Ceramic Materials and Components for Energy and Environmental Applications

Ceramic Transactions, Volume 210

A Collection of Papers Presented at the 9th International Symposium on Ceramic Materials for Energy and Environmental Applications and

the Fourth Laser Ceramics Symposium November 10-14, 2008, Shanghai, China

Edited by Dongliang Jiang

Yuping Zeng Mrityunjay Singh Juergen Heinrich

®WILEY A John Wiley & Sons, Inc., Publication

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Ceramic Materials and Components for Energy and Environmental Applications

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Ceramic Materials and Components for Energy and Environmental Applications

Ceramic Transactions, Volume 210

A Collection of Papers Presented at the 9th International Symposium on Ceramic Materials for Energy and Environmental Applications and

the Fourth Laser Ceramics Symposium November 10-14, 2008, Shanghai, China

Edited by Dongliang Jiang

Yuping Zeng Mrityunjay Singh Juergen Heinrich

®WILEY A John Wiley & Sons, Inc., Publication

Copyright © 2010 by The American Ceramic Society. All rights reserved.

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Contents

Preface xv

Acknowledgements xvii

I. Basic Science, Design, Modeling and Simulation

FRACTURE STATISTICS OF SMALL SPECIMENS 3 Robert Danzer and Peter Supancic

STRUCTURE AND PROPERTY OF Ti-AI-C/TiB2 COMPOSITE 13 CERAMICS

Xinmin Min, Gang Xu, and Bin-Chu Mei

THE EFFECT OF DOPED SINTERING AIDS FOR Nd(Mg0 5Ti0 5)03 17 MICROWAVE DIELECTRIC CERAMICS PROPERTIES

Kok-Wan Tay and Teng-Yi Huang

MICROWAVE DIELECTRIC PROPERTIES OF 25 (1-x)(Mg0.6Zn0.4)o.95Co005Ti03-xSrTi03 CERAMIC SYSTEM

Jun-Jie Wang, Chun-Huy Wang, Ting-Kuei Hsu, and Yi-Hua Liu

OXYNITRIDE GLASSES: EFFECTS OF COMPOSITION ON GLASS 31 FORMATION AND PROPERTIES WITH IMPLICATIONS FOR HIGH TEMPERATURE BEHAVIOUR OF SILICON NITRIDE CERAMICS

Stuart Hampshire and Michael J. Pomeroy

THE HYDROLYSIS OF ALUMINIUM NITRIDE: A PROBLEM OR AN 39 ADVANTAGE

Kristoffer Kmel and Tomaz Kosmac

PREPARATION AND COMPARISION OF TWO TYPICAL CVD FILMS 47 FROM CH4 AND C3H6 AS CARBON RESOURCES

W. B. Yang, L. T. Zhang, L. F. Cheng, Y. S. Liu, and W. H. Zhang

v

KINETIC INVESTIGATION ON THE DEPOSITION OF SiC FROM 55 METHYLTRICHLOROSILANE AND HYDROGEN

Cuiying Lu, Laifei Cheng, Chunnian Zhao, Litong Zhang, and Fang Ye

II. Nanomaterials and Nanotechnologies

SYNTHESIS OF HEMATITE-ZIRCON-SILICA NANO COMPOSITE AS 65 A NON TOXIC CERAMIC PIGMENT BY SOL-GEL METHOD

Maryam Hosseini Zori

FORMATION OF NANOCRYSTALLINE α-ALUMINAS IN 71 DIFFERENT MORPHOLOGY FROM GEL POWDER AND BOEHMITE POWDER: A COMPARATIVE STUDY

Xiaoxue Zhang, Yanling Ge, Simo-Pekka Hannula, Erkki Levänen, and Tapio Mäntylä

SYNTHESIS AND IN VITRO RELEASE OF GENTAMICIN FROM 79 CaMCM-41/PLLA COMPOSITE MICROSPHERES

Yufang Zhu and Stefan Kaskel

HIGHLY ORDERED CUBIC MESOPOROUS COBALT OXIDE BY AN 85 ACCURATELY CONTROLLED INCIPIENT WETNESS TECHNIQUE

Limin Guo, Xiangzhi Cui, and Jianlin Shi

PREPARATION OF Fe304 NANOPARTICLES BY TWO DIFFERENT 93 METHODS

Mingxin Geng, Futian Liu, and Zengbao Zhao

NANO-ZIRCONIA/MULLITE COMPOSITE CERAMICS PREPARED 99 BY IN-SITU CONTROLLED CRYSTALLIZATION FROM THE Si-AI-Zr-0 AMORPHOUS BULK

Liang Shuquan, Zhong Jie, Zhang Guowei, and Tan Xiaoping

PREPARATION AND CHARACTERIZATION OF Er:Gd203 109 POWDERS

Rong Zhang, Lian-Jie Qin, Bo Wang, Zhi-Qiang Feng, and Ru Ge

III. Ceramics in Energy Conversion Systems

CMC MATERIALS AND BIOMORPHIC SiSiC FOR ENERGY 117 APPLICATIONS

B. Heidenreich, J. Schmidt, Sandrine Denis, Nicole Lützenburger, J. Goring, P. Mechnich, and M. Schmücker

CRYSTALLIZATION, MICROSTRUCTURE AND PHYSICAL 125 PROPERTY OF NEW TYPES OF BOROSILICATE GLASS-CERAMICS

Shufeng Song, Zhaoyin Wen, Liu Yu , Qunxi Zhang, Jingchao Zhang, and Xiangwei Wu

vi · Ceramic Materials and Components for Energy and Environmental Applications

A STUDY OF Al203 AND YSZ CERAMIC SUPPORTS FOR 131 PALLADIUM MEMBRANE

M. Kitiwan and D. Atong

SYNTHESIS OF OLIVINE (LiFeP04) and Ni/OLIVINE (LiFeP04) 139 CATALYSTS FOR UPGRADING SYN-GAS PRODUCTION

D. Atong, C. Pechyen, D. Aht-Ong, and V. Sricharoenchaikul

FABRICATION AND CHARACTERIZATION OF CERMET 147 MEMBRANE FOR HYDROGEN SEPARATION

S. Vichaphund and D. Atong

POROUS CERAMICS FOR HOT GAS CLEANING; DEGRADATION 155 MECHANISMS OF SiC-BASED FILTERS CAUSED BY LONG TERM WATER VAPOUR EXPOSURE

