPS method, induce similar sintering process-activating mechanisms to those occurring in the PAS, SPS, and FAST processes, except that, thanks to the high energy delivered in a pulse (of the order of 320 MVA = 40 kA-8 kV), i.e. manifold greater than that achieved in the other techniques, the PPS processes are much more intensive. As seen in Table 1, the electric parameters Table 1. Electric Parameters of the PPS and SPS of the PPS processes differ substantially Sintering Processes from those used in the SPS processes. The Parametr PPS SPS [71 differences include the electric current Current (A) 40 000 5000 intensity, electric voltage, pulse duration, Voltage (V) 8 000 10 and the pulse repetition frequency. In PPS, Pulse duration (ms) 0.6 36* the instantaneous electric current (I) is Pulse repetition frequency (ms) 500 6* several times higher than in SPS, whereas the voltage (U) is several hundred times as high, so that the instantaneous electric power in PPS is about 320 MVA (UT) compared with 50 kVA in SPS. The PPS pulse duration is also about 60 times shorter and the inter-pulse interval is about 80 times as long as those in SPS. APPLICATIONS OF THE PPS METHOD The PPS method has been used for sintering a wide variety of materials, such as e.g. WC/diamond [8, 9] and Cu/diamond [10, 11] composites, nanocrystalline sintered parts [12-15] and with the participation of the SHS reaction for fabricating high-melting ceramics [16-18]. Diamond/WC Composites Intended for Cutting Tool Edges Diamond/cemented carbide containing 30 vol% of diamond particles was produced using a mixture of a 6 wt% Co added-WC powder, with a WC grain size of 0.8 μπι and a diamond powder with a grain
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size ranging from 40 to 60 μπι. The mixture was sintered to produce a two-layer plate, 20mm in diameter, in which a layer (0.5 mm thick) composed of WC6C0 composite + 30% of diamond was formed on a WC6C0 substrate. The sintering process was conducted at a temperature of 1100 °C under a load of 60 MPa for 5 min. Figure 5 shows a diffraction pattern obtained for the diamond/cemented carbide sintered by PPS.
Figure. 5. The XRD patterns for a cemented carbide with diamond particles. The phases identified in the sintered composite were tungsten carbide, diamond, and a cobalt phase. Figure 6 shows an SEM micrograph of the surface of the sintered diamond/cemented carbide composite and Fig. 7 is a SEM image of the surface of a fracture through the cemented carbide/diamond composite.
Figure 6. SEM image of surface of the composite.
Fi
8- 7. SEM image of the surface of a fracture through the diamond/WC6Co composite.
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The diamond particles distributed uniformly within the cemented carbide matrix do not form a skeleton because they only constitute 30 % of the matrix volume. No graphite precipitates can be seen around the diamond particles and these particles are in very good contact with the WC6C0 matrix. We can see in the figure that, on fracture, only few diamond particles were torn out from the matrix, whereas most of them clove along the fracture plane. Table 2 compares the hardness of the diamond/cemented carbide composites produced by PPS and their cemented carbide matrix with the hardness of the composites and their matrix produced by the SPS method as reported by H. Moriguchi et al. [19]. Table 2. Properties of the Sintered Composites Produced by PPS and SPS Method Temperature Time Composition [min] 5 30 vol% diamond/WC-6 wt% Co PPS 1100 PPS 1100 5 WC-6 wt% Co 1400 3 20 vol% diamond/WC-10 wt% Co SPS 3 SPS 1400 WC-10wt%Co
m
Hardness [GPa] 23 20 18 17
Ref. 9 9 19 19
The hardness of the diamond/WC6Co composite consolidated by PPS is higher about 3 GPa than that of the cemented carbide without diamond particles and also higher than the hardness of the diamond/carbide sintered by H. Moriguchi et al. who used the SPS method [19]. The lower hardness values of the sintered composites produced by H. Moriguchi et al. may be explained in terms of the smaller diamond content and the lower hardness of the WClOCo matrix. It is however worth noting that, in order to avoid graphitization, H. Moriguchi et al. also pre-covered the composite with a thin SiC film before its sintering. Wear of the milling cutter edge has been studied through machining of melamine faced boards. Figure Tabele 3. Parameters of machining 8 shows milling cutter with edges of diamond/W6Co composite used for investigations of durability. Table 3 Speed of rotation 18000 rpm shows the parameters of machining of the milling cutter Speed of machining 1130m/min edge. Figure 9 shows decrement of the milling cutter Feed per tooth 0,25 mm/tooth edge as a function of a machining distance.
Figure 8. A milling cutter ended with a diamond/cemented carbide. The critical wear value was taken to be ΙΟΟμπι. The wear of the sintered carbide milling cutter measured after cutting along a length of 32m was 126μηι which is greater than the critical wear value, whereas the wear of the milling cutter with edges made of a diamond/W6Co composite reached the critical value after the cutting length exceeded about 128m. Hence, at the critical wear assumed to be
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ΙΟΟμπι, the milling cutter edges made of a diamond/W6Co sinter can be run along the cutting distance 4 times as long as that available for the sintered carbide cutting edge.
E
E
32 -Sintered carbides
64 96 Machining distance Cm] -Diamond/WCSCo
160 — — The critical wea
Fig.9. Decrement of the milling cutter edge as a function of a machining distance. Diamond/Cu Composite Intended for Heat Sink Applications The diamond/Cu composite was produced from a mixture of the Cu0.8Cr (wt%) alloy powder with the grain size from 10 to 15μπι and a synthetic diamond the particle diameter between 177 and 210 μιη. The mixture was subjected to sintering to form a plate, 30 mm in diameter and 3 mm thick, built of a Cu0.8Cr alloy matrix with the 50% diamond content. The sintering process was conducted at a temperature of 900 °C under a load of 50 MPa for 20 min.
τ~· < n n ™ , ,-. ,-.Fig.10 SEM image of the surface of a fracture through the diamond/Cu composite.
Fig. 10 shows the surface of a fracture through the diamond/Cu0.8Cr composite. As can be seen, the diamond particles torn out from the copper matrix are only few, whereas most of them have cleaved along the fracture plane. This gives evidence that the bond at the diamond/Cu0.8Cr interface is mechanically strong. Chemical analysis of these pellets (Fig. 11) performed using Energy Dispersive Spectroscope, revealed chromium. This suggests formation of chromium compounds at the interface, in particular formation of carbides. The formation of interfacial carbides in this type of materials was observed by Schubert et al. [10] who identified the ^ ^ ^ ag
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Figure 11 .Pellets at the diamond particle surface The density of the Cu0.8Cr-diamond composite was equal to 99.7% of the theoretical and its thermal conductivity amounted to 640W/mK. Nanocrystalline Composites The nanocrystalline NiAl-TiC composites containing 25 wt% or 40 wt% of TiC were sintered using a mixture of a nano-crystalline NiAl-TiC powder. The powder mixture was prepared from an NiAl powder milled to reduce its grain size from about 50 μιη to 25 nm and a TiC powder milled to reduce the grain size from about 2-5 μιη to 60 nm. The powders were milled in a Fritsch Pulverisette P5 planar mill. The density of the composites sintered at a temperature of 1130 °C under a load of 60 MPa was 99.9 %. Fig. 12 shows TEM images of the NiAl-TiC composite. The NiAl-TiC composites containing 25 wt.% of TiC had a hardness of 750 HV1 and a stress intensity factor KiC of 7 MPa-m"2, whereas those containing 40 wt.% of TiC had a hardness of 1070 HV1 and Kic of 11.8 MPa-m"2.
Figure 12. Microstructure of the composites: a) NiAl+25wt%TiC, b) NiAl+40%TiC.
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Sintering with the Participation of the SHS Reaction An original energy-saving technique of producing ceramic materials from elementary powders is the self-propagating high-temperature synthesis (SHS). This method was used for producing N1AI-AI2O3 composites with 13, 38 and 55 vol. % contents of AI2O3. The starting materials were aluminum, nickel and AI2O3 powders. The synthesis combined with consolidation was conducted at a temperature of 1250 °C under a load of 60 MPa for lOmin. Irrespective of the volumetric content of AI2O3, the relative density of the composites was 99 %. By way of example, Fig. 13 shows the microstructures of the composites with 13 and 55 vol.% of AI2O3. The hardness of the composites was 480 HV10 with 13vol% of AI2O3 and 680 HV10 with 55 vol% of A1203. As to the fracture toughness, it markedly depends on the content of the dispersed AI2O3 phase. The composite containing 13 % of AI2O3, showed no cracking at all.
Figure 13. SEM images of the N1AI2O3 composites with various AI2O3 contents: a) 13 vol.%, b) 55 vol.%. In the composite with 38 % of AI2O3, the stress intensity factor KJC was 9.1 MPam"2 and in the composite with 55 % of A1203 it was 8.2 MPam1'2. CONCLUSION Pulse Plasma Sintering (PPS) is a new sintering technique involving the action of an electric field. This method utilizes pulsed high electric current discharges to heat the powder subjected to pressing. The PPS process has a very high thermal efficiency, since the powder is heated directly by the pulse arc discharges. The use of capacitors as the source of energy permits generating periodic current pulses, with a duration of several hundred microseconds with energy of several kJ. These specific conditions permit producing sintered parts with a density close to the theoretical value in a short time. The results have shown that the PPS sintering technique can be used for producing dense sintered parts from a wide variety of materials such as e.g.: diamond/cemented carbide, diamond/cooper, nanocrystalline intermetallic phases. This method can also be used for producing refractory alloys by reactive processes with the participation of the SHS reaction. ACKNOWLEDGEMENT The work was supported by the grant no N507 017 32/0586 from the Polish Ministry of Science and Higher Education. REFERENCES 'S.H. Risbud, Ch.H. Shan, Fast Consolidation of Ceramics Powders, Mater. Sei. Eng., A204,1461-151 (1995). 2 S.L, Cha, S.H. Hong, and B.K. Kim, Spark Plasma Sintering Behavior of Nanocrystalline WC-lOCo Cemented Carbides Powders, Mater. Sei. Eng., A351,31-8(2003).
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3
P. Feng, W. Xiong, L. Yu, Y. Zheng, and Y. Xia, Phase Evolution and Microstructure Characteristics of Ultrafine Ti(C,N)-Based Cermets by Spark Plasma Sintering, Inter. J. Refractory Met. Hard Mater., 22, 133-38 (2004). 4 L.H. Zhu, Q.W. Huang, and H.F. Zhao, Preparation of nanocrystalline WC-IOC0-O.8VC by Spark Plasma Sintering. J. Mater. Sei. Lett. 22, 1631-33 (2003). 5 J.R. Groza, A. Zavaliangos, Nanostructured Bulk Solids by Field Activated Sintering, Adv. Mater. Sei., 5, 24-33 (2003). 6 J.R. Groza, A. Zavaliangos, Sintering Activation by External Electrical Field, Mater. Sei Eng., A287, 171-77(2000). 7 W. Chen, U. Anselmi-Tamburini, J.E. Garay, J.R. Groza, and Z.A. Munir, Fundamental Investigations on the Spark Plasma Sintering/Synthesis Process I. Effect of DC Pulsing on Reactivity, Mater. Sei. Eng., A394, 132-138(2005). 8 A. Michalski, D. Siemaszko, M. Rosinski, and J. Jaroszewicz, Fabrication of Nanocrystalline WC5Co Carbide with a WC-5Co/Diamond Composite Surface Layer Using the Impulse-plasma Sintering Method, Inzynieria Materialowa, 5, 327-329 (2005). (Polish). 9 A. Michalski, M. Rosinski, Sintering Diamond/Cemented Carbides by the Pulse Plasma Sintering Method, J. Am. Ceram. Soc, 1-6, (2008) (in press). 10 T. Schubert, L. Ciupinski, W. Zielinski, A. Michalski, T. Weißgarbera, and B. Kieback, Interfacial Characterization of Cu/Diamond Composites Prepared by Powder Metallurgy for Heat Sink Applications, Sprita Mater., 58 263-266,(2008). n L . Ciupinski, D. Siemiaszko, M. Rosinski, A. Michalski, and K.J. Kurzydlowski, Heat Sink Materials Processing by Pulse Plasma Sintering, Advanced Materials Research, (2008) (in press) 12 A. Michalski, D. Siemaszko, Nanocrystalline Cemented Carbides Sintered by the Pulse Plasma Metod, Inter. J. Refractory Met. Hard Mater., 25, 153-158 (2007). 13 A. Michalski, J. Jaroszewicz, M. Rosinski, D. Siemaszko, K.J. Kurzydlowski, Nanocrystalline CuAI2O3 Composites Sintered by the Pulse Plasma Technique, Solid State Phenomena, 114, 227-232 (2006). 14 A. Michalski, M. Rosinski, D. Siemaszko, and J. Jaroszewicz, K.J. Kurzydlowski, Pulse Plasma Sintering of Nano-Crystalline Cu Powder, Solid State Phenomena 114, 239-244 (2006). 15 M. Rosinski, A. Michalski, Nanocrystalline NiAl-TiC Composites Sintered by the Pulse Plasma Metod, Solid State Phenomena, 114,233-238 (2006). 16 A. Michalski, J. Jaroszewicz, M. Rosinski, and D. Siemaszko, N1AI-AI2O3 Composites Produced by Pulse Plasma Sintering with the Participation of the SHS Reaction, Intermetallics, 14,603-606 (2006). 17 A. Michalski, J. Jaroszewicz, and M. Rosinski, The Synthesis of NiAl Using the Pulse Plasma Method with the Participation of the SHS Reaction, Int. J. Self-Propagation High-Temp. Synth., 12, 237-246 (2003). 18 J. Jaroszewicz, A. Michalski, Pulse Plasma Sintering Combined with a Combustion Synthesis of a TiB2 Composite with a Nickel Matrix, J. Europ. Ceram. Soc, 26, 247-2430 (2006). 1 H. Moriguchi, K. Tsuduki, A. Ikegaya, Y. Miyamoto, and Y. Morisada, Sintering Behavior and Properties of Diamond/Cemented Carbides," Int. J. Refract. Met. Hard Mater., 25,237-243 (2007).
