Functionally Graded Materials 1996

FUNCTIONALLY GRADED MATERIALS 1996 Organized and sponsored by THE FCM FORUM THE SOCIETY OF NON-TRADITIONAL TECHNOLOGY...

Author: I. Shiota | Y. Miyamoto

29 downloads 1633 Views 45MB Size Report

This content was uploaded by our users and we assume good faith they have the permission to share this book. If you own the copyright to this book and it is wrongfully on our website, we offer a simple DMCA procedure to remove your content from our site. Start by pressing the button below!
Report copyright / DMCA form

DOWNLOAD PDF

FUNCTIONALLY GRADED MATERIALS 1996

Organized and sponsored by THE FCM FORUM THE SOCIETY OF NON-TRADITIONAL TECHNOLOGY Supported by SCIENCE AND TECHNOLOGY AGENCY, JAPAN

FUNCTIONALLY GRADED MATERIALS 1996 Proceedings of the 4th international symposium on Functionally Graded Materials, AIST Tsukuba Research center, Tsukuba, Japan, October 21-24,1996

Edited by

ICHIRO SHIOTA Department of Environmental Chemical Engineering, Kogakuin university, 2665-1, Nakanocho, Hachioji, Tokyo 192, Japan

YOSHINARI MIYAMOTO The Research center for Cyclic Loop Systems for Processing and iviaintenance. Joining and welding Research institute, Osaka university, ibaraki, Osaka 567, Japan

ELSEVIER Amsterdam - Lausanne • New York - Oxford - Shannon - Singapore - Tokyo 1997

ELSEVIER SCIENCE B.V. Sara Burgerhartstraat 25 P.O. Box 211,1000 AE Amsterdam, The Netherlands

ISBN 0 444 82548 7 © 1997, ELSEVIER SCIENCE B.V. All rights reserved. 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 or otherwise, without the prior written permission of the publisher, Elsevier Science B.V., copyright & Permissions Department, P.O. BOX 521,1000 AM Amsterdam, The Netherlands. Special regulations for readers in the u.S.A.-This publication has been registered with the copyright Clearance Center inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923. information can be obtained from the CCC about conditions under which photocopies of parts of this publication may be made in the U.S.A. All other copyright questions, including photocopying outside of the U.S.A., should be referred to the copyright owner, Elsevier Science B.V., unless otherwise specified. No responsibility is assumed by the publisher for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions or ideas contained in the material herein. This book is printed on acid-free paper Printed in The Netherlands

PREFACE

A formulated concept of functionally graded materials(FGMs) was proposed in 1984 by material scientists in Sendai area, Japan, as a means of preparing thermal barrier materials, and a coordinated research was developed in that country since 1986. The idea, that continuously changes in the composition, microstructure, porosity, etc., of these materials resulting in gradients in such properties as mechanical strength and thermal conductivity, has spreaded world-wide during the past ten years through the research. Aiming at opening channels among researchers working in state-of-the-art FGM topics and at discussing further developments in the FGM field, the first FGM symposium was held in Sendai, the birthplace of FGMs, in 1990 followed by the 2nd in San Francisco, 1992, and then the 3rd in Lausanne, 1994. Through these activities, the idea of graded structures and functions has attracted the attention of many scientists and researchers for its boundless scope in materials science and engineering. In this symposium, nearly three hundreds participants joined in order to exchange information which covers all aspects of functionally graded materials including their design, process and evaluation of structure, function, and integration, as well as applications. In particular, it should be noted that fifty five of these participants were from many countries in the worid. As a chairman of this symposium, I expect that this proceedings will be useful for FGM scientists and engineers, and will contribute to promote the research and development of FGMs in future.

V*^' Mitsue Koizumi Chairman

This Page Intentionally Left Blank

LIST OF ORGANIZING COMMITTEE

Chairman: Vice-Chairman:

Prof. M. Koizumi (President of the FGM Forum, Ryukoku University) Prof T. Hirai (Tohoku University)

Advisory Committee Dr. L. I. Anatychuk Prof F. Erdogan Dr. R. Ford Prof A. Glaeser Mr. T. Hirano Prof N. Ichinose Prof B. Ilschner Mr. R. Imoto Dr. M. Kamimoto Prof W. Kaysser Mr. T. Kurino Dr. A. Mazurenko Prof A. Merzhanov Prof Z. Munir Dr. Y. Nikolaev Dr. B. Rabin Prof S. Suresh Prof R. Watanabe Prof R. Yuan

Institute of Thermoelectricity, Ukraine Lehigh University, Pennsylvania, USA Materials Technology, New York, USA University of California, Berkeley, USA Daikin Industries, Ltd., Kusatsu, Japan Waseda University, Tokyo, Japan Swiss Federal Institute of Technology, Lausanne, Switzerland Science and Technology Agency, Tokyo, Japan Electrochemical Laboratory, Tsukuba, Japan German Aerospace Research Establishment, Koln, Germany The Society of Non-Traditional Technology, Tokyo, Japan Institute of General & Inorganic Chemistry, Kiev, Ukraine Institute of Structural Macrokinetics, Chemogolovka, Russia University of California, Davis, USA Research Institute of SIA LUCH, Moscow, Russia Idaho National Engineering Laboratory, Idaho Falls, USA Massachusetts Institute of Technology, Cambridge, USA Tohoku University, Sendai, Japan Wuhan University, Wuhan, China

Executive Committee Prof Y. Tada (Chairman) Nihon University, Chiba Dr. K. Eguchi National Aerospace Laboratory, Tokyo Dr. R. Fukuda Electrotechnical Laboratory, Tsukuba Prof Y. Miyamoto Osaka University, Osaka Dr. M. Niino National Aerospace Laboratory, Kakuda Dr. I. A. Nishida National Research Institute for Metals, Tsukuba Prof I. Shiota Kogakuin University, Tokyo Ms. S. Tsuda The Society of Non-Traditional Technology, Tokyo Dr. S. Yatsuyanagi National Aerospace Laboratory, Kakuda

Program Committee Prof. I. Shiota (Chairman) Dr. N.Cherradi Prof. M. Gasik Prof T. Kawasaki Dr. A. Kumakawa Prof Y. Miyamoto Prof J. Yoshino

Kogakuin University, Tokyo, Japan Swiss Federal Institute of Technology, Lausanne, Switzerland Helsinki University of Technology, Helsinki, Finland Tohoku University, Sendai, Japan National Aerospace Laboratory, Kakuda, Japan Osaka University, Osaka, Japan Tokyo Institute of Technology, Tokyo, Japan

Tsukuba Regional Committee Dr.R.Fukuda (Chairman) Dr.T.Fujii Mr.Y.Imai Mr.Y.Kasuga Dr.K.Kato Dr.I.Kojima Ms.M.Maeda Mr.A.Negishi Dr.I.A.Nishida Mr.Y.Nishio Mr.T.Ohta Dr.Y.Shinohara Mr.J.Teraki Mr.A.Yamamoto

ElectrotechnicalLaboratory,Tsukuba National Research Institute for Metals,Tsukuba National Research Institute for Metals,Tsukuba ElectrotechnicalLaboratory,Tsukuba National Institute of Materials&Chemical Research,Tsukuba National Institute of Materials&Chemical Research,Tsukuba The Society of Non-Traditional Technology,Tokyo Electrotechnical Laboratory,Tsukuba National Research Institute for Metals,Tsukuba Daikin Industries, Ltd.,Tsukuba Electrotechnical Laboratory,Tsukuba National Research Institute for Metals,Tsukuba Daikin Industries, Ltd.,Tsukuba Electrotechnical Laboratory,Tsukuba

CONTENTS

GENERAL TOPICS

FGM research programs in Japan -from structural to functional uses Mipmoto, Njino and Koizumi ............................................................................

1

Research program on gradient materials in Germany R&je/ and A. Neubrand.. ..............................................................................................

9

Lessons learnt in 7 years of FGM research at Lausanne

6.//schner .............................................................................................................................. PART I

15

STRUCTURAL MATERIALS

Design and Modeling

Local fields in functionally graded materials Y.D. Bi/otsky and M.M. Gasik ............................................................................................

21

Computer-aided process design for forming of pore-gradient membranes

c.w.

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

29

Mathematical model for axial-symmetrical FGM and C.C. ..................................................................................... X.D.

35

Stress analysis in a two materials joint with a functionally graded material y- Yang and D.Munz .........................................................................................................

41

Optimum design and fabrication of TiC/Ni,Al-Ni functionally graded materials Q- Shen, X.F. Tang, R. T", L.M. Zhang and R.Z. Yuan ..................................................

47

A mathematical model for particle distribution in functionally graded material produced by centrifugal cast B. Zhang, J. Zhu, Zhang, Z. Ying, H. Cheng and G.An ............................................

53

Modeling and measurement of stress evolution in FGMcoatings during fabrication by thermal spray S.Kuroda, y. Tashiro and Fukushima .........................................................................

59

Artificial neural network used for TiB,-Cu FGMdesign cao and C.C. .................................................................... Z C. Mu,Z.X.

65

Deformation analysis of graded powder compacts during sintering Shinagawa .......................................................................................................................

69

Simulation of the elasto-plastic deformations in compositionaily graded metalceramic structures: Mean-field and unit cell approaches H.E. Pettermann, E. Weissenbek and S. Suresh

75

Large deflections of heated functionally graded clamped rectangular plates with varying rigidity in thickness direction F. Mizuguchi and H. Ohnabe

81

Model investigation of ceramic-metal FGMs under dynamic thermal loading: Residual stress effect, thermal-mechanical coupling effect and materials hardening model effect O.J. Zhang, P.C. Zhai and R.Z. Yuan

87

Fractal geometry and it's implications to surface technology D.P. Bhatt, O.P. Bahl, R. Schumacher and H. Meyer

93

Database system for project of the functionally graded materials K. Kisara, A. Moro, Y.S. Kang and M. Niino 1-2

99

Fracture Analysis

Fracture mechanics of graded materials F. Erdogan Microstructural effects in functionally graded thermal barrier coatings M.J. Pindera, J. Aboudi and S.M. Arnold

105 113

Micromechanical failure criterion for FGM architecture studied via disk-bend testing of Zr02/Ni composites T. Ishizuka, Y. Ohta and K. Wakashima Thermomechanical response characteristics of ZrOg/Ni functionally graded materials: An experimental study to check model predictions T. Ishizuka, C.S. Kang and K. Wakashima Micromechanical approach to the thermomechanical analysis of FGMs S. Nomura and D.M. Sheahen Effect of gradient microstructure on thermal shock crack extension in metal/ceramic functionally graded materials A. Kawasaki and R Watanabe Thermal fracture mechanisms in functionally graded coatings K. Koklnl, Y.R. TakeuchI and B.D. Choules 1-3

123

131 137

143 149

Powder Metallurgical Process

Fabrication of AIN/W functionally graded materials K. Sogabe, M. Tanaka, T. Mlura and M. Tobloka Graded casting for producing smoothly varying gradients in materials B.R. Marple and S. Tuffe

155 159

XI

Gradient components with a high melting point difference M. Joensson, U. Birth and B. Kieback

167

Fabrication of pore-gradient membranes via centrifugal casting aw. Hong, F.Muller and P. Greil

173

Mechanical properties and microstructure of insituTiCp reinforced aluminum base FGM by centrifugal cast a Zhang, J. Zhu, Y. Zhang, Z Ying, H. Cheng and G. An

179

Dispersion and fabrication of ZrOj/SUSSIG functionally graded material by tape casting process J.G. Yeo, Y.G. Jung and S.C. Choi

185

Fabrication of ZrOj/Ni and ZrOj/AljOg functionally graded materials by explosive powder consolidation technique A Chiba, M. Nishida, K. Imamura, H. Oguraand Y. Morizono

191

Development of metal/intermetallic compound functionally graded material produced by eutectic bonding method S. Kihhara, T. Tsujimoto and Y. Tomota

197

Mechanical performance of Zr02-Ni functionally graded material by powder metallurgy J.C. Zhu, S.Y. Lee, ZD. Yin andZH. Lai

203

Fabrication of PSZ-SUS 304 functionally graded materials H. Kobayashi

209

Preliminary characterization of interlayer for Be/Cu functionally gradient materials - thermophysical properties of Be/Gu sintered compacts S. Saito, N. Sakamoto, K. Nishida and H. Kawamura 1-4

215

Deposition and Spray Process

Electrophoretic forming of functionally-graded barium/strontium titanate ceramics P. Sarker, S. Sakaguchi, E. Yonehara, J. Hamagami, K. Yamashita and T. Umegaki Processing and properties of electrodeposited functionally graded composite coatings of Ni-AI-AljOg K. Barmak, S.W. Banovic, H. M.Chan, L.E. Friedersdorf, M.P. Harmer, A.R. Marder, CM. Petronis, D.G. Puerta and D.F. Susan Functionally graded materials by electrochemical modification of porous preforms A Neubrand, R. Jedamzik and J. Rode! Thermal management of carbon-carbon composites by functionally graded fiber arrangement technique Y. Kude and Y. Sohda

221

227

233

239

Xll

Formation and properties of TiC/Mo FGM coatings T. Fukushima, S. Kuroda, S. Kitahara, K. Ishida and M. Sano Formation of a Ti-AlgOa functionally graded surface layer on a Ti substrate with the use of ultraflne particles A Otsuka, H. Tanizaki, M. Niiyama and K. Iwasaki

245

251

Oxidation-resistant SiC coating system of C/C composites N. Sato, I. Shiota, H. Hatta, T. Aoki and H. Fukuda

257

AljOg-ZrOj graded thermal barrier coatings by EB-PVD-concept, microstructure and phase stability U. Leushake, U. Schuiz, T. Krell, M. Peters and WA. Kaysser

263

Microstructure characteristic of plasma sprayed ZrOj/NiCoCrAlY graded coating Z Yin, X. Xiang, J. Zhu and Z Lai 1-5

269

Reaction Forming Process

Formation of functionally-graded materials through centrifugally-assisted combustion synthesis W. Lai, ZA. Munir, BJ. McCoy and S.H. Risbud

275

SHS - a new technological approach for creation of novel multilayered diamondcontaining materials with graded structure E.A. Levashov, LP. Borovinskaya, A.V. Yatsenko, M. Ohyanagi, S. Hosomi and M. Koizumi 283 Graded dispersion of diamond in TiB2-based cermet by SHS/dynamic pseudo isostatic compaction(DPIC) M Ohyanagi, T. Tsujikami, M. Koizumi, S. Hosomi, E.A. Levashov and l.P. Borovinskaya

289

Annealing of ceramic/metal graded materials fabricated by SHS/QP method A.N. Pityulin, Z.Y. Fu, M.J. Jin, R.Z. Yuan and AG. Merzhanov

295

Thermodynamic calculation and processing of TiBg-Cu FGM C.C. Ge, Z.X. Wang and W.B. Cao

301

Fabrication of Al-Cu system with functionally graded density profiles R. Tu, O. Shen, J.S. Hua, L.M. Zhang and R.Z. Yuan

307

AlgOgto Ni-superalloy diffusion bonded FG-joints for high temperature applications L IHeikinheimo, M. Siren and M.M. Gasik 1-6

313

Novel Process

Advances in the fabrication of functionally graded materials using extrusion freeform fabrication G.E. Hilmas, J.L. Lombardi and R.A. IHoffman

319

Novel routes to functionally graded ceramics via atmosphere-induced dopant valence gradients M Kitayama, J.D. Powers and AM Glaeser

325

The growth of functionally graded crystals by verneuil's technique M Ueltzen, J.F. Fournie, C. Seega and H. Altenburg

331

Excimer laser processing of functionally graded materials Y. Uchida, J. Yamada, Y.P. Kathuria, N. Hayashi, S. Watanabe, S. Higa, H. Furuhashi and Y. Uchida

337

Development of stainless steel/PSZ functionally graded materials by means of an expression operation K. Taka, Y. Murakami, T. Ishikura, N. Hayashi, S. Watanabe, Y. Uchida, S.Higa, T.lmura and D. Dykes 343 Microwave sintering of metal-ceramic FGM M A Willert-Porada and R. Borchert

349

Residual stress control of functionally graded materials via pulse-electric discharge consolidation with temperature gradient control H. Kimura and T. Satoh

355

Study on the composition graded cemented carbide/steel by spark plasma sintering A Ikegaya, K. Uchino, T. Miyagawa and H. Kaneta

361

Phase composition profile character of a functionally-graded AljTiOg/ZrOj-AljOa composite S. Pratapa, B.H. O'Connor and IM Low

367

The use of a functionally graded material in the manufacture of a graded permittivity element S. Watanabe, T. Ishikura, A. Tokumura, Y.Kim, N. Hayashi, Y. Uchida, S. Higa, D. Dykes and G. Touchard 373 1-7

Material Evaluation

Evaluation and modelling of the residual stresses generated on functionally graded materials - Two examples N. Cherradi, D. Delfosse and P. l\/loeckli Residual strains and stresses in an AljOg-Ni joint bonded with a composite interlayer: FEM predictions and experimental measurements B.H. Rabin, R L Williamson, H.A. Bruck, X.L. Wang, T.R. Watkins and D.R.Clarke Residual thermal stresses in functionally graded Ti-TiCx materials N. Frage, M.P. Dariel, U. Admon and A. Raveh

379

387 397

The effect of constituent and microstructure of composites on the residual thermal stress in TiC-NigAI FGMs J.H. Wang and LM Zhang 403 New application of FGMto identification of unknown multicomponent precipitates /. Itoh, H. Yamada, Y. Kojima, Y. Otoguro, H. Nakata and M. Matubara Evaluation of graded thermal barrier coating for gas turbine engine M Kawamura,Y. Matsuzaki, H. Hino and S. Okazaki Mechanical and electrical properties of multilayer composites of silicon carbide J. Hojo, F.Hongo, K. Kishi and S. Umebayashi

409 413 419

The effect of thermal shock on the thermal conductivity of a functionally graded material A J. Slifka, A Kumakawa, B.J. Filla, J.M. Phelps and N. Shimoda

425

Non-destructive evaluation of carbon fibre-reinforced structures using high frequency eddy current methods G. Mook, O. Koserand R. Lange

433

Thermal diffusivity measurement forSiC/C compositionally graded graphite materials J. Nakano, K. Fuji! and R. Yamada High-temperature ductility of TiC as evaluated by small punch testing and the effect of CrgCg additive L M Zhang, J.F. Li, R. Watanabe and T. Hirai Mechanical and thermal properties of PSZ/Ni-base superalloy composite S. Akama Processing-working stress unified analysis model and optimum design of ceramic-metal functionally graded materials P.C. Zhai, Q.J. Zhang and R.Z. Yuan

439

445 451

457

Evaluation test of C/C composites coated with SiC/C FGM, under simulated condition for aerospace application Y. Wakamatsu, T. Saito, F Ono, K. Ishida, T. Matsuzaki, O. Hamamura, Y.Sohda andYKude 463 Durability and high altitude performance tests of regeneratively cooled thrust engine made of ZrOg/Ni functionally graded materials Y. Kuroda, M. Tadano, A Moro, Y. Kawamata and N. Shimoda

469

XV

PART II 11-1

ENERGY CONVERSION, MATERIALS

ELECTRONIC AND ORGANIC

Thermoelectric Materials

Research on enhancement of thermoelectric figure of merit through functionally graded material processing technology in Japan T, Kajikawa

475

A design procedure of functionally graded thermoelectric materials J. Teraki and T. Hirano

483

Transport properties in multi-barrier systems Y. Nishio and T. Hirano

489

Theoretical estimation of thermoelectric figure of merit in sintered materials and proposal of grain-size-graded structures J. Yoshino

495

Computer design of thermoelectric functionally graded materials LI. Anatychuk and LA/. Vikhor

501

Anisotropic carrier scattering in n-type BijTejgsSeo 15 single crystal doped with HgBr^ I.J. Ohsugi, T. Kojima, H.T. Kaibe, M. Sakata and LA. Nishida

509

Percolation design of graded composite of powder metallurgically prepared SiGe and PbTe R. Watanabe, M. Miyajima, A. Kawasaki and H. Okamura

515

Design of multi-functionally graded structure of cylindrical Rl heat source for thermoelectric conversion system S. Amada, J. Terauchi and T. Senda

521

Fabrication of N-type polycrystalline Bi-Sb and their thermoelectric properties M Miyajima, G.G. Lee, A. Kawasaki and R. Watanabe

527

Development of functionally graded thermoelectric materials by PIES method A Yamamoto and T. Ohta

533

MIcrostructure and thermoelectric properties of p-type BiogSbigTea fabricated by hot pressing D.M. Lee, J.H. Seo, K. Park, I. Shiota and C.H. Lee

539

Microstructural and thermoelectric properties of hot-extruded p-type BiosSbigTeg J.H. Seo, D.M. Lee, K Park, J.H. Kim, I.A. Nishida and C.H. Lee •'• • Effect of dopants on thermoelectric properties and anisotropies for unidirectionally solidified n-BigTeg N. Abe, H. Kohri, I. Shiota and LA. Nishida Thermoelectric properties of arc-melted silicon borides L.D. Chen, T. Goto and T. Hirai

545

551 557

XVI

Graded thermoelectric materials by plasma spray forming J. Schilz, £ Muller, W.A. Kaysser, G. Langer, E. Lugscheider, G. Schiller and R.Henne • 563 Preparation of PbTe-FGM by joining melt-grown materials M Orihashi, Y, Noda, LD. Chen, Y.S. Kang, A. Moro and T. Hirai

569

Improvement and thermal stability of thermoelectric properties for n-type segmented PbTe S. Yoneda, H.T. Kaibe, T. Okumura, Y. Shinohara, Y Imai, LA. Nishida, T.Mochimaru, K. Takahashi, T. Noguchi and I. Shiota

575

Preparation and thermoelectric properties of IrSbg M Koshigoe, I. Shiota, Y. Shinohara, Y. Imai and LA. Nishida

581

p-n joining of melt-grown and sintered PbTe by plasma activated sintering Y.S. Kang, Y. Noda, LD. Chen, K. Kisara and M. Niino

587

Trial manufacture of functionally graded Si-Ge thermoelectric material T. Noguchi, K. Takahashi and T. Masuda

593

Microstructure and property of (Si-MoSigVSiGe thermoelectric converter unit J.S. Lin, K. Tanihata, Y. Miyamoto and H. Kido

599

Temperature dependence of the porosity controlled SiG/B4G+PSS thermoelectric properties K. Kato, A. Aruga, Y. Okamoto, J. Morimoto and T. Miyakawa Preparation of B4G-B system composites adding PSS and their thermoelectric properties A Aruga, K. Tsuneyoshi, Y. Okamoto and J. Morimoto

605

611

Joint of n-type PbTe with different carrier concentration and its thermoelectric properties Y. Imai, Y. Shinohara, LA. Nishida, M. Okamoto, Y. Isoda, T. Ohkoshi, T. Fujii, L Shiota and H.T. Kaibe 617 Effects of plasma treatment on thermoelectric properties of SigoGejo sintered alloys K. Kishimoto, Y. Nagamoto, T. Koyanagi and K. Matsubara Gontrol of temperature dependence of thermoelectric properties of manganese silicide by FGM approach T. Kajikawa, S. Suzuki, K. Shida and S. Sugihara Heat sensing device with thermoelectric film laid on insulated metal sheet T. Amano, N. Kamiya and S. Tokita 11-2

623

627 633

Thermionic IVIaterials

Recent developments in oxygenated thermionic converters J. L. Desplat

639

Development of refractory metal oxide collector materials and their thermionic converter performance R Fukuda, Y. Kasuga and K. Katoh

647

Thermionic properties and thermal stability of emitter with a (0001) oriented rhenium layer and graded structure M Katoh, R. Fukuda and T. Igarashi

655

Development of efficient thermionic energy converter T. Kato, K. Morimoto, K. Isogai, M. Kato, T. Fukushima and R. Fukuda

661

Radiation dose reduction by graded structures in the heat source of a ®°Sr radioisotope battery A Ohashi, K. Ueki and T. Senda

667

Output increase of thermionic energy converter due to the illumination of xenon short arc lamp Y. Shibahara and M. Kando

673

Hybrid mode concept of a thermionic converter with a FGM structured collector M Iwase and Y. Hirai

681

11-3

Electronic Materials

Thermoelectrically modulated/nanoscale multilayered gradient materials for application in the electromagnetic gun systems M A Otooni, J.F. Atkinson and LG. Brown Synthesis of In-Sb alloys by directional solidification in microgravity and normal gravity condition H. Minagawa, Y. Suzuki, K. Shimokawa, Y. Ueda, J. Nagao and J. Kawabata Full-colored zinc gallate phosphor with graded composition T. Endo, K. Uheda and H. Takizawa Synthesis and characterization of a model CuO/SnOg oxygen sensor P.J. Mailer, Z.S. Li, Q.L Guo

687

695 701 707

Fabrication of magnetic functionally graded material by martensitic transformation technique Y. Watanabe, Y. Nakamura and Y. Fukui

713

Characterization of single-crystalline Cu/Nb multilayer films by ion beam analysis S. Yamamoto, H. Naramoto, B. Tsuchiya and Y. Aoki

719

Enrichment of ^^Si by infrared laser irradiation T. Tanaka, I. Shiota, H. Suzuki and T. Noda

725

11-4

Natural, Organic and Intelligent Materials

Adaptive and functionally graded structure of bamboo S. Amada and N. Shimizu

731

XVlll

Learning about design of FGMsfrom intelligent modeling system in natural composites F.Nogata Development of the fire door with functionally graded wood H. Getto and S. Ishihara Elemental mapping of functionally graded dental implant in biocompatibility test F. Watari, A Yokoyama, F. Saso, M Uo, S. Ohkawa and T. Kawasaki Characteristics of epoxy-modified zirconium phosphate materials produced by an infiltration process AM Low, S. Yamaguchi, A. Nakahira and K. Niihara Preparation and properties of PVC/polymethacrylate graded blends by a dissolution - Diffusion method Y. Agari, M. Shimada, A. Ueda, T. Anan, R Nomura and Y. Kawasaki Preparation and properties of polyimide/Cu functionally graded material M Omori, A. Okubo, G.H. Kang and T. Hirai Smart functionally graded material without bending deformation J. Qiu, J. Tani and T. Soga

737 743 749

755

761 767 773

I. Shiota and M.Y. Miyamoto (Editors) Functionally Graded Materials 1996 ® 1997 Elsevier Science B.V. All rights reserved.

FGM research programs in Japan —from structural to functional uses Y.Miyamoto^ M.Niino^ and M.Koizumi'' ^ The Institute of Scientific and Industrial Research, Osaka University, Japan ^ National Aerospace Laboratories, Kakuda, Japan "^ Faculty of Science and Technology, Ryukoku University, Japan The FGM concept can be applied to various material fields for structural and functional uses. In Japan, several five-year programs have been conducted over the past ten years in order to develop the architecture of FGMs, and also to develop these materials for high temperature applications (e.g., components for the hypersonic space plane) and for functional applications (e.g., thermoelectric and thermionic converters). These programs are discussed with respect to the construction of FGM architecture and the future of FGMs. 1. APPLICATION OF THE FGM CONCEPT A functionally graded material (FGM) is a material in which the composition and structure gradually change resulting in a corresponding change in the properties of the material. This FGM concept can be applied to various materials for structural and functional uses. In order to create FGMs, the architecture of design, processing, and evaluation needs to be developed because no comprehensive study of such nonuniform materials has been carried out previously. The concept of integrating incompatible functions such as the refractoriness of ceramics and the toughness of metals with the relaxation of thermal stress, lead to a research project for the development of FGM architecture in 1987 [1]. In fact, it is possible to integrate a variety of dissimilar materials and properties if the thermal expansion mismatch or lattice mismatch can be relaxed and chemical compatibility can be maintained. Many applications exist that require high temperature resistance or thermal shock resistance, where the FGM concept can be applied. 2. THE DEVELOPMENT OF FGM ARCHITECTURE 2.1. For structural uses~the integration of refractoriness and toughness A five-year research program entitled "Fundamental Study on the Relaxation of Thermal Stress for High Temperature Materials by the Tailoring of Graded Structures" was established in 1987 with a total budget of 1,215 million yen under the auspice of the Science and Technology Agency. The goal was to develop the architecture of FGMs for structural uses and for high temperature components for the future hypersonic space plane. About 30 research organizations from national institutes, universities, and companies participated in the

Major Results of The FGM Program for 1987 -1991 CAD System: Inverse design model Selection of composition & microstructure Optimization of gradation Fuzzy function ,

Micromechanical Modeling: Correlation of graded microstructures & properties

Small Punch Test for Fracture energy

(3 Evaluation of Heat Shock: Xenon lamp irradiation. Burner Heating

immmm

r Stress Analysis by FEM J

Fractal & Percolation Theories: Quantitative analysis of gradation

Process Developments: CVD, PVD, PM, Plasma Spray, SHS, GalvanoForming, CVD/CVI, PM/CVD, SHS/HIP PS/GF

FGM Samples: Disk: SiC/C, PSZ/SUS, PSZ/Ni, AlN/SiC,TiC/Ni, Cr3C2/Ni, TiB2/Ni Nose cone: SiC/CC Rod: PSZ/Ni

Figure 1. Major results of the 1987-1991 FGM research program on the "Fundamental Study on the Relaxation of Thermal Stress for High Temperature Materials by the Tailoring of Graded Structures."

program as a member of one of three major groups: design, processing, or evaluation. Each investigation was coordinated for the purpose of developing the fundamental architecture of FGMs and their applications. Figure 1 illustrates the major results of the research program [2, 3]. For example, with respect to design and modeling, a CAD system using an inverse design model was developed that can produce an overall design architecture including selecting compositions and microstructures and optimizing the graded arrangement. Thermophysical parameters measured or calculated to minimize thermal stress both under process and service conditions were used for this optimization. A fuzzy function was used to combine different microstructures and properties smoothly, and a micromechanical approach to correlate graded microstructures and properties was established. Fractal and percolation theories were introduced for the quantitative analysis of the spatial change in graded microstructures, and FEM was used to model the distribution of internal stress. A number of processes were developed that use CVD, PVD, plasma spray, powder metallurgy, SHS, and galvanoforming. Several combined processes were also developed including CVD/CVI, PM/CVD, SHS/HIP, and plasma spray/galvanoforming. Various FGM samples were fabricated such as disks of SiC/C, AlN/SiC, PSZ/stainless steel, PSZ/Ni, TiC/Ni, Cr3C2/Ni, TiB2/Cu; nose cones of SiC/CC; and rods of PSZ/Ni. A small punch test was devised to evaluate the fracture energy of a thin FGM disk. Two methods were developed for the evaluation of thermal shock resistance up to 2000 K: irradiation by a strong xenon lamp and heating using an oxygen/hydrogen mixed-gas flame burner. Small combustion chambers for rocket engines made of SiC/CC by CVD/CVI and of Zr02/Ni by plasma spray/galvanoforming are undergoing combustion tests at the National Aerospace Laboratory. Although this program did not extend beyond fundamental research, it established the future direction for continuing FGM research worldwide. The FGM concept has been applied by several industries to a variety of products. To date, high performance cutting tools of TiCN/WC/Co, Ni FGM [4] and shaving blades of Al-Fe intermetallics/stainless steel FGM [5] have been commercialized. However, other commercial applications are still limited. 2.2 For functional uses ~ the direct conversion of thermal energy to electric energy Because the FGM concept was expected to be applicable to materials for functional uses as well as for structural applications, a new five-year project was initiated in 1993 with the aim of applying the FGM concept to the development of highly efficient thermionic and thermoelectric energy conversion materials. Both a themionic converter (TIC) and a thermoelectric converter (TEC) can produce electric power directly from thermal energy by the electron flow generated in space or in a solid under a high temperature differential. Figure 2 illustrates this ongoing program. In this Hybrid Direct Energy Conversion System, a TIC and a TEC are combined, and solar energy is used as the heat source to create a large temperature differential from ~2000K to ~300K. The design and optimization of the graded fields with respect both to the electronic and the elastic potential should lead to higher conversion efficiency with the relaxation of thermal stress. Thus the development of FGM architecture that would combine structural and functional properties is another goal of this program.

• C/C heat reservoir Mo radiation shield cyhnder TIC emitter Re graded coating TIC collector

SiGePbTeBi2Te3-

2.2.1. The design and processing of graded components for TICs and TECs In order to develop efficient and long lasting TICs and TECs, or combinations of these devices, an optimized system with lower heat loss and less degradation must be assembled using high performance TIC and TEC materials and devices. This will require solving various interface problems with respect to heat and carrier transportation, materials joining, thermal stress, electric contact, and insulation under extreme thermal conditions.

1) Graded C/C heat reservoir In order to achieve efficient heat accumulation and transfer from solar rays, Figure 2. A schematic illustrating the Hybrid Direct a composite FGM consisting of a 3-D Energy Conversion System. graded alignment of carbon fibers and pitch infiltration has been developed at Nippon Oil Company Ltd. [6]. Carbon fibers are highly anisotropic with respect to thermal conductivity along and across their length. Therefore, the graded alignment of fibers is designed to have a higher fiber density along the heat flux at the inner layer. A woven carbon fiber cup with a graded texture was infiltrated with pitch and hot isostatically pressed (HIP) to graphitize the pitch and densify the structure. Figure 3(a) shows the graded alignment of carbon fibers, and Figure 3(b) is a photo of the dense, graded C/C heat reservoir after HIPing. Solar rays are concentrated in this graded C/C heat reservoir by a large parabolic mirror, and the bottom and lateral sides are uniformly heated to 1680°C and 1380°C, respectively. The heat reservoir is covered with a radiat ion shield made of a highly polished Solar Rays

1380 x:

o ^^\\\\\\\

J680 Tj. As a matter of fact, the setup of the experiment imposes a constraint inasmuch as all coaxial shells have to have identical elongation at any moment, independent of their respective temperature T(r). One part of this elongation is due to the thermal expansion, the other part to the creep strain. We consider the material to be in a visco-elastic state. A transient stress distribution will therefore occur after each change of the applied stress and/or temperature profile. Only very small local deformations and, thus, short times are necessary to adjust local stresses to the general continuity condition. After the transition, the whole specimen will creep in tension under the action of a radial distribution of axial stresses a(r) which assures, respecting the creep rate equation, an equal creep rate for the whole specimen. From the viewpoint of continuum mechanics, a chemically homogeneous specimen with a radial temperature gradient is indeed a "graded material" inasmuch as each coaxial shell offers a different resistance to the applied stress and has a different time constant for relaxation. We may speak of a "thermally graded material". This work led to the idea of adapting the alloy composition to the temperature profile; this must be an iterative process, because the radial composition profile implies an inhomogeneity of thermal conductivity and is thus influencing the primary temperature profile. As a next step, it was felt that the mechanical behavior of a compositionally graded material at homogeneous temperature should be studied. Consequently, after taking up a new academic position in Lausanne, the author filed a research proposal with the Swiss National Funds [2]. This project was, incidentally, not approved in the first time, but later granted thanks to an initiative taken by Prof. V. Franzen, who at that time was the director of the National Research Program on "Materials for the Demands of Tomorrow". This was the first project in Lausanne on what later became known as FGM. The funding was modest and permitted to hire just one PhD. student, who was to be D. Delfosse, joining the lab on July 1,1985. Insights: The Japanese Model The fact that the above-mentioned Ph.D. project was part of a program on materials "for the demands of tomorrow" obliged us to go beyond the original guideline of obtaining valid scientific results and to seriously consider the potential for technical applications. Our primary concern was, however, to develop an experimental method for making fully dense continuously graded specimens in a sufficiently large number to allow for subsequent study of composition profiles, microstructures, and mechanical behavior. Although a number of alternatives were briefly studied, the process of "centrifugal powder metallurgy" as originally proposed in [2] emerged as the most efficient and reliable one. It was first published in [3,4]. At this stage, Prof. W. Bunk, at that time director of the materials division of the German Aeronautical Research establishment near Cologne (now DLR) established close contracts with the pioneering FGM research activities in Japan. These were centered at the National Aerospace Research Center (with Dr. Niino) and patronized by the Japanese Society for Non-Traditional

17 Technology. In the framework of these early contacts, a group of scientists from Japan under the direction of Prof. Koizumi visited Germany in 1988 and came subsequently also to the author's laboratory at EPFL Lausanne. This encounter proved to be of great importance for the future work of this group, The first insight gained from this visit was that the Japanese colleagues had a real national program, had a goal (at that time: thermal barrier coatings for future commercial space shuttles); they had generous funding, industrial resonance, an efficient organization - and all of this was practically nonexistent in Europe (and the rest of the world). One might illustrate this situation by depicting the Japanese FGM-program as a strong tree, and the other research activities in graded and layered structures as individual flowers distributed all over the world. By and large, this picture is still valid today. One exception - also going back to an initiative of W. Bunk - may be seen in the priority program on graded materials which has been launched in Germany in 1995 [5]. The Impact due to the discussion with the Japanese colleagues during their visit to Lausanne was reinforced by the insights which the present author gained during his participation in the first international conference on FGM in Sendai, 1990. It became clear that in order to achieve a visible result it was necessary to go beyond the limits of the traditional European university research style ("one topic - one thesis - one student"), which had, by the way, already been abandoned In other fields like nuclear physics or semiconductor research. Thus, in spite of serious difficulties to obtain funding, a small group of highly motivated young researchers [6] could be formed, which was since 1991 coordinated by N. Cherradi [7,8], who also made a very important contribution to the visibility of the FGM concept in his capacity as secretary general of the 3rd International. Symposium at Lausanne, 1994 [9]. On the other hand, the attempt to bring together a FGM Working Group on a national scale in Switzerland was not met by success. In retrospective, it appears that 2 necessary conditions for such a plan could not be established: a) to find a key person ("locomotive") of high reputation and sufficient political influence in the national community, being able to devote a major part of his energy and time to overcome the "activation barriers" during the incubation phase, and b) a fair amount of "seed money" which would enable the pioneer research group to produce preliminary results on which to base further funding applications. Again, both of these conditions were fulfilled in Japan! Functionally Graded Materials on the Marketplace During the 7-year period of FGM research in Lausanne, several other lessons had to be learnt. Among these is one which could already be sensed while working on the "thermally graded materials" project: The necessity of linking the experimental and microstructural aspects of graded (or layered) materials to the methods and results of continuum mechanics. Clearly, each inhomogeneous material is subjected to complex multi-axial stresses originating from the local differences in basic properties, in particular Young's modulus, the limit of elasticity, and the coefficient of thermal expansion. In this

18 field, it is therefore particularly important to coordinate expertise from both communities, such as demonstrated in a workshop in Davos organized in 1995 [10]. Probably the most important lesson which had to be learnt came in recent years only, and it came from outside of our community. As researchers and academic teachers in the field of materials we have to face an embarrassing fact: Materials and manufacturing actually are not in a dynamic growth phase comparable to the period 1960 to 1980. The so-called New Materials, in spite of the fascination originating in their often astonishing mechanical or electromagnetic behavior, do not find It easy to present themselves as an attractive value on the "marketplace". Too many of this kind, with sometimes exotic structures and compositions, have been announced with much ado, without finally living up to (exaggerated) expectations. The actual situation on the marketplace of our industrial society appears to be such that improved property values are no more considered to be a natural justification for Increased prices; this holds except for the field of telecommunication and for some "niche" applications which are not characteristic for the general status of materials science and engineering. Quite generally. Industrial leaders adhere more and more to a philosophy which states that the shareholder value - being their primary responsibility - is not essentially increased by research into new materials and technologies, but rather by skillful use of existing technology in combination with computerized design strategies and "lean assembly". The decisive battles, they say, are won or lost by commercial or financial moves. In parallel, governments (or parliaments ) are less and less Inclined to spend public money in scientific research as a "culture". This tendency is not likely to change in the next 10 years. As all sectors of our society, materials science and engineering must continuously discuss, redefine and justify its aims and ways. This general analysis may lead us to the following insight: If functionally graded materials, or FGM, are advertised as a wonderful new class of materials for the 21st century, they risk to be marginalized (as others before), except if they yield really spectacular results within the next few years. This is not impossible, but it Is not very likely either that this will happen. It has to be admitted that at the present stage of knowledge, graded materials with designed functions are too difficult and too expensive to make so that they cannot be produced in large quantities for industrial use; moreover, the means to ascertain their quality, reproducibility, reliability and lifetime by accepted standards with corresponding testing procedures are insufficient. There are no accepted design rules, and the community of design engineers (conservative as it is obliged to be) has little or no knowledge at all of the advantages, problems and limits of gradients in solid materials. The conclusion which we derived from this lesson at Lausanne is that the aforementioned limiting conditions reflect the reality and that a twofold strategy appears to be appropriate: I) To encourage basic studies of the physical, chemical and mechanical behavior of graded materials in general, of their cross

19 links with microstructure, and of the mechanisms likely to control possible fabrication routes. II) To consider the above-mentioned shortcomings as a challenge to resolve the associated technical problems by intelligent engineering, taking advantage of all the impressive knowledge on FGM which has been accumulated worldwide. In the following two sections, these two parallel strategies will be more closely described and discussed. Beyond FGM: The Function of Gradients in l\âteriais There is no doubt that it can be of great advantage to design technical components using different materials for load-bearing, surface-protecting, electromagnetic and decorative functions. Fiber reinforcement and the whole surface treatment as well as joining technologies are excellent examples. Likewise, many scientific and manufacturing arguments can be brought fon/vard in favor of graded transitions inside such multi-material components, instead of abrupt property changes. The FGM concept has provided a new quality of understanding of these phenomena. In particular, it has demonstrated that compositional or microstructural gradients can not only serve to avoid undesirable effects (such as tensile stress concentrations) but can also serve to generate unique positive functions: focusing light in fibers, channeling heat in computer chips, implant-tissue transitions in biomedical engineering. Many others can be conceived. In a general way, the FGM concept has taught how to optimize concentration profiles. "Opening the lens" towards a broad view on "The Function of Gradients in Materials" may thus lead beyond the current scope of FGM as a special class of materials. The topic of gradients (and also multilayers) in solid materials presents itself as a promising perspective, very timely after a century of practical exercises and after 10 years of intensive work on FGM. The whole field Is urgently needing a coherent scientific infrastructure In all its chemical, electronic, mechanical aspects. Obviously, such a methodical approach envisages and enables applications in many traditional and non-traditional fields. Where a scientific background is in demand, there is no reason to shy away from topics such as welding and brazing, segregations after casting of liquid alloys, diffusion controlled hardening of steel surfaces and glasses; the analysis needs extension into polymer systems and natural materials such as wood, bone, teeth and shells. The Engineering Chaiienge: Fast, Cheap, Reiiabie - Conclusion The present shortcomings of graded materials from an engineering point of view have been listed above. Real progress can be achieved only if the following tasks are being fulfilled: Define applications which appear adapted for gradient solutions and establish a complete list of properties needed for their satisfactory function.

20 Specify candidate systems of graded materials/structures to comply with as many as possible (If not all) of the properties in demand. Evaluate feasible fabrication routes which yield either a semifinished product (strip, wire, etc.) or even near-net shaped components. Assess the materials systems and fabrication routes envisaged with respect to quality, reproducibility, available equipment and cost per piece. Define quantitative criteria for reliability (or admissible scatter) and durability (in terms of total service time or cycle number to failure). Find or design testing methods (preferably non-destructive, and as close as possible to currently standardized methods) which appear suitable to control the validity of the above-mentioned criteria. Evaluate possible environmental hazards as well as problems related to recycling. This package of tasks contains a considerable number of problems which belong to the modern field of manufacturing science. On the other hand, manufacturing science has not yet dealt at all with graded materials. So there is an "open sky" before us, and a rich and realistic source of motivation for young scientists and engineers to join the field which has been opened by the introduction of the FGM concept. Acknowledgment The author gratefully acknowledges financial support from the Swiss National Funds and the Priority Program on Materials Research (financed by BSFIT). Moreover, he thanks his collaborators for their successful work and many colleagues In the international FGM community for enlightening discussions. References [1] U.Engel, Z. Werkstofftech. 10 (1979) 243-248, see also U.Engel, B. Ilschner, Z. Werkstofftech. 17 (1986) 299-307 [2] B. Ilschner, Projet No. 4.834-(1985) du Fonds National Suisse [3] B. Ilschner, in: M. Yamanouchi, M. Koizumi, T. Hirai, I. Shiota (Eds.), Proc. 1st Internatl. Symposium on FGM, Tokyo 1990, pp. 101-106 [4] B. Ilschner, D. Delfosse, H.U. Kuenzi, Acta metall.mater. 40 (1992) 2219-2224 [5] J. Roedel, D. Neubrandt, Proc. 4th Internatl. Symposium on FGM, Tsukuba 1996 [6] The group consisted (in alphabetical order) of K. Barthel, M. Blumm, D. Delfosse, N. Desmonts, P. Li, X. Ding, K. Dollmeier, M. Probst-Hein, W. Thiele; important advice in theoretical and experimental questions is due to M. Cans, H.U. Kuenzi, and N. Merk. Most of their work hasa been published in the Proc. 3rd Internatl. Symposium FGM, Lausanne 1994. [7] N. Cherradi , A.Kawasaki, M.Gasik, Composite Engineering. Current Trends in Composites Research, Vol.4 (1994) 883-894 [8] N. Cherradi, D.Delfosse, B.Ilschner, A. Kawasaki, Rev. de MetallurgieCIT (1996) 185-196 [9] S. Suresh, F. Needleman (Eds.): Mechanics and Physics of Layered and Graded Materials (Proc. Of an Engineering Foundation Conference Davos 1995, Special Issue of J. of the Mechanics and Physics of Solids


21

Local fields in functionally graded materials Yevgen D. Bilotsky^ and Michael M. Gasik^^ Înstitute of Physics, 252650 Kyiv, Ukraine ^Helsinki University of Technology, 02150 Espoo, Finland

The structure and basic properties of the FGMs of different systems have been studied theoretically. There is a need for theoretical basis, which would allow to describe the structure and properties of materials from first principles, while remaining simple and easy to use. In this work, such theoretical principles are suggested and their applications to heat flow and respective stress fields in FGMs are considered as example. These principles can be spread out for other materials.

1. INTRODUCTION The functionally graded materials (FGMs) are characterised by a non-linear 3D-distribution of phases and corresponding properties [1,2]. They are distinguished from isotropic materials by gradients of composition, phase distribution, porosity, texture, and related properties (hardness, density, resistance, thermal conductivity. Young's modulus, etc.) [3-5]. The FGM is characterised not only by the presence and appearance of compositional or other gradients but also by the sophisticated behaviour of FGM component in comparison with conventional (macroscopically uniform) materials. In the simplest case, the structure of a material is represented or replaced by the model-like system of a matrix with embedded particles or grains. For such composites the microstructural fields are assumed to be homogeneous, whereas for FGMs they are heterogeneous. Due to the gradients in FGMs, the "normal" approximations and models, used for traditional composites, are not directly applicable to FGM. The situation becomes even more complicated, when an FGM has gradients on several levels, i.e. macro-, micro- and nano-scale, where defects such as vacancies and dislocations start to play an important role in the transfer processes and mechanical behaviour of the specimen. The main method actually used is based on the finite element approach (FEM) and its variations. Most numerical schemes are bases on discrete distribution models, not all of them taking into account possible non-isotropic phase distribution. When this distribution is not isotropic but complies with a certain law, the same observation of measurement process yields This work was partially supported by Technology Development Centre of Finland (TEKES) and the Commission of European Communities (COST-503 project)

22

different results depending on the way the sample is placed. It is obvious that the resources necessary to define, conduct, and interpret such an analysis, are prohibitive for complex structures [4]. Another opportunity would be in a modelling of the FGM structure and in a deducing of "structure-property" relationships, e.g. as micromechanical model. This, however, is limited to simplified structures with quite a lot of assumptions. The explicit description of any material (not only FGM) from the first principles can be obtained from its consideration over an arbitrary domain, where every inclusion, defect, anisotropy, etc., is precisely taken into account [6,7,15]. This task could be solved theoretically, but its application would be certainly useless in practice, since it will involve a vast number of calculations and measurements. In this connection, there is a need for theoretical basis, which would allow to describe the structure and properties of materials from first principles, while remaining simple and easy to use. In this work, such theoretical principles are suggested and their applications to FGM heat flow and respective mechanical stresses are considered as example. These principles, however, can be spread out for other materials.

2. THEORETICAL BASIS FOR FGMS A comparative analysis of such structures, involving the evaluation of their "effective" properties, e.g. with a "pointwise" homogenisation, with some micromechanical models [4], as well as numerical methods (combined models, FEM calculations, etc.) was reported elsewhere [4,6,7]. In this respect, the following issues might be formulated for an "ideal" theory that is able to describe and to solve these problems: (i) it should be a first-principle theory, involving as less as possible or none fitting assumptions or parameters, e.g. do not require an artificial representative volume element or grid introduction; (ii) this theory should be easily applicable for any material with the structure of any complexity; (iii) the solution procedure should be rather fast and reliable, and be asymptotically free (i.e. all asymptotic cases have to have finite solutions without singularities); the calculations themselves should be "error-resistant" (e.g., a small error should be compensated on the next iteration) [6,12]. This kind of a theoretical approach could be based on the local field analysis [6,7,10,15]. The external and local fields in materials can alter in a significant way such processes as the dislocations motion, solid-state reactions kinetics, sublimation, oxidation, etc. In many of the reported findings, the attempts were made to provide basic explanations for the experimental observations, but in general they were failed to give a consistent picture of the role of the fields in the various processes [9]. For instance, one of the main problem for polycrystalline specimens is in high non-linearity and inhomogeneity of the fields between the grains and near the defects. Resulting singularities usually do not allow the differential equations to be solved numerically. 2.1. Local stress and strain fields in FGMs Let's consider first a defect-free grain of one phase in a two-phase composite. The state of this crystal can be described by the equation of motion of elastic media [11]:

23

where vector f describes the density of the volume forces, applied to crystal, p is the crystal density, ui are components of the distortion (shift) vector

= l(î^k-^^kî) \^Xk

(2)

^îj

and tensor Ojî is bound with strains e^-^ by Hooke's lawCJ-j^ — A-^^^ £^^ . Let's consider now a crystal with a dislocation. In this crystal a single-valued vector of elastic shift u can be always introduced, where function u(r) will have a leap b on the surface SQ, laying on the dislocation loop or interface D:

5u = u^ - u ~ = b

(3)

where superscripts "+" and "-" refer to values of u(r) on upper and lower side of Sj) respectively. It is important that the same form of this equation is valid for a leap of u(r) on the grain boundaries and well as interfaces in the solid. In the latter case (3) does not specify a general appearance of the leap over S, whereas strain 8^-^ keeps its continuity and remains differentiable. Thus (3) transforms to

where the quantities e^ and R can be determined from the equilibrium conditions of the force and moment, i=l,2,...,N is the number of layers in the joint, E is Young's modulus, u is Poisson's ratio and a is thermal expansion coefficient. Fkt. 3

Fkt. 2

-^ ^^

Fkt. 4

4—e-^^ ^r;/y ^ = 0) qi^y = 0)

0 OQ 0.2

0.4

0.6

0.8

I 0.2

-O a^y = h,) 1 1.0

I 0.4

i 0.6

0.8

1.0

f

f

Fig.2 (left) Stresses versus f for hi/H=O.Ol {Ei = 200 GPa, u^ =: u^ = 0.3, cî = 5 * 10-yK, E2 = 100 GPa, 0^2 = 10 * IQ-yK), Fig.3 (right) Stresses versus f for hi/H=0.05. In Fig.la, we assume that in FGM the transition function of E and a is the same, i.e., E{y) = g{EuE2, y),

a{y) = g{au 0^2, y)

(2)

where Ei, ai is the value of the material at y=0 and ui = iy2- We define a quantity

f = ^j\ifuf2,y)dy

(3)

43 with / i = 1 and /2 = 0. The quantity f is the average value of material 1 in the FGM. f = fi = 1 means that FGM is the homogeneous material 1, f = /2 = 0 means that FGM is the homogeneous material 2 and a linear transition function corresponds to f=0.5. The different value of f means that in FGM the transition function form is different. For hi/H =0.01 (H=/ii + /12), the stresses at different positions are plotted versus f in Fig.2 and for hi/H =0.05 in Fig.3. It can be seen that for a very thin FGM layer (thickness of FGM = 1% H) the transition function form in FGM has a negligible effect on the stresses, whereas for a thickness of FGM = 5%H the transition function form in FGM has a significant effect on the stresses. Generally, it is impossible to reduce the stresses at any position of the joint for thermal loading. Therefore, the optimization of the stress in a joint with FGM is not unique. There is no general rule for the optimization of the stress in a joint with FGM. The optimization of the stress in a joint with FGM may be: (a) reduce the maximum stress in the joint; (b) move the location of the maximum stress from the interface; (c) reduce the stress at a special location, e.g., at the upper surface, at the lower surface, at the interfaces, etc. Some studies on (a) and (b) have been given in [2]. As an example for the case (c), we use the transition function (coordinates see Fig.lb) E{y) = g{Ei, ^ 2 , y) = E2 - (^2 - ^1)

hi +

h2-y

(4)

where n can be varied to reach a optimization of the stress. Our aim regarding the optimization of the stress is that, for example, at the lower surface (y=0) or at the interface (y=î) the stress in the middle of the joint equals zero. We can vary n and the geometry ^ 1 , ^2, hs. For a given geometry hi, /i2, /13, the corresponding values of n have been found and they are plotted in Fig.4 for cTxiv = 0) = 0 and in Fig.5 for crîy = hi) = 0, where U—hi + /12 + ^3- From these figures we can see that for some geometries it is impossible to reach the optimization, if this transition function form is used.

n 0.125

0.25

0.375

0.5 h,/H

0.625

1

r

0.75

0.875

1.0

0.375

Fig.4 (left) The possible n for a^{y = 0) = 0 {h2 = H - hi - /13). Fig.5 (right) The possible n for aîy — hi) — 0.

0.5 h,/H

0.625

0.75

0.875

1.0

44

3

Stresses near t h e free edges of a joint with F G M

For thermal loading, the stress function $ in a homogeneous material must satisfy V^^ + V2(gT) = 0

(5)

aE for plane stress aE ^ Î 7(1-^) ^ ^ for plane strain ' where q is independent of the coordinates and T is the temperature change. Now, in a graded material (i.e. q is not a constant, but q=q(x,y) =q(f, ^)), we can imagine that qT is the effective temperature change and the material is homogeneous. Under this assumption, we obtain the same equation as Eq,(5) for the stress function in a graded material. To get the solution for $, the Mellin transform method is used. The Mellin transform of a function (f, 6) is defined as _{

—\

roo

^s,e)=

/

^{r,e)f^'-^^df

(6)

Jo

where s is the Mellin transform parameter and f = r/L, L is a characteristic length of the joint. The basic equation Eq.(5) in the Mellin domain is [«' + ^ ] [ ( ^ + 2)' + ^]Ms,

with

0) + [is + 2f + ^]f{s

f{s + 2,6>) = / q(f, e)Tr^'-^^^df = To J

+ 2,9) =0

(7)

q{f, e)f^'^Ûf,

(8)

0

where the temperature change is T=To for f < RQ and T=0 for f > RQ. Its solution is

^,{s,e) = ¥,{s,o) + ^'(s,e) with

4^(5,9) = Aks''^ + AkC-''^ + Bke'^'"^^^^ + 5^6-^(^+2)^

4^^(s, 0) = — Lin{se) jfk{s

(9) ^^Ô)

+ 2, e)cos{sO)de - cos{se) ffk{s -h 2,0)sin{se)de\ (11)

where the coefficients Ak and Bk can be determined from the boundary conditions (k=l, 2 for material 1 and 2). For the case of a polymonial as the transition function, i.e. E{f, e) = A-\- Bfsm{0) + Cr^ sin2(6>) + Df^ sm\0) + Er^ sin^(l9) + ... the stresses in the Mellin domain are obtained [3] as

(12)

45 where Sn is the solution of A*A2 = 0 and dijk{sn, 0) / 0, The stresses in a polar, coordinate system can be calculated from

Sn) ,GPa 0^2 = [2.5 -h 5f'^si'n?{e)] * 1 0 - 7 ^ ^ . The materials data for example 2 are El = 100 GPa, 1^1 = 1 = 1^2,^1 = 2.5 * I O ' V K ,

E2 = 100 + 50f5m(i9),GPa 0.2 = [2.5 + bf^sinîO)] * 1 0 - V K .

For example 1 we have ^ = 0, therefore, the poles of aij{s, 6) are independent of u. They are s = -2, -3, -4, -5, -6, ..,, where s=-2, - 3 , -5 are the first-order poles of Gij{s,9) and

46 s=:-4, -6 are the second-order poles of dij{s,6). The stresses calculated from Eq.(16) and by FEM are compared and given in Fig,6. For example 2 we have B ^ 0, therefore, the poles of dij{s,6) depend on the values of v and B, They are s== -2, -3, -4, -4.1529, -5, ..., where s=-2, -4.1529 and -5 are the first-order poles, and s=-3 and -4 are the second-order poles of cFij{s, 9). The stresses calculated from Eq.(16) and by FEM are compared and given in Fig.7. From Figs.6 and 7 we can see that in the range of r/L < 0.1 Eq.(16) can describe the stresses very well. 0.030-

O.OlbO-i

0.020-

0.0100-

—™««niaBBB»»n»™«»»»R'^

0.00500.010H \

0.0000-

CO

o.oooH -0.0050-0.010-

...,.^V \

-0.0100o—

-0.020- TTT 1 lE-04

1 I II 1 lE-03

1 I I I 1 1 I Ir 1E-02 1E-01 1E+00 r / L along the line 8 = 0

p -0.01501E-04

"' "^'^1

1—TTT

1E-03

BBiuiiuuumMiii!™::::;^^

^

r-

m — 1 — 1 -I 11—^^t—1 1 11 1E-02 1E-01 1E+00 r / L along the line 8 = - 4 5

Fig.6 Stress distribution along ^ = 0 and 9 =-45 for example 1. U.UJUUt WHiHHHtHtfWHHBIfflgmfflîqw^ge

0.0200-|

0.0250-

0.0150-

^

^

\

™ ^ 6

/

0.0100-

0.0200-

0.00500.01500.0000-

\

0.0100-

5^ a

-0.00500.0050-

-0.0100o

-0.0150- J

0.0000-^ -0.0050- W T

. 1E-03 2

t-r-n 1 r—r-n \ 1^• i - n 4 lE-02 2 4 1E-01 2 4 1E+00 r / L olong the line 8 = 0

C «•>,

lE--03 2

•W 1\ ^ 4

1E-02 2 4 lE-01 2 4 1E+00 2 r / L along the line 8 = - 4 5

Fig.7 Stress distribution along ^ = 0 and 9 = - 4 5 for example 2. Acknowledgement:The financial support of the Deutsche Forschungsgemeinschaft is gratefully acknowledged. The authors would like thank Mr. Schaller for some calculations.

References 1. D.Munz, Y.Y.Yang, Proc. of 3rd Int. Symposium on Structural and Functional Gradient Materials, 1994, pp.465-471. 2. Y.Y.Yang, D.Munz, Fracture Mechanics: Vol.26, ASTM STP 1256 (1995) pp.572-586. 3. Y.Y.Yang, Stress analysis in a two materials joint with a functionally graded material under thermal loading by using the Mellin transform, submitted to J. Solids & Structures.


47

Optimum Design and Fabrication of TiC/NijAl-Ni Functionally Graded Materials Q. Shen , X.-F. Tang , R. Tu , L.-M. Zhang and R.-Z. Yuan State Key Lab. of Materials Synthesis and Processing, Wuhan University of Technology, Hubei, 430070 P.R. China

TiC/Ni3Al-Ni system was chosen for the potential use as the first wall materials of thermonuclear experimental reactors. The residual thermal stresses during fabrication were calculated by finite element inethod. Based on the consideration of minimum stress, minimum ratio of stress to fracture strength and proper distribution of thermal stress in pure TiC side, the optimum design with the distribution exponent P=1.6 was reached. According to the design result, TiC/Ni3Al-Ni FGM samples were then successfully fabricated.

L IISTRODUCTION In recent years functionally graded materials(FGMs) have received considerable attention. Ceramic/metal type FGMs are believed to be hold promise in applications for advanced technology, especially in aerospace and nuclear engineering, where the materials encounter high heat loads[l-2]. On the basis of the traditional cermet TiC-Ni, we chose TiC/NiaAl-Ni FGM system, which was composed of Ni as the metal phase, TiC as the ceramic phase and TiC-Ni3 Al composites with various Ni3Al ( has a lower thermal expansion coefficient and a better wettability with TiC[3] ) volume fraction as the graded interlayers.