Pirjo Laurila and Tapio Mantyla

IV. Solid Oxide Fuel Cells (SOFCs): Materials and Technologies

DEVELOPMENT OF NANO-STRUCTURED YSZ ELECTROLYTE 165 LAYERS FOR SOFC APPLICATIONS VIA SOL-GEL ROUTE

Feng Han, Tim Van Gestel, Robert Mücke, and Hans-Peter Buchkremer

DEVELOPMENT OF SINGLE-CHAMBER SOLID OXIDE FUEL 173 CELLS: PERFORMANCE OPTIMIZATION AND MICRO-STACK DESIGNS

Bo Wei, Zhe Lü, Xiqiang Huang, Mingliang Liu, Dechang Jia, and Wenhui Su

DEVELOPMENT OF BUNDLE/STACK FABRICATION 179 TECHONOLOGY FOR MICRO SOFCS

Toshio Suzuki, Toshiaki Yamaguchi, Yoshinobu Fujishiro, Masanobu Awano, and Yoshihiro Funahashi

AN OVERVIEW OF SCANDIA STABILIZED ZIRCONIA 185 ELECTROLYTE DEVELOPMENT FOR SOFC APPLICATION

K. Ukai, M. Yokoyama, J. Shimano, Y. Mizutani, and O. Yamamoto

FABRICATION OF Ni-GDC ANODE SUBSTRATE BY TAPE 191 CASTING PROCESS

Fu Chang Jing, Chan Siew Hwa, Liu Qing Lin, and Ge Xiao Ming

V. Ceramics in Environmental Applications

INFLUENCE OF LATTICE STRAIN ON THE Ce0 5Zr0 5 0 2 AND Al203 199 DOPED Ce0.5Zr0.5O2 CATALYTIC POWDERS

Chia-Che Chuang, Hsing-I Hsiang, and Fu-Su Yen

Ceramic Materials and Components for Energy and Environmental Applications · vii

MICROSTRUCTURE AND PROPERTIES OF CORDIERITE- 207 BONDED POROUS SiC CERAMICS PREPARED BY IN SITU REACTION BONDING

Shifeng Liu, Yu-Ping Zeng, and Dongliang Jiang

FABRICATION OF LIGHTWEIGHT CLAY BRICKS FROM 213 RECYCLED GLASS WASTES

Vorrada Loryuenyong, Thanapan Panyachai, Kanyarat Kaewsimork, and Chatnarong Siritai

THE PERFORMANCE OF GEOPOLYMER BASED ON RECYCLED 221 CONCRETE SLUDGE

Z.X. Yang, N.R. Ha, M.S. Jang, K.H. Hwang, B.S. Jun, and J.K.Lee

STRUCTURE AND MICROWAVE DIELECTRIC PROPERTIES OF 225 THE 2.02L¡2O-1Nb?O5-1T¡O2 CERAMICS

Qun Zeng, Wei Li, and Jing-kun Guo

PHOTOLUMINESCENCE PROPERTIES AND X-RAY 231 PHOTOELECTRON SPECTROSCOPY OF ZnO MICROTUBES SYNTHESIZED BY AN AQUEOUS SOLUTION METHOD

Liwei Lin, Masayoshi Fuji, Hideo Watanabe, and Minoru Takahashi

THE DYNAMICS OF WATER MOLECULES ON YV04 PHOTO- 237 CATALYST SURFACE

Mitsutake Oshikiri, Akiyuki Matsushita, Jinhua Ye, and Mauro Boero

PREPARATION OF SILICON CARBIDE HOLLOW SPHERES BY A 243 TEMPLATE METHOD

Lei Zhang, Jiu-jun Yang, Xue-ping Wang, and Feng-chun Wei

NONDESTRUCTIVE TESTING OF DEFECT IN A C/SÍC 249 COMPOSITE

Hui Mei, Xiaodong Deng, and Laifei Cheng

VI. Advanced Structural Ceramics

FABRICATION OF BARIUM ALUMINOSILICATE-SILICON 259 NITRIDE-CARBON NANOTUBE COMPOSITES BY PRESSURELESS SINTERING

Bo Wang, Jian-Feng Yang, Ji-Qiang Gao, and Koiichi Niihara

NONLINEAR FINITE ELEMENT ANALYSIS OF CONVECTIVE 265 HEAT TRANSFER STEADY THERMAL STRESSES IN A Zr02/FGMATi-6AI-4V COMPOSITE EFBF PLATE WITH TEMPERATURE-DEPENDENT MATERIAL PROPERTIES

Yangjian Xu, Daihui Tu, and Chunping Xiao

viii · Ceramic Materials and Components for Energy and Environmental Applications

EFFECT OF MULLITE GRAINS ORIENTATION ON TOUGHNESS 273 OF MULLITE/ZIRCONIA COMPOSITES

Y. K. Tür, A. E. Sünbül, H. Yilmaz, and C. Duran

CONTROLLED CRYSTALLISATION OF GRAIN BOUNDARY-TYPE 279 Y-SIALON GLASS TYPICAL OF THOSE FOUND IN SILICON NITRIDE CERAMICS

Michael J. Pomeroy and Stuart Hampshire

HIGH TEMPERATURE COMPRESSION CREEP BEHAVIOR OF 285 AMORPHOUS Si-B-C-N CERAMICS IN CONTROLLED ATMOSPHERE

Ravi Kumar, C. Eswarapragada, A. Zimmermann, and F. Aldinger

FABRICATION AND PROPERTIES OF SÍ3N4/BN COMPOSITE 291 CERAMICS BY PRESSURELESS SINTERING WITH Yb203-Al203-Y203 AS SINTERING ADDITIVES

Yongfeng Li, Ping Liu, Guanjun Qiao, Jianfeng Yang, Haiyun Jin, Xiangdong Wang, and Guojun Zhang

EFFECT OF B4C ADDITIONS ON THE PRESSURELESS SINTERING 297 OF ZrB2-SiC ULTRA-HIGH TEMPERATURE CERAMICS

Hui Zhang, Yongjie Yan, Zhengren Huang, Xuejian Liu, and Dongliang Jiang

TRANSLUCENT AND TOUGHENED Dy-a-SiAION CERAMICS WITH 303 LiF AS SINTERING ADDITIVE

Qian Liu, Junming Xue, and Wei He

PROPERTIES OF SILICON CARBIDE CERAMIC FROM 309 GELCASTING AND PRESSURELESS SINTERING

Jingxian Zhang, Dongliang Jiang, Qingling Lin, Zhongming Chen, and Zhengren Huang