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INFLUENCE OF ELECTRIC TECHNIQUE (FAST)
FIELDS
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THE
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SINTERING
Michaela Müller and Rolf Ciasen Saarland University, Department of Powder Technology Geb. C6 3, 66123 Saarbruecken, Germany ABSTRACT The Field Assisted Sintering Technique (FAST) has become popular since the 1990s. Since then, many investigations have been effected on materials that can be sintered by this technique, numerical simulations of the processes have also been performed. Several theories about the influence of the electric current during sintering have been established, but up to now the activation due to the pulsed electric current in the powder still remains uncertain. In this paper a modified FAST equipment has been developed allowing to separate the electric circuit from the heating loop. With this setup we were able to investigate the amount of current passing through the powder and its influence on sintering. INTRODUCTION Since the late 1990s there have been many investigations on the Field Assisted Sintering Technique (FAST) which is also known as Spark Plasma Sintering (SPS). This powder technology process involves pressing loose powders uniaxially in a graphite die connected to a pulsed electric field allowing the flow of high current densities. The application of an electric current to the graphite die results in high heating rates up to 600 K/min due to the heat developed by Joule effect. The main advantage of this technique is the rapid densification of loose powders, which can be consolidated without additives. FAST has become very popular because it permits to sinter dense materials (near 100 % of theoretical density (%TD)) at lower temperatures than those normally used. Soak times are also reduced. As a consequence FAST has been applied to a wide range of materials ' and special attention has been drawn to ceramic and composite materials. Dense AI2O3, Z1O2 and T1O2 2-6 have already been successfully sintered. The role of the electric current during this process has not been clarified yet. Several theories have been set up. One of them claims that electric current builds up some sparks that form a plasma between the powder particles, promoting the transport of matter. Other theories state that the current activates the surface of the powder particles by means of removing surface impurities which may be present. Some numerical simulations have been performed7"9 stating that the current's path through the powder or die depends mostly on the material. If the powder is an insulating ceramic material, most of the current will pass through the die whereas in the case of metallic powders a considerable fraction of the current will flow through the particles. The problem of the experimental verification of these results lies in the way the FAST equipment is built. There is no isolation between the powder bed and the surrounding graphite die. Therefore the amount of current passing through the die - used for heating and the amount passing through the powder - activating the sintering process - can only be estimated by theoretical formulations. In this paper the role of the electric current during FAST is investigated by separating the heating loop from the electric circuit. To this end, a new equipment was built which guarantees current flow only through the powder. The employed heating rates are relatively low (25 K/min) compared to those normally used. But in this way, the thermal effects due to heating can be widely suppressed.
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EXPERIMENTAL PROCEDURE The experiments were carried out in a specially designed equipment depicted in figure 1. A laboratory press (Flexi-Press 16 t, Stenhoj, Denmark) was employed along with two pressing punches made of dense silicon-infiltrated SiC. This material was selected because of its good electrical conductivity at high temperatures and its high compressive strength. The supports for both punches are made of high-temperature-resistant steel. They act as electrodes once connected to the current. As pressing die a dense, high purity (99.7 %) alumina pipe was employed to guarantee that the applied current passes only through the powder. The electrical resistivity of this pipe is higher than 10 14 Ωαη. The samples consisted of Titania nano-powder (P25, Evonic Degussa, Germany). The material was selected for the following reasons: Its electrical resistivity is about 1010 Ωαη and sinks with increasing temperature, because T1O2 is a semiconductor. In this way the sample resistivity is lower than that of the alumina, guaranteeing the flow of current through the powder and not through the die. Besides the high ratio of surface to volume of the powder particles helps to activate the surface. The pressing equipment was positioned inside a metallic heating tube that could be independently regulated. Doing so, the separation of the heating circuit from the electric circuit was achieved. The current passing through the die was measured with a multimeter (METRAtop 52, Gossen-Metrawatt, Germany) and also mapped with an oscilloscope (Oscilloscope OS-9020G, LG Precision Company, South Korea).
Figure 1. Scheme of built FAST-equipment The powder was filled in the 10 mm inner diametre die and heated up to the sintering temperature with a heating rate of 25 K/min. For the sake of comparison, sintering temperatures of 575, 725, 750, 825 and 850 CC were chosen (5 samples at each temperature). Former investigations showed that at a sintering temperature of 775 °C with a soak time of 45 min, a density of 79 %TD (%TD = % of the theoretical density) could be reached 10. Therefore the soak time was extended to
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60 min. After reaching the sintering temperature, a pressure of 15 MPa was applied to the samples and then held during the whole soak. After finishing dwell time, the pressure was released. During heating and soak, a pulsed voltage of 4 V was applied and the current passing through the sample was measured and registerd. The duration of one pulse was 3 ms and the ratio pulse-on-time/pulse-off-time was 5/1. Additional samples were sintered with a soak time of 5 min to compare with the samples sintered in the commercially available FAST-equipment. These samples were labeled "A-i-j", where i stands for the sintering temperature and y for the holding time. To study the influence of the electric current, 10 samples were processed similarly but without application of electric current. They were labeled "B-i-j". In order to study the performance of our equipment, experiments were carried out in a commercially available FAST equipment (FCT HP D 25/1, FCT Systeme, Germany). The powder was filled in the die with an inner diameter of 20 mm, prepressed with 15 MPa for 30 s and then put into the furnace. While applying a pressure of 15 MPa, it was heated up to 450 °C during 1 min, then heated up to the sintering temperature at 25 or 100 K/min. Sintering temperatures of 650, 700, 750 and 850 °C were chosen. Samples were held at the sintering temperature during 5 min. A pressure of 15 MPa was applied during the soak time. The applied pulses had a duration of 3 ms with a pulse-on-time/pulse-offtime ratio of 5:1. Those samples were labeled "C-i" ( heating rate of 25 K/min) and "D-i" (heating rate 100 K/min). To study the role of sintering temperature, heating rate, pressure and electric current during FAST a Design-of-Experiments method (DOE) called "comparison of variables for process optimization" was used. A high density was chosen as target value. Estimated "good" and "bad" levels were then given to the four factors as can be seen in table I. The statistical spreading of the target value due to the action of all factors was estimated during preliminary tests. During these tests all factors were set on the level "good" and afterwards all factors were set on the level "bad". Each preliminary test was repeated once. Based on this estimation, single experiments were carried out in which one factor was set to the "good" level while the others were set to the "bad" level. With this method the influence of each factor on the target value can be estimated looking out for dominances or interactions between factors. More details on this method can be found elsewhere 12. The sample density was measured by the Archimedes' method and the microstructure of fractured surfaces was investigated by SEM (Jeol SEM-7000, Japan). Table I. Factor steps for Design of Experiments examination Level Level Factor "good" "bad" Sintering 800 °C 600 °C temperature Heating rate 25 K/min 10 K/min Pressure 5 MPa 15 MPa Current on off RESULTS The current passing through the powder as a function of time during the type A experiments (see table II) is shown in figure 2. At the beginning the current increases slightly to 0.1 mA. When a temperature of 400 °C is reached, the current decreases to a value of 0.008 mA followed by an increase up to several mA. From 600 to 800 °C fluctuating current values can be observed. After 40 min, when reachmg 850 °C, the current goes up from 0.1 mA and reaches about 300 mA at the end of the dwell time. At this point the applied voltage was removed.
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Figure 2. Temperature profile during sintering cycle "with current" and current passing through the sample against time Table II. Characteristics of samples produced using different sintering techniques Sintering Heating Rate Dwell Time Density Grain Size Sample Temperature (min) (K/min) (%TD) (nm) (°C) 60 49 32,5 575 25 60 93 725 25 77 60 90 112 750 25 A (with current) 825 60 92 160 25 850 60 95 176 25 5 62 750 25 77 5 130 850 87 25 77 725 60 80 25 60 89 103 750 25 825 60 92 161 B (without 25 current) 60 93 171 850 25 5 81 79 750 25 132 5 86 25 850 5 112 750 77 C 25 5 86 (FAST 25 K/min) 850 271 25 5 69 69 100 650 5 74 100 700 89 D (FAST 100 K/min) 123 5 80 750 100 5 87 268 850 100
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The densities and grain sizes of the samples prepared using the sintering techniques A and B in the new-built equipment, and C and D in the commercially available FAST equipment are shown in table II. Applying electric currents results in densities increasing from 49 %TD to 95 %TD when sintering at temperatures increasing from 575 °C to 850 °C, respectively (samples A-575-60 to A-85060). The grain sizes increase in the same way from 33 nm to 176 nm. The samples B-725-60 to B-850-60 reach densities from 80 %TD to 93 %TD and grain sizes between 77 nm and 171 nm. Shorter soak times result in lower densities and grain sizes for the samples sintered in our equipment with and without applied electric current (samples A-750-5, A-850-5, B-750-5 and B-850-5). The obtained densities vary from 77 %TD to 87 %TD, the grain sizes from 62 nm to 132 nm. The samples sintered in the FAST equipment (C-i and D-i) have densities from 69 %TD to 87 %TD and grain sizes between 69 nm and 271 nm. Figure 3 plots the comparison of the densities obtained with the different techniques. It shows that the sample A-850-60 has the highest sintered density. The samples A-750-60 to A-850-60 and B750-60 to B-850-60 reach the highest densities. The densities for the samples sintered in the conventional FAST equipment and in our new equipment for 5 min are in the range of 69 to 87 %TD and at equivalent temperatures in the same order of magnitude. Grain sizes of the sintered samples are shown in figure 4. All samples sintered at temperatures equal to or lower than 725 °C present grains with average diameters smaller than 100 nm. At a sintering temperature of 750 °C the samples A-750-60, B-750-60, C-750 and D-750 show grains with average diameters between 110 nm and 140 nm and a standard deviation of 45 nm (same order of magnitude). The samples A-750-5 and B-750-5 present smaller grains with mean diameters of 62 nm and 79 nm respectively. Significant differences are found at 850 °C, the samples C-850 and D-850 present grain sizes of around 270 nm, whereas die samples A-850 and B-850 show grains with average diameters of around 170 nm. The SEM micrographs shown in figure 6 depict this difference.
Figure 3. Measured densities against sintering temperature obtained by A) sintering with applied current, B) sintering without applied current and C) and D) in a conventional FAST equipment
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Figure 4. Measured grain size against sintering temperature obtained by A) sintering with applied current, B) sintering without applied current and C) and D) in a conventional FAST equipment SEM micrographs of fractured surfaces of the preliminary tests performed during DOEmeasurements are shown in the in figure 5. Figure 5.a presents a quite dense microstructure when sintering with all factors set on step "good" in contrast to a loose powder packing with no visible sintering progression for the "bad" test shown in figure 5.b.