2. EXPERIMENTS AND CALCULATION Pure metal Ni and TiC-Ni3Al composites with Ni3Al volume fraction of 0, 20%, 40%, 60%, 80%, 100% were sintered by HP method for 2h at ISOO^C and 30MPa under Ar gas protection( the same as the conditions for sintering TiC/'Ni3Al-Ni FGMs). The samples were then cut and ground into 36x4x3mm strips, the mechanical properties including Young's modulus, Poisson ratio and the fracture strength, were measured by a four-point bending test method. The thermal expansion coefficient was tested by a non-loaded thermal dilatometer. The tested v ^ e s are indicated in Table 1.

48 Table 1 Properties of Ni and TiC-Ni3Al composites with various Ni3Al volume fraction Ni3Al volume fraction (%)

0

Young's modulus (GPa) Poisson ratio Fracture strength (MPa) Thermal expansion coefficient (xl0"%-l)

20

40

60

320

318

340

267

0.195

0.195

317

587

0.225 1351 9.15

0.253 1261 9.46

7.40

7.55

80

100

100(Ni)

266

199

206

0.270 0.295 0.30 1468 1346 1322 11.46 11.90 13.30

The residual thermal stresses were calculated by a finite element computer programme Super-Sap. The model is 10mm in diameter, 6mm in thickness and has 11 graded layers. Due to the axisymmetric problem, an axisymmetric finite element modle is used and 1/4 part of the material is considered. The FE model includes 1200 elements and 1275 nodal points. The thermal load is raised from the sintering temperature 1300 ^C to room temperature. Moreover, an insulated heat condition is considered at the flank boundary. The compositional distribution of the metal and ceramic in the graded layers was assumed to take the form C=(x/d)P[4], where C is the volume fraction of Ni3Al, d is the distance to the graded layers, x is the layer location coordinate, and P is the distribution exponent. In the calculation, the material properties at the graded layers were obtained by using the tested values.

3. THERMAL STRESS ANALYSIS AND OPTIMIZATION 3.1. Thermal stress analysis of TIC-Ni two layers material It can be seen from Table 2 that the stresses at the metal-ceramic interface are extremely high. For the radial stress GJ^ and the circumferential stress 099, the metal side is in compressive state and the ceramic side in tensile state, which due to the difference thermal expansion coefficient. The stress state of the axial stress a^z in Z-axis direction is quite the contrary. Such large stresses at the interface can easily lead to rupture failure of the two layers material. Also, the experimental results prove to be the same. Table 2 Calculated results of the thermal stress for TiC-Ni t(vo layers material an- (MPa) Metal side Ceramic side

-1930 1550

099 (MPa) -1930 1550

GZ^

(MPa)

1870 -837

49 3.2. Thermal stress analysis and optimization of TiC/NijAl-Ni FGMs The thermal stresses of TiC/Ni3 Ai-Ni FGMs were calculated for different exponent values ranging from 0.6 to 2.2. Fig.l presents the tensile stress a^r and Cjri with respect to the distribution exponent P. From Fig. 1, it is seen that within the exponent values tfie thermal stress in any of the FGMs is relaxed compared with that in the two layers material. In particular, when P=1.8, the stress a^- is a minimum (280MPa), and the stress relaxation is a maximimi, up to 75%, whereas the stress Cjz reaches the minimum value (290MPa) at P=1.6, the stress 1000

1.2 1.6 diBtributtonttxponontP

2

24

Fig. 1 Relationship between tensile stress and the distribution exponent P

1.2

1.6

2.4

oiscnxjDon oixporioni r

Fig. 2 Relationship between the ratio of stress to fracture strength and the distribution exponent P

50 relaxation in FGM is nearly 80%. According to the minimum stress rule, P=1.6~1.8 can be the optimum points for the FGM compositional design. It k noticed that the FGM interlayers have differentfracturestrength. If the thermal stress occurs at any interlayer was not optimized, the FGM could be damaged. By examining the ratio of the stress to the corresponding layer fracture strength, an optimum P can be obtained. From Fig. 2, the ratio for c^ is found to reach its minimum value (0.27) at P=1.8, but for Oj^ it is at P=1.4. Therefore, the optimum result for the FGM compositional design is P=1.4~1.8. To verify the reasonableness of the FGM compositional optimum design, one must also check the stress state at the pure ceramic side since it is usually damaged first. Fig. 3 provides the relationship between the stress at the TiC side and the exponent P. From Fig. 3, it is observed that the residual stress at the pure TiC side decreases with increasing of P, and it experiences a transition at P=1.6 from tensile to compressive, where the stress is zero. This is favourable for FGM fabrication. Therefore, P=1.6 is indeed an optimum design for TiC/Ni3Al-Ni FGMs. 800

•soo

dtatributlonflxponontP

Fig. 3 Relationship beween the stress in pure TiC side and the distribution exponent P 4 FABRICATION Table 3 Constituent (vol%) and density (g/cm^) of FGM layers layer Ni3Al TiC Density

1 100(Ni) 0 8.90

2

3

97.5 92.4 2.5 7.6 7.47 7.23

4

5

6

7

8

9

10

11

85,4 76.9 67.0 55.8 43.5 30,0 15.5 14.6 23.1 33.0 44.2 56.5 70.0 84.5 7.13 6.94 6.67 6.52 6.21 5.85 5.47

0 100 5.03

51 According to the optimum design result P=1.6, the constituent and density of each layer is determined, as shown in Table 3. The mixtures were prepared by mixing a 5pm average sized Tie powder, 5S3puxk sized Ni3Al and Ni powder, fhen sintered under the same conditicms stated previously.

(a) Layers near the metal side (b) Layers near the ceramic side (c) the 4th and 5th layers

Fig. 4 SEM micrographs of the FGM Fig.4 gives the SEM micrographs of the FGM specimen. From Fig.4a,4b, the layered projSle is clear. The SEM micrograph of the FGM interface between the 4th and the 5th layer is shown in Fig. 4c, the transition crossing the layer interface is smooth, no cracks and pores are observed. It is indicated that the expected design has been achieved during the fabrication process.

5. CONCLUSIONS (1) Within the exponent values ranging from 0.6 to 2.2, the theimal stress in any of the FGMs is relaxed compared with that in TiC-Ni two layers material.

52 (2) By analysing the thennal stress and its distribution, an optimum design with the exponent P=1.6 was reached. (3) TiC/Ni3Al-Ni FGM samples were successfully fabricated via a HP method.

REFERENCES [1] M.Niino, T.Hirai, and R. Watanabe, J. Jpn. Soc. Compos. Mater., 13(1987),257 [2] Edited by B.Dschner and N.Cherradi, Proc. 3rd Int. Sym. on SFGM, Presses Pofytechniques et Universitaires Romandes,1995. [3] L.M.Zhang, R.Tu and R.Z.Yuan, Acta Materiae Compositae Sinica, 12(1995),22 [4] A.Kawasaki and R.Watanabe, J. Jpn. Soc. Powder Metall., 37(1990),253


53

A Mathematical Model for Particle Distribution in Functionally Graded Material Produced by Centrifugal Cast Zhang Baosheng Zhu Jingchuan Zhang Yongjun Ying Zhongda Cheng Hongsheng An Geying School of Material Science and Engineering, Harbin Institute of Technology, Compus Box 434, Harbin 150001,P.R.China 1. Introduction Functionally Graded Materials (FGMs), with gradiently distributed reinforcement particles, can be produced conveniently by centrifugal cast due to the segregation phenomena which is caused by the different specific gravities of reinforcement particles and alloy liquids J ^'^'^^ To produce FGMs with accurately distributed particles, the sedimentation procedure of reinforcement particles in centrifugal fields should be theoretically grasped. For this purpose, the paper applies the continuous theory and builds up the mathematical and physical model for reinforcement particle distribution by considering the influence of alloy viscosity and solidification on particle sedimentation as well as the interrelation of particles.^"^^ Then the author solves this model numerically and simulates the sedimentation procedure with aids of numerical analysis and computer graphics. At last, a SiCp/A356 FGM is prepared to rectify the results of theoretical analysis. 2. Mathematical Model Figure 1 shows the microelements filled with melt of reinforcement particles and alloy liquid in the cenrifugal force field. The initial concentration of this microelement is C and the densities of particles and alloy are Pp and pi, respectively. The gravity is omitted because it is * far smaller than the centrifugal force. Thus, the ^^^' ^ J^^^^ eiawfit reinforcement particles can only move in radius " ^^^ ^^ "*® ^ direction. If the particle concentration distribution is axisymmetrical, it can be considered as the function of radius r and time t. At any time t, in a microelement Ar, the volume concentration of particles is C, and the sedimentary velocity is Uc. The unit volume flux J of reinforcement particles in unit time is

J=CUc

(1 )

According to continuous theory, in time At, the change of concentration in the microelement is

[{J + dl/a-) - j]dt = -{dCla)drdt. Adjusting Equation (2), one can write * School of Material Science and Technology, Harbin Institute of Technology, Harbin , China, 150001

(2 )

54

[{J + dJ/a-) - J]dt = -{dCla)drdt.

(3 )

From Robison^^', the sedimentary velocity of particles with concentration C in centrifugal force field is

Uc=U^x{\-CY

(4)

with KdîPp - Or)

^

M where k is the shape coefficient of particles, d is the average diameter of particles, ^ is the viscosity, ps and PL are the specific gravities of particles and liquid, respectively, co is the rotation angular velocity, and r is the centrifugal radius. The change of melt viscosity caused by the increment in volume portion of reinforcement particles (Vp) is /^^P=A(I + | ^ ' . + 7 . 6 F / ] where |ii is the viscosity of alloy liquid. ^^^ Using equation (4) and (5), we may write equation (1) in the form aC o[Ar(l-CyC] —- + ——^^ —^ = 0

ar with

(6)

(7)

aA=

^^-—^-^co\

which is the mathematical model for particle sedimentation. Equation (7) is a nonlinear partial differential equation. According to conditions of convergence and stability, applying against wind differential scheme, it may be discretized as Ari C."-^' ^ ^ « | [ ^ r ( l - C ) ] . -\Ar{\-Cyc\ \ (0 twin plasma torch

Figure 1. Twin plasma torches to spray FGM coatings and the instrument to measure the curvature of a substrate during deposition. 2.3 Modeling The ntmierical model we used was originally developed by Gill and Clyne [6] and has been modified to handle multi-layered deposits. It is a 1-dimensional model and consists of two parts: thermal profile calculation and stress calculation. By regarding the torch motion as a fluctuation in the heat and mass flux onto a reference point on the substrate and assuming biaxial stress state, the program calculates both the through-thickness thermal profile and stress distribution during thermal spray as fimctions of time.

61

Table 2 Thermal and mechanical properties used for modeling. E: elastic modulus, kithermal conductivity, a:thermal expansivity, Gqi quenching stress. NiCrAlY

YPSZ (bulk)

YPSZ (deposit)

190 18

192 4 10 20

19 0.8 8.3 20

E(GPa) k(W/m/K) a(10-6/K) CTq(MPa)

12.2

250

Figure 2. Cross section of FGM coating. *—• 10|im ^

preheat

cool down

spray

^ o.3r — ^ -0.2

;=o.i 2

3 Timelmin]

400r _300 •^200 2

3 Time[min]

Figure 3. Measured curvature and temperature of a substrate during spra3dng of a NiCrAlY coating.

62 3. RESULTS 3.1 Experimental results Fig.3 shows the curvature and temperature records when NiCrAlY was sprayed onto a mild steel substrate. The high-frequency oscillations in the curvature and temperature traces are due to the heating and cooling by the plasma and cooling air jets. From the slope of the gradual curvature change with respect to time, i.e. the coating thickness, quenching stress in sprayed deposits can be evaluated[7]. Quenching stress arises because the thermal contraction of individual splats is constrained by the underljdng solid and is therefore always tensile. The value of quenching stress is independent of substrate material but depends on the substrate temperature. In the case of a substrate temperature around 600K, aq=250MPa for NiCrAlY and 20MPa for YPSZ were obtained. The values of aq as well as the elastic modulus of the deposits with several mixing ratios were also measured too. For the modulus determination, 3-point bending test was performed for deposits detached from substrates. Fig.4 shows the curvature and temperature data when a graded coating was sprayed onto a mild steel substrate by gradually changing the volume ratio of YPSZ from 0 to 1. It is evident that the slope, i.e. the quenching stress, decreases as more YPSZ is mixed. 3.2 Thermal and mechanical properties of sprayed deposits Table 2 lists the thermal and mechanical property data used for the model calculation. The thermal conductivity and elastic modulus of sprayed YPSZ are often an order of magnitude smaller than the bulk values. This is due to extensive microcracks and unbonded gaps between lamellae. 3.3 Model calculation Fig.5 shows the calculated curvature and temperature evolution for an FGM deposit with thickness of about 180|jm, which is consistent with the experimental results shown in Fig.4 except for the transient oscillations. Fig.6 (a) shows the calculated stress distributions in 2-layer and FGM deposits. The gradual stress variation in the FGM can be observed. In Fig.6 (b) effects of model parameters such as the substrate temperature and elastic modulus of YPSZ on the stress distribution in 2-layer deposits are demonstrated. As the substrate temperature is raised from 600 to 825K, the tensile stress in the NiCrAlY layer is significantly reduced. If a value of elastic modulus of 190GPa of a dense bulk material was used, the compressive residual stress in the YPSZ is excessively overestimated. This example clearly demonstrates the importance of using realistic values for modeling thermal and mechanical behavior of sprayed deposits. 4. CONCLUSION To predict the residual stress distributions in sprayed FGM, in-situ curvature measurement is necessary because the values of quenching stress are difficult to

63 preheat

YPSZ vol ratio 0 p400

cool doown

spray

0.1

0.2

0.3

0.4

0.5

0.6

0.7

6

7

8

9

0.8

0.9

1

|ii|iiMM^^^^

3*200'

0 1

2

3

4

5

10

11

12

Time[nnin]

Figure 4. Measured curvature and temperature of a substrate during spraying of a NiCrAlY/YPSZ FGM coating.

Time (min) ûu

:

—

I

-

—

\

—

'

—

i

^

—

•

—

*

—

1

—

•

—

-

'

'^~

T

•

^

'

_ _^^^^^^^^ ^

._ _

300

'

1 1 t

U

j j 1

•

200

V

100 n

j

*-. ^

*

•

•

•

*»

1 -

1

1

1

1

1 — 1 — 1 .

8 Time (min)

•

J

1

•

n

•

•

1

12

Figure 5. Predicted curvature and temperature of a substrate during spraying of a NiCrAlY/YPSZ FGM coating.

64

200

l-^

-^""""""lA^^

^ -100 -200 0.0

0.5

1.0

1.5

2.0

Position (mm) (b) Figure 6. Calculated residual stress distributions in deposits, (a) 2-layer deposit and 9-layer FGM, (b) effects of the substrate temperature and elastic modulus of the YSPZ deposit.

obtain theoretically. Proper evaluation of thermal and mechanical properties of sprayed deposits is also important for modeling because these can be remarkably differed from the values of bulk materials. Using numerical models, the influence of the property data on the stress distributions can be studied easily. REFERENCES 1. L.Pawlowski, The Science and Engineering of Thermal Spray Coatings, Wiley, Chichester, 1995. 2. T.Fukushima, S.Kuroda and S.Kitahara, Proc. 1st Int. Symp. FGM, Sendai, Oct., 1990, p. 145. 3. N.Shimodaet al., i6irf, p.l51. 4. H.StefFens, M.Dvorak, and M.Wewel, ibid, p. 139. 5. S.Kuroda, T.Fukushima and S.Kitahara, Thin SoHd Films, 164(1988)157. 6. S.C.Gill and T.W.Clyne, Thin Solid Films, 250(1994)172. 7. S.Kuroda and T.W.Clyne, Thin Sohd Films, 200(1991)49-66.


65

Artificial neural network used for TiB2-Cu FGM design Z.C.Mu', Z.XWang', W.B.Cao', C.C.Ge' ^School of Automation and Information Engineering, University of Science and Technology Beijing, Beijing, 100083, P.R.China ^Laboratory of Special Ceramics and Power Metallurgy, University of Science and Technology Beijing, Beijing, 100083, P.R.China As FGM is a kind of complex heterogeneous composites, the underlying relationship among various factors (composition, constitution, processing parameters etc.) affecting its properties such as density, hardness, strength, fracture toughness, hot shock resistance, elastic modulus and grain size etc. of the bulk or certain layer of FGM are subtle, complicated and very difficult to describe as formulas or rules. Artificial neural network (ANN) does not require any explicit knowledge rules to construct, and can learn by itself to form "mapping" from inputs to outputs. In this work, ANN is first applied for density estimation of the FGM. 1. INTRODUCTION Knowing the effective material properties is essential for the FGM design especially in its earlier stages. Traditionally these properties are obtained mainly by using some classical rules of mixture. More recently some papers have presented the methods that use Expert System and/or Fuzzy Logic as alternatives for the property estimation. However, the FGM is a kind of complex heterogeneous composite, its properties are affected by various factors such as composition, constitution, and processing parameters etc. The underlying relationship among these factors are subtle, complicated, and very difficult to find and describe as formulas or rules. To solve these problems which lack existing solutions, we have applied the Artificial Neural Network (ANN) technology into property estimation of the FGM design. The result from this trial looks quite promising. 2. BACKGROUND OF THE ANN The ANN is mathematical model that simulates many characteristics of actual neurons in the brain. Generally, an ANN is a structurally multi-layered network which links a large number of nodes (the neuron-like computational elements) and operates dynamically. Although mathematical neurons were conceived as early as 1943, only recently have largescale real-world applications become practical. Unlike rule-based Expert System and Fuzzy Logic, the ANN can find relationships among the inputs and outputs of the network without the need for training by an expert. It does not require any explicit knowledge rules to construct. It applies a weight-adaption algorithm to a representative sample of training data to correlate inputs with desired outputs, i.e. it can learn by itself to form "mapping" from inputs to outputs. Another advantage of the ANN over Expert System is that it has the ability to generalize — to produce a reasonable response to data for which the system has not been explicitly trained. In a rule-based Expert System, if a situation occurs for which there is no applicable knowledge rule, it may be unable to give any response.

66 In short, the motive that we have applied the ANN into the FGM design was inspired by the ANN'S distinct characteristics-its noniinearity, ability of self-learning, and ability of generalization. 3. APPLICATION TO THE FGM DESIGN According to our application purpose, the development of the ANN can be described as follows: If defme xêK" (i=l,2,...,n) as the network inputs which represent the factors that have significant influence on the properties of the FGM and yjGR"" (j=l,2,...,m) as the network outputs which represent the estimated properties, the goals of the work are to choose the network architecture, train the network with data from real experimental process, and make the network act mathematically as an underlying function Y=F(X) which maps network inputs to network outputs. density

hardness

gram size output layer hidden layer

Ti

input layer pressure

B particle size Fig. 1 The Architecture of ANN Network

Development of the ANN for the FGM design consists of two phases. In the first phase, or the training session, an ANN network is trained for the property estimation after its network architecture is determined. The architecture of the network is shown in Fig. 1 . It is a layered, feed-forward network. A supervised learning algorithm — Back-Propagation Algorithm (BPA) is used for the training. The algorithm compares the calculated outputs of the network to the expected outputs, and readjust the weights in the network so that the next time that same input is presented to the network, the network's output will be closer to the expected output value. The training error is defined as: 1

(1)

^^ k=\ f=i

where m is the number of output nodes; n is the number of training data sets; T^^, is the expected output value of the network which is measured from experimental process; and Oi,, is the calculated output value of the network. The network is trained step by step according to the equation : AW(t) = -y\VE{t) + a A ^ ( / -1)

(2)

where the arguments t and t-1 are used to indicate the current and the most recent training step

67 respectively, W represents the weights which interconnect the network nodes, r| is the learning constant, and a is an user-selected positive momentum. During the training session, the equation (2) is applied iteratively until convergence of the calculated and expected outputs. In general, the specific architecture of the network and the optimum value of y\ and a depend on the problem being solved, and there is no single solution suitable for different applications. Therefore, the number of hidden layers, the number of hidden nodes, learning constant r\ and momentum a must be chosen experimentally for the application during the training session. Experimental results have shown that the effectiveness and convergence of the BPA depend significantly on these factors. In the second phase of the development, the ability of property estimation of the network is examined with the data samples which are measured from the experimental process but never used in the training session. Based on the experimental data which were available for the trial, we trained and tested the ANN network to predict densities of FGM. Table 1 shows the comparison of measured and the network estimated densities of as-synthesized TiB2-Cu FGM using the Self-propagating High-temperature Synthesis (SHS) technique. The result indicates that the ANN network can give quite good estimations to the FGM properties. Apart from density, other properties of FGM such as hardness, strength, fracture toughness, hot shock resistance, elastic modulus and grain size etc. of the bulk or certain layer of FGM can be predicted and designed.

Table 1 The Comparison of Measured and BPA Estimated Densities estimated values Samples measured values 1 79.00 80.20 70.83 2 71.33 63.95 3 64.40 80.93 4 79.10 63.74 5 63.70 In order to further improve the ability of generalization of the network, a more complex ANN network was developed. This network combined two companion networks using the Double Back-Propagation (DBP) algorithm which improves the network performance by forcing the output to be insensitive to incremental changes in the input. The improvement is quite significant. The mean estimation error of the network decreases by 30% compared with the network using the BPA[3]. 4. CONCLUSIONS The ANN is an artificial intelligent technique that has several distinct advantages over rulebased Expert System and Fuzzy Logic. The technique has been shown to be a feasible technique that estimates the material properties for the FGM design. The estimation accuracy is satisfactory.

68 5. ACKNOWLEDGMENT This work is supported by China National Natural Science Foundation, The Doctorial Program Fundation of State Education Commission, and National Committee of High Technology New Materials. REFERENCES 1. T.Hirano et al. Proceedings, The First International Symposium, FGM, Sendai, (1990) 5. 2. T.Hirano et al. International Workshop on Artificial Intelligence for Industrial Application, (1988)245. 3. Z.C.Mu et al. Pattern Recognition and Artificial Intelligence, Vol. 8, No. 1 (1995) 51. 4. H.Drucker and Y.L.Cun, IEEE Trans. Neural Networks, Vol. 3, No. 6 (1992) 991.


69

Deformation analysis of graded powder compacts during sintering K. Shinagawa Department of Mechanical Engineering, Anan College of Technology Minobayashi, Anan, Tokushima 774, Japan

A method for simulating the deformation behavior of graded powder compacts during sintering is proposed. A constitutive model for sintering of metal and ceramic powder mixtures is presented. The constitutive equation is applied to the viscoplastic finite element method. The shape change in graded powder plates during sintering is predicted. The effects of sintering properties of the powders and their combinations on warpage in the sintered plates are examined.

1. INTRODUCTION Powder metallurgy is one of the methods to produce functionally graded materials (FGM) with metals and ceramics. In general, shrinkage behavior of ceramics during sintering is different from that of metals. Difference in shrinkage rate often induces distortion or cracks in sintered bodies. Sintering process should be controlled to avoid such defects. Powders may be coordinated by selecting particle size or adding elements to get almost homogeneous shrinkage rate all over the layers in FGM powder compacts [1,2]. In another way, graded heating may be imposed to the powder compacts to adjust the sintering balance of the layers [3]. Conditions of the process, however, seem to be determined by trial and error. Thermal stress in FGM has been studied because it is important to avoid the fracture due to thermal shock. However, the defects in the powder compacts during sintering is caused by sintering stress, which arises from surface tension. Therefore, the structure of FGM made by sintering should be designed with both thermal stress and sintering stress taken into consideration. Analysis of the sintering process of FGM powder compacts has not been conducted. The author has proposed a constitutive equation for sintering of a single powder and applied it to the prediction of deformation behavior of powder compacts during sintering using the viscoplastic finite element method [4-6]. In this paper, a constitutive model for sintering of metal/ceramic mixed powder compacts is developed. The shrinkage behavior of metal and ceramic powder mixtures is expressed on the basis of the sintering behavior of each component powder and the mixing ratio. The constitutive equation is applied to the finite element method and the deformation behavior of cylindrical graded powder plates during sintering is simulated. The effects of the balance of sintering properties of two component powders and the size of powder compacts on the warpage in the graded powder plates are examined.

70 2. CONSTITUTIVE MODEL FOR GRADED POWDER COMPACTS 2.1. Constitutive equation for sintering Sintering can be described as the deformation process of viscous porous bodies under the action of the sintering stress, which is an apparent hydrostatic stress [4-6], Based this theory, the constitutive equation for sintering is given by = _1_ en = 2rj (1) hj=x,y,z 9/^ «=2.5, f=l/2.5fi7p, where rj is the viscosity, p the relative density, ^ , rr' are the strain rate and deviatoric stress, respectively, 6 is the Kronecker symbol, Om is the hydrostatic stress, as is the sintering stress. The sintering stress is evaluated from surface tension and pore geometry as follows;

îrl^'^^^^V^'^'^^H

as=p^-y, 1P(1-PO)I

(2)

'

N=6, A:=0.5, po=0.52,

where y is the surface tension,} is the effective pore radius, R is the radius of a powder particle, po is the initial relative density. If the mechanism of material transport in sintering is grain boundary diffusion, the viscosity can be expressed as a function of the temperature and the grain size. From a model for boundary diffusion controlled creep M2 1 proposed by Coble [7] and the temperature 70 C2 dependence of diffusion coefficients, we obtain 4U}

rj=ciT'exp(f\d\

where T is the temperature, d is the grain size and ci, C2 are constants. The grain growth during sintering is assumed to be given by d^=do^^C3t'exp(^],

I

/Ml 10 /

C/3

5

(4)

do=2R, where do is the initial grain size (= the diameter of powder particles ), t is the time (sec) and cs, CA are constants.

^Cl

15

(3)

n

j

/

j

-

C/ 1 i 600 800 1000 1200 1400 0.5 1.0 Temperature /°C Holding time /h Figure 1. Shrinkage curves.

2.2. Sintering behavior of metals and ceramics powder compacts Figure 1 shows shrinkage curves of metals Ml(Mo), M2(Mo with 0.1mass%Ni) and ceramics Cl(Zr02), C2(PSZ) calculated by Eqs. (1)'^(4), which are employed as components of FGM. The rate of heating up is 100°C/min. After the temperature reaches 1400 °C, the sintering is carried on at the same temperature for one hour. The material parameters used in Eqs. (1) ^^(4) are shown in Table 1. These component materials were referred to the research on molyb-

71 Table 1 Material constants. Metals

Ml

?;[Pa-s]

1.5628 x l O '

16415 d[m]

1.2794x10"'"

Ceramics

M2

7.3919x10'' 15426

CI

C2

5.4445x10'' 1.4454x10'' 47921

40043

1.2569x10"" 4.6148x10"' 2.5493x10"'

R[m]

-34804 1.0x10"^

-29041 1.0x10"^

-72213 0.025x10"^

-65313 0.025x10"^

)4mN/m]

1000

1000

1000

1000

denum / zirconia system by Watanabe et al. [1,2] and the parameters ci'-C4 were determined from their experimental data by the method of least squares. 2.3. Constitutive model for metal and ceramic powder mixtures Let us express the shrinkage behavior of powder mixtures MCI composed of Ml and CI, and MC2 composed of M2 and C2 by the shrinkage curve of each component shown in Figure 1. It is assumed that there is no reaction between the metals and the ceramics. The powder mixtures are described as two porous bodies mechanically engaging with each other. Using this assumption, the sintering stress of the mixtures may be given by Osmc=VmOsm-^VcOsc^

(5)

where Vmy Vc are the volume fractions of metal and ceramic, respectively (Km +Fc =1), Osmy Osc are the sintering stresses of metal and ceramic, respectively. When two kinds of particles with different diameters fill up a container, the bulk density may change with the ratio of mixture. Variation of the initial relative density with the volume fraction of ceramic is set as shown in Figure 2. The relative densities of metallic and ceramic parts of powder compacts are assumed to be given by p,=((1-a)Fc+a>-p , a=0.8, (6) where a is a parameter to express the reduction in relative density due to mixture. The viscosity of the mixtures is assumed to be evaluated by m=^mrjm-^Vcric, m

rjm rjc'

20 40 60 80 100 Volume fraction of ceramic /% Figure 2. Variation of initial relative density with ratio of mixture of metal and ceramic.

72

25 20 ^15

1400°C^

u

xôo°c 1

I 10 c/5

5

1200°C

k

r O ^ — /\• _ 1 0

1

1

iioo°c[ &—-

0 -^ lOOO^C 1

1

1

20 40 60 80 100 20 40 60 80 100 Volume fraction of ceramic /% Volume fraction of ceramic /% (b) MC2 (a) MCI Figure 3. Variation of sintering behavior with ratio of mixture of metal and ceramic.

MCI: ^=1, MC2: y5=.0.0625+0.863 V^ The actual shrinkage behavior of the mixtures was also referred to the research of Watanabe et al. [1,2] and the initial relative densities in Figure 2 and the parameters a, fi were determined from their experimental data. Figure 3 shows shrinkage behavior of powder mixtures calculated by Eqs. (1)'^(7) with the heating rate of 100°C/min. The sintering balance of MC2 is better than that of MCI. The shrinkage does not follow the law of mixture, that is, the minimum shrinkage is obtained at the low volume fraction of ceramic [1,2]. This is considered to be because of the increase in the average radius of pores due to mixture. This phenomenon was expressed as the reduction in relative density in Eq. (6) in the present work. 3. FINITE ELEMENT ANALYSIS OF SINTERING PROCESS 3.1. Theory The finite element method with the sintering stress taken into account has been formulated [4,6]. In this case, the equilibrium equation is given by dXi

dXi

'

hj=x,y,z

(8)

where Sij is the sintering stress. From the principle of virtual work, the nodal forces for each element are given by

{P)=\[BY{o)dV^\

[B7{S)dV

(9)

73

Figure 4. Model of graded cylindrical powder compacts.

{a} = {ajc Oy Oz x^y Tyz T^Y where [B] is the matrix correlating the strain-rate components with the nodal velocity components. The stresses are given by (10) {a) = [D]{e) = [D][B]{u) s] = { ex

£y £z Yxy Yyz Yzx]

[D] = 3r/mao2''-l 0 0 0 0

0 0 0 c 0 0

0 0 0 0 0 0 0 0 c 0 0c

2c = i 9' 3 where {u} is the nodal velocity. Substituting Eq. (10) into Eq. (9) gives

a=f^^,b=f-

•.j[BnD][B]dV[u]^j[ {P]=\[BnD][B]dV{u]^\[BY{S)dV

(11)

Adding together the nodal forces of the surrounding elements at each nodal point gives simultaneous linear equations. The nodal velocities are obtained as solutions of these equations. 3.2. Sintering simulation Deformation of two types of graded cylindrical powder compacts having different diameters as shown in Figure 4 were analyzed in the same sintering conditions as Figure 1 (section 2.2). Figure 5 shows calculated distorted grid patterns of the sintered cylinders with the small diameter. The shape of MCI is not strait because the shrinkage of metal Ml is much smaller than that of ceramic CI. The middle of cylinder MC2 with the small diameter is slightly swelled because the initial density of this part is high and the shrinkage is small. However, a sound shape may be obtained in MC2 due to the good sintering balance of the component layers.

74 Figure 6 shows calculated shapes of the sintered cylinders with the large diameter. MCI, having an inferior sintering balance, is considerably warped because a difference in shrinkage exerts more significant influence on a large size. Even MC2 suffers from some warpage. During the process of MCI heating up, the cylindrical plate MC2 is warped once and deformed again in the opposite direction. This may produce a defect within the sintered body. These results suggest that the MC2 size effect should be taken into consideration for suitable design of FGM. 900X

1200X

ISOO'C

1400*C

4. CONCLUSIONS A constitutive equation to simulate the deformation of the graded powder compacts during sintering was proposed. The sintering stress of each layer in the powder compacts was evaluated from powder properties. The constitutive equation with the sintering stress was applied to the prediction of the deformation behavior of graded powder plates. Warpage in the plate during sintering was predicted by the viscoplastic finite element method.

UOOV (Ih)

Figure 5. Distorted grid pattern in cross section of cylindrical FGM with small diameter.

izoo'C 1300X:

MCI

MC2

Figure 6. Warpage in cylindrical FGM with large diameter.

REFERENCES 1. R. Watanabe, A. Kawasaki and N. Murahashi, J. Asso. Mater. Eng. Resour., (in Japanese), 1 (1988) 36. 2. R. Watanabe, Micromeritics, (in Japanese), 33 (1989) 76. 3. M. Yuki, M. Toshikazu, I. Toshio, A. Kawasaki, R. Wtanabe, J. Jpn. Soc. Powder Metall., (in Japanese), 37-7 (1990) 929. 4. K. Shinagawa, Trans. Jpn. Soc. Mech. Eng., A, (in Japanese), 62-539 (1996) 240, 246. 5. K. Shinagawa, JSME Int. J., A, 39-4 (1996) 565. 6. K. Shinagawa, Proc. 3rd Asia-Pacific Symp., AEPA'96, (1996) 439. 7. R. L. Coble, J. Appl. Phys., 34-6 (1963) 1679.


75

Simulation of the Elasto-Plastic Deformations in Compositionally Graded Metal-Ceramic Structures: Mean-Field and Unit Cell Approaches* H.E. Pettermann^, E. Weissenbek"^ and S. Suresh^ Înstitute of Light Weight Structures and Aerospace Engineering, Vienna University of Technology, Austria, Gusshausstr. 27-29/E317, A-1040 Vienna, Austria ^Department of Materials Science and Engineering, MIT, 77 Massachusetts Avenue, Cambridge, MA USA 02139-4307 1. I N T R O D U C T I O N The elasto-plastic behavior of a compositionally graded metal-ceramic structure is investigated. The deformation under uniaxial loading is predicted using both an incremental Mori-Tanaka method and periodic as well as random microstructure extended unit cell approaches. The latter are able to give an accurate description of the local microfields within the phases. Furthermore, the random microstructure unit cell model can represent the interwoven structure at volume fractions close to 50%. Due to the high computational costs, such unit cell analyses are restricted to two-dimensional considerations. Computationally less demanding mean-field methods provide a tool to account for the out-of-plane constraints, but have the disadvantage of using phase averaged stress and stain fields. In the present work, an incremental Mori-Tanaka approach is employed, which is implemented as a constitutive material law in a finite element code. Both twodimensional and three-dimensional investigations are performed and the results are compared to the predictions of the extended unit cell approaches. 2. M O D E L I N G OF T H E F G M - S T R U C T U R E The investigated structure (cf. fig. 1) consists of a pure nickel top layer (1.2mm thick), an FGM zone with a linear variation of the volume fraction (2.2mm thick), and a pure alumina bottom layer (0.45mm thick). Material data of the constituents are given in table 1, where Eh denotes the strain hardening modulus. The boundary conditions force all cross sections perpendicular to the monolithic/FGM interfaces to remain plane, i.e. the lefthand and the righthand side (as well as the viewing plane for three-dimensional considerations). The uniaxial load (which causes extension and bending for the present *This work was supported by the Grant DE-FG02-93ER45506to MIT from the US Department of Energy. The post-doctoral study of EW at MIT was supported by an Erwin Schrodinger Fellowship from the AUSTRIAN NATIONAL SCIENCE FOUNDATION. HP'S visit to MIT was supported by a scholarship for

Overseas Scientific Study from the AUSTRIAN FEDERAL MINISTRY OF SCIENCE, TRANSPORT AND ART. ^present address: BMW Entwicklungszentrum Steyr, Hinterbergerstr. 2, A-4400 Steyr, Austria

76 Table 1 Material data for alumina '* and nickel ^ [GPa] 380 0.25

[GPa] [MPa] 214 0.31 148

[MPa] 668

case) is applied centered at and perpendicular to the left- and righthand side, respectively. All calculations are performed with the finite element code ABAQUS [1]. 2.1. Extended Unit Cell Models Periodic Packing In the field of metal matrix composites a number of models are used to characterize both, macroscopic behavior as well as local microfields. The present section deals with plane models, the three packing cases shown in [2] are used as the basis to extend the unit cell method for graded structures with hexagonal packing, square edge packing^ and square diagonal packing [3]. Nine subcells with different volume fractions (corresponding to linear grading) are combined to represent the graded part (fig. 1, left and middle). Due to the fact that these models can only represent a pure matrix/inclusion structure, a switch from nickel-matrix to alumina-matrix is necessary. To investigate the particular influence of the eflfective matrix phase for the center sublayer two diflFerent cases are considered, viz. the 50% layer shows a nickel-matrix (marked as Ni) or an alumina-matrix (marked as A1203). Random Micro structures Usually the microstructure of an FGM does not show a matrix/inclusion type topology throughout the thickness. Typically, in the range between 30 and 70 % volume fraction an interwoven type microstructure exists. To account for this, a further two-dimensional plane stress approach is used where the grading within the FGM layer is divided into 11 sublayers each having a fixed volume fraction. In each row the proper number of hexagonal "grains" are assigned to the nickel and alumina phases, according to the volume fraction. The locations with the pertinent row are chosen randomly (fig. 1, right). The bottom and top layers, consisting of pure nickel and alumina, respectively, show the same finite element mesh topology, viz. each grain comprises six triangular elements. Eight diflFerent randomly generated microstructures are studied. 2.2. Incremental Mori-Tanaka Method (IMT) As a complementary approach a mean-field method is used in combination with the finite element method to investigate the FGM. To compare the predictions with the periodic unit cell simulations, the FGM part is divided into nine sublayers. Each of them consists of two bi-quadratic 8-node plane elements over the thickness, and only one element is used in the horizontal direction. The parts of pure alumina and pure nickel are modeled by three and 12 elements, respectively. In each sublayer the volume fractions of the phases are constant. In addition, the center sublayer can be split into a metalmatrix and a ceramic-matrix half sublayer. The properties of the particular material on the meso-structural level within the finite element calculation are described via a con-

77

Figure 1. Extended unit cell finite element models; hexagonal arrangement and detail of center subcell (left); square edge arrangement and detail of center subcell (middle); random arrangement (right)

stitutive material law. This is an incremental Mori-Tanaka approach [4] (representing an matrix/inclusion topology) which is based on Eshelby's equivalent inclusion method. Herein, the Eshelby tensor is a function of the inclusion aspect ratio and the (instantaneous) material properties of the matrix phase. For a general behavior of the matrix material (i.e. elasto-plasticity or anisotropic elasticity) the Eshelby tensor is calculated numerically, based on an implementation developed by Gavazzi/Lagoudas [5]. The IMT method is implemented as a "user supplied material routine" [4] for the finite element package ABAQUS [1]. The mesoscopic, instantaneous material data of the microscopically heterogeneous materials are calculated individually for each integration point at each increment within the finite element analysis. In contrast to the extended unit cell models, the IMT-method does not provide detailed information about the micro-fields. The computational requirements, however, are much lower. Furthermore, this method can be employed to predict the complete deformation of a three-dimensional graded layer and to perform structural analyses for components made from composite materials. Within the present method a pure matrix/inclusion type micro-topology is assumed (no interwoven structure can be represented). Hence, a sudden change of the properties occurs, when the matrix material changes from alumina to nickel. The IMT-method as implemented performs a fully three-dimensional analysis on the micro level independently of the global finite element analysis option.

78

IQ

0)

U

CQ

•H

H

IMT reduced constr. (Ni) IMT reduced constr. (A1203) Square-diagonal (Ni) Square-diagonal (A1203) Square-edge (Ni) Square-edge (A1203) Hexagonal (Ni) Hexagonal (A1203) 2.0

Axial Strain (%)

Figure 2. Predicted axial strain response for the extended unit cell models and the corresponding incremental Mori-Tanaka approach (IMT); the matrix of the center sublayer being nickel (Ni) or alumina (A1203)

3. RESULTS The deformation is given in terms of axial strain and bending strain which are the mean value of the strains in loading direction and in proportion to the curvature of the layered structure, respectively. The global behavior of the periodic packing models with respect to the axial strain is displayed in fig 2, considering both an alumina and a nickel center sublayer. (The responses with respect to the bending strains are equivalent.) The square diagonal packing and the hexagonal packing show similar response, but the square edge packing model is stiffer. The results coincide with the findings in [2,6,7] for equivalent periodic packing arrangements. The overall stress vs. axial and bending strain prediction of the random microstructure models are displayed in fig 3. A slight variation for different randomly generated models can be observed; the global behavior, however, does not deviate markedly. Compared to the periodic unit cell approach the random microstructure models show a more compliant behavior. Mainly responsible for the overall stiffness of the FGM is the portion of interconnected alumina matrix. The periodic unit cell results are directly comparable to the IMT predictions, because both approaches represent the same matrix/inclusion type microstructure. However, such comparisons have to be done carefully since some assumptions regarding the finite element calculations are not equivalent for the extended unit cell approaches and the present mean-field method. The plane stress analysis of the unit cell models does not take into account the constraints in the out-of-plane direction. In contrast, within the present IMT formulation the inclusions are enclosed three-dimensionally by the matrix material. In contrast to the plane stress unit cell models, the constraint in the out-of-plane direction is accounted for. Accordingly, these predictions are denoted as full internal constraint. To overcome this internal constraint in order to "simulate" the plane stress model assump-

79 J

1

1

1

1

_i

1

1

L

(0

0) 0)

4.)

a^

"^St^^

•H

X

(d •d 0)

•H

n

0.0

^

1

4.0

,

1

8.0

^

Arrangement Arrangement Arrangement Arrangement Arrangement Arrangement Arrangement Arrangement 1 ' 12.0

8 7 6 5 4 3 2 1 r

16.0

Axial/Bending strain (%)

Figure 3. Predicted axial (stiffer) and bending (more compliant) strain response for eight different random microstructure models tions, the inclusions are introduced as infinite fibers in out-of-plane direction and the elastic material parameters of the ceramic phase in out-of-plane direction are reduced by several orders of magnitude. Such models are denoted as internally reduced constraint. A center layer with alumina matrix and nickel matrix, respectively, is modeled. It is well known that incremental mean-field methods show a tendency to over-predict the hardening behavior, but the general features are captured in a qualitative as well as quantitative way (cf. fig. 2). Additional calculations are performed where the center sublayer is subdivided. These results and the stress-strain behavior of a global plane stress and full internal constraint analysis (considering spherical inclusions and unmodified material data throughout) are displayed in fig. 4. A marked stiffening as the result of the full constraining on the micro level can be observed. Furthermore, the predictions of a generalized plane strain analysis are shown. This way, mesoscopic interaction between the sublayers is accounted for and a second set of strains can be calculated, describing the axial strain in the out-of-plane direction and the out-of-plane rotation (see fig. 4). These results show that a plate under the assumed loading is deforming to a saddle shape. 4. CONCLUSIONS The deformation behavior of a compositionally graded metal-ceramic structure has been investigated by numerical and (semi)analytical simulations. Random microstructure models are able to predict the response of an FGM-structure in a more accurate way than the other approaches. The interwoven structure in the "middle" of the FGM can be accounted for using this modeling strategy. For the extended periodic unit cell models the predicted stress strain response depends strongly on the micro-arrangement of the inclusions. Detailed information on the microfields of the stresses and strains can only be obtained by the extended unit cell models. The incremental Mori-Tanaka method

80 1

,

I

i

.

I

.

I

0)

u

GPE GPE GPE GPE PST PST PST PST

'

Id 0) •H H

& 1

'

1 -0.5

1 0.5

b e n d i n g / o u t of p l a n e a x i a l / o u t of p l a n e bending/in plane axial/in plane full c o n s t r . red.constr. r e d . c o n s t r . (Ni) r e d . c o n s t r . (A1203)

|

'

1

1 1.5

•

Axial/Bending strain (%)

Figure 4. Predicted axial strain response for plane stress (PST) calculations with internally full and reduced constraint and predicted axial and bending strain response for interally fully constraint generalized plane strain (GPE) calculations by the incremental Mori-Tanaka approach

shows a tendency to over-predict the hardening behavior, but, it is numerically less intensive. In addition, the three-dimensional interaction between matrix and inclusions can be considered, and it can be employed to predict the complete deformation of an FGM-structure. Acknowledgments The authors thank Drs. H. J. Bohm, M. Finot, A.E. Giannakopoulos, A. Needleman and F. G. Rammerstorfer for many helpful discussions during the course of this work. REFERENCES ABAQUS User's Manual; HKS Inc., Pawtucket, RI (1994). T. Nakamura, S. Suresh.: Acta metall.mater. 41, 1665 (1993). E. Weissenbek, H.E. Pettermann, S. Suresh: submitted to Acta.mater. H.E. Pettermann, H.J. Bohm, F.G. Rammerstorfer: In "Proceedings of the General Workshop in Materials Science and Engineering", 1996, Ed: M. Rappaz, European Commission, in press. A.C. Gavazzi, D.C. Lagoudas: Comput.Mech. 7, 13 (1990). E. Weissenbek., H.J. Bohm, F.G. Rammerstorfer: Comp.Mat.Sci. 3, 263 (1994). E. Weissenbek: VDI Fortschrittsberichte (Reihe 18, Nr. 164), VDI Verlag, Diisseldorf, Germany (1994).


81

Large Deflections of Heated Functionally Graded Clamped Rectangular Plates with Varying Rigidity in Thickness Direction F. Mizuguchi^^ and H. Ohnabe**^ ^Dept. of Mechanical Engineering, Japan Maritime Safety Academy, 5-1, Wakaba-cho, Kureshi, Hiroshima-ken,737 Japan. ^CompositeNfeterials Center, AeiD-Engine & SpaceOperations, Jshikawajima-Haiirna Heavy Inciustries Co., lid, 3-5-1, Mukodai-cho, Tanashi-shi, Tokyo, 188 Japan. The governing equations for the large deflection of heated functionally graded elastic, rectangular^plates with varying Young's modulus in thickness direction are derived by Berger and K i m ^ approach. We assume that the functionally graded Young's modulus varies symmetrically with respect to the middle plane according to the nth power of the nondimensional thickness. For a clamped rectangular plate affected by an arbitrary symmetrical temperature and load distribution about midpoint of the plate and prevented from inplane motions on the boundary, the governing equations are solved by means of the Galerkin method. As a numerical example, the cases as seen in aerodynamic heating are analyzed. The influence of functionally graded Young's modulus and temperature change on the large deflection are shown in the graphs. 1. INTRODUCTION Recently, the functionally graded materials (FGM) of the thermal relaxation type, adaptable to a super-high-temperature environment like a super and hyper sonic transportation and a space plane, have received considerable attention. An approximate method for investigating the large deflections of isotropic plates has been proposed by Berger [1] in 1955. Since then much research has been conducted on large deflections by Nowinski [2] in 1962 and on thermal buckling by Kamiya [3] inl976. Nowinski and Ohnabe [4] in 1972 pointed out that the relative exactness of the Berger method is closely associated with the restriction imposed on the in-plane displacement of the boundary conditions. The mathematical justification for this statement has been given by Schmidt [5] in 1974 using a proper perturbation method. Recently Horibe [6] in 1990 proposed a new iterative solution of the Berger equation. The solution is derived by utilizing both the idea of the Kantrovich method and the boundary integral equation method. Following Berger, Ohnabe and Mizuguchi [7,8] derived the governing equations for the large deflection and the non-linear vibration of heated non-homogeneous circular plates with radially varying rigidity. They were solved for the clamped boundary condition by using the Galerkin method. The governing equations for large deflections of heated functionally graded elastic, rectangular clamped plates with varying Young's modulus in thickness direction were also derived by Berger and Karman approaches. Assuming the functionally graded Young's modulus in thickness direction symmetrical with respect to the middle plane, for a rectangular simply supported plate due to a temperature distribution as seen in aerodynamic heating, they are solved by employing the Poincarc method [9]. In the present study, appling the same procedure, for a case of a rectangular clamped plates, they are solved by employing the Galerkin method. The influence of functionally graded Young's modulus and temperature change on the large deflection are shown in the graphs. The solutions for Berger and Karman approaches are compared.

82

2. GOVERNING EQUATIONS We consider a functionally graded, elastic, heated rectangular plate, with a lateral load q. Let the deformation be axisymmetric with respect to the center .We assume that the functionally graded Young' s modulus varies symmetrically with respect to the middle plane according to the nth power of and is given by According to Berger, eliminating the second strain invariant and applying the Euler-Lagrange variational principle for minimum potential energy, the Euler-Lagrange differential equations become the following governing equations for large deflection of heated functionally graded elastic, rectangular plates with varying Young's modulus in thickness direction [9] B V^ (V^w) + a( 1 + V ) i | (V^nu, + pV^m ') - K^v\ h^

- -5L ^0

(2) (3)

where fh/2 thil B = l + - ^ ^T-, , n u ,- - |I Tzdz,PT,= Tdz nu, Tzdz , PT = I| n.-3 ^ |_^2 T j_^^

1+-^, n+1 h/2 tV2

rh/2 tY\l2

1

h/2 equations with large ^^W.h/2 The von Karman-type deflection can also be12(1derived from the equations of equilibrium and compatibility referring to[9]

^ V ^ ^ ^ r ^ (^^"h-+P^^"^T')=^^'p) ^ ^ V"^ + aEQ ( v \ + PV^P^') = - 1 AEQh^w, w)

(4)

(5) ^^^

where the operator L applied to the functions w, F is 3x2 3y2 "^ ay2 9x2 ' ax9y dxdy

^^^

3. EXAMPLES OF SOLUTION OF GOVERNING EQUATIONS The approximate expression for w is selected directly from the linear theory of plates with small deflections, and is given by w(x, y) - f sin^ axsin^ Py /gx where f is the maximum deflection and ^

a,

*^ b

Boundary conditions for a plate clamped on all edges are, at X - 0, a

at y - 0, b

(9)

83

w

3w

^ 0

w

3w

^ 0

ax ay (10) The temperature distribution over the plate is assumed to be symmetrical with respect to the center of the plate and is given as oo oo

I

Px = h i: E Tij COS iax cos jpy ijieven Pj = h S E Tij cos iax cos jPy ijreven and the load is also given as

oo oo

I

m j - h^ | S Z Tpq sin pax sin qPy + Tg (p,q:odd ) m j ' = h^ ! S S Tpq sin pax sin qPy .+.T^ ;! \p,q:odd (11)

q = X S qij sin iax sin jPy ijiodd Substituting Eqs. (8) and (11) into Eq. (3) and integrating with respect to x and y, K^ is obtained _

(12)

Obtaining a general and a particular solution of Eq. (2) and using the boundary conditions of Eq. (10), we then determine the integral constants. Wefinallyobtain the following expression for maximum deflection

_2_ 128

T^C ^?K^!Î*^(^* J ^ t ^ C *^)Kf^lT(».*Poo)|;p,q:odd

p2 + >.V .= 64 £ % X2pq(p2 - 4)(q2 - 4) ^^-^j^J''^ ' "^^^ ' "^^ (14) ^=^

where

h, (15) We consider the case where the temperature distribution on the xy-plane of the plate takes a parabolic form and the temperature distribution through the thickness is linear and the temperature on the lower face is one-half on the upper face , that is, the temperature distribution is expressed as follows: T(x,y,z|)= T „ + T , (0 1L

•(vfi'-i^*" ^ a ' J L V b / JiM'^si ' 3h'

(16)

Then if a lateral load is uniform, q(x,y) - QQ , the above equation (14) becomes

128l-v2l »15

j,2| '^ j i2(i.v2)(^4\2'^'| 4 ( l - v ) P 5 ^ 2 H T , ^ 9 l U " ' • | ' '

-E_ Hfn2.4¥n2-4rh' '"'^'"^.;;idd^'(p^)^(p^-4X'^^-4)

_SQ_ - l (y)î2-4)(j2-4) 7l4 . l l.i ij:odd

(17)

84 where Qo* - qob''/(Eoh'') stands for non-dimensional loading. In case of Karman, Eq. (14) becomes the following

^dJ 9 i + 2vx.^ + x'^ I 1 / n i + x"^, 4 , 1 I 1 (Irî ^128(l-v2) ^4 3 2 | 8 ^4 (^^^2)2 (^^^^^2)2 (4,;,2)2|J^

• { 4(T02 + PT'02) - (TO4 + pTo4)| + HTIO + PT'20) -(T40 + pT'4o)ll + ^ ^ / ^ ^0?^ " J 2(1+X2)

IX'

i |(T24+PT'24) ^ (T42 + PT'42)|

^-(ftlh)"^ 6

(Tpq-PTpq)

p,q:odd = 64 Ji2 U

i,j:odd

p2 + x V 5^ pq(p2-4Kq2-4)

'lij ij(i2-4)(j2-4)

(18) In case of /?= 0, this equation becomes the same equation as Eq. 26 of [10] and for aerodynamic heating with a uniform load, q(x,y) = qo, it becomes as follows 128(l-v2)

,4

12(l-v2)l;^4

^2

& JtMl+x2 = 21^ Z ^Î'l

i,j:odd

32|8

,4

(^^^2)2

(^^^^2)2

(^^^2)2|

U s 2 (l+J^)(Io^.l| + ^ | l + X U [4{l-v)(

5^2)17,

(t)25-TAr2ll^ L_._i 1 + 4)L2 4 + X^,

9l 4;t2| ^2J Z

P2.M2

(h)2^T,

* (iJ)î2-4)(j2-4)

where qo* = qobVCEgh^) stands for non-dimensional loading.

(19)

4. NUMERICAL CALCULATIONS AND DISCUSSION OF RESULTS First we present the comparison with the solutions of the Berger and Karman equations for large deflections due to the temperature distribution through the thickness by means of the same Galerkin method in Fig. 1. The results by the Berger equation are thick lines and the solutions by the Karman equation are shown as thin lines. The solid lines are for the homogeneous elastic plate (/9 - 0) and the dashed lines are for the functionally graded plate (/9 - 1, n-2). It shows the relation between the maximum deflection(f ) and the temperature difference ((b/hfaT^) with TQ/TJ as the parameter and without a lateral load for a rectangular

85 clamped plate. The deflection due to heating according to the Berger method is lower than the Karman method. Nevertheless the two methods do show the good agreement over a wide range of temperature difference. When a temperature distribution as seen in aerodynamic heating which causes the deformation , f =0.7, at a plate with uniform elastic modulus (/? -0), is applied to the graded plate ( ^ = 1 , n=2), the amount of deformation can be reduced by 26% at To/Ti=0, 36% at 0.5, 40% at 1.0 and 49% at 2.0 in case of Berger approach. Figure 2 represents the maximum deformation due to uniform external loading QQ* using Berger and Karman. It may be seen that the deformation of the plate with the graded ekstic modulus in thickness direction is smaller by 20 % at (b/h)'aT^ = 0 and 15 % at (b/h)âTi = 2.0 for QQ* =200 than the ones with a constant elastic modulus in case of Berger. It is observed from these figures that the graded elastic modulus can decrease the deformation of the plate.

5. CONCLUSION Assuming the Young's modulus and the temperature distribution through the thickness, the governing equations by Berger and Karman with the boundary condition of the edges clamped were solved by employing the Galerkin method. ^ A comparison with ^ e numerical results by the Karman -type non-linear governing equations showed sufficient agreement to verify the much simpler Berger approach. The graded elastic modulus can control the deformation of the plate. ACKNOWLEDGMENT The authors are deeply indebted to Dr. J. L. Nowinski, H. Fletcher Brown Distinguished Professor Emeritus, Department of Mechanical Engineering, University of Delaware for his helpful suggestions.

REFERENCES 1. H. M. Berger,. "A new approach to the analysis of large deflections of plates," J. Appl. Mech. 22 (1965) 465. 2. J. L. Nowinski, "Note on an Analysis of Large deflections of Rectagular Plates," Appl. Sci. Res., Sec. A, Vol. 11(1962)85. 3. N. Kamiya, "Large Thermal Bending and Thermal Buckling," ACTA TECHNICA CSAV, 1(1982)33. 4. J. L. Nowinski, and H. Ohnabe, "On certain inconsistencies in Berger equations for large deflections of elastic plates," Int. J. Mech. Sci. 14 (1972) 165-170. 5. Schmidt, R. 1974. "On Berger's method in the nonlinear theory of plates," J. Appl. Mech. 14:521. 6. T. Horibe, "Boundary Strip Method for Large Deflection Analysis of Elastic Rectangular Plates," Transaction of the Japan Society of Mechanical Engineers, 56(532) (1990) 140 (Japanese). 7. H. Ohnabe and F. Mizuguchi, "Large deflections of heated non- homogeneous circular plates with radicaUy varying rigidity," Int. J. Non-Linear Mechanics, 28, (4) (1993) 365. 8. H. Ohnabe and F. Mizuguchi, "Non-Linear Vibrations of Heated Non-Homogeneous Elastic Circular Plates with Radially Varying Rigidity," Proc. American Soc. Composites, 9th Technical Conference, (1994) 1147.

86 9. F. Mizuguchi and H. Ohnabe, "Large Deflections of Heated Functionally Graded Simply Supported Rectagular Plates with Varying Rigidity in Thickness Direction/* Proc. American Soc. Composites, 11th Technical Conference (1996) 957. 10. M. Sunakawa, ^Thermal Deformation of Clamped Rectangular Plate Subjected to Aerodynamic Heating," Transaaion of the Japan Society of Mechanical Engineers, Vol, 9, No. 85, (1961) 37 (Japanese).

A = 0, »/»0.3.qQ*-0 I

.

I

I

.

.

L

1 Fig. 1 Relation between maximum deflection( f ) and temperature difference ((b/h)âTj) with TQ/TI ' '

\j,

Berger ^«0 - —-^/?-l,n-2 Karman /?.l.n-2

A=1,

y=0.3,

T/T=1 0

i—•—I—I—I—I—I

100

200

I

1

L

300

400

500

Fig.2 Maximum deformation due to uniform external loading QQ*

600


87

Model investigation of ceramic-metal FGMs under dynamic thermal loading: Residual stress effect, thermal-mechanical coupling effect and materials hardening model effect Qing-Jie Zhang, Peng-Cheng Zhai and Run-Zhang Yuan State Key Laboratory of Materials Synthesis and Processing Wuhan University of Technology, Wuhan 430070, P.R.China

ABSTRACT The analysis model for the response of ceramic-metal FGMs under dynamic thermal loading is investigated. Emphasis is put on the effects of the residual stress, thermalmechanical coupling and hardening model for the materials. It is shown that the three effects are significant when the materials' response is inelastic and should carefully be considered in constructing the analysis model.

l.THE STATEMENT OF THE PROBLEM The key issue in developing ceramic/metal FGMs is to identify an optimum compositional gradation or micro structure according to the response to service loads or environments. Since different responses may lead to different conceptions of the optimum design, it is important to establish a correct model for the response analysis. There have been some studies on the service stress and optimum design of FGMs under some service environments, but a detailed investigation of the analysis model is lacking. The present paper focuses on the model investigation of the service stress of the materials under dynamic thermal loading. The loading history considered is indicated in figure 1 which simulates a wide range of service environments. In figure 1, the thermal loading history consists of two phases: phase I corresponds to the cooling phase after sintering and this phase is steady one; phase II corresponds to the service phase and this phase is dynamic one, either thermal shock process or thermal fatigue process. Phase II is illustrated in more detail in figure 2. The model investigation involves three important effects: • the residual stress effect. The residual stress is produced in phase I and may exert a significant effect on the service stress in phase II. This should be considered in a correct way. • the thermal-mechanical coupling effect. The thermal-mechanical coupling results from phase II and is an important phenomenon for the dynamic thermal loading process. This effect depends on the thermal loading rate and the plastic deformation of the material.

88 • the material hardening model effect. For ceramic-metal FGM, there are two hardening models which can be used to describe the plastic deformation: one is the kinematic hardening model and the other is the isotropic hardening model. Under dynamic loading circumstances, the effect of the two hardening models becomes important since they may predict very different responses of the materials. 2.MODEL DESCRIPTION FOR THE THREE EFFECTS 2.1.The residual stress effect There are two methods that can be used to treat the residual stress effect: one is so-called separate analysis model and the other is an unified analysis model. The two methods can be explained in a simple way as follows: separate analysis model: the resultant stress = the residual stress in phase I only + the service stress in phase II only; unified analysis model: the resultant stress = the stress obtained through an unified analysis for phase I and phase II (namely the two phases are treated as one unified loading process). 2.2. The thermal-mechanical coupling effect The thermal-mechanical coupling model for suddenly-heated ceramic-metal FGMs has been developed by the present authors in Ref [1]. To consider the plastic deformation effect on the heat conduction in the materials, the coupled heated conduction equation in Ref [1] is now modified as: ^

^

JT

JT

d

- (A(z) —) - Q (z) - - -f 3/:, (z)a(z)r[3a(z) — + -

G (TTTTT)]

d

" ^:^

G

G

(TT

- -)

The signals in the above equation have been defined in Ref [1]. If the coupling terms(the second and third terms on the right hand side) in the above equation are abandoned, the coupled heat conduction equation is reduced to the common uncoupled heat conduction equation. The motion equation of the model remain the same as those in Ref [1]. 2.3.The materials hardening model effect The stress-strain relationship for FGMs is assumed to be a bilinear form and can be described by the isotropic hardening model and kinematic hardening model as: \G\- G + Hs for the isotropic hardening model J{G- HS^ ) - cr^, = 0 for the kinematic hardening model where H = EE^/(E - E^)\ errand s^ are the yield stress and effective plastic strain of the materials, respectively; E and E^ are the elastic modulus and the elastic-plastic modulus.