MICROWAVE DIELECTRIC PROPERTIES OF Nb203- 315 Zn0.95Mg0.05TiO3+0.25TiO2 CERAMICS WITH Bi203 ADDITION

Ying-Chieh Lee, Hui-Hsiang Huang, Wen-Hsi Lee, Yen-Lin Huang, and Shin-Feng Chien

FABRICATION OF YTTRIA-STABILIZED ZIRCONIA CERAMICS 321 WITH RETICULATED PORE MICROSTRUCTURE BY FREEZE-DRYING

Yuan Zhang, Kaihui Zuo, and Yu-Ping Zeng

THE NOTCHED BALL TEST—A NEW STRENGTH TEST FOR 327 CERAMIC SPHERES

Peter Supancic, Robert Danzer, Zhonghua Wang, Stefan Witschnig, and Oskar Schöppl

Ceramic Materials and Components for Energy and Environmental Applications · ix

LIQUID PHASE SINTERED α-SILICON CARBIDE WITH AIN-Re203 337 AS SINTERING ADDITIVE

Yuhong Chen, Laner Wu, Yong Jiang, Youjun Lu, and Zhenkun Huang

PREPARATION OF Si3N4 CERAMICS FROM LOW-COST Si3N4 345 POWDER WITH HIGHER ß PHASE AND OXYGEN CONTENT

Yong Jiang, Laner Wu, Fei Han, and Zhenkun Huang

MICROSTRUCTURE OF LIQUID PHASE SINTERED SILICON 349 CARBIDE CERAMICS WITH HIGH FRACTURE TOUGHNESS

Yong Jiang, Laner Wu, Yuhong Chen, and Zhenkun Huang

VII. Advanced Ceramic Coatings

DEVELOPMENT OF ELECTROSPINNING TITANIA WEB FROM 357 SUSPENSION

W. D. Teng and Nassya M. Said

HIGH-SPEED ENGINEERING CERAMIC COATING BY LASER 363 CHEMICAL VAPOR DEPOSITION

Takashi Goto, Teiichi Kimura, and Rong Tu

A REVIEW OF NANOCRYSTALLINE DIAMOND/ß-SiC COMPOSITE 371 FILMS

Vadali. V. S. S. Srikanth, Thorsten Staedler, and Xin Jiang

EFFECT OF TEMPERATURE FIELD ON DEPOSITION OF BORON 379 CARBIDE COATING FORM BCI3-CH4-H2 SYSTEM

Yongsheng Liu, Litong Zhang, Laifei Cheng, Wenbin Yang, Weihua Zhang, and Yongdong Xu

EFFECT OF DEPOSITION RATE ON MICROSTRUCTURE AND 387 THERMAL CONDUCTIVITY OF YSZ FILMS PREPARED BY MOCVD

Rong Tu and Takashi Goto

VIII. Novel Processing of Ceramics

PREPARATION OF Na-ß"-AI203 GREEN BODIES THROUGH 397 NONAQUEOUS GEL-CASTING PROCESS

Xiaogang Xu, Zhaoyin Wen, Ning Li, Xiangwei Wu, Jiu Lin, and Zhonghua Gu

ROD-LIKE ß-SIALON POWDER PREPARED BY A NEW 403 N2-ASSISTED CARBOTHERMAL REDUCTION OF CARBON AND ALUMINUM NANOCASTED MESOPOROUS SILICA

Tongping Xiu, Qian Liu, Minghui Wang, and Qiang Yan

x · Ceramic Materials and Components for Energy and Environmental Applications

CERIA-STABILIZED ZIRCONIA/ALUMINA NANOCOMPOSITE 407 SUITABLE FOR ELECTROPHORETIC DEPOSITION IN THE FABRICATION OF DENTAL RESTORATIONS

Takashi Nakakmura, Hisataka Nishida, Tohru Sekino, Xuehua Tang, and Hirofumi Yatani

PREPARATION OF POROUS ALUMINA BY GEL-CASTING 413 PROCESS USING COMMERCIAL STARCHES AS A GELLING AGENT

Vorrada Loryuenyong, Ajcharaporn Aontee, Daruni Kaeoklom, and Adisorn Sridej

THE EFFECT OF POLYVINYL ALCOHOL ON THE 417 MICROSTRUCTURE OF THE POROUS Ti02 SHEETS FABRICATED BY FREEZE TAPE-CASTING

Linlin Ren, Yu-Ping Zeng, and Dongliang Jiang

PRECERAMIC PAPER DERIVED FIBRILLAR CERAMICS 421

Cynthia M. Gomes, Bjoern Gutbrod, Nahum Travitzky, Tobias Fey, and Peter Greil

IX. Composites

IN-SITU SYNTHESYS AND PROPERTIES OF TiB2/Ti3SiC2 431 COMPOSITES

Wei Gu, Jian Yang, and Tai Qiu EFFECT OF La203 ADDITIVE ON MICROSTRUCTURE AND 437 PROPERTIES OF Si3N4-AIN COMPOSITE CERAMICS

Peng Xu, Jian Yang, and Tai Qiu

VAPOR SILICON INFILTRATION FOR FIBER REINFORCED 443 SILICON CARBIDE MATRIX COMPOSITES

Qing Zhou, Shaoming Dong, Haijun Zhou, and Dongliang Jiang

TAILING PROPERTIES OF C/SiC COMPOSITES VIA 449 MODIFICATION OF MATRIX COMPOSITION

Shaoming Dong, Zhen Wang, Yusheng Ding, Xiangyu Zhang, Ping He, and Le Gao

STATUS AND CRITICAL ISSUES OF SiC/SiC COMPOSITES FOR 455 FUSION APPLICATIONS

Zhou Xingui, Yu Haijiao, Cao Yingbin, Liu Rongjun, Wang Honglei, Zhao Shuang, and Luo Zheng

PREPARATION AND CHARACTERIZATION OF C/SiC-ZrB2 467 COMPOSITES VIA PRECURSOR INFILTRATION AND PYROLYSIS PROCESS

Jun Wang, Haifeng Hu, Yudi Zhang, Qikun Wang, and Xinbo He

Ceramic Materials and Components for Energy and Environmental Applications · xi

FABRICATION OF Cf/SiC-BN COMPOSITES USING 473 POLYCARBOSILANE(PCS)- BORON-SiC FOR MATRIX DERIVATION

Zhen Wang, Shaoming Dong, Le Gao, Haijun Zhou, Jinshan Yang, and Dongliang Jiang

SINTERABILITY, THERMAL CONDUCTIVITY AND MICROWAVE 479 ATTENUATION PERFORMANCE OF AIN-SiC SYSTEM WITH DIFFERENT SiC CONTENTS