Figure 5. SEM micrographs of fractured surfaces of samples sintered during preliminary tests of Design of Experiments measurements a) all factors on factor step "good", 800 °C, 25 K/min, 15 MPa, with applied current b) all factors on factor step "bad", 600 °C, 10 K/min, 5 MPa, without current application
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Figure 6. SEM micrographs of fractured surfaces, samples sintered a) with applied current at 850 °C, 25 K/min, 60 min, b) without applied current at 850 °C, 25 K/min, 60 min, c) conventional FAST at 850 °C, 25 K/min, 5 min, d) conventional FAST at 850 °C, 100 K/min, 5 min Micrographs of fractured surfaces of the samples where the variation of one factor was performed are shown in figure 7 (One factor is set on the step "good" the others stay on step "bad"). Figure 7.a shows larger grains than the others, 7.b shows neck formation between the small particles. Figure 7.c shows a quite dense particle arrangement and the apparition of "molten zones". Figure 7.d presents a quite dense compaction without any formation of interparticle connections like "sinter necks". The influence of the factors on the density during DOE-measurements is shown in figure 8. During preliminary tests Gl, G2, Bl and B2 the range of the target value for "good" and "bad" test is evaluated. The "good" tests result in target values of 78 %TD, the "bad" tests in 40 %TD. The variation of the factor temperature leads to a complete inversion in the target value (samples TgRb and TbRg). Pressure variation results in an approximation of the values (samples PgRb and PbRg). DISCUSSION With this newly developed equipment it is possible to determine the amount of current flowing through the powder because its electrical conductivity is several orders of magnitude higher than that of the alumina die, as shown in figure 2. The initial increase in current can be attributed to the
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semiconducting properties of titania. The second major increase starting at 600 °C followed by a slight decrease is due to particles rearrangement and densification during the phase transformation from anatase to rutile. Literature values describing the transformation are in good agreement with this result ". For this reason all samples sintered at temperatures higher than 800 °C consist exclusively of rutile, which has a theoretical density of 4.26 g/cm3. Such results have already been presented in , where the X-ray diffractograms, used to analyze the samples, are shown. The increase in the flowing current during the soak step can then be ascribed to densification processes. The electrical resistance sinks with a denser particle arrangement. With our equipment, the highest densities are attained at temperatures 750 °C and 850°C for the type-A and type-B samples and for soak times of 60 min whether current is applied or not (figure 3). The slightly higher densites determined for the samples A-750-60 to A-850-60 (compared to samples B-750-60 to B-850-60) lie in the range of measurement error and this difference is too small to be ascribed to a current effect. At sintering temperatures lower than 750 °C, the commercially FAST equipment (100 K/min heating rate, samples D-650 to D-750) and the newly developed equipment lead to almost the same densities. The variation of dwell time seems to have more influence on the density
Figure 7. SEM micrographs of fractured surfaces of samples sintered during Design of Experiments measurements a) high sintering temperature: grain growth, b) high heating rates: formation of "sinter-necks", c) high pressure: "molten zones", d) applied current: no visible influence
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Figure 8. Influence of factors on target value "density" during DOE. Bl, B2: Preliminary "bad" test, Gl, G2: preliminary "good"test, b = bad, g = good, T = Temperature, H = Heating rate, P = Pressure, C = Current than applying current or varying heating rates, because all samples sintered with holding times of 5 min achieve comparable densities, whereas the samples sintered with 60 min holding time present about a 10 % increase in density. The longer holding times seem to favor densification by diffusion mechanisms. Some hints that may support this conclusion are observed by comparing the grain sizes of fractured surfaces (diagramm in figure 4). Up to 750 °C all grain sizes are smaller than 150 nm. At 850 °C, samples C-850-5 and D-850-5 result in a mean grain size of 270 nm. Samples A-850-60 and B-850-60 show smaller grains (175 nm) and samples A-850-5 and B-850-5 still smaller ones (130 nm). It seems that longer soak time lead to longer diffusion times and therefore to grain growth. The samples sintered with the conventional FAST equipment show quite large grains even at short soak times what can be explained by the optimal sintering temperature being exceeded in this furnace. Grain growth takes place rapidly, because the heat generated by the current flow through the graphite die leads to an overheating of the sample due to difficult temperature when those high heating rates are applied. The results of the DOE-method allowed evaluating the effects of the different factors on the density and microstructure of the samples. With all factors at the "good" level, the samples can be sintered to densities around 78 %TD, meaning that sintering proceeds favorably (Figure 8). A loose compaction without any sintering takes place when all factors are kept at the "bad" level. The final densities are close to the green densities, that is around 40 %TD (figure 6,b and figure 8). When comparing the microstructures obtained with the single experiments (figure 7) to that of figure 6.b the effects of each "manipulated" factor can be determined. High sintering temperatures lead to an enhanced grain growth by favoring diffusion. Figure 8 supports this theory, because a complete inversion in the target values due to the variation of one factor means that this factor is dominant u. Higher heating rates accelerate sintering by formation of "sinter-necks" between the particles, but have no direct influence on the final density as shown in figure 8. The application of a pulsed current shows
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no influence on the microstructure of the fractured surfaces, as well as on the sintered density. When applying high pressures, there is an approximation in the target value shown in figure 8, meaning this factor is important, but not independent of the others. "Molten zones" are found in the microstructure (figure 7.c), but this phenomenon could not be related necessarily to the high pressure. Further investigations have to be done on this subject to quantify the influence of the factors and to generalize the results for less conducting materials. CONCLUSION AND OUTLOOK Investigations on the effect of the applied electric current during the Field Assisted Sintering Technique were carried out in a newly developed equipment. The equipment allows to measure the amount of current passing through the powder independently from that used for heating the sample. Initial tests showed no visible effect of the current on the sintered densities and grain sizes. A Designof-Experiments method was used to investigate the effect of sintering temperature, heating rate, pressure and current on density and microstructure. Sintering temperature was found to be the dominant factor on density and led to higher grain growth. Heating rate influences the formation of sinter necks, while pressure affects mostly the sample density and is also an important factor to promote sintering. The electric current passing through the sample, had no apparent influence on either microstructure or density. Further investigations will be performed to support these results and to study the influence of electric current pulses on insulating powders. REFERENCES 'M. Tokita, Mechanism of Spark Plasma Sintering. Proceedings of the International Symposium on Microwave, Plasma and Thermochemical Processing of Advanced Materials, ed. S. Miyake and M. Samandi. (1997), Osaka Universities Japan. 69-67. 2 Z. Shen, M. Johnsson, Z. Zhao and M. Nygren, Spark Plasma Sintering of Alumina, J. Am. Ceram. Soc, 85, 1921-1927(2002). 3 L. Gao, Z. Shen, H. Miyamoto and M. Nygren, Superfast Densification of Oxide/Oxide Ceramic Composites, J. Am. Ceram. Soc, 82, 1061-1063 (1999). 4 R. Chaim, Z. Shen and M. Nygren, Transparent nanocrystalline MgO by rapid and low-temperature spark plasma sintering,/. Mater. Res., 19, 2527-2531 (2004). 5 G. D. Zhan, J. Kuntz, J. Wan, J. Garay and A. K. Mukherjee, A novel processing route to develop a dense nanocrystalline alumina matrix (< 100 nm) nanocomposite material, J. Am. Ceram. Soc, 86, 200-202 (2003). 6 Y. I. Lee, J.-H. Lee, S.-H. Hong and D.-Y. Kim, Preparation of nanostructured T1O2 ceramics by spark plasma sintering, Mat. Res. Bull., 38, 925-930 (2003). 7 K. Vanmeensel, A. Laptev, J. Hennicke, J. Vleugels and O. V. d. Biest, Modelling of the temperature distribution during field assisted sintering, Acta Mater., 53,4379-4388 (2005). 8 K. Vanmeensel, A. Laptev, O. V. d. Biest and J. Vleugels, Field assisted sintering of electroconductive Zr02-based composites, J. Eur. Ceram. Soc, 27, 979-985 (2006). 9 U. Anselmi-Tamburini, S. Gennari, J. E. Garay and Z. A. Munir, Fundamental investigations on the spark plasma sintering/sythesis process II. Modeling of current and temperature distributions, Mat. Sei. Eng., 394, 139-148(2005). I0 M. E. Müller, Untersuchungen zum feldunterstützten Sintern, Diplomarbeit, Universität des Saarlandes, Saarbrücken (2007). "N. Masahashi, Fabriction of bulk anatase T1O2 by the spark plasma sintering method, Mat. Sei. Eng., 452-453, 721-726 (2007). 12 W. Kleppmann, Taschenbuch Versuchsplanung, Carl Hanser Verlag, ISBN: 3-446-40617-4 (2006)
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SINTERING OF COMBUSTION SYNTHESIZED TIB2-ZR02 COMPOSITE POWDERS IN CONVENTIONAL AND MICROWAVE FURNACES Hayk Khachatryan2, Alok Vats', Zachary Doorenbos1, Suren ICharatyan2, and Jan A. Puszynski1 'South Dakota School of Mines and Technology, Rapid City, SD, USA, Yerevan State University, Yerevan, Armenia ABSTRACT Comparative pressureless sintering studies of Τ1Β2-Ζ1Ό2 composite powders with different compositions of Y2O3 stabilized Z1O2 were conducted in an inert atmosphere using conventional and microwave sintering furnaces. Composite powders were prepared in one step combustion synthesis (CS) also called self-propagating high-temperature synthesis (SHS) process using two different initial reactant compositions: i) Ti- 2B- 0.2 Z1O2 (unstabilized) and ii) Zr-Ti02-2B. In both cases, Y2O3 powder was added as a stabilizer. Attrition milled submicron product powders were dried and pressed to the desired green density in uniaxial or cold isostatic presses. For comparison commercial T1B2 and Z1O2 (yttria stabilized) powders of the same composition were subjected to attrition milling and green samples were sintered together with those obtained from combustion synthesized powders. Sintering experiments were done in a conventional pressureless graphite furnace for one hour at 1500°C, 1700°C, and 1850°C under the flowing argon gas. The sintering results have shown that combustion synthesized composite powders have better sinterability, CS-T1B2 rich composite sinters up to 99% of relative density at 1700°C. Sintering studies in a microwave furnace have shown that the same results can be achieved at much faster rates and lower temperatures as compared to the conventional furnace. INTRODUCTION Ceramic materials offer many excellent properties, such as high hardness, high melting point, chemical inertness, high compression strength, and impact resistance, etc. [1,2]. Mechanical properties of ceramic materials, especially fracture toughness, can be improved by the addition of other phases into a material's matrix to form a composite structure [3]. Ceramic parts are generally produced by cold die compaction with subsequent sintering and finishing or by hot pressing or hot isostatic pressing and finishing. Among these procedures, sintering or densification is the most important process for fabricating ceramics [4-6].