89 3.RESULTS AND DISCUSSION A TiC/Ni FGM is used as an example. The graded layers in the FGM are treated as homogeneous with effective properties. The properties, geometrical sizes and the compositional distribution function in the graded layers were given in Ref.[l]. The dynamic thermal load in the service phase is taken as q = 4 MW/m^ and t^ = Is for the residual stress effect analysis and the hardening model effect analysis, and as q = 6 MWlm^ and t^ = 0.5s for the thermal-mechanical coupling effect analysis, where q is the magnitude of the heat flux and IQ is the duration of one thermal cycle. The sintering temperature in phase I is taken as 1300A^. The compositional distribution exponent is taken SLS P = 1.6. The residual stress effect is considered by the separate analysis model and unified analysis model, and the results are shown in figures 3(a) and (b). Figure 3(a) corresponds to the elastic analysis and it is seen that the separate analysis model and unified analysis model give the same resultant stress; Figure 3(b) corresponds to the elastic-plastic analysis and it is seen that the resultant stresses found from the two models are different. This is because in the elastic analysis the two responses in phase I and phase II are both linear and the resultant response can be obtained from a direct superposition of the two separate ones. In the elastic-plastic analysis, however, the two separate responses are both nonlinear and the separate analysis model based on the direct superposition of the two separate responses is no longer suitable. The thermal-mechanical coupling effect is shown in figure 4. The difference between the coupling model and uncoupling model for the presented thermal loading is about 7%. Different thermal loadings have also been examined and the results indicate that the difference between the two models increases when the loading rate and plastic deformation increase. The material hardening model effect is demonstrated in figure 5. From figure 5, the kinematic hardening model and isotropic hardening model produce the same material response in first thermal cycle and different ones in the subsequent cycles. The first difference between the two responses after the first cycle is the compressive history at the ceramic surface: the compressive history predicted by the isotropic hardening model is longer than that predicted by the kinematic one. The second difference between the two responses is the maximum tensile stress at the ceramic surface: it is nearly the same in every thermal cycles for the isotropic hardening model, and it changes and increases in the subsequent cycles for the kinematic hardening model. ACKNOWLEDGEMENTS This work was supported by the National Science Foundation of China REFERENCES 1. Q.J.Zhang, G.H.Zhang and R.Z.Zhang, Proc. 3rd Int. Symp. on FGMs, 1994, 235-240

90 T(K)

time phase I

phase n

Figure 1: Thermal loading history of ceramic-metal FGMs phase I: cooling phase after sintering phase II: service phase

heat flux ,

1

X

ceramic graded layers

1

metal liquid cooling

tmie

Figure 2: Dynamic thermal loading simulating the service phase in figure 1

91 o

time (s)

^

o o (N

O

S o

-K3- unified analysis model —i^ separate analysis model

o o

a: elastic case o o

o o cd

T3

o a o (N B

I

o B o

• unified analysis model • separate analysis model

o o

b: elastic-plastic case Figure 3: processing-service stress obtained from the unified analysis model and separate analysis model

92

_ 1

a

uncoupled theory coupled theory

O rsi in

PLH

s rn C/1 d)

o 0^

^ ^

h

0

0.5

1

1.5

time t(s) Figure 4 : Effect of the thermal-mechanical coupling model

o o o

- isotropic hardening model • kinematic hardening model

o o o

Figure 5 : Effect of the materials hardening model


93

Fractal geometry and it's implications to surface technology D.P.Bhatf, O.P. Bahl^ R. Schumacher^ and H. Meyer^ ^Carbon Technology Unit, National Physical Laboratory, New Delhi 110 012, India Âtotech Deutschland GmbH, Erasmusstrasse 20-24, 10553 Berlin, Germany The basic know-how is presented to simulate impedance diagrams of complex equivalent circuits by viewing the electrode surface through fractal patterns. The implications of this model for electrochemical surface technology are also reported in this paper. 1. INTRODUCTION In the recent years fractal geometry has made considerable advances in the surface problems of many scientific disciplines^'^. Fractals (a word coined by Mandelbrot in the seventies) which mean basically for either irregularity orfragmentation,are more than the topographical dimensions, or these are the geometrical objects of non-integer dimensions which always exhibit the rule of self-appearance characteristics in contrary to the conventional elements of Euclidean-geometry. One of the first steps of the development of systematic fractal geometry, including its computer graphic aspects have blossomed tremendously on the basis of a simple system of Z = x^+C in order to subsequently demonstrate how one could calculate Mandelbrot set^'"^ in a particular plane of Cp,q. Assemblance of ZiZ2,Z3 Zn, under varying conditions of the square of the hypotenuse of the p,q plane while put together in the plane by applying the simulation principles, could generate two categories of points viz. White and black, leading to the formation of the strange figure, nick-named as apple tree owing to its appearance (Fig.l). Any fiirther modelling of Cp,q points in different shorter ranges from the Fig. 1 could give rise to ensemble offinerdiagrams^

A

B

n^T;r-A>Q.

. ^ ^

3^

^-^

Brtjcr^tZt^

(a) Figure!.

(b) "^'Ûre

2.

94 Traditional electrochemical concepts of the interface usually proceed by assuming an ideal smooth electrode surface ( e.g. Mercury). In other words, the ideal homogeneous electrode surface plane is often the worst assumption on the part of the electrochemist to prepare their interfacial experiments. Decisive factors associated with irregular heterogeneous surfaces are governed in various processes for e.g. the growth of crystalline and amorphous materials, heterogeneous catalysis, galvanic processes, corrosion, general decomposition processes, surface rich adsorbance, surface enhanced Raman spectroscopy, etc. Distinct features of the fractal surfaces in comparision to those of the non-fractal ones have been exemplified in Fig. 2A-E^:SituationA: Here is a case where atoms or molecules (o-o) go alongwith the surface only. In case (a) having the smooth surface, the distance between the molecules or species is shorter within the same length of the electrode and hence could be considered as the better situation as compared to the situation with fractal surface (b) Situation B: In this situation atoms or molecules go to the surfaces by diffusion controlled mechanism. Fractal electrode (b) is better than the smooth electrode (a) because the ionic species have got relatively more paths in the former situation and could thereby possess more ionic mobility to get themselves transported to the electrode surface. Situation C: Edges, cracks, etc. (b) could place at disposal energy richer reaction centres than the surfaces with the normal number of free valencies (a). Therefore, the active centres can be distributed more in case of fractal surface (b) than the non-fractal surface (a). This is a prominent case applicable to electrocatalysed systems likefiielcells. Situation D: When the surface has many neighbouring atoms or species, one may then expect two neighbouring atoms or species to interact. In (b) situation, one has choice for the atoms to make more neighbours and hence the system possesses more neighbouring atoms. Because of the multiple choice, the interaction could,therefore, result more in the fractal electrode than in the case of smooth surface (a). Situation E: Both (a) and (b) planes here belong to the real surfaces (fractal). However, the dimension of the molecular species would be the detrimental parameter of the reactions in the real surfaces, i.e. having the same surface, either more or less number of molecules can be absorbed. The size of the molecules is apparantly smaller in the former one and hence more number of molecules can be accommodated in the structure (a) than (b). Fractal dimension, D is considered as an effective number that characterises the irregular electrode surface. The term has been related to physical quantities such as mass distribution, density of vibrational stages, conductivity and elasticity. If we consider a 2-D fractal picture in its self-similar multi-steps, one can draw various spheres of known radii at various points of its structure and may thus count the number of particles, N inside the sphere by microscope, following relation will then hold good : N(r) - r^ (1) where D = Fractal dimension and N = Number of lattice points inside a sphere of radius, r The plot of r vs. N could give rise to a straight line, the slope of which equals the value of fractal dimension. Equation (1) is, however, not valid for the 3-D geometry of the structure. A general simulation programme for the calculation of Nyquist plots with

95 respect to the 3-dimensional fractal electrode-electrolyte interface is included in the next section. ^4

/

0 STAGE 6=30.13 D = 2.50 1st STAGE — I \—I

^

>—^ ^^—11nd STAGE

Sc

.^JLAJ Figure 3.

^ A j X A - m r d STAGE Figure 4.

2. STRUCTURAL MODELLING OF THE NYQUIST CURVES FOR FRACTAL ELECTRODE/ELECTROLYTE INTERFACE The simplest model to describe the impedance behaviour of the metal/solution interface can be the Koch curve. Fig.3 illustrates the view of the irregular surface in terms of fractal geometry. Each interface consists of long parallel V-shaped grooves filled with electrolyte (black shaded region). Working electrode is depicted by the white portion. The metal/electrolyte interfacial boundary forms a generalised Koch-curve, the fractal-dimension of which can be measured by various methods described elsewhere^'^. Roughness of the surface is the measure of the fiinction of 0 (angle of the grooves). In this example, we consider a four-stage Koch-curve wherein 4 peaks of different sizes are present (Fig.4). Dilatational symmetry is one of the feature of the Koch-curve. Each peak could thus possess different impedance characteristic, which are named as Z4, Z3, Z2 and Zi according to the falUng sizes. Besides these peaks, there are 16 flat regions which show pure capacitive behaviour (Zo). As the impedances are all connected in parallel, the whole impedance, Zt is composed of the reciprocal values of the individual impedances. If the different regions of these peaks are taken into account, Zt may be written as : 1/Zt =16/Zo+8/Zi +4/Z2 + 2/Z3 +I/Z4 (2) 2.1. Calculation of the impedance of a flat region (Zo) If we permit charge penetration to the interface, the simplest equivalent circuit diagram is then a parallel circuit composed of R^ and Cai in series with Rbuik- Its impedance is calculated as : 1/Z = (jcoCdi + 1/Rct) (3) or Z = Rct/GcoCdiRct+1) = RcAo'Cdi 'Rct'+ 1) - j [(o)CdiRct')/(«'Cdi'Rct'+ 1) (4) Taking into consideration Rbuik gives :Z = Ret/(co'Cdi 'Rct'+ 1) - j [(cDCdiRct')/(«'Cdi'Rct'+ 1) + Rbuik

(5)

96 2.2.

Calculation of the impedance of smallest peak (Zi) Conical shape as divided into K number of slices is the drawing of the smallest peak [Fig. 5(a)]. Equivalent circuit of these different slices is an ensemble of branched resistance/capacitance ladders [Fig.5(b)]. The parameters like ro,ri,r2, r/; ro',ri',r2', n' and Co,Ci,C2, Ci are the K different values of bulk resistances, charge-transfer resistances and the capacitances, respectively. Wang^ did not consider these additional charge-transfer resistances. Considering the circled last parallel connection (Fig. 6), the impedance of the last but one slice could be calculated. This rule can be further followed to other equivalent circuit diagrams in a similar manner till one gets Zo which would be the total impedance of the peak. Following the analogy of the apple tree, in this situation too, one could do with a recursive calculation in order to formulate the following derivation to calculate the impedance of all the sHces : 1/Zi.i = l/{(ai +ri) + bj)} + l/r/.i + JCOCM (6) where i is the index for K and varies from K to 1. Substitution of uj = ai + n in equation (6) followed with suitable mathematical changes gives :1/Zi.i = Ui/(ui' + bi') - j [(bi/(ui' + bi')] + l/r'i.]jcoCi.i (7) Separating into real and imaginary parts gives :1/Zi.i = Ui/(ui' + bi') + l/r-.i + j[coCi.i - {bi/(ui' + bi')}] Substitution of Ci = Ui/(ui ^+ bi^) + l/r'i-i as real part and di = coCi. imaginary part gives :l/Zi.i = Ci+diJ or Zi.i = l/(ci + dij) = Ci/(Ci' + di') - j[di/(Ci' + di')]

Thus, we obtain > New real part: New imaginary part

ai-i = Ci/(ci^ + diO bi.i-di/(Ci' + di')

bi/(Ui' + bi')

(8) as

(9) (10)

(11) (12)

4=hÎ3TCI]TCIh (b)

-^^Y^'fg"f(]

^^-o-

Figure 5. Figure 6. Now ri, r'i and Ci are to be calculated. The length and the depth of the electrode has been originally assumed as 1 cm. Capacitance of the interface may be calculated by multiplying the standard capacitance and the length of the Koch-curve. Both sides of the groove structure are considered here in constrast to the flat smooth surface. Using the geometrical principles, further steps with respect to the calculations of length of the fractal electrode, number of peaks, bulk resistance, etc. have been followed in the numerical

97 model. With this knowledge, it could be then possible to calculate the impedance of the cone (Zi) in any multiple number of the structure. 2.3.

Modelling of a rough electrode with equivalent electrical circuits Z2 is the impedance of the second smallest network as shown in Fig. 7(a). Parallel placements of three branches each having the Zi impedance could give rise to the resultant impedance of Zi/3 at the intersection. The latter, in turn, becomes the terminating impedance at the end of the network for the calculation of Z2 [Fig. 7(b)]. The branched resistance/capacitance network can be solved by using the same equation as employed previously for the calculation of Zi. The impedances of the next higher grooves such as Z3, Z4, Z5,.... Zn, can also be calculated in similar manner depending upon the branching configuration. In this work, a general programme has been thus developed using Turbopascal 5.0 language in order to simulate the impedance of the many peak irregular surface with n number of stages. The details of this software are to be published.

(a)

(b) 0

^00 200 REAL PART(ohm)

Figure 7. 3. PRESENTATION OF THE MODEL CALCULATIONS

Figure 8.

The assessment of the reported model for experimental passivation systems of say magnesium/magnesium perchlorate^^'^^ and titanium/or titanium dioxide/sulphuric acid has been made from the view-point of fractality of the electrode surface and a good agreement between the model calculated complex plane impedance (Fig. 8 being a typical simulated plot) and the measured Nyquist-plots is obtained. The charge transfer resistance (Ret) values in respect of magnesium AZ31 alloy in 2 M Mg(C104)2 have been measured as 4154 , 338, 238 and 150 ohm for the applied potentials of 0,10,30 and 50 mV, respectively^^. Increase of the passivation potential from 0 to 50 mV has brought about the gradual decrease of the radii of the semi-circle - an anomalous observation because in any normal circumstance, the Ret of the electrode surface should have increased with the rise in the passivation (a case of oxide film formation). In order to rationalise this unusual polarisation behaviour, one could imagine the interpretation based on the concept of anion adsorption in the surface oxide layer wherein afieldassisted transport of ions through the passive layer is introduced to account for the ion current density increase upon raising the oxidation potential. These interpretations are, however, not valid for systems containing no chloride in the base electrolyte. High corrosion rate accounts the reason of the non-employment of MgCb

98 electrolyte in the cells developed by us in India ^'*•^^ Different parameters such as the groove angle, number of slices, number of different peaks, capacitance, series/and parallel resistors and the thickness of charge transfer resistor have been varied during the simulation by the programme so as to obtain the series of semicircled impedance diagrams. The important findings are such that decrease of the groove angle brings about the decrease in the Ret which has been found valid for 10 < 9 < 75 and 5 < N (number of different peaks) < 20. It is thus envisaged qualitatively that during passivation, morphological changes in the electrode take place and this change becomes effective for the charge flux to diffuse which thereby explain the cause of anomalous behaviour. This model, however, requires much more refinement as the small lateral branches remain still unconsidered and the number of slices (K) must be selected so large that the impedance is constant i.e. Z ^ f (K). Also the simulation of the diffusion controlled interfacial processes has not been possible through the present model. These are some of the open areas wherein modelling research could be further pursued . Acknowledgements. Correspondence and discussions with M. Wicker is highly acknowledged. DPB is obliged to DST , Govt, of India and Klaus Hagen, Atotech, Tokyo 141 for providing partial financial aid in attending FGM96 symposium. Grateful thanks are accorded to the Director, NPL, New Delhi for giving permission to publish this paper. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.

L. Pietronero and E. Tosatti (eds.). Fractals in Physics, Elsevier Science Publishers B.V.,Netherland, 1986. M. Gardner, Scientific American, 238 (1978) 16. B.B. Mandelbrot, The fractal geometry of nature. Freeman W.H. and Co., New York, 1982. H.-O.Peitgen and P.H. Richter (eds.). The beauty of fractals - Images of complex dynamical systems. Springer Verlag, New York Inc., 1986. H.-O. Peitgen and D. Saupe (eds.). The Science of fractal images. Springer Verlag, New York Inc., 1988. P. Pfeifer, Chimia, 39 (1985) 120. D. Avnir and P. Pfeifer, J. Chem. Phys., 79 (1983) 3566. R.F. Voss, Physica Scripta, T13 (1986) 27. J.C. Wang, Electrochim. Acta, 33 (1988) 707. R. Udhayan and D.P. Bhatt, In International Conf on Magnesium alloys and their applications, Germisch-Partenkirchen, Germany (1992) 59. R. Udhayan, Ph.D. thesis, M.K. University, Madurai, India, 1991. M. Wicker, Ph.D. Dissertation, University of Kiel, Kiel, Germany, 1991. D.M. Drazic, S.K. Zecevic, R.T. Atanasoki and A.F. Despic, Electrochim. Acta, 28(1983)751. D.P. Bhatt and R. Udhayan, Indian Pat. 749/DEL/l 991. R. Udhayan and DP. Bhatt, J. Power Sources, 39 (1992) 323 ; J. Appl. Electrochem., 23 (1993) 393.


99

Database System for Project of the Functionally Graded Materials K. Kisara, A. Moro, Y. S. Kang, M. Niino National Aerospace Laboratory, Kakuda Research Center, Japan. ABSTRACT This report will introduce the concept and status of a database system for a national project entitled: "A Study in the Development of Energy Conversion Materials through the Formation of Gradient Structures" , which project is being promoted by some thirtyodd industrial, academic and governmental organizations. While the database system will be, organizationally speaking, somewhat loose-knit, it is ejected that the project's initial goal will be realized within a fixed period of time. In order to provide a convenient means of comunication for researchers working in various organizations to exchange information, complete their work assignment in a short space of time and maintain a common perspective, the establishment of some method of information-sharing is essential. At the same time the report will describe measures of the need for maintenance of the database and a network to make use of it in real time so as to promote support for the project and, additionally, show that the use of the Internet is a viable method of operating the system at this present time.

1. INTRODUCTION The Fimctionally Graded Materials Database System was established to manage the entire body of data arising out of the Science and Technology Agency funded project: "A Study in the Development of Energy Conversion Materials throu^ the Formation of Gradient Structures" (Phase I: 1993-1995; Phase II: 1996-1997, hereafter referred to collectively as the FGM Part 2 Project), and to maintain such so as to facilitate effective access to said data. The project aims at dividing materials into thermal areas and developing the most efficient energy conversion elements for each individual area, all the while keeping to the fore the concept of a compound system that would convert thermal into electrical energy at a high level of efficiency. Some thirty-odd industrial, academic and governmental orgEinizations are participating in the project, the activities of which are carried out by subcommittees. As the fimction of these subcommittees is to make use of e)q)erimental data found in the published reports and minutes of seminars held in various fields of study, an information centre to collect

100 and maintain this data assumes an important role in enabling the project's participant organizations to share and effectively access such information resources. Additionally, the centre play s a vital role in preventing the loss of project assets. Also,fromthe very early stages of the project, maintaining and actually operating such a centre as a base for accessing information is vital to the project's receiving adequate support.

2. FGM PROJECT AND DATABASE The following is an outline of the role of the database within the project as a whole. The research being conducted under the project has as its principle aim the development of fundamental technological skills essential to the creation of new materials, these skills being developed by sharing results of research among the various specialist subcommittees dealing with planning, synthesis (creation of new materials) and evaluation into which the thirty-odd participating organizations are divided. By means of this co-operation, participating bodies become part of a loose-knit organization working together to achieve common goals and thus it can be seen that the adoption into the system of a groupware concept whereby these bodies engaged in research can mutually access each other's published data would be effective. The relative position of the database as seen against the background information outlined here is illustrated in Figure 1. As described above, within theframeworkof a looseknit organization where participant bodies work together to achieve common goals, the database needs to provide an operating system for the groupware, desiga the system platform that serves as its base and, at the same time, fulfill the primary function of the database, namely to prevent the loss of the fruits of project research so that individual researchers may mutually access this information. The different duties involved in this information distribution are classified variously as: data gathering and maintenance, standardization, access environment maintenance and educational.

^ ,

plaiming(designing)

.•^

estimate of characteristic estimate of performam design of FGM ^ 3 ^ 3 ^ ^ ^ Ithennoelectru material

Thermal andl Mechanical evalution total evaluation laracteristic of FGM iterial

S Ithermionic database material |(FGM emittei a te collector] radiator o insulator electrode heat collecter

, ^

synthesisofinaterials

'^.

Fig.l The relative position of the database

In order to accomplish all this, the FGM Database manages the entire body of project data and maintains a network for effectively accessing this data. The relationship between the database and the project is shown in Figure 2. Basically speaking, the database is made up of three groups of data shown in Figure 2.: data from written sources, that from electronic conferences and measurement datafromexperiments.

101 characteristic of FGM material Icharacter of thermal and | mechanical evalution FGM database (three groups) f Database server ^ database *«ct data management system store data

electronic filing report data (Optical memory disc) logging data of BBS (first class) communication

JI

provide data multi platform -interface—! subcommittees mtemet planning or modem [Network systeiji WWW e-mail ftp —news—

thermoelectric material thermionic generator synthesis of materials evaluation

-support system for planning-

knowledge base of FGM (example based)

theory, experence simulation technique of use of database] technique of designing

expert system

Fig.2 The relationship between the database and the project

3. OPERATION AND THE NETWORK 3.1. Design of the System Platform In the early stages of the project, a database system centering on personal computer communication was constructed to enable infonnation to be shared and accessed. At the present moment a different approach is possible with group ware making use of the Internet, and machine interface is possible by means of hypertext browsers such as the World Wide Web. As the database is constructed to gather and maintain information, questions such as the following are pertinent: What information is gathered in the database? How is it compiled? Who uses it? How do they use it? What is needed is a database that will make the optimum use of limited resources, in other words, one that will increase the efficiency of the brainwork of its users.

102 In the area of what information is gathered, the following data has been collated: information and actual experimental data on the physical properties, methods of making and measuring the performance of new materials being developed; graphs, tables and photographs published in seminar journals and subcommittee reports together with data in written form from monographs and the published minutes of subcommittee conferences. As to how it is compiled, keywords are assigned to assembled data from e^qjeriment measurement values, images, written works such as monographs and this data is maintained in electronic files as a means of managing project information. Also, the results of information exchanges using electronic bulletin boards are stored and accumulated as further resources of information. As to the envisaged users of the system, for the duration of the project, the idea is to provide timely information to researchers belonging to organizations involved in the project and, upon the project's completion, make this information available to public users in an open database. On the matter of method of access, direct access via the Internet has been chosen. At the inception of the project, a network was deployed using modems connected to the public telephone lines but, in response to changes in the network environment cause by the growing availability of the Internet, a switch was made to direct access via the net. In summary, the database was assigned the following three information management roles: To serve as a database in the narrow sense of the term - simply gathering, organizing and recording data. To provide a system for dissemination timely information - enabling participants to share groupware data. To maintain an environment for access and a users' service (support for researches on how to make use of the system). These three roles are dealt with morefrillybelow. 3.2. Maintaining an Environment for Information Access In order to keep the project moving forward it is vital that participant organizations not only share the same goal but also share information and maintain a common perspective. The project maintains a closed networksystem, excluding access to all but participant org3nizations, as a base for information sharing whilst protecting portions thereof that may need to be kept secret. Operation of the original service begun at the Japan National Aerospace Laboratory's Quaked Research Centre with the construction of a personal computer communication host computer (BBB) using four public telephone lines. Subsequently, with the availability of the Internet, a BBB using Window and Macintosh to support TCP/IP protocol was put into operation. At the present moment, a switchover is taking place in the mode of operating the database access environment from the old C/S (client server) system to a method employing the concept of a distributed database such as the World Wide Web using the Internet. A distributed database is being constructed hat uses data and monographs in the

103 possessionof the various individual participating organizations to create home pages, and then serves as a database centre, consolidating these pages into a single home page for convenient access. 3.3. The Functionally Graded Material Database in the Narrow Sense of the Term Gathering, organizing and recording data contributes to the accumulation of the project's immaterial assets. Data is principally assembled from the published monogr^hs of researchers and from subcommittee reports. These are recorded on electronic files. Data is organized at the time of recording according to information or keywords necessary to reference it. Additionally, in order to manage this information, a search application is provided to facilitate researchers' access to the data from their own personal computers. Also, as measurement data from eêriments is used in designing new materials or inferring their physical properties, it is vital that such measurement data be kept up to date in a systematic fashion so that the database may fulfill its role in the narrow or restricted meaning of the term "database*' and the maintenance of such a body of experimental data increases the value of the database's support operations. 4JTJTURE PROSPECTS In these days when the dual concepts of the Intemet and group ware are being brou^t more and more to the fore, a base whereby project researchers can make optimum use of needed information is being put in place. Formerly, a WWW browser would read and display a specified file but, from the spring of 1995, the Hot JAVA browser developed by the Sun Microsystem Company has deployed a form of programming called "Applet" . By means of CGI (Common Gateway Interface) procedures org3nically linking h i ^ processing level database servers such as SQL together with the WWW server, the construction of a distributed database able to conduct sophisticated dialogue has become possible. Always adjusting to progress in the network environment, the Functionally Graded Materials Database will continue to gather data and support the project. It will also continue to frmction as an attractive centre for information pertaining to frmctionally graded materials by translating the tables and the abstracts of principal monographs into En^sh, thereby fiilfilling its role as an internationally valuable information source and contributing to the standardization of research data and, additionally, it is intended that it will serve as a news centre educating the public regarding the concept of fimctionally graded materials.

104

NAL KRC LAN Macintosh TCP/IP H

Macintosh

GatorBox Filing system

UNIX

Windows

LocalTalk

llU EtherNET

AppleTalk TCP/IP DataBase BBS;First Class

^ ^ ^ '

IBM/AT DOS/V Modem (4 ports)

Macintosh

TEL NTT

IBM/AT Windows

PC98/DOS

WWW databese homepage http://fgin.kakuda-splab.go.jp/

Fig.3 Network System for FGM Database

References 1) R. Watanabe ,Fimctionally gradient material(Japanese),The society of non-traditional technology


105

Fracture Mechanics of Graded Materials F. Erdogan Department of Mechanical Engineering and Mechanics Lehigh University, Bethlehem PA, 18015, USA In this article after a brief review of elementary principles of fracture mechanics, certain issues concerning the applications to graded materials are identified and some examples are given. 1. INTRODUCTION In recent past there has been a great deal of interest in the concept of material property grading as a tool for new material design. This is usually accomplished by suitably varying composition and/or microstructure of the medium. Thus far most of the work in the field has been on metal/ceramic composites, various intermetallics and electronic materials with current and potential applications as interfacial zones and coatings. From a mechanics view point the main advantages of material property grading appear to be improved bonding strength, toughness and wear and corrosion resistance, and reduced residual and thermal stresses. Some typical applications include thermal barrier coatings of high temperature components in gas turbines, surface hardening for tribological protection and graded interlayers used in multilayered microelectronic and optoelectronic components [1-3]. An important aspect that needs to be addressed in various engineering applications of FGMs is the question of reliability and durability in general and fracture related failures in particular. This article is concerned primarily with fracture mechanics as applied to structures involving FGMs. After a brief description of some basic notions of fracture mechanics, certain critical issues relating to FGMs are discussed and some examples are given. 2. FRACTURE MECHANICS The quantitative theories of fracture which are currently in use are based on a fundamental principle of continuum thermodynamics, namely the first law or the energy balance which states that dU_ _ dV^ dJ^ dD_ dt dt dt dt where t is the time U the external work, V the recoverable (elastic) energy, T the kinetic energy and D the sum of all irreversible energies associated with the creation of new fracture surfaces such as surface tension, plastic work and viscous dissipation. If the solid contains a

106 dominant flaw which may be represented by a planar crack having a surface area A(t) and if the fracture process is taking place in a quasi-static manner and A(t) can be characterized by a single length parameter a{t), then dT/dt = 0 and defining dD/da = Qc, (1) may be expressed as ±(U-V)=

Gc,

(2)

where the left hand side is the rate of energy available for fracture (also known as Q, the crack driving force or the strain energy release rate) and Qc represents the energy required for unit crack extension. If the fracture can be characterized as a low energy or brittle phenomenon, then it can be assumed that the size of the inelastic region around the crack tip (also known as the fracture process zone) where all the dissipative processes take place is small compared to the crack size a, Qc is independent of a and the energy flowing into the crack tip region comes from the elastic bulk of the medium and is insensitive to the details of the stress and deformation states in the fracture process zone. The significance of this last observation lies in the fact that a purely elastic solution may be used to calculate the crack driving force. For example, by observing that under normal opening or mode I loading the asymptotic values of the cleavage stress and crack opening displacement at the crack tip x = a, y = 0 are given by [4] ^^^^^'^^ ~ ~J2(i^'

^y ~ ^y = ^^y(^'^) = " ^

hy/2{a-x),

(3)

by using the concept of crack closure energy, the energy available for fracture can be expressed as 1 pa+da

d{U-V)

= -

J

ayy{x,0)IÛy{x - da,0)dx,

Z Ja

ki = ^mJ2{x

—{U -V) aa

- a)ayy{x,0),

1 4- /c

= Qi = - ^ n k l Qfi

(4)

where ki is known as the mode I stress intensity factor, /x is the shear modulus and « = 3 - 4z/ for plane strain and « = (3 - i/)/(l +1/) for plane stress, i/ being the Poisson's ratio. Similarly under mode II, the in-plane shear and mode III, the anti-plane shear loading conditions, the stress intensity factors, the corresponding energy release rates and the total strain energy release rate for co-planar crack growth are given by /C2 = MiJ2{x

-a)(7a;y(x,0),

^// = ^ 7 r A : | ,

Giii = ^7rkl

ks = ]im^y2{x - a) ayz{x,0), Q = Qi+Qii + Qiii.

(5)

Referring to the general expression (2), in brittle fracture the critical value of Qc corresponding to the co-planar crack growth is known as Qic, the fracture toughness, with G = Qic being the fracture criterion. In practice, very often Kj = ^J^k\, Kjj = ^Jl^hi, Km = v^/cs and Kj = Kic are used as the stress intensity factors and the fracture criterion. In addition to their successfiil applications to fracture stability problems, the stress intensity factors have been widely used as correlation parameters in analyzing the subcritical crack growth rates da/dn (in fatigue) and da/dt (in corrosion), n and t referring to the number of

107 load cycles and time, respectively. In the presence of large scale inelastic deformations the general energy balance criterion described by (2) is still valid. However, in this case since Qc is no longer independent of the crack size, the fracture propagation can not be described by a single parameter criterion. In high energy fracture, the fracture process zone, and consequently Gc usually grows with the growing crack size. Hence, for fracture stability problems it becomes necessary to use a criterion based on variable Qc such as a crack extension resistance curve or a R-curve approach. Unlike the linear elastic fracture mechanics dealing with brittle fracture and subcritical crack growth, the tools of the so-called elastic-plastic or nonlinear fracture mechanics dealing with high energy or ductile fracture are not well-developed and universally accepted. In some cases the J-integral is used with some success to compute the crack driving force, Q = d{U — V)lda. In all cases the application of the criterion G = Gc requires extensive numerical and experimental work. 3. MAJOR ISSUES IN FGMS The principles of fracture mechanics described in the previous section are applicable to inhomogeneous as well as homogeneous materials. In FGMs the difficulties arise in the solution of elastic or elastic-plastic crack problems to evaluate G or ki, ki, k^ and in characterizing the material to determine Kjc, Gic or Gc where the fracture toughness Gic is no longer a material constant [5]. The definitions of stress intensity factors and expressions of the strain energy release rates given by (4) and (5) are still valid provided the elastic parameters /i and K are evaluated at the crack tip. Following are some of the major issues concerning the fracture mechanics of FGMs. (a) Elastic singularities. As long as the elastic parameters ^ and K are continuous ftinctions of the space variables with piecewise continuous derivatives, the stress state around the crack tips has the standard square-root singularity. For example, in plane isotropic elasticity problems for r -• 0 the leading terms of the stresses are given by [6-8] -

-'^^'"'^^[fci/iyW + fc2/2i,W], {ij) = ir,e)

(6)

where (r, 9) are the polar coordinates at the crack tip, ki and k2 are the modes I and II stress intensity factors, (f>{r,6) is a smooth function with 0 and the crack is located along 0 < x < a, y = 0. (b) Analytical methods/benchmark solutions. Even though there are no known closed form solutions for crack problems in FGMs, for simple property variations the formulations leading

108 to singular integral equations are straightforward and accurate solutions can be obtained [7]. (c) Computational methods. Finite element method is the major computational tool. However, to improve efficiency and accuracy the development of enriched crack tip and transition elements and ordinary inhomogeneous elements will be needed [10]. (d) Material orthotropy. In many cases the material orthotropy seems to be the consequence of processing technique. For example, FGMs processed by using a plasma spray technique tend to have a lamellar structure. Flattened splats and relatively weak splat boundaries result in an oriented material with higher stiffness and weaker cleavage planes parallel to the boundary [11]. On the other hand graded materials processed by an electron beam physical vapor deposition technique have usually a columnar structure giving higher stiffness and weak fracture planes in thickness direction [12]. These oriented materials can generally be approximated by an inhomogeneous orthotropic medium. (e) Inelastic behavior. Because of the length scales involved in FGM coatings and interfaces, in addition to conventional plasticity, one may have to use a microplasticity approach which accounts for the effect of strain gradients on strain hardening coefficients. The resulting nonlinear elastic-plastic crack problems require a numerical approach with special inhomogeneous elements. (f) Rheological effects. Invariably FGMs are used in high temperature environments. As a result the time-temperature effects may not be negligible and the material may have to be modeled as an inhomogeneous viscoelastic or viscoplastic medium. (g) Dynamic effects. Generally, high velocities in propagating cracks and high rates of loading (e.g., impact) in stationary cracks would necessitate the consideration of inertia effects in solving the fracture problem. However, even for the uncracked linear elastic inhomogeneous bounded medium, the stress wave phenomenon is not fully understood. The existing solutions are restricted mostly to one dimensional problems in materials with certain simple property gradings. (h) Material characterization. This is still the most important issue in studying the fracture mechanics FGMs. The knowledge of thermomechanical and fracture mechanics parameters of the material is essential for any realistic predictive reliability study of FGM components. 4. EXAMPLES In this section we will briefly discuss three groups of examples. The first two are concerned with FGM coatings on homogeneous substrates in which for simplicity it is assumed that the bond coat has the same thermomechanical properties as the substrate. The third group deals with the effect of material orthotropy on the stress intensity factors. 4.1. Surface Cracking In FGM as well as homogenous (ceramic) coatings the fracture related failures may take place in various ways. One way would be under cyclic mechanical and/or thermal loading the initiation of a fatigue crack at a surface defect, the subcritical growth of the crack in thickness direction, fracture of bond coat and opening an oxygen path to the substrate. This may happen if there are no weaker fracture planes in the coating and the coating/bond coat interface is

109 sufficiently strong. Such crack initiation and growth in thickness direction have been observed in FGM coatings by several investigators (e.g., [13,14]). A variation of this mode of failure would be multiple (or eventually, periodic) surface cracking. Multiple cracking is clearly in evidence in the work reported in [14]. In practice, because of the long hold times under high temperature, the crack growth process would be heavily enhanced by the environmental effects. Even in the simplest case of low temperature and relatively high cycle fatigue for which a simple two-parameter crack propagation model such as ^=C{AK)\ C = C{a), b = b{a) (8) an may be applicable, in FGMs the parameters C and b would be dependent on the material composition and the microstructure. This would mean that in surface crack problems C and b would be functions of the crack length a. For modeling and any quantitative analysis, these functions must be determined from the fatigue data on homogenous cupons with various composition. The surface crack problem is one of mode I and the determination of the stress intensity factor ki is sufficient for fracture stability and fatigue analysis. For a FGM coating on a homogenous substrate some sample results are given in Figures 1-3 [15] where hi and /12 are the thicknesses of coating and the substrate, respectively, c is the crack length, K is constant and the shear modulus of FGM is given by /i(x) = /ioexp(/3a:), ^0 being the modulus of the substrate. Figure 1 shows the effect of material inhomogeneity on /ci in a medium loaded by fixed grips or constant strain EQ. The normalizing stress is given by CTQ = 8/ii£o/(l + /^), /ii := /ioexp(-/5/ii). Figures 2 and 3 show ki for PSZ/Rene 41 FGM coating (/5/ii = 0.375) on Rene 41 substrate loaded by constant strain £0 or constant temperature change AT, respectively. Figure 2 shows the influence of the thickness ratio h2/hi on ki. The effect of the uniform temperature change AT is shown in Figure 3 where To corresponds to the stress-free state and T] and To are the surface temperatures. This is a special case of a general problem in which Ti 7^ To and the medium is under steady-state heat conduction.

. 7.0 6.0 ,

kl

i ; i !

y

h2/h,=0.5 h/h,=1.0 h/h,=2.0 h^h,=10.0

/-

5.0

y/

ic

\

Ôy 2.0 1.0

U—\

,^^^^^^:

-

-'-"'IT-

c/Zii

Figure 1. Mode I stress intensity factor for a surface crack in FGM coating, h\ —h^.

Figure 2. Mode I stress intensity factor for a surface crack in FGM coating, phi = 0.375.

4.2 Spallation Another mode of failure would be the transformation of the surface crack to a T-shaped crack at a relatively weak fracture plane parallel to the surface. This may be microcracks forming along the oxidized splat boundaries or the interface between the thermally grown

no oxide and the coating. There seems to be some evidence of such branching in the results given in [14]. For the T-shaped crack the stress state at the crack tip is one of mixed-mode. Therefore, in the fatigue model, for example, one would have to use A^ rather than Ai^ as the correlation parameter.

Tj=T,=5To Tj=T,=10To T,=T.=20T„

~».^

y

"^^

•r.^

^pL

N

0.025 o 0.020

TT

O^ 0.015

\

arxA"^ "*"-«.»

\

0.010

t\-

0.005

-^^ ^^ *^

1

0.003

^ ^

0.002

1

r_ f

'

0.4

0.6

0.8

1.0

Figure 4 Strain energy release rate for a T-shaped crack under uniform temperature change.

1

\CR2

f

1

LN

r

1

MR1

/^ '

1

0.2

CR1

f

0.001

•

\\.

0.0

- p=:CO

b/l

c/hi Figure 3. Normalized stress intensity factor under uniform temperature rise, ar = 8/ioQ:oTb/(l + K,)

0.004

0.000

p=0.2 p=0.5 p=1 p=3 p=5 p=8

MR2 .

1

1

.HM 1

1

1

"^

Figure 5 Normalized strain energy release rate due to uniform temperature change, ijhi = 5, ^0 = (1 - i^Dids^TfEs-Khi.

Figure 6 Mode I stress intensity factor in an orthotropic FGM subjected to uniform crack surface pressure o-ii(0, X2) = -po, z^ = 0.3

In [14] it was reported that spallation cracks develop in the graded region due to the change in residual stresses caused by the oxidation of the metallic lamellae. Similar observations were made in [16] where a candidate design for an abradable seal was tested 242 hours at 1000°C The seal consisted of a 0.13mm NiCoCrAlY layer, 2.54mm NiCoCrAlY/YSZ FGM region and a 1.27mm low density YSZ. The substrate was a MM247 superaUoy. The spallation occurred in FGM 0.5mm from the initial substrate surface. It was observed that most of the metallic phase in the spalled region was oxidized whereas the part of the seal remaining on the substrate was not. This appears to be due to connectivity of the oxidized region. The continuous oxide layer seems to create a weak fracture plane as well as preventing further oxygen diffusion. Figures 4 and 5 show the strain energy release rate for a T-shaped crack and symmetric edge cracks, respectively. In these examples the substrate is Rene 41 (E5 = 219.7 Gpa,

Ill 1/3 = 0.3, as = 1.67 IQ-^K ) the coating is FGM ( Rene 41 / YSZ, ^Jc = 151 Gpa, Uc = 0.3, Qc = 10"^/°K), h2/hi = 0.16, £/hi = 5,the loading is uniform temperature change AT and the normalizing strain energy release rate is QQ = {1 - u^)(asAT)Ês7vhi. For the FGM coating the modulus variation is given by E{y)

-{

Es, E, -h {Es - Ec)il + ihi/h2) - (y//l2))^

0 400 200

0.4 0.6 0.8 Volume fraction of PSZ,j^s2

Fig. 8 Fracture strengths, in terms of in-plane macrostress (triangles) and maximum "equivalent normal stress" in PSZ phase (circles), plotted against PSZ volume fraction. Solid and open markings refer to the cases with and without taking account of residual stresses.

In view of the particle cracking observed in most composite specimens, we focus attention on the microstress {ojp^^, ^^ ^^^ ^^^ phase, and suppose that fracture occurs when a latent microcrack starts to grow. Since {a)psz is triaxial ((cîi)psz "(^22)PSZ ^^' (^33)PSZ ^^^^ we define the stress triaxiality /3 as j3 = (^33)^^^/ ( K^c y where a

is the crack radius. Accordingly, our task now is to examine the maximum value of a^ given

a^ /((îi)psz = JsinÔ + p^cos^6 + ih + 2{( 1 - p)/(2 - v)}'Isin'O cos'0

(4)

where 6 is the angle between the crack surface normal and the .Xg-axis. In Fig. 9, o^ /(îi)psz is plotted against 6 for several different /3 values (in the range -1^/3 :s 1) with V = 0.25. From the diagram, we see the following: if -0.53 ^ j8 < 1, then (a^) = {o^^)^^ and a latent crack oriented at 0 = Jt/2 will extend; otherwise (-1 ^ /3 < -0.53), a mixed-mode crack extension results {ji/4

1 /; /'

Mercury-porosimetry data for sintered specimens at lOOO^C for 3 h

d in jLim (log) (b) pH=4,5 vol%, 1 mm cut-off

-s?

^TL

1 1 ,1

s 6

1 ' 1' 1 11 1'

o -

a 3

11

o

> C •"

/( //

o

cd

d in jLim (log) (c) pH=4, 5 vol%, no cut-off

OH

.

J. V

"

O

>

d in jim (log) (e) pH=4,10 vol%, no cut-off

Figure 4: Cumulative pore-size distribution of sintered specimens made by different suspensions with different degree of bottom cut-off.

178 A c k n o w l e d g m e n t : The authors would like to thank the German Science Foundation (Deutsche Forschungsgemeinschaft, DFG) for the financial support. REFERENCES [1] A. Grull, Prospects for the Inorganic Membrane Business^ Key Engineering Materials Vols. 61 & 62 (1991) pp. 279-288, Trans Tech Publications, Switzerland. [2] A. Larbot, J.-P. Fabre, C. Guizard, L. Cot and J. Gillot, New Inorganic Ultrafiltration Membranes: Titania and Zirconia Membranes, J. Am. Ceram. Soc, 72[2] 257-61 (1989). [3] K. K. Chan and A. M. Brownstein, Ceramic Membranes - Growth Prospects and Opportunities, Am. Ceram. Soc. Bull., 70[4] 703-7 (1991). [4] R. Kohl, G. Tomandl, A. Larbot, L. Cot, Herstellung und Charakterisierung von keramischen Membranen aus Titanoxid zur Cross-Flow-Ultrafiltration nach dem Sol-GelVerfahren, Kurzreferate pp. 64-66, DKG-Jahrestagung, Bayreuth, 4.-7. Oktober 1992. [5] C. Miiller, S. Gottschling, R. Kohl, G. Tomandl, Zr02 Ultrafiltration Membranes Processed by the Sol-Gel-Route, Ceramic Transactions, Vol.51: Ceramic Processing and Technology, American Ceramic Society, (1995) pp. 689-93. [6] R. Kohl, G. Tomandl, A. Larbot, L. Cot, Herstellung und Charakterisierung von keramischen Membranen aus Titanoxid zur Cross-Flow-Ultrafiltration nach dem Sol-GelVerfahren, Kurzreferate pp. 64-66, DKG-Jahrestagung, Bayreuth, 4.-7. Oktober 1992. [7] M. Zhou, G. Meng, D. Peng, G. Zhao, Studies on the Sol Gel Process for Ti02 Membrane Formation, Key Engineering Materials Vols. 61 & 62 (1991) pp. 387-390, Trans Tech Publications, Switzerland. [8] A. Larbot, J. A. Alary, C. Guizard, L. Cot and J. Gillot, New Inorganic Ultrafiltration Membranes: Preparation and Characterization, Int. J. High Technol. Ceram., 3, 143-51 (1987). [9] C. Guizard, A. Julbe, A. Larbot, L. Cot, Nanostructures in Sol-Gel Derived Materials. Application to the Elaboration of Nano filtration Membranes, Key Engineering Materials Vols. 61 & 62 (1991) pp. 47-56, Trans Tech Publications, Switzerland. [10] S. Kruyer, The Penetration of Mercury and Capillary Condensation in Packed Spheres, Trans, of Faraday Society, Vol.54, 1758-67 (1958). [11] G. Mason, A Model of the Pore Space in a Random Packing of Equal Spheres, J. of Colloid and Interface Science, Vol.35, pp.279-287 (1971). [12] C.-W. Hong, Computer-Aided Process Design for Forming of Pore-Gradient Membranes, paper presented at the 4th International Symposium on Functionally Graded Materials (FGM), Tsukuba/Japan, October 20 - 24, 1996.


179

Mechanical Properties and Microstructure of in-situ TiCp Reinforced Aluminum Base FGM by Centrifugal Cast Zhang Baosheng, Zhu Jingchuan, Zhang Yongjun, Ying Zhongda, Cheng Hongsheng, An Geyin School of Materials Science and Engineering, Harbin Institute of Technology, Harbinl50001,P. R.China ABSTRACT The TiCp/2020Al FGM was fabricated by in-situ reaction in melted Al alloy and the following centrifugal cast, and was investigated by means of microscopy observation and mechanical property test. The hardness and bending strength of the FGM gradully varied corresponding to the composition gradient, and the wear resistance was remarkably improved due to the formation of TiCp-rich surface layer that is strongly bonding with 2024A1 substrate through the TiCp/2024Al graded interlayer. KEYWORDS functionally graded material, centrifugal cast, microstructure, mechanical property, TiC, Al alloy

1. INTRODUCTION Particle reinforced in-situ metal matrix composites (MMCs), with fme and clear in-situ reinforced ceramic particles generated by the exothermic reaction between elements and compounds, possess better mechanical properties than conventional composite materials^^^'. At present, carbides, borides, nitrides and oxides have already successfully been generated on bases of Al, Ti, Ni, Fe and other intermetallic compounds^^'^l By centrifugal cast, the reinforcement particles can be arranged gradiently along the direction of centrifugal force field due to their difference in specific gravity^^l In this paper, the TiCp/2024 FGM was fabricated by in-situ reaction in melted materials and centrifugal cast, and its microstructure and mechanical properties were investigated. 2. EXPERIMENTAL PROCEDURE Firstly, a TiCp/2024 compounded material was prepared by in-situ reaction in the melt. The raw materials are listed in Table 1. Then, the TiCp/2024 composite was put into a special iron crucible. After the composite melting and being refined, the crucible was taken out and

180 put into a centrifuger quickly. The centrifugal cast apparatus was shown in Figure 1, which maximum rotating speed was 5000 rpm and maximum centrifugal acceleration was 5180g. A layer of asbestos was placed in the crucible as insulating material to keep the melt from solidifying too fast for the TiC particles to move. Under the centrifugal force field, the crucible axis, which was initially vertical, became horizontal gradually. Due to the distinction of specific gravity between TiC particles and 2024 Al alloy, TiC particles can move in the direction of centrifugal force. The gradient distribution of TiCp can be controlled by adjusting such parameters as rotating speed, temperature, solidification condition and time of centrifugal cast.

Roter

Fig.l Schematic drawing of centrifugal cast

Table 1. The raw materials used in experiments material size (|im) Al Ti

C Al-Cu-Mg

29 100 45 147 0.5 45 Igot

Composition (wt%) Fe Cu Si H,0 O H 'v^

(0

«.

v__

•

- •-

SUS316-f0.1PMAA

*

SUS316-fO.SPMAA

- '-

SUS316-f0.1Na-CMC

-

SUS316-»0.5Na-CMC

«-

''^•"•~'•-.'••..-.-.^^

.••

•••...-••-.'• '^

'\v.

-30

"'~"-v-,,,^^^^-^*'' -40

*-o..^ 3

4

5

^0-°'*' 7

PH

(a)

8

9

PH

(b)

Figure 2. Zeta potential of (a) TZP and MZP, (b) SUS316 with pH variation respectively

(Na-CMC) + 0.015wt% PMAA at pH 8.0. When all the additives are added, the viscosity of slurry is about 4,000—5,000 cps. At that time, soHd loading of TZP, MZP and SUS316 are 25, 40 and 80 volume percent(vol%), respectively. Heating schedule is determined by TG-DTA data[7], from which most of the binder is bumed-out below 500 °C.

3.2. Control of the sintering defects & optimization of compositional gradient In the fabrication of FGM, it is essential to control the sintering defects. So, the adjustment of particle size and phase type of ZrOi, that is, TMP/SUS316 FGM(rather than TZP/SUS316) can prevent defects generated in FGM. This result is ascribed to two things, one is the larger particle size of MZP, which plays a role in releasing the difference of shrinkage rate between ceramics and metal. The other is 3—5 vol% expansion on cooling[8]. From the data about the influences of metal volume fraction and sintering temperature on shrinkage rate[4], we can estabhsh the suitable number of stacking layer and compositional gradient. The number of stacking layer is 16.

3.3. Microstructure and continuity of interface Some discontinuity created frequently in multilayer materials, are investigated at the interface of the fabricated FGM but the continuous compositional change throughout FGM is observed with optical microscope as shown in figure 3. As it were, the composition changes continuously from the Zr02-rich region to the SUS316-rich region. We observe the dispersive structure in the metal side which ceramic particles are dispersed in the metal matrix. Dispersive structure is shown in the ceramic side to the contrary, in other words, metal particles are dispersed in the ceramic matrix, as if dispersing particle and matrix are woven each other. For intermediate composition, network structure is observed, which two phases are Unked respectively as the volume

189 ZrOi

SUS316

Figure 3. Multilayer and interface structure

a) lOOjm thick, pressureless sintering b) 200/M thick, pressure sintering c) 400/m thick, pressure sintering Figure 4. Photograph of FGM(16 layers)

SUS316

ZrOz

'/«y#iiliftlfeM a)

b)

Figure 5. Distribution of a) Fe and b) Zr in ZrOz/ SUS316 FGM with WDS

fraction of each phase increases. These microstructure are consistent with the model designed theoretically and proposed by R. Watanabe et al[2]. Because of the different soUd loading of each phase in each layer, it shows the different shrinkage rates. Therefore, it is Hkely to cause the various flaws in the sintered sample such as warping, crack, delamination and so on. Besides, ZrOz particle is smaller than SUS316 particle, therefore, shrinkage of ZrOi is larger, so the warping to ceramics happens easily. As shown in figure 4, this is relieved appreciably by pressing and increasing the layer number. Pressure sintering just means that sintering is performed under some load to specimen. In pressureless sintering, warping appears toward the cerainics-rich region although we control the difference of shrinkage and the sintering behavior between ZrOi and SUSS 16. It is thought that it is effect of the difference of soHd loading. This is verified by the observation of optical microscope as well. Consequently the difference of shrinkage rate and sintering

190 behavior between each layer can be decreased by the adjustment of the particle size and phase type of ZrOz so that sintering defects are minimize. Figure 5 shows the distribution of Zr and Fe.

4. CONCLUSION Zr02/SUS316 FGM was fabricated by tape casting method in an aqueous system. The dispersion state of ZrOa depended on the electrostatic stabiUzation and that of SUS316 depends on the steric stabilization, respectively. We could control the sintering defects due to different shrinkage rates of starting materials by adjusting particle size and phase type of Zr02. It was a key factor to press specmiens and increase the layer number, specially in problem of warping. Furthermore, the residual stresses induced on FGM were relaxed as the thickness and the number of compositional gradient layer was increased. Also, the continuity of interface and the microstructure of Zr02/SUS316 FGM were observed.

REFERENCES 1. R. Watanabe, Powder processing of functionally gradient materials, MRS Bull., (1995) 3 2 - 3 4 2. R. Watanabe and A. Kawasaki, Development of FGMs via powder metallurgy. Powder and Powder Met., 39(4) (1992) 279-286 3. M. Takemura and M. Tamura et al., Mechanical and thermal properties of FGM fabricated by thin sheet lamination method. In Proc. 1st. Int. symp. FGM, edited by M. Yamanouchi, M. Koizumi (1990) 97-100 4. A. Kawasaki and R. Watanabe, Fabrication of sintered functionally gradient materials by powder spray forming process. In Proc. 1st. Int. symp. FGM, edited by M. Yamanouchi, M. Koizumi, (1990) 197-202 5. M. Itoh, The fluidity of zirconia slurries as a function of ammonium polyacrylate molecular weight. Ceramic powder science vol. 4, (1991) 251—256 6. M. Hashiba et al. Dispersion of ZrOi particles in aqueous suspensions by ammonium polyacrylate, J. Mat. Sci., 24 (1989) 873 — 876 7. P. Calvert and M. Cima, Theoretical models for binder burnout, J. Am. Ceram. Soc, 73[3] (1990) 575-579 8. A. H. Heuer, Transformation toughening in ZrOi-containing ceramics, J. Am. Ceram. Soc, 70[10] (1987) 689-698


191

Fabrication of Zr02/Ni and Zr02/Al203 Functionally Graded Materials by Explosive Powder Consolidation Technique A. Chiba, M.Nishida, K Imamiira, H.Ogura and Y. Morizono Faculty of Engineering, Kumamoto University, Kumamoto City 860 Japan Zr02/Ni and Zr02/Al203 functional gradient materials(FGMs) were fabricated by our newly developed underwater-shock consolidation technique. The experimental assembly consists of three parts, i.e. explosive container, water tank and powder container from top to bottom. The energy of shock wave increased by the convergence of shock wave due to the reduction of the cross section area of water tank. The increased shock pressure and long shock duration facilitated the consohdation of difficult-to-consohdate powders to fuU density. The pressure level obtained was estimated to be 7 GPa. The 5 to 10-layered FGMs for both systems were fabricated in an overall cross section without any discontinuity and defects. The obtained FGMs could withstand the thermal stress by cyclic differential thermal load testing. 1. INTRODUCTION Functional gradient materials characterized by the materials having continuously varying material property from one surface to the other, have been prepared via several methods such as CVD, PVD, ion plating, plasma spraying, sintering and self-propagatuig high temperatures synthesis[l]. Shock consolidation is known as a technique to produce the bulk materials from powders. However, it was hitherto difficult to obtain sound specimens without any cracks and/or central hole by using an axisymmetric explosive consolidation technique. The authors have so far developed the dynamic consolidation of difficult-toconsolidate powders such as Zr02 and Si3N4 ceramic powders, utilizing underwater-shock wave generated by the detonation of explosive as a pressure medium of water. And they have reported that sound specimens can be fabricated without using any sintering additives[2]. The advantages of the shock consolidation are that the compact with full density can be fabricated within nano second order and lots of defect induced and fresh surface exposed by shock pressure can reduce the post-sintering temperature in comparison with the conventional process. The purpose of the present study is to establish the technique for fabricating two kinds of FGMs, i.e. Zr02/Ni with 10 layers and Zr02/Al203 systems with 5 layers, by using the underwater-shock consohdation technique mentioned above and to investigate microstructures and thermo-mechanical properties.

192 2. EXPERIMENTAL PROCEDURE 2.1. Materials Partially stabilized zirconia powder (TZ-3Y)was supplied from Tosoh Co., Tokyo, Japan. The content of Y2O3 in the powder was 3.64 mass% and the average particle size was about 0.3 \im. Ni powder was supplied from Nilaco Co.,LTD. Tokyo J a p a n and the average size was about 5(jim. AI2O3 powder was supplied from Sumitomo Chemical Industry LTD. Tokyo, Japan and the average size was about O.Sîm. 2.2. Underwater-shock consolidation assembly The assembly used in the present study consists of explosive container, water tank and powder container from top to bottom as illustrated in Figure 1. The mixed powders with prescribed ratio were tapped into the powder container as illustrated in the right hand side of Figure 1. Hard steel powder in the top side was used to prevent the scattering of FGM powders from the powder container and SUS304 powder in the bottom side was used for momentima trap.

water

hard steel powder (100 i/m)

SU$304 powder •AlaOipavfiti 30ZrG2-70AJ2d3, ;5fnm-50M2O3 TOZirdi-aOAliOJ

ZrOz powder SUS304 powder

no[Mixing ratio:vol% , Unil:mm]

Figure 1. Schematic illustration of underwater-shock consolidation assembly. All containers are made of mild steel. The magnitude of the shock wave associated with the explosive detonation increases by convergence of shock wave due to the reduction of cross section area and reflection on the conical wall of the water tank. The pressure level and shock duration can be easily controlled by adjusting the mass and detonation velocity of explosive and the conical angle of the water container. The explosive used in the present study was SEP (provided by Asahi Chemical Industry Co.LTD.) mainly consisting of nitric ester and the detonation velocity was 6900m[/s. The Zr02/Ni FGM was sintered at 1673K for 2h. The Zr02/Al203 FGM was firstly degassed at 1673K for 2h and then sintered at 1823K for 4h.

193 2.3 Estimation of shock pressure The shock velocity at the powder container was measured by the ion gap method, and the shock pressure was calculated using the equations by Cole [3] and Penny and Dasgupta [4] expressing the relationship between the shock pressure and velocity of water. The shock velocity was measured by arrival time difference of shock wave between pins with different height. The velocity of the shock wave was measured to be about 4600m/s, so t h a t the shock pressure obtained by this assembly was estimated to be 7 GPa in the powder container. 2.3. Microstructural investigation and thermomechanieal testing Microstructural charaterization of the obtained FGMs were performed by optical microscopy, scanning electron microscopy (SEM:JSM-6100) with EDX analysis (JED-2000). Thermomechanieal property of Zr02/Ni FGM was investigated by the cyclic differential thermal load testing. 3. EXPEraMENTAL RESULTS AND DISCUSSION 3.1. Microstructures of as-consolidated state Figure 2 shows the cross sections of 10-layered Zr02/Ni and 5-layered Zr02 /AI2O3 FGMs cut parallel to the shock wave direction.

EISBl

W'Ma Smm "^ *^

Figure 2. External views of FGMs. The thickness of the consohdation state reduced to about 11/19. in Zr02/Ni, and 11/16 in Zr02/Al203 system compared with the tapping state. From macroscopic observations, no cracks were found in the specimens and continuous compositional change were confirmed. Figure 3 shows the results of EDX analyses of the two systems. Both the back electron images in (a) and Ka-line images of constitutional elements clearly indicate that the continuous compositional changes were achieved in each system. It is concluded that the FGM produced by the underwater-shock consolidation has fiilly densified microstructure eveiywhere in an overall cross section without any discontinuity and defects. 3.2 Microstructures of annealing state Scanning electron micrographs of bonding interface of the Zr02/Al203 FGM are shown in Figure 4. All of the interface completely bonded. In the 70%Al2O3-30%ZrO2 layer, the both grains of AI2O3 and Zr02 are fine about 2 \IWL in diameter due to the inhibiting the grain growth each other by

194 'M

mZt~K a X
10 fi m. 3. RESULTS AND DISCUSSION At first, the thermal diffusivity, a , and the specific heat, Cp, on sintered compacts of Be/Cu mixture are shown in Fig. 3 and Fig.4, respectively. From these results, it appeared that the thermal diffusivity on sintered compacts which contained less than 50at. %Cu was lower than that of lOOat. %Be. The thermal diffusivity increased with increase of Cu containing ratio and the specific heat gradually decreased with increase of Cu containing ratio.

•o

To

0 10 20 30 40 50 60 70 80 90 100 Composition of Be/Cu sintered compacts, at.%Cu

Fig. 3 Thermal diffusivity of Be/Cu sintered compacts. The thermal conductivity, K , of sintered compacts was obtained by calculation from the following equation:

0 10 20 30 40 50 60 70 80 90 100 Composition of Be/Cu sintered compacts, at.%Cu

Fig.4 Specific heat of Be/Cu sintered compacts. 300 r E

K = a X Cp X f)

The p is dencity. This is shown in Fig.5. The tendency of the thermal conductivity was similar to the thermal diffusivity. Particularly, the thermal conductivity of sintered compacts which contained more than 50at.%Cu was higher than that of lOOat %Be. Therefore, it is considered that these sintered compacts are advantageous to apply those to FGM

0 10 20 30 40 50 60 70 80 90 100 Composition of Be/Cu sintered compacts, at.%Cu Fig.5 Thermal conductivity of Be/Cu sintered compacts.