Wenhui Lu, Xiaoyun Li, Weihua Cheng, and Tai Qiu

EFFECT OF ALKALINE EARTH OXIDES ON DIELECTRIC 485 PROPERTIES OF POLYCRYSTALLINE BaTi205 PREPARED BY ARC MELTING

Xinyan Yue, Rong Tu, Takashi Goto, and Hongqiang Ru

JOINING AND INTEGRATION OF ADVANCED CARBON-CARBON 493 AND CARBON-SILICON CARBIDE COMPOSITES TO METALLIC SYSTEMS

M. Singh and R. Asthana

JOINING OF ZIRCONIUM DIBORIDE-BASED CERAMIC 505 COMPOSITES TO METALLIC SYSTEMS FOR HIGH-TEMPERATURE APPLICATIONS

M. Singh and R. Asthana

X. Bioceramics

PREPARATION AND CHARACTERISATION OF PLGA-COATED 517 POROUS BIOACTIVE GLASS-CERAMIC SCAFFOLDS FOR SUBCHONDRAL BONE TISSUE ENGINEERING

Timothy Mark O'Shea and Xigeng Miao

CERAMIC MATERIALS FOR BONE TISSUE REPLACEMENT AND 525 REGENERATION

W. Swieszkowski, Z. Jaegermann, D.W. Hutmacher, and K. J. Kurzydlowski

CHEMICAL INTERACTION BETWEEN HYDROXYAPATITE AND 531 ORGANIC MOLECULES IN BIOMATERIALS

K. Tsuchiya, T. Yoshioka, T. Ikoma, and J. Tanaka

POROUS Al203 PREPARED VIA FREEZE CASTING AND ITS 537 BIOCOMPATIBILITY

Jing Li, Kaihui Zuo, Wenjuan Liu, Yu-Ping Zeng, Fu-Qiang Zhang, and Dongliang Jiang

xii · Ceramic Materials and Components for Energy and Environmental Applications

XI. Laser Ceramics

PREPARATION OF TRANSPARENT CERAMIC Nd:YAG WITH MgO 547 AS ADDITIVE

Yongchao Li, Tiecheng Lu, Nian Wei, Ruixiao Fang, Benyuan Ma, and Wei Zhang

SYNTHESIS OF La, Yb CODOPED Y203 POWDER AND LASER 553 CERAMICS

Yihua Huang , Dongliang Jiang , Jingxian Zhang , and Qingling Lin

MICROCRYSTALLIZATION IN OXYFLUORIDE Nd3+ DOPED GLASS 561 DUE TO LASER IRRADIATION

S. González-Pérez, P. Haro-González, and I. R. Martin

OPTICAL GAIN BY UPCONVERSION IN Tm-Yb OXYFLUORIDE 567 GLASS CERAMIC

P. Haro-González, F. Lahoz, I. R. Martin, S. González-Pérez, and N. E. Capuj

FEMTOSECOND LASER MODIFICATION ON STRONTIUM 573 BARIUM NIOBATE GLASSES DOPED WITH Er3+ IONS

P. Haro-González, I. R. Martín, S. González-Pérez, L. L. Martin, F. Lahoz, D. Puerto, and J. Soli's

INFLUENCE OF POWDER TYPE ON THE DENSIFICARON OF 579 TRANSPARENT MgAI204 SPINEL

Adrian Goldstein, Ayala Goldenberg, and Meir Hefetz

SINTERING EVOLUTION OF NOVEL Nd:YAG POWDERS WITH 585 TEOS AS ADDITIVE

Ruixiao Fang, Tiecheng Lu, Nian Wei, Yongchao Li, Wei Zhang, and Benyuan Ma

THE EFFECT OF La203 ON THE PROPERTIES OF Nd3+-DOPED 591 YTTRIUM LANTHANUM OXIDE TRANSPARENT CERAMICS

Hongxu Zhou, Qiuhong Yang, and Jun Xu

Lu203:Eu3+ ULTRADISPERSED POWDERS AND TRANSLUCENT 597 CERAMICS

R.P. Yavetskiy, E. A. Vovk, M. B. Kosmyna, Z. P. Sergienko, A. V. Tolmachev, V. M. Puzikov, B. P. Nazarenko, and A. N. Shekhovtsov

FABRICATION AND SPECTROSCOPIC PROPERTIES OF Nd:Lu203 605 TRANSPARENT CERAMICS FOR LASER MEDIA

Ding Zhou, Yan Cheng, Yu Ying Ren, Ying Shi, and Jian Jun Xie

FABRICATION AND LASER PERFORMANCE OF (Ybo.osYo.gs-xLa^Os 611 CERAMICS

Qiuhong Yang, Chuanguo Dou, Hongxu Zhou.Qiang Hao, Wenxue Li, and Heping Zeng

Ceramic Materials and Components for Energy and Environmental Applications · xiii