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Specific surface area of the powder among other properties plays a crucial role during sintering, as it provides additional driving force for densification, smaller initial size of the powders normally results in higher densities or in some cases may lead to lower firing temperatures due to faster sintering kinetics [3,5,6]. The friction between the powder and the die wall during powder compaction typically leads to residual stresses and nonuniform green density in ceramic compacts. The variation in density distribution in powder compacts results in nonuniform shrinkage during sintering process. These residual stresses cause micro cracks in the powder compacts during the sintering process and thus affects the mechanical properties of the compacts. The density that can be achieved during a cold compaction of ceramic powder in a die is lower compared to metal powders. Therefore, the effects of nonuniform density distribution and residual stresses in ceramic compacts are more serious than those associated with sintering of metal powders [5,6]. This work was focused on i) investigation of pressureless sintering of combustion synthesized TiB2-Zr02 composites [7-9]; ii) feasibility study of sintering TiB2-Zr02 composites in a microwave furnace. EXPERIMENTAL PROCEDURE In this sintering study, four different TiB2-Zr02 composite powders were used as shown in Table 1. The first two composites powders were synthesized using combustion synthesis technique with Zr0 2 concentration being 25wt% and 75wt% [6, 7]. The first composite (PI) was synthesized from titanium and boron reactants with the addition of unstabilized zirconia. In this case, the amount of magnesium present in boron was sufficient to stabilize zirconia during the combustion process [7]. The second composite powder (P2) was formed from Zr, B and T1O2 as reactants with the addition of unstabilized zirconia. In this case, yttria was added in addition to the already present magnesium in boron powder in order to fully stabilized zirconia in the T1B2Z1O2 composite [7]. For comparison, identical compositions (P3 and P4) were also prepared by mixing T1B2 and fully stabilized zirconia powders. Combustion synthesized titanium diboride powder was used in P3 and P4 composite compositions. The average particle size of combustion synthesized T1B2 was 5 μηι. Fully stabilized zirconia used in P3 and P4 composite compositions was obtained from the Zircar Company with the average particle size less than 5μπι. All four compositions were subjected to mechanical milling in an attritor mill (01-HDDM Union Process, Szegvari Attritor System). Dense zirconia grinding media (1.2-1.4 mm in dia)
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was used with distilled water. A constant shaft speed of 3,200 rpm and a total milling time of 40 min was used to mill each composition. Table 1. Compositions of composite powders used in sintering experiments. Name
Composition
PI
75%wt T1B2 - 25wt% ZrC"2 (stabilized) combustion synthesized powder
P2
25%wt T1B2 - 75wt% ZrC>2 (stabilized) combustion synthesized powder
P3
75%wt TiB2 - 25wt% Z1O2 (stabilized) mixed powder
P4
25%wt TiB2 - 75wt% Zr0 2 (stabilized) mixed powder
The ratio of the grinding media to milled powder was 10:1 by weight. After milling, the composites powders were separated from media and dried. The final drying was done at 8090°C in a vacuum oven. Next, cylindrical pellets with a diameter of 12 mm and 7-8 mm height were prepared using both cold isostatic and uniaxial presses. Samples in the cold isostatic press (CIP 32260, Avure Autoclave Systems, Inc.) were pressed at 60, 137, 210, 275, and 345MPa. The pressing in an uniaxial press was done at 87.5MPa pressure. Pressureless sintering studies were conducted in two different sintering furnaces: i) conventional sintering furnace with a graphite heating element (FP20 from Astro Industries, Inc.) ii) microwave furnace (VIS300001B from CPI Inc.).The sintering atmosphere in a graphite furnace was argon, while the inert gas used during the sintering in microwave was high purity helium. The reason for using helium instead of argon in microwave furnace was to inhibit gas ionization which led to a plasma formation. Sintering studies in the conventional graphite furnace were carried out at 1500°C, 1700°C, and 1850°C. Heating rate was set at 5°C/min in the graphite furnace and soak time was 1 hr. In order to determine sintering kinetics, additional experiments were conducted with different soak times of 15, 30, 45, 60, and 75 min. Densities of sintered samples were determined using Archimedes method. In order to minimize experimental error, three samples of each composition were used in the analysis. Sintering studies in the microwave furnace were curried out at 1300°C, 1400°C, and 1500°C. Heating rate was 70-100°C/min and soak time was 15 min. Samples were placed in a specially designed highly porous alumina box. The box cap had a small hole to determine samples temperature using a pyrometer.
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The Vickers hardness of the sintered specimens was measured on a hardness tester (model Micrometer 4 micro, Buehler Ltd.) with an indentation load of 1,000 kg. Specimens were polished on a diamond-grinding wheel (type Cameo disk Platinum 1, 3 and 4 purchased from Leco Co.). Phase composition analyses were carried out on the sintered test specimen using electron dispersive X ray analyzer (EDX) on SEM (Supra40VP from Zeiss Co.) and X-ray diffractometer (Rigaku Ultima Plus). The stability of these composites to oxidation was measured by heating the samples in air at temperature of 800 and 1000°C for 4 hours. RESULTS AND DISCUSSION SEM photographs of TiB2-Zr02 composite powder (PI) before and after attrition milling are shown in Figure 1. It is clear from these micrographs that the combustion synthesized composite powder was fused during synthesis. According to EDX analysis, gray and well defined crystals are titanium diboride, while light gray phase is zirconia (Figure la). After attrition milling, the average particle sizes of composite powders was reduced below 2 μηι (Figure lb). X-ray analyses did not show any changes in phase composition due to the milling and drying of composite powders.
Figure 1: Microstructure of PI powders; a) before milling, b) after 40 min milling. Figure 2 shows the final relative densities of the pellets as a function soak time (1500°C) and powder pressing technique. The PI powder was pressed using both CIP and uniaxial press. The samples were pressed at 210 MPa and 87.5 MPa, respectively. The pressed pellets were sintered in the graphite sintering furnace at 0.1 MPa argon pressure.
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Figure 2: Relative density of pellets made from 75 wt%TiB2-25 wt%Zr02 composite (PI) at ]50(fC temperature as the function of soak time. As can be seen from Figure 2, the densification of this composite material at 1,500°C reached much higher density for the pellets pressed using cold isostatic press as expected. The final density of pellets prepared by uniaxial press was 82% and for the pellets prepared using cold isostatic press a density of 90% was obtained. - 50
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Figure 3: Relative density (Δ) and volumetric shrinkage degree (Θ) of composite powder (PI) as a function of a consolidation pressure in CIP. Samples were sintered in a graphite sintering furnace at 150(fC in argon atmosphere with a soak ofl hour. It is important to note here that for all future experiments a soak time of 1 hour was used. Relative density and degree of volumetric shrinkage of PI composite pellets formed in a cold isostatic press and later sintered at 1500°C for 1 hr in a pressureless graphite furnace as a function of green consolidation pressure is shown in Figure 3. This Figure indicates that the
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initial green density has a significant effect on the final density and volumetric shrinkage of the TiB2-Zr02 composite. It should be noted that the composite (P3) with the same composition prepared by mixed T1B2 and fully stabilized ZrC>2 powders resulted in significantly lower relative densities (78-85%) under identical sintering conditions. Figure 4a shows SEM photograph of a green sample of PI composite prepared in CIP at 210 MPa whereas Figure 4b shows the microstructure of the sintered body of the same pellet at 1,500°C for 1 hr in a graphite furnace in an argon atmosphere.
Figure 4: Microstructure ofPI powders a) sintered at 1500PC temperature b) initial powder after attrition milling. In order to increase the relative density of sintered composites, additional sintering experiments were conducted at 1,700°C. Figure 5 shows the relative density (Δ) and the volumetric shrinkage degree (Θ) of PI and P3 composites sintered for 1 hr in a graphite furnace in argon atmosphere as a function of green consolidation pressure in a cold isostatic press. Again in this case, the combustion synthesized powders did show much higher relative density after 1 hr soak time than the pellets made by mixed TiB2 and Zr0 2 powders, 98% vs. 88%). The faster sintering rates for combustion synthesized powders can be explained by the fact that the composite powders obtained via the SHS (self-propagating high-temperature synthesis)process have higher percentage of nonequilibrium phases which are formed due to high cooling rates during the synthesis. According to XRD analysis done on sintered samples, no phase changes in the samples were observed, only phase composition comprises of two phases T1B2 and stabilized ZrC>2. Figure 6(a) shows the microstructure of SHS synthesized composite powder which was sintered at 1700°C.
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Figure 5: Relative density (Δ) and degree of volumetric shrinkage (Θ) ofPI and Pi samples as the function ofgreen consolidation pressure in CIP. Sintering was done in a graphite sintering furnace at ¡70(fCfor Ihr in argon atmosphere (a) P3 composite (b) PI composite. PI and P3 composite powders were also sintered in a microwave furnace. In this case, dense composite materials were obtained in much shorter time and at lower sintering temperatures. For PI and P3 powders 95-98% relative densities were obtained for the samples sintered at 1400°C for 15 min in the microwave furnace. This level of densification was obtained in a conventional graphite furnace at 1700°C for only PI type composite. We believe the high relative densities achieved for P3 type composition sintered in the microwave furnace is caused by the high selectivity of the microwave coupling with the T1B2 phase in the P3 composite microstructure. It can be observed that the TiB2 grains had grown selectively over the Z1O2 grains as shown in Figure 6(b).
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Figure 6: a) Microstructure of PI powders sintered in conventionalfurnace at 170(fC temperature, b) Microstructure ofP3 Powders sintered in microwave furnace at 140(fC temperature. P2 and P4 composite powders were also sintered at 1700 and 1850°C using conventional furnace with the soaking time of 1 h. Figure 7 shows the relative density (Δ) and the volumetric shrinkage degree (Θ) of P2 composite sintered for 1 hr in a graphite furnace in argon atmosphere as a function of green consolidation pressure in cold isostatic press.
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- 35
400
Figure 7: Relative density (A) and degree of volumetric shrinkage (Θ) ofP2 composite as a function ofgreen consolidation pressure in C1P. Sintering was done in a graphite sintering furnace at 1700° C and 1850° Cfor Ihr in argon atmosphere. The relative densities of P2 samples sintered at 1700°C were between 95 to 96% and at 1850°C between 97to 98%. P4 composite which was prepared by mixing TiB2 and stabilized Z1O2 after sintering at same conditions showed lower relative densities (~ 90%). SEM image of P2 samples sintered at 1700°C is shown in Figure 8. It can be seen in this micrograph that TiB2 crystals are homogeneously distributed in a well sintered zirconia matrix. Also in this case XRD analysis, reveled no other peaks associated with phase other that T1B2 and stabilized ZrC>2.
Figure 8: Microstructure ofP2 powders sintered at 1850 °C temperature in a graphite furnace under argon atmosphere for 1 hour. In order to study the stability of TiB2-Zr02 composites in oxidizing atmosphere the sintered samples were heated at 800 and 1000°C temperature in air, Figure 9 presents weight change of
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different composite samples at the 1000°C temperatures. The samples heat at 800°C showed very high oxidation resistance, no weight change was observed at this temperature range after 4 hours exposure. However, weight changes for the samples heated at 1000°C were observed as it is evident from Figure 9. The weight change of 3 ~ 3.5% was observed at these conditions. It should be noted that weight changes were more pronounced during the first stage of heating. According to these results, P3 composites, which was obtained by mixing, started oxidizing comparatively earlier then composites obtained by SHS method (PI and P2). This can be caused by lower porosity of (PI and P2) SHS synthesized composites as compared to P3.
I
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Figure 9: % Weight change associated with different composition at 100(fC. The Vickers hardness analysis has shown that the hardness strongly depend on the composition of TiB2-Zr02 composites. The PI composite has shown the highest hardness of 1750±50 kg/mm2 for samples sintered at 1500°C and 2400±50 kg/mm2 for samples sintered at 1700°C. While P3 type composite has shown hardness of 1750±50 kg/mm2 for samples sintered at 1700°C. For P2 composite compacts which are zirconia rich, the hardness of 1600±50 kg/mm2 was when sintered at 1850°C and 1200±50 kg/mm2 for samples sintered at 1700°C. CONCLUSIONS In this investigation, it was established that one stage SHS synthesized composites possess higher sinterability then composites obtained by mixing method. It has been clearly
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shown that that higher relative densities were obtained for composites prepared using cold isostatic press as comparing to uni-axial press. The titanium diboride rich composites (75wt%) were successfully densified by pressureless sintering at 1700°C, while the samples with 75wt% zirconia needed higher sintering temperature of 1850°C. Composites samples sintered using microwave furnace showed much faster sintering kinetics at lower sintering temperatures as compared to samples sintered using conventional furnaces. The faster sintering kinetics is attributed to the diffusional drift term due to electromagnetic coupling with the samples in the microwave furnace. It was established that sintered composites are very resistant against oxidation up to 800°C. It is important to note that samples made from SHS derived composite powders exhibit higher stability towards oxidation. It has been also shown that T1B2- ZrC>2 composites exhibit higher hardness as compared to dense zirconia. ACKNOWLEDGEMENT The authors acknowledge the financial support endowed to Dr. Hayk Khachatryan by CIES/ Fulbright scholarship. REFERENCES [1]
J. M. Leger and J. Haines, "The Search for Superhard Materials", Endeavour, 21, 1997.
[2]
R. J. Brook, "Superhard Ceramics", Nature, 400, 1999.
[3]
W.E. Lee, W.M. Rainforth, Champman&Hall, London-Glasgow-Weinheim-New York, Tokyo-Melbourne, Madras, 1994.
[4]
R.M. German, "Sintering Theory and Practice", ISBN 0-471-05786-X. Wiley-VCH, January 1996.
[5]
S Kang, "Sintering-Densification, Grain Growth and Microstructure", ISBN 07506 63855, Elsevier Butterworth- Heinermann, 2005.