218 interlayer. On the other hand, thermal conductivity of sintered compacts which contained less than 50at%Cu was lower than that of 100at.%Be. It is considered that this phenomenon was due to decrease of thermal conduction with free electron by formation of Be-Cu intermetalHc phases or lattice strain. Thermal conductivity of lOOat.% Cu was about 270W/m/K. This value agreed with measured value in literature [4]. (0 E The thermal expansion coefficient of sintered compacts are shown in Fig. 6. From 0 10 20 30 40 50 60 70 80 90 100 these results, between 300°C and 400''C, it Composition of Be/Cu sintered compacts, at.%Cu appeared that thermal expansion coefficient of these compacts gradually increased with Fig.6 Thermal expansion coefficient increase of Cu containing ratio and the of Be/Cu sintered compacts. compacts which contained less than 60at.%Cu was lower than that of DS-copper and higher than that of HP-Be. The bonding interface will be used at this temperature range. Therefore, it is possible to reduce thermal stress of bonding interface by applying those sintered compacts to FGM interlayer.

Fig. 7 SEM photographs of as manufactured Be/Cu sintered compacts.

219

Fig. 8 SEM photographs of Be/Cu sintered compacts used for the measurement of thermal expansion coefficient. The measurement were performed at RT to 700 °C .(The arrows indicate cracks.)

From the SEM observations on sintered compacts of Be/Cu mixture, it became clear that the sintered compacts contained residual beryllium, copper and two kind of intermetallic compounds, namely, Be->Cu( o ) and BeCul/ ). SEM photographs of the as manufactured compacts , which composition are (a)90at.%Cu (b)50at.%Cu and (c)10at.%Cu, are shown in Fig. 7. These compacts were composed of those four phases and the ratio of these phases varied with varying the composition. Fig. 8 shows SEM photographs of the compacts used for the measurement of thermal expansion coefficient. The measurement were performed at RT to 700°C.From this observation, many cracks were observed at the interface between BeCu( / )phase and Cu phase in these compacts. It is considered that these cracks were generated by the transformation of BeCu(/j)phase into BeCu( / )phase and Cu phase with large shrinkage[5,6]. Therefore, the fomiation of Be-Cu(/j )phase, occurred at 620°C, should be avoided when beryllium and DScopper would be joined by diffusion bonding or HIP bonding method.

220

4. CONCLUSIONS In this study, thermal diffusivity and specific heat of Be/Cu mixture sintered compacts were measured by laser flash method, then thermal conductivity was obtained from calculation of those measured values. And thermal expansion coefficient was measured by laser interferometry method. These thermophysical properties were measured in order to characterized those compacts as interlayer between beryllium and copper alloy used in the plasma facing components. The obtained results are as follows. (1) From the results of thermophysical characterization, thermal conductivity of Be/Cu sintered compacts which contained more than 50at.%Cu were higher than that of 100at.%Be. And thermal expansion coefficient of compacts which contained less than 60at.%Cu were lower tlian that of DS-copper and higher than that of HP-Be. Therefore, it appeared that Be/Cu sintered compacts which contained 50-60at. %Cu were advantageous to apply those to FGM interlayer. (2) From the metallographical observations, it became clear that Be/Cu mixture sintered compacts contained residual beryllium, copper and two kind of intermetallic compounds, Be2Cu( d^) and BeCu( / ). And the ratio of these phases varied with varying the composition. (3) SEM photographs of the compacts annealed to 700°C show many cracks due to the transformation of Be-Cu( /^ )phase into BeCu( / )phase and Cu phase with large shrinkage. Therefore, joining with beryllium and DS-copper by diffusion bonding or HIP bonding method should be performed below 620 °C in order to avoid the formation of BeCu( i3 )phase. And the bonding interface also should be used below 620°C. From these results, thermal designs of beryllium and copper alloy bonded plasma facing components using Be/Cu sintered compacts as FGM interlayer became possible. However, it is necessary to give full consideration to effect of brittle intermetalhc compounds in FGM interlayer on bonding strength of beryiiium/copper alloy interface. Mechanical properties tests will be performed in order to estimate themial stress at bonding interface.

REFERENCES [1] D.W.Doll, etal., J.Nucl.Mater., 85-86(1979)191. [2] T.Kuroda and G.Vieider, ITER Plasma Facing Components, ITER Documentation Series N30 (IAEA, Vienna, 1991). [3] K.Nakamura, etal., J.Nucl.Mater., 212-215(1994)1201. [4] C. Carmichael (ed.), Kent's Engneere's Handbook, (John Wiley&Sons, Inc.) [5] N.Sakamoto, H.Kawamura and R.Solomon, to be published in Proc. I9th Symposium on Fusion Technology, Lisbon, 1996. [6] N.Sakamoto, S.Saito, M.Kato, R.Solomon and H.Kawamura, to be pubUshed in Proc. 5th international workshop on Ceramic Breeder Blanket Interaction, Rome, September 23-25, 1996.

I. Shiota and M.Y. Miyamoto (Editors) Functionally Graded Materials 1996 1997 Elsevier Science B.V.

Electrophoretic Forming of Functionally-Graded Barium/Strontium

221

Titanate Ceramics

Partho Sarkar Ceramic Research Group, Department of Materials Science and Engineering McMaster University, Hamilton, Ontario, Canada L8S4L7 Sumie Sakaguchi, Eiko Yonehara, Jun-ichi Hamagami, Kimihiro Yamashita and Takao Umegaki Department of Industrial Chemistry, Tokyo Metropolitan University Hachioji, Tokyo

Abstract Single phase BaTiOa (BT) and SrTiOs (ST) have sharp Curie Point at 393K and lOK respectively. ST forms solid solution with BT and shifts the Curie Point toward the lower temperature. In a multilayer sample varying the BT/ST ratio among the layers it would be possible to fabricate a fiinctionally-graded laminated dielectric composite which will exhibit a board transition temperature and as a result it will have a low temperature coefficient and high dielectric constant in a wide temperature region. Laminated BT/ST composites thick films and bulk samples were synthesized by electrophoretic deposition (EPD). Two types of solvents were tested for the EPD suspensions, alcohol/acetylacetone mixed solvent and ethanol. Microstructure of the sintered samples was characterized by optical and SEM. Dielectric properties as a fiinction of temperature were measured using an impedance analyzer. /.

Introduction EPD is an effective technique to synthesize monolithic as well laminates thick film [1-8] and bulk samples [9-13]. Sarkar and Nicholson [9,10] are thefirstto demonstrate the EPD can be successfiiUy use for fabrication of laminated and fiinctionally graded materials. There are few reports on fabrication of BaTiOj monolithic thick film by EPD [1,5,6]. Yamashita et al [7] is the only one used EPD to synthesize BaTiOj/SrTiOj laminated composite with varying BT/ST ratio and observed board Curie temperature response in the sample. EPD technique uses electrostatically stabilized suspension. It is a combination of two processes, electrophoresis and deposition. Electrophoresis is the motion of a charged particle in a suspension under the influence of an electric field. It was discovered around 250 years ago by the Indian Scientist, G.M. Bose. The Russian Scientist, Reuss, was the first to observe electric field-induced motion of clay particles in the water. The second process is deposition, i.e., the coagulation of particles into a dense mass. In the present study alcohol/acetylacetone mixed solvent is used for fabrication of thick films. It was found that mixed solvent is good for making thick film but the deposition voltage is high, the rate of deposition is low and also suspension stability is low. To overcome these problems a new suspension, i.e., titanates/ethanol system is being investigated.

222 //. Experimental Procedure Starting powders are BaTiOj (Kanto Chemical Co., Tokyo, Japan). SrTiOj powder used with mixed solvent is from High Purity Chemicals Laboratory. Since this SrTiOj has a large particle size (average size ~ 10//m), therefore for ethanol solvent system SrTiOa (average Size ~ l / / m ) form a different source (Transelco Division o f Ferro Corporation, ^ U S A ) is used. Suspensions are characterized 's by measuring their electrophoretic mobility "^ using Coulter DELSA 440SX and deposition ^ rate. Microstructure of the sintered samples g* is characterized by SEM and dielectric properties measured as a function of temperature using HP impedance meter. HI Results and Discussion 0 20 40 60 80 100 Figure 1 shows the deposited weight Acac PrOH Composition (v/o of Acac) o f BT, ST and 80w/o BT-ST mixed powder Fig1 Deposited weight of BT, ST and BT/ST mixture as in mixed solvent as a function of an a function of solvent composition of the suspension. alcohol/acetylacetone ratio. Depositions were conducted using constant voltage (400 V/cm) for 180 sec from a suspension o f 10 g/1. ST forms good deposit in pure alcohol but deposited weight decreases as the alcohol/acetylacetone ratio decreases in the solvent and no deposition occurs in pure acetylacetone. B T does not deposit either of the pure solvents but deposited weight increases departure from pure solvent and shows maximum deposition rate in 30-50 v/o acetylacetone. Mixed powder deposition behavior is similar to BT. Mixed powder deposition has some anomaly, it does not deposit in pure alcohol though ST has a maximum deposition rate. Pure alcohol ST particles positively charged. It is speculated here that in pure alcohol BT particles are slightly negatively charged and as a result of that the heterogeneous coagulation occurs between ST and BT. Since B T

L

BaTiOa/Ethanol Suspension -j

if A

r ^

^

A

/^

k

H

A

""

[ I

H

A

A

[

\ \

A

L

A

A

A A

L

\

'' : -

A

A

1 . .-. 1 . . . 1 . . • 1 . . . 1 . , . 1 4

6

8

10

12

14

pH Fig. 2. Electrophoretic mobility as a function of pH of (a) BaTiOs/ethanol and (b) SrTiOa/ethanol suspension.

223 powder is finer (BT -l/zm, ST ~10//m), therefore BT form an envelope on ST particles BT/ST multilayered thick film. and as a result of this mixture powder behave like BT and form no deposit in pure alcohol. Figures 2a and 2b are the ^ ^ A • electrophoretic mobility of BT and ST powder in ethanol as a function of pH of the A ^ • • 1kHz ^ ^ A A suspensions. Both the materials below pH 9 *^ A A A 10 kHz show positive mobility ie. particles are • • • • • - • -100kHz positively charged. The BT and ST has a basic 100 150 surfaces. Since the absolute value of the Temperature ("C) mobility is higher at low pH (positive mobility) than at high pH (negative mobility), therefore it is decided that deposition will be conducted Fig. 3. Temperature dependance of capacitance of from a positively charged suspension. These Bi.ySJ FGM multilayered thick film. suspensions provide good deposition in the pH range between 5 and 4. The temperature dependence of the dielectric of the multilayer thick film deposited from titanate /mixed solvent (alcohol/acetylacetone) system is shown in Figure 3. This multilayer (5 layers) FGM sample was made using the suspension of composition 0, 30, 46, 63 and 100

Fig. 4. Cross-sectional SEM micrographs of multilayer BT/ST bulk sample: (a) low magnification is showing multiple BT(dense) and ST(porous) layers and (b) high magnification is showing the grains structure of dense BT layers.

v/ of BT. It is clearfromthisfigurethat there is no sharp Curie point and as a result of that the sample has a smaller temperature coeflScient than that of pure BT. Bulk multilayer BT/ST and as well as thick films were fabricated from tatinates/ethanol suspension (100 g/1). The deposition was conducted at pH'-4 to 5 at constant current. The sample was sintered at HOOT for 2 H in air with a 300 °C heating/ cooling rate. Figures 4 is a cross sectional micrograph of a poUshed and thermally etched (1300°C for IH) multilayer of 100% BT/100% ST sample. In Figure 4(a) porous layers are SrTiOj and dense layers are BaTiOj. The thickness of the ST

224

Fig. 5. Cross-sectional SEM micrographs of non-planner laminates. Sequentionally deposited from BT-ST/ethanol suspensions of composition 100, 75, 50 and 25 v/o of BT. (a) is a low magnification micrograph showing thefibre-electrodesposition and (b) is a high magnification micrograph showing the details of layers microstructure. layer is ~20//m and BT -SO/zm respectively. Figure 4(b) is the high magnification micrograph of the BT region showing high density of the region with average grain size - 18//m. Non planner laminates were also fabricated using Nicalon fibres as a depositing

Fig. 6. Cross-sectional SEM micrographs of non-planner laminates with 3-fibre electrodes. Each electrode has 37 layers, (a) is a low magnification micrograph showing the fibre-electrodes position and (b) is a high magnification micrograph showing the details of layers microstructure.

electrode. Four suspensions of composition 100 v/o BT, 75 v/o BT, 50 v/o BT and 25 v/o BT are used. There are deposited in the following sequences 100, 75, 50, 25, 50, 75, 100, 75.... etc. Figures 5a and 5b are the microstructure of a nonplanner laminates where fibre electrodes

225 125

IkHz

$i

BTS5

1.00

\

A

1 Q

0.50

_

•

• S

• ^ * •

Q

•

•

•

•

•

r

5

\• •

40

A

«

•

80

-'

A A •'

50

1 I 25

A

a.J_J_. 1 .1 .1 .1 . 1 .1. 1 . 1, 1 . 60

'

/

E

'-

20

A

75 pL

^

•

0.25

nnn .1.1.1.1.1

^ A A "

r

••

•A • •

F BTST Solid Solution

100 E-

• • •

A •

0.75

&

^ ^

BT95 BT100

100 120 140 160 180

Temperature (C)

~

70

'

'

'

80

85

•

•

•

. . 1 . . i

90

III 95

1 .1

v/o Barium Titanate

Fig. 7. Normalized capacitance as a function of c- © r^ • temperature of monolithic B„S.T samples ^'^ ^- J""" temperature of Ba,.Sr,TiO:'3 as a containing 85 (BT85), 95 (BT95) and 100 ^^'^^'^'^ of composition. (BTIOO) v/o of BT. are placed in a plane. In this sample each fibre has 31 layers. 25 v/o BT has the maximum porosity and lOOv/o BT has nearly no porosity. Between two porous layers (25 v/o) there are 5 layers (50, 75, 100 (thick), 75, 50 v/o BT). Figures 6a and 6b are the BT/ST FGM Thick Film on Pt 6000 microstructure where 3-fibres electrodes were used, two of them in a 5000 plane and one ofthem out of plane. In 'fe A IkHz 4000 this case each fibre has 37 layers. To determine the Curie 3000 + 10 kHz temperature, monolithic samples of the 42000 composition 75v/o, 80 v/o, 85 v/o, 90v/o, 95 v/o and 100 v/o BT were H 1000 made and their capacitances were . I • I • I • I • I • I • I • I • I • I • I • I • I • I • I 0 measured as a function of temperature. 100 120 140 160 180 60 80 20 40 F i g u r e 7 Temperature (C) is a plot of normalized capacitance of 85, 95 and 100 v/o BT. All these Fig. 9. Capacitance/Dielectric constant of a 160/^m multilayer thick fihn deposited from 100, 75, samples show sharp transition. Figure 50 and 25 v/o BT suspension. 8 is a plot of Curie temperature as a function of composition. 75 v/o sample shows a Curie point - 16°C. Figure 9 is a dielectric response of a multilayer thick fihn on a Pt substrate made from titanate/ethanol suspensions of composition 100, 75, 50 and 25 v/o BT. This sample shows broad transition temperature (80°120°C). Although pure BT has a transition temperature ~ 120T and next nearest transition temperature by 75 v/o BT(~ 16°C). This indicates inter-layer diffusion of the cation resuhed the broadening as well as shifting of the peak towards lower temperature. Dielectric constant at transition temperature is -5,000 in IkHz. This preliminary results indicate that by chosing appropiate suspension composition, individual layer thickness and sintering time and

I

226 temperature it would be possibe to control the position and broadening of the transition temperature. IV Conclusion Mukilayer thick films of BaTiOj, SrTiOj and their mixture are fabricated by EPD technique. It was demonstrated mixed solvent system is good for thick film deposition. Bulk and thick film multilayer samples were fabricated from titanates/ethanol system. Multilayer samples with varying composition shows board Curie temperature and as a result of that it has low temperature coefficient. References 1. V.A. Lamb and H.I. Salmon, "Electrophoretic Deposition of Barium Titanate" Am. Ceram. Soc. Bull. 41 (1962) 781-782. 2. P. Sarkar, S. Mathur, P.S. Nicholson and C.V. Stager, "Fabrication of Textured Bi-Sr-CaCu-0 Thick Film by Electrophoretic Deposition", J. Appl. Phys. 69 (1991) 1775-1777. 3. P. Sarkar and P.S. Nicholson, "Magnetically Enhanced Reaction Sintering of Textured Yba2Cu30x", Appl. Phys. Lett. 61 (1992) 492-494. 4. S. Sugiyama, A. Takagi and K. Tsuzuki, "(Pb, La)(ZrTi)02 Film by Multiple Electrophoretic Deposition/Sintering Processing", Jpn. J. Appl. Phys. 30 (1991) 21702173. 5. S. Okamura, T. Tsukamoto and N. Koura, "Fabrication of Ferroelectric BaTiOj Films by Electrophoretic Deposition", Jpn. J. Appl. Phys. 32 (1993) 4182-4185. 6. M. Nagai, K. Yamashita, T. Umegaki and Y. Takuma, "Electrophoretic Deposition of Ferroelectric Barium TiTanate Thick Films and Their Dielectric Properties" J. Am. Ceram. Soc. 76 (1993) 253-255. 7. K. Yamashita, E. Yonehara and T. Umegaki, "Dielectric Properties of Electrophoretically Layered Barium Strontium Titanate Films" K. Yamashita, E. Yonehara and T. Umegaki, to be published in the IEEE proc. 8. P. Sarkar, J. Hamagami, K. Sakaguchi, K. Yamashita and T. Umegaki,"Multilayers BaTiOj/SrTiOj Thick Films and Bulk Ceramics", proc.of the 16th Electronic Division Meeting by Electronic Division of Jpn. Ceram. Soc, pp.43-44 (1996). 9. P. Sarkar, X. Huang and P.S. Nicholson,"Structural Ceramic Microlaminates by Electrophoretic Deposition", J. Am. Ceram. Soc. 75 (1992) 2907-2909. 10. P. Sarkar, X. Huang and P.S. Nicholson,"Zirconia-Alumina Functionally-Gradiented Composites by Electrophoretic Deposition Techniques", J. Am. Ceram. Soc. 76 (1993) 1055-1056. 11. P.S. Nicholson, P.Sarkar and X. Huang,"Potentially Strong and Tough ZrOj-Based Ceramic Composites ^ 1300°C by Electrophoretic Deposition", Science and Technology of Zirconia V; Edited by S.P.S. Badwal, M.J. Bannistar and R.H.J. Hannik, (Technomic Publishing Company, Inc. (1993)) pp.503-516. 12. P. Sarkar, O. Prakash and P.S. Nicholson, "Micro-Laminate Ceramic/Ceramic Composites (YSZ/AI2O3)", Ceramic Engineering and Science Procedings 15 (1994) 1019-1027. 13. M. Whitehead, P. Sarkar and P.S. Nicholson,"Non-Planar AI2O3ATSZ Laminates by Electrophoretic Deposition using AI2O3 Fibre Electrodes", Ceramic Engineering and Science Procedings 15 (1994) 1110.


227

Processing and Properties of Electrodeposited Functionally Graded Composite Coatings of Ni-Al-AÔa K. Barmak^ S. W. Banovic^ H. M. Chan^ L. E. Friedersdorf, M. P. Ha^ner^ A. R. Marder\ C. M. Petronis^ D. G. Puerta^ and D. F. Susan^ ^ Materials Research Center, Lehigh University, 5. E. Packer Ave.,. Bethlehem, Pennsylvania 18015, USA ^ Energy Research Center, Lehigh University, 117 ATLSS Dr., Bethlehem, Pennsylvania 18015, USA

1. ABSTRACT Single- and dual-particle, uniform and graded composite coatings of Ni-Al-AUOs, with Ni as the matrix and primarily Al and AI2O3 as second phase particles, were fabricated via electrodeposition. During the electrodeposition process, Ni was plated from an electrolytic bath to which the particles had been added. For single particle baths, the codeposition of AI2O3 was more strongly affected by current density and bath particle content than was the codeposition of Al. In the mixed particle bath, codeposition of AI2O3 was suppressed at low current densities, whereas codeposition of Al was not affected at any of the current densities studied. When coatings containing Al were annealed, the reaction of the two elements resulted in the formation of either single phase y solid solution or two phase y-y', in agreement with the equilibrium phase diagram. In addition to current density and bath particle content, the shape and size of the particles was found to affect the electrodeposition process. Here, angular nickel aluminide particles resulted in porous coatings. The microhardness of the Ni-Al and NiAI2O3 coatings showed a complex behavior with volume fraction of particles as a consequence of the effect of these particles on the microstructure of the Ni matrix.

2. INTRODUCTION The introduction of gradients of chemical composition, phase distribution or microstructure represents a now fervently pursued concept in the design of engineering components for optimum performance [1]. The occurrence of the Fourth International Symposium on Functionally Graded Materials (FGMs) bears witness to this fact. FGMs can be made by a variety of techniques - see, for example, the proceedings of the

228

previous international symposium on these materials [1]. The fabrication of graded coatings by electrochemical methods has the advantages of versatility, ability to coat complex shapes, and low cost. In addition, particles that are added to the electrolytic bath codeposit with the electroplated metal, thus creating a metal matrix particulate composite. The volume fraction of codeposited particulates depends on many parameters. These include the nature of the electrolytic bath, the current density and the type (metaUic, ceramic, etc.), size, shape and amount of particles. Here we report the effect of a variety of these parameters on processing and the resultant microhardness of uniform and graded, single- and dual-particle composite coatings of Ni, with primarily Al and AI2O3 as the second-phase particles.

3, EXPERIMENTAL The details of our electrochemical deposition process are given elsewhere [2]. Here we give a brief summary. The substrate for all the coatings was pure Ni 200 plate. The electrodeposition bath was sulfamate type and contained 400 g/l of nickel sulfamate tetrahydrate, 30 g/l boric acid, 5 g/l nickel chloride hexahydrate, 0.5 g4 sodium lauryl sulfate and 0.1 g/l Coumarin. For most experiments a-alumina powder, with an average size of 0.60.8 )Lim, and Al powder, with majority of the particles in the 1-4 |im size range, were added to the electrolytic bath for codeposition with Ni. In some experiments large nickel aluminide particles (with average size 7.1 fim) were used to study the effect of particle shape and size on the codeposition process. The bath was sonicated prior to the deposition run and was mechanically agitated during the run. The starting pH of the electrolyte was 4 ± 0.2 and the bath temperature was maintained at 50 ± 2°C. The volume percent of the incorporated particles was measured through quantitative image analysis of the pohshed cross sections on a LECO 2001 image analyzer. The microhardness of the as-deposited and annealed coatings were measured using a LECO-M 400FT microhardness tester in accordance with ASTM E384 standard using loads of 25 g on polished cross sections.

4. RESULTS AND DISCUSSION Figure 1 presents scaiming electron micrographs of the second phase particles used for producing the coatings on the left and optical micrographs of the cross-section of the resultant coatings on the right. As can be seen in the figure, the smaller particles resulted in dense coatings, while the large, angular nickel aluminide particles gave a porous coating. Thus, at given deposition conditions and electrochemical cell set-up, the shape and size of the particles Fig.l - (Opposite page) Second phase particles used for producing the composite coatings and the resultant coatings. Scanning electron micrographs of (a) alumina, (c) aluminum and (e) nickel aluminide particles. Optical micrographs of the cross sections of the resultant coatings (b) Ni-alumina with 225 g/l alumina in bath, (d) Ni-Al with 225 g/l Al in bath and (f) Ni-nickel aluminide with 200 g/l aluminide in bath. All coatings were deposited at 5 A/dm^.

229

1^ ^t,»M

IW^

230

can have a significant impact on the quaUty of the coating, with dense coatings being obtained for "rounder", smaller particles, particularly when the particles are metallic. Figure 2a is a plot of volume percent alumina in Ni-Al203 coatings as a function of volume percent in the bath for a range of current densities. It can be seen that increasing the amount of alumina in the bath resulted in a steep increase in vol.% alumina in the coating. A maximum of 39 vol.% alumina in Ni was achieved at 1 A/ dm^ for a bath loading of 5.3 vol.%. This value is almost twice the maximum reported by Ding et al. [3] for Ni electrodeposits that contained 2.7 jim a-alumina particles. The decrease in volume percent as a function of current density for our coatings followed a similar trend to that found by Ding et al. [3] for Ni-a alumina and Cua alumina and Celis et al. [4] for Cu-y alumina deposits. Compared with AI2O3, the codeposition of Al was less strongly affected by current density and bath particle content. The amount of Al in the coating ranged from 5 to 17.5% only, as can be seen in Fig. 2b. Comparison of the structure of the Ni matrix at high current densities (> 10 A/dm^) with and without the presence of Al showed that codeposition of Al resulted in refinement of the structure. Comparable studies in Ni-Al203 coatings were not possible, because the etchant preferentially attacked the interface [2]. However, from the variation of hardness of the coatings (see below) with particle vol.% we believe that at lower current densities the alumina particles result in a coarsening of the Ni grain structure. Note that grain structure of Ni for sulfamate bath becomes finer with decreasing current density. [2] In mixed particle baths, the codeposition of Al was not affected by the presence of alumina whereas the codeposition of alumina was suppressed at lower current densities so that the two lines shown in Fig. 2a for low and high current density regimes collapsed onto the latter. The reason for this behavior, we believe, is related to the distortion of the field lines around metallic (conducting) versus ceramic (insulating) particles during deposition. Graded coatings of Ni-Al-Al203 were produced by varying the bath particle content at a fixed current density of 5 A/dm^. A light optical micrograph of one such coating is shown in Fig. 3a and the annealed structure of the same coating in Fig. 3b. When coatings containing Al

2

4

6

8

Vol.% Alumina In Bath

10

2

4

6

8

10

Vol.% Aluminum In Bath

Fig. 2 - Volume percent (a) AI2O3 (b) Al in coatings as a fiinction of particle volume percent in the bath for a series of current densities in the range 1 - 25 A/dm^.

231

Fig. 3 - Light optical micrographs of a graded Ni-Al-Al203 coating, (a) From bottom to top, the three layers in the coating contain approximately 12-0, 9-16, 9-24 Al vol.%-Al203 vol.%., respectively, (b) Same coating as in (a) annealed at 635° C for 1 hr.

2^500

1

I

O Ni • Ni-AI O 2

I

1 1 -

600

a

£ 500 -O > I ^400i

3

X ^400 0)

g 300

•

*

O

O

1 200 inn

•

•

o

o

1

5

10

15

•

o •

- (/> I 300|; :

0

1

' 1 '

1

1 1

b

u

(0

•

'

Ni Ni-Ai

• 1

# •

o

0

5

10

* •

#

-

o

o

o

:

15

20

25

30

^ 200|

1

20

25

Current Density (A/dm^)

30

0 100'

Current Density (A/dm^)

Fig. 4 - Vickers hardness as a function of current density for (a) Ni-Al203 and (b) Ni-Al coatings. In both figures, the hardness of Ni with no particles is given for comparison.

232 were annealed, the reaction of the two elements resuhed in the formation of either single phase Y sohd solution or two phase y-Y, in agreement with the equilibrium phase diagram. The sample in Fig. 3b, annealed for 1 hr at 635 "C, was a two phase mixture of y-Y, with the alumina particles residing in the y phase. Figures 4a and 4b present the hardness of single-particle, uniform coatings of respectively Ni-Al203 and Ni-Al as a function of current density. Two points are worth noting. One, at high current densities ( > 10 A/dm^) the "soft" metalhc Al particles resulted in greater hardening than the "hard" ceramic AI2O3 particles. Two, at lower current densities that the incorporation of alumina resulted in a smaller increase in hardness than at higher current densities, even though the volume percent of the incorporated particles was larger at the lower current densities. In other words, for both types of coatings the hardness did not follow a simple rule of mixtures. The reason for this, we believe, is the change in microstructure of the Ni matrix when the second phase particles are incorporated.

5. CONCLUSIONS Electrodeposition offers an attractive method for the fabrication of uniform and graded particulate composite coatings. Here we demonstrated the use of this method in the fabrication of single- and dual-particle Ni-Al-Al203 coatings. In doing so we delineated the effect of current density and bath particle content on the volume percent of particles in the resultant coating. The hardness of the single-particle coatings shows significant deviations from the rule of mixtures. This was believed to be a result of the effect of the particles on the microstructure of the matrix during deposition. This work was made possible by research subcontract DE-FC21-92MC29061 sponsored by the U.S. Department of Energy - Morgantown Energy Technology Center through a cooperative agreement with the South Carolina Energy Research and Development Center at Clemson University. The authors thank A.O. Benscoter for help with metallography and microscopy, and X. M. Ding and Profs. B. Ilschner and R. Chaim for helpful discussions.

REFERENCES 1. B. Ilschner and N. Cheradi FGM '94, Proc, of the 3rd international symposium on structural andfunctional gradient materials, (Ed. by B. Ilschner and N. Cheradi, Presses polytechnique et universitaires romandes) pp. V-IX (1995). 2. K. Barmak, S.W. Banovic, C. M. Petronis, D. F. Susan and A. R. Marder, J. Micros., (in press). 3. X. M. Ding, N. Merk and B. Ilschner, FGM *94, Proc, of the 3rd international symposium on structural and functional gradient materials, Ed. by B. Ilschner and N. Cheradi, Presses polytechnique et universitaires romandes, 365 (1995). 4. J. P. CeHs, J. R. Roos, and C. Buelens, C, J. Electrochem. Soc. 134, 1402 (1987).


233

Functionally graded materials by electrochemical modification of porous preforms A. Neubrand, R. Jedamzik, and J. Rodel Fachbereich Materialwissenschaft, Technische Hochschule Darmstadt, PetersenstraBe 23, 64287 Darmstadt, Germany A novel method to produce gradient materials based on the infiltration of refractory porous preforms with a molten metal or polymer has been developed. The porosity gradient in the preform is created by electrolysis. For this purpose, a gradient of the electrochemical potential is set up inside the porous preform, leading to a gradient in the rate of electrochemical dissolution or deposition of the preform material and thus to a graded porosity. A macroscopic electrokinetic model of the gradation process is developed, and the influence of experimental parameters like current density, electrode and electrolyte resistivity and geometrical factors on the gradation profiles are discussed and compared to experimental observations. W/Cu graded materials have been produced and some of their properties have been determined as a function of position.

1. EVTRODUCTION In the last decade, a variety of processing methods for functionally graded materials including powder processing, thermal spraying and deposition processes have been developed. Infiltration techniques are a very promising method for material combinations with very different melting points. A preform of the more refractory phase possessing a porosity gradient is produced and infiltrated with the melt of the lower melting component at elevated temperatures. The main advantages of the method are the low porosity levels that can be achieved without the need of developing sophisticated densification techniques like sparkplasma or microwave sintering, which have to be adapted to the material combination and gradient. The main challenge lies in the production of suitable preforms in a one-step process. An ideal preform should have a large porosity gradient with minimum closed porosity and sufficient mechanical stability. The lower porosity limit for a preform with equiaxed phase elements is about 8% (below this limit most porosity will be closed). The upper porosity limit is given by the need of mechanical stability of the preform - using fibres a porosity as high as 95% is achievable. Thus, infiltration processing can produce gradient materials with smooth gradients from 92% to 5% volume fraction of the more refractory phase. A variety of methods has been used to prepare graded preforms. For example sintering of powder compacts with a graded grain size leads to the formation of a porosity gradient. However, in tungsten preforms large deformations due to uneven sintering shrinkage have been observed unless different layers of the compact were pressed separately to different green densities [1]. Porosity gradients can also be introduced in the compact by admixing variable

234

amounts of non-equiaxed elements. As an example, Al2Ti05/Al203 preforms with graded porosity have been produced by sequential casting of slips with different content of short alumina fibres [2]. Plasma spraying has been employed for the production of graded AI2O3 preforms [3]. The method yields materials with some closed porosity and only moderate gradients in open porosity of 5-14%. Another method uses open-celled polymer foams as precursor materials. The polymer foam is coated with a ceramic slip while rotating in a centrifuge. Afler burning out the polymer a ceramic foam with a porosity gradient is retained [4]. In the present study an electrochemical process is used to introduce a porosity gradient into a homogeneous preform. The method is able to produce a large variety of gradient materials in a simple two-step process consisting of gradation and infiltration thus making it attractive for large-scale industrial processes.

2. THEORETICAL BACKGROUND Electrochemical gradation of porous preforms is based on an electrochemical reaction taking place in a porous electrode where the solid phase of the electrode takes part in the electrochemical reaction - it is either dissolved or deposited during the process. The apparatus for the gradation process is sketched in Fig. 1.

Galvanostat

Referenceelectrode

Electrolyte Porous preform

Insulation

Fig. 1 Experimental setup for the electrochemical gradation process

235

For tungsten as porous anode material the anodic half reaction is W + 80H-

-^

w o / " + 4H2O + 6e'

During the reaction current passes through the pores of the electrode. According to Ohm's law this leads to a potential gradient in the electrolyte. In simple cases, the current density j depends on the overpotential rj (the difference between actual potential and equilibrium potential) according to the Tafel relation j=j^J^

(1)

For the anodic dissolution of tungsten in alkaline solution Jo = 5.8*10"^ A/m^ and k= 38.4 V "^ [5]. This means that a change of 60 mV in overpotential causes the reaction rate to increase by a factor of 10. Such potential differences occur in the electrolyte within a few millimetres distance at current densities of a few mA/cm^, which are easy to realise for the electrode reaction mentioned above. Using the Tafel relation, the distribution of the current (and thus reaction rate) inside the anode at the beginning of the experiment can be calculated analytically [6]. In the present paper a refined numerical model was used for the calculation of the dissolution rate which can use experimentally determined current-potential-relations and can take into account the change of pore radius during the dissolution process. The model shows that the current distribution and thus the gradation profile is controlled by a number of experimental parameters like initial porosity, current density, conductivity of electrolyte and electrode material, kinetics of the electrode reaction and temperature. By changing these and the geometry of the experiment, a variety of different gradation profiles can be produced.

3. EXPERIMENTAL Tungsten preforms of 16 % and 42 % porosity containing about 1% nickel (Tridelta AG, Hermsdorf, Germany) were used for the gradation experiments. The area of the preforms was 30 X 24 mm^, the thickness was either 5.2 mm or 5.8 mm. The preforms were first weighed and then graded by using them as anode in an electrolytic cell. For this purpose the preform was infiltrated in vacuum with the electrolyte and contacted on the back. The platinum cathode was mounted parallel to the anode surface at a short distance. It had the same area as the anode giving rise to a nearly uniform electrolyte potential at the front surface of the anode. The cell current was kept constant during experiments by means of a galvanostat. The electrolyte was commercial grade NaOH. Under the experimental conditions tungsten was dissolved at the anode while hydrogen was generated at the cathode. After completion of the experiment the tungsten anodes were flushed several times with water in order to remove sodium hydroxide and reaction products, dried in a drying chamber and weighed. The resulting graded preforms were infiltrated in vacuum with either molten copper or the molten alloy CuNi2Si. An overview of the processing sequence is shown in Fig. 2. The volume content of the different phases was determined from optical micrographs using an image analyser. EDX analysis of the elemental composition was performed on some of the samples. Hardness tests were carried out using a Vickers indenter using a load of 49N.

236

anodic dissolution >

porous tungsten

infiltration with copper

tungsten with porosity gradient

tungsten/copper gradient material

Fig. 2 Overview of the processing sequence 4. RESULTS A porous tungsten sample (A) was electrochemically graded under experimental conditions given in Table 1. Its microstructure after copper infiltration is shown in Fig. 3. As a result of the electrochemical gradation process a one-dimensional gradient in tungsten content (dark areas) from the side away from the cathode (left) to the side close to the cathode (right) is observed. This is in accordance with theory which predicts that the electrochemical reaction will always be faster on the side close to the counter electrode if the electrode material has a higher conductivity than the electrolyte. The gradient is continuous and accompanied by an increase in the size of the copper ligaments (light areas). A slight step is only observed at the former outer surface of the tungsten preform on the right of the micrograph. No signs of porosity are observed even at higher magnifications.

Fig. 3 Microstructure of W/Cu FGM

237

Table 1 JExgerimental conditions for Sample Initial Porosity A 16% B 42%

electrochemical gradation Electrolyte Duration of Anodisation IMNaOH 23 5h 2MNaOH 23 5h

Current density 6.25mA/cm2 6.25mA/cm2

Current yield 103 % 103 %

The chemical composition of the tungsten-copper FGM as a function of position as determined by optical micrography is shown in Fig.4a. From weight loss data a current yield close to 100% was determined for the experiments - showing that there were very little side reactions during the electrochemical dissolution of tungsten. Modelling the gradient is therefore straightforward and a theoretical prediction of the composition profile is in good agreement with the observed one, if one assumes that the BET surface remains constant during the dissolution process. In reality one would expect that the BET surface first increases and then decreases with material removal. It appears that the assumption of no change in time average still yields good results. The gradient in composition is also reflected in a change of Vickers hardness. However, close examination shows that the tungsten content shows little variation on the side away from the cathode, whereas the hardness decreases significantly. The reason for this behaviour is yet unclear, but macrostresses at the tungsten-rich side of the graded interface may be responsible for the apparent hardness increase. In general, the observed hardness values compare favourably with ungraded W/Cu composites (possessing a Vickers hardness of 2.8 GPa at 85% tungsten content) indicating a low porosity level of the produced FGM. Theory predicts shallower composition gradients for electrolytes with higher conductivity. This has been demonstrated by grading a second sample (B) under different conditions - in this case the composition profile (determined by optical microscopy and EDX) extends over several millimetres (Fig.4b). Again the composition gradient is well predicted apart from a small increase in tungsten content close to the surface which existed already in the untreated preform. The gradient is again reflected by the Vickers hardness. As can be seen from Table 1 the only parameters changed were the initial porosity of the sample and the concentration of the electrolyte. The increased porosity and electrolyte conductivity leads to smaller potential a)

b) 60

100

i B

"c o O

o^

(0 (0 0)

>

c

50

•D

(0

^

Content Experimental Content Theoretical

3

ro

a. O

^

Vickers Hardness

Position [mm]

±(0

L5$2;^^

o• 0)

Q-

40

c o c

o

^

Content Experimentar

ac

Z3

Content Theoretical 20

A

Vickers Hardness

Position [mm]

Fig. 4 Hardness and composition gradients in two tungsten/copper-FGM's

Cathode -

238 differences in the liquid phase when the cell is operated, which in turn leads to shallower gradients. 5. CONCLUSION Electrochemical gradation of porous preforms is a versatile and cost-effective method to produce gradient materials. It is suitable for the production of gradient materials from two components with very different melting points. The method yields graded tungsten-copper composites of high density in a simple two-step process. The electrochemical gradation process of tungsten is adequately described by a macroscopic model of the electrode kinetics.

ACKNOWLEDGEMENT This work was supported by the German Research Society (DFG) as part of the „Schwerpunktprogramm Gradientenwerkstoffe". We also thank Tridelta AG for kindly supplying the tungsten preforms.

REFERENCES [1] M. Takahashi, Y. Itoh, M. Miyazaki, H. Takano, and T. Okuhata, p. 17-28 in Proceedings of the 13 th International Plansee Seminar, H. Bildstein and R. Eck (eds.),Metallwerk Plansee, Reutte 1993 [2] W. Henning, C. Melzer and S. Mielke, Metall 46 (1992) 436-439 [3] W. Schultze, S. Schindler, F.-U. Deisenroth, German patent DD 300 725 A5 (1990) [4] Y. Miura, H. Yoshida, Y. Takeuchi, K. Ito, German patent DE 3527 872 Al (1986) [5] J.W. Johnson and C.L. Wu, J. Electrochem. Soc. 118 (1971) 1909-1912 [6] A. Neubrand, B. Kastening and J. Rodel, p.488-497 in Elektrochemie der Elektronenleiter, GDChMonographienBd.3, F. Beck(Hrsg), GDCh-Verlag, Frankfurt 1996


239

Thermal management of carbon-carbon composites by functionally graded fiber arrangement technique Y. Kude and Y. Sohda Central Technical Research Laboratory, Nippon Oil Company, Ltd., 8, Chidori-cho, Naka-ku, Yokohama, 231, Japan Next to mechanical properties, the most important characteristics of a carboncarbon composite(C/C) are thermal conduction and thermal expansion. In this paper, several investigations have been made into carbon fiber arrangement relationships for different carbon-carbon composite materials. Pitch-derived carbon matrix-carbon fiber composites have been used, processed by means of the hot isostatic pressing (HIP) technique for converting pitch into a dry carbon fiber preform. Repeated HIP cycles are required to build the composite matrix up to an acceptably high density/low porosity for deployment in severely ablative environments. The effects of heat treatment temperatures on thermal conductivity, thermal conductivity at high temperatures and thermal expansion behavior have been studied. At room temperature, the value of thermal conductivity for unidirectional (UD) carbon-carbon composites is 700 W/m-K. In the case of three-dimensional (3D) carbon-carbon composites, this value is determined by the volume of the fiber arrangements. On the other hand, the thermal expansion of carbon-carbon composites in the fiber axial direction is chiefly governed by the thermal expansion of the fiber. On the basis of this fundamental research, a functional graded fiber arrangement technique has been proposed which presents the opportunity to 'tailor' thermophysical properties into carbon materials. 1. INTRODUCTION A lot of investigations have been made in the field of high performance carbon/carbon composites for aerospace applications. Most of these composites wêre associated with their superior mechanical properties at high temperatures. In addition, thermal conduction and thermal expansion of carbon-carbon composites are also important for some applications, e.g., re-entry vehicles or aero-engine components. On the other hand, it is expected that the positive thermal management technology of carbon/carbon composites will provide excellent heat receivers or heat radiators, especially in fields that require severe thermal shock resistance. In this paper, first the thermal properties of carbon fibers are described, and second the thermal properties of carbon-carbon composites are presented. Finally, the application to sunshine heat receivers by a functionally graded fiber arrangement technique is also described. One of the important aims of this research is to prove that carbon-carbon's

240 properties are capable of being tailored to specific applications by this functionally graded fiber arrangement technique. 2. THERMAL PROPERTIES OF PITCH-BASED CARBON FIBERS Graphite shows very anisotropic thermal properties as a result of its crystal structure. This is because graphite possesses two-dimensional hexagonal network structures and the layers are held together very loosely by weak forces. For example, chemical vapor deposited carbon, which is manufactured with heat treatment at 3000°C after the deposition and possesses almost ideal graphite structures, has a thermal conductivity of 2,000 W/m'K (at room temperature) parallel to the layers and 10 W/m-K in the perpendicular direction as shown in figure 1. This value in the parallel direction is approximately 4-5 times more than the value of silver or copper, which are typical high thermal conductivity metals. Carbon fibers, which utilize the preferred orientation of the graphene layers, show not only high modulus and high strength but also high thermal conduction and low thermal expansion along the fiber axis. On the basis of these properties, fiber reinforced materials present the opportunity to design the thermal properties into materials. Figure 2 shows the thermal conductivity of pitch-based carbon fibers for each modulus grade (value [XN-**] means its tensile modulus) in comparison with other high thermal conductivity materials. High modulus carbon fibers, that is, carbon fibers which have high degrees of preferred orientation of the graphene layers, show high thermal conductivity. Those values are more than the value of silver as a typical high thermal conductivity metal or silicon nitride as a typical high thermal conductivity ceramic. Incidentally, pitch-based carbon fibers show much higher thermal conductivity than PAN-based carbon fibers with the same modulus. Carbon fibers show negative thermal expansion behavior at temperatures between 20°C and around 500°C as shown in figure 4. This behavior depends on each fiber's grade. By utilization of this negative behavior, materials whose coefficient of thermal expansion is zero can be created when quasi-isotropic laminates are controlled with an optimum fiber volume fraction and are incorporated with matrices which have positive coefficient of thermal expansion. In practice, those materials can be used in satellites or space telescopes which demand severe thermal environment resistance. 3. FABRICATION METHOD OF CARBON/CARBON COMPOSITES In this work, all carbon-carbon composites were fabricated by using pitch-based carbon fibers and pitch-derived carbon matrices. Two types of preforms, were mainly used. One is unidirectional (UD) preforms, and the other is 3-dimensional (3D) fabrics. 3D fabrics normally contain 55 vol.% of fibers that are introduced in three directions. Each volume fraction of fibers is 40 vol.% in the x-direction, 10 vol.% in

241 the y-direction, and 5 vol.% in the z-direction. After matrix impregnation, the pitch was converted to carbon by a process of pyrolysis in high isostatic inert gas pressure. This densification process was repeated several times. After densification processing, the matrix was graphitized by controlled heating to temperatures above 1700°C. 4. THERMAL PROPERTIES OF CARBON/CARBON COMPOSITES 4.1. Thermal conductivity Thermal conductivity was evaluated by the product of the density, specific heat, and thermal diffusivity. Thermal diffusivity was measured by the Laser Flash method. Figure 5 shows the thermal conductivity of UD-C/C compared with that of 2D-C/C. At room temperature, the thermal conductivity value is 700 W/m-K parallel to the fibers in the case of UD-C/C. The values of conductivity rise significantly as the final heat treatment temperature increases. This is not only because the size of the graphite crystallites became bigger, but also because the orientation of the crystallites along the fibers increased. UD-C/C possesses roughly twice as great a value of thermal conductivity as 2D-C/C. This result also proves that the matrices in UD-C/C greatly contribute to the thermal conductivity because the orientation of the matrices' crystallites along fibers increased. Figure 6 shows the temperature dependence of the thermal conductivity for UDC/C in comparison with copper. As the temperature is increased, the thermal conductivity falls. This is because the amount of phonon scatter is due to the vibration of the crystal lattice. The thermal conductivity data of 3D-C/C are presented in figure 7 correlated with the fiber volume fraction for each direction. The direction with 40 vol% of the fiber has a thermal conductivity of 470 W/m-K. On the basis of the good relationships between the fiber volume and the thermal conductivity, it is considered that the design and the regulation of the heat flow in C/C would be possible. In this case, there are two noteworthy points for the design as can be seen from 3D-C/C type A and type B in Figure 7. First the density of C/C greatly contributes to the thermal conductivity. Second, the fiber volume valance influences the contribution of the matrices to the thermal conductivity more than the actual fiber volume dose. In other words, the more isotropic the fiber volume valance in C/C is, the more dependent on the fiber itself in C/C the thermal conductivity is. 4.2. Thermal expansion Thermal expansion was measured by the laser light interference method. Figure 8 shows thermal expansion behavior of UD-C/C with the heat treatment at 3000°C. There are large differences in the thermal expansion between the fiber axial direction and the fiber vertical direction. Figure 9 shows the relation between the coefficient of thermal expansion and the

242 measurement temperature in UD-C/C. The value of the coefficient in the fiber axial direction is almost zero. In contrast, the value of the coefficient in the fiber vertical direction is close to the value of the coefficient in copper. This fact means that the joining between copper and C/C is easy when limited to this direction. The thermal expansion in the fiber axial direction is chiefly governed by the thermal expansion of the fiber, and the thermal expansion in the fiber vertical direction is chiefly governed by the thermal expansion of the matrix. Figure 10 shows the coefficient of thermal expansion in 3D-C/C. There is a small difference for each direction, but all of the values are almost zero. Therefore, the joining between copper and C/C is expected to be quite difficult in the case of 3DC/C. 4.3. Application to sunshine heat receivers of functionally graded fiber arrangement technique As mentioned previously, the heat flow through C/C composites by conduction can be controlled by the design of the fiber architecture. The most suitable design method is by using the functionally graded fiber arrangement technique. Figure 11 shows a C/C composite cavity manufactured with the functionally graded fiber arrangement technique for a sunshine heat receiver. This C/C cavity is manufactured from 3D carbon fiber fabrics which are designed for getting the optimum heat flow. Solar rays are irradiated by a large parabolic mirror into the inner surface of this C/C cavity. Since the heat is utilized from the back bottom wall, efficient heat flow to the back bottom wall is required. At the side, the fiber volume of the inner side in the bottom direction is larger than the outer side. At the bottom, the fiber volume of the center to the back bottom direction is larger than the outer. The fiber volume of each intermediate part is graded. This cavity was tested by the solar ray concentration equipment at Tohoku University. The results are shown in figure 12. C/C composites made with the FGM method have higher performance than isotropic graphite. 5. SUMMARY Carbon-carbon composites made with the functionally graded fiber arrangement technique present the opportunity to 'tailor' thermo-physical properties into carbon materials. In this paper, the changing of the fiber architecture is the method for FGM. Fibers or matrices are other options for FGM. This functionally graded fiber arrangement technique can be applied to a wide range of materials processing. ACKNOWLEDGEMENT The authors would wish to thank Prof. Arashi and Dr. Naitou of Tohoku University for evaluating the C/C composite cavity.

243 2 0 0 OW/mK

Cu

(a-axial)

Ag AIN PANKT

'

-rt

I

I

• - •• I

• ,

,

V

:

•:

,

• •,.

iilllllliilllllllll iiiiiiMiiiiii

]

1

•

1

XN50A XN70A XN80A 0

1 OW/mK (c-axial)

100

200

300

400

ITiermal conductivity W/mK

Figure 1 Difference in thermal conductivity of graphite between a-axis and c-axis.

Figure 2 Thermal conductivity of carbon fibers and various materials.

_ _ 0 3 ' ° /CO-"^ O^-^-^.A A— A

:5

100

200

-

-

—O— Granoc - A - PAN

A 0

A

300

400

500

600

700

Young's rroduius of carbon fibers

800

200

GPa

Figure 3 Thermal conductivity of carbon fibers.

300 400 500 Temperature °C

600

Figure 4 Thermal expansion of carbon fibers.

800

E (i> JC

1500

2000

2500

3000

3500

Final heat treatment temperature °C

Figure 5 Thermal conductivity of C/C composites at room temperature.

250

500

750

1000

1250

1500

Measurement temperature °C

Figure 6 Thermal conductivity of UDC/C composites as a function of temperature.

244 90

•

/oo £

2.0g/cm3

600

/^

400

/

300 200 .

y /

X ^

70

60 V

1.92g/cm3

50

(Vv=8.5%)

S

40 r

g

3D-C/C B 1.82g/cm3

^-^"^^^"^^

(Vv=13.3%)

n 40

60

80

100

18 16 UD-C/C

14 12 10

A

X

/ . / •Fiber vertical

1 20 I 10 ' ^ 0{ 1 -10 i

i

y

6

y

Fiber axial direction ^-o—o—o—o—o—o—o-o—o 1

—1

1

1

4

400

500

600

700

1

Figure 8 Thermal expansion of UD-C/C composites after heat treatment at 3000°C. y

2.5 (-

o

2.01 1.5

Vf 5% direction

Vf 10% direction Vf 40% direction

PV--^-^"^

-1.0 300

1

-0.5

Fiber axial direction

0 200

1

100 200 300 400 500 600 700 800 Measurement temperature °C

0.0

100

direction

/

i

0.5

0

./

/•

1.0

Fiber vertical direction

8

2|-

y

/•

/ •

30

0

Figure 7 Thermal conductivity of 3DC/C composites.

UD-C/C

L

Fiber volume %

9

1

0

Q.

^

20

^ .2

3D-C/C A

500

100

80

UD-C/C

800

-1.5

o^%^^^

•

0

100

Measurement temperature "C

Figure 9 Coefficient of thermal expansion of UD-C/C composites after heat treatment at 3000°C.

0-

e

0. 0. 0. 0.

10

12

14

Temperature

16

O

: TiC

•

: Uo

18

coaling substrate

20

22

(xlO'K)

Fig. 3 Emissivity of TiC coating and Mo substrate 3.2 Formation of TiC/Mo FGM coatings Both TiC and Mo powder feeding rates were controlled for the formation of TiC/Mo composition graded coatings. The macrostructure of cross section of TiC/Mo FGM (coating thickness : 500 '^ 600^m) sprayed under those operating conditions is shown in Fig. 4. To compare with the characteristics of TiC/Mo FGM coatings, TiC coatings Fig. 4 Structre of TiC/Mo FGM coating (coating thickness : 320 ~ 330juLm ) and TiC-Mo two layer coatings ( coating thickness :320 ~ 330fxm) were formed onto Mo substrate. 3.2.1. Thermal stability and thermal resistance of coatings TiC, TiC-Mo two layer and TiC/Mo FGM coatings were heat-treated under conditions of 1473K, 16h and 72h, in a vacuum (2 X 10 "^ Pa) .

248 Firstly, figure 5 shows the typical cross sections of TiC and TiC-Mo two layer coatings observed by SEM. As shown in this figure, some cracks were found in the heat-treated TiC coatings and the TiC layer peeled from Mo substrate after the heat-treatment.. In the heat-treated two layer coatings, there were no cracks in both TiC and Mo layers and the interface between TiC and Mo layers was sound. These results were caused probably by thickness difference of TiC layers between TiC coatings and combination coatings as shown in Fig. 5.

Fig. 5 Structures of coatings by heat treatment Secondly, figure 6 shows the distributions of Ti, C, O and Mo near the interface of the TiC and Mo layers in the two layer coatings for the as sprayed and the heat-treated coatings. Elements Ti, C and Mo did not diffuse to the other layer. From the results and observations of micro structures, it was found that TiC and Mo showed no chemical reaction in the two layer and FGM coatings. Horiguchi et al. carried out diffusion bonding of TiC with Mo and reported a kinetic expression for the diffusion between the two materials ^^ . Extrapolating their results to the present conditions of heat treatment, it is expected that a diffusion layer of at least 5 jU m thickness is formed at the TiC/Mo interface possibly resulting in a reaction product such as Mo 2 C. Lack of diffusion or reaction layer between the TiC and Mo in the sprayed specimens may be because sprayed Mo particles were covered with thin oxide film . Further study is necessary to confirm this hypothesis, however. Finally, figure 7 shows the scheme of a solar heating test carried out by Prof Arashi's laboratory at Tohoku Univ. In this test, the specimen was vacuum-encapsulated in a quartz cell and the coating surface was heated by a condensed solar radiation. The surface of FGM coatings reached 1775K where as the rear surface reached 1725K during the test. No micro-crack and peeling between the coatings and Mo substrate were observed after the test.

249 3.2.2. Thermal cycle resistance of coatings Thermal cycle resistance of Tie, TiC-Mo and TiC/Mo FGM coatings were investigated by the thermal cycling test of temperature range between room temperature and 1223K in 5 times ( heating, cooling speeds were 100 K/s ) in air . These experimental results were summarized in Table 2. The cracks in TiC layer and peeling between TiC layer and Mo substrate were observed in TiC coatings and the peeling was observed at some part of the interface between Mo and TiC layers in the TiC - Mo coatings. In TiC/Mo FGM coatings, there were no recognizable defects. From these results, it was found that thermal stress , caused by different expansion coefficients between TiC and Mo ^^' ^^ , was significantly reduced in TiC/Mo FGM coatings. As mentioned above, TiC/Mo FGM coatings formed by thermal spraying in the air were effective for the emitter element of the thermionic generator.

Mo-TiC two layer coating | i I" • As sprayed

Heat-treated

r

L_.

Mo w ...;--

—— |-

.--.

—

f->

— — — —' - ----- - - _:..

Lc'

—

—

^1

u

i.

i -o

•^r- — — "^ .a_. T T Z ; Analysis results of coatings by EPMA -_i_i.

Solar radiation Thermocouple Ho-TiC two-layer coating

100 jum

Pyrometer Fig. 7 Scheme of a solar heating test

TiC coating

Fig. 8 Surface and cross-sectional structures of coatings after thermal cycle test

250

Table 2 Results of thermal cycle test of coatings FGM coating TiC/tto coating TiC coating

Substrate/ coating Sound Sound Peeling

TiC/Mo coating boundary Sound Peeling

Coating surface Sound Sound Crack

Evaluation

0 A X

4. CONCLUSIONS Formation of graded coatings (FGM) was carried out with the plasma twin torch spraying method in air. TiC and Mo powder (particle size ilO to 44 fi m) were sprayed onto Mo substrate to obtain coatings with high thermal absorptance in order to improve the performance of the thermal energy conversion system. The results are summarized as follows. 1) Graded coatings are obtained by stepwise control of each powder feeding rate. 2) The compositional gradient in the coating is nearly smooth and linear. 3) After the heat treatment of the sprayed coatings in a vacuum ( at 1473K, 16h, 10 ~^ Pa ), there are no recognizable reaction products between Mo and TiC in the coatings. 4) There are no recognizable defects in the FGM coatings after the thermal cycle test (from R.T. to 1223K, 5 cycles) while there are defects in the TiC single coating onto the Mo substrate. REFERENCE 1) Journal of the Society of Materials Science : An Extreme Situation and Materials, Syokabo, 134, 1987 (in Japanese ) 2) T. Fukushima : Proceedings of the first Int. Sympo. on FGM, 145, 1990 3) Y. Watanabe : Journal of the Japan Society for Aeronautical and Space Sciences Vol. 42, No. 482, 141, 1994 ( in Japanese ) 4) A. Horiguti : The Materials, Vol. 35, No. 388, 35, 1986 the Japan Society for Aeronautical and Space Sciences, vol. 42, No. 482, 141, 1994 (in Japanese ) 5) Journal of the Society of Materials Science : An Extreme Environment and Materials, Syokabo, 123, 1987 (in Japanese ) 6) National Astronomical Observatory : Chronological Scientific Tables, Pyhs.49 (463 ), 1985 (in Japanese)


251

Fonnation of a Ti-Al203fimctionallygraded surface layer on a Ti substrate with tlie use of ultrafme particles A. Otsuka, H. Tanizaki, M. Niiyama and K. Iwasaki Steel & Technology Development Laboratories, Nisshin Steel 7-1 Koyashinmachi, Ichikawa, Chiba, 272 Japan A Ti-Al203 functionally graded surface layer of about 0.5 mm in thickness is formed by dryjet spraying of ultrafine particles produced by radio-frequency plasma onto a cylindrical Ti rod. The spraying is made by continuously changing the ratio r = Ti/(Ti+Al203) from 1 to 0 or from 0.5 to 0 in the outward radial direction. The obtained green composite is sintered in the temperature gradient condition, where the Ti-rich and the Al203-rich sides are sintered at about 1400 K and 1800 K, respectively. The ratio r in the sintered composite is found to change gradually from 1 to 0 independent of the starting r value. The r region omitted in the spraying is considered to be compensated by abnormally rapid diffusion of Ti. The size of voids found in the layer is much smaller when the starting r value is set at 0.5 than when it is set at 1. The number of cracks in the layer is reduced by adjusting the sintering conditions and by adding Zror Ti-hydride powders to the substrate. The layer has a fine metallographic structure and the adhesion strength between the substrate and the layer is measured to exceed 60 MPa. 1. INTRODUCTION Though the sintering of ultrafine particles (UFPs) are known to proceed at low temperature and to give rise to fine-grained materials, their industrial applications are still very few. By taking these advantages of UFPs into account a trial to fabricate a functionally graded material (FGM) with the use of them is undertaken in this work, where an artificial tooth root is chosen as an example. It consists of a cylindrical core rod of Ti and a Ti-Al203 surface-coated FGM layer. The composition ratio, r = Ti/(Ti+Al203), is set to decrease gradually in the outward radial direction from 1 to 0. The mechanical strength of the tooth root is sustained by the Ti rod, while the AI2O3 surface serves as a biochemically stable (bioinert) layer. If bioactivity is required, the AI2O3 surface is fijrther coated with hydroxyapatite (HAP) [1-3]. Since metals and ceramics exhibit quite different sintering behavior from each other, a special

252

care must be taken when a green compact of their mixture is sintered. Otherwise there ^sually appear many defects such as voids and cracks due to sintering unbalance [4]. One of the most popular methods to suppress the defect formation is to use processes operated at high pressure and temperature such as hot pressing (HP) and hot-isostatic pressing (HIP) [5]. The cost performance of these methods, however, is very low and the size and the shape of the composite are limited. If it comes to the sintering of an FGM where the sintering temperature should be varied corresponding to the composition, the difficulty in sintering increases greatly and the HP and the HIP methods are not any more appropriate. In order to cope with these problems temperature gradient sintering as will be described in Sec. 2 below is tried in this work. 2. FABRICATION PROCEDURES Figure 1 shows schematically a closed system used for the production and the deposition of UFPs. Raw powders of Ti (average diameter = 27 jam) and AI2O3 (10 fim) are fed into the plasma flame with two mutually independent dispersion feeders, where Ar gas is used as carrier. By adjusting the feeding rates of the two feeders the ratio r of the raw powders can be adjusted at any value between 0 and 1. The total feeding rate is kept at 2 g/min. As for the details of UFP production, see refs. [6-8]. The produced UFPs are homogeneously mixed in an aerosol form, cooled in the cooler and fed into the deposition chamber, where the UFPs are deposited onto the cylindrical surface of the substrate rod by dry-jet spraying [9]. The velocity of the spraying gas is about 200 m/s estimated at the exit of the nozzle. A newly developed L-shaped nozzle is used to increase the deposition efficiency [10]. The cylindrical substrate rod is made of Ti powder of 27 |im and Ti- and Zr-hydride powders of 4 fim in average diameter. The powders are compacted in a polyurethane die at 200 MPa by cold isostatic pressing (CIP) to obtain the substrate of about 3 mm in diameter and about 40 mm in length. It is located in front of the nozzle, where the distance between them is kept at 15 mm. In order to make the spraying homogeneous it is rotated at 30 rpm and simultaneously moved back and forth along the rod length direction with the amplitude of 30 mm and at the frequency of about 0.05 Hz. The total spraying time is about 30 min, during which the ratio r of the UFPs changes gradually from 1 to 0 or from 0.5 to 0. The total thickness of the deposited layer is about 1 mm, which shrinks to about 0.5 mm after sintering. The deposited specimen is sintered in a vacuum (10"^ Pa) furnace shown in Fig. 2. It consists of a W-mesh heater to heat the atmosphere, YAG laser to irradiate the specimen surface, and a thermotracer and a thermocouple to measure temperatures. The YAG laser is

253 first switched-on at the beginning of the sintering to irradiate the outermost AI2O3 surface of the specimen that needs higher temperature for sintering than the Ti core. Then the W-mesh heater is additionally switched-on to heat the whole part of the specimen. It should be emphasized here that the heating sequence is very important. If it is reversed, that is, if the W-mesh heater is switched-on first and then the YAG laser irradiation follows, the FGM layer often flakes off from the substrate. The outermost AI2O3 surface of the specimen is heated to about 1800 K and the central core is heated to 1400 K in this way. The temperature difference of about 400 K is attained between the outer and the inner part of the specimen. The specimen rod is rotated at about 10 rpm and the laser is scanned along the rod axis at 2000 mm/sec to make the irradiation homogeneous.