A STUDY ON THE ZnO-AI203-Si02 SYSTEM NdF3-DOPED 617 TRANSPARENT FLUORIDE-OXIDE GLASS-CERAMICS

Jing Shao, Guohui Feng , Hongbo Zhang , Guangyuan Ma , and Chunhui Su

SYNTHESIS OF NANO-SIZED Lu203 POWDER FOR 623 TRANSPARENT CERAMICS FABRICATION USING CARBONATE DERIVED PRECURSORS

Xiaodong Li, Xudong Sun, Ji-Guang Li, Zhimeng Xiu, Di Huo, and Yan Liu

PREPARATION AND INVESTIGATION OF TRANSPARENT YAG 629 CERAMICS DOPED WITH d1 IONS

V. B. Kravchenko, Yu. L. Kopylov, S. N. Bagayev, V. V .Shemet, A. A. Komarov, and L. Yu. Zaharov

PREPARATION AND CHARACTERIZATION OF NEODYMIUM- 635 DOPED LZS TRANSPARENT GLASS-CERAMICS

Hongbo Zhang, Yimin Wang, Guang Cui, Jing Shao, Huashan Zhang, and Chunhui Su

PREPARATION AND CHARACTERIZATION OF ZnO-AI203-Si02 639 TRANSPARENT GLASS-CERAMICS

Jing Shao, Guohui Feng, Hongbo Zhang, Guangyuan Ma, and Chunhui Su

LUMINESCENCE OF Yb3+, Ho3+: Lu203 NANOCRYSTALLINE 645 POWDERS AND SINTERED CERAMIC

Liqiong An, Jian Zhang, Guohong Zhou, and Shiwei Wang

MIRRORLESS CONTINUOUS WAVE LASER EMISSION FROM 649 Nd:YAG CERAMIC FEMTOSECOND-WRITTEN WAVEGUIDES

A. Benayas, D. Jaque, A. Rodenas, E. Cantelar, L. Roso, and G. A. Torchia

Author Index 655

xiv · Ceramic Materials and Components for Energy and Environmental Applications

Preface

The global population growth and tremendous economic development has led to increasing demand for energy from all over the world as well as increasing con-cern for environment and global warming. The energy efficient and eco-friendly systems and technologies are critically needed for the further global growth and sustainable development. Advanced ceramics are enabling materials for a number of demanding energy efficient and eco-friendly applications in aerospace, power generation, ground transportation, nuclear, and chemical industries. These materi-als have unique properties such as high strength, high stiffness, long fatigue life, low density, and adaptability to the intended functions. Significant achievements have been made worldwide in the design, development, manufacturing, and appli-cation of these materials in recent years and considerable innovative research and technology development is still continuing to address technical and economic challenges.

9th International Conference on Ceramic Materials and Components for Energy and Environmental Applications (9th CMCEE) in Shanghai, China was continua-tion of series of international conferences held all over the world over the last three decades. The major goal of CMCEE was to bring together academicians, re-searchers, and end users in various disciplines from all over the world to share knowledge and exchange views leading to industrial applications of these technolo-gies. The current volume contains selected peer reviewed papers from more than 300 presentations from all over the world. The papers in this volume also highlight and emphasize the importance of synergy between advanced materials and compo-nent designs. This volume also contains selected papers from 4th International Laser Ceramics symposium which was held during the same time period. We would like to thank organizers and sponsors of this symposium.

We would like to acknowledge the financial support from Chinese Academy of Sciences, Shanghai Municipal Corporation, and Shanghai Institute of Ceramics. Our special thanks to Abhishek Singh from Case Western Reserve University, Cleveland, Ohio for the editing of the manuscripts. We would also like to thank Mr. Greg Geiger, Technical Content Manager of The American Ceramic Society for all

XV

the help in the production of this volume. We would like to thank all the contribu-tors and reviewers from all over the world.

Dongliang Jiang Yuping Zeng Shanghai Institute of Ceramics, Shanghai, China

Mrityunjay Singh Ohio Aerospace Institute, Cleveland, USA

Juergen Heinrich Clausthal University of Technology, Germany

xvi · Ceramic Materials and Components for Energy and Environmental Applications

Ac kn ow led g ernen t s

9th International Conference on Ceramic Materials and Compo- nents for Energy and Environmental Applications (9th CMCEE)

Hosted by: Shanghai Institute of Ceramics, Chinese Academy of Sciences

Endorsed by: The Chinese Ceramic Society The American Ceramic Society The European Ceramic Society The Ceramic Society of Japan The Korean Ceramic Society The Australian Ceramic Society

Conference Committee: Conference Chair (Asia): Prof. Dongliang Jiang Shanghai Institute of Ceramics, Chinese Academy of Sciences Chna

Co-Chair (America): Dr. Mrityunjay Singh Ohio Aerospace Institute NASA Glenn Research Center USA

Co-Chair (Europe): Prof. Jurgen Heinrich Clausthal University of Technology Germany

xvii

International Advisory Committee F. Aldinger (Germany) Longtu Li (China) José Ferreira (Portugal) J. Martinez-Fernandez (Spain) C.X. Ding (China) S. I. Milieko (Russia) Ludwig Gauckler (Switzerland) Dong-Soo Park (Korea) Jingkun Guo (China) Mrityunjay Singh (USA) Jürgen Heinrich (Germany) Louis Winnubst (The Netherlands) Zhanping Jin (China) Paolo Zannini (Italy) Walter Krenkel (Germany)

M.H. Lewis (U.K.) Jean Baumard (France) L.M. Manocha (India) Yibing Cheng (Australia) G.L. Messing (USA) Ruiping Gao (China) Dale E. Niesz (USA) Peter Greil (Germany) Yoshio Sakka (Japan) Stuart Hampshire (Ireland) Derek Thompson (U.K) Dongliang Jiang (China) Koichi Niihara (Japan) K. Komeya (Japan) Hasan Mandal (Turkey)

G.N. Babini (Italy) H.T. Lin (USA) I-Wei Chen (USA) S. Mathur (Germany) M.K. Ferber (USA) R. Naslain (France) Takashi Goto (Japan) Pavol Sajgalik (Slovakia) Victor Gusarov (Russia) N. Sobczak (Poland) S.I. Hirano (Japan) M. Yoshimura (Japan) A. Kohyama (Japan) L.T. Zhang (China)

4th International Laser Ceramics symposium (4th LCS)

Local Organizing Committee

Chair: Prof. Lidong Chen Shanghai Institute of Ceramics Chinese Academy of Sciences

Secretariat: Prof. Yu-Ping Zeng Shanghai Institute of Ceramics Chinese Academy of Sciences

Secretariat assistant: Mr. Hui Tong Shanghai Institute of Ceramics Chinese Academy of Sciences

Hosted by Shanghai Institute of Ceramics, Chinese Academy of Sciences

Endorsed by The Chinese Ceramic Society The American Ceramic Society The European Ceramic Society The Ceramic Society of Japan The Korean Ceramic Society The Australian Ceramic Society

xviii · Ceramic Materials and Components for Energy and Environmental Applications

Conference Chairman: S. W. Wang, Shanghai Institute of Ceramics, Chinese Academy of Sciences, China

Co-chairs and Program Committee A. A. Kaminskii, Institute of Crystallography, Russia K. Ueda, Institute for Laser Science, University of Electro-Communications, Japan Q. H. Lou, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of

Sciences, China A. Ikesue, World-Lab. Co. Ltd., Japan W. Strek, Dept of Excited State Spectroscopy, Poland Academy of Sciences,

Poland V. Lupei, Institute of Atomic Physics, Romania Bruno Le Garree, CEA CESTA, France

International Advisory Committee T. Taira, Laser Research Center for Molecular Science, Institute for Molecular