[6]
M.W. Barsoum, " Fundamentals of Ceramics", ISBN 0-07-005521 -1, McGraw Hill series in Materials Sciences, 1997.
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[7]
H. Khachatryan, J Puszynski, S. Kharatyan "Combustion Synthesis of Titanium Diboride and Zirconia Composite Powders. Part I" J. Am. Ceram. Soc, 1-6, 2008.
[8]
A.G. Merzhanov. "Twenty Years of Search and Findings". In: Combustion and Plasma Synthesis of High-Temperature Materials, Eds. Z.A. Muñir, J.B. Holt, N.Y.: VCH Publ. Inc., pp.1-53, 1990.
[9]
Z.A. Munir, U. Anselmi-Tamburini. "Self-propagating Exothermic Reactions: the Synthesis of High-Temperature Materials by Combustion". Mater. Sei. Reports., vol.69, No.7-8, pp. 277-365, 1989.
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PRODUCTION AND CHARACTERIZATION OF WC-Co CEMENTED CARBIDES BY FIELD ASSISTED SINTERING Rafet Emre Özüdogru1, Filiz Cinar Sahin1'2, Onuralp Yucel1'2 'Istanbul Technical University, Metallurgical & Materials Eng.Dept. Maslak, Istanbul, 34469, Turkey Istanbul Technical University, Applied Research Center of Materials Science & Production Technologies, Maslak, Istanbul, 34469, Turkey ABSTRACT Cemented WC-Co bulk materials were obtained from mixed WC-Co powder by using Field Assisted Sintering technique. Powder mixtures were sintered at 1300°C, 1350°C and 1375°C under 50MPa pressure in order to determine the effects of sintering temperatures. Sintering behavior and mechanical properties such as density, hardness, fracture toughness and modulus of elasticity of fine-grained WC-5 wt% Co and WC-10 wt% Co hard metal were investigated. Microstructural observations were carried out by Scanning Electron Microscopy (SEM) technique. Test results show that densities of bulk materials sintered at 1375CC are higher than 99 % of theoretical density. Mechanical test results point out that hardness, fracture toughness and modulus of elasticity are more dependent on composition of cobalt content than sintering temperature. INTRODUCTION WC-Co is a well known hard material used for cutting tools and dies due to its high wear resistance and strength1. They consist of a high volume fraction of the hard WC phase embedded within a soft and tough Co binder phase. These materials can be densified by liquid phase sintering and their mechanical properties depend on their compositions and microstructure. Increasing the volume fraction of Co increases the fracture toughness, but decreases hardness and wear resistance . When the grain size of the WC particles is reduced to a range of submicrometer or nanometer, the hardness and the strength of the cemented carbides increase remarkably, and the toughness improves greatly as well, thus showing excellent combined mechanical properties of the hard materials. Extensive WC grain coarsening occurs when sintering nanometer sized WC-Co starting powder mixtures by the conventional pressureless sintering. The additions of small amounts of WC grain growth inhibitors, typically <0.1 wt.% of a metallic carbide such as VC, Cr2C3,NbC or M02C to the starting powder mixture helps control the WC grain growth3. In addition to the effect of grain growth inhibitors, many researches are focused on the development of new sintering techniques that obtain better mechanical properties due to lower sintering temperature, and a shorter thermal cycle such as hot pressing1,4, microwave sintering5 and field assisted sintering6'7. Field assisted sintering technique (FAST) is also called spark plasma sintering (SPS) and it enables a powder compact to be densified by Joule heating when the pulsed direct current goes through the sintering specimen8"10. Generally, the FAST process applies simultaneously a low voltage, pulsed direct current of high intensity and uniaxial pressure, which offers the high heating rates (100-500°C/min) and short holding times (3-5 min.) used to obtain fully densified bulk materials. Owing to the rapid heating and cooling rates, and short holding time, powder samples can be densified at relatively lower temperatures than in the conventional methods. Thus, the grain growth during sintering can be effectively inhibited. Recently, FAST applications to optimize processing parameters of WC-Co cemented carbides and binderless WC is rapidly increasing6·7·11-15. In the present paper, WC-Co powder mixtures containing two different volume fraction of Co binder are densified by FAST. The effect of the FAST temperature and Co volume fraction on the densities of cemented carbides and some mechanical properties such as hardness, fracture toughness and elastic modulus will be discussed by through microstructural observation.
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EXPERIMENTAL PROCEDURE Commercial WC powder (Dr. Fritsch, Germany) and Co powder (Dr. Fritsch, Germany) were used as the raw materials and some of their physical and chemical properties are given in Table I. The morphologies of the starting powder are shown in Fig. 1. Table I. Physical and chemical properties of starting materials. WC Co
Particle Size d5o (μπι) 1 0.85
Purity (wt. %) >99.6 >99.6
Density (g/cm3) 15.8 8.71
0 2 Cont. (max. wt. %)) 0.6 0.6
(a) (b) Figure 1. SEM micrographs of starting powders, (a) WC powders, (b) Co powders. The attrition ball milling was carried out for mixing WC and Co particles, with the ball-milling apparatus Attritor 01-HDDM (Union Process, US) using a tefzel coated tank and WC balls. Ethanol was used as the milling medium to prevent agglomeration of powder. Attrition milling was carried out for 2 hours at the rotating speed of 500rpm, and the ball to powder ratio of 3:1. Sintering procedure conducted with FCT HP D25/1 (FCT System GmbH, Germany) apparatus including a 10 V, 10000 A DC power supply and a 250 kN uniaxial press. The dried powder was poured into a graphite die 40 mm in diameter with graphite paper inserts. Both powder mixtures were sintered by applying constant pressure of 50 MPa, with a holding time of 2 min. at final sintering temperatures of 1300°C, 1350°C and 1375°C with a heating rate of 100°C/min. A thermal carbon felt insulation was used around the die to avoid thermal gradients inside the sample during the sintering. The temperature was controlled by a pyrometer focused at the bottom of a central core hole in the upper punch about 2 mm from the top surface of the sample. After sintering, the samples had a thickness of 4 mm and were sand blasted, ground and polished. The relative densities of the sintered samples were measured by the Archimedes method. The Vickers hardness was measured on the hardness tester (Leica VMHT, Germany) with a load of 1 kg. The fracture toughness was calculated from the length of the radial cracks originating in the corners of the Vicker's indentations according to the Anstis equation [15]. Elastic modulus of sintered samples was obtained using an acoustic resonance method (Grindosonic MK 5 Industrial Instrument). Microstructural observations were carried out field emission scanning electron microscope (JEOL JSM 7000F, Japan) on polished sample surfaces. RESULTS AND DISCUSSION The variation of FAST parameters such as sintering temperature, absolute pressure, displacement speed, piston displacement, and force during sintering process were monitored during the experiments and given in Fig.2 and Fig. 3 for samples containing 5 % Co and 10 % Co,
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respectively at 1300°C final sintering temperature. The whole FAST process for each sample, including heating up, densification and holding at sintering temperatures takes less than 18 min. Liu. et al. explained the FAST process by displacement speed. According to displacement speed, the whole FAST process can be divided into three stages, as shown in Fig.2 and Fig. 3. In the first stage (marked as I in Fig.2), the displacement rate has a very small change. This stage ends when the temperature reaches 850°C and displacement and displacement speed increase. In the second stage (marked as II in Fig.2), from the increase of temperature, powder samples start shrinking, resulting in the increase of the displacement and displacement speed. The external pressure is applied when the temperature reaches 1000°C and the displacement and displacement speed increase sharply. The atomic diffusion becomes stronger, which results in the bonding of powder particles, hence the formation of sintering necks. In this stage when the temperature is increased to 1300°C, the displacement speed reaches the maximum value, where Co binder phase connects the WC powders. When displacement speed becomes zero, the main densification process is basically finished. The last stage (marked as III in Fig.2) is the isothermal holding period. In this stage, powder compact density improves, the porosity reduces by the effect of binder phaseflowing,and WC grains re-arranging. The change of the displacement speeds of both samples containing 5 % and 10 % Co is similar by increasing time, temperature and force. However, due to the displacement speed of the sample containing 10 % Co decreases to zero earlier than that of the sample containing 5 % Co, densification is completed in shorter time within sample containing 10 % Co.
Figure 2. Variation of the temperature, force, vacuum pressure, displacement and displacement speed with time during sintering of the WC-5% Co cemented carbide at 1300°C for 2 minutes.
Figure 3. Variation of the temperature, force, vacuum pressure, displacement and displacement speed with time during sintering of the WC-10% Co cemented carbide at 1300°C for 2 minutes.
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Fig. 4 and Fig. 5 show the influence of the sintering temperature on the density and relative density of the WC-5 %Co and WC-10% Co cemented carbides, respectively. In both figure, density and relative density of cemented carbides increases with increasing sintering temperature and they reach full density at 1375°C.
1290
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Temperature (°C) Figure 4. The variation of density and relative density of WC- 5 % Co as a function of sintering temperature applying 50 MPa pressure for 2 min.
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Figure 5. The variation of density and relative density of WC- 10 % Co as a function of sintering temperature applying 50 MPa pressure for 2 min.
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The measured hardness value of WC-5 % Co and WC-10 % Co cemented carbides as a function of sintering temperature are given in Fig.6. Vickers hardness of both cemented carbides increase with increasing sintering temperature, due to increase in density of samples. However WC-5 %Co samples having lower soft binder Co phase shows higher hardness values than that of WC-10 % Co samples. The hardness values of WC-5 % Co and WC- 10 % Co cemented carbides sintered at 1375CC by applying 50 MPa for 2 min. are 2087 kg/mm2 and 1795 kg/mm2, respectively.
-"-WC-5%Co -*-WC-10%Co
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Temperature (°C) Figure 6. Hardness of the WC-5 % Co and WC-10 % Co cemented carbides as a function of sintering temperature. 750 -B-WC-5%Co
700 --
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650 -C600 ¡550 W
500 450
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1330 1350 1370 1390 Temperature (°C) Figure 7. The variation of elastic modulus of the WC-5% Co and WC- 10 %Co cemented carbides as a function of sintering temperature.
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Fig.7 shows elastic modulus of the WC-5 %Co and WC-10%Co cemented carbides sintered at different temperatures. As the temperature increases from 1300°C to 1375°C, the elastic modulus of the WC-5 %Co cemented carbide increases from 608 GPa to 625 GPa. The same temperature change in the WC-10 %Co cemented carbide sintering results in an increase in the elastic modules from 545 GPa to 565 GPa. These increases in elastic modulus values result from the increase in density of cemented carbides by increasing sintering temperature. However, the theoretical elastic modulus values of WC-5 %Co and WC-10 %Co are not achieved by the FAST experiment. Fracture toughnesses of cemented carbides according to the hardness are presented in Fig. 8. Fracture toughness values of the samples are most dependent on the Co content of the cemented carbides. The samples containing 5 % Co, having high hardness show lower fracture toughness than that of the samples containing 10 % Co. Fracture toughness of values of the samples containing 5%Co change between 11.3 MPa.m"2 and 12.9 MPa.m"2 where as 10 % Co containing samples between 14.6 MPa.m"2 and 15.9 MPa.m1'2. 19 ■ WC-5%Co m tx
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t < [Λ
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Figure 8. Fracture toughness of samples WC-5 % Co and WC-10 % Co versus hardness. A typical indentation with the resulting radial crack pattern for samples spark plasma sintered at 1375°C, containing 5 % Co and 10 % Co are shown in Fig.9(a) and Fig.9(b). Higher magnification views of portions of typical radial cracks in WC-5 %Co and WC-10% Co are shown in Fig. 9(c) and Fig. 9(d), respectively. The crack induced by Vicker's indentation propagates along the Co binder phase as shown in Fig. 9(c) and Fig. 9(d). Therefore, the deformation behaviour of Co binder phase in cemented carbides is the most critical factor determining the fracture toughness of cemented carbides. Low Co content in cemented carbides resulted in longer crack length representing brittle structure. Microstructures of polished surface of the WC-5 % Co and WC-10 % Co cemented carbides sintered at 1300CC and 1375°C under a pressure of 50 MPa for 2 min were observed by field emission scanning electron microscope (FE-SEM) and given in Fig. 10. EDS analysis indicates that dark areas are Co phase and white particles are WC. As it can be seen as Fig. 10, increase in field assisted sintering temperature from 1300°C to 1375°C does not significantly effect an increase in WC grain size. This may be due to the high heating rate and short sintering time. Concerning starting powder size, abnormal grain growth is not observed in the samples spark plasma sintered at 1375°C.