Carrier gas

Thermocouple

Plasma gas

W-mesh heater

Optically flat window 1.06//m band gap filter

YAG laser

Deposition chamber

Specimen holder

Plasma chamber

Fig. 1 Schematic view of the system for UFP synthesis and deposition.

Specimen

Fig. 2 Schematic view of the temperature gradient sintering furnace.

3. EXPERIMENTAL RESULTS AND DISCUSSION Figure 3 shows the difference in the size of voids (black area) between the two cases where the deposition starts from r = 1 (a) and from r = 0.5 (b). It is clearly seen that the void size is much smaller in the latter than in the former. Since the Ti-rich region with r ranging from 1 to 0.5 showed very large shrinkage during sintering in the previous preliminary experiments, the decrease in the void size is considered to be mainly due to the elimination of this region in the deposition process. The ratio r of the sintered specimen deposited from r = 0.5, however, changes from 1 to 0 as shown in the results of electron probe micro analyses (Fig. 4). The

254

region of r in the range between 1 and 0.5 is considered to be constructed by abnormally rapid diffusion of Ti from the substrate to the FGM layer. Diffusion of this kind is supposed to take place along the surface of the small voids.

FGM surface FGM surface

*'''^' Substrate-FGM boundary

Substrate-FGM boundary

) 00 fi m

100 ;em

(a) r changed from 1 to 0 (b) r changed from 0.5 to 0 Fig. 3 Optical photos of the cross section of FGM perpendicular to the rod axis.

FGM surface

Substrate-FGM, boundary

Signal intensity(Arbitrary unit) Fig. 4 Results of EPMA across the FGM layer. Relative size changes of the substrate and the AI2O3 UFP compact during the sintering are shown in Fig. 5(a). The AI2O3 compact is taken as a representative component of the FGM layer. Temperature profiles during the sintering are shown in Fig. 5(b). The substrate and the AI2O3 compact are sintered at 1400 K and 1800 K, respectively, in consideration of the temperature gradient sintering. The final value of the relative shrinkage of the Ti substrate is about 4 %, which is about half of that of the AI2O3 UFP compact (dotted line). If 5 % hydrides are added to the Ti substrate the amount of shrinkage increases and comes very near

255

to that of the AI2O3 UFP compact, where Zr-hydride seems to be more effective than Tihydride. It should be noted here, however, that the reproducibility of their concentration dependence is rather poor. Though the amount of the relative shrinkage has a tendency to increase with increasing hydride addition up to about 5 %, the relation between them becomes quite complicated above 5 %. This is partly due to the difficulty of uniform compaction because of the high hardness of the hydrides powders. Then it is difficult to determine the proper amount of hydride addition exactly. Since the appearance of cracks in the FGM layer perpendicular to it after sintering is considered to be mainly due to the difference in the relative values of shrinkage between the substrate and the FGM layer, their agreement by the addition of hydrides is expected to be very effective for the suppression of the number of cracks. This is actually seen in Fig. 6, where the decrease in the number of cracks is clearly observed by comparing (a) with (b) as expected.

AI2O3 UFP

Ti+5%Ti-hydride Ti+5%Zr-hyderide

100 Sintering time / min

100 Time/min

(a) Relative size change (b) Temperature profile Fig. 5 Shrinkage behavior during sintering.

(a) Without Zr-hydride (b) With Zr-hydride by 5% Fig. 6 SEM photos of the cross section of FGM perpendicular to the rod axis.

256 As shown above, a fine-grained FGM is obtained with the use of UFPs and by the temperature gradient sintering. Advantages of the present method lie in the high speed formation of an FGM layer and one-process sintering at low temperature and low pressure. The important factors are the distribution of r during the spraying, the sequence of heating with a W-mesh heater and YAG laser, and the adjustment of the difference in the relative shrinkage between the substrate and the FGM layer. The procedures developed here are expected to be extend to the production of various kinds of FGMs. ACKNOWLEDGMENT This work was conducted in the program "Advanced Chemical Processing Technology" consigned to Advanced Chemical Processing Technology Research Association (ACTA) from New Energy and Industrial Technology Development Organization (NEDO), which was carried out under the Industrial Science and Technology Frontier Program enforced by the Agency of Industrial Science and Technology. Authors would like to express their gratitude to these institutions for supporting this work. Dr. S. Koura, Messrs. K. Ohsaki and T. Tanaka and Ms. E. Kobayashi of the authors' laboratory are also acknowledged for their help in performing this work.

REFERENCES 1. K. Ohsaki, H. Tanizaki, K. Iwasaki, M. Ueda, T. Kameyama and K. Fukuda, Proc. 7* Symp. Plasma Sci. Mater., (1994) p.83. 2. T. Kameyama, M. Ueda, K. Onuma, K. Ohsaki, H. Tanizaki and K. Iwasaki, Proc. 14* Int. Thermal Plasama Conf ,(1995) p. 187. 3. H. Tanizaki, A. Otsuka, M. Niiyama, K. Iwasaki, M. Ueda and A. Motoe, Trans. Materi. Res. Soc. Jpn., (1996) in press. 4. R. Watanabe, Materi. Res.Soc. Bull. (Jan. 1995) 34. 5. R. Watanabe, J. Jpn. Industri. Materi.,38(Dec. 1990) 39. 6. S. Koura, H. Tanizaki, M. Niiyama and K. Iwasaki, Materi. Sci. Eng. A208(1996)69. 7. H. Tanizaki, A. Otsuka, M. Niiyama and K. Iwasaki, Materi. Sci. Eng. A, in press. 8. A. Otsuka, S. Koura, H. Tanizaki, M. Niiyama and K. Iwasaki, Nisshin Steel Tech. Rep. 72(1995)11. 9. S. Kasyu, E. Fuchita, T. Manabe and C. Hayashi, Jpn. J. Appl. Phys., 23(1984) 1900. 10. Jpn. Patent H6-336271, (Dec. 1994).


257

Oxidation-Resistant SiC Coating System of C/C Composites N.Sato'^, I.Shiota'\ H.Hatta'^ T.Aoki'\ H. Fukuda'^ 1) Kogakuin University,Tokyo,Japan 2)The Institute of Space and Astronautical Science,Kanagawa,Japan 3) Science University of Tokyo,Tokyo,Japan ABSTRACT C/C composites are easily oxidized to evaporate above 500°C. Anti-oxidizing SiC coating on a surface of C/C composites is known to be an effective measure against oxidation. However weakness in bonding strength often become a serious problem in actual applications. In this paper optimal fabrication technique of SiC coating on C/C composite was explored based on two kinds of criteria; bonding strength and oxidation resistance. Thus a parametric study was carried out experimentally in terms of thicknesses of the coating layer and the conversion FGM layer and CVD temperature. It was shown that the optimal condition of the coating is low CVD temperature, thick conversion FGM layer, and intermidiate coating thickness. 1. INTRODUCTION C/C composites are unique material which possess exceptional high heat resistance along with lightweight, high stiffness and high strength [1,2]. For this reason, C/C composites have been expected to be applied to high temperature structures, in such as aerospace and nuclear fusion industries. However C/C composites are known to possess a serious shortcoming; easily oxidized to evaporate above a temperature as low as about 500''C[3,4]. To overcome this defect, anti-oxidizing SiC coating on the surface of C/C composite was a quite effective measure in an oxidizing environment up to about 1700''C[5]. However weakness in bonding strength and coating cracks due to thermal mismatch between the substrate C/C composite and the SiC coating still often become a serious problem in actual applications. In this paper optimal fabrication technique of SiC coating on C/C composite using CVD (Chemical Vapor Deposition) process was explored based on two kinds of criteria; bonding strength and oxidation resistance. 2. EXPERIMENTAL 2.1 Material (1) C/C composite

258 The examined C/C composite was fabricated via. preformed yarn method[6]. The reinforcing fiber, fiber volume fraction, stacking sequence, and dimensions of specimens of it are Toray M40, 50%, 0790°, and 30mm x 30mm x 3mm, respectively. In the laminated C/C composite, periodical cracks along the fiber axis direction, transverse cracks (TCs), frequently appear as shown in Fig. 1. The surface layers of the TCs especially affect characteristics of the coating on C/C composites. (2) SiC coating The SiC coating was composed of two layers; a thin SiC conversion layer (several \xm) and a thick CVD coating layer. The conversion layer was formed by chemical reaction of gas phase Si with carbon in the substrate. The gaseous Si was provided by thermal decomposition of bubled SiCl^, in which carrier gas was H,. The aim of the conversion layer is to make bonding strength of the coating higher. The CVD layer was thermally deposited at three kinds of temperatures, 1800, 1600 and 1200°C, named hereafter CVD-18, -16 and -12, respectively. The SiC coating with three kinds of nominal thicknesses, 60, 100, 200!LAm were formed.

a^g^TO"

Fig. I Cross sectional view of CVD-SiC coated C/C composite with 0/90 stacking sequence

Fig.2 SEM micro-photograph of surface of SiC-coatin5

Typical cross sectional and top views of the SiC coating are shown in Fig. 1 and Fig. 2. It is obvious from these figures that a lot of cracks appeared in the coating. These cracks were formed in the cooling down process from CVD to room temperatures due to thermal expansion mismatch between the SiC coating and the C/C substrate. SEM and optical microscope observations revealed that the coating cracks appeared first just above the TCs to the direction parallel to the TCs and then perpendicular branch cracks developed from them. The apertures of the former cracks are normally larger, about lOjim, than the latter, several \xm. 2.2 Oxidation Test Oxidation tests have been carried out under xenon lamp heating and natural convection of air, where weight loss under constant temperature was monitored. The temperature was monitored by an infrared thermo-viewer and was calibrated with that of the tungsten-rhenium or platinum-rhodium thermo-couples. Temperature range examined was from 600 to 2300°C. Main features of this apparatus are that a large size specimen can be exposed and equilibrium constant temperature is rapidly attained (about 20s).

259 2.3 Bonding Strength of SiC Coating Evaluation method for bonding strength between a hard and thin cx)ating and the C/C composite of the substrate has not been established. In this study the method illustrated in Fig. 3 was tried to be applied, i.e., shear stress is directly applied to the interface between a coating and a substrate by the plunger. We hereafter call the method as "shear load method" and abbreviates as SLM. A typical load-displacement curve obtained by the SLM is shown in Fig. 4. It is obvious from this figure that shear fracture, at the maximum load point, can be easily attained even for thin brittle coating. However several problemes were anticipated in this method; 1) How to apply precisely compressive load along an interface 2) The sample must be processed into a quite thin plate but whether residual stress in the thin sample is same as the thicker original one. To confirm the formar problem, the interfacial strength was evaluated as a function of loading place, X in Fig. 5. The correct value is considered to be the value at the clearance. Therefore from this figure it is concluded that 0.03mm is sufficient clearance between the interface and the plunger edge. Thus in the present study it is tried to maintain the clearance 0 (t > z / v) and U (x) = 0 for X < 0 (t < z / v). In Eq(3), v is the terminal velocity of the particle, t is time, and z is distance. Assuming f^ to be in the form fo(r) = br^

(4)

the expressions for the volume fraction of particles in the sample, F^(z, t = o) and F(z, t) are: (5)

(6) Normalization of the volume fraction (at any t) relative to the initial value gives

where r,^ and rj^ are the maximum and minimum particle size, respectively, and r^ is defined by

where L is the length of the graded zone, t is time, and (j) is defined by Stokes' law as (9) The terminal particle velocity, v, is in turn defined by v-^(P.-P.)-r'

(10)

where p^, p^. are the densities of the solid (AI2O3) and liquid (Cu) phases, respectively, g (= agj is the centrifugal acceleration, |LI is the liquid phase viscosity, and r is the particle radius. The normalized volume fraction, E, can be calculated from experimental results. The calculation requires knowledge of F(z, t) and F^ (z, t = 0) at any given z value. The former can be obtained from image analyses of sections of samples (i.e. at various z values). However, F^ cannot be determined experimentally but an approximate value can be calculated from the initial

280 stoichiometry, Eq(l), assuming the product to be a fully dense mixture of AI2O3 and Cu. For x = 6 and 7, F^ is 28.74 and 26.63% by volume AI2O3. Thus assuming the 2-dimensional image analyses to represent volumetric distributions, E values are calculated as a function of z, as shown in Figures 4(a) and (b) for systems with x = 6 and 7, respectively.

Best-^hline •

-T—I 0.06

O.i

Distance (cm)

Figure 4(a) Normalized volume fraction of AI2O3 particles with the graded region, x = 6

0.03

1

1

1

0.04

Experiment

I

• •

0.05

0.06

0.07

Distance ( cm)

Figure 4(b) Normalized volume fraction of AI2O3 particles with the graded region, x = 7.

Through a least-squares fit of the E values, two experimental parameters of the separation process can be calculated from Eq(7). These are the particle size exponent, a, and the separation time, t. The last parameter is implicit in the definition of r^ in Eq(7). The calculated values for "a" and t for x = 6 are -1.8 and 0.61s, respectively. The corresponding values for x = 7 are 2.8 and 0.27s. The calculated times are the durations of the separation process for the two x values. The separation process, of course, takes place only when the copper is in the liquid phase, and thus the total time when the sample temperature is at or above 1083°C is important. Attempts to measure the temperature profile during the centrifuge experiments were not successful. Determinations of temperature profiles made at 1 g^ and in a non-flowing argon atmosphere showed that the duration when T > 1083°C is 12 and 7s for the systems with x = 6 and 7, respectively. These times are higher than the calculated separation times by factors of about 20 and 26, respectively. A complete phase separation would take place if the copper remained in the molten state for the times indicated by the 1 g^ temperature profiles. However, a simple heat transfer analysis [12] shows that in the presence of a flow of argon gas, convective heat loss could reduce the times by a factor of about 30 [14]. When taken into account, heat loss would reduce the length of the separation process to 0.4 and 0.21s for the cases of x = 6 and 7, respectively. These approximately calculated values are in general agreement with those obtained from Eq(7).

281 ACKNOWLEDGMENTS This work was supported by a grant from the National Science Foundation (Division of Materials Research).

REFERENCES 1. N. Sata, K. Nagata, N. Yanagisawa, O. Asano, and N. Sanada, Proceeding of the First USJapanese Workshop on Combustion Synthesis, Tokyo, Japan, Y,. Kaieda and J. B .Holt, (eds.), 1990, p. 139. 2. S. E. Niedzalek and G. C. Stangle, /. Mater. Res., 8 (1993) 2026. 3. Y. Miyamoto, H. Nakanishi, I. Tanaka, T,. Okamoto, and O. Yamada, Proceeding of the First US-Japanese Workshop on Combustion Synthesis, Tokyo, Japan, Y. Kaieda and J. B. Holt, (eds.), 1990, p. 173. 4. Y. Matsuzaki, H. Hino, J. Fujioka and N. Sata, Proceeding of the First US-Japanese Workshop on Combustion Synthesis, Tokyo, Japan, Y. Kaieda and J. B. Holt, (eds.), 1990, p.89. 5. Z. Fu, R. Yuan and Z. Yang, Proceedings of the First International Symposium, FGM, Sendai, Edited by M. Yamanouchi, M. Koizumi, T. Hirai and I. Shiota, 1990, p. 175. 6. J. B. Holt, M. Koizumi, T. Hirai, and Z. A. Munir, Editors, "Functionally Gradient Materials", Ceramic Transactions, vol. 34, American Ceramic Society, 1993. 7. O. Odawara, J. Amer. Ceram,. Soc, 73 (1990) 629. 8. O. Odawara, K. Nagata, K. S. Goto, Y. Ishii, H. Yamasaki, and M. Sato, J. Jpn. Inst. Met., 52(1988) 116. 9. A. G. Merzhanov and B. I. Yukhvid, Proceedings of the First US-Japanese Workshop on Combustion Synthesis, Tokyo, Japan, Y. Kaieda and J. B. Holt, (eds.), 1990, p i . 10. B. B Serkov, E. I. Masksimov, and A. G. Merzhanov, Combust. Explos. Shock Waves, 4 (1968)349. 11. S. A. Karataskov, V. I. Yukhvid, and A. G. Merzhanov, Fiz. Gor. Vzryra, 6 (1985) 41. 12. W. Lai, MS thesis. University of California, Davis, CA, 1996. 13. D. M. Himmelblau and K. B. Bischoff, "Process Analysis and Simulation-Deterministic System", Wiley, 1968, Chap. 4. 14. R. B. Bird, W. E. Stewart, and E. N. Lightfoot, Transport Phenomena, Wiley, N. Y., 1960.


I. Shiota and M.Y. Miyamoto (Editors) Functionally Graded Materials 1996 1997 Elsevier Science B.V.

283

SHS - A NEW TECHNOLOGICAL APPROACH FOR CREATION OF NOVEL MULTILAYERED DIAMOND-CONTAINING MATERIALS WITH GRADED STRUCTURE E.A.Levashov^, I.P.Borovinskaya^, A.V.Yatsenko^, M.Ohyanagi^, S.Hosomi^, M.Koizumi*' ^SHS-Center of Moscow Steel and Alloys Inst, and Inst, of Structural Macrokinetics RAS, Leninskypr., 4, Moscow, Russia ^Russian Ministry of Science and Technical Policy, Tverskaya str., 11, 103905, Moscow, Russia ^'Ryukoku University, Yokotani 1-5, Seta, Ohtsu City 520-21, Japan ^Tomei Diamond Co. Ltd., Joto 4-5-1 Oyama 323, Japan

L INTRODUCTION Functionally gradient method is that same process allowing the solution of three problems simultaneously while manufacturing diamond tools and development of new materials [1-4]. Additional demands are made to the production of multi-layered diamondcontaining and functionally gradient materials with a gradually from layer-to-layer changing diamond concentration. Those demands include: the increase of a material impact resistance and strength, reduction of the expensive diamond powder input, the increase of the expensive diamond powder input, the increase of the diamond boundary concentration in the working layer. The SHS-method allowed to produce 6-layer composites with (Ti,Mo)C ceramic binder and from layer-to-layer changing diamond concentration from 0 to 12 % with a step of 3 % and from 0 to 25 % with a step of 5 %. Regardless the composition of the exothermal mixture there is a boundary concentration of diamond powder in the mixture above which the SHS-process in the layer can't proceed. This can be explained by the fact that being an inert diluent diamond possesses a relatively high coefficient of thermal conductivity (X) as compared to the charge X. The growth of its concentration results in the increase of heat losses from the diamond heating up and from the heat transfer through the diamond grains to the environment and finally the combustion process is interrupted. However it's possible to produce a thin (1-2 mm) diamond layer with the diamond concentration up to 90 % when diamond is introduced into the charge layer of the metal powder with a melting temperature much low than the combustion temperature of the mixture in the diamondless layer. After the metal melting in the diamond layer in course of the combustion process the melt saturates the porous skeleton of the capillary forcer. The diamond layer reduces and the diamond concentration sharply grows because the metal binder leaves the layer. The authors of the present work studied FGM in the system (Co+diamond)/(TiC+Co) obtained under various ratio of the layer masses. The behaviour of natural diamond in the combustion wave of various SHS-systems (Ni-Al, Ti-Mo-C, Ti-Al-C, Ti-B, Ti-B-Si) was studied also for the production of bi-layered compositions with a FGM structure.

284

2. EXPERIMENTAL PROCEDURE The following powders were used in the experimental: carbonyl cobalt of a dispresity less than 40 |j,m; titanium powder produced by NPO "Tulachermet"(Russia) with the size of the dominant fraction in the range 63-7-160 (xm; brown amorphous boron 98,5 %; molybdenum - less than 50 ^m; carbonyl nickel of a dispresity less than 50 |im; aluminium - less than 10 fxm; carbon (lamp soot) with the particles measured about 0,2 |im; synthetic diamond AC 20 brand 160/125 jim (Russia); synthetic diamond IRV brand 150/125 |im produced by Tomei Diamond Co., Ltd (Japan); natural diamond A5 brand 250/200 [im of a medium strength as much as 38 N (Russia). Initial powders were dried out in specific drying chambers under the temperature 85-95° C. The reactant powders were weighed out in the proper stoichiometric proportions keeping a constant equimolar ratio of Ni-Al; 80 % (Ti-C) + 20 % (mass) Co; 84 % TiB + 16 % Ti; (Ti - aC) + 30 % (mass) Mo. Reactive mixtures of various compositions were prepared in ball mills of a volume of 6 litres. The necessary amount of diamond (from 3 to 25 % mass.) was introduced into the charge and was mixed up with it without grinding balls. The ready mixture was pressed into bi-layered and multi-layered pellets of a diameter of 48 mm and of a height 10-20 mm with a relative density of 50-60 %. Nine compositions with the diamond concentration of 3, 5, 7, 9, 10, 12, 15, 20, 25 mass % were mixed with the charge Ti-C-Mo to produce multi-layered semi-products. The ready mixtures were placed layer-by-layer into a pressform in the following order: diamondless layer weighing 25,5 g; 3 mass % diamond layer, weighing 10 g; 5 % layer 10 g; 7 % layer - 10 g; 9 % layer - 9,9 g; 12 % layer - 9,9 g. After densification pellets were obtained 48 mm in diameter with the thickness of the layers 5.0, 2.0, 2.0, 2.0, 2.0, 2.0 mm correspondently. Multilayered pellets with the diamond concentration from layer to layer as much as 0, 5, 10, 15, 20, 25 % mass were prepared similarly. The final pellet was placed into a reactional mold. An SHS reaction was initiated from the lateral face of the cylindrical pellet by a tungsten spiral. After accomplishment of the combustion reaction and propagation of the combustion synthesis wave, the hot SHSproducts were compacted in a hydraulic press at P > 400 MPa for no more than 10 s. The time of exposure to pressure was chosen dependent on the combustion temperature and reology of the products, e.g., on their plasticity and the amount of the liquid phase formed. Usually this time is 0.5 -^ 2 sec. SHS-products were cooled at the room temperature. To produce FGM with cobalt varied concentration a mixture was prepared of the following composition: 64 % Ti + 16 % C + 20 % Co. The mixture weighing 56 g was placed into a mold. Then cobalt powder was added. Three pellets were obtained with the diameter of 48 mm with various mass ratio of the mixture and cobalt layers: 13/56 (0.23); 20/56 (0.36); 28/56 (0.5) correspondently. The relative density of the mixture layer was 0.58; of cobalt layer - 0.65. The SHS-densification was carried out in the reactional mold with the values of the delay time ti = 2 -r 5 sec; pressure Pk = 30 MPa and time of exposure t2= 5 -r 10 sec. Concentration profile of cobalt distribution throughout the sample thickness were constructed by means of micro-X-ray-spectral analysis (MXSA). The regime with the optimal correlation of the parameters: mco/m(Ti-c); Pk; ti; t2 was determined. A complex of parameters was considered as the optimal one when the cobalt layer was melted at the expense of the heat of chemical reaction Ti + C + Co -> TiC + Co and

285 all the melt penetrates through the synthesis products TiC + Co. The next series of experiments when diamond was introduced into the cobalt layer with the concentration equal to 10 and 20 % mass was carried out under the optimal regimes. The methodics used in the experiments with the natural diamond A5 was similar to that in the paper [3], The ratio of the masses mi/m2 varied (mi - the mass of the exotthermal mixture with diamond concentration equal to 25 % vol.; m2 - diamondless layer), Pk = 30 MPa, t2 = 1 sec, ti = 2 -=- 5 sec. The phase analysis was carried out on an X-ray diffractometer DRON-3M (CuKa and FcKa radiation) with the rate of X-ray photographing 2 °/min. The morphology of the products synthesised and diamond grains was studied on electron scanning microscopes JSM-35 (JEOL), and JSXA-733 (JEOL). The strength of layer-by-layer recuperated diamond grains was determined by the standard method by crushing. The wear resistance test was performed in comparison with the volume loss of the diamond grinder against the volume loss the samples, using a resin bond diamond grinder. The ratio in the grinding test, volume loss of the sample test piece, was measured as one of the index for the wear resistance degree. The ratio in samples against that is cemented carbide (WC-Co, K-10) was evaluated as the wear resistance index. The test was performed under wet grinding condition (wheel speed: 1500 m/min, table speed 5.0 m/min, down feed: 0.02 mm/pass).

3. RESULTS AND DISCUSSION 3.1. Multilayered version Figure l,a and b present the distribution profiles of diamond concentration and strength through the thickness of multilayered samples. The figure shows that the diamond strength grows from 3 % layer to 12 % layer (fig.la) and is the maximum one in the layer with the diamond concentration equal to 15-20 % (fig.lb). The analysis of the synthesis products' mixture as well as the conclusions of the proper [3] allowed to explain the scientific results. Low values of the diamond strength in the synthesis products when its' concentration in the layer is small can be explained by a powerful heat stroke on every grain from the diamondless layer. The heat transfer from layer doesn't produce any noticeable effect on the velocity of the combustion wave propagation in the diamond layer. The heat stress on every diamond grain decreases with the growth of the diamond concentration and the diamond strength reduces inconsiderably. There is one more important feature which is the diamond protection against oxidation by the heat-resistant synthesis products (Ti,Mo)Ca, that limit the access of oxygen to its' surface. However when diamond concentration in the layer exceeds 20 % mass then the convention rate in the combustion process reduces (initial reagents are present in the layer) because of the high heat losses from the diamond heating up and heat transfer through the diamond grains into environment. The porosity of the layer with the diamond concentration more than 20 % is raised. The diamond isn't protected from the oxidation and the grain strength decreases. Such an approach - the production of multi-layered composites - allows to determine the limit of combustion with the growth of diamond concentration in the mixture and to construct multi-layered diamond containing materials for tools of various destination. Besides, the multilayered materials are characterised by the raised impact viscosity and strength as comparing to the homogeneous and bi-layered diamond-containing composites. The mentioned materials find their applications in industry for the production of cutting and grinding tools.

286

3.2. FGM - a version in the system Co+diamond (TiC+Co) Figure 2 presents the concentration profiles of cobalt distribution through the thickness of FGM samples, produced by the SHS-densification technology with the 12

P, N

mass % dia 10-

6H

2H

0+ 8

9

10

' thickness, mm

a) mass % dia

thickness, mm b)

Fig. 1. Distributions of diamond grains AC20 (160/125 |im) concentration and diamond grains strength (P) in the SHS products with (Ti,Mo)Ca ceramic binder on the thickness of FGM-compositions with 12 %(a) and 25 % (b) of diamond.

287 various ratio of the masses of the charge layers of pure cobalt and of the exothermal mixture Ti+C+Co. When the mass ratio is equal to 0.5 (curve 1), cobalt is not melted completely, there is only its' partial fusion on the division boundary between two layers. The decrease of the cobalt charge layer mass (curve 2) results in its' complete melting at the expense of the heat of the chemical reaction. Cobalt penetrates into layer of the synthesis products by two ways: capillar impregnation and migration. The capillar impregnation of the porous hot combustion products by cobalt starts in the process of the combustion wave propagation before the application of densification pressure and proceeds during the stage of the products' densification (after the pressure application) while the existence of capillar-porous space. The consequent migration of cobalt possibly occurs by the migration mechanism. In the third case (curve 3) cobalt penetrates through the reagents and the layer of pure cobalt hot formed in the final products. The mass proportion equal to 0.23 was taken as the optimal one. In such a regime the diamond-containing FGM-samples were produced with diamond concentration in the cobalt layer equal to 90 % volume. No softening of diamond brands AC 20, IRV, IMS, A5 can be noticed. Such a FGM approach is recomended for manufacturing grinding tools. 100

I

I { I I I I I I I I I I I I I I I » r r I I

0,0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 J^J^ Fig.2. Cobalt distribution on the thickness of diamond containing FGM with (TiC+Co) binder, produced at the different relationship of mass layers mco/mTi+c+coi 28/56(1); 20/56 (2); 13/56(3).

3.3. Application of natural diamond One of the peculiarities of the natural diamond is a considerably lower content of admixtures Ni, Mn, oth. as compared to the synthetic diamond. It is this feature that determines its' raised resistance to the action of high temperature in the combustion wave. Figure 3 shows the dependencies of the recuperated synthetic and natural diamond strength on the mass proportion of the charge layers mi/m2 with diamond concentration equal to 25 % vol. on the example of the bi-layered composite with the ceramic binder (Ti,Mo)Ca. The strength of diamond grains is also affected by mi/m2 is the composites with the binder of NiAl, TiB+Ti, TiC+TiAl, TiBz+Si.

288 The tests of the produced materials for the abrasive wear showed that the composition 20 % TiB2 + 25 % Si-natural Dia possesses the highest wear resistance. The wear resistance index is equal to 206.

50

P,N 40 30

initial n a t u r a l diamond

initial synthetic diamond

20: 10- J — I — 1 — 1 — I — I — I — 1 — I — I — I — I — I — r

0.0

0.8

0.4 ml/inZ

Fig 3

Dependencies of the diamond grain strength in the FGM SHS-composition on the mass ratio of the Ti+Mo+C-f25 vol % diamond (mj) and Ti+Mo+CC/Wj) layers

CONCLUSIONS The paper presents the new technological opportunities of SHS for the production of diamond containing ceramic multilayered and FGM composites.

ACKNOLEDGEMENT The present work was carried out within the frame of the joint investigation program between the Moscow Steel and Alloys Institute, Ryukoku University and "Tomei Diamond" Inc., and supported by the Russian Ministry of Science and Technical Policy.

REFERENCES 1. E.A.Levashov, I.P.Borovinskya, A.S.Rogachov, M.Koizumi, M.Ohyanagy and S.Hosomi. Intern. Journal of SHS, vol.2, 2 (1994) 189. 2. E.A.Levashov, A.V.Trotsuk, I.P.Borovinskaya, M.Ohyanagy, M.Koizumi and S.Hosomi. Abstr. of the 3rd Intern. Symp. on Structural and Functional Gradient Materials, Laus'atine, Switzerland, October 10-12 (1994) 57. 3. E.A.Levashov, B.V.Vijushkov, E.V.Shtanskaya, I.P.Borovinskaya, M.Ohyanagy, S.Hosomi and M.Koizumi. Intern. Journal of SHS, vol.3, 4 (1994), 287. 4. M.Ohyanagy, T.Yoshikawa, M.Koizumi, S.Hosomi, E.A.Levashov and I.P.Borovinskaya. Intern. Journal of SHS, vol. 4, 4 (1995) 387.


289

Graded Dispersion of Diamond in TiB2-based Cermet by SHS/Dynamic Pseudo Isostatic Compaction (DPIC) M.Ohyanagi^), T.Tsujikami^), M.Koizumil), S.Hosomi^), E-A-Levashov"^) and I.P.Borovinskaya^) l)Dept. of Materials Chemistry, Ryukoku University, Japan. 2)Dept. of Mechanical and System Engineering, Ryukoku University, Japan. 3)Tomei Diamond Co., Ltd., Japan. 4)Center of SHS, Moscow Steel & Alloys Institute, Russia. 5)Russian Academy of Sciences, ISMAN, Russia

Graded dispersion of diamond in TiB2/Si cermet (70vol% diamond layer / 40vol% diamond layer / matrix) was carried out by dynamic pseudo isostatic compaction (DPIC) just after self- propagating high temperature synthesis (SHS). The DPIC was performed using commercial casting sand as the pressure transmitting medium for the densification of cermet. The process enabled to simultaneously synthesize and densify the cermet matrix within a few minutes. Diamond (an average particle size, approximately 30)j,m) mixed with the reactant was fixed in the matrix produced after the SHS. The maximum combustion temperatures were controlled to be approximately 2000 K to prevent the diamond to graphite transformation. X- ray diffraction patterns and Raman spectra indicated that the diamond was embedded in the matrix mostly with no damage. The diamond particles were strongly fixed in the matrix even after lapping with a diamond abrasive. The primitive calculation for residual stress based on graded structure of diamond in the matrix was also performed. 1. INTRODUCTION Diamond being optical, high thermal conductive, semiconductive and very hard materials, itself is widely expected to become an industrial materials of twenty first century. Metal alloys and ceramic materials containing diamond with such a useful feature will be also developed as new materials. The bonding is one approach to fabricate diamond composite materials. Instantaneous bonding of diamond and metal has been studied by new cost- effective SHS method. Another approach is to disperse diamond particles into the material matrices. ' We, herein, perform the latter approach. In case of using SHS process, the reaction does not occur in diamond- highly concentrated reactant without external energy support because the diamond works as the reaction diluent. The diamond- locally dispersed matrix reactant containing the side layer without diamond as an energy supply source is required to synthesize the material. However, in two layer system consisting of diamond highly- dispersed and the matrix layers, there would be residual stress in the interface. So, graded dispersion of diamond m the matrix reactant is required to fabricate diamond-containing materials. On the other hand, diamond with a meta- stable structure usually transforms into graphite by exposing for long time above 1800K even under an inert gas atmosphere or in vacuum. Accordingly, the fabrication of diamond- dispersed ceramics with high melting temperature such as TiC, TiB2 is considered to be difficult because the sintering and the densification are often performed over 2000K, conventionally using hot press and hot isostatic press. However, the cost- effective short processing, one of the advantages in SHS, is very effective to prevent diamond to graphhe transformation in course of the SHS processing even if the the maximum combustion temperature raises up to over 2000K. The SHS products

290 in highly dense form can be also fabricated using a combination technique of this SHS and an external pressure such as hot pressing, hot isostatic pressing (HIP), pseudo- HIP, explosive consolidating, and high-velocity forging. ^^ Dynamic pseudo isostatic compaction (DPIC) was applied for the hot and partially molten samples after the SHS of the matrix materials. The DPIC technique using commercial casting sand as the pressure transmitting medium was developed for the densification of cermets by Russian scientist and was also applied for the fabrication of diamond- dispersed cermets by the DPIC apparatus newly developed. In the equipment, a slender sheet of carbon ribbon as the heat device only for ignition is embedded with a sample in commercial casting sand, which is contained in a pressure vessel. The compaction was performed by quickly pressing the sand containing the sample just after the SHS reaction. A pseudo- HIP using sand as the pressure medium is well- known to cause pseudo isostatic pressing. Similarly, herein, the pressing of the sand by high speed auto-pressing machine was applied to perform the DPIC. One of the objective of this research is to fabricate diamond- gradually dispersed cermets by the combination technique of SHS for short time processing and following dynamic compaction for densification. The other is to support for the fabrication by the calculation of residual stress based on graded structure of diamond in the matrix. 2. EXPERIMENT PROCEDUE 2.1 Evaluation of residual stresses using finite element method The finite element method (FEM) has been used to evaluate thermal residual stresses at interface of Diamond/TiB2/Si composites. Axisymetric cylindrical specimens were used, allowing two dimensional models to be employed. A model system composed three layers, Diamond, Diamond/(TiB2/Si) and TiB2/Si. The finite element analysis was performed using the original developed software SACOM for composite materials^^'-^^. In this simulation, thermal residual stresses, considering only elastic behavior were calculated, and the Diamond/riB2/Si composites was cooled from the assumed high temperature service (2000K) to room temperature (293K). Time and temperature dependent properties were neglected. Table 1 shows physical and mechanical properties of Diamond, TiB2 and Si relevant to the calculation. The specimen's dimensions were 5 nmi long and 16 mm in diameter. Constitutive properties for the composite material mterlayer were computed using a rule-of-mixtures.

Diamond TiB2 Si

Table 1 physical and mechanical properties of Diamond, TiB2 and Si Elastic modulus E Coef. of thermal Poisson s ratio v (GPa) expansion (K' ) 0.3 1050 1.00X10"^ 6.39X10"^ 0.2 365 4.2X10-^ 105 0.3

2.2 Materials and procedure The reagents used were elemental powders of Ti (an average particle size: approximately 22.5 |j,m, >99.5%, Osaka Titan Inc.), B (- 325 mesh, >99%, High Purity Chemicals Laboratory Inc), Si (-10 |am, >99.9%, High Purity Chemicals Laboratory Inc) and C (diamond: artificial, an average particle size: approximately 30.0 )j-m, >99.9%, Tomei Diamond Co. Ltd.). The reactant powders were weighed out m the proper stoichiometric proportions, keeping a constant equimolar ratio of Ti- 2B. The mixing ratio of Ti- 2B/Si was kept at 70/30 in vol%. Diamond powder was added so that it occupied 40 to 70 vol% of the reactants in the locally dispersed layer. The powder batches were mixed dry by auto agate mortar for half an hour. Cylindrical compacts (approxunately 16 mm in diameter and 25 mm long) were formed in a stainless steel die with double- acting rams so that diamond powder was dispersed in the 1/3, 1/5, 1/8 bottom layer of the compacts. In case of the graded dispersion, the composition of each layer was mixed individually, then layered in the steel die in the green pellet. The compacts were pressed uniaxially at the pressure of

291 approximately 5.0 MPa. DPIC was performed by a special SHS/DPIC equipment.^'^^ A stainless steel pressure resistant vessel of 30 mm inside diameter, 100 mm outside diameter and 60 mm deep was filled with commercial casting sand. An ignition heating device made of the slender carbon ribbon was placed on top surface of the sample. Each compact was ignited by a passage of current through the carbon heating ribbon under an atmosphere. In the delay time for 1 to 3 sec after the reaction, the sand containing the sample was pressed by a piston from top by using high speed auto- pressing machine (a piston moving velocity: 60 mm/s). The total applied pressure was approximately 255 MPa. The pressure was maintained for 10 sec after the pressing. A temperature profile was measured by a thermocouple (W- Re5%AV-Re 26%)- ^he vohage outputs from the thermocouple and the transducer indicator for pressure were monitored using a data acquisition recorder (OMUNIACE RT3200, highest sampling rate: 200kHz, NEC). This recorder made h possible to measure and store the data during the SHS/DPIC. The product surfaces lapped using a diamond abrasive were observed by SEM (JSM T- 330A, JEOL) and identified by X- ray diffraction equipment (RAD- C system, Rigaku Inc). 3. RESULTS AND DISCUSSION 3.1 Evaluation of residual stresses using finite element method The finite element method (here, triangle linear element method) has been used to evaluate thermal residual stresses at interface of Diamond/TiB2/Si composhes. Axisymmetric cylindrical specimens were used, allowing two dunensional models to be employed. A model system composed three layers. Diamond, Diamond/(TiB2/Si) and TiB2/Si. Figure 1 shows the scheme of the Diamond/riB2/Si composites. Figure 2 shows the axisymmetric mesh model for the Diamond/TiB2/Si composites. The finhe element mesh consisted of 12857 elements and 6610 nodes. At first, the effect of varying the diamond volume fraction of the top layer were studied. Different diamond volume fractions of top layer were changed from 50% to 100% for the evaluation. Constitutive properties for the composite material interlayer were computed using the rule- of- mixtures. The diamond volume fraction of middle layer is 40%, and the TiB2 volume fraction is 50% in TiB2/Si matrix in all layers. Figure 3 shows the behavior of maximum radial, axial and shear stresses of the top layer whh varying the diamond volume fraction. It is found that the stresses become larger with increasing diamond volume fraction. The contour plot in Figure 4 shows the distribution of the radial stress when the diamond volume fraction of top layer is 70%. Since the thermal expansion coefficient of diamond is smaller than that of Diamond/rriB2/Si, there are compressive in the Diamond and tensile in Diamond/riB2/Si. The contour plot in Figure 5 shows the distribution of the axial stress. The maximum stress concentration occurs at the free surface of the top layer. The contour plot m Figure 6 shows the distribution of the shear stress. The maximum stress concentration occurs at the interface between the top layer and the middle layer on the free surface side. The results suggest that the stresses become larger as a result of the property mismatch.

Figure 1. Scheme of Diamond/TiB 2/Si composite.

Figure 2. Finite element mesh for Diamond/ TiB2/Si composite.

292 3500 3000 ^2500 a.

D . • : Radial stress A , A : Axial stress : Shear stress

^2000 1^1500

11000 (D 500 •S

0

i-500 m E-IOOO

1-1500 ^2000 -2500 -3000 -3500

50 60 70 80 90 Diamond volume fraction of tfie top layer

Figure 3. The maximum axial, radial and shear stress of diamond layer with varying the diamond volume fraction.

Figure 4. The distribution of the radial stresses for the material when the diamond volumefractionof the top layer is 70%.

Figure 5. The distribution of the axial stresses for the material when the diamond volume fraction of the top layer is 70%.

Figure 6. The distribution of the shear stresses for the material when the diamond volume fraction of the layer is 70%.

Next, in two layers system consisting of diamond- dispersed layer and only matrix, effect of thickness of the diamond layer on the residual stresses was evaluated. In radial stress, the maximum compressive and tensile stresses in the diamond layer and in the interface of the layers became smaller in the thinner layer. In three layers system consisting of diamond- high, low dispersed layers (40 and 70 vol%) and matrix, influence of insertion of middle layer on the maximum stresses was compared with the two layers system. The residual stresses in each layer seems to become reduced by the insertion of middle layer. 3.2 Graded dispersion of diamond in TiB2/Si-diamond system by SHS/DPIC The SHS/DPIC of diamond- gradually dispersed TiB2/Si cermets was performed. In case of fixing diamond in cermet matrix, there are two methods. One is the physical fixing just like a diamond ring, and the other is the chemical fixing by covalent bond between diamond and metal in the cermet. In this work, we studied the latter system and considered that a metal carbide is very suitable as an interlayer to form the covalent bond.. There are many metals in periodic table to form the metal carbide. However, the

293 metals are desirable to have low melting temperature for suppression of the graphitization of diamond and acceleration of the densification in rather low temperature. Consequently Si were chosen as a metal portion for the cermets. The combustion maximum temperatures {Tmax) were controlled to be approximately 2000 K to prevent the diamond to graphite transformation. 255 MPa of the pressure was applied to the sand filled in the pressure vessel in the delay time for 1- 3 sec after the reactions. The pressure was maintained for 10 sec after the pressing. The sample could be taken out from the reaction vessel within a couple of minutes after ignition. The sand works as the pressure transmitting medium,

Figure 7. SEM photograph of lapped surface of diamond layer (TiB2/Si/diamond70vol%), BEL

(a) Cross section.

Figure 8. SEM photograph of lapped cross section in two layersTiB2/Si-Diamond(70vol%) and the matrix, (ratio of each thickness: 1 to 4)

(b) Interface between diamond layers, 70 and 40vol%.

(c) Interface between diamond layer, 40vol% and the matrix Figure 9. SEM photograph of lapped cross section in three layers of TiB2/Si- diamond (70vol%) and TiB2/Sidiamond (40vol%), and the matrix.

294 which suggests that Tmax to be measured is difficuh to reach the adiabatic temperature {Tad) of the reaction system. Figure 7 shows SEM photographs of the lapped surfaces of the specunens in TiB2/Si/diamond(70vol%), (a) SEI, (b) BEL The darkest part in the each SEM corresponds to diamond. The adhesion between diamond and the each matrix seems to be smooth and good. In EPMA analysis, the X- ray Kp spectrum of Si measured on the diamond surface in lapped cross section of TiB2/Si/diamond cermet agreed with the spectrum of SiC. The spectrum of Si in the cermet matrix also agreed with that in Si wafer. These suggest the formation of strong covalent bond layer, SiC between diamond and Si. The Raman spectrum based on diamond shows an intense and sharp peak in 1335 c m - 1 . The X- ray diffraction patterns also indicated in any cases that the diamond was embedded in the each matrix mostly with no damage. Figure 8 shows SEM photograph of lapped cross section in two layers composite of TiB2/Si- Diamond (70vol%) and the matrix (ratio of each thickness: 1 to 4). The lateral crack along the interface and almost perpendicular crack were observed in the specunen. Figure 9 shows also SEM photograph of lapped cross section in three layers of TiB2/Si- Diamond (70vol%), TiB2/Si- Diamond (40vol%), and the matrix (ratio of each thickness: 1 to 1 to 6). In each interface, the crack-based on residual stress was not observed. 4. CONCLUSION Graded materials of diamond- dispersed TiB2/Si composite were fabricated by SHS/DPIC method. Each diamond fraction in the graded composite was 0, 70vol% in two layers system, and 0, 40, 70vol% in three layers system. In the two layers composite, some cracks occur in the matrix and also in the interface of the layers. On the other hand, in the three layers, crack did not occur in the diamond layers and did not often occur in the interface between middle layer containing 40vol% of diamond and matrix. The tendency corresponds to the results of evaluation of residual stresses using finite element method. ACKNOWLEDGMENT This work was performed in High- Tech. Research Center (HRC) of Ryukoku University. One of the authors, M.Ohyanagi thanks for partial supports by Grand- in Aid for Scientific Research on Priority Area Physics and Chemistry of Functionally Graded Materials , The Ministry and Education, Science and Sports and Culture, and also by the Science Research Promotion Fund from Japan Private School Promotion Foundation.

REFERENCES 1. M. Ohyanagi, M. Koizumi et al., Am. Cer. Soc. Bull., 72, 86 (1993) 2. E.A. Levashov, LP. Borovinskaya, A.S. Rogachov, M. Koizumi, M. Ohyanagi, S. Hosomi, Intern. J. SHS, 2, 189 (1994) 3. E.A. Levashov, B.V. Vijushkov, E.V. Shtanskaya, LP. Borovinskaya, M. Ohyanagi, S. Hosomi, M. Koizumi, Intern. J. SNS, 3, 287 (1994) 4. M. Ohyanagi, M. Koizumi, S. Hosomi, E.A. Levashov, K.L. Padyukov, LP. Borovinskaya et al.. Trans. Mat. Res. Soc. Jpn., 14A, 685 (1994) 5. A G . Merzthanov, Ceram. International, 21, 371 (1995) 6. O.Yamada, Y.Miyamoto, and M.Koizumi, Am. Ceram. Soc. Bull, 64, 319 (1985) 7. Y. Miyamoto, Am. Ceram. Soc Bull, 69, 686 (1990) 8. P.H. Shingu, K.N. Ishihara, F. Ghonome, T. Hyakawa, M. Abe and K. Tagushi, Pro. of 1st US- JAPAN Work-shop on Combustion Synthesis (Tsukuba), 65 (1990) 9. L.J. Kecskes, T. Kottke, and P.H. Netherwood, J.Am. Chem.Soc ,73, 383 (1990) 10.J.C. LaSalvia, L.W. Meyer, and M.A Meyers, J.Am.Chem.Soc ,75, 592 (1992) 11. M. Zako, T. Ttujikami, Development of Personal Computer Program of Stress Analysis for Composite Materials, Journal of the society of material science, 38, No.438, (1990) 12. M. Zako, T. Ttujikami, M. Hibino, M. Ichikawa, M. Uemura, Development of Structure Design System for Composites, Reinforced plastics, 38, No.2, (1992) 13. M.Ohyanagi, M.Koizumi, S.Hosomi, E.ALevashov and I.P.Borovinskaya, Intern. J. SHS, 4, 387 (1995)


295

Annealing of cermic/metal graded materials fabricated by SHS/QP method A. N. Pityulin% Z. Y. Fu^ M. J. J i n \ R. Z. Yuan^ and A. G. Merzhanov' ^ Institute of Structural Macrokinetics, Russian Chernogolovka, 142432 Moscow Region, Russia

Academy

of

Sciences,

^ State Key Lab of Advanced Technology for Materials Synthesis and Processing, Wuhan University of Technology, Wuhan 430070, China

SHS/QP is an efficient method for preparing FGM. But in synthesis process, high temperature and high velocity may result in some results not expected by us, which as a consequence will affect the FGM's performance. Al so, repeatability of the concentration distribution is not good. In this work, FGMs were prepared by SHS/QP and heat treating, which had very thin gradient layer and wide range concentration distribution. The manufacturing was carried out as following: the pellet including mixture-metal layers was processed by SHS/QP, and then the product was treated longer than two hours at 700 "C -1200 °C . Quantitative and qualitative analyses were carried out to different points in the gradient layer. The result indicates that the thickness of the gradient layer is decided by the heat treatment to a great extent. The chemical and phase composition, and the connection between grains show no great change.

1. INTRODUCTION Modern industry needs hard alloys with both good wear-resistance and highstrength. Ceramic/metal layered materials, with the structures as shown in Figure 1, are very promising. However, because of the difference of the heat expansion coefficients between ceramic and metal, it is very difficult to sinter the two parts together by traditional methods. SHS compaction (hydraulic pressing) or SHS/QP method with its features shows potential in the fabrication of such layered materials [1,2]. In their experiments, Pityulin and his coworkers obtained two kinds of layered structure: symmetrical profiles (SYGMA-1) and nonsymmetrical profiles (SYGMA-2) [1]. SYGMA-2 materials, one layer is pure metal and the other side is ceramic (Figure 1), can have very good wear-resistance on the ceramic side and good overall ductility owing to the metal part. In this paper, SYGMA-2 with Ti as the metal side and TiB-45wt%Ti

296 as the ceramic side made by SHS/QP was heated at different temperatures. Variations of structures and properties of the sample with annealing temperatures were studied.

2. EXPERIMENTAL PROCEDURES Ti (grain size < 60|im, purity > 99%) and amorphous B (grain size < lOfam, purity > 94%) powders were used in the experiment. Thoroughly mixed powders with determined composition were pressed into plate (70mmx70mmxl0mm) with 50% relative density, which was then put into a special die as shown in Figure 2. Between the raw plates and die, there are Si02 powders with average particle size 0.5mm, which serve both to protect the die and to transform the mechanical force from the hydraulic press to the sample in a pseudo-isostatic way. The SHS reaction was ignited by a tungsten coil with a short electric pulse. Thermocouples were used to determine the reaction temperatures and propagating time. Immediately after reaction, the hot product was pressed by a lOOOkg/cm^ force. By this way dense layered sample with determined structure, one side Ti and the other side TiB-45wt%Ti, as shown in Figure 1 was produced, which was then cut and polished into small strips (5x5x30mm). The small strips were heated in a vacuum stove (vacuum degree 10'^ Torr). Maximum heating temperature and time were 1500 °C and 5 hours respectively. Hardness and ultimate bending strength were tested by standard procedures. Structure and element distribution were analyzed by EPMA and SEM.

3. RESULT AND DISCUSSION Ti and the hard alloy linked well with each other in the two-layer sample made by SHS/QP as shown in Figure 3. Porosity of Ti side is 0.5%.There is no pore in the intermediate layer. XRD proves that the two layers are composed of TiB-Ti and Ti respectively. Gradient intermediate layer between Ti and the hard alloy is lOOfam in thickness as shown in Figure 4, which is independent of thickness ratio of the two layers. The sample was etched with 36% HCl. Etched structures of the sample were shown in Figure 5. Structure of the hard alloy is quite uniform, in which TiB grains are in a long-flake shape with maximum length up to 30)Lim. Structure in the gradient layer is not uniform. Thickness of the gradient layer increases with annealing of the sample as shown in Figure 6. There are three regions in the chart. At low-temperature (< 900 °C ), thickness of the gradient layer (about lOOfim) does not change with annealing temperature. Thickness of the gradient layer will increase to 350~400|im, when the annealing temperature rised to 1200 "C , but the sample's shape does not change. When the annealing temperatures are higher than 1300 °C , the thickness of the gradient layer will increase obviously. At an annealing temperature 1 500 °C , Ti layer will

297 totally melted and migrated into the hard alloy, which forms a 4mm gradient layer and makes the sample shrink to a certaim extent. Distribution of element concentration of the sample treated at 1500 °C is shown in Figure 7. The gradinet distribution is similar to ordinary FGMs made by other methods [3,4]. Hardness variations across the sample are shown in Figure 8. The sample presents a sudden change in hardness distribution, when it is heat treated at 700 °C . Hardness changes gradiently along the sample, when the sample is heat treated at 1500 °C . Strength of the sample increases with treatment temperature. The ultimate bending strength can be rised by 25% as shown in Figure 9.

4. CONCLUSIONS Annealing of the SYGMA-2 type sample can change structure and thickness of the gradient intermediate layer. 1500 °C annealing results in the migration of melted Ti totally into the hard alloy, which forms a 4mm gradient layer. Sudden and gradient variations in hardness distributions across the sample were observed after 700 °C and 1500 °C teratment, respectively. Ultimate bending strength of the sample increases with annealing temperature.

REFERENCES 1. A. N. Pityulin, Y. V. Bogatov and A. S. Rogachev, Inter. J. SHS, 1(1992)111 2. Z. Y. Fu, W. M. Wang, H. Wang, R. Z. Yuan and Z. A. Munir, Inter. J. SHS, 2(1993)307 3. M. Koizumi, Ceramic Transactions, 34(1993)3 4. Z. Y. Fu, R. Z. Yuan and Z. L. Yang, Proceed. 1st Inter. Sym. on FGM, Sendai, (1990)175

298

Reactants

Gradient layer

'Mh Ceramic

Thermocouple

Metal SiOa powers

Figure 1. Schematic representation of ceramic/metal layered materials

Figure 2. Schematic representation of SHS/QP die

3 alloy

0

Figure 3. Structure of two-layered sample by SHS/QP

0. 2 0. 4 0. 6 0. 8 1. 0 X>mm

Figure 4. Element concentration profiles in two-layered sample

299

Figure 5. SEM micrographs of sample. a. Gradient region b. Region 1mm from the gradient layer c. Region 3mm from the gradient layer

lOOi

300 600 900 1200 1500 T/C Figure 6. Dependence of thickness of gradient layer on annealing temperature

Figure 7. Element concentration profiles in sample treated at 1500 °C

300 ^

10 o

»

1

y\

8

r-H

X CO

> X

• —700°C 4

• ^ ^ l

t

. 1

o—1500°c1

. 2 X)inm

3

4

Figure 8. Hardness variations across samples treated at different temperatures

0

300

600

900

1200 1500

Figure 9. Effect of treating temperature on ultimate bending strength


301

Thermodynamic calculation and processing of TiB2-Cu FGM C.C.Ge, Z. X. Wang and W. B. Cao Laboratory of Special Ceramics & Powder Metallurgy, University of Science and Technology Beijing, Beijing 100083, P. R. CHINA Thermodynamic calculation and SHS/HIP were successfully used for making TiB2-Cu FGM without macro-defects from element and diluent powders. In this case, SHS/HIP was used not only to create "a chemical oven" for densification of FGM, but also to combustion synthesize the foundmental constitute of FGM~TiB2. 1. INTRODUCTION Since 1984 Japanese scientists proposed the idea of "Functionally Graded Materials" (FGM), research on FGM is developing rapidly. For commercial applications of FGM, problems on design and processing have to be solved. In designing of FGM, not only the thermal stress in FGM under service conditions should be minimized, but also the thermal stress during processing should be reduced in order that macro-defects of FGM can be prevented. SHS/HIP(self-propagating high-temperature synthesis/hot isostatic processing) is an advanced technology proposed by Y. Miyamoto and M. Koizumi[l] for making FGM, which has following advantages: 1. high reaction rate and short duration at high temperatures of SHS/HIP process are very beneficial for keeping the designed constitute gradient in FGM; 2. Simultaneous synthesis and densification are realized; 3. Product with large dimensions or complicated shapes can be made; A series of FGM including TiB2-Ni, TiC-Ni, MoSi2-SiC/TiAl, Cr3C2-TiC etc. has been successfully made with SHS/HIP[2]. In most of these works ,the exothermic reaction of SHS was used to form a chemical oven for densification of FGM, while the fundamental constitutes (such as Cr3C2 in Cr3C2-Ni FGM, MoSi2, SiC in MoSi2-SiC/TiAl FGM etc.) in FGM were used as commercial raw materials which had been beforehand synthesized. The problems of forming and preventing macrodefects in FGM samples have not been reported. This work was undertaken for making TiB2-Cu FGM without macro-defects from element and diluent powders through thermodynamic calculation and SHS/HIP. SHS/HIP was used in this case not only to create "a chemical oven" for densification of FGM, but also to combustion-synthesize the fundamental constitute of FGM-TiB2. 2. EXPERIMENTAL PROCEDURES Processing of TiB2-Cu FGM was based on our work of non-graded homogeneous TiB2-Cu composites by SHS/HIP technology for investigating the effects of processing parameters on the microstructures, constitutes, properties and sinterability of as-synthesized products[3].

302

Commercial powders of Ti (~ 42 jn m), amorphous B( ~ 5 jn m) and Cu( ~ 7 ja m),and selfmade SHS TiBj powder as diluent are used as raw materials. As the first step, graded green compacts with a dimension of (^ 17mm x lOmm and a relative density of - 60% of the theoretical value were made by stacking of mixed powders in the die in proper order of Cu content. Green compacts were combustion-synthesized in Ar under 5MPa in a combustion chamber of a self-designed SHS/HIP assembly (SHA). Preliminary experiment in making 6-layered FGM in SHS assembly led to frustum samples, expanding in TiBj-rich side and shrinking in Cu-rich side, while in making 8- and 11-layered FGM serious cracks, warping and delamination occurred in samples. These defects of samples were attributed to high thermal stress due to great difference in combustion temperatures between layers. Thermodynamic calculation was carried out before the following experiments with the aim to adjust the combustion temperature of different layers for reducing the thermal stress during processing and preventing the macro-defects of products. On the basis of our previous work on analysis model and mathematical calculation for design of thermal-relaxed TiB2-Cu FGM[4], graded green compacts with dimensions of cj) 17 X 10mm and cj) 26 x 10mm and with - 60% of the theoretical density were made by stacking of mixed powders in the die in proper order of Cu content, according to the optimized parameters: Cu content changes from 0-100%, thickness of graded layers t = 8mm, thickness of surface layers = 1mm (TiB2 layer and Cu layer respectively), thickness of each graded layer was designed with the volume distribution function / = (

-y,

while

constitute distribution factor p=0.8. Both green compacts with number of layers n=ll and n=15 were pressed and encapsulated with glass and embedded into a Ti ignition agent in a graphite crucible under nitrogen pressure. In order to make the process less-expensive, the gas pressures of 5MPa and 1 IMPa were used for different samples. The synthesized TiB2-Cu FGM samples were longitudinally cut, polished and observed with SEM. The distributions of element Ti and Cu were line-scanned and area-scanned with EDX. The densities of layers were measured with image-analysis method. 3. RESULTS AND DISCUSSION 3.1. Thermodynamic calculation While the SHS process has high reaction rate and short duration, it can be regarded as an adiabatic process in our calculation:

40 60 80 Cu content, wt%

100

Fig. 1 Variation of adiabatic temperatures with Cu content for TiB2-Cu system

303

Fig. 1 is the calculation result for variation of adiabatic temperatures with Cu content in Ti2B-Cu system : Ti + 2B + bCu = TiB2 + bCu

(1)

where b is the mole content of Cu. During SHS, this exothermic reaction consists of following processes: (1) melting of Cu (endothermic) (2) melting of Ti(endothermic) (3) Phase transformation of Ti (endothermic): a -Ti(hcp) ^^^^\ p -Ti(bcc); (4) Formation of TiB2 (strong exothermic) Fig.2 is the variation of enthalpy with temperature for Ti-2B-Cu system from our calculation according to:

-A//;,,^^=£;c,(5yr+*Atf„,, (2)

where: -AH^ j ^ .-the formation enthalpy of TiB2 at 298K; C {s) -heat capacity under constant pressure for TiB2(solid state); A//^ ^„ -melting enthalpy of Cu.