Science, Japan T. Yanagitani, Konoshima Chem Co Ltd, Takuma, Japan J. Kawanaka, Osaka University, Japan R. L. Gentilman, Raytheon Company, USA T. F. Soules, Lawrence Livermore National Laboratory, USA M. Dubinskiy, US Army Research Laboratory, USA G. J. Quarles, II-VI Corp./VLOC, USA S. B. MIROV, University of Alabama at Birmingham, Birmingham, USA G. C. Wei, Osram Sylvania Inc., USA D. L. Jiang, Shanghai Institute of Ceramics, Chinese Academy of Sciences, China Z. Y. Xu, Institute of Physics, Chinese Academy of Sciences, China D. Z. Shen, Research Institute of Synthetic Crystals, Beijing, China D. Y. Tang, School of Electrical & Electronic Engineering, Nanyang

Technological University, Singapore S. N. Bagayev, Institute of Laser Physics, Novosibirsk, Russia V. B. Kravchenko, Fryazino, FIRE RAS, Russia T. T. Basiev, Laser Materials and Technology Research Center, Moscow, Russia G. Boulon, LPCML, CNRS, Lyon, France M. Mortier, Ecole Nationale Supérieure de Chimie de Paris, France J. F. Baumard, SPCTS, Limoges, France Y. Rabinovitch, CILAS, ESTER Technopole, France H. J. Kong (Korea), Laser Science Research Lab, Korea Advanced Institute of

Science and Technology Witold Lojkowski, Institute of High Pressure Physics, Polish Academy of

Sciences, Poland R. Chaim, Department of Materials Engineering, Israel Institute of Technology,

Israel A. Krell, Fraunhofer Institute for Ceramic Technologies and Systems (IKTS),

Germany

Ceramic Materials and Components for Energy and Environmental Applications · xix

Local Organizing Committee H. J. Luo, Shanghai Institute of Ceramics, Chinese Academy of Sciences, China J. Q. Zhu, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of

Sciences, China J. T. Zhao, Shanghai Institute of Ceramics, Chinese Academy of Sciences, China Y. B. Pan, Shanghai Institute of Ceramics, Chinese Academy of Sciences, China D. Y. Jiang, Shanghai Institute of Ceramics, Chinese Academy of Sciences, China J. Zhang, Shanghai Institute of Ceramics, Chinese Academy of Sciences, China G. H. Zhou, Shanghai Institute of Ceramics, Chinese Academy of Sciences, China

xx · Ceramic Materials and Components for Energy and Environmental Applications

I. Basic Science, Design, Modeling and Simulation

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FRACTURE STATISTICS OF SMALL SPECIMENS

Robert Danzer, Peter Supancic

Institut tur Struktur- und Funktionskeramik, Montanuniversität Leoben, Peter-Tunner Strasse 5, A-8700 Leoben, Austria

and Materials Center Leoben, Roseggerstrasse 12, A-8700 Leoben, Austria. E-mail: isfk@unileoben.ac.at

ABSTRACT Strength data of brittle materials show significant scatter. Therefore designing with brittle materials has to be made with probabilistic methods. So far this is done using Weibull statistics, which is based on the weakest link hypothesis. It (implicitly) implies a particular type of defect distribution, which can be observed in many (but not in all) ceramic materials. It is shown that for very small specimens the Weibull assumptions claim unrealistic high densities of flaws. Then the flaws will interact, they are not longer statistically independent and the weakest link hypothesis is not valid. Consequently the Weibull distribution predicts too high a strength for very small specimens.

INTRODUCTION Fracture of ceramics usually initiates from flaws which are randomly distributed in the material. The strength of the specimen then depends on the length of the major flaw, which varies from specimen to specimen. The strength of brittle materials has to be described by statistical means [1 -3]. It follows from experiments that the failure probability increases with load amplitude and with size of the specimens [1-5]. The first observation is trivial. The second observation follows from the fact that it is more likely to find a major flaw in a large than in a small specimen. Therefore the mean strength of a set of large specimens is smaller than that of small specimens. This size effect of strength is the most prominent and relevant consequence of the statistical behaviour of the strength of brittle materials. Weibull developed his statistical theory of brittle fracture on the basis of the weakest link hypothesis, i.e. the specimen fails if its weakest element fails [6, 7]. In its simplest form and for an uniaxial homogenous and tensile stress state, σ, and for specimens of the volume, V, the so called Weibull distribution of the probability of failure, F, is given by:

F(a,V) = l-exp

The Weibull modulus, m, describes the scatter of strength data: the distribution is the wider the smaller m is. σ0 is the characteristic strength and V0 is the corresponding reference volume. Of course the probability of surviving (the reliability, R) is: R = 1 - F . Freudenthal [8] showed for sparsely distributed flaws, that the probability of failure only depends on the number of destructive flaws, NcS, occurring in a specimen of size and shape, S :

Fs(°) = l-exP{-Nc) ·

NcS is the mean number of destructive (critical) flaws in a large set of specimens (i.e. the value of expectation). Jayatilaka et al. [9] showed, that, for brittle and homogeneous materials, the distribution of the strength data is caused by the distribution of sizes (and orientations) of the flaws.

V[cr_ ~νΛση

3

mailto:isfk@unileoben.ac.at

Fracture Statistics of Small Specimens

A Weibull distribution of strength will be observed for flaw populations with a monotonically decreasing density of flaw sizes. Danzer et al. [10 - 12] extended these ideas to flaw populations with any size distribution and to specimens with an inhomogeneous flaw population. On the basis of these ideas a direct correlation between the flaw size distribution and the scatter (statistics) of strength data can be defined. The Weibull distribution is the state of the art statistics in the mechanical design process of ceramic components [1 - 3]. Strength testing and data evaluation are standardised. A sample of at least 30 specimens has to be tested. The range of "measured" failure probabilities increases with the sample size [3, 13] and is - for a sample of 30 specimens - very limited (it is between 1/60 and 59/60). To determine the design stress, the measured data have to be extrapolated with respect to the volume and to the "tolerated" failure probability. This often results in a very large extrapolation span [3]. In this paper the Weibull theory is applied to very small specimens. The analysis follows the ideas presented in [13]. The relationships between flaw population, size of the fracture initiating flaw and strength are discussed. It is shown that a limit for the applicability of the classical fracture statistics (i.e. Weibull statistics based on the weakest link hypothesis) exists for very small specimens (components).