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Figure 9. Micrographs of Vickers indentation pyramids on polished surfaces of samples spark plasma sintered at 1375:(a) WC-5 % Co (b) WC-10 % Co (c) crack tip of WC-5 % Co and (d) crack tip ofWC-10% Co.
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Figure 10. Scanning electron microscope image of polished surface of (a) WC-5 %Co sintered at 1300°C and (b) WC-10% Co sintered at 1300°C, (c) WC-5 % Co at 1375°C and (d) WC-10% Co sintered at 1375°C under a pressure of 50 MPa for 2 min. CONCLUSION By using field assisted sintering technique (FAST), fully densified WC-5 % Co and WC-10 % Co cemented carbides were prepared at 1375°C under a pressure of 50 MPa for 2 min starting with attrition milled submicrometer size WC and Co powder mixtures. Increasing FAST temperature resulted in increasing density, hardness and elastic modulus in WC-Co cemented carbides. Cemented carbides containing high Co shows high fracture toughness. The highest hardness and elastic modulus was obtained with WC-5 % Co cemented carbide whereas the highest fracture toughness was reached in WC-10 %Co cemented carbide. Increasing sintering temperature from 1300°C to 1375°C in FAST, does not cause to abnormal grain growth due to high heating rate and short sintering time. REFERENCES 'C.Jia, L.Sun, H.Tang, X.Qu, Hot Pressing of Nanometer WC-Co Powder, Int.J.Ref.Met.&Hard Mat., 25, 53-56 (2005). 2 H.C.Kim, I.KJeong, I.J.Shon, I.Y.Ko, J.M.Doh, Fabriaction of WC- 8 wt.% Co Hard Materials by Two Rapid Sintering Process, Int.J.Ref.Met.&Hard Mat. ,25,336-340, (2007). 3 S.G.Huang, L.Li, K. Vanmeensel, O.Van der Biest, J.Vleugels, VC, Cr3C2 and NbC doped WCCo
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Cemented Carbides Prepared by Pulsed Electric Current Sintering, Int.J.Ref.Met.&Hard Mat., 25,417-422,(2007). 4 Z. Qiao, X.Ma, W.Zhao, H. Tang, B.Zhao, nanostructured Novel Cemented Hard Alloy Obtained by Mechanical Alloying and Hot Press Sintering and Its Application, J.Alloy.Comp. doi.l0.1016/j.Jallcom. 2007.08.062,(2007). 5 E.Breval, JP. Chen, DK.Agrawel, P.Gigl, M.Dennis, R.Roy, Comparison between Microwave and Conventional Sintering of WC-Co Composites, Mat.Sci. Eng.K 391, 285-295, (2005). 6 X.Liu, X. Song, J.Zang, S.Zhao, Temperature Distribution and Neck Formation of WC-Co Combined Particles During Spark Plasma Sintering, Mat.Sci.Eng.A 488, 1-7,(2008). 7 SI. Cha, SH. Hong, BK.Kim, Spark plasma Sintering Behaviour of Nanocrystalline WC-10 Co Cemented Carbide Powders, Mat.Sci. Eng. A, 351, 31-35, (2003) 8 M.Tokita, Trends in Advanced SPS Spark Plasma Sintering Systems and Technology, J. Soc. Pow. Tech. Jap., vol.30 11, 790-804,(1993). 9 Z.A. Munir, U.Anselmi-Tamburini, M.Ohyanagi, The Effect of Electric Field and Pressure on the Syntehsis and Consoludation of Materials: A rewiev of the Spark Plasma Sintering Method, J.Mat.Sci. 41, 763-777, (2006). 10 M.Tokita, Development of Square-shaped Large-size WC/Co/Ni System FGM Fabricated by Spark Plasma Sintering Method and Its Industrial Application, Mat.Sci. For. , Vol. 492-493, 711718,(2005). 11 K.Vanmeensel, A Laptev, J.Hennicke, J.Vleugels, O.Van der Biest, Modelling of the Temperature Distribution During Field Assisted Sintering, Acta. Mater. 53, 4379-4388, (2003). 12 I.Cha, S.H. Hang, Microstructure ofBinderless Tugstencarbides Sintered by Spark Plasma Sintering Process, Mat. Sei. Eng. A, 356, 381-89, (2003). 13 C.C. Jia, H. Tang, X.Mei, F. Yin, H.Qu, Spark Plasma Sintering on Nanometer Scale WC-Co Powder, Mat. Lett. 59, 2566-2569, (2005). 14 S.G.Huang, K. Vanmeensel, L.Li, O. Van der Biest, j . Vleugels, Influence of Starting Powder on the Microstructure of WC-Co Hardmetals Obtained by Spark Plasma Sintering, Mat. Sei.Eng. A, 475,87-91,(2008). 15 H.C.Kim, LJ.Shon, J.K.Yoon, J.M.Doh, Consolidation of ultra fine WC and WC-Co hard materials by pulsed current activated sintering and its mechanical properties, Int.J.Ref.Met.&Hard Mat.,25, 46-52, (2007). 16 W. Liu, X. Song, J.Zhang, F.Yin, G.Zhang, A Novel Route to Prepare Ultrafine-Grained WC-Co Cemented Carbides, J. Alloy. Comp. 458, 366-371, (2008).
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MICROWAVE RAPID DEBINDING AND SINTERING OF MIM/CIM PARTS P. Veronesi*, C.Leonelli*, G. Poli*, L. Denti°, A. Gatto0 Dept. of Materials and Environmental Engineering, University of Modena, Via Vignolese 905,41100, Italy ° Dept. of Mechanical Engineering, University of Modena, Via Vignolese 905,41100, Italy ABSTRACT Thermal debinding of parts obtained by Metal Injection Moulding (MIM) or Ceramic Injection Moulding (CIM) can benefit from the rapid, volumetric and selective microwave-assisted heating, having the organic binder or the metallic powders to preferentially absorb microwaves. This is particularly useful when dealing with ceramic powders having low thermal conductivity, but also more conductive materials can be treated faster if the maximum temperature difference inside each part is kept low. Microwave assisted debinding and sintering of MIM/CIM parts, made of stainless steel and alumina, has been optimized by means of numerical simulation, in order to determine the most favorable load configuration, in terms of heat generation homogeneity and energy efficiency. Rapid microwave-assisted debinding, in the optimized loading conditions, was experimentally achieved, with time reduction from 6 to 8 times, compared to conventional processes. Moreover, in case of MIM, presintering of the brown part occurred, despite the temperature lower than 600°C. The occurrence of this beneficial phenomenon, which improves the brown part mechanical properties, has been ascribed to the electromagnetic field concentration which takes place in the space between the conductive particles, thus promoting rapid binder removal and neck formation. INTRODUCTION The debinding process is a preliminary step, prior to sintering, which consists of the removal of the organic binder used during forming of metal or ceramic "green" parts. Debinding can be performed either by chemical methods (solution) or thermal methods (melting or oxidation), or a combination of the two. Maximum debinding temperature depends on the organic binder nature, and it is usually lower than 600°C. Generally, the thermal debinding process requires a very slow and controlled heating in order to avoid generating overpressure in the green parts which could induce distortions, cracking or unwanted porosity and roughness. The debinding step results particularly demanding for products obtained by Metal Injection Moulding (MIM) and Ceramic Injection Moulding (CIM), where the weight percentage of the binder can reach 40%. Microwaves interact with matter, generating in the material a power density distribution given by: Pj(x,y ,z) = ω EoéegErn? + ω μ0μ "egHrms
(1)
where: Pd = power density in the material (W/m3), at the position (x,y,z) ω = 2πΐ (Hz), f = frequency of the incident microwaves 6"eff = effective loss factor, including conductivity losses, μ" eff= imaginary part of the effective magnetic permeability Elms= local (x,y,z) electric field intensity (V/m), Hrms= local (x,y,z) magnetic field intensity (A/m),
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In case of good conductors, like metals, this conversion of the electromagnetic field energy into heat occurs only in a very thin layer, whose thickness can be described by the skin depth, in equation (2)
d = skin depth (m), σ = electrical conductivity (S) μ3 = absolute magnetic permittivity Considering a typical ISM frequency for microwaves, i.e. 2.45 GHz, the skin depth value, for most metals, is of the order of micrometers, but it can be significantly increased as temperature increases, due to the conductivity variations. Moreover, in case of conductive powder compacts immersed in relatively high intensity electromagnetic field, other phenomena can occur, leading to a more pronounced and deeper heating of the conductive material, like arcing and plasma formation1"4. Besides, the oxide layer which can be present on the metallic powders can give a further heating contribution by dielectric heating5 Thus, depending on the organic binder dielectric properties, on the particles dielectric, electric and magnetic properties and on the electromagnetic field distribution, microwaves could be successfully applied to perform rapid thermal debinding treatments on MIM green parts. In particular, microwave assisted thermal debinding can benefit from the heating selectivity, having the organic binder or the metal particles to preferentially absorb microwaves, thus accelerating the conventional process, which has to rely on heating by conduction6'7. This is particularly useful when dealing with powders and binders having low thermal conductivity, but also more conductive materials can be treated effectively, provided the maximum temperature difference inside each part is kept low. One of the main drawbacks in using microwaves to perform thermal debinding treatments lies in its intrinsically low reproducibility and strong dependence on the materials properties. Many factors affect the way a load can be heated in a microwave applicator, and small compositional unhomogeneities (variations of ε, μ and σ), or not well designed electromagnetic field distributions (spatial distribution of Επ^ and Hnns) contribute in perturbing the heat generation, according to eq. 1. In case of multiple variables and conflicting objectives, Design of Experiment (DoE) techniques can help reducing the number of experiments needed to find a possible correlation between the variables and the response of the studied system. As a matter of fact, DoE uses experimental methods to quantify interactions between factors, statistically, through observance of forced changes made methodically and experiments run in a random order, to avoid introducing bias into the results. As a result, mathematical models describing the factors (variables) interactions can be obtained, and local maxima or minima can be calculated (optimisation) and experimentally tested for validation. In the present work, DoE techniques are applied to numerical simulation, in a procedure which consists in a series of virtual experiments ("virtual", as the experiment is firstly performed trough numerical simulation), and the simulation results are used as a measure of the expected results. This approach is particularly useful when a large number of physical experiments is not feasible, due to lack of time or high experimental costs, and when optimisation procedures involve many interacting variables and multiple conflicting objectives. Moreover, numerical simulation allows to calculate the electromagnetic field distribution in each part of the system, and especially inside the materials, i.e. it is able to provide data which are practically impossible to measure on large systems, or without significant perturbation.
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Aim of the present work is the optimisation of the microwave-assisted thermal debinding of green parts obtained by CIM and MIM, coupling DoE techniques with numerical simulation, in order to achieve a highly efficient and effective process, experimentally validated. MATERIALS AND METHODS Ring-shaped CIM green parts (Bettini S.p.A., Milan, Italy) for textile use, made of AI2O3 powders, containing up to 35 wt% of binder and complex ring-shaped MIM green parts made of 430L stainless steel (PM-Tech, Fiorano, Italy), containing up to 35 wt% of binder, were used as representative samples for the optimisation of the microwave assisted debinding process. The binder of the MIM parts is made of a high percentage (80%) of water soluble compounds blend. This allows to perform a relatively rapid chemical debinding in warm water (60°C) prior to the thermal one, thus reducing the amount of binder to be removed from the green part. The samples were chosen since they present pronounced thickness and dimensional variations in radial and longitudinal direction. Dielectric properties of the CIM green parts and of the MIM green parts after chemical debinding in water and drying were measured in the 1-3 GHz range using an Agilent 8753D Vector Network analyzer connected to the Agilent 85070E Dielectric probe kit. Smooth disc-shaped samples were prepared in order to favour the probe contact with the material during measurement. The room temperature dielectric properties were used as input data for the numerical simulation of the microwave heating of the green parts in two different existing multimode applicators, operating at 2.45 GHz. The software Concerto 4.0 (Vector Fields, U.K.) was used to model the electromagnetic field distribution in the applicator varying the load configuration in terms of its spatial arrangement, number of CIM/MIM parts simultaneously treated and presence of possible auxiliary microwave absorbers. Figure 2 shows the model geometry of the two loaded microwave furnaces, one simulating a CEM-MAS 7000, and the other a self constructed8 two-ports (WG1 and WG2) microwave applicator. The room temperature equivalent dielectric properties of the materials used in the model are shown in Table I.