Ti (P) + 2B( S)

r^-'Tif^

+ 2B (S)

o

e

Ti (a) + 2B (S)

>> u. (0

ri

TiB2+Cu T

\ Cu(S)

^^-^ Cu(l)

A Hf"

W

At,Ti

im.Cu

Tm,Ti

Temperature, K

Fig.2 Variation of enthalpy with temperature for Ti-2B-Cu system For adjusting the combustion temperature of different layers in FGM, we use the reaction product phase-TiB2 as diluent, then: Ti + 2B + aTiB2 + bCu=(l+a)TiB2 + bCu and

(3)

304

where a is mole content of TiB2. From equation (4) it is shown that through adjusting the metal and diluent content of the reaction mixture, the control of combustion temperature can be realized.

I Metal Cu Content , wt%

Fig.3. Composition design of TiB2-Cu FGM compositions at different Tc

H

20

40

Time, sec

Fig.4. Tc profiles of some kinds of compositions according to Tc=2000k Fig.3 is our calculation results for composition design of TiB2 -Cu FGM at different combustion temperatures. Fig.4 is the experimental results for combustion temperature profiles of some kinds of compositions according to Tc = 2000K and corresponding design of compositions of reaction mixtures. Fig. 5 is the comparison of measured temperatures(Tm) and designed temperature (Td). It is proved that through thermodynamic calculation and adjust of constitutes ratio of graded layers, control of combustion temperature and composition design can be achieved. 3.2. Processing of TiBj-Cu FGM in self-designed combustion chamber 11-layered and 15-layered TiBj-Cu FGM samples with dimensions (|) 17 x 10mm free of macro-defects were successfully processed with SHS/HIP technology under gas pressure of

305 5MPa in self-designed combustion chamber. It is seen that through reasonable designing the constitutes ratio of each layer, SHS of different layers could be controlled in the same combustion temperature region and similar shrinking behavior between layers , this led to SHS/HIP TiB2-Cu FGM which is free of macro-defects.

p

94% is achieved at the rich-Cu end of samples processed under llMPa in HIP-apparatus.R120. The porosities of these samples are 50% lower than the porosities of rich-Cu end of samples processed under 5MPa. For the low-

306 Image analysis for density measurement was made on the longitudinal cross-section of 11layered TiB2-Cu FGM processed under 5MPa (in self-designed combustion chamber) and processed under 1 IMPa in HIP apparatus R120. The results are shown in table 1. It is noticed that relative density of >94% is achieved at the rich-Cu end of samples processed under llMPa in HIP-apparatus R120. The porosities of these samples are 50% lower than the porosities of rich-Cu end of samples processed under 5MPa. For the lowtemperature end of thermal-relaxed FGM, higher density favors heat conductivity and strength of the material. Though the relative density at the rich-TiB2 end of samples processed under 1 IMPa increased inconsiderably comparing with samples processed under 5MPa, yet for thermal-relaxed FGM some porosity is beneficial for heat insulation ability of the ceramic end. The processed TiB2-Cu FGM may fulfill the requirement of relaxation of thermal stress for certain applications. Table 1 Measured porosity is various regions along the longitudinal cross-section

Cu Content low

1

high

Porosities in Synthesized Porosities in Synthesized! Products Made in HIP(%) Products Made in Selfmade Apparatus(%) | 51.84 50.89 35.82 41.25 13.85 25.88 5.95 13 17

4.CONCLUSIONS Through thermodynamic calculation for adjusting the combustion temperatures of different layer of TiB2-Cu FGM, SHS/HIP was successfully used both for combustion-synthesis of the fundamental FGM constitute and for densification of FGM in one step, and TiB2-Cu FGM samples without macro-defects has been obtained. 5. ACKNOWLEDGMENT This work is supported by China National Natural Science Foundation, The Doctorial Program Fundation of State Education Commission, and National Committee of High Technology New Materials. REFERENCES 1. Y. Miyamoto and M. Koizumi, Proc. Int. Symp. on Sintering '87, Tokyo, Elsevier (1988), 511. 2. Y. Miyamoto, Int. J. SHS, V.l, No. 3, 1992 3. Z. X. Wang, Dissertation of Univ. Sci. Tech. Beijing, 1995. 4. Z. X. Wang, C. C. Ge, W.B. Cao and X. D. Zhang, Proc. 4th. Int. Symp. on FGM, Tsukuaba, Elsevier (to be published).


307

Fabrication of Al-Cu system with functionally graded densitj^ profiles* R. Tu^ Q. Shen^ J.-S. Hua^ L.-M. Zhang^ R.-Z. Yuan^ ^ State Key Lab. of Materials S>^thesis and Processing, Wuhan University of Technology, Wuhan, P. R. China, 430070 ^ Laboratory of Shock Wave and Detonation Physics Research, Southwest Institute of Fluid Physics, Chengdu, P.R.China, 610003

To lower the temperature-enhancement inside the target material and achieve higher pressure and velocity is important in dynamic high-pressure technology. It can be realized through quasi-isentropic loading by density functionally graded materials (DFGM). A kind of .^-Cu DFGM was hot-pressed by powder stacking with adjusting soaked temperature, load interval and pressure et al. The FGM has quasi-continuous density variation along the thickness direction.

1. INTRODUCTION Recently, researches in the world have extended progresses in thermal stress relaxation FGMs[l] and energy conversion materials [2]. But they all can not be put into practice at present time. In the same teims, a new kind of FGM with density gradient(DFGM), which can be used in dynamic high-pressure technology has been prepared in America [3]. The DFGM was applied to the shock-wave loading technology in order to carry out quasiisentropic loading on target materials [4], from which can offer extreme experimental conditions of pressure or velocity^ for thermodynamics and dynamic physics study. In this paper, the Al-Cu system which has large density difference was chosen to prepare DFGM on a trial basis.

2. EXPERIMENTS 2.1. Materials designation The volume fraction C of gradient layers of Al-Cu FGMs was defined as the form [5]: C=(x/d)P

(1)

Where, d is the total thickness of FGM, x the location coordinate of any gradient layer, and P the distribution exponent. In order to gain the linear density distribution, P is fixed at 1.0. This work is supported by National Natural Science Foundation of China.

308 According to the phase diagram of Al-Cu system, it is noticed that many intermetallics will be formed in the range of 15-50 weight^'b.Al. The high brittleness of the intermetallics [6] and their phase transformation wiU degrade the materials. Therefore, the layer in the above range, i. e. the layer of 50 vol% .\1 + 50 \T)l?b Cu was eliminated from the design for avoiding intermetallics as much as possible. In addition, the eutectic point of Al-Cu is much low (821K) and a great deal of liquid phase would occurr at the temperature, so the sintering temperature was fixed at 800K or so. The temperature 800K is too low^ for the densification of pure copper powder. In order to protect liquid from flowing out and avoid the difficulty to sinter pure Cu layer densely, a solid Cu disk and Al disk were employed to replace the pure copper and pure aluminium powder layer respectively. The designed compositional distribution of materials is given in Table 1. Table 1 Composition of the .Al-Cu system FGM layers 1 Al voI% 0 .\latom% 0

2 10 7.31

3 4 5 6 7 8 9 10 20 30 40 (50) 60 70 80 90 100 15.06 23.31 32.10 41.49 51.55 62.66 73.94 86.46 100

2.2. Materials preparation Commercialh^ available average particle size 75 j.im and high-purit>^ 99.5% aluminium and copper powders were used as raw materials. The ground .Al-Cu mixtures were loaded in the grapliite mould as designed and hot pressed. The thickness of each layer is 0.5mm except that the Cu and M layers are 1mm. Previous expeiiments showed that melted metal flowed out when hot-pressed at 900K for 1.5 hours directfy. UTiile at 800K, it can not be sintered densely. To avoid the above phenomena, the experimental procedures as Fig.l was proceeded. It can be seen that the specimen was first heated to 900K and soaked for hatf an

300

1.0

1.5

2.0

t(hours)

Figure 1 Diagram of experimental procedure. hour with no applied pressure. Then the temperature was decreased to 800K and soaked for one hour with the pressure ot 15 Nfiâ. The as-hot-pressed FGM was cut along the diameter and polished. A scanning electron microscopy (S£M) was used for microstructure of the materials, and a electron probe microanahsis (EPMA) for its elemental macro linear

309 distiibution. Under the same sintering conditions, each layer of the FGM was prepared. Their densities were measured by the water-immersion technique.

3. RESULTS AND DISCUSSION Fig. 2 is the cross-section of Al-Cu densit>^ functionally graded material. It shows that there were no micro cracks, and the transition between layers was in a good state. Fig. 3 gives the result of elemental macro linear analysis. From Fig. 3, it can be seen that the Cu element content increases along FGM's thickness, while that of Al decreases. The relative density of gradient layers are low but the solid aluminium layer and copper layer are high, which due to the oxidization of aluminium powder on the surface [7]. It can reject the reaction of aluminium and copper. The detailed anah'sis of oxide content in aluminium particles will be

Figure 2 Cross-section of .Al-Cu DFGM. 8000

0

1

2

3 A D(mm)

5

6

7

8

Figure 3 Compositional distribution of Al-Cu DFGM along its thickness. performed in future. For investigating the densit\' variation of FGM, each layer was hot pressed under the same conditions. Theii* densities were measured and was shown in Fig. 4. It can be found that the density^ of FGM along the thickness direction increases with copper content. But relative densitv^ of the layer containing 10 vol^^b Al decreases obviously. Except for the oxidation of aluminium powder, it could be thought that aluminium and copper did

310 not fbrm the eutectic compound in that composition range. At this time, the densification temperature between aluminium and copper is so large that the relative densit\' decreases. When content of aluminium increases to 60 vol% (51.55 atom%), the relative density increased. Especiall>^ when the content of aluminium is over 70 atom%, low-melting-point compound is formed between aluminium and copper, and the relative densities of the layers increase. The FGM has quasi-continuous density- variation.

^0 60 Cu Content (vol*/.)

Figure 4 Designed and practised density of graded layers of .\1-Cu DFGM. One of the future works is to solve the problem of aluminium oxidation so that the graded layers can be sintered denseK. Adding some active metal, e. g. Mg and Sn, to the Al-Cu mixture may be a feasible ways.

4. CONCLUSIONS (1) A kind of Al-Cu density FGM coinciding with designed composition is prepared. (2) The low relative density of graded layers is due to the oxidation of aluminium powder on the surface.

REFERENCES

3. 4.

L. M. Zhang, M. Oomori, R. Z. Yuan and T. Hirai, J. Mater. Sci. Lett., 14(1995) 1620 M. Niino, M. Koizumi, in proceedings of 3rd International Symposium on Structural and Functional Gradient Materials, Lausanne, Switzerland, 1994, 601 L. M. Barker and D. D. Scott, SAND 84-0432 L. C. Chhabildas, in BuUetin of the 1995 APS Topic Conference on "Shock Compress of Condensed Matter", Scatter, Washington, 1995

311 5. 6. 7.

A. Kawasaki and R. Watanabe, J. Jpn. Soc. Powder Metall., 37(1990) 253 L. F. Mondolfo, Aluminium Alloys: Structure and Properties, Butterworths, Boston, 1976 C. N. Cochran and W. C. Sleppy, J. Electrochem. Soc, 108(1961) 984



313

AI2O3 to Ni-superalloy diffusion bonded FG-joints for high temperature applications* Liisa Heikinheimo^ Mika Siren^, Michael M. Gasikt* ^Technical Research Centre of Finland - VTT Manufacturing Technology, FIN-02150 Espoo, Finland ^'Helsinki University of Technology, FIN-02150 Espoo, Finland

The aim of this study is to manufacture alumina-superalloy joints for high temperature applications using direct diffusion bonding process with metallic interlayers and with functionally graded plasma spray coatings. In the study for the first graded joints with interlayers the bending strength values were found to be three to seven times higher than for the direcdy bonded materials. The funcdonally graded joints (FGJs), the transient produced coating, are characterised by a non-linear 3D-distribution of phases and corresponding properties, the results show a great potential in respect with the high temperature properties.

1. INTRODUCTION Manufacturing of ceramic-metal joints (AI2O3 to Ni-superalloy) for high temperature applications in power generation can be performed using solid state bonding technologies, either high temperature brazing or direct diffusion bonding (DB) with interlayers. In this study DB-technique that is suitable for joining of highly mismatching materials is developed. First joints (with Ti and Cr active layers combined with Ta and Nb interlayers) were prepared at 1050-1150°C for 1 - 3 hours under axial pressure of 5 - 20 MPa. The graded layers in these preliminary experiments were formed during the bonding cycle. Second, specimens with graded layers were manufactured by plasma spray (PS) coating procedure, where alumina content was decreased in the coating layers and the metal phase content was simultaneously increased. It was shown that use of functionally graded materials (FGM), characterised by a non-linear 3D-distribution of phases and corresponding properties, allows to decrease the residual stresses and to improve the properties of the joint [1-3,5]. The joint integrity was examined using mechanical testing with four-point bending test. The joint microstructures were studied using LOM and SEM+EDS methods. The results of strength measurements show that specimens with graded layer exhibit higher fracture strength three to seven times more than those without the layers.

* This study has been supported by the European Commission through the project BE-7249 under the contract BRE2-CT94-0928.

314 2. ALUMINA-NICKEL ALLOY JOINTS FABRICATION The alumina-superalloy joints are intended to withstand high service temperatures (700 1000°C) and thermal cycles typical in power generation processes. The fabrication of a joint should provide a relatively good strength but more important that it will remain relatively stable in the service conditions. Therefore, experimental studies for the joint design optimisation should be carried out and the data for novel procedures and for modelling the FGstructure and FE-analysis should be created. 2.1. Fabrication of joints by diffusion bonding The DB-procedure was optimised in respect with the kinetic requirements and the hightemperature mechanical properties of the Ni-superalloy. From the kinetic point of view, the bonding temperature should be over 1000°C when alumina and transition metals are directly bonded [6]. The bonding procedure was always carried out in high vacuum, better than 2-10'^ mbar (0.2 mPa). The typical thermal and axial compression cycles are presented in Fig.la. It was experimentally found that the ambient bonding temperature is llOO^C or less due to the fast creep of the superalloy beyond this. The compression for the tests was selected as 10 MPa in ceramic-metal joints and 20 MPa in ceramic-ceramic joints [6]. The initial approach in this study was to demonstrate the use of metallic interlayers and/or coatings in the bonding procedure. For the first layer (intended for the metallurgical bonding of the ceramic), Ti and Cr were found to be the most promising metals. Here both coatings (by PVD, 1-10 |Lim thick) and layers of foils (25 |Lim thick) were used. The function of the second Ta layer of 25 |Lim thickness was to suspend the diffusion of Ti between the foils. In all of the experiments the third layer of niobium of 2 mm thickness was applied for thermal residual stress relief. The multilayered joint microstructure is shown in Fig. lb [7]. The bonding process and joint structure optimisation are resulting in a four-point bending strength (sample 12x12x60 mm^) of 7.5 MPa/4.3 MPa (tested at 25''C/400°C) for Al203/Nb/Al203-joints, 22.5 MPa/- for AlzOa/Cr/Ta/Nb/Ta/Cr/AlzOa-joints and 50 MPa/27.3 MPa for Al203/Ti/Ta/Nb/TayTi/Al203-joints. In AI2O3 to Ni-superalloy (PK33) -joints the strength values decrease about to one fourth of the above listed ones: Al203/Cr/Ta/Nb/PK33 5.6 MPa and Al203/Ti/Ta/Nb/PK33 12.6 MPa at 25 ""€. Thus the combination of Ti-, Ta- and Nb-layers is considered to be most promising, reported in details in [8]. However, the formation of the thermal residual stresses in ceramic-metal joints and the diffusion at the aimed service temperature leads to the deterioration of this potential joint configuration at the ceramic interface [9]. The use of functionally graded layers instead of the pure metallic ones seems to be the optimal solution. However, it includes two manufacturing processes, namely thermal spraying and diffusion bonding, which must be optimised for the materials and conditions considered. The first benefit claimed is in a gradient in mechanical properties providing the minimum of thermal stresses. The second one provides more stable composition at high temperatures, in comparison to the metal layers, such as Ti or Cr. 2.2. Fabrication and studying of FG-joints In this study several graded joints were fabricated. All of them were produced by low pressure plasma spray method at 800-900°C over alumina substrate (A-479, Kyocera Co.+ powder Metco 105SFP). In the experiments, variations of concentration of metal component, namely Ni-20%A1 (Metco 404NS) and NiCoCrAlY (Amdry 995) alloys were applied [6].The resulting profiles of graded coatings are shown on Fig.2. The microstructure of these coatings

315 was studied by optical microscopy and SEM. The majority of the specimens were of a good quality, although some surface cracks were observed in specimens in series 58, 59 and 63. The most possible origin of these cracks was due to higher residual thermal stresses after the spraying.

-2400

1200

/

1000

1

O 800

»/*\^

1 /

0)

w 600 0) Q.

E £ 400

200

\ \ \

A*

-2000

\

-1200 "g i4; o

\

/

-800

/

l^

-1600

\

-400

I

\ \

rw vA, •N

_

Time [15 min/div]

a)

b)

Figure 1. The typical thermal cycle for diffusion bonding of AI2O3 ceramic to Ni-superalloy (a) and the joint microstructure with the optimised joint configuration using interlayers (b).

100

'^n '=:o

oojOy

80 h

61,62 63 65

o

>

60 h

iS 40 20

V ^ y < ^ ^ ^ -

1

2

1

1

3

4

5

Relative coating thickness Figure 2. Profiles of metal-alumina FGM coatings produced for joining experiments. Numbers indicate different experimental series: Ni-20%A1 (58,61), and NiCoCrAlY (59, 62-65).

316 The crack-free coated alumina specimens were subjected to a diffusion bonding (DB) procedure, described above. The parameters of the process were same as for non-graded specimens. After the bonding to IN-738 superalloy the joints were examined by their appearance and microstructure. For some specimens it was found that good, crack-free microstructure does not guaranteed high mechanical properties, in particular at elevated temperatures under external mechanical load. A complete series of mechanical testing of these joints shall be made after the whole array of the data will be obtained. In order to disclose the general peculiarities of FG-joints, the calculations of their basic properties were made by a micromechanical model [2,4].

3. CALCULATION OF PROPERTIES OF FG-JOINTS In these calculations of properties of FG-joints, the micromechanical model was applied as developed by Gasik e.a. [2-4]. The calculated equations of temperature dependence of source materials data were integrated in "FGM for Windows"-program files to use them for analytical properties evaluation instead of expensive FEM methods. The following properties were calculated: elastic and shear moduli, CTE, thermal conductivity, specific heat, density, thermal diffusivity, etc., versus temperature at 20 - 820°C and volume fraction of alumina in the "metal-ceramic" graded composite. Taking into account the particular geometry of the joint, the following initial conditions were established (Fig.3): (i) FG-joint has only one-dimensional gradient (in X-direction), (ii) the composition in the joint will follow the rule Yue = x^, VAI2O3 = 1 - x^, where Vi - volume fraction of component (NiAl, NiCoCrAlY or alumina), x = X/L is relative coordinate, p - anisotropy coefficient (0.7...1.3), (iii) only thermoelastic behaviour is considered and temperature distribution in FG-joint is assumed to be uniform and steady, and the joint has no external forces applied.

Figure 3. The model for FG-joint calculations.

The results are partially shown here as contour plots for NiCoCrAlY-alumina joints (Fig.4). These values are the mean ones of the respective tensor in certain direction (X or Y/Z). As far as the specimen is assumed to be free, the graded composition in X direction will be sufficient

317 for the relaxation of the whole specimen in order to satisfy thermal and mechanical equilibrium criteria.

200

400

600

800

Temperature, °C

200

400

600

Temperature, °C

200

400

600

800

Temperature, °C b

800

200

400

-r 600

800

Temperature, °C Figure 4. Calculated properties vs. temperature and anisotropy coefficient (p): elastic modulus, MPa, along Y/Z-axes (a) and its relative difference, %, to X-axis (b); thermal conductivity, W/mK, along Y/Z-axes (c) and its relative difference, %, to X-axis (d). The main bottleneck in this case will be in relaxation on the Y-Z plane (perpendicular to gradient), since there will be the most property mismatch and restricted movement of the parts of the whole specimen. Interesting, that relative anisotropy in elastic module between X and Y/Z components is not large (2-3%), but depends on temperature and anisotropy coefficient in a complicated way (Fig.4a and b). On the other hand, differences in values of thermal conductivity between X and Y/Z are almost the same for different anisotropy, but change strongly with the temperature (Fig.4c and d). The results for Y/Z-plane could be summarised in Table 1.

318 Table 1. Properties of the FG-joint at the Y/Z plane. Increasing of... Elastic modulus, GPa Anisotropy p Increases Temperature T Decreases

Thermal conductivity, W/mK Decreases Decreases

CTE, x 10^ 1/K Decreases Increases

These calculations show sources and values of the possible properties mismatch in properties of the graded joints. For instance, such large differences and anisotropy in thermal conductivity confirm that heat flow in non-steady conditions would affect the temperature distribution in the joint quite significantly. In this case additional thermal stresses could be generated by internal gradients of temperature.

4. CONCLUSIONS Two types of approaches to produce FG-joints by the DB-method have been presented, the use of metallic interlay ers and the use of graded PS-coatings. The results show that quality joints can be obtained with the optimisation of interlayers and the bonding process. However, the joints with the graded coatings/layers are evident to meet the high service temperature requirements. The calculations and experiments also reveal the origin and the magnitude of possible properties mismatches in the graded joints.

ACKNOWLEDGEMENTS The authors would like to thank the BE-7249 project consortium and especially Dr. G. Kleer, Fraunhofer-Institut IWM Freiburg, Germany, and Dr. M.Tului, GSM Rome, Italy.

REFERENCES 1. M.Koizumi, Ceram. Trans.: Functionally Gradient Materials, Ed. B.Holt e.a., ACerS., Ohio, 34(1993)3-10. 2. M.Gasik and K.Lilius, Comp. Mater. Sci., 3 (1994) 41-49. 3. N.Cherradi, A.Kawasaki, and M.Gasik, Compos. Eng. 4 (1994) No. 5, 883-894. 4. M.Gasik, Acta Polytech. Scand., Ch 226 (1995) 73 p. 5. M.Gasik, FGM News, 31 (1996) 6-9. 6. L. Heikinheimo (Ed.). Report No.VALC154 for project BE-7249, VTT Manufacturing Technology, Espoo (1995), 60 p. 7. Report No.VALC253 for project BE-7249, VTT Manufacturing Technology, Espoo (1996), 42 p. 8. IWM-Report No. V54/96 for project BE-7249. IWM Freiburg (1996), 38 p. 9. L.Heikinheimo, Thesis Dr., VTT Publications 218, Espoo, Finland, (1995), 166 p.


319

Advances in the Fabrication of Functionally Graded Materials using Extrusion Freeform Fabrication Greg E. Hilmas, John L. Lombardi, and Robert A. Hoffinan Advanced Ceramics Research, Inc. 851 E. 47th Street, Tucson, Arizona, USA ABSTRACT The Extrusion Freeform Fabrication technology (EFF), developed by Advanced Ceramics Research, Inc. (ACR) offers tremendous potential for net shape rapid prototyping of polymers, metals, and ceramics, as well as their hybrids such as functionally graded materials (FGMs). Two unique EFF systems capable of rapid prototyping monolithic polymer, metal, and ceramic parts have been developed and entail the sequential deposition of layers of self supporting viscous suspensions or highly loaded thermoplastics using a computer controlled extrusion head. In particular, the extrusion head builds up a 3D body by sweeping out a path based on a CAD virtual image. For the fabrication of FGMs, the EFF systems are modified to contain two extruders which dispense dissimilar materials into a small mixing head. The composition of the bi-component extrudate is controlled by proportioning the raw material feedrate from the two extruders. In this manner, the composition can be continuously graded to produce a FGM component. The ACR EFF technique offers the advantages of being able to form the body into almost any shape which can then be processed through traditional powder metallurgical or ceramic firing routes. This approach is inexpensive and potentially feasible for grading between any thermodynamically compatible ceramic-metal, ceramic-ceramic, or metal-metal material combination. 1. INTRODUCTION Functionally Graded Materials (FGMs) are currently receiving considerable attention from the materials science community, particularly in Japan, where the concept originated[l]. FGMs consist of a synergistic combination of different materials and are typically composed of ceramics graded to metals. Unlike conventional coated materials and composites, FGMs have a continuous grade in composition between their respective end members. FGM materials therefore take advantage of the properties of two different materials within the same body. The graded composition eliminates many of the problems associated with the presence of discrete interfaces in conventional composites such as poor mechanical integrity, transport losses due to low interfacial adhesion, and can also eliminate problems associated with thermal expansion mismatch which is a significant problem for many conventional high temperature composites. The use of highly loaded slurries or thermoplastic formulations combined with state-of-the-art freeform fabrication technologies also enables the rapid prototyping of FGM components.

320 A host of industrial and military applications can benefit from FGMs, consequently there is substantial interest in devising an inexpensive and versatile process for their fabrication. A unique process for FGM fabrication is under development at ACR and is an extension of Solid Freeform Fabrication (SFF) techniques which have been previously developed for the rapid prototyping of monolithic and composite ceramic components [2-5]. SFF is a rapidly developing technology destined to have a large commercial effect on the manufacturing industries. It is a computer controlled process where the desired part being prototyped is first reduced to geometric sections through the use of Computer Aided Design (CAD) software and then built up sequentially, layer by layer, out of its raw material(s). The method for transferring the CAD design to the fabrication of an actual component is quite complex and dependent on the particular SFF technology being utilized. The SFF field has rapidly progressed from producing simple models to producing complex functional prototypes. Prototypes which were once solid freeformed using waxes can now be made from high strength structural materials such as thermoplastics, thermosets, metals, ceramics and discontinuous fiber reinforced composites. ACR is actively involved in developing its own SFF technology known as Extrusion Freeform Fabrication (EFF) which has been shown to be a rapid and flexible prototyping and manufacturing process [6,7]. Two in-house systems have been developed which successfully freeform CAD designed complex parts using polymer and ceramic engineering materials including AI2O3, Zr02, Si3N4 and SiC, as well as filled and unfilled PEEK and polycarbonate thermoplastics. The next technological breakthrough lies in gaining the ability to rapidly EFF fabricate FGM prototypes for use in the design of potential mass produced FGM components. When a successful FGM composition is found, direct application of the technology can be utilized to prototype functional 3D parts. The goal of this study was to develop a rapid, flexible, and precise fabrication method for producing and evaluating potential FGM compositions. Nine different ceramic-to-metal graded compositions were successfully prepared during this study, resulting in a method which appears promising as a low-cost, high pay-off approach for fabricating and screening potential FGMs. 2. EXPERIMENTAL PROCEDURE 2.1 CAD/CAM Capabilities Similar to other rapid prototyping techniques, ACR's EFF process begins with a 3D drawing (AutoCAD, .DXF, etc..) of the component to be fabricated. The file is imported into ACR proprietary software and sliced into the individual layers and fill patterns which will be utilized to build the part. The fill pattern in each successive layer ultimately becomes an extrusion path for the EFF machine to follow while extruding the chosen material in the shape of the component being fabricated. The EFF machines utilize a 3-axis gantry with a piston extruder mounted on the z-axis. Extruder motions are driven by stepper motors and are indexed with a 4-axis motion control card which drives the x-axis, y-axis, z-axis, and one proportional axis. The 3D drawing of the desired component is converted to indexer code in an AutoCAD environment using proprietary ACR subroutines. During fabrication the extrusion piston is indexed at a rate proportional to movement on the x-y planes.

321 A second extrusion piston was required in order to fabricate FGMs, subsequently requiring precise control over a fifth axis or second proportional axis, one for each material required to form the gradient. This required multiple software and hardware modifications beyond just the creation of a dual extrusion head. The modifications included calculations associated with the ratio of material simultaneously extruded from each of the two heads. Code was written to calculate the proportions and write the values to each path definition along with code for x-y-z movement. Once the code was generated using these programs, it was downloaded to the controller card. In order to run two proportional axes on the AT6400 controller, a custom operating system was required which substituted a proportional axis for the z-axis. Movement on the z-axis was then controlled by a stand alone controller which raised the extrusion head (z-axis) a predefined amount when triggered by a statement in the indexer code. 2.2 Extrusion Freeform Fabrication (EFF) The processes for manufacturing FGMs at ACR are based on the deposition of self supporting viscous suspensions ('liquid feedstocks') or highly loaded thermoplastics ('solid feedstock') from a computer controlled moving head. The extrusion head sweeps out a path while depositing either viscous liquid slurries or a ceramic or metal loaded thermoplastic strand to fabricate the desired 3D body. In order to produce FGMs, the EFF machine is configured with dual extrusion cylinders which control the flow of two materials into a small mixing head containing an in-line static mixer connected to a deposition needle. In order to produce a 3D part, a virtual image of the desired final body is drawn in CAD. The image is then sectioned into layers and extrusion paths are generated to sweep each layer. Ultimately, the desired composition at each point can be controlled in the CAD package by proportioning the rate of feedstock flow from the two extruders utilizing the indexer code. The viscous suspensions used in the 'liquid feedstock' EFF process are thermally polymerizable acrylate gel casting formulations, very heavily loaded suspensions (>50 vol.%) of ceramic or metal particulate in polymerizable monomer solutions [8-10]. The suspensions are prepared at sufficient viscosity to maintain the shape of the body during the forming process while still able to be extruded at low pressures (50 to 150 psi). The gel casting suspensions are loaded to such an extent that very little shrinkage occurs during thermal curing thus, the shape of thefi-eeformedbody is maintained. The ceramic or metal particulate loaded thermoplastics used in the 'solid feedstock' EFF process are similar to formulations utilized in conventional powder injection molding processes and contain >50 vol.% solids. The solid feedstock approach drastically increases the variety of materials that can be used to fabricate FGMs using the EFF technique, however the extrusion process requires considerably higher pressures (500 to 1000 psi). A large number of particulate raw materials can be blended with a thermoplastic and extruded in controlled manner since the rheology of the mix can be precisely regulated by the temperature and pressure utilized during extrusion. For either EFF approach, the free formed bodies are processed through traditional powder metallurgical or ceramic firing routes. The main advantages of the ACR's EFF techniques over other FGM fabrication processes are that it has the ability to control the composition of the body in both the horizontal and vertical orientations, the ability to prepare complex shapes directly, and that

322

the process is amenable to a large variety of materials systems. Any material system that can be prepared as a gel casting formulation or blended with a thermoplastic can be used to fabricate FGMs using the ACR EFF process. 2.3 Fabrication of Functionally Graded Materials by EFF Ten different functionally graded material combinations have been currently fabricated using the ACR EFF process including the following: AI2O3 to NiAl, Zr02 to NiAl, AI2O3 to 304 S.S., Zr02 to 304 S.S., AI2O3 to Inconel 625, Zr02 to Inconel 625, WC to NiAl, TiB2 to NiAl, Tie to Inconel 625, and AI2O3 to tungsten. The majority of the compositions were fabricated in this study as flat billets to demonstrate the EFF FGM techniques and for preliminary mechanical property evaluations [10]. However, the AI2O3 to tungsten FGMs were being fabricated as W-AI2O3-W rings for potential insulating columns for heavy ion fusion accelerators containing in-situ electrodes [11]. 3. RESULTS The 'liquid feedstock' (low pressure) and 'solid feedstock' (high pressure) EFF machines utilized in ACR's FGM fabrication processes are shown in Figures 1 and 2, respectively. Figure 3 shows a scanning electron micrograph (SEM) of the cross-section of a typical FGM billet fabricated on the ACR EFF machines as square billets for mechanical testing purposes. The AI2O3-304 Stainless Steel billet shown was hot pressed for 1 hour at 1250°C and a 25 MPa load. It can be seen from the SEM micrograph that the EFF process is capable of producing a uniform transition between the ceramic and metal end members.

Figure 1. 'Liquid feedstock' low pressure EFF machine

Figure 2. 'Solid feedstock' high pressure EFF machine

323

^ 304 SS

A\p,

Figure 3. SEM micrograph of a cross-section of the AI2O3-304 Stainless Steel FGM billet. The majority of the FGM compositions were linearly elastic to failure when tested in four-point bending, however the 304 S.S. and Inconel 625 containing compositions exhibited high strengths and nonlinear fracture behavior. Figures 4 shows the load-deflection curves for the AI2O3-304 S.S. FGM system. The bars were tested separately having both the ceramic and metal side placed in tension in the four-point bend test fixture. With ceramic side in compression, the ceramic actually spalled off the compressive side of the bars prior to failure during many of the flexure tests. With the ceramic side in tension, the crack would pop in on the tensile side of the bar at a low load but would then be deflected several times by the ceramic-metal graded layers. The latter tests resulted in low strengths but extremely high work-of-fracture. In the end, these bars were visibly bent and cracked but remained intact (see inset of AI2O3-304 S.S. flexure bar).

o

2 3 Crosshead Displacement, mm

Figure 4. Load-deflection curves for AI2O3-304 S.S. four-point bend test bars. The bars were tested individually with the 304 S.S. side and AI2O3 side of each bar placed in tension.

324 4. CONCLUSIONS This study demonstrated that ACR's EFF technique is a versatile method for the rapid prototyping of functionally graded materials. The myriad of ceramic-metal FGMs produced shows that the technology is a viable method for both screening and producing potential FGM systems and components. In addition, preliminary mechanical property measurements on the FGM compositions demonstrated both high strength and high toughness with some unique failure characteristics. The FGM systems developed in this program and many other systems which have yet to be fabricated have a large number of potential commercial and government applications which may be realized through this technology. 5. ACKNOWLEDGMENTS The authors wish to graciously acknowledge the Ballistic Missile Defense Organization for their support of this research under grant #DAAH04-95-C-0049. REFERENCES 1. M. Koizumi, Ceram. Eng. Sci. Proc, 13 (1992) 333. 2. P. Jacobs, "Fundamentals of Stereolithography," Society of Manufacturing Engineers, Dearborn, MI. 1992. 3. P.M. Dickens (ed.), Proc. Third European Conf on Rapid Prototyping and Manufacturing, University of Nottingham, England, 1994. 4. H.L. Marcus, J.J. Beaman, J.W. Barlow, D.L. Bourell, and R.H. Crawford (eds.), SoHd Freeform Fabrication Symposium, University of Texas, Austin, TX, 1994. 5. H.L. Marcus, J.J. Beaman, J.W. Barlow, D.L. Bourell, and R.H. Crawford (eds.). Solid Freeform Fabrication Symposium, University of Texas, Austin, TX, 1993. 6. P. Calvert, R. Crockett, J. Lombardi, J. O'Kelley, and K. Stuffle, pp. 50-55, in Solid Freeform Fabrication Symposium, H.L. Marcus, J.J. Beaman, J.W. Barlow, D.L. Bourell ,and R.H. Crawford (eds.). University of Texas, Austin, TX, 1993. 7. K. Stuffle, A. Mulligan, P. Calvert, and J. Lombardi, pp. 60-63, in Solid Freeform Fabrication Symposium, H.L. Marcus, J.J. Beaman, J.W. Barlow, D.L. Bourell, and R.H. Crawford (eds.). University of Texas, Austin, TX, 1993. 8. M. A. Janney, Method for Molding Ceramic Powders, U.S. Patent No. 4 895 194 (1990). 9. A. C. Young, O. O. Omatete, M. A. Janney, and P. A. Menchofer, J. Am. Ceram. Soc, 74 [3] (1991) 612. 10. G. E. Hilmas, J. L. Lombardi, R. A. Hoffman, and K. L. Stuffle, pp 443-450, in Solid Freeform Fabrication Symposium, D.L. Bourell, J.J. Beaman, H.L. Marcus, R.H. Crawford, and J.W. Barlow (eds.). University of Texas, Austin, TX, 1996. 11. DOE Contract # DE-FG03-95ER82105.


325

Novel Routes to Functionally Graded Ceramics via Atmosphere-Induced Dopant Valence Gradients M. Kitayama, J. D. Powers and A. M. Glaeser Department of Materials Science and Mineral Engineering, University of California, & Center for Advanced Materials, Lawrence Berkeley National Laboratory Berkeley, CA 94720-1760, USA

Alumina compacts, when doped with Ti, can be made to develop a dopant valence gradient during or after firing through control of the sintering/annealing atmosphere. The dopant valence, Ti^+ (vacuum) versus Ti"^"^ (air), has a pronounced effect on the resulting microstructure, and on the rate of grain boundary migration. It is possible to generate microstructures in which a transition from fine equiaxed grains to elongated facetted grains occurs. Grain boundary migration characteristics have been investigated by monitoring the growth of an oriented single crystal sapphire seed into Ti-doped and undoped AI2O3. An enhancement of the grain boundary mobility, relative to behavior in undoped AI2O3, is indicated for Ti^+-doped AI2O3. Opportunities for more widespread use of the furnace atmosphere as a means of producing microstructurally graded ceramics suggest themselves.

1.

INTRODUCTION

A broad range of materials can be described by the general term functionally graded material (FGM). Hirai [1] has recently provided a review summarizing the various types of FGMs. One form of FGM involves a continuous or nearly continuous variation in microstructure and properties that is achieved by continuously or nearly continuously grading the phase contents. An example of such a structure might be one in which a transition from a pure metal to a pure ceramic is achieved. Similarly, a gradient in the volume fraction of fiber reinforcement may be developed to optimize the performance (and reduce cost). When ceramic materials are used, such gradients are generally established in the green structure. There are other classes of material in which there are chemical discontinuities and discontinuities in selected physical properties, but continuous or nearly continuous variations in a specific property. An example of such a material would be a thermal barrier coating in which the thermal expansion coefficient is graded. Such gradients could be achieved by varying the coating composition during deposition, for example from the vapor phase. An additional category of FGM is one in which the chemical composition is essentially constant, as is the phase content, but a microstructural gradient develops that induces a property gradient. Processing in a temperature gradient is one route to achieving such microstructurally graded materials. Such materials are also referred to as fine composites [1]. The range of processing techniques that can be employed to produce FGMs is also broad [1]. Vapor-phase methods {e.g.y CVD, CVI, and PVD methods), liquid-phase methods {e.g.y electrodeposition, sol-gel, plasma spraying and molten metal infiltration methods), and a variety of solid-phase methods based on powder metallurgy are available. The solid-state methods include powder stacking techniques, powder infiltration techniques, slurry techniques {e.g.y sedimentation

326 and electrophoretic deposition methods). In contrast to the vapor-state and liquid-state methods, which yield a final product, the solid-state methods generally lead to green structures with builtin gradients that must be retained during subsequent firing and densification. One interesting variation of powder metallurgy methods is that reported by Rosier and Tonnes at FGM '94 [2]. In this work, a microstructural gradient was produced by introducing a spatial variation in the Cr content of a TiAl powder. Subsequent processing was isothermal. One can anticipate that similar variations could be produced in ceramics. Another approach, one that has not been explored extensively, is to vary the valence 0^2. multivalent impurity through control of the sintering atmosphere. The use of valence gradients is likely to provide substantial opportunities for microstructural design because one can anticipate that the local valence state will affect the local solubility, grain boundary diffusivity, surface diffusivity, lattice diffusivity, and grain boundary mobility, and thereby, the density, grain size, grain size distribution, and grain shape. Several prior studies of sintering and grain growth attracted us to exploration of Ti-doped AI2O3. Bagley et al. [3] showed that the addition of Ti"^"^ led to significant increases in the sintering rate; apparently the much more soluble isovalent Ti^+ form had no interesting effect on densification. Brook [4] proposed a defect model in which Ti4+ substitutes for AP"*", and introduces Al vacancies as a charge compensating defect; Ti^+ would not produce a similar defect. Horn and Messing [5] have studied grain growth in high-density aluminas containing between 0.15 and 0.4 wt % Ti02. Normal grain growth, anisotropic grain growth, and abnormal grain growth occurred within specific ranges of temperature, composition, and time, and models linking this to the anisotropy of the grain boundary energy were proposed [6]. Work by Glaeser and coworkers has shown that the morphological stability of surfaces in alumina [7], and the Wulff shape of alumina [8] are changed by Ti doping. Thus, Ti-doped alumina provides an interesting and challenging model system for study, with the potential for using the atmosphere to produce microstructural and property gradients. The present work was undertaken to isolate the effects of small amounts of Ti on sintering behavior and the anisotropy in grain boundary motion. Low levels of Ti dopant ( P-Al2Ti05

(3)

at approximately 1390° C^^l The figure shows that the intensity of aluminium titanate (AT) lines decreases gradually from the surface to the center of the sample. On the other hand, the intensities of a-alumina peaks increase with depth. The tetragonal zirconia peak intensity appears to increase slightly with depth. The figure shows no other titania-related peaks which indicates that Ti02 (rutile) had reacted completely with a-alumina to form AT. The quantitative phase analysis results are shown in Figure 2 and Table 1. As can be seen from the figure, the amount of AT is 44.5 wt% on the surface and reduces Unearly with depth to 9.5 wt% at 0.3 mm, and then to 5.3 wt% at 1.5 mm. By contrast, the a-alumina content increases linearly with depth from 44.4 wt% at the surface to 80.2 wt% at 0.3 mm, and then 85.7 wt% at 1.5 mm. This suggests that the kinetics of infiltration are time-dependent and thus the amount of infiltrant reduces with depth. Clearly, liquid infiltration is a useful method to produce FGMs, as also indicated by other researchers^^'^l

370 100

80

-

60

h

40

li

I

I

I

I I I

+ Alumina oAT

I

20

5 0.0

5

i

1

0.2

0.4

5

5 1 0.6

1 0.8

1 1.0

1 1.2

5 1

1.4

Sample Depth (mm)

Figure 2. Weight ifraction of aluminium titanate (AT) and a-alumina according to depth in the functionally-graded aluminium titanate/zirconia-alumina composite. Error bars indicate 2x estimated standard deviations.

Table 1 Weight Fraction of Minor Phases and Mass Attenuation Coefficient of Aluminium Titanate/Zirconia-Alumina Composites as a Function of Sample Depth. Depth (nun) Wt(t-Zr02) Wt(Amor.) MAC 1 Wt(m-ZK)2) % % % cmV' i 5.3(3) 1.0(2) 5(2) 0.0 56.2(12) 5.8(2) 0.7(1) 0.1 52.0(10) 3(2) 7.0(2) 0.3 2(2) 41.6(8) 1 1.2(1) 7.0(2) 0.4 41.2(9) 5(2) 1.0(1) 0.8 6.8(2) 4(2) 41.2(9) 1.1(1) 6.5(2) 2.4(1) 1.2 0(2) 40.2(5) 6.7(2) 2.1(1) 0(2) 39.4(5) 1.5 Wt : weight fraction. m-Zr02 : monoclinic zirconia. t-Zr02 : tetragonal zkconia. Amor. : amorphous phase. MAC : mass attenuation coefficient of specimen at CuKa wavelength. Parenthesised figures represent the estimated standard deviation in terms of the least-significant figure to the left.

371 There is some indication of a marginal increase in the weight fraction of tetragonal zirconia (Table 1) with depth. In the alumina-zirconia (90:10 by weight) control sample, the content of the t-phase is approximately 5 wt%. On the surface of the FGM sample, where AT is approximately 45 wt%, the weight fraction of t-phase is 1.0% and this value increases up to 2.4% at a depth of 1.2 mm. It is suggested that the presence of AT has induced tensile residual stresses which are responsible for enhancing the t-->m phase transformation. The graded character is also shown by the change with depth of the mass attenuation coefficient (MAC) values (Table 1). The theoretical MAC values of AT, alumina, and zirconia are 72.9, 30.4, and 101.5 cmV\ respectively^^^l This suggests that AT has a significant contribution to the final MAC value at each depth. Since the amount of AT decreases with depth, the MAC value should also decrease with depth. The Rietveld 'external standard' method has allowed the amount of amorphous material to be computed. The presence of this phase is probably due to the incomplete crystallisation of the infihrant precursor during calcination. Table 1 depicts the content of this phase at each depth with average value of 3 wt%. Calculation shows that the MAC value of this material at each depth is between 69.8 and 125.8 cmV^ Since the theoretical MAC values for Ti02 and AliTiOs are respectively 127.3 and 72.9 cmV^ ^^^\ the detected amorphous phase could be either amorphous Ti02 or Al2Ti05^^^l Energy-dispersive x-ray microanalysis was used to qualitatively verify the graded character. Figure 3 shows the plot of the x-ray emissions of TiKa, AlKa, and ZrLa versus sample depth. Titanium emissions gradually reduce with depth whereas those of aluminium and zirconium are fairly constant. The titanium emission reduction agrees with the composition measurement using x-ray diffraction. This suggests that the infiltration has led to the formation of an FGM. Similar graded profiles were obtained for muUite/alumina system by infiltration^^l Therefore, these resuhs complement the result of x-ray diffraction quantitative phase analysis.

15

120

Al - ^ 96

12

H72

rV ^^

48

124

1

1

1

0.2

0.4

1

1

1

1

1

0.6

0.8

1

1.2

1.4

1

Sample Depth (mm)

Figure 3. X-ray characteristic emissions of TiKa, AlKa, and ZrLa with depth of FGM sample measured using energy-dispersive microprobe analysis. Error bars indicate 3x estimated standard deviations.

372 SUMMARY It can be concluded from the study that: 1. A functionally-graded aluminium titanate/zirconia-alumina composite has been synthesised by a liquid infiltration. 2. X-ray diffraction Rietveld analysis, with attenuation corrections applied using x-ray emission Compton scatter measurements, provided a powerful means for revealing the graded composition character of FGMs. Its ability in analysing phases rather than elements makes this method superior over the electron-probe microanalysis technique, especially for determining tetragonal zirconia and the amorphous phase contents. 3. The presence of aluminium titanate appears to reduce the content of tetragonal zirconia possibly due to the formation of AT-induced residual stresses in the microstructure. ACKNOWLEDGMENTS One of us (S.P.) is very grateful to the Australian Agency for International Development (AusADD) for scholarship support. We thank our colleagues Prof Deyu Li and Arie van Riessen for useful discussion. REFERENCES L Hirai, T. (1996). "Functional Gradient Material." In: Processing of Ceramics (Part 2). Ed. Brook, R.J., VCH Verlagsgesellschafift mbH, Weinheim. 2. Marple, B.R. and Green, D.J. (1989). "Mullite/Alumina Particulate Composites by Infiltration Processing". J, Amer. Ceram. Soc. 72[11], 2043-2048. 3. Low, I.M., Skala, R, Richards, R. and Perera, D.S. (1993). "Synthesis and Properties of Novel Mullite-Zirconia-toughened Alumina Composites". J. Mater. Sci. Lett. 12, 19851987. 4. Low, I.M., Skala, R.D. and Zhou, D. (1995). "Synthesis of Functionally-gradient Aluminium Titanate/Alumina Composites". J. Mater. Sci. Lett. 15, 345-347. 5. Pratapa, S. and Low, I.M. (1996). "Synthesis and Properties of Functionally-gradient Aluminium Titanate-Mullite-ZTA Composites". J. Mater. Sci. Lett. 15, 800-802. 6. Pratapa, S., O'Connor, B.H. and Low, I.M. "Use of Compton Scattering for Attenuation Corrections in Rietveld Phase Analysis". In preparation. 7. Jordan, B., O'Connor, B.H. and Li, D. (1990). "Use of Rietveld Pattern Fitting to Determine the Weight Fraction of Crystalline Material in Low Quartz Specimens". Powder Diffraction 5(2), 64-69. 8. Latella, B.A., Burton, G.R. and O'Connor, B.H. (1995). "Use of Spodumene in the Processing of Alumina-matrix Ceramics - Influence on Microstructure and Mechanical Properties". /. Amer. Ceram. Soc. 78[7], 1895-1899. 9. Pratapa, S. and Low, I.M. (1996). "The Effects of Spodumene Addition on Properties of Functionally-graded Aluminium Titanate/Zirconia-toughened Alumina Composites". In: Proceedings of the 2nd International Meeting ofPacific Rim Ceramic Societies. 10. O'Connor, B.H. and Thomas, A.G. (without year). X-ray Analysis Toolkit. Version 3.0. 11. Feltz, A. and Schmidt, F. (1990). "Preparation Study of Amorphous Al2Ti05". J. Eur. Ceram. Soc. 6, 107-110


373

The Use of a Functionally Graded Material in the Manufacture of a Graded Permittivity Element S.WATANABE*. T. ISHIKURA*, A. TOKUMURA*. Y. KM**. N. HAYASHl*, Y. UCHIDA*, S. HIGA*, D. DYKES***. G. TOUCHARD**** * Aichi Institute of Technology, Yachikusa Yakusa-cho Toyota 470-03 Japan. ** Yongwol Institute of Technology, Yongwol Kangwondo. 230-800 Korea. *** Yokkaichi University, Kayo-cho, Yokkaichi, 512 Japan. ****Universit6 de Poitiers, 40 av. du Recteur Pineau, Poitiers 86022 France.

1. ABSTRACT The authors of this paper have previously developed a vacuum filtration technique for the manufacture of functionally graded materials (FGMs) by a progressive lamination method. For this, they have been granted a U. S. patent. Using this method, it is possible to manufacture FGMs with thicknesses ranging from several millimetres to several centimetres. The authors have already produced an iron ( m ) oxide-kaolin FGM. the graded condition of which they have verified by means of a scanning electron microscope. In addition, they have performed measurements to determine this material's electrical properties viz: conductivity, relative permittivity and magnetic permeability. The present paper reports an experiment to create a different type of FGM, characterised by graded permittivity. The constituent materials used are titanium oxide and kaolin. The graded condition of manufactured specimens was investigated by mean of scanning electron microscope photographs and measurements of relative permittivity. Relative permittivity was found to vary between 2 and 5, while the photographs confirmed that the specimens were smoothly graded. On the basis of these results, it seems probable that graded permittivity elements can be manufactured using the authors' method.

2. INTRODUCTION Technology has recently been developed in Japan to manufacture materials which combine two or more constituent substances in graded proportions, as a means to achieve thermal relaxation. Such materials are known as functionally graded materials (FGMs). Application fields for such materials are found in mechanical, chemical, biological and

374 electrical engineering. In electrical engineering, they have utilisation potential in feeler sensors, resisters, magnetic shields, lossless optical fibres and superconductors. Methods of manufacture vary, but include the chemical and physical vapour deposition methods, the electrolytic deposition method, the atomised metal spray method, and a method in which powdered material is first melted in a plasma jet and then deposited ^\ But none of these methods or other previously existing ones, allowed the manufacture of a comprehensive range of FGM thicknesses extending from less than 1 millimetre to several centimetres. The authors have developed a new method of FGM manufacture, for which a US patent has been granted ^^. Using this method, it has became possible to produce FGMs across the whole range of thickness from a few millimetres up to several tens of centimetres. The authors have manufactured functionally graded materials consisting of iron ( m ) oxide-kaolin and copper-kaolin, using a successive layer accumulation method. The present research aims to develop a type of element permitting electric field relaxation, consisting of constituent materials graded for electric permittivity. The constituents used are titamium oxide and kaolin. 15 combinations of titamium oxide and kaolin in differing relative proportions were produced by a vacuum filter prcess, and tests were conducted to measure the permittivity and conductivity of each. A simple field distribution calculation was then performed for the assumed case of an element composed of these 15 combinations in graded sequence.

3. METHODS OF MANUFACTURING FGMs In order to manufacture this kind of FGM, Korean kaolin of uniform granular diameter is mixed with titanium oxide and dissolved in distilled water, agitating well. The mixture is put into a cylinder and then vacuum filtered. The filtering (extraction) rate is 120 1/min. When the first cake has been formed, fresh materials are put into the cylinder and thus successive layers are added. After the final cake is formed, the whole FGM mass is subjected to applied pressure for 24 hour. For a 60 mm diameter cylinder, the pressure applied is 3. 6 kg/cm ^. The FGM is then dried naturally, and baked to firmness in a reducing furnace. The furnace temperature is regulated in accordance with JIS R8101 1959^^. The sintering temperature itself is determined by the use of a Seger cone and a test piece. The titanium oxide used for the present experiment was first grade experimental TiO 2. The Korean kaolin used was a clay primarily consisting of kaolin ore, having the chemical formula SiO 2 -Al 2 0 3.

4. THE EQUIPMENT USED FOR THE MANUFACTURE OF FGMs The apparatus was constructed in bronze and comprised four parts, an upper and a lower cylinder, a piston and two perforated plates. The dimensions of the upper cylinder were

375 oxide-kaolin FGM after sintering. The layered manufacture of the FGM is recognisable from the photograph. A scanning electron microscope photograph of the same material is shown as Photograph 2. The graded condition of the titanium oxide and kaolin particles in successive layers can be verified in this photograph.

Photograph 1 The titanium oxide-kaolin FGM

:«?*#'i-«; .,^-- .••J -S.'H

.i^

Photograph 2 Scanning electron microscope photograph of the titanium oxide-kaolin FGM

s J

Fig. 3 Electrodes for measurement of relative permittivity.

6. MEASURED PERMITTIVITY OF FGMs In view of the possible use of FGM elements for electric field relaxation, the permittivity

376 60 X 130 X 95 mm. The lower cylinder was 40 mm in length, with an outlet port for the extraction of filtered water. The piston was 60 mm in diameter with a port in its upper portion for the extraction of air. The two perforated plates were 5 mm in thickness. The cylinder plate had a diameter of 52 mm, the piston plate a diameter of 66 mm. A schematic diagram of this apparatus is seen in Fig. 1. Fig. 2 shows the pressing operation after the successive accretion of layers.

cuum ump

Fig. 1 Apparatus for the manufacture of FGMs

5. METHODS OF SINTERING THE FGMs For sintering, the FGM was heated in a furnace using butane fuel. Following this, a Seger cone was placed inside the furnace to determine the desired temperature, the gas pressure was set at 0. 05 kg/cm ^ and the furnace was ignited. The gas pressure was raised gradually in steps of 0. 05 kg/cm ^, and at 30 minute intervals measurements of the furnace temperature were taken. C o m p re s s ion 3. 6 K g f / c m ^ Layer 1

Natural

Si n t e r e d Temp.lSOOC

dry

f rWYYvWYVJ

UMMMM

m

mMMMM

--

mMm^

Fig. 2 Manufacturing operation Two sintering methods could then be used. In the reducing method, the flow of air into the furnace was cut off after the furnace temperature reached 900 °C. The sintering temperature was determined by observing the melting down of the Seger cone. After the sintering was completed, the furnace was left to return very gradually to normal temperature while a plentiftil air circulation was assured. Photograph 1 shows the titanium

377 e r of the materials was measured using a Q-meter. A schematic representation of the electrodes used is to be seen in Fig. 3. The measurement frequency adopted was 50 MHz, The FGM sample to be tested was placed between the electrodes, and measurements were taken of the distance between the electrodes (L) and the electrostatic capacity Cm. The sample was then removed and the electrostatic capacity Co was measured for the same value of L without the test piece. The relative permittivity was obtained from a comparison of Cm and Co. The results of this comparison are shown in Fig. 4 for the various types. It can be seen that the relative permittivity changes from about 2 on the kaolin side to about 5 on the titanium oxide side. O CO

6

>

o

i

4 0

\— (U

>

^ ^ ^

2

05

1

1

Cd

2

4 6 8 10 1 2 1 4 Samp 1 e No.

Fig. 4 Relation between relative permittivity and titanium oxide-kaolin ratio in samples

7. CALCULATION OF THE FIELD DISTRIBUTION For calculation purposes, the field distribution was taken for the case of a uniformly composed (non-FGM) insulating material. The model used for the calculation is shown in

Potential Fig. 5

OV

Simulation model for numerical analysis

378 Fig. 5. The equipotential line was found by means of a conformal mapping procedure, using the following formula. 4C(1-C) 3C-1-—^ ~ b _ , 2 C + C - i b ^ _^ C-C -] + —-ja Z=—[cos — —sm C+i 2 7C a C+i where C=a/(a ^ +2b ^ ) and a=2b. For numerical analysis, the Y axis was divided into 18 segments, and the X axis into 12. The results are shown in Fig. 6.

^

f9900 V f7500 V 5000 V

Potent iai Fig. 6 Results of electric field calculation The symbols O, @, O and • represent the equivalent potentials for 2500 V, 5000 V, 7500 V and 9900 V respectively. It is to be anticipated that with the use of an FGM composed of materials of differing relative permittivity, the same kind of difference between relaxation and concentration areas will be found within a single piece of material. If an FGM of especially high relative permittivity is used, a greater relaxation effect ought therefore to be attainable. In future experiments, the authors plan to manufacture FGMs of higher relative permittivity, and to perform detailed measurements in order to verify this hypothesis.

8. REFERENCES 1. The Functionally Graded Material Forum and The Society of Non-Traditional Technology : Functionally Graded Materials, p. 351, Kogyochosakai, Tokyo, 1993. 2. U.S. patent. No. 5167813(1992). 3. Japan Industrial Standard: JIS-R-8101(1959). 4. Prinz(Masuda, Kouno, trans.) : "The Calculation of Electric Fields" pp. 37-168, Asakurashoten, Tokyo, 1974.


379

Evaluation and Modelling of the Residual Stresses Generated on Functionally Graded Materials -Two examplesN. Cherradil, D. Delfosse^ and P. Moecklil iSwiss Federal Institute of Technology, CH-1015 Lausanne, ^Swiss Federal Laboratories for Materials Testing and Research, EMPA, CH-3602 Thun, Switzeriand

1. ABSTRACT A parametric study was carried out to determine the influence of the compositional gradient on the residual stress distribution. The calculations were based on a cylindrical geometry for WCyCo samples and a rectangular geometry for CuNi samples with stepwise compositional variation at the interlayers. The effects of the gradation size and composition profile of the graded materials were investigated by a visco-elasto-plastic finite element analysis using the ABAQUS code. It was found that the degree of residual stress is mostiy determined by the compositional distribution and its thickness, but not by the thermal history. The calculated stress values were compared with those measured experimentally either by Xray diffraction on graded WC/Co specimens or by deflection measurements during electrochemical removal of subsequent layers for graded CuNi samples. The comparison with experimental methods showed good agreement, thus validating the results obtained by the parametric finite element study.

2. INTRODUCTION A functionally graded materials (FGM) is an engineered composite which is designed to optimize materials properties for use under complex loading conditions by local control of composition and microstructure. The intentionally introduced constitutional gradation can be tailored for specific requirements. However, the different material combinations will generally have dissimilar thermal expansion coefficients that can lead to the generation of significant residual stresses, whenever the part is exposed to a thermal cycle (e.g. during processing). Residual stresses are commonly considered a nuisance or even a potential danger to the integrity of the part. In certain cases, however, they may have a beneficial effect on the performance of a component. The FGM concept offers an altemative method to design a part with a well defined, built-in stress state. By judiciously tailoring the composition and the microstructure, thermal stresses can be either dispersed or minimized during both the processing cycle and the in-service use. The purpose of this research work is to develop a fundamental understanding of the effect of a graded structure on stress distribution and thus an efficient tool for optimized profile design.

380 The theoretical results were compared with those obtained from the experimental techniques using two different FGM systems, namely Cu-Ni and WC-Co, as examples. 3. STUDIED MATERIALS The materials used in this study were fabricated following two different techniques (figure 1). The WC/Co graded samples were fabricated by a stepwise compositional control It consists on layering the mixed powders with different composition ratios in a die. Then, they were

Stepwise compositional

Continuous

control

compositional control

i

I

Stepwise stacking

Dosage system

Pre-compaction

Preform

I

1

1

Pressureless sintering

1

1

CIP/Compaction

Hot pressing

compacted uniaxially and sintered. Figure 2 shows an optical micrograph of the polished cross section at the interface between two different layers. The samples under consideration are a bi-layer part 75WC/25Co 95WC/5CO and a tri-layer part 75WC/25Co 85WC/15CO - 95WC/5CO.

|

Hotlsostatic Pressing

The Cu/Ni graded samples were fabricated by a continuous compositional control based on the centrifugal method described elsewhere [1]. An optical micrograph of the microstructure shown in the figure 3 exhibits a smooth variation of the composition.