FRACTURE STATISTICS AND DEFECT SIZE DISTRIBUTION The function NcS (σ) is obtained by integrating the local density, nc (σ, r), of destructive flaws

nc(a,r)= J g (a , r )da α,.(σ)

over the volume of the specimen: NcS = ¡ncdV [3, 8 - 10]. For simplicity, but without loss of generality [8], it is assumed that size and orientation of a flaw are described by a single variable (the flaw size, a). The frequency distribution of the density of flaw sizes, g(a,r), may depend on the position vector, r . A local fracture criterion (e.g. the Griffith criterion, [1, 2]) correlates stress amplitude and flaw length: the critical flaw size is the smallest flaw length, which - under the action of the stress - causes failure (the size of the smallest destructive flaw). Since ac depends on the magnitude of the applied stress, so do the values of nc and also Nc¿ (σ). For a homogeneous material loaded under uniaxial homogeneous tension the volume integral is trivial. For a flaw population with relative frequencies decreasing with a negative power the flaw size, a ,

8(a)=g0-(a/a0)"

a Weibull distribution (eq. 1) occurs [9]. This function has only two independent parameters: the exponent ( - r ) and the coefficient (g0 ·α0''). Using these assumptions and after some algebra the density of destructive flaws in terms of a critical flaw size is: n(ac) = (ac · g(ac)) / (r - 1 ) . The critical flaw size can be defined using the Griffith/Irwin criterion [1 - 3]:

c π \Υ·σ)

KIc is the critical stress intensity factor (the fracture toughness) and Y is a dimensionless geometric factor. Inserting in the above expression analytical equations for the Weibull parameters results: The Weibull modulus is only related to the path of the flaw size distribution:

m = 2 - ( r - l ) .

4 ■ Ceramic Materials and Components for Energy and Environmental Applications

Fracture Statistics of Small Specimens

The second parameter in the Weibull statistics is: V0-a0m = ( ( r - l ) / gQ -a0MKIC/ Υ^π·α0 V \

In the following a material behaving in the way as described above (eq. 1, eq. 4, etc.) is called "Weibull material". A Weibull type strength distribution also may arise for inhomogeneous stress and non uniaxial stress states (then the volume has to be replaced by an effective volume, [1 - 3]). If failure is caused by surface flaws, the volume has to be replaced by the surface [1,3, 12]. Danzer et al. have discussed the influence of other types of flaw populations (e.g. of bimodal distri-butions) on strength [11, 12]. In these cases the Weibull modulus might depend on the applied load amplitude and on the size of the specimen. Then the determination of a design stress in the usual way may become problematic. A stress and size dependent modulus occurs for materials with an R-curve behaviour [11] and may also be caused by internal stress fields [11]. It should be noted that on the basis of a small sample size, e.g. only 30 specimens, it is not possible to differentiate between a Weibull, a Gaussian, or any other similar distribution functions, as shown by Lu et al. [14] using statistical measures or by Danzer et al. [12] using Monte Carlo simulations. This is caused by the inherent scatter of the data and the difference between sample and true population. The ultimate test for the existence of a Weibull distribution is to test a material on different levels of (effective) volumes.

THE CORRELATION BETWEEN STRENGTH AND FLAW POPULATION In the following, the relationship between fracture statistics and defect size distribution is discussed for the simple case of tensile tests (uniaxial and homogeneous stress state) on a homogeneous brittle material. The tests are performed on specimens of equal size. It is assumed that the volume of the specimens is: V = V0. The number of tested specimens (the sample size) is X . In each test the load is increased up to the moment of failure. The strength is the stress at the moment of failure. In each sample the strength values of the individual specimens are different, i.e. the strength is distributed. If data determined in that way are evaluated the specimens are ranked according to their strength, / being the ranking parameter. To estimate the failure probability for an individual specimen an estimation function is used [1,3, 13]:

Fi=(i-\/2)/X , i = l,2,? X

Inserting eq. 7 into eq. 2 and making a few rearrangements, we get: NcS(σ,) = h 2X/(2X - 2i +1). In this way the mean number of critical flaws per specimen (volume VQ; stress ai) can be read from the ranking number and the sample size. For the weakest specimen (i = 1) of a sample the estimator for the probability of failing is: FY = F(al) = l/2X . That specimen contains on average NcS(al) = \ñ2[x/(2X-l)] destructive flaws. For the strongest specimen of the sample (i = X) it holdsthat: Fx = F(ax) = (2X -\)/2X and NcS(ax) = h2X. A special situation occurs if the strength is equal to the characteristic strength (i.e. for V =V0 and σ = σ0). Then the probability of failure is F(a0) = \-\/e and NcS(a0) = \ and the density of critical flaws is: nc (σ0, V0) = NcS (σ0) / V0 = 1 / V0 · If the calculations made for σ = σ0 and V = V0 are generalized for any stress value

Fracture Statistics of Small Specimens

The use of this equation opens a simple possibility to determine the frequency distribution of flaw sizes in a wide range of parameters by testing specimens of different volume. In the following these ideas are applied to describe bending test results of a commercial silicon nitride ceramic.

FRACTURE AND FLAW STATISTICS OF A TYPICAL COMMERCIAL SILICON NITRIDE MATERIAL

A typical commercial gas pressure sintered silicon nitride ceramic is used as model material. Its hardness (HV5) is 15.5 ± 0.3 MPa, the fracture toughness (SEVNB, [15, 16]) is 5.0 ± 0.2 MPaVm, the Young's Modulus is 297 ± 2 GPa and the Poisson ratio is 0.27. More details can be found in [19]. A sample of 30 bending specimens was machined out from large discs (diameter 250 mm, thickness 5 mm). The specimen preparation and the tests were done according to EN 843-1 and evaluated according to EN 843-5 [17, 18]. The characteristic strength of this sample is σ0 = 871 MPa and the Weibull modulus is m= 14.1. The effective volume [1] of the bending specimens is Vejf =V(ra+2)/ 4(m + l)2 =8.5·10"9 m3. This value is used as scaling parameter V0 = V. The Weibull distribution is shown in Fig. l.a. The measured data are nicely distributed around the straight line, which describes the Weibull distribution.

Fig. 1: a) Strength data of a silicon nitride ceramic tested in four point bending (4PB) in a Weibull plot and b) the relative frequency distribution of flaw sizes. The data points were determined by fracture experiments.

By fractographic inspection fracture [20, 21 ] origins within the volume (inclusions) were found in 3 specimens. In the other 27 specimens no clear evidence for the type of fracture origin was found. It is assumed that all flaws are small surface flaws, i.e. their geometric factor is Y = 1.12.