Figure 1. Model geometry in one possible loading condition of: a) CEM-MAS furnace with 4 CIM green parts; b) two ports applicator with 16 MIM green parts. The symbols indicate: ports position (WG1, WG2), applicator geometry (walls indicated by A), a supporting plate (P), a removable SiC Cshaped ring (C), a refractory board (R) and a closed alumina fibre lining (L).
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Table I - Model materials with lettering according to Figure 1 and equivalent dielectric properties at 2.45 GHz; (m)= measured * 1 ι ΐΐ-π 1 Part Material Dielectric properties9'11 Applicator walls (A) Perfect electric conductor Waveguides (WG1 and WG2) Perfect electric conductor Supporting plate (P) 6-J1.2 Borosilicate glass Lining (L) Alumina fibre 9.5-J0.000285 Refractory plates (R); C-shaped element (C) Alumina or SiC 8.9-J0.009 or 30-jll Load (green parts) (CIM) A1203 + 25 wt% binder 12-J0.2 (m) Load (green parts) (MIM) AISI430L + 3 wt% binder 18.7-j0.6(m) ¿
The software Design Expert v.6 was used to reduce the number of numerical simulations (virtual experiments) needed to gather information regarding the optimisation, in terms of speed, heating homogeneity and energy efficiency. The Response Surface Method was chosen, as particularly useful in the study and optimization of complex systems12. For a given part material and geometry, independent variables were: number of samples in the applicator (ranging from 6 to 20), sample minimum reciprocal distance (from 5 to 30 mm), refractory boards type (SiC, alumina), sample position in the applicator. Responses, obtained as outputs from the numerical simulation, were the Specific Absorption Rate (SAR, in W/kg) mean value and gradient and the SAR variance in each green part and in the whole load, as well as the overall dissipated power, the latter as a direct measure of the energy efficiency referred to the load. It is important to consider not only SAR variance but also its gradient, since for the samples integrity and shape retention's sake it is important that no significant heat generation difference occurs in neighbouring regions of the green part. As a matter of fact, SAR is a measure of the amount of heat generated in the load and usually only small SAR differences can be tolerated, depending on the green part thermal conductivity. Experimental validation of the optimised debinding conditions was performed in a CEM MAS 7000 Digestor (CEM, U.S.A.) for CIM parts, and in the self constructed applicator for MIM parts. The obtained brown parts were sintered in industrial kilns, and a second series of samples, conventionally debinded in a Nannetti PK70 resistance furnace, was also prepared, for the comparison's sake. Temperature was measured by a Neoptix Reflex optical fibre in the range 20-250cC, and by a Mikron sapphire fibre to assess that the samples reached and maintained the 600°C debinding temperature. In both cases, fibres were placed in contact with the central sample, but the lowtemperature one was removed soon after reaching 250°C. In principle, this temperature measurement setup does not guarantee that all the CIM or MIM parts are subjected to similar heating schedules, due to the non homogenous electromagnetic field distribution in the applicator, demonstrated by numerical simulation. For this reason, a series of preliminary heating tests, up to 250°C, were performed with optical fibres placed on 4 different samples positioned, in the optimised arrangement, at different distances from the centre of the applicator. The measured maximum temperature difference between the samples was less than 20°C during heating-up, and much lower in case of isothermal treatments or use of auxiliary microwave absorbers (SiC elements). Thus, the use of a single temperature signal to control the furnace is expected to induce only trivial errors, and for each experimental run at least one sample thermal history is known. The MIM samples (brown parts) density was measured according to ASTM B328. Brown parts were subjected to an uniaxial increasing compressive load (Instron 5567), applied on the ring basis, in order to have an estimate of the load at which rupture occurs. Surface area of the brown parts was measured by the B.E.T. method, using a Micromeritics GEMINI instrument. The sintered samples surface morphology was studied by SEM (PSEM XL 40, Philips, The Netherlands).
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RESULTS AND DISCUSSION Numerical simulation: CIM
Figure 2 - Response analysis in case of SiC (left column) or AI2O3 (right column) presence
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Numerical simulation, conducted according to the plan of virtual experiments required by the response surface method, led to the results shown in figure 2. As expected, the overall dissipated power results maximum in case of SiC element surrounding the samples, since SiC constitutes an auxiliary microwave absorber, which thus reduces power reflections. However, the presence of a heating element not directly involved in the process causes an increase of the thermal capacity of the whole load, which could lower the efficiency of heating if referred to the CIM parts only. As a matter of fact, the second row of Figure 2 shows that the power absorbed by each CIM part is almost sixteen times higher in case of absence of SiC. Rather unexpectedly, there is only a weak dependence of the power dissipated per CIM part by the number of parts constituting the load, while there is a strong influence of the reciprocal distance. Parts placed nearer tends to present a higher power generation, no matter how many parts are present in the furnace. This phenomenon can be ascribed to the peculiar distribution of the electromagnetic field inside the microwave furnace, whose electric component tends to have a higher intensity near the centre of the applicator. Thus, a reduced distance of the parts, placed in the centre, allows a better coupling of the whole load with the microwaves. The lack of dependence on the parts number could be explained considering their dielectric properties, which makes them poor microwave absorbers, meaning that the electromagnetic field results poorly attenuated when passing trough the studied CIM green parts. As far as the homogeneity indexes are concerned, i.e. the average SAR gradient and the SAR variance, their value is minimum in case of SiC element surrounding the samples. As a matter of fact, the C-shaped SiC element attenuates significantly the microwaves directed towards the CIM parts, and the resulting SAR is lower, which leads to a lower variance and average gradient. Moreover, the presence of SiC is expected to help homogenizing the temperature distribution with respect to alumina lining only. SiC presents a relatively high thermal conductivity and in case of not homogeneous heat generation due to the uneven microwave distribution, heat is rapidly conducted towards the colder regions. Thus, the presence of SiC is likely to help improving temperature distribution, even if not proved by the studied models, which refer only to heat generation. Based on these relationships, an optimised debinding treatment has been found requiring the highest homogeneity (lowest SAR variance and SAR average gradient), the maximum number of parts simultaneously treated and the higher energy efficiency, the latter with a lower relevance with respect to the homogeneity indexes. The load configuration corresponding to the optimised conditions is made of 20 CIM green parts, spaced 2 mm, surrounded by the C-shaped SiC element. This solution has a desirability of 0.504. The Corresponding simulated SAR distribution is shown in Figure 3.
Figure 3- optimised debinding conditions: calculated SAR distribution, including the SiC element
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Debinding and sintering: CIM The optimised debinding conditions were experimentally applied and the resulting processing times in case of 5 mm thick rings were 6 hours, using microwaves. It must be pointed out that industrial debinding times for such samples are in the range of 80-140 hours, depending on the shape and dimensions of the products. Trying to further reduce the microwave assisted debinding time resulted in blistering and distortion of the samples. For slightly larger samples, 13 mm thick, the optimum debinding time resulted 20 hours. It was impossible to obtain non cracked or broken samples by conventional heating when applying heating cycles similar to the microwave-assisted ones. The obtained brown parts are apparently similar to the parts which can be achieved after 140 hours in conventional furnace, but after identical conventional sintering it emerged that the surface roughness of the two samples is different: figure 4 shows that the microwave-treated samples, after sintering, present a much higher surface roughness, which could be detrimental in case of special applications, like in the textile industry. This phenomenon could possibly be reduced by extending the time of microwave exposure.
Figure 4 - SEM micrograph of the surface after conventional sintering of the samples subjected to microwave assisted debinding (left, 6 hours) and conventional debinding (right, 140 hours) Numerical simulation: MIM Numerical simulation, conducted according to the plan of virtual experiments, led to the results shown in figure 5. Overall dissipated power is once again maximum when an auxiliary absorber, like SiC, is used. However, the difference of heat generation per each ΜΓΜ part results significantly lower than in case of CIM: when the samples are leaning on SiC, their power dissipated per part is almost one fourth of the power achievable using an alumina support. This can be ascribed to the different geometry of the auxiliary absorber: in the CEM furnace used for CIM parts, the SiC element surrounds the parts, while in this case the SiC plate is simply underneath the samples. This reduces significantly the attenuation suffered from the electromagnetic field before interacting with the MIM parts. In case of MIM parts placed in the two port applicator, there is also a strong dependence of the heat generation per each part on the samples distance and quantity. The maximum dissipated power per parts can be achieved when the parts are at the maximum distance and if their number is high. In case of SiC presence, the number of samples in the applicator becomes less important. Considering the nature of the MIM parts, which present a strong microwave absorption, much stronger than the CIM ones, it is expected that a higher distance favours the microwave coupling of each part.
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Figure 5 - Response analysis in case of SiC (left column) or AI2O3 (right column) presence
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As far as the homogeneity indexes are concerned, again the use of SiC reduces both the SAR variance and its gradient. However, comparing the numerical values with the CIM ones, it is evident that there is a much stronger lack of homogeneity of heat generation in case of MIM parts. However, due to the higher thermal conductivity of the MIM parts, especially as debinding proceeds, it is expected that the samples will be able to withstand SAR gradients larger than CIM parts one. Moreover due to the use of the water soluble compound in the binder composition, only 3 wt % remains to be removed from the MIM part, and the empty spaces left by the chemically removed binder can further help the outward diffusion of the gaseous products of the oxidation and the inward diffusion of oxygen. The SiC element results effective in reducing the lack of homogeneity, which, however, results higher, independently on the supporting material, in case of many samples placed at a large distance. Numerical simulation results demonstrate the existence of conflicting objectives: the heating homogeneity is favoured by the use of SiC boards, but a large number of samples, placed at a large distance, leads to higher lack of homogeneity; the energy efficiency is maximum in case of alumina boards, since this configuration leads to the maximum of heat generation per green part; in case of SiC board, the maximum power dissipated per part is reached with many samples at a large distance. Optimisation, thus, requires a trade-off between the two conflicting objectives: heat generation homogeneity and efficiency. The optimisation of the microwave assisted de-binding process was conducted assigning the highest priority to the SAR distribution homogeneity of each single part composing the load, in order to reduce the risk of cracks or distortions caused by uneven heating during the treatment. It was considered important, but not mandatory, that the highest energy efficiency could be obtained and it was set as a preferable configuration that the maximum number of samples could be treated simultaneously. The optimum treatment resulting from the optimisation, with a desirability of 0.573, resulted to be 16 green parts, on a SiC board, placed at 20 mm distance. The corresponding SAR distribution is shown in Figure 6.
Figure 6- optimised debinding conditions: calculated SAR distribution, including the SiC board Debinding and sintering: MIM The optimised debinding conditions were experimentally applied and the resulting processing times were 120 minutes, using microwaves. It must be pointed out that industrial debinding times for such samples usually are 720 minutes. The obtained brown parts appear different from industrial
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reference samples, presenting a less oxidised surface, probably due to the reduced treatment times. For the comparison's sake, debinding treatments were conduced by conventional heating applying a 120 minutes heating cycle. The obtained samples resemble the microwave treated ones, but with more defects and tendency to cracking. Density, maximum compressive load and surface area of microwave treated samples (120 minutes=MWO), conventionally treated samples (120 minutes=C) and industrial reference samples (720 minutes= I) are shown in figure 6.