Figure 1. FGM production by P/M routes

Figure 2. Bi-layer sample 75WC/25Co-95WC/5Co

Figure 3. Cu/Ni graded sample

4. FINITE ELEMENT ANALYSIS For the finite element analysis, the following assumptions were made: - The geometrical details of the bodies: For the WC/Co it was a cylinder with 10 mm diameter and 6 mm height, and for the CuNi, it was a rectangular plate with 3 mm thickness, 14 mm

381 width and 32 mm length. The mesh configuration was modeled by a finite element strip of isoparametric eight-node elements with 4 integration points. We have considered a fixed geometry for each sample and changed either the composition of the gradation and its size. The model is divided into a number of geometric elements which are in contact with one another and considered as layers, each layer being assigned slightly different materials properties. For the 1-phase-system (Cu-Ni), the composition of the Cu-Ni-alloy changes by 10% from layer to layer, whereas for the graded 2-phase-systems (WC-Co), the step-wise nature of the gradient is reproduced in the analysis. - We used an elasto-plastic analysis for WC/Co and visco-elasto-plastic analysis for Cu/Ni samples. Then, the physical and mechanical properties as function of the temperature and composition were compiled from the literature or determined by mechanical tests. - The boundary conditions were imposed following the symmetry taken. - The temperature was considered to be uniform over the whole sample at each calculation step, and the sample was considered to be stress free at the starting temperature. It was set up at 800°C. In fact, above this temperature, Cu, Ni as well as Co are too soft to build up a load and residual stresses disappear by local creep/stress relaxation. - Numerical solutions are obtained using the ABAQUS code [2]. 4.1. WC/Co analysis - The axi-symmetric specimen geometry allowed two-dimensional models to be employed. In order to illustrate the stress generated in a WC/Co part,figure4 shows contour plots of the radial and shear stress distribution in a three layer sample based on 95, 85 and 75 wt.% of WC. The highest concentration of the radial stresses are between the 95 and 85% layers in comparison with the interface between the 75 and 85% layers. This is due to the plastic deformation which could occurs in the Corichregion, whereas in the 95% layer, the relaxation mechanism is effectively prohibited due to the high WC content. This layer is essentially elastic even at high temperatures. Also, since this composition exhibits high elastic moduli, a small displacement in these areas generates a large stress. Regarding shear stresses in the left figure, we can notice that the peaks values are mostly located at the free surface between the 95 and 85 layers.

Figure 4. Contour plots showing the radial and shear stress distribution

382 Figure 5 shows the peak values of the axial andradialresidual stresses for different types of profiles. As expected, the peak stresses depend strongly on the gradient profile, but they are always larger in the non-graded material as a result of the large property mismatch.

Profile A

Profiles

Thickness

^

Profile A

Profile B

Profile D

Thickness

Thickness

Profile C

Profile D

Figure 5. Predicted peak values of radial and axial residual stresses within different WC/Co FGM parts. Figure 6 summarizes the numerical results of the axial stresses for different types of profiles. As we can see, the evolution of the stresses are higher at the edge interface between 95 and the other compositions, and that is true for all the profiles. However, the evolution of the stress through a graded sample from 90_85_80_75 is lower. In fact, if the upper limit of the WC content is lower then 95% (e.g. 90%), then the residual stresses are reduced. This is due to the relaxation mechanism which is more efficient. 800t

^9f'5fi[

^75

i

rhrh ^ ^75

4.

u I I t I I I I I I I II

I I I I I I I I

2 3 4 Thickness (mm)

5

^75

D=^

Thickness

Thickness

^.9:

E^

•90!

i r h ^ ^751 I M l ^ Thickness

Figure 6. Influence of the profile shape on the axial stress distribution

Thickness

383 4.2. Cu/Ni analysis For this analysis, symmetrical parts have been considered. Figure 7 shows the contour plot of Oy stress. As expected the Ni-rich layers at the surfaces are under compression and the Copper -rich layers in the central part under tension. The peak values varies between 100 and -100 MPa. From the contour plot of the plastic deformation shown in figure 10, we can see that all of them occur in the pure metal layers in both Ni and Cu. This is explained by the low yield strength of pure Cu and Ni which are soft metals as compared to the solid solutions hardened CuNi alloys. 4 = -100MPa 10 = 0MPa 14 = 100 MPa

epl

2 = -0.07% 4 = -0.01 % 6 = +0.05%

3 = -0.04 % 5 = +0.02% 7 = +0.08%

Figure 7. 2D analysis for a graded Ni/Cu/Ni sample (lower right quarter of the sample is shown) Figure 8 shows the calculated stress distribution in NiCuNi part. The peculiar form of the curve is due to the solid solution strengthening effect that occurs while changing from a soft, pure metal to an alloy. In the pure metal layers, the thermal stresses are relaxed by visco-plastic deformation. In the adjacent layers, the yield stresses of the alloys (for example Cu-20Ni and Ni-20Cu) are higher and thus are the residual stresses.

-2001

0.00

0.50

1.00

1.50

2.00

2.50

3.00

Position through thickness (mm) Figure 8. Residual stress a n in graded Ni/Cu/Ni

384 5. RESIDUAL STRESS MEASUREMENT 5.1. WC/Co sample The chosen technique was X-ray diffraction that is widely used for non-destructive surface measurement of applied and residual stresses. Stress analysis relies on the determination of the lattice strain using the interplanar spacing as a gauge by measuring the peak shifts in a fixed O direction for different \j/-tilt of the sample [3]. Stresses are calculated from measured strains using diffraction elastic constants which were calculated theoretically. As the Co phase takes up a certain amount of W and transforms after cooling into a solid solution with a variable W content, the measurements were limited to the WC phase. The X-ray measurement is confined to the surface of the specimen. Therefore, in order to investigate the residual stresses trough the thickness, we applied a method that measures the radial stresses at the outer surface of a specimen and tried to correlate them to the intemal stress state [4]. It is known that for a materials with two or more phases the stress field is the superposition of stresses at two levels : Macroscopic stresses which exist between the different layers and resultfi*omthe intemal force balance through the whole material. Microscopic stresses which appear between grains or phases in the material. Thus, the micro residual stresses stemming from the two-phase system have to be added to the results from finite element analysis (where only macro residual stresses are determined) allowing direct comparison with the total stresses experimentally measured. Figure 9 shows the macro residual surface stresses from the numerical analysis for the two and three layer specimens. One can see that the resuhs from Xray measurements agree fairly well with the predicted values. 1000 1

Two-layer-spec imen

^500

K^ 1 1-500 -1000J 0

,

1 2

,

,.

\

1


1

6

Macro stresses X-ray measurements

-1000


"• Total stresses for WC phase V X O Samples

Figure 9. Comparison between the predicted and the measured total residual stress within the WC phase of a two and three layer WC/Co part. X-ray measurements of surface stresses offer a reasonable tool to check the validity of numerical predictions. The method is, however, not fine enough to pick up all the stress

385 maximas and minimas that occur over small distances. It is also not possible to extrapolate from measurements of residual surface stresses to the stress state in the interior of the part. For a non-destructive, more in-depth determination of the residual stress state, neutron diffraction method with its much higher penetration depth has to be employed [5]. 5.2. Cu/Ni sample Copper and nickel exhibit a simple one-phase diagram characterized by complete solid solubility. Thus, it was not possible to apply the X-ray diffraction method. The residual stresses were determined by continuously removing thin layers of materials by an electrochemical technique while monitoring the resulting deformation of the sample [6]. The experimental device consists mainly of a clamp in which a copper cathode, the specimen and a linear voltage displacement transducer (LVDT) are fixed. The amount of bending of the specimen is measured with the LVDT and therefrom, the original stress distribution calculated. Figure 10 shows the measured deflection of some investigated gradient samples. As we can see, the deflection sign changes following the material that is removed at the surface. IDU

NCN-part

£^100 ^

50

X/i

S 0 "I -50

—•—FE-Analysis Experim. 1 Experim. 2 Experim. 3

1-100 0.1

0.2

0.3

0.4

0.5

Removed thickness (thickness of original specimen = 1) Figure 10 Measured deflection of three different Cu/Ni parts as function of the thickness of the removed layer

-150 0.00

0.50

1.00

1.50

2.00

\L • \>s*^^ ^SST *^ 2.50

3.00

Position through thickness (mm) Figure 11. Comparison between the predicted and measured residual stress

In figure 11, the residual stress distribution in the "NCN" part obtained from the analysis is plotted against the experimental results from the electrochemical thinning method. The agreement between the results is highly satisfactory and validates the visco-elasto-plastic approach taken in the FE-analysis as well as the values of the input data. 6. CONCLUSION Residual stresses are often impossible to avoid as a result of manufacturing operations. The graded concept shows, however, that a desired stress state can be designed allowing the dispersion or even optimization of these stresses. Furthermore, the finite element analysis tums

386 out to be a useful tool for mapping residual stresses in the bulk and at the surface of the components non-destructively, providing information which can be used for manufacturing process optimization, analysis of structural integrity, improving mechanical behavior and for service life prediction. Residual micro stresses have to be taken into account for the comparison with experimental results, if two or more phases are present within the FGM. ACKNOWLEDGMENT I would like to express my sincere gratitude and thanks to Professor B.Ilschner who introduced the FGM concept and initiated the work in Switzerland. He gave me the opportunity to create my own group and work in such an exciting field. Also, my thanks go to all my colleagues and collaborators for their help and assistance, the Swiss National Fund and the Swiss Priority Program on Materials Research for their financial support.

REFERENCES [1] Delfosse D. and Ilschner B., "Pulvermetallurgische Herstellung von Gradientenwerkstoffen", Materialwissenschaft und Werkstofftechnik 23,1992,235-240. [2] Hibbitt, Karlsson and Sorensen, Computer Code ABAQUS, Inc., Providence, RI, 1994 [3] Noyan I.C. and Cohen J.B, "Residual Stress, Measurement by Diffraction and Interpretation", Material Research and Engineering Series, Springer-Verlag, New York, 1987 [4] Delfosse D., Cherradi N. and Ilschner B., "Numerical and Experimental Determination of Residual Stresses in Graded Materials", Comp. Eng., Special issue, 1997 [5] Williamson R.L., Rabin B.H. and Byerly G., "Residual Stresses in Joined CeramicMetal Structures: FEM Studies on Interlayer and Creep Effects", in 3rd International Symposium on Structural and Functional Gradient Materials, ed. Ilschner, B. and Cherradi, N., PPUR, Lausanne, (1994), 215-221. [6] Delfosse D., Kiinzi H.-U. and Ilschner B., "Experimental Determination of Residual Stresses in Materials with a One-Dimensional Gradient of Composition", Acta Metallurgica et Materialia 40, (1992), 2219-2224.


387

Residual Strains and Stresses in an AliOa-Ni Joint Bonded with a Composite Interlayer: FEM Predictions and Experimental Measurements Barry H. Rabin, Richard L. Williamson and Hugh A. Bruck Idaho National Engineering Laboratory, Idaho Falls, ID Xun-Li Wang and Tom R. Watkins Oak Ridge National Laboratory, Oak Ridge, TN David R. Clarke University of California, Santa Barbara, CA Abstract A cylindrical Al203-Ni joint bonded with a 4.0 mm thick composite interlayer of 40 vol.% AI2O3-6O vol.% Ni was fabricated by powder processing and the residual stresses and strains in the specimen were studied experimentally using neutron diffraction, x-ray diffraction and optical fluorescence spectroscopy. Experimental measurements were compared with finite element method (FEM) modeling results obtained using a variety of different constitutive assumptions. The predicted residual strain distribution within the AI2O3 along the center of the specimen was in excellent agreement with neutron diffraction measurements. Alternatively, the predicted peak strains and stresses within the AI2O3 along the specimen surface were significantly higher than those measured, suggesting stress-relief occurred near the free-edge during cooling. The mechanisms of stress-relief are uncertain, however localized plasticity and damage within the composite interlayer are believed to play a role. Introduction Ceramic-metal joining has recieved considerable recent attention [1,2]. Numerous studies have focussed on residual stresses in ceramic-metal joints [3-5]. Residual stresses have also been measured experimentally in a several cases, however these studies involved joints fabricated using brazing techniques [6-11]. The goal of this work was to experimentally measure the residual strains and stresses in a ceramic-metal joint that is more characteristic of typical FGM structures, and to compare the results with modeUng predictions. In this study, a ceramic-metal joint bonded with a thick composite interlayer was produced by powder processing. Strains and stresses were measured using a variety of experimental techniques. Experimental results were compared with FEM predictions from a detailed elastic-plastic, temperature-dependent model. Al203-Ni was selected as a model system because the properties of the pure materials are well characterized, there is a large mismatch in properties, and Al203-Ni composites are amenable to diffraction methods of residual strain measurement. Rather than examining a complicated, multi-layered FGM structure, this model study was conducted using a cylindrical Al203-Ni joint containing a single, homogeneous composite interlayer approximately 4.0 mm thick. Experimental Specimen fabrication involved powder processing techniques described in detail elsewhere [12, 13]. The steps included powder selection, incorporation of sintering aids and binder, powder mixing, die compaction, sintering, and final consolidation by hot isostatic pressing (HIP). The cylindrical specimen examined in this study is shown in Figure 1, along with photomicrographs showing the microstructure of the composite in the regions near the ceramic-composite and metal-composite interfaces. The 40 vol.% AI2O3-6O vol.% Ni composite interlayer was approximately 4.0 mm thick.

388 The neutron diffraction measurements were conducted at the High Flux Isotope Reactor of Oak Ridge National Laboratory using a triple-axis spectrometer operated in the diffractometer mode. The details of the experimental method have been described elsewhere [10,14]. Slits of dimensions 0.8 X 4 mm^ and 0.8 x 30 mm^ were inserted before and after the specimen, which together defined a sampling volume of approximately 2,6 mm^. Radial and axial strain (Crr and e^z) distributions were investigated in this study. For each strain component, a series of measurements was taken along the specimen axis of symmetry through the AI2O3 and composite layers. For the purpose of illustration, the specimen orientation for the measurement of e^z is shown in Figure 2. To improve the ability of detecting the predicted steep strain gradient, an overlapping sampling volume was employed, with a step size of 0.25 mm between analysis points in the vicinity of the interfac. The AI2O3 (3 0 0) reflection (20-72.0°) was used for strain determination according to e=

Figure 1. The powder processed specimen examined in this study, consisting of pure AI2O3 joined to pure Ni using a 40 vol.% AI263-6O vol.% Ni composite interlayer approximately 4.0 mm in thickness. Micrographs of the composite and the interface regions are also shown.

d-do _ sin 60 ^0

sin 0

where d is the lattice spacing and 20 the diffraction angle of AI2O3 (3 0 0). do and 20o are the corresponding stress-free values. In general, strains measured with diffraction methods are a superposition of macro- and microstrains [15]. Since in this study we were solely concerned with the macrostrain distribution resulting from the thermal expansion mismatch between the bonded dissimilar materials, the data points farthest from the interface were assumed to correspond to zero macrostrain. In this way, effects of any microstrains due to the thermal expansion anisotropy within the single phase AI2O3 were removed. However, data in the composite layer still contain a microstrain contribution due to the thermal expansion mismatch between AI2O3 and Ni phases, and this contribution was not taken into account in the analysis. Details of the x-ray diffraction strain measurements can be found elsewhere [14]. Measurements were performed on a 4-axis goniometer* in the "Q-goniometer geometry" [15]. Cu Ka^ radiation (X = 1.54060 A) was used. A pinhole collimator with a 0.5 mm opening was used to define the sampling volume, and soller slits were and to minimize sample displacement errors. The (1 4 6) AI2O3 reflection at -136° 20 was step-scanned using three azimuthal angles ((|) = 0, 45, and 90°) and seven tilt angles, {\\f = 0, ±28.2, ±42, and ±55 °) corresponding to sin^Xj/ values of 0, 0.22, 0.45, and 0.67, respectively. In order to map the strain gradients along the length of the specimen, the sample was translated and the above measurements were repeated at various points along the cylindrical axis of the sample. The penetration depth of Cu Ka^ radiation in a-Al203 depends upon the tilt angle; a depth of * PTS goniometer, Scintag, Inc., Cupertino, CA.

(1)

389 about 35 |im was calculated and can be taken as an average value for the current experiments. The sample was rotated about its cylindrical axis to improve particle statistics for some of the measurements. Careful goniometer and sample alignment procedures were employed. The average strain free interplanar spacing, d^, was determined from annealed powder the same as that used to fabricate the specimen. Strains and stresses were calculated using the procedure of Winholtz and Cohen [16].

Figure 2. Schematic illustrating the specimen orientation for neutron diffraction axial strain measurements, and the overlap of sampling used to improve spatial resolution of the measurements.

Optical Fluorescence Spectroscopy Details of the optical fluorescence technique used to measure residual stresses in polycrystalline AI2O3 have been published previously [17, 18]. A portion of the sample was excited using an argon ion laser and the fluorescence peak of the Cr^^ impurity present in the AI2O3 is detected using a Raman spectrometert. The shift of the Rl and R2 fluorescence lines in Cr^^ doped AI2O3 can be related to the stress state in the excited volume using the relation

Av = (2n,-fn,)(îi±^|i±^) where Av is the average frequency shift, and Hy are the piezospectroscopic coefficients relating frequency to stress. The numerical values of the piezospectroscopic coefficients Fla and lie have been determined previously by direct experimentation [17, 18], and are 2.7 and 2.15 cm"^ GPa~^, respectively for the R2 line, which was used in this study. For these experiments, a high spatial resolution laser probe was used, having a diameter of approximately 50 |im. The excited volume from which stress information was obtained is determined by the penetration depth of the argon ion laser in polycrystalline AI2O3, which has been measured experimentally to be on the order of 50 fim. FEM Modeling Strains and stresses were computed for the joined specimen cooled uniformly to room temperature from an assumed stress-free elevated temperature using numerical models described in detail previously [19, 20]. The coordinate system and an example of the finite element mesh utilized are shown in Figure 3. Elastic-plastic response was permitted in both the Ni and Al203-Ni composite materials; a von Mises yield condition and isotropic hardening were assumed.

t Model T64000, Instruments SA, Inc.

(6)

390 Calculations were performed for four different cases as described below. In all cases, pure AI2O3 was assumed to remain elastic with a temperature independent Young's modulus of 380 GPa and Poisson's ratio of 0.25. The thermal expansion coefficient of AI2O3 decreased linearly from 9.4 x 10"^ K'^ at 1100 K to 5.4 x 10'^ K"^ at room temperature. For pure Ni, all cases assumed the same temperature dependent Young's modulus, which decreased from 208 GPa at room temperature to 166 GPa at 900 K, and the same Poisson's ratio of 0.31. The thermal expansion coefficient of Ni decreased linearly from 17.8 x 10"^ K"^ at 1100 K to 13.4 x 10"^ K"^ at room temperature. Two different sets of Ni strength properties were examined, corresponding to properties taken from the literature for both fine grained and coarse grained microstructures [21, 22]. These simulations are referred to in Table I as Case 1 and Case 2, respectively. The temperature dependent yield strength and the flow strength at 2% strain are listed in Table I. Linear hardening behavior was assumed in both cases. For Case 1 and Case 2 the properties of the composite material interlayer were computed as follows. The thermal expansion coefficient of the composite was estimated using a simple volume fraction based mixture rule. The temperature dependent composite stress-strain curves were constructed using an modified rule-of mixtures approach first proposed by Tamura, et al. [23]. Also listed in Table I are the properties used in a calculation referred to as Case 3. This calculation was performed using a set of material properties intended to be representative of the actual material behavior. Most of these properties were determined through direct experimental measurements made on bulk Ni and composite specimens, although some of the temperature dependent values that were not measured directly were estimated by extrapolation based on trends observed in literature data, as well as unpublished research. The notes provided along with Table I describe in detail the origin Figure 3. Coordinate system and example of these data. of FEM mesh used to model the specimen. Calculations for Cases 1 through 3 were all performed assuming a stress-free temperature of 1100 K. Recent model calculations performed including creep deformation constitutive laws for an Al203-Ni bimaterial joint indicated that creep strains in the pure Ni exceeded the plastic strains for all temperatures above about 700 K [24]. Since creep deformation in the Ni at high temperatures effectively lowers the stress-free temperature, a final calculation was performed assuming a stress-free temperature of 700 K in an effort to account for this effect. This calculation, referred to as Case 4, was performed using the same material properties as in Case 3.

391 Table 1. Temperature Dependent Mechanical Properties of Ni and the 40% Al2O3-60% Ni Composite used in the FEM Calculations for Three Different Cases. 900K

300K Case

Material

E

E

V

(MPa) 1

2

3 a. b. c. d. e. f. g. h.

(MPa)

1

V

(MPa)

(GPa)

(MPa)

Ni

208.0'

0.31'

148.0'

161.0'

166.0'

0.31'

69.0'

72.0'

interlayer

254.0'

0.29'

148.6'

230.7'

214.8'

0.29'

69.4'

134.0'

Ni

208.0'

0.31'

25.0''

53.7'

166.0'

0.31'

11.9'

25.6'

interlayer

254.0'

0.29'

25.r

133.2'

214.8'

0.29'

12.0'

94.8'

Ni

208.0'

0.31'

18.0^

75.0^

166.0'

0.31'

15.3^

63.8^

interlayer

219.0^

0.29'

80.0^

192.0«

171.0^

0.29'

56.0^

134.4^^ 1

from [221 from [21] linear rule-of-mixtures modified rule-of-mixtures for fine grained Ni [22] and q = -4.5 GPa modified rule-of-mixtures for coarse grained Ni [21] and q = -4.5 GPa temperature dependence assumed to be same as that of fine grained Ni from direct experimental measurement estimate based on unpublished research

Experimental Results The results of neutron diffraction strain measurements made along the axis of symmetry and within the vicinity of the interface between the AI2O3 and the composite are shown in Figure 4 as a function of axial position within the sample. Both the radial strain (EJ and axial strain (EZZ) are shown, along with errors estimated from the standard deviations of the least-squares fitting of the recorded diffraction profiles. The errors in this experiment were dominated by the unfavorable scattering intensity due to the small sampling volume used. Within the experimental precision, the experimental data provide evidence of a steep strain gradient across the interface, extending to a distance of approximately 2 mm on either side of the interface. In general, the magnitudes of the measured strains are quite small, on the order of 10' . In the AI2O3 layer, E^ becomes increasingly compressive as the interface is approached. A maximum compressive strain of approximately 3 x 1 0 ' was measured within the AI2O3, approximately 1 mm from the interface. The axial strain (E^^) is compressive in the AI2O3 layer, becoming tensile only when the interface is approached. Measurements of £22 across the interface were not attempted because in this measurement geometry, an artificial peak shift was anticipated when the sampling volume was partially buried in the AI2O3 layer [25]. This artifact leads to an apparent strain and adds ambiguity to the determination of e^z. The results of x-ray diffraction strain measurements made along the specimen surface near the interface between the AI2O3 and the composite are shown in Figure 5 as a function of axial position along the sample. In this figure, the axial strain and hoop strain components are shown. The peak axial strain value was quite small, approximately 2 x lO"^ tensile within the AI2O3 and very little variation with distance from the interface was observed. The hoop strain values exhibited considerable scatter and larger errors, but the peak value appears to be compressive within the AI2O3 and occurs within 1 mm from the interface.

392 The results of stress measurements made along the specimen surface using optical fluorescence spectroscopy are shown in Figure 6 as a function of axial position along the sample surface. In this figure, the stress reported is the sum of the three principal stresses. As a result of the high spatial resolution (-50 îm diameter spot size) and small errors (estimated to be ±20 MPa), the entire stress distribution within the AI2O3 as the interface is approached is well characterized. The stress increases smoothly and gradually as the interface is approached. The maximum stress measured was on the order of 100 MPa and occurred at a location approximately 1 mm from the interface. —

1

—

1

—

1

—

(

—

Modeling Results FEM modeling results showing the predicted strain and stress distributions within the pure AI2O3 are J 11 '1 li r ' also shown in Figures 4-6 for each of the different cases (i.e. different constitutive assumptions) examined. Significant differences in the predicted peak strain and [ 'NI^T stress values were observed depending upon the '\ J constitutive assumptions. In all cases, the magnitude of the predicted peak strain/stress values decreased in the order Case l>Case 3>Case 4>Case 2. Case 1 resulted in the highest predicted strain and stress values whereas Case 2 resulted in the lowest values. These results can be explained by recognizing Figure 4. Neutron diffraction results showing the distribution of that in these analyses the thermal strains and stresses in the AI2O3 were dictated by the plastic flow properties of the volume averaged (a) radial the metal and composite. Case 1 used properties taken strain and (b) axial strain as a from the literature for fine grained Ni (approximately 50 function of axial position along îm grain size) resulting in a relatively high value for the the interior of the specimen. assumed yield strength, and since the composite properties were calculated using the modified rule-of-mixtures, the composite also exhibited a relatively high yield strength. In contrast, Case 2 used Ni properties characteristic of a coarse grained Ni microstructure (greater than approximately 1 mm grain size), resulting in very low estimates of the flow strength for both the pure metal and the composite. It is clear that the flow strength of the metal and composite play an important role in determining the magnitude of the residual stresses in the joint. The flow strength of Ni is determined primarily by grain size. In contrast, the flow properties of a composite material are generally influenced by additional microstructural aspects, such as amount and size of second phase, its spatial arrangement, interfacial characteristics, etc. These effects are considerably more difficult to assess, and this information is not readily included in simple, empirical models such as the rule-of-mixtures. portion of the specimen experienced significant grain growth during elevated temperature processing and had a final grain size of approximately 1 mm. Its properties were thus expected to be similar to those assumed in Case 2. In contrast, within the composite interlayer the presence of the AI2O3 particles limited the extent of grain growth and the final grain size was on the order of the interparticle spacing, approximately 35 |Lim. Therefore, when estimating the composite properties using ^ e rule-of-mixtures approach it would make sense to utilize the fine grained pure Ni properties assumed in Case 1. Although this calculation was not performed, it would be expected that the results would fall between those of Case 1 and Case 2. The point is that use of a single set of Ni flow properties for estimating the 1

1

1

Cm 1

•

1 . 1 1

—, / IH / 1

nnriron dlffraairon

flu

: 1'" AI2O3

1

1

^

60Ni-40Al203

D l i l o n e i from Intarfact ( m m )

393 behavior of both the pure metal and the composite would not be expected to result in accurate residual stress predictions. Note that near the r Microstmctural examination of the powder processed materials indicated the pure Ni adial freesurface (Figures 5 and 6) the differences in the peak stresses within the AI2O3 between the Case 1 and Case 2 predictions were significantly greater than within the specimen interior (Figure 4). This result is due to the fact that the plastic strains are predicted to be considerably larger at this location, and differences in the assumed flow characteristics of the composite therefore become more obvious. Case 3 was a calculation performed using properties actually measured for the bulk Ni and composite materials. As expected, the predicted strain and stress values fell between the Case 1 and Case 2 results. Case 4 used the same properties as in Case 3, except the assumed stress-free temperature was lowered from 1100 K to 700 K. Reducing the simulated temperature change during cooling resulted in a concomitant reduction in the peak strain and stress predictions. This result clearly indicates the importance of understanding and accounting for possible stress-relief mechanisms operating in any of the materials within the joint during cooling from elevated temperatures.

52 /«m from rodlol frw ijrfoc« 1 ^ ^ — Can 1 .

—

'1

—

•

f

Cait 2

y /

xray (Xffriiotisn

___-iiresf5i^'

. \\, . . . 1

/N\I

' %

^"1\

iK

-1

1 r

I

AIÔj

i

1 Composite

Dlitonct from InUrfae* (mm)

52 /im trom radial frat surfaiiB

Di*tone« from Inltrioc* (mi

Figure 5. X-Ray diffraction results showing the distribution of (a) axial strain and (b) hoop strain as a function of axial position along the surface of the specimen, at a fixed depth of 52 fim.

Discussion Figure 4 compares the strains measured using neutron diffraction with the FEM predictions. Due to the large sampling volume used in the neutron diffraction experiments it was necessary to manipulate the FEM results in order to directly compare the measured strains with those predicted by the model. This was accomplished by calculating an average value of strain from the elements that would have contributed to the diffracted intensity. The predicted strains shown in Figure 5 are the volume averaged results. Note that, within the experimental errors, both the magnitudes of the experimentally measured maximum strains, as well as the shape of the strain distribution, are in reasonable agreement with the FEM predictions for all of the numerical cases examined. Overall, these results suggest that the strain distribution within the interior of the specimen is relatively insensitive to differences in material properties, and therefore reasonably accurate modeling predictions can be expected using relatively simple constitutive assumptions. This can be explained by the fact that limited plasticity occurs in this region of the specimen, therefore the strain distribution is governed primarily by the thermal expansion coefficients and the elastic modulii of the materials, which are relatively independent of microstructure (i.e. to a first approximation they depend only on volume fraction). Of course, this conclusion is only valid for this particular specimen geometry since the fonnation and spreading of plastic zones during cooling is highly geometry dependent.

394 Due to the larger plastic strains predicted locally close to the interface near the surface of the specimen the situation is significantly different. Consequently, less satisfactory agreement between the measured and predicted strains and stresses was observed. Figure 5 compares the strains measured in the AI2O3 along the surface of the specimen using x-ray diffraction with the FEM results. The FEM results shown correspond to the strains predicted within a row of elements at a fixed distance of 52 |im from the radial free surface. This depth Composite compares reasonably well with the calculated - 4 - 3 - 2 - 1 0 penetration depth of Cu Ka^ radiation in Oistanco from interfoce (mm) AI2O3, approximately 35 |im. The FEM predictions of the axial strain appear to overFigure 6. Optical fluorescence spectroscopy predict the strain values measured using x-ray results showing the sum of the principal diffraction for all numerical cases studied. stresses as a function of axial position along The stresses measured in the AI2O3 the surface of the specimen, at a fixed depth along the surface of the specimen by optical of 52 |im. fluorescence spectroscopy are shown in Figure 6, along with the FEM predictions. These FEM results are also presented for a depth of 52 fim from the radial free surface, comparable to the penetration depth of the laser in AI2O3, which has been measured to be --50 jim. Note that the shape of the stress distribution is well predicted by the FEM model, and the measured distribution is in reasonable agreement with the FEM predictions for Case 2 or Case 3. However, the peak value of stress is overestimated by the model for all cases, and the location of the maximum stress is predicted to be much closer to the interface between the AI2O3 and the composite. The calculations predict a significantly steeper strain gradient immediately adjacent to the interface than was observed experimentally. These results suggest that a localized stressrelief mechanism operates in this region of the specimen in response to the large concentration of strains and stresses (including significant plasticity) near the intersection of the interface with the free-edge. There are several possible strain/stress relief mechanisms that could be considered to explain these results. For example, microcracking in the AI2O3, partial debonding at the interface, or damage accumulation within the composite, each could result in lower peak strain and stress values in the AI2O3. No microstructural evidence for any of these mechanisms has yet been found within as-fabricated joints. However, mechanical property studies carried out on bulk 40 vol.% AI2O3-6O vol.% Ni composites has demonstrated that damage does accumulate during large-scale plastic deformation, and that models incorporating microstructural damage (in the form of fractured particles, separation of contiguous AI2O3 particles, or particle-matrix interfacial decohesion) can adequately explain the observed deformation and fracture behavior of this material [26]. It is difficult to quantitatively assess the effects of any potential stress-relief mechanisms using the continuum models presented here, since the edge-stress concentration and its effects occur on a size scale comparable to the microstructure. Additional experimental work is needed to characterize the evolution of the residual strain and stress state in this area of the specimen during cooling, and new modeling methodologies incorporating detailed microstructural information will be required to allow local material response to be predicted. 52 /im from rodiql free surface

395 Summary Residual strains and stresses were studied experimentally using a variety of techniques in a model ceramic-metal joint containing a thick, homogeneous composite interlayer. An elastic-plastic FEM model was used to investigate the residual strains and stresses in the joint, and to investigate the role of the assumed interlayer properties on the predicted strains and stresses. The elastic strains measured in the specimen interior using neutron diffraction were found to be in excellent agreement with model predictions made using a simple, modified rule-of-mixtures approach to estimate the joint interlayer properties. It is therefore demonstrated that, excluding edge-effects, FEM models can be used to reliably predict strain and stress distributions within composite and graded interlayer joints, provided reasonably accurate material property estimates are available. Using two independent measurement techniques (x-ray diffraction and optical fluorescence spectroscopy) it was shown that the strains and stresses in the Al2C)3 measured along the specimen surface are lower than what was predicted by the FEM model, suggesting that stress-relief occurs during cooling from the joint fabrication temperature. No experimental evidence for the occurrence of any stress-relief mechanisms has been found, however, it is believed that large, localized plastic strains may have induced damage within the composite interlayer. Acknowledgments Research sponsored in part by the U. S. Department of Energy, Office of Energy Research, Office of Basic Energy Sciences, under DOE Idaho Operations Contract DE-AC0794ID13223, and in part by the Assistant Secretary for Energy Efficiency and Renewable Energy, Office of Transportation Technologies under DOE Oak Ridge Operations Contract DE-AC05-96OR22464. References A. H. Carim, D. S. Schwartz and R. S. Silberglitt (eds.). Joining and Adhesion of Advanced Inorganic Materials, Mater. Res. Soc. Symp. Proc, Vol. 314. Materials Research Society, Pittsburgh, PA, 1993. A. J. Moorhead, R. E. Loehman and S. M. Johnson, Structural Ceramics Joining II, Ceramic Trans., Vol. 35. The Amercian Ceramic Society, Westerville, OH, 1993. T. Suga, K. Mizuno and K. Miyazawa, "Thermal Stresses in Ceramic-to-Metal Joints"; pp. 137-142 in Metal-Ceramic Joints, Proc. MRS International Meeting on Advanced Materials, Vol. 8. Edited by M. Doyama, S. Somiya and R. P. H. Chang. Materials Research Society, Pittsburgh, PA, 1989. D. Munz, M. A. Sckuhr and Y. Yang, "Thermal Stresses in Ceramic-Metal Joints with an Interlayer," /. Amer. Ceram. Soc., 78 [2] 285-290 (1995). H.-Y. Yu, S. C. Sanday and B. B. Rath, "Residual Stresses in Ceramic-Interlayer-Metal Joints," /. Amer. Ceram. Soc., 76 [7] 1661-1664 (1993). 1. M. Kurita, M. Sato, I. Ihara and A. Saito, "Residual Stress Distribution of CeramicMetal Joint"; pp. 353-362 in Advances in X-Ray Analysis, Vol. 33. Edited by C. S. B. e. al. Plenum Press, New York, 1990. S. Tanaka and Y. Takahashi, "Effects of X-ray Beam Collimation on the Measurement of Residual Stress Distribution in a Si3N4/Steel Joint," ISIJInternational, 30 [12] 10861091 (1990). O. T. lancu, D. Munz, B. Eignemann, B. Scholtes and E. Macherauch, "Residual Stress State of Brazed Ceramic/Metal Compounds, Determined by Analytical Methods and Xray Residual Stress Measurments," /. Amer. Ceram. Soc., 73 [5] 1144-1149 (1990). L. Pintschovius, N. Pyka, R. Kubmaul, D. Munz, B. Eigenmann and B. Scholtes, "Experimental and Theoretical Investigation of the Residual Stress Distribution in Brazed Ceramic-Steel Components," Mater. Sci. Eng., A177 55-61 (1994).

396 10. X.-L. Wang, C. R. Hubbard, S. Spooner, S. A. David, B. H. Rabin and R. L. Williamson, "Mapping of the Residual Stress Distribution in a Brazed Zirconia-Iron Joint," Mat ScL Eng., A211 45-53 (1996). 11. H. Li, L. Z. Sun, J. B. Li and Z. G. Wang, "X-ray Stress Measurement and FEM Analysis of Residual Stress Distribution Near Interface in Bonded Ceramic/Metal Compounds," Scripta Materialia, 34 [9] 1503-1508 (1996). 12. B. H. Rabin, R. L. Williamson, R. J. Heaps and A. W. Erickson, "Powder Processing of Nickel-Aluminum Oxide Gradient Materials"; pp. in press in PM' 92, Proceedings of the 1992 Powder Metallurgy World Congress. Edited by Metal Powder Industries Federation, Princeton, NJ, 1992. 13. B. H. Rabin and R. L. Williamson, "Design and Fabrication of Ceramic-Metal Gradient Materials"; pp. 145-154 in Processing and Fabrication of Advanced Materials III. Edited by V. A. Ravi, T. S. Srivatsan and J. J. Moore. The Minerals, Metals and Materials Society, Warrendale, PA, 1994. 14. B. H. Rabin, R. L. Williamson, H. A. Bruck,. X.-L. Wang, T. R. Watkins and D. R. Clarke, "Residual Strains and Stresses in an Al203-Ni Joint Bonded with a Composite Interlayer: FEM Predictions and Experimental Measurements," to be published in /. Amer. Ceram. Soc, 1996. 15.1. C. Noyan and J. B. Cohen, Residual Stress, Measurement by Diffraction and Interpretation, a) p. 101-2, b) p. 118, Springer-Verlag, New York, 1987. 16. R. A. Winholtz and J. B. Cohen, "Generalized Least-squares Determination of Triaxial Stress States by X-Rays Diffraction and the Associated Errors," Aw^t. /. Phys., 41 189-99 (1988). 17. Q. Ma and D. R. Clarke, "Stress Measurement in Single-Crystal and Polycrystalline Ceramics Using Their Optical Flourescence," / Amer. Ceram. Soc., 16 [6] 1433-1440 (1993). 18. Q. Ma and D. R. Clarke, "Piezospectroscopic Determination of Residual Stresses in Polycrystalline Alumina," /. Amer. Ceram. Soc., 77 [2] 298-302 (1994). 19. R. L. Williamson, B. H. Rabin and J. T. Drake, "Finite Element Analysis of Thermal Residual Stresses at Graded Ceramic-Metal Interfaces, Part I: Model Description and Geometrical Effects," / Appl Phys., 74 [2] 1310-1320 (1993). 20. J. T. Drake, R. L. Williamson and B. H. Rabin, "Finite Element Analysis of Thermal Residual Stresses at Graded Ceramic-Metal Interfaces, Part II: Microstructure Optimization for Residual Stress Reduction," /. Appl. Phys., 74 [2] 1321-1326 (1993). 21. W. Betteridge, Nickel and its Alloys. Ellis Harwood, Ltd., West Sussex, UK, 1984. 22. M. A. Meyers and K. K. Meyers, Mechanical Metallurgy: Principles and Applications, p. 345, Prentice Hall, Inc., Englewood, NJ, 1984. 23.1. Tamura, Y. Tomota and H. Ozawa, "Strength and Ductility of Fe-Ni-C Alloys Composed of Austenite and Martensite with Various Strength"; pp. 611-615 inProc. 3rd Int. Conf. Strength of Metals and Alloys. Edited by Institute of Metal and Iron, London, 1973. 24. R. L. Williamson, B. H. Rabin and G. E. Byerly, "FEM Study of the Effects of Interlayers and Creep in Reducing Residual Stresses and Strains in Ceramic-Metal Joints," Composites Eng., 5 [7] 851-863 (1995). 25. S. Spooner and X.-L. Wang, unpublished research, Oak Ridge National Laboratory, Oak Ridge, TN, 1995. 26. H. A. Bruck and B. H. Rabin, "Deformation and Fracture Modelling of Nickel-Alumina Composites for FGMs," Acta Metall. Mater., submitted for publication (1996).


397

Residual Thermal Stresses in Functionally Graded Ti-TiCx Materials. N. Frage^, M.P. Dariel^, U. Admon and A. Raveh Department of Materials Engineering, Ben-Gurion University, Beer-Sheva, Israel, Nuclear Research Center-Negev, P.O.Box 9001, Beer-Sheva, Israel. ABSTRACT Graded Ti-TiC nanoscale multilayers transform after an appropriate interdiffusion anneal into a functionally graded (FG) region between a TiC hard coating and a Ti substrate. Using the available database regarding the properties of the TiC^ solid solution, it was possible to develop analytical expressions for the residual thermal stresses that develop in the FG-material. It was shown that by appropriate design of the graded concentration in the initial multilayer, it is possible to generate compressive stresses in the vicinity of the ceramic-like edge of the FGtransition zone.

1. INTRODUCTION AND BACKGROUND A functionally graded material (FGM) is a composite, consisting of one or more phases, with its composition varying in some spatial direction. The design is intended to take advantage of certain desirable features of each of its constituents. We are focusing our attention on the titanium (metal) - titanium carbide (TiCx) combination. According to the Ti-C phase diagram, the carbide phase has a wide homogeneity range that extends from TiCg 43 to TiCg gg. The extended composition range of the TiCx phase is a key element in the approach we suggest for interface tailoring and which consists of diffusion anneal of a graded Ti-TiC multilayer. The multilayer is produced by sputter-coating on an appropriate Ti substrate of Ti-TiC bilayers with constant thickness. Whereas the thickness of each bilayer is kept constant, the thickness of the individual components in each bilayer, namely that of Ti and of TiC, varies according to the required design, as shown schematically in Fig. la. A hypothetical but plausible outcome of a short diffusion anneal will result in a different configuration of the two phases, as shown in Fig. lb. During the cooling stage after the diffusion anneal, thermal stresses, that may impair the performance of the system, are generated within the thin layer coating. The object of this study was to examine whether an appropriate design of the FGM region may alleviate the effect of the residual thermal stresses. Consider an ordinary substrate-ceramic coating combination. Such a composite system, prepared at elevated temperatures and subsequently cooled to room temperature, will be thermally stressed due to the usually large difference in thermal expansion and elastic moduli of the substrate and coating. These stresses often exceed the fracture strength of the ceramic component, particularly in regions close to free surface near the interface. This leads to either cracking of the ceramic part or to failure at the substrate-coating interface.

398 component, particularly in regions close to free surface near the interface. This leads either to cracking of the ceramic part or to failure at the substrate-coating interface. The residual thermal stresses in a substrate-coating combination are due to the interfacial forces arising from the thermal expansion coefficient mismatch between coating and substrate and from the presence of a lending moment [1]. The former are uniformly distributed over the film thickness while the laUe'" arises from the requirement to balance the external bending moment induced by the interfacial force in a coating-substrate combination and varies across the film thickness [2]. Functionally graded materials by virtue of the gradual change in the thermal expansion mismatch over the transition region offer a solution and can minimize the thermal stresses arising from cooling or heating (a) Multilayer Coating (n layers)

[Substrates, k y y y y y yl

KTiC fcoatingi

(b) Single phase Ti(C) solid solution -• •Two-phase region

Ti Substrate H

Single phase Tie region

[Tie

3

[Coating j

't A rt rt rt rt rt

Fig.l. (a) Schematic view of graded multilayer. The two basic components of;the multilayer are Ti and TiC layers. The basic unit of the multilayer is a juxtaposed double layer of Ti and Tie. This basic unit has a constant L width. The relative width of the two components of this basic unit varies, however, as one proceeds from one end of the multilayer to its other. In the vicinity of the Ti substrate, the Ti component makes up most of the basic unit; on side, this basic unit consists mostly of the TiC component, (b) Schematic drawing of the possible outcome of the diffusion anneal on the microstructure of the functionally gradient region. 2. THE MODEL We have used one-dimensional model [3] to calculate the residual stresses in the system involving a ceramic-like (TiC) coating connected to a metal-hke (Ti) substrate by an inter-mediate PGM region, consisting (ultimately after the interdiffusion anneal) of titanium carbide with a carbon concentration that varies with distance. The PGM plate has a thickness 2c, unit dimension in depth (z-direction) and is infinitely long in the x direction, as shown in Fig. 2. The composition in any xz plane is held constant. The carbon concentration, actually the titanium carbide composition, x in TiC^, varies within the transition region in the y direction according to a given functional form. We have used such a function after Wakashima et al. [4], Eq.(l), where y^ and y2 are border regions of pure phase 1, Ti, and phase 2, TiC, respectively. This function has the ability, depending on the single parameter, N, of being either "concave upward" and "concave downward".

399

c,max

/(y) =

[y2-yi J

(1)

FGM

Knowledge of / (y), and the composition-dependent microstructure, allows to determine the y-dependence of the effective values of the coefficient of Tie thermal expansion and Young's Figure 2. A schematic view of the modulus. These, in turn, can be used to Functionally Graded Material system calculate the stress distribution across the transition layer. In principle, this allows to establish a linkage between FGM design and performance, where/ (y) is related to design, while the calculation of the residual stresses is related to performance. We have adapted this function to a single-phase FGM based on nonstoichiometric titanium carbide TiCj^. It is possible to treat the nonstoichiometric carbide as a solution of titanium carbide of high carbon content (TiCo.98) and added titanium. Note that x^Mc/Mxi where M stands for the number of moles, and JA, the molecular weight is equal to 48, 12 and 59.76 g/mole for Ti, C and TiCo.98, respectively. The value of x can written as :

59.76 AS

xO.98

4704(1-m^.) 48 + 11.76m„.

(2)

59.76

where rrij.. is the titanium wt. fraction in Ti - TiCo.98 mixture (in the pre-diffusion anneal stage, as shown in Fig.la). When mj.= 0.456, x=0.48, and mj.=0, jc=0.98. Assuming that wt. fraction of titanium in mixture varies according to the function (3), we obtain for the dependence of x in the y direction (eq.4), within FGM region: S my.. = 0 4561

^

•^'"°

(3)

1-0.456 [ y-ynnn 1 ^ jc=47. 04|

b

-V-I

I 48 + 5.363 - ^ - ^ \

L -'max

-î

I ^1

jJ

(4)

The dependence of m xi and x on the distance (>') for a transition region 10 /<m is shown in Fig.3, for several values of N (0.2, 1,5), values that determine both the curvature and the steepness of the dependence. The relevant thermophysical parameters (expansion coefficient and Young modulus) of the TiC phase vary with the carbon content and, therefore, along the yaxis in the FGM region. Using reported data values in the literature [5], one can plot the xdependence of these parameters that can be approximated by the following expressions: a=(9.61-2.09jc)xl0"^^"'

(5)

E=l94 + 293.6x,GPa

(6)

400 and using expression (4) for x, we can deduce the y-dependence of a and of E,

f

147.04

a{y) = 9.61-2.09^

u

iri

y-Vm

Li>«Hil2™2iJi_^ ^ 10^j^-' f y-y^n 1 48+5363 147.0411 - ; - ^ ^"^

£(j)= 194.4+293.61

\

[..^min

1)'^^

^m

- KGi'^ 48+5.363' ^ ^™ ' L-^min

0'>

(7)

(8)

^max J

-0—m(Ti), N=1 1 -x--x{y), N^Tl --B--m(Ti),N=5 I - ^ - - x ( y ) , N=5 1 • ••- -mcro, N=0.2| —M- x(y), N=0.2|

d*

'^•Vr**',iiMy 60 urn

Optics microscope photo

Figure 3. Photomicrostructure of TiC-NisAl with various mixing ratios of TiC and NisAl.

405 3.MICROMECHANICAL MODEL FOR THERMAL STRESS CALCULATION In this paper, a spherical-shaped micromechanical model is considered. The diameter of the inside sphere is 5|am, the thickness of the outside spherical shell can be changed. The calculation condition for the thermal load is sintered at 1300°C and cooled down to room temperature (25°C). 3.1 Formulation Due to the spherical symmetrical problem, an spherical symmetrical equilibrium equation can be written as:

=0

dR - + - R The strain-displacement relations are expressed as

(1)

dUo

^'~

dR

(2)

The stress-strain relationship are expressed as aET l + ju 1 - 2 / / E

M

\ + ju , 1 - 2 / /

"

1-2;/

(3)

oET -O+Sj.

1-2//

Substituting expression (2) into equation (3) yields E \

fi

_ du„\ du,^

oET \-2ju

E

(7r =

Ur M -e+1 + //U-2//

(4)

oET 1-2//

Introducing expression (4) into equation (1) and applying expression (2), we find Un=-—-a—j] TR^dR + CR^—:r ^ \-ju R^ J^ R^ 2aE 1 EC 2ED 1 TrdR + c r „ = - \-juR' 1-2// l + ^R'

(5)

f

oE C7r =

1-//

U

EC TR^dR + 1-2//

ED

(6)

1

oET

\ + juR'

\-ju

(7)

The integrating constants C and D are to be determined by the condition of compatibility of the interface of the TiC sphere and the outside spherical shell NisAl.

406 3.2 The radial displacement of TiC ceramic sphere Considering a TiC ceramic sphere as shown in figure 4, the sphere is subjected to a uniform load qi, the radius is equal to a.

Figure 4. TiC ceramic sphere

Figure 5. NisAl spherical shell

The boundary conditions are given by (8) (9) Substituting equation (8) and (9) into expression (5) and (6) yields

1+A

r ^ l z M \^(Ê,T

(10)

*«i

3.3 The radial displacement of NiaAl spherical shell Considering a NiaAl spherical shell as shown in figure 5, the inside of the spherical shell issubjected to a uniform load qi, the inside radius and the outside radius of this spherical shell are equal to a and b respectively. The thickness of NisAl is equal to subtracting afromb. The boundary conditions are given by

(o-«X^, = - ^ 2

(11)

(^«L*=0

(12)

Substituting equation (11) and (12) into expression (6) and using expression (5) leads to MR2=-

4l-2/^)

laÊJ'

a

3(l-//.)^^-«

r92

(i+;^VV lEâ%^-a')

(13)

3.4 The determination of the interface stress When the temperature varies , the TiC ceramic sphere and NisAl spherical shell are deformed simultaneously. The displacement of the interface between TiC sphere and NiaAl spherical shell are equal, namely, it must satisfy the condition of compatibility of the interface displacement, and the radial stress is equal and opposite in the interface.lt can be written as "/?] = ^R2

(14)

qx=qi=q

(i5)

407 From expression (14) and (15), we can obtain 1+M 3(1-A)

^ ^ 1 - 2A

^(1-2//^) laÊjT

2«i£ir 3(1-A)

-^

a^q

3(1-/^)" (16)

4.ANALYZING RESULTS AND DISCUSSION In this study, the properties of TiC and NisAl are for TiC, ai=7.4xlO"^/K, Ei=320GPa, m=0.195 for NisAl a2=11.9xlO-^/K,E2=199GPa, 1^2=0.295 When a=2.5|im, b=3.0|im, t=0.5|Lim andT=-1275K, substituting the upon data into equation (16) and solving , we find q =— 460.5MPa. For the same reason, we can obtain the results that when t is equal to 0.4|im, 0.3|im, 0.2|im and 0.1|im, q is equal to -392.1MPa, -313.8MPa, -223.9MPa, -120.2MPa, respectively. Based on the evaluated interface stress, the radial residual thermal stress and tangential residual thermal stress of different NisAl thickness are calculated. Figure 6 shows the relationship between the radial stress and NisAl thickness. In this figure, the radial stress in the TiC ceramic sphere is uniform compressive stress and the magnitude of this stress increases with the increment of thickness of NisAl. The radial stress is equal to zero on the outside surface of NisAl spherical shell. Figure 7 shows the relationship between the tangential stress and NisAl thickness. In this figure, the tangential stress in the TiC ceramic sphere is also uniform compressive stress and the magnitude of thes stress increases with the increment of thickness of NisAl. However, the tangential stress suddenly becomes tensile stress in the NisAl spherical shell area. The magnitude of this stress is increased with the decrement of the thickness of NisAl. For the thickness of NisAl is proportional to the content of NisAl, in other words, the radial compressive stress and tangential compressive stress increase with increment of the content of NisAl; the tangential tensile stress is decreased with the increment of the content of NisAl. This is a very important phenomenon and in agreement with the previous test results in which the strength of TiC-NisAl composites is increased with the increase of the content of NisAl. The larger the radial compressive stress, the harder to fracture in the radial direction in the material; the larger the tangential tensile stress, the easier to fracture in the tangential direction in the material. So, the failure mechanics of TiC-NisAl composite may be different in different content of NisAl. 5.CONCLUSIONS Through the analysis of a spherical-shaped micromechanical model of TiC-NisAl, the following conclusions can be drawn (1) The radial and tangential residual thermal stress in TiC sphere is a uniform compressive

408

(2)

(3)

stress and increase with the increase of the thickness of NisAl; The radial stress in NisAl spherical shell is rapidly decrease and equal to zero on the surface of the sphere, the tangential tensile stress is decrease with the increase of the thickness of the thickness of NisAl; The different content of NisAl may cause different failure mechanics. 100 0 -100^1\D

—1

0.5

1.0

m

i_

1.5

2.0

2

-200

•'•'!

-300

••!!

-400 -500 -600

t=0.1 t=0.3 t=0.5

t=0.2 t=0.4

-700 Radial length,|Lim

Figure 6. The relationship between radial stress and thickness of Ni3Al(t, |Lim) 1800 c« 1400

1=0.1 t=0.2

. 1000

1=0.3 t=0.4 t=0.5

200 ^

-200o[er -TQ:^-r.WT.TX-Jr.z.t.^r. ^.5

3

-600 Radial length,|;im

Figure 7. The relationship between tangential stress and thickness of Ni3Al(t, |im)

ACKNOWLEDGEMENTS This work was supported by the National Science Foundation. REFERENCES 1. J.H.Wang, Q.J.Zhang and D.H.Wu, J.Compos. Soc.,Vol.l3,No.2, (1996),89-93. 2. L.M.Zhang, J.Liu R.Z.Yuan and T.Hirai, Materials science & engineering, A203 (1995) 272-277.


409

New application of FGM to identification of unknown multicomponent precipitates I. Itoh% H. Yaraada', Y. Kojima', Y. Otoguro% H. Nakata' and M. Matubara' ^Department of Mechanical System Engineering, Gunma University 1-5-1, Tenjin-Chou, Kiryu-Shi, Gunma, 376, Japan ''Graduate Student, Gunma University

1. INTRODUCTION It is well known that FGM is developed to relax the thermal stress which generates near the bonding interface of metal and ceramics. Recently FGM has been actively applied to many other fields. For example, .there is a research project on the development of energy conversion materials through the formation of gradient structures(Research periodiPhase 1 Fiscal 1993 to 1995)[1]. We have joined the project and studied the diffusion bonding of AI2O3 and Mo using the Al-Sn bonding method which we developed[2]. The objective of this research is to offer the new application of FGM that is the compositionally graded material(CGM). It is difficult to identify multicomponent precipitates because of the lack of multicomponent phase diagram and X-ray diffractometer's data. Then we try to develop the method by which the precipitates can be easily identitified, that is, the method using CGM. When the diffusion couple of Cu-10 mass^Sn and Al-0.5 mass%Sn is heated at 773 K which is lower than the eutectic temperature of 821 K in Cu-Al system, 4 intermetallic compounds are formed in the diffusion layer[3]. In this research, these compounds are judged by using CGM.

2. EXPERIMENTAL METHOD Diffusion couple of Cu and Cu-10 mass%Sn is pressed with screws of a clamp and treated at 1173 K for 360 ks in a vacuum of about lO^^Pa. Each specimen size is 10 mm cube. One of the 10x10 mm surfaces is selected as the bonding surface. The bonding surfaces of Cu and Cu-lOmass^Sn are polished with a #800 polishing paper. After bonding, the couple is cut perpendicularly to the bonding interface and separated into two pieces. These pieces have the same size of 20 mm in length, 10 mm in width and 5 mm in thickness. The cross section of one piece is polished with 1 //m-diamond powder for analysis of each element near the interface using EPMA. The other piece is used for identification of the intermetallic compounds as mentioned later. Both pieces change gradually in concentration of Sn from 0 to 10 mass%, that is, CGM.

410 Next the CGM is used as one piece of diffusion couple bonded to the other piece of Al-0. 5 massJKSn whose size is 20 mm in length, 10 mm in width and 5 mm in thickness. We call this couple the compositionally graded diffusion couple(CGDC). The bonding surfaces of the couple are 10 mmx20 mm in size and polished with jJSOO polishing paper. This couple is heated at 773 K for 7.2 ks under the pressure of 2MPa in the atmosphere. After this treatment, the couple is cut perpendicularly to the bonding interface and in parallel to the direction of the length at the middle point(Ref. Figure 1). The cross section of one piece is polished for the observation of the structure using SEM and optical microscope, and for analysis of each element near the bonding interface. From now on, we will adopt the simple expression of CGDC which contains the concrete heat treatment, that is, in this case Cu:eu-10Sn(1173K-360ks)/Al-0. 5 Sn(773K-7. 2ks).

3. EXPERIMENTAL RESULTS

Figure 1, (a) Schematic diagram of the method to make the compositionally graded diffusion couple. (b) Schematic view of the intermetallic compounds formed in the couple mentioned in (a). (c) and (d) Composition images using EPMA on Cu side and Cu-lOSn side near the bonding interface, respectively.

411 Figure l-(a) shows the schematic diagram of the method to make the compositional ly graded diffusion couple. The couple of Cu/Cu-10 mass^Sn has the diffusion zone of 2 mm in length after heating. Figure l-(b) shows the schematic view of the intermetallic compounds formed in the couple mentioned above. Figures l-(c) and l-(d) show the composition images using EPMA on Cu side and Cu-lOSn side near the bonding interface, respectively. The concentration of Sn gradually increases from 0% on Cu side to IQ% on Cu-lOSn side. Such intermetallic compounds as 7 2, 772 and 6 are formed at the interface of Cu side from Cu to Al-0. 5Sn alloy[4]. 4 intermetallic compounds of a'^d are formed at Cu-lOSn side. The intermetallic compounds of b, c and d are identified as r 2, V2 and 6 according to the continuation of structure from Cu side to Cu-lOSn side, respectively. Each thickness of these intermetallic compounds almost does not change throughout the couple and the total thickness of those keeps about 20 jim in width. The intermetallic compound of a, which is produced in the concentration range of Sn over 2.5%, shows an island having 20 to 30//m in length and 5 to 10 //m in width. This compound is cleared to be d phase(Cu-32 mass%Sn) in CuSn system by a quantitative analysis of EPMA. Figure 2 shows SEM and Sn X-ray image at the interface of the couple of Cu and Cu-lOSn bonded at 773 K for 14. 4ks. Sn concentrates at the interface of Cu and r 2. Thus the concentration of Sn on Cu-lOSn side is considered to create the intermetallic compound of 6,

Figure 2. SEM and X-ray image at the interface of the couple of Cu/Cu-lOSn bonded at 773 K for 14. 4ks.

4. APPLICATION OF CGDC TO OTHER CASE Figure 3 shows the structures throughout CGDCs of Cu:Cu-8Al(1173K-360ks)/ Cu-52Zn(/S-brass, 973K-57. 6ks) and Cu:Cu-4Si(1173K-360ks)/Cu-52Zn(973K-57. 6ks). In both couple, the growth of )S-brass into Cu alloy increases with increasing the content of Al or Si, and the width of /S-brass on Al or Si rich side is about two times compared with that on Cu side. Moreover, a structure like martensite is formed in yS-brass on Al or Si rich side. Also, the layer

412 of new precipitate is recognized at the interface of Cu and )S-brass on Si rich side. Thus, many information can be obtained by only one CGDC and will be available in the field of surface-treatment. 1. Itoh also reported the effect of the moving direction of the interface on morphological stability of al fi phase interfaces in the Cu-Zn system using the CGDC of Cu:Cu-52Zn(973K-72ks)/Cu(973K-57. 6ks)[5]. The details will be omitted here.

Weld I Interlace Cu-SAl

Figure 3. CGDCs of Cu-Al alloy or Cu-Si alloy and )8-brass.

5. CONCLUSION As a new application of FGM, the identification of unknown multicomponent precipitates in the system of Cu-Al-Sn is studied. Three among four intermetallic compounds can be identified as r 2, ?7 2 and Q in the system of Cu-Al with using the compositionally graded diffusion couple(CGDC). Also, CGDC is expected to use in many fields. As one example, the surfacetreatment is proposed to fit this case.

REFERENCES 1. S. Sasaki, FGM News No. 31(1996) 2. Journal of FGM Forum. The Society of Non-Traditional Technology. 2. I. Itoh, H. Yamada, T. Ichiba, Y. Kozima and Y. Otoguro, Proc. of 17mm Diameter of heated area: -1 0 1 a z(GPa) .

i

1000 1

Figure 2. Distribution of residual stress in SiC-TiC-Ni system. T : tension, C : compres.