6 · Ceramic Materials and Components for Energy and Environmental Applications

Fracture Statistics of Small Specimens

In the following, the strength data are used to determine the frequency distribution function of the defects. Using eq. 5 the size of the critical flaw for the characteristic strength is ac0 = 26· 10"6 m. This value is used in the following for the arbitrary scaling parameter: a0 = ac 0 . For the exponent r we get using eq. 6: r= 8.05. With these data the factor in eq. 4 is: g0 = 3.21013m~4, and therefore all parameters in eq. 4 are determined. The relative frequency distribution of flaw sizes is shown in Fig. l.b. The transformation of strength into flaw size data was done using eq. 8. Again the data are nicely distributed around the straight line. This is characteristic for a Weibull material. An extremely strong dependency of the relative frequency on the critical flaw size can clearly be recognized: although the size of the critical flaws in the samples only varies by a factor of around 2.2 the corresponding relative frequency of the flaw sizes varies by a factor of around 500. That means that flaws with a radius of 21 μηι are about 500 times more frequent than flaws with a radius of 46 μπι.

SIZE EFFECT ON STRENGTH; APPLICATION TO VERY SMALL SPECIMENS As discussed in the introduction a size effect on strength exists [1 -3] , which - for a Weibull material - is described by:

Vvalm =V2-a2m

The probability of failure in a sample of specimens of volume V2 is equal to that in another sample containing specimens of volume V], if the stresses applied to the specimens are related according to eq. 9. Using the Griffith criterion we get [13]:

ac,xlaca={VxIV2)2lm

For the specimens with volume Vx the corresponding relative frequency of flaw sizes at σ = σ0 is g(ax) = gQ-{axlaQyr and the density of destructive flaws is ηα(σΟΪ,νϊ)= 1/Vlt The analogue holds for specimens of volume V2. In Fig. 2 the diameter (2ac) of the critical flaws (for the characteristic strength of the specimens) is plotted versus the (effective) volume in a double logarithmic scale (eq. 10) using the example of the silicon nitride material described above. The slope of the line is: l/(m/2) = l/(r — 1) = 1/7.05 . The dashed line describes a typical scaling parameter for the volume of the specimen. For simplicity the edge length of a cube with volume V is taken as the characteristic length: / = V1/3. For materials with a modulus m > 6, there exists a point of intersection between both lines, which is - in the selected example - at a volume of about V~ 4.210"17 m3 (this corresponds to the diameter of the critical flaw of about 2a c « 3.4 μπι). Obviously the assumption made in eq. 4 (the relative frequency of flaws follows an inverse power law) can only approximate the behaviour of materials for large flaws. It fails for very small flaws: the relative frequency goes to infinity if the flaw size goes to zero: a —* 0, g(a) —> oo [13]. At the intersection point in Fig 2, the density of dangerous flaws gets so high that the volume of the specimens is completely filled with flaws and, left of that point; the "volume of dangerous flaws" even exceeds volume of the specimens. For obvious reasons this is not possible in real materials. Another inconsistency is caused by the fact, that the derivation of the fracture statistics (eq. 1 and eq. 2) assumes non-interacting flaws [8]. This will only be true in the case of a low flaw density. If fracture statistics are applied to very small specimens made of a Weibull material the density of dangerous flaws gets high and the interaction between flaws cannot be neglected any longer [22]. For that case it can be assumed that interacting flaws link up. This would cause an upper limit for

Ceramic Materials and Components for Energy and Environmental Applications · 7

Fracture Statistics of Small Specimens

Table 1: Strength test on specimens of different size. Data set

Specimen dimension /mm

Charact. strength / MPa

2ar 0 /μηι Weibull modulus / -effective volume /

1012m3

x, /μπι

V2 ßr .O '-

4PB

45x3.95x2.98

871

52 14.1 [11-17]

8500

2041 39

A (B3B-test) 0 43;

t = 2.484

1053

36 12.4 [9-15]

280

654 18

B (B3B-test) 0 20;

t= 1.983

1123

31 15.9 [12-19]

65

402 13

C (B3B-test) 0 10.8,

t= 1.054

1226

26 21.7 [16-26]

4.3

163 6.3

D (B3B-test) 0 4.7;

t = 0.445

1275

24 17.7 [13-22]

0.6

84 3.5

4PB: four point bending test; B3B: ball on three balls test; 0 : diameter; t: thickness; 2ac0: diameter of the critical flaw corresponding to the characteristic strength, / : reference length (defined to be the third root of the effective volume). Numbers in square brackets are limits of the 90 % confidence interval.

the strength, if the distance between the flaws gets too close, say 2 - 3 times their diameter. Further strength tests (data sets A- D) were made in biaxial bending on specimens of different size. Specimens were cut from the same plates as used for the bending specimens. Tests and results are described in [19]. Key results are summarised in Table 1. The data show a significant size effect, i.e. the characteristic strength is much larger for small than for large specimens (Fig. 3). The straight line shows the size effect as predicted by eq. 9 based on the bending test data. Although the data sets A and B are in the 90 % confidence interval of the extrapolation, the sets C and D show a significantly lower strength than predicted. The behaviour of small specimens is discussed in more detail in [13]. A possible reason for this drop of strength is the fact that machining of very small specimens (as is the case of set D) is very demanding and some machining damage cannot be excluded in this case. Additional damage would cause a reduction of strength as observed in Fig. 3. Further possible reasons for the (apparent) deviation of the strength of small specimens from the Weibull behaviour are experimental measure-ment uncertainties, which become large for small specimens and which are not included in the scatter bars shown in Fig. 3. The plotted scatter bars refer to the uncertainties due to the sampling procedure (the sample is different from the underlying population, [12]). Another reason would be the interaction between flaws, as described above. The last line in Table 1 shows the ratio of the size parameter (corresponding with the effective volume; it is the length of the edge of a cube with the effective volume) divided by the diameter of the critical Griffith flaw for the characteristic strength. This ratio is larger than 10 for the sets 4PB, A and B. Here an interaction seems not to be likely. But for set D the ratio is as small as about 3. Here some overlapping of local stress field and linking of micro defects may become possible. But at present it is not clear if this really happens or not. Bazant formulated a statistical theory of fracture for quasibrittle materials [5, 23, 24]. He assumed that there exist several hierarchical orders which each can be described by parallel and serial linking of so-called representative volume elements (RVEs). For large specimens (and low probability of failures) the fracture statistics is equal to the Weibull statistics , i.e. if the specimens size is larger than 500 to 1000 times of the size of one RVE. In the actual case this is similar to the diameter of the critical flaw. For smaller specimens the volume effect disappears and the fracture

8 · Ceramic Materials and Components for Energy and Environmental Applications