Figure 6 - density, maximum compressive load and surface area of: microwave treated samples, for 120 minutes, in the optimised conditions (MWO); conventionally treated samples, for 120 minutes (C); industrial samples, conventionally treated for 720 minutes (I) It is evident that the microwave treated samples present a much higher compressive strength, accompanied by a substantial surface area decrease, while density is almost unaffected, considering the experimental errors. This apparently unexpected behaviour can be explained considering that probably pre-sintering occurred while debinding by microwaves. As a matter of fact, it has been demonstrated in previous works2'13,14 by some of the authors that electromagnetic field concentration occurs in the space between the conductive particles, leading to a very localised overheating in the space between the particles themselves, according to eq (1). In some cases, the electric field intensity can reach the dielectric strength of the medium, leading to breakdown phenomena. This favors binder removal, but triggers also more efficient mass transport mechanisms in the liquid or vapour phase, which promote the formation of necks. This very localised overheating does not affect significantly the measured overall sample temperature, which then results much lower, as confirmed by the minimal oxidation of the samples. Selected samples deriving from microwave assisted , conventional or industrial debinding were sintered in an industrial furnace to investigate if the accelerated treatments somehow affected the microstructure or properties of the samples. The maximum tensile load bearable by the sintered parts
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was measured and no significant difference emerged: the industrial (I) samples can withstand 2445±335 N load, the conventional ones (C) can resist up to 2712±205 N and the microwave treated samples do not break up to 2939±42 N. This similarity demonstrates that microwave assisted debinding of MIM parts leads to stronger brown parts but that the obtained pre-sintering does not affect the final parts tensile properties. CONCLUSIONS The combined use of DoE techniques and numerical simulation helped determining the best sample arrangement to conduct rapid microwave assisted debinding treatments in two different microwave furnaces operating at 2.45 GHz. The study allowed to find the optimum arrangement of the microwave load in terms of number of samples, reciprocal distance and supporting material. Optimisation was conducted giving priority to heating generation homogeneity in the green parts and in the whole load and maximizing energy efficiency. Optimum treatment, either in case of MIM or CIM parts, consisted of the maximum number of samples, placed on a microwave-absorbing support (SiC), at the maximum allowable distance (in case of MIM) or at the minimum distance (in case of CIM). This different behaviour is ascribed to the different electromagnetic field distribution in the two applicators and to the different dielectric properties of the two materials. In case of CIM parts, the microwave heating in presence of a C-shaped SiC element led to a reduction from 140 to 6 hours of the processing time, but the conventionally heated samples surface, after conventional sintering, resulted smoother, and thus suitable for textile applications. The fast microwave debinding, instead, cannot be used for samples destined to textile use, since the main requirement is the absence of asperities which could damage the filaments. However, it can be successfully applied to other industrial applications, not so demanding as far as surface quality is concerned, or employed to drastically reduce the testing time (forming, debinding and sintering) required for the development of new moulds. Microwave thermal de-binding of MIM green parts, made of stainless steel containing a 3%wt binder after a pre-treatment in water to remove the water-soluble binder compounds was successfully achieved, leading to a process time reduction of more than 5 times with respect to a typical industrial cycle. Numerical and experimental validation of the model lead to the production of brown parts whose density is slightly higher than the industrial reference, and able to withstand a compressive load 5 times higher, due to pre-sintering promoted by the electric field concentration in the space between the unnecked conductive particles. The presintered brown parts can be able to withstand more severe mechanical stresses, which help maintaining their integrity during conveying or transportation prior to sintering. After conventional sintering in industrial furnace, the samples present similar mechanical properties, measured in terms of maximum bearable tensile load. ACKNOWLEDGEMENTS Authors are grateful to Dr. Luca Colombini for providing the MIM green and industrial brown parts and to Eng. Marco Montorsi for performing the ANOVA and his valuable help in the experimental validation. REFERENCES 1 A.G. Whittaker and D.M.P. Mingos, Arcing and other microwave characteristics of metal powders in liquid systems, J. Chem. Soc, Dalton Trans., 1521-1526 (2000). 2 P. Veronesi, C. Leonelli, E. Bossoli, A. Gatto, and L. Iuliano, Microwave assisted sintering of SLS green metal parts', in Proc. Sintering 2003, September 15-17, 2003, Perm State University, Pennsylvania, USA, CD-ROM (2003). 3 G. Veltl, F. Petzoldt, and P.A. Pueschner, Effects of microwaves on sintering processes, Proc. PM2004 World Congress, October 17-21, Vienna, EMPA (2004).
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M. Gupta, and E.L. Wong, Microwave and Metals, Wiley and sons (Asia), (2007). K.I. Rybakov, V.E. Semenov, S.V. Egorov, A.G. Eremeev, I.V. Plotnikov, and Y.V. Bykov, Microwave heating of conductive powder materials, J. Appl. Phys., 99, 023506 (2006). 6 P. Veronesi, M. Orlandi, C. Leonelli, and G.C. Pellacani, Microwave assisted fast dewaxing of technical ceramics, Proc. of the Intl. Conf. on microwave chemistry, 315-318 (2000). 7 K.Y.L., E.D. Case, J. Asmussen, and M. Siegel, Binder bum-out in a controlled single-mode microwave cavity, Scripta Materialia, 35 [1], 107-111 (1996). 8 P. Veronesi, C. Leonelli, C. Siligardi, and V.M. Sglavo, Microwave assisted toughening of soda-lime glasses, Proc. 9th AMPERE International Conference, 1-5 September 2003, Loughborough, U.K., 6770 (2003). 9 A.C. Metaxas, R.J. Meredith, Industrial microwave heating, Peter Peregrinus, London (1983). 10 R.F. Schiffmann, Principles of industrial microwave and RF heating, in: Microwaves: theory and applications in materials processing IV, Ceramics transactions, 80, 41-60 (1997). M. Sato, Insulation blankets for microwave sintering of traditional ceramics, in Microwaves: theory and applications in materials processing V, Ceramics transactions 111, 277-285 (2001). 12 J.S. Shang, S. Li, and P. Tadikamalla, Operational design of a supply chain system using the Taguchi method, response surface methodology, simulation, and optimization, Int. J. Prod. Res. 42 [18]. 38233849 (2004). P. Veronesi, C. Leonelli, and G. Poli, Microwave enhancement of the early stages of sintering of metallic powder compacts and metal-containing composites, in: Microwaves in the engineering and applied science, E. Caponera' Editor, 125-138 (2007). 1 C. Leonelli, P. Veronesi, L. Denti, A. Gatto, and L. Iuliano, Microwave assisted sintering of green metal parts, Journal of Materials Processing Tech., 205 [1-3], 489-496 (2008) 5
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Sintering of Biomaterials
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ANALYSIS OF SINTERING OF TITANIUM POROUS MATERIAL PROCESSED BY THE SPACE HOLDER METHOD L Reig, D. Ingeniería Mecánica y Construcción, Universidad Jaime I. Av. de Vicent Sos Baynat, s/n, 12071 Castelló de la Plana, Spain V. Amigó, D. Busquets, M.D. Salvador Instituto de Tecnología de Materiales. Universidad Politécnica de Valencia, Camino de vera s/n. 46022 Valencia, Spain J.A. Calero AMES, C/ Laurea Miró, 388, Sant Feliu de Llobregat 08980 Barcelona, Spain ABSTRACT In this work the sintering behaviour of TÍ-6A1-4V titanium alloy porous materials prepared by the space holder (SH) method have been analysed in terms of mechanical properties and microstructural characterisation. The porous materials were processed under vacuum and different sintering cycles were analysed. Other variables studied were space holder size fraction and content, and compaction pressure. The influence of these factors on bending strength was analysed. Microstructural observation was carried out by means of optical and electron microscopy in order to correlate microstructure to the observed mechanical behaviour. Results showed that different processing conditions were to be used for different SH content to obtain better properties. Furthermore, minimising the contact time between alloy powders and space holder resulted to be a critical point in the processing of these materials. INTRODUCTION Thanks to their inherent properties (corrosion resistance, biocompatibility, lightness and specific strength) the applications of Titanium and its alloys in Biomedicine are very wide1' . However, despite of all this, the stiffness of this alloy is too high (110 GPa) with regard to the human bone (10-30 GPa, cortical), which introduces some difficulties regarding its use as a implant4"5. Because ofthat, different methods to produce porous titanium have been developed in last years. These methods are intended firstly to reduce its Young's modulus, and secondly to improve osteointegration6" 9
Several manufacturing processes have been used for producing porous metallic pieces 5 ' 8 n , i.e. gas injection into the melt, plasma spray, decomposition of foaming agents, vapor deposition, sintered metal powders, space holder method... Main differences between them are the state of the raw material used (solid, liquid or gaseous) and porosity parameters (opened or closed; homogeneous or random). Because of titanium high reactivity3, a solid raw material method is needed. Between them, with the spacer holder process is possible to make components with a high level of porosity (50 - 60 %), distributed thorough all the volume, and not only near from the surface, allowing to a significant modulus reduction. Furthermore, this method has proven to be simple and easy to industrialize. The objective of the present work was to manufacture TÍ6A14V porous specimens by the space holder method, in order to achieve the best combination of properties to be used as a biomaterial. For this purpose the role of the process variables in the manufacture of porous components made from Ti6A1-4V by the Space Holder Method using ammonium carbonate (NH4HCO3) have been analyzed. These comprised sintering temperature and time, compacting pressure, size and content of space holder and were correlated to the bending strength.
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EXPERIMENTAL PROCEDURE Titanium alloy selected for this research was TÍ-6A1-4V, whereas ammonium carbonate was used as space holder (SH). The titanium alloy powder was supplied by Se-Jong Materials (South Korea). This powder is fabricated by means of the Hydride-DeHydride (HDH) technology, giving a characteristic angular morphology to the particles. The composition of the original alloy powders is given in Table I. Element
%
Table I. Composition of TÍ-6A1-4V HDH powders used in this study V Al O Zr H N Fe 6.63 4.57 0.55 max 0.03 0.3 max 0.5 max 0.03
Ti Bal.
Ammonium carbonate (Scharlau, reagent grade) was used as space holder. After previous work, appropriate ranges for the different parameters to be studied were selected12. Base material was sieved to three different size ranges (125-250 μπι, 250-500 μπι and 500-1000 μπι), and added up to 70% volume percentage, using compacting pressures of the powder mix up to 300 MPa. The sintering cycle was carried out under vacuum (10^ mbar) at 1275, 1300 or 1325°C from a period of time ranging from 1 to 4 hours, as summarized in table II.
Figure 1. SEM Micrograph showing polygonal morphology both alloy and space holder powders, a) Ti cp3. b) Ammonium carbonate, 500-1000 μπι size fraction. Table II. Variables and ranges studied. 125-250,250-500, 500-1000 Space holder size range (μπι) Vol. Pet TÍ6A14V- Vol. Pet. SH 100-0,75-25,60-40,30-70 Compacting pressure (MPa) 100,200,300 Sintering temperature (°C) 1275, 1300, 1325 Sintering time (h) 1,2,4 Alloy and SH powders were mixed in a V-type lab mixer for 20 min at 38 r.p.m. Five samples for flexural testing (dimensions 32x12x6 mm) were compacted and sintered for each combination of variables.
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After compaction, the samples were treated at 80°C for 21 hours to eliminate the space holder and then sintered. Delay time after compaction was to be reduced to a minimum after proven the deleterious effect of this factor in the mechanical behaviour of the specimens as discussed below. Mechanical properties of the materials were evaluated following ASTM E290-97a for flexural strength in all the samples and ASTM E9 89A for compression testing in some of them, using INSTRON universal testing machine model 4204. Fractured samples were observed by means of a JEOL JSM6300 scanning electron microscope (SEM). Chemical analysis to analyze carbon, oxygen and nitrogen content on both the base powders and the specimens after sintering was carried out by means of a LECO CS200 apparatus. RESULTS AND DISCUSSION There was found a maximum allowable content of space holder for the correct handling of the green samples after evaporation of the same. In fact, for ammonium carbonate contents higher than about 55%, the samples were unable to be handled without damage. Porosity of the samples produced by the space holder was even and homogeneously distributed. There were small amount of interconnected pores coming from touching particles of the space holder prior to evaporation. Also, this effect diminished with as the size fraction increased, as seen in Figure 2, because of the lower surface area of the bigger space holder particles. Furthermore, this facilitated these of being surrounded by the much smaller size of the titanium alloy particles during compaction and then after sintering, producing sound interpore walls. Porosity consisted of large pores coming from the space holder and small ones, produced inherently in the conventional powder metallurgy process. These last can be observed in any specimen, in bulk material and large pore walls, as seen on figure 2, a) to d)
Figure 2. Low magnification micrographs showing the different size of pores depending on the space holder size fraction used (40 vol. pet.) a) no space holder b) 125-250 μπι size fraction c) 250-500 μπι
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size fraction and d) 500-1000 μπι size fraction. technique used is also present in all samples.
Tiny porosity inherent to the powder metallurgy
Chemical analyses performed on different selected samples after sintering revealed important increases in carbon and oxygen content, both in samples with and without space holder. However a higher contamination levels were found on the samples as long as the addition of ammonium carbonate was higher. In fact, in table III a significant increase in carbon content is observed for specimens with 40 and 55 vol. pet.