500^ 3 5 1

1

^^-^°^^^^—^11:^ —o o 1

1

10 15 Layer number

1

20

Figure 3. Change in residual stress with the number of layers.

ent materials, in which the composition was linearly graded between SiC and TiC, and between TiC and Ni. In the present system, the thermal expansion coefficient varies in the following order: SiC(4.8xlO-^rC) < TiC(8.0xlO-V°C) < Ni(16.8xlO-^rC). When the SiC-TiC part was mechanically polished after hot-pressing, cracks were sometimes formed on the surface of TiC layer, especially in samples (a) and (b). This is caused by residual stresses generated from the gap in thermal expansion coefficient between SiC and TiC. After bonding to the TiC-Ni part, cracks were also formed in the ceramic part of SiC-TiC-Ni system of samples (a) and (b). The example is shown in Figure 1. Cracks proceeded typically in the perpendicular direction from SiC surface and in the parallel direction along the interface in SiC layer. Cracks were not observed in samples (c) and (d). 3.2. Residual stresses The stress distributions, which cause cracking in the ceramic part, are typically characterized by two stress components as follows: tensile stress parallel to interface near disk center; tensile stress perpendicular to interface near disk edge [2]. The residual stresses were calculated for cooling process after bonding of the ceramic part to the metallic part. Figure 2 shows one example of the stress distributions along gradient direction (z-axis). ax is the residual stress parallel to interface. Large tensile stress exists on the surface of SiC layer. This stress causes cracking in the perpendicular direction from SiC surface, a z is the residual stress perpendicular to interface at disk edge. Large tensile stress also exists in the range from TiC to SiC. This stress causes cracking in the direction parallel to interface. These calculations can explain the cracking behavior of layer composite of SiC-TiC-Ni system as indicated with a x and az in Figure 1. The variation of residual stresses with the number of layers was evaluated with respect to tensile stresses on the surface of SiC layer and in the middle of SiC-TiC part at disk edge in the stacking model seen in Figure 2. The results are shown in Figure 3. It is confirmed from the calculations that the residual stresses are effectively reduced by increase of the number of layers.

422

iKjc(//)

H100M,m Figure 4. Vickers indentation on section surface of SiC+TiC layer.

Figure 5. Fracture toughness of section surface of SiC-TiC part (sample (c)).

Crack propagation by the Vickers indentation was observed to prove the presence of residual stresses. When the surface of SiC layer was indented, the crack propagation was serious near disk center. This means that tensile stress expanded the cracks on SiC surface. Figure 4 shows the crack propagation on the section of the ceramic part. It was found that the cracks parallel to interface were longer than those perpendicular to interface. This means that tensile stress was large in the perpendicular direction to expand the cracks. These results are well consistent with the expectation from the calculation of stress distributions. The fracture toughness of section surface was evaluated from the crack length in each direction, that is, parallel or perpendicular direction, by using Niihara's equations [3]. The result of sample (c) is shown in Figure 5. The fracture toughness was smaller in the parallel direction than in the perpendicular direction over the range from SiC to TiC, because large tensile stress existed in the perpendicular direction. The fracture toughness exhibited the maximum around 50vol% TiC in both directions. Such an improvement of fracture toughness has been reported in the particulate composite of SiC-TiC system [4, 5]. In the present work, the cracks were formed especially at or near SiC layer although large tensile stress was imposed over the whole range of the ceramic part as seen in Figure 2. It is thought that some strengthening effects work in other layers. 3.3. Electrical properties of SiC-TiC system The multilayer composite of SiC-TiC system was sintered in N2 to make SiC semiconductive by nitrogen doping. It is known that nitrogen is incorporated into SiC and works as electron donor [6]. However, N2 atmosphere retards the sintering of SiC. Figure 6 shows typical microstructures of SiC+TiC layers sintered in N2. Many pores were observed when the content of SiC was above 70vol%. In Figure 6, black matrix is assigned to SiC and white grains to TiC. With increasing content of TiC, TiC grains connected to each other and formed the network. The V-I curve of the multilayer composite, which had the same structure as in the

423

TiC : 10vol%

TiC : 50vol%

Figure 6. Section surface of SiC-TiC multilayer composite (sintering atmosphere : N2).

i a -0.4

-0.2

0.0

0.2

0.4

0.6

Voltage (V)

Figure 7. V-I curves of SiC-TiC systems. Specimen size : d=10mm-^. \^^ '>^. .>\. .y\.

/y // =//

r

// =//

f/ =/y

// =^/^ ff =/y

ff =/y

.Main/Inner-Guard Heater Plate -Control RTD Plate W

ff =

-Heat Flux Transducer

Figure 3. Schematic of the measurement stack of the one-sidedguarded-hot-plate. is used in our apparatus, rather than two. Figure 3 shows the important features of the measurement system. Heat-flow calculations show that the one-sided nature of the apparatus reduces heat losses. Details of the apparatus design are found elsewhere [5, 6]. The principle of operation is to create one-dimensional axial heat flow through the specimen so that the Fourier heat conduction equation may be used to determine thermal conductivity: q = -kA

dx

(1)

where q is steady-state heat flow, k is thermal conductivity, A is the specimen cross-sectional area and -dT/dx is the temperature gradient [7]. Heat is injected electrically into the main / inner guard heaters at a constant power density over the plate surface. The plate below the main / inner guard plate has a platinum resistance temperature detector (RTD) embedded in it to measure the absolute control temperature for the measurement stack. The outer guard cylinder is controlled to the same temperature as that of the main / inner guard plate. The inner and outer guards keep heat from the main heater from flowing radially. The bottom heater plate is also controlled to the same temperature as the main / inner guard plate so that heat from the main heater cannot flow downward. Therefore, all of the heat generated by the main heater flows upward, through the thermocouple plates and the specimen, and into the heat sink, where the heat is radiated away to the cooler furnace. Knowledge of the specimen's crosssectional area, coating thickness, temperature difference across the specimen as determined from the thermocouple plates, and steady-state heat flow as measured using the electrical power input to the main heater, yields the raw data needed to calculate the thermal conductivity.

428 This raw data, when used in equation 1, gives total I I I I I I I I I I I thermal conductivity, E which is shown in figure 4. The total thermal 5 . i....Q..O..O-.6.^.conductivity data 6 o o o p '^ represent essentially five •>
•p 23 stainless steel substrate, o we use data obtained "a previously on 410 stainless steel [8]. Figure 5 shows thermal conductivity as a function E 21 of temperature for 410 stainless steel as measured 20 in the guarded hot plate. 400 500 600 700 $00 900 1000 We extrapolated the quadratic fitting function Temperature, K to 1200 K for this work. Figure 5. Thermal conductivity of 410 The properties of 403 and stainless steel. 410 stainless steel are similar since 403 and 410

429 stainless steels have the same 0.000 28 composition, except 403 stainless steel has a narrower 0.000 26 acceptable chromium range [9]. We also use 0.000 M data measured previously on the interfacial resistance 0.000 2 Z L between stainless steel 410 and the upper thermocouple 0.000 2 plate for the interfacial resistance o between the t : 0.00018 substrate and measurement plate 0.00016 required here. 500 600 700 800 900 1000 400 Again, we extrapolate our data Temperature, K to 1200 K for use Interfacial resistance between 410 Figure 6 here. Figure 6 shows the substrate- stainless steel and the measurement plates. coating interfacial resistance function. The interfacial resistance between the coating and the lower thermocouple plate is different from the interfacial resistance between the substrate-measurement plate due to light oxidation of the steel substrate, which is not observed for the coating. We have observed that the interfacial resistance of ceramics depends primarily on the surface finish of the ceramic material, since ceramics are chemically stable. Therefore, we use an interfacial resistance that was previously measured between Pyroceram 9606, of the same surface finish as the FGM coating, and the upper thermocouple plate as our interfacial resistance function for the coating-measurement plate interface [6]. Tliermal conductivity of the FGM coating can then be extracted from the total conductance data by using these mterfacial resistances and the thermal conductivity data for 410 stainless steel. The estimated uncertainty of the measurement system is 5%. 3.

RESULTS

Figure 7 shows thermal conductivity data for 5 test cycles of the specimen. A test cycle entails a conditioning thermal ramp, where the specimen is heated from 473 K to 1173 K in steps of 100 K, and a final thermal ramp. At each temperature of interest, the system is allowed to thermally equilibrate for a minimum of 3 hours. The conditioning ramp is used to allow complete heUum diffusion between the plates, mechanical settling due to thermal expansion differences, and stable formation of oxides on metallic specimens. Since the interfaces between measurement plates and the specimen are changing during this ramp, we do not use any of the data during this ramp in the analysis. Following the conditioning ramp, the temperature is dropped to 373 K, then the final thermal ramp is done in 50 K steps, up to 1173 K. The thermal cycling due to the testing itself is a mild form of thermal shock. Thermal conductivity dropped by an average of 12% from the first test to the second test, probably due to significant microcracking from differential thermal expansion of the two components in the coating. At lower temperatures, test 1 yielded thermal conductivity data that were appreciably higher than corresponding data from any of the four subsequent tests. Since the coating had

430 not yet been subjected to high temperatures, the coating would have had a 2.5 low microcrack density o t95t Tl until sufficiently high test i\ n temperatures would give test 3l o £ enough thermal stress X test 4l from the mismatch in the test sl + thermal expansion coefficients of the two coating components to •S 1.5 o oO start generating o microcracks. After the © 3 specimen had been tested QH = C twice, each successive 2*+ + — 1 test was preceded by an -»*additiond moderate _i_ ~ thermal shock to the specimen outside the apparatus before re0.5 I testing by heating the 200 1000 400 600 800 1200 1400 specimen to 473 K and Temperature K quenching into water at 295 K to induce a small Figure 7 . Thermal conductivity of the FGIVI amount of microcracking coating, showing data from 5 tests. in the specimens. Figure 7 shows that the thermal conductivity did not change appreciably from test 2 to test 3, which would be due to this moderate thermal shock. The first external thermal shock appears to have had no effect on the thermal conductivity of the coating. The next test (test 4) showed an additional average drop in thermal conductivity of 17%, while thefinaltest (test 5) showed an additional average drop in thermal conductivity of 9%. Even a moderate thermal shock is seen to significantly decrease the thermal conductivity of this coating. Since the thermal conductivity does not increase from test to test, the upper temperature limit of 1200 K is probably too low to allow sintering of the splats.

xji+

of

An interesting feature of figure 7 is the large drop in thermal conductivity between 1050 K and 1100 K. A possible explanation for the drop in thermal conductivity could be based on differences in the thermal expansion coefficients of 8YSZ and Ni20Cr. Since the thermal expansion of zirconia is about half that of Ni20Cr, there could be a separation at the zirconiaNi20Cr splat boundaries as temperature increases and the metal expands more rapidly than the 8 YSZ. Tliis phenomenon would only occur in the metal-rich portion of the coating, though. The coating is deposited at approximately 725 K to 925 K. Since the discontinuity in thermal conductivity occurs above this temperature range, this explanation is at least plausible. A more likely explanation for the sharp drop in thermal conductivity between 1050 K and 1100 K is the occurrence of a phase change in the coating. One thing to note is the repeatability of the drop in thermal conductivity. We observed a small, -50 K temperature hysteresis in this thermal conductivity transition upon cooling. The repeatability over many thermal cycles and the small temperature hysteresis upon cooling points toward a phase transition occurring, causing the decrease in thermal conductivity. The mechanism here would be a splat-boundary opening occurring when monoclinic 8YSZ material transforms to a tetragonal crystal structure. The monoclinic-to-tetragonal phase transformation in zirconia results in a volume contraction of 3 to 4%. Even a small volume contraction in the 8 YSZ splats could result in a much more

431 efficient thermal barrier at the splat boundaries. The thermal hysteresis of the zirconia phase transformation has been observed in polycrystalline zirconia [10]. The phase transformation possibly observed here occurs at a lower temperature, which could be due to fine grain structure. Since plasma-spray is a non-equilibrium process, grain sizes of material within the splats may be very fine. The monoclinic-to-tetragonal phase transformation in zirconia is loiown to be a function of grain size [11]. We plan to powder some of the coating and do xray diffraction analysis at room temperature, to determine whether a significant amount of monoclinic material exists in the coating. As Httle as 2% monoclinic phase may be enough to cause the discontinuity in thermal conductivity because the effect would not be due to a difference in phonon transport through different crystallographic phases, but due to the opening of splat boundaries. If we observe a significant amount of monoclinic 8 YSZ at room temperature, we plan to do high-temperature x-ray diffraction analysis on the coating to determine the phase transformation temperature in our plasma-sprayed material. The increase in thermal conductivity as temperature increases from 400 K to 1050 K is probably due to the Ni20Cr, as we have observed virtually no temperature dependance of thermal conductivity for pure 8YSZ coatings from 400 K to 800 K [8]. The strong temperature dependance of thermal conductivity above 1100 K is probably due to a radiative component of thermal conductivity in the 8 YSZ. If a radiative contribution is becoming a significant contributor to thermal transport in this temperature region, these data should be viewed as apparent thermal conductivity, composed of both conductive and radiative heat transfer. 4. CONCLUSIONS We have direcdy measured the thermal conductivity of a plasma-sprayed Ni20Cr / 8 YSZ FGM. Thermal conductivity decreased about 12% after the first test, probably due to microcracking from differential thermal expansion between the two coating components. Subsequent tests showed no drop, then a 17 % drop, then a 9 % drop, on average, of the thermal conductivity of the coating. We observe a sharp drop in thermal conductivity of the coating between 1050 K and 1100 K, probably due to a phase transformation or thermal expansion effects. We plan to do future work investigating this phenomenon.

432 REFERENCES 1. R.L. Williamson and B.H. Rabin, "Numerical Modeling of Residual Stress in NiAI2O3 Gradient Materials," Ceramic Transactions, 34, American Ceramic Society, pp.55-65 (1993). 2. R. Watanabe, A. Kumakawa and M. Niino, "Fabrication of Panel Assembly of Functionally Gradient Material with Active Cooling Structures," Ceramic Transactions, 34, American Ceramic Society, pp. 181-188 (1993). 3. N. Shimoda, H. Hamatani, Y. Ichiyama, S. Kitaguchi and T. Saito, "Fabrication of PSZ / Ni-Alloy FGM by Applying Low Pressure Plasma Spray," Advanced Materials '93, III/ B: Composites, Grain Boundaries andNanophase Materials, M. Sakai et al. Ed., Trans. Mat. Res. Soc. Jpn., 16B, pp.1263-1266 (1994). 4. "Standard Test Method for Steady State Heat Rux Measurements and Thermal Transmission Properties by Means of the Guarded-Hot-Plate Apparatus," C 177-85, Annual Book ofASTM Standards, 6, ASTM, pp. 17-28 (1988). 5. B.J. Filla, "Design and Fabrication of a Miniature High-Temperature Guarded-HotPlate Apparatus," Thermal Conductivity, 21, Plenum Press, pp.67-74 (1990). 6. B.J. Filla, "A Steady-State High-Temperature Apparatus for Measuring Thermal Conductivity of Ceramics," submitted to Review of Scientific Instruments. 7.

W.H. McAdams, Heat Transmission, 2nd Ed., McGraw-Hill, p.7 (1942).

8. A.J. Slifka, B.J. Filla, J.M. Phelps, C.C. Berndt and G. Bancke, "Thermal Conductivity of a Zirconia Thermal Barrier Coating," submitted to Journal of Thermal Spray Technology. 9.

R.A. Lula, Stainless Steel, ASM, p.37 (1986).

10. G.M. Wolten, "Diffusionless Phase Transformations in Zirconia and Hafnia," Journal of the American Ceramics Society, 46:9, pp.418-422 (1963). 11. D.J. Green, R.H.J. Hannink and M.V. Swain, Transformation Toughening of Ceramics, CRC Press, p.24 (1989).


433

Non-Destructive Evaluation of Carbon Fibre-Reinforced Structures using High Frequency Eddy Current Methods G. Mook, O. Koser, R. Lange Institute of Materials Science and Materials Testing, Otto-von-Guericke-University Magdeburg, POB 4120, 39016 Magdeburg, Germany Eddy current (EC) inspection of carbon fibre-reinforced structures bases on their anisotropic electrical properties. Great differences in conductivity between carbon fibres, polymer matrix and integrated functional components contribute to this circumstance. The paper describes suitable eddy current probes, the fundamental idea of modelling and measurement of EC distribution and provides a short survey of application potential to characterise CFRP nondestructively.

1. EDDY CURRENT PROBES The essential idea of EC inspection of CFRP is to use the anisotropic conductivity of the material [1,2]. Along the carbon fibres much higher conductivity is found than in the opposite direction (9... 15 kS/m and 0.07... 0.7 kS/m respectively). Additionally, capacitive couplings between the fibres can be used at high test frequencies. Non-axial EC probes (Fig. i) are necessary to detect these anisotropic effects [3,4]. Differential probes (Fig. 2) are capable to detect local inhomogeneities due to their gradients in conductivity. The comparatively low conductivity of the material lets eddy currents penetrate deep into the material thus opening the opportunity of volume inspections. The range of test frequencies starts at about 500 kHz and actually ends with the limitations of commercial EC devices at about 10 MHz. For higher frequencies network anaFig. 1: Non-centric eddy current probe for lysers can be used. Fig 2: Differential probe and CFRP inspection

sensitivity profile

434 2. MODELLING AND MEASUREMENT OF EDDY CURRENT DISTRIBUTIONS

S (x,y+dy) infinitesimal current loops

y+dy

S(x,y)

S (x+dx,y)

X

x+dx

Fig. 3: Model for the relation between current distributions and the magnetic field

In order to develop eddy current measurement techniques for CFRP it is necessary to understand the effect of the anisotropic resistance on the eddy currents. A method was developed which enables the visualisation of eddy currents in CFRP. In this method the z-component of the magnetic field was measured using a receiver coil. From the two-dimensional magnetic field distribution the current distribution can be calculated. The method bases on a formulation of the current density in form of a grid consisting of elementary current loops (Fig. 3). Each loop has a current flow with the size S(x,y). The current density J is then the result of the partial derivations ofS: ^ . . d S(x,y) J,(x,y) = — dy

. J, . d S(x,y) and J,(x,y) = — d X

Each elementary current loop produces a magnetic field which is proportional to S, The magnetic field of the current distribution is the sum of the magnetic fields of the elementary loops. The relation between S and B can be formulated as a convolution because the magnetic fields of the elementary current loops are equally shaped. The relation between the zcomponent of the magnetic field measured with a coil and S can be written as: B(x,y) = b^*S . The distribution of b^ in a plane close to the plane of the current distribution has ^^ approximately the shape of a delta function. Substituting this in Eq. (2) gives: (3) B^(x,y) = C'S(x,y) with C being a proportional constant. For this reason the current density can be evaluated directly by forming the partial derivations ofB^.

435

Experimental setup receiver coil

scan area

transmitter coil Fig. 4: Magnetic field and current distribution of unidirectional CFRP specimen

The eddy currents inside the CFRP were induced using a transmitter coil. The coil had a ferrit core with a diameter of 3 mm and a length of 5 mm. The magnetic field was measured directly above the CFPR using a small receiver coil so that Eq. (3) is valid. The magnetic field was measured with and without specimen. The difference between both measurement results gives the magnetic field of the eddy current distribution. The method was applied first to investigate current distributions in unidirectional CFRP. Fig. 4 left hand side shows the z-component of the magnetic field in form of grey values. The picture size corresponds to a scan area of 2.4 cm square 7.6 cm. Next to the magnetic field the current distribution evaluated with Eq. (1) and (3) is shown. It can be seen that the currents induced in fibre direction are dominating as expected for reasons of the anisotropic conductivity. In an additional experiment four layers of CFPR having different fibre orientation were stacked. Fig. 5 shows the measured magnetic field. The picture size corresponds to a scan area of 2.8 cm square 3 cm. The fibre orientation is clearly visible.

Experimental setup scan area

transmitter coil Fig. 5: Magnetic field of multidirectional CFRP specimen

436 3. APPLICATION TO CFRP 3.1. Detection of fibre orientation

Mil LA/ Fig. 6: Eddy current polar diagrams of unidirectional (left) and multidirectional CFRP (right)

Fig. 7: Eddy current image of bidirectional CFRP (above), Hanning masked and Fourier transformed image (below)

Fig. 6 shows the EC signal in a polar system obtained by a rotating non-centric probe [3]. Obviously, the diagram on the left represents unidirectional CFRP. The signal maximum correlates with fibre orientation. Special probes have been developed to detect the accuracy of fibre orientation in fatigue specimen up to 0.5°. The diagram on the right results from multidirectional laminate with 0, +45, 90 and -45° fibre orientation. The signal amplitude decreases with increasing distance between probe and layer. These diagrams have been recorded at 10 MHz. Higher frequencies provide sharper separation of fibre directions but require special equipment like network analysers [5] which hardly can be used for in-field inspection. The diagram in Fig. 6 on the left shows another interesting effect. Perpendicular to the fibre direction side maxima can be observed. In an ideal CPRP material, all fibres are parallel and isolated each from another. In reality, the manufacturing process leads to a certain fibre deformation and redistribution. Both the fibres within a layer and the fibres of neighbouring layers can contact each other thus causing variations in the eddy current field. This effect can be used for evaluating some matrix and bonding properties. Another way of evaluating fibre orientation is to scan a certain area with stationary differential probes. Fig. 7 presents the result of bidirectional CFRP specimen (RTM system) scanned in a 15x15 mm^ area. The pattern above results from natural inhomogeneities always occurring parallel with the fibres [4]. The image below indicates the fibre orientation very clearly. It was obtained by Hanning masking the original image and subsequent Fourier transform [6].

437 3.2. Ageing Effects The complex conductivity across the fibres changes with materials ageing. A set of specimen was thermally aged using a cycle between -160 and +120 degrees centigrade. The ageing process was interrupted after defined numbers of cycles and EC signal has been recorded. A significant growth of the side maxima during the ageing process could be found (Fig. 8). 3.3. Local Inhomogeneities To locate and analyse local inhomogeneities rotating EC probes scan the material. The m e a s u r e m e n t signal is on-line visuaUsed in a Fig-8: Eddy^current inspection of thermally aged C F ^ ^ Number of thermal cycles (from inner to outer polar coordinate system on a PC screen. Two loop): 0, 10, 200 cursors allow to choose angle positions of the probe where measurement signals should be taken. These two values whether can be recorded directly or they can be processed before recording [7]. Commonly, the ratio between the maximum and the adjacent minimum is the most suitable choice. Fig. 9 shows changing fibre orientation covered by unidirectional material twice as thick as the layer of interest. Another type of local inhomogeneity is a gap remaining between two tapes during the manufacturing. Fig. 10 demonstrates the potential of EC method to evaluate these gaps nondestructively. Although the CPRP is made from pregregs both figures clearly show varying conductivity across the fibres resulting from slightly varying fibre fraction.

Fig. 9: Eddy current detection of covered changes of orientation

Fig. 10: Eddy current detection of a gap between fibre tapes

438 3.4. Impact damage The impact damage combines fibre braking and delamination. Both inhomogeneities influence the EC signal. Fibre braking interrupts the conduction current and delamination significantly reduces the interlayer connection. Fig. 11 displays an 40x40 mm^ area including an impact not visible from the front side.

3.5. Adaptive structures Recent developments in materials science and technology try to integrate active components into the structure. Among a wide variety of possible combinations piezoceramic foils laminated into CFRP are of great interest. At first stage, the manufacturing of these structures should be optimised. Non-destructive methods help to characterise the material immediately after manufacturing and after certain static and dynamic load. High resolution eddy current methods are capable to detect, for instance, inhomogeneous fibre distribution, impact damages in fibres and actuators. Fig. 12 reflects an eddy current image of a broken piezoceramic actuator (44x30 mm^ ) under CFRP covering. Eddy current spreading bases on the thin metallisation of the piezoceramic foil which is necessary for electrical contacting.

Fig. 11: Eddy current image of an impact

Fig. 12: Eddy current image of a broken actuator in an adaptive CFRP structure

ACKNOWLEDGEMENTS This work was supported from the Deutsche Forschungsgemeinschaft and the Kultusministerium of Sachsen-Anhalt. REFERENCES [1] [2] [3] [4] [5] [6] [7]

S.N. Vernon, Materials Evaluation 46(1988)11, p. 645 S.N Vernon, J.M. Liu, Materials Evaluation 50(1992)1, p. 36 R. Lange, G. Mook, NDT&E International 27 (1994) 5, p. 241 G. Mook, R. Lange, Materialprtifung 36(1994)9, p. 345 M.P. de Goeje, K.E.D. Wapenaar, Composites 23 (1992) 3, p. 147 G. Mook, H. Heyse, J. Simonin, A. Tchemov, J. Berger, R. Lange, DACH-Jahrestagung ZerstCrungsfr. Materialpr., Lindau, 13.-15.5.1996, proc, p. 99 G. Mook, R. Lange, ICCE/2,21.-24.8.95, New Orleans, proc, p. 519


Thermal diffusivity

439

measurement for SiC/C compositionally graded

graphite materials O J. Nakano, K. Fujii and R. Yamada Japan Atomic Energy Research Institute, Tokai-mura, Naka-gun, Ibaraki-Ken, Japan

ABSTRACT Thermal diffusivity of oxidation-resistant SiC/C compositionally graded graphite materials has been measured by using the laser flash method. In order to study the effect of the SiC/C graded layer on the diffusivity, the thickness of the graded layer and the SiC content were changed. In addition, the specific surface areas of the SiC/C materials have been measured. It is shown that the effect of the SiC/C graded layer on thermal diffusivity was small within SiC contents (0.27-8.52 mass%) used in this study. 1.

INTRODUCTION In various fields including nuclear energy systems, graphite materials have been well used although they have a drawback of high reactivity to oxygen. To improve oxidation-resistance, SiC/C compositionally graded graphite materials with a gradual change in concentration between SiC and C have been fabricated, and have shown good oxidation-resistance and thermal shock resistance! 1-4]. Since they are used at a high temperature, it is important to study the thermal properties. This report describes the results of thermal diffusivity measurement for the SiC/C compositionally graded materials with different thicknesses of the SiC/C graded layer and SiC contents. 2. EXPERIMENTAL PROCEDURE 2 . 1 . Materials Isotropic fine-grained nuclear grade graphite (IG-110 graphite, Toyo Tanso Co., Ltd., Japan) and solid SiO of 99.9% purity (Wako Pure Chemical Industries Co., Ltd., Japan) were used for the formation of the SiC/C materials. Sample dimensions were

440

1.5, 2.0, and 3.0 mm in thickness and 10 mm fixed in diameter. The SiC/C graded layer was formed by the following reaction: 2C (s) + SiO (g) -^ SiC (s) + CO (g), where the graphite heated at 1380 °C was exposed to SiO molecules that were gasified at 1300 °C and carried by high purity helium gas. Here, all the external surfaces of the sample were graded with SiC. The formed SiC had the /? structure identified by X-ray analysis (RINT-1000, Rigaku Co., Ltd., Japan). After the above reaction, sample weights increased because of the formation of SiC. The average SiC content in the SiC/C graded layer was calculated by the following equation: M, w — w X Average SiC content (mass%) ^^ after ^^ before-xioo. (1) ^Si

^C

w.

where A^^ , A^, and M^j^ are the atomic weight of silicon, that of carbon, and the molecular weight of SiC, respectively. W^gf^^^^ and W^^^^ are the sample weights before and after the SiC/C layer formation, respectively. Fig. 1 shows wavelength-dispersive analysis of X-ray (WDAX) maps for Si for samples with 1.5 mm thickness. Si atoms penetrated a depth of about 500// m from the surface in Fig. 1 (a), and reached the center of the sample in Fig. 1 (b).

Laser Beam Direction

I

SiC/C Graded Area

Observed Area Fig. 1 X-ray maps for Si for the SiC/C graphites cross-sectionally cut (thickness: 1.5 mm); (a) SiC content 1.95% and (b) 6.87%. 2.2. Measurement of thermal diffusivity Thermal diffusivity was measured by using a laser flash equipment, PS-2000 (Rigaku Co., Ltd., Japan) which has a ruby laser of maximum 20 J in power. The sample temperature was changed from room temperature to 1320 °C . Thermal

441 diffusivity was obtained by t^/g method using the following equation: (2)

a=1.388LV7r't,

where t^/g is the time required to reach half of the total temperature rise on the back surface of the specimen and L is the sample thickness. SiC contents are 0.37-7.61% for 1.5 mm sample thickness and accordingly, 0.27-6.82% for 2.0 mm, and 0.30-8.52% for 3.0 mm. Before the thermal diffusivity measurement, the specific surface area for each sample was measured (AcceSorb2100E, Shimazu Co., Ltd., Japan) using Kr as an adsorption gas. IG-110 graphite and CVD SiC (Toshiba Denko Co., Ltd., Japan) were also used for the measurements for comparison. 3.

R E S U L T S AND DISCUSSION

3 . 1 . T h e effect of SiC c o n t e n t on t h e r m a l

diffusivity

In Fig. 2, the volumetric change and the bulk density after the formation of SiC/C graded layer are shown as a function of SiC content. It is seen that the sample volume was expanded with an increase in SiC content, but the bulk density hardly changed with SiC content. No variance of the density is reasonable when the weight gain due to the formation of SiC is taken into account. Fig. 3 shows the results of measured specific surface areas. The fact that the specific surface area increased with increasing SiC content means that the porosity in the surface layer also increased with SiC content. As shown in Figs. 2 and 3, these tendencies did not depend on the sample thickness.

+8

o

sz

E

1.5 2.0 3.0 • #

o 0

9.4

"co c CD

E o >

+2

A

Q ^^

13 CO

oo ^

0 O CO

o

t:

ZJ o CO 1_ A

o

4

6

'

8

1(?

SiC content(mass%) Fig. 2 Volumetric change and bulk density after the formation of SiC/C graded layer.

o o o o o

O O "" J^

o

^ o

o CO 13

%2

0 0

^

0

•

^

mm)l 3.0 • ' A •

--^-13-110 Graphite -^ SiC/C graded material (SiC cont.:0.3-8.5mass%) ^-CVD SiC

010X3.0 £1.5 o

.R.T.

b 750

E

im9^<m^

fi>OQ^ < ^ Q

^^

^0

0

0

,^340°C '

i«2S(3DA D ^ D ^ as the temperature became higher. The form of the flow curve in same temperature changed D^ t = > D ^ F ^ B as the concentration of PSZ became higher. From the load-deflection curves, the yield strength of each composite was obtained in elevated temperature as shown in Fig.6. It was found that the yield strength in the PSZ/INIOO composites became lower as the temperature became higher but the relationships between yield strength and temperature can be distinguished into two groups. Namely, where the concentration of PSZ is under 50%, the yield strength abruptly decreases over 1123 K. Over lb% PSZ, that slowly decreases. The yield strength is one of the most important design parameters where "no plastic deformation" is design criterion. But in case of the rotating parts, the specific yield strength (yield strength/density) becomes one of the most important design parameters. Fig. 7 shows the relation between the specific yield strength and temperature. In this picture, the specific yield strength of the Single Crystal (CMSX-2) which is recently used for the turbine blades of the aero jet engines is plotted simultaneously. It is recognized from Fig.7 that the specific yield strength of composites with more than 15% PSZ is nearly equal to that of the CMSX-2 in the temperature range from 1173 K to 1273K.

4.CONCLUSIONS 1.The relationships between the thermal expansion coefficient and the concentration of PSZ and the thermal conductivity coefficient and the concentration of PSZ at elevated temperature were obtained. 2. 4-point bending tests were carried out at temperature range from 1073K to 1373K, the change of the form of Load-deflection curve was obtained.

454 3.The yield strength of composites, where the concentration of PSZ is under 50^, abruptly decreases over 1123K. 4. The specific yield strength is nearly equal to that of the Single Crystal (CMSX-2) which is recently used for the turbine blades of the aero jet engines, where the concentration of PSZ is over 75^. ACKNOWLEDGEMENT The author wish to thank Mr. Y. Tada and Dr. R. Ishikawa of National Aerospace Laboratory, Science and Technology Agency, JAPAN for their contribution to the bending test program. REFERRENCE 1.M. Yuuki, H. Nakanishi et al, Proc. of FGM'93 symposium of Functionally Graded Materials Forum. 47-50, (1993) 2. M. Yuuki, H. Nakanishi et al, Proc. of the 22th annual conference of Gas Turbine Society Japan. 185-189, (1994)

CONCENTRATION OF PSZ

wt%

Fig. 1 Thermal expansion coefficient of PSZ/INIOO composites

455 ^ 30 CONCENTRATION OF PSZ

2

CONCENTRATION OF PSZ

20

673

WT%

-—-—-j—-1-

©

1 CO Q_

^

2

1

E

®

1

50 1

©

1

—-i-©---H— • ® © ^ I

U_ CD

^

1273 1473

Fig. 3 Relation of thermal conductivity coefficient and temperature

N9

L/;

1073

TEMPERATURE

Fig. 2 Thermal conductivity coefficient of PSZ/INIOO composites

®

873

1— =2: CJ5

1

1

1

-—(i>--i1

1

1

1

CD

" 100 .

Fig. 4 Classification of loaddeflection curve

-—[—\—^®

1073

1173 1273 TEMPERATURE

1373K

Fig. 7 Specific yield strength of PSZ/INIOO composites


457

Processing-working stress unified analysis model and optimum design of ceramic-metal functionally graded materials Peng-Cheng Zhai, Qing-Jie Zhang and Run-Zhang Yuan State Key Laboratory of Materials Synthesis and Processing Wuhan University of Technology, Wuhan 430070, P.R.China

The processing-working unified analysis model and optimum design of ceramic-metal functionally graded materials are studied. Emphasis is placed on the effect of the residual stress on the working stress and optimum design of the materials. Two analysis models for the residual stress effect are examined: one is a separate analysis model and the other is an unified analysis model. It is indicated that the effect of the residual stress is significant and the optimum design of the FGMs should be based on the processing-working unified analysis model when the materials response is inelastic. 1.INTRODUCTION The stress analysis of ceramic-metal FGMs constitudes a basis for the materials optimum design, either in the processing process or in the working process. There have been many studies on the residual stress and the optimum design process of the materials, for instance Ref [1-3], and some studies on the working stress and the optimum design process, such as Ref [4-5], but few studies have been reported to deal with the processing-working stress unified analysis. Therefore, the optimum design for the working process considering the residual stress effect is not well established at present. The present study concerns the working stress and optimum design of ceramic-metal FGMs considering the residual stress effect. The residual stress effect is examined with two analysis models: one is a so-called separate analysis model and the other is an unified analysis model. The difference between the two analysis models is discussed. When the response of the materials is inelastic, the separate analysis model is proved to be unsuitable and the unified analysis model is proposed for the processing-working stress analysis and the optimum design of the compositional gradation. 2.M0DEL DESCRIPTION Consider a ceramic-metal FGM which undergoes a thermal load history as shown in figure 1. The thermal loading history consists of two phases: phase I corresponds to the cooling after sintering(processing phase), the stress in this phase is called residual stress; phase II

458 corresponds to the working phase and the stress is called working stress. There are two methods that can be used t6 treat the residual stress effect on the working stress: one is so-called separate analysis model and the other is an unified analysis model. In the separate analysis model, the residual stress and working stress is analyzed separately and I he resulted stress is obtained from a direct superimposition of the two separate ones. It is obvious that this method is correct only when the two responses are linear and the material remains elastic in the two phases. For the unified analysis model, the processing phase and the working phase are treated as an unified loading process and the resulted stress is obtained through an unified analysis for the two phases. l.RESULTS AND DISCUSSION A TiC/Ni FGM is used as an example. The material properties, geometrical sizes and compositional function were given in Ref [6]. The thermal load in the working phase is thermal a shock with heat flux magnitude q = 5 AffV/m^ and duration ^^ = 2.0^. The sintering temperature in the phase I is taken as 1300K. The effect of the residual stress is considered by comparing the results of the separate iiuilysis of phase II(which abandoned the residual stress effect) and unified analysis of phase I mill II. Numerical results are indicated in figure 2. It is obvious that the effect of the residual stress is significant. For the case of not considering the residual stress effect, the stress is compressive during the heating process and decreases with the time increases. During the unloading process, the stress becomes tensile and then decreases with the time increases and becomes compressive again. The maximum tensile stress at the ceramic surface is about 7M)lVIPa. For the case of considering the residual stress effect, the stress is compressive during I lie heating process and increases with the time increases. During the unloading process, the stress becomes tensile and remains tensile. The maximum tensile stress at the ceramic surface is about 350MPa. It is suggested that the residual stress exerts significant effect on the working stress and it will reduce the maximum tensile stress at the ceramic surface obviously. Figures 3(a) and (b) compare the results from the separate analysis model and the unified analysis model. Figure 3(a) corresponds to the elastic analysis and it is seen that the two models give the same resulted stress. Figure 3(b) corresponds to the elastic-plastic analysis \\H\ it is seen that the results found from the two models are different. This is because in the eListic analysis the two responses in the phase I and II are both linear and the resulted response can be obtained from a direct superimposition of the two separate ones, but in the I'liLstic-plastic analysis, the two separate responses are both nonlinear and the separate analysis model based on the direct superimposition of the two separate responses is no longer suitable. Figure 4(a) and (b) give an important relationship for the optimum design of the FGM: the relationship between the maximum tensile stress at the ceramic surface and the compositional L'.xponent. Figure 4(a) shows the effect of the residual stress on the optimum design. From figure 4(a), it is seen that the effect of residual stress is very significant. When the effect of the residual stress is considered, the maximum tensile stress at the ceramic surface almost

459 decreases monotonously with the compositional exponent increases but if the effect of the n'sidual stress is abandoned, the maximum tensile stress has a minimum value at P = 0.6 . It is suggested that the effect of the residual stress on the optimum design of the FGMs can not l)c igonred. Figure 4(b) compares the results from the separate analysis model and unified analysis model. From figure 4(b), there exist some difference between the two analysis models.. 4.CONCLUSIONS The thermo-elastic-plastic response and optimum design of ceramic-metal FGMs under thermal shock loading are studied. An unified analysis model is used to consider the effect of residual stress on the working stress and optimum design of the FGMs. In this model, the cooling process and working process is treated as an unified thermal loading process. A TiCNl FGM is taken as a numerical example. Emphasis has been put on two aspects: the effect of (he residual stress on the working stress and the optimum design of the graded composition. The main conclusions obtained are as follows. i 11 fhe effect of the residual stress on the working stress and optimum design of FGMs is very significant. It not only changes the stress history but also changes the magnitude of the tensile stress at the ceramic surface. If this effect is abandoned, it will overestimate the tensile stress at the ceramic surface. (2) In the elastic analysis, the separate analysis model and the unified analysis model give the same result because the two responses of the cooling and working phases are both linear. In this case, the direct superimposition is suitable. I}) In the elastic-plastic analysis, the separate analysis model and the unified analysis model give the different results because the two responses of the cooling and working phases are both nonlinear. In this case, the separate analysis model is no longer suitable and the unified analysis model should be used..

\ ( KN OWLEDGEMENTS This work was supported by the National Science Foundation REFERENCES I

R.L.Williamson and B.H.Rabin, Proc. 2nd Int. Symp. on FGMs, 1992, 55-66

> ^ 4. 5. 6.

R.L.WilHamson and B.H.Rabin, Proc. 3rd Int. Symp. on FGMs, 1994, 215-222 N.Cherradi, P.Moechli and K.Dollmeier, Proc. 3rd Int. Symp. on FGMs, 1994, 253-258 J.Teraki, T.Hirano and K.Wakashima, Proc. 2nd Int. Symp. on FGMs, 1992, 67-74 T.Maruyama, M.Harada, etal., Proc. 2nd Int. Symp. on FGMs, 1992, 433-440 P.C.Zhai, Q.J.Zhang and Y.Z.Yuan, Acta Mechaica Solida Sinica, vol.9, 1996,in press

460 T(K)

time

phase I

phase n

Figure 1 : Thermal loading history of ceramic-metal FGMs phase I: cooling phase after sintering phase II: working phase o o o

• working stress • resulted stress o o

o o

o o o

Figure 2 : Influence of processing stress(residual stress) on working stress (P=1.0)

461 o o (N

1 1

t

^

^s-

time (s) \. '

2

'

'

3^*-»..^ 4

5

• o o (N

—^r- unified analysis model -•— separate analysis model

O

o

a: elastic case O O

o o

0, the functional derivative should be negative. Therefore (e -î)' + ^ ( 1 +Z)(e -î) + 2 ^ ( 1 +Z) > 0.

(4)

Equation (4) determines the height of potential barrier Eg and the solution of eq.(4) is

Therefore if we make the potential barrier below E^_ or above £3+, the change of figure of merit 6Z becomes always positive. However the effect of the barrier above 63+ is neglected in following analysis, since the expression of 6Z contains the derivative of Fermi distribution function (eq.(2)) and therefore the contribution of carriers above £3+ is considered to be small. It is easy to see that eq.(5) gives the generalization of height of the optimal barrier derived earlier[4] 3. ENHANCEMENT OF Z IN TWO BAND SYSTEM In this section we estimate the enhancement of Z and characteristic feature of this method by using Kane model. In Kane model, the transport coefficient, when the particular type of scattering mechanism is pre-dominant, is given by[5]: a = Z cJi, a = i 5^ Gitti, K = LaT+ K^^, + KL, i=e,h

i=e,h

(6)

491

o. = A 0^3 ,j(Ti,p),

a,a. = - ^ A [ G ; . 3 /,(Ti,p) - I]GI, /^(Ti.p)], [GJ.3,,(TI,P)

(7)

(8)

G;.3/2(^.P)

(9) (10)

(11) Here the suffix e denotes electron and the corresponding expression for holes is obtained by substituting T] -> - T| - x^ in above equations(the expression of hole contribution for thermopower is required to change the sign in addition to the substitution). We have used the relaxation time approximation in above expressions and assumed the energy dependence of relaxation time is given by[5]: T(X) = X?

x^(l + px)^ (1 + 2px) '

(12)

and r depends on the scattering process, i.e. r=-l/2 corresponds to acoustic phonon scattering, r=l/2 to optical phonon scattering, and r=3/2 to ionized impurity scattering[5]. To perform the numerical calculation, we use the semi-empirical formula of energy gap forBii_ySby [6] with y=0.1 as a typical example: E^ =270y - 15 + 4.0 x 0.032T (meV), and set the temperature at 100K(therefore x^ = 2.878). We also fix the ratio K^ / KL = 1.

(13)

492 Figure 1 shows the ratio of the contribution between electrons and holes to thermopower as a function of reduced chemical potential. We have also shown the results in the case of parabolic band(|5 set to be zero while x^ kept fixed value corresponds to the parabolic band). KambJK total, 1

10^ -•-Acoustic Phonon -'-Optical Phonon -•-Ionized Impurity -^Parabolic Band

10^

'

'

!

'

•

•

'

1

1

.

.

T-

r-1

-•-Acoustic Phonon ] i - ' - Optical Phonon 1 j -•-Ionized Impurity f 1 -©-Parabolic Band | ]

0.8 ?!?i8^ 0.6

H^^^^H'^'"'^ 1

0.4

10' 0.2

10°

-1

01 -1 -0.5

0

0.5

1

-0.5

1

I

1

i

0

1

>

>

•

i

1

0.5

•

i

•

i

1

>

1

•

>

i

I

1

1

1

1.5

1.5

Figure 1. Ratio of contributions between electrons and holes to thermopower as a function of reduced chemical potential.

Figure 2. Ambipolar contribution to thermal conductivity devided by total thermal conductivity as a function of reduced chemical potential.

Z From Fig.l the contribution from minority -Acoustic PhononI 1.5 -Optical Phonon carriers to thermopower is comparable -Ionized Inipurity with that of majority carriers near T] = - 1. -Parabolic Band 1.25 This reflects the increase of the ambipolar contribution toward r| = - 1 as seen from Fig.2. Therefore the rapid decrease in Z 0.75 toward r| = - 1 is due to the minority carriers in this model. We also see the properties near r| = 2 correspond to be single band. 0.25 Next we estimate the enhanced figure of merit as a function of reduced chemical potential simply by setting the lower limit of integral in eq.(lO) by corresponding Figure 3. Thermoelectric figure of merit as barrier height using eq.(5). Figure 4-7 a function of reduced chemical potential for various scattering processes. shows the effect of energy filter. We see the influence of elimination of minority carriers has considerable effects on thermopower and thermal conductivity.

493 Since, from Figs.4-6, the effect of increase in thermopower and of decrease in thermal conductivity is superior than that of decrease in electrical conductivity, the figure of merit increases toward T] = - 1. Comparing Fig.3 and Fig.7 we see that the enhancement of figure of merit comes from two different origin. The enhancement near Ti = - 1 is due to the elimination of minority carriers and that near r| = 2 is due to the elimination of harmful majority carriers. a Filtei ^Klteicd/Ô

J%

1 -Acoustic PhononI -Optical Phonon - Ionized Impurity I -Parabolic Band

0.9 I 0.8 [•• 0.7 -•-Acoustic Phonon -^-Optical Phonon 0.6 H -•-Ionized Impurity o-Parabolic Band 0.5

-1

-0.5

0

0.5

1.5 -0.5

Figure 4. Electrical conductivity with barrier divided by that without barrier as a function of reduced chemical potential.

0

r| Figure 5. Thermopower with barrier divided by that without barrier as a function of reduced chemical potential.

^Filterec/S

11

• . . . , . . . . , , . . . , . .

.

.

j • .

-•-Acoustic Phonon i 0.8 11 ^ ^ Optical Phonon [ 1 -^•-Ionized Impurity \ |-«-Parabolic Band y\ 0.6

XJr-^

0.4 -

. 1 j .

• • • 1

1

j

A———^"^

T

3.5 3

•

•

•

'

j

:

i

bs^

j

'

'

•

'

1

i"*

\ 2.5 \ ^ ^

-0.5

'

1

•

•

•

'

I

'

'

' •'

j

'

- ^

^ ^

kj^^^î—-•—T^*—~t^——-i

^!tite}^

1.5 1

• i .

'

-•-Acoustic Phonon ...J - ^ - Optical Phonon -•-Ionized Impurity j... ^^ Parabolic Band

2

t

. .

•

'

•

J

0.2 Ol.. ,1 -1

1

.

. •. . i . . . . i . . . . i . . •. 1

• .

0

0.5

1.5

Figure 6. Thermal conductivity with barrier divided by that without barrier as a function of reduced chemical potential.

0.5

'

-1

1

1

•

•

i

•

-0.5

•

•

•

i

0

•

1

.

•

i

.

0.5

•

•

I

i

1

I

•...•

i

1.1

1

•

1

1.5

Figure 7. Thermoelectric figure of merit with barrier as a function of reduced chemical potential.

494 Although our results of calculation are rather qualitative one, Efimova et.al.[7] estimated the influence of the minority carriers on Z for n-type PbTe in more realistic fashion and indicated the minority carriers are responsible for a decrease of Z by 40-50% around T « 500-600°C. 4. DISCUSSION AND CONCLUSION It has been proved that the elimination of lower energetic carriers brings the enhancement of Z and the optimal height of potential barrier within the two band model is given analytically. Such elimination (confinement) of minority carriers has already studied in GaAs/AlAs systems and it has been known that the use of graded alloy composition at interfaces of hetero-junction are important to confine the minority carriers effectively[8] due to decrese in the defect density near interfacial region. Finally we note that the possibility of destroying the effect of enhancement of Z by internal electric field, which is produced by blocked carriers located near the barrier interface. Such internal electric field is inevitable and may degrade the effect of enhancement by this method. We expect the cancellation of positive and negative blocked carriers located at the interface of barrier makes this internal electric field weaker, to some extent. However the effect of internal electric field is left as a future problem. ACKNOWLEDGMENTS One of the author (Y.N.) would like to thank Professor J. Yoshino of Tokyo Institute of Technology and Professor T. Koyanagi of Yamaguti University for helpful discussions. This work is partly supported by a grant from the Science and Technology Agency of Japan for the Development of Functionally Graded Materials for Energy Conversion. REFERENCES 1. B. Y. Moizhes and V. A. Nemchinsky, 11th Int. Conf, on Thermoelectrics, Texas, 1992, (University of Texas Press, Texas, 1993), p.232. 2. L. W. Whitlow and T. Hirano, J. Appl. Phys. 78(1995)5460. 3. D. M. Rowe and G. Min, 13th Int, Conf. on Thermoelectrics, Kansas, 1994, (AIP Press, New York, 1995), p.339. 4. Y. Nishio and T. Hirano, Jpn. J. Appl. Phys., submitted. 5. A. Anselm, Introduction to Semiconductor Theory, Prentice-Hall Inc., New Jersey, 1981, Chapter 9. 6. B. G. Martin and L. S. Lemer, Phys. Rev. 86(1972)3032. 7. B. A. Efimova, L. A. Kolomoets, Yu. I. Ravich and T. S. Stavitskaya, Sov. Phys. Semicond. 4(1971)1653. 8. L. W. James, J. Appl. Phys. 45(1974)1326.


495

Theoretical estimation of thermoelectric figure of merit in sintered materials and proposal of grain-size-graded structures. Junji Yoshino Department of Physics, Tokyo Institute of Technology, Meguro-ku, Tokyo 152, Japan

Thermoelctric figure of merit for n-type sintered materials of SiGe and PbTe has been calculated based on Boltzmann equation and a heterostructure grain boundary model. The results reveals that thermoelectric figure of merit are expected to be improved in both materials reducing the grain size. However, maximum thermoelectric figure of merit is expected to achieve at different grain sizes for SiGe and PbTe, owing to difference of their sound velocities.

1. INTRODUCTION Recently, thermoelectric energy conversion has paid a great attention in terms of energy saving once again. However, improvement of its energy conversion efficiency is still a essential issue. Since thermoelectric quantities, which determine thermoelectric figure of merit, Z, strongly depend on temperature, functionally graded (FGM) structures, where impurity concentration or/and alloy concentrations are changed along temperature gradient in a thermoelectric element to achieve maximum dimensionless thermoelectric figure of merit, ZT, at each point, are expected to improve Z, effectively. However, it is probably inevitable to adopt sintered materials to prepare such practical FGM thermoelectric elements. Therefore it is important to examine the energy conversion efficiency of sintered materials theoretically. Although extensive theoretical studies have been made to clarify the grain boundary effect on thermal conductivity, the effects on electric properties have not been well examined. In this paper, thermoelectric figure of merit for n-type sintered materials of SiGe and PbTe has theoretically been estimated considering effects of grain boundaries on carrier mobility and Seebeck coefficient based on a model.

2. THEORETICAL MODEL In this paper thermoelectric figure of merit, Z, for sintered materials are evaluated based on theoretical calculation of bulk properties. The framework employed in present study to calculate bulk properties is similar to Vining's model [1], except some small modification mentioned in the following. Scattering processes included in Boltzmann equation are ionized impurity scattering, acoustic phonon scattering, alloy scattering and intervalley scattering for

496 calculations of electronic properties, and three phonon scattering, carrier scattering and alloy scattering for calculation of thermal conductivity. Since the effect of non-parabolic band is essential especially in narrow gap semiconductors, following non-parabolic effective mass is introduce in the calculation of PbTe properties. m :\ + In present calculation, it is assumed that the effects of grain boundaries for Z are brought only through electric conductivity, Seebeck coefficient and thermal conductivity. Namely, grain boundaries effects on these three important properties are taking account independently, and then thermoelectric figure of merit, Z, are obtained by using the equation, Z = cra^/fc, where cr, a and K are electric conductivity, Seebeck coefficient and thermal conductivity, respectively. The effects of grain boundaries for thermal conductivity is accounted by a simple relaxation time formula, r = L/v^, where v^ and L are velocity of phonons and grain size, respectively [2]. On the other hand, mean free path of charge carriers is fairly smaller than grain size, as typical grain size of sintered thermoelectric materials is about 1-100 |nm. Therefore, carrier scattering at grain boundaries is not essential. However, grain boundaries contain a lot of defects and sometimes it is consisted of amorphous materials. Then carrier mobility in grain boundaries is expected to be smaller than that of grain inside. Furthermore, localized energy levels which are created by dangling bonds, expected to pin Fermi level and form band bending. Several models have been proposed to account for temperature dependence of mobility in polycrystalline silicon. In this paper, a crystalline-amorphous-crystalline heterostructure model for grain boundaries presented by Kim et al. [3] has been accepted to take account of grain boundary effects on electric properties of sintered thermoelectric materials. Figure 1 presents the grain boundary model used in this study. The carrier transport in grain boundaries are assumed to take place by Brownian motion and the carrier mobility is inversely proportional to temperature. Several interface parameters, which characterize its band profile are also indicated in fig. 1. The meanings of these parameters are the same as that presented in Kim's paper. Figure 1. Energy band profile of sintered Since Seebeck coefficient is depend on Fermi materials based on heterostructure grain energy, it is position dependent, if one assumed a boundary model. band profile as shown in fig. 1. Overall Seebeck coefficient is calculated as follows. Total output voltage of single grain is estimated integrating Seebeck coefficient over a single grain. Position dependent Seebeck coefficient is obtained as a function of Fermi energy based on calculation for bulk, Then overall Seebeck coefficient is obtained by dividing total output voltage by a grain size. Major parameters used in

497 this calculations are summarized in table 1.

Table 1. Important parameters used in present calculation. SiGe anhrmonicity parameter of alloy scattering for phonon: y rate constant ratio related to intervalley scattering: W2/W1 band discontinuity at grain boundary: A thickness of grain boundary: S localized energy level around grain boundary: Ei

PbTe

0.91

1.5

1.0

0.5

OeV

OeV

lxIO"'m

IxIO'^m

- 0.5 eV

- 0.5 eV

3. RESULTS Electric and thermal properties of bulk materials have been calculated to examine reliability of our calculation. Figures 2(a) and (b) indicate temperature dependence of calculated electron mobility for bulk Sio.yGeo.s and PbTe, respectively. The mobility of SiGe is almost inversely proportional to temperature, while that of PbTe is almost proportional to T~^. It is notable that strong temperature dependence of PbTe, which is experimentally obtained, is successfiilly achieved. Although the effect of grain boundaries on Seebeck coefficient have been examined, it is found that the effect is only to become significant at a grain size less than 0.1 fim and it is negligible in common sintered materials. Therefore, the effect on Seebeck coefficient is neglected in the following calculation. Figures 3(a) and (b) indicate grain size dependence of Z r for sintered SiGe and PbTe, respectively. We can find significant difference in the grain sizes,

1000 Temperature (K)

1000 Temperature (K)

Figure 2. Temperature dependence of calculated carrier mobility for (a) SiGe and (b) PbTe.

498

10-6

10-5

Grain size (m)

Figure 3. Grain size dependence of dimensionless thermoelectric figure of merit, ZT ^ for (a) SiGe and (b) PbTe

which give maximum ZT. Namely, maximum ZT is obtained at a grain size around 0.1 jim for SiGe, while that of PbTe is achieved at a smaller grain size. Origin of the notable difference can be easily understood, if one examine grain size dependence of electric conductivity and lattice thermal conductivity show in fig. 4. Lattice

"T

100000

'"1

I

400 K

(b) PbTe

600 K 50000 800 K

•H«j—I I IHIH]

1 I Mllll|—t I l l l l l l l — I I I mil

400 K

600 K 800 K

10-8

10-7

10-6

10-5

Grain size (m)

10-4

10-3

10-8

10-7

10-6

10-5

10-4

10-3

Grain size (m)

Figure 4. Grain size dependence of electric conductivity a and lattice thermal conductivity KL for (a) SiGe and (b) PbTe.

499 thermal conductivity of sintered SiGe and Nd= 1 X 10 26 PbTe decrease with decreasing grain size as Si Ge 0.7 0.3 Nt= 3.2 X 10 28 shown in fig. 4. However, it is notable that J-400K grain size, where suppression of thermal 1.0 1200 K conductivity is take place, is not identical 1000 K for SiGe and PbTe. Lattice thermal 0.5 conductivity decrease gradually below a 800 K grain size of 10 \\.vci in SiGe, while it begin 600K below a grain size of 1 |Lim in PbTe. The nn significant diflTerence can be attributed to 10-6 10-5 large difference of sound velocity. Grain size (m) So far, extensive experimental studies on grain size effects have been made [4]. Figure 5. Grain size dependence of dimensionless thermoelectric figure of merit ZT for cases of high Although reduction of thermal conductivity locaHzed level density. Density of localized level is due to reduced grain size has been 3.2xl0^^m•^ confirmed by many authors experimentally, results on ZT are still controversial [4,5]. The calculated grain size dependence of thermal conductivity shown in fig.4(a) is in good agreement with experimental results obtained by Vining et al. [4]. On the other hand, their results indicate that degradation of electric conductivity takes place below the same grain size, while present result predicts that it takes place below one order of magnitude smaller grain size. This large discrepancy is due to the difference of electric conductivity in grain boundaries. The grain size dependence of electric conductivity is strongly affected by mobility ratio between grain inside and grain boundary, deference of their temperature dependence, and band profile. Therefor the grain size itself, which gives 2 7 maximum, shown in fig. 3 are not meaningful. The inconsistency of experimental results is also attributable to difference of grain boundary quality, since it strongly depends on preparation procedures. Therefor a great effort should be given not only to clarify the structure of grain boundaries, but also to control the quality of grain boundaries, in terms of thickness and defect concentration. Furthermore, interesting behavior on grain size dependence is expected. Figure 5 shows grain size dependence of ZT for a case of high localized level density. The grain sizes, which give maximum ZT, shift toward smaller grain size as increasing temperature. This results offer a new concept of a FGM structure, namely a grain size graded structure. However, band bending at grain boundaries reduces the peak value of ZT, and control of defect density at grain boundaries is essential problem.

4. SUMMARY Thermoelectric figure of merit for sintered materials has been investigated theoretically based on classical transport equation and a grain boundary model. The calculations reveals that enhancement of ZT by phonon scattering at grain boundaries are expected to be dominant at grain sizes of below 10 |im for SiGe and 1 îm for PbTe. Since such enhancement is strongly affected by quality of grain boundaries, fijrther effort to control the quality of grain boundaries is expected to result in enhancement of Z r due to grain size reduction.

500 ACKNOWLEDGMENTS This work was performed through Special Coordination Funds of the Science and Technology Agency of the Japanese Government.

REFERENCES 1. 2. 3. 4. 5.

C.B. Vining, J. Appl. Phys., 69 (1991) 331. J.E. Parrott, J. Phys. C2, (1969) 147. D.M. Kim et at., TEEE Trans. Electron Device, ED-31 (1984) 480. C.B. Vining et al., J. Appl. Phys., 69 (1991) 4333, and references therein. D.M. Rowe et al, J.Appl. Phys., 73 (1993) 4683.


501

Computer design of thennoelectric fimctionally graded materials L.I.Anatychuk, L.N.Vikhor Institute of Thermoelectricity, General Post-Office, Box 86, 274000, Chemivtsi, Ukraine Abstract The results of the optimal control theory use have been presented for program creation of functionally graded material computer modeling. Modeling results such as limiting values for FGM generators efficiency, fimctionally graded material advantages resulting from the computer modeling have been. Problem solution Achievements in thermoelectricity during the recent 30-40 years are first of all due to the progress in the creation of a thermoelectric material with high figure of merit values Z = ^

(1)

The maximum figure of merit is achieved by way of material optimization. It is well known that in semiconductors Seebeck coefficient a, conductivity a and heatconductivity K are the fiinctions of current carrier concentration «, p which in their turn are the fimctions of impurity concentrations Ne, Np a = a(n,p)= a(NeNp) a=a(n,p)=c7(NeNp) K= K(n,p)^

(2)

K(NeNp)

To reach the maximum of Z, one must find the optimal concentration fi-om the extremum condition —

=0

(3)

Thus, the result of optimization is a number, namely the value of the optimal concentration of donor or acceptor impurities. Naturally, the theory cannot indicate the exact figure of doping impurity concentration. Therefore the optimal concentration is experimentally determined by way of creating materials with different impurity concentrations and determination of their Z. This method served as the basis for highly efficient thermoelectric material technologies and guaranteed the progress of thermoelectricity on the whole. However, by the present time these ways of improving the thermoelectric figure of merit have practically exhausted themselves. Despite the numerous efforts, the increase in the figure of merit is insignificant. Therefore, it is only natural to ask whether this situation is a casual one or there are vaUd reasons for these restrictions.

502 To answer this question, special investigations were carried out. The value of Z was calculated for the model thermoelectric materials from which the best possible values of microscopic constants were taken in crystalline structures. The calculated values of ZT lie between 2 and 3. In reality this value will be considerably lower, therefore one can assume that this way of improving the thermoelectric figure of merit of material seems to have exhausted itself What are the further possible ways of increasing the efficiency of materials for the thermoelectric energy conversion? At present one of the most challenging trends of increasing the efficiency of thermoelectric materials is the transition from a classical thermopile model where legs are made of the homogeneous material, to the thermopiles where legs are made of materials whose properties are coordinate functions. The prospect of using the inhomogeneous legs was already indicated by academician loffe in his book [1]. A large series of investigations on the use of the inhomogeneus materials in cooling batteries has been conducted in Ukraine. A theory of computer-aided design of materials with a programmable inhomogeneity has been developed. Fig. 1 shows an example of the optimal inhomogeneity functions for the materials based on Bi-Te. These investigations have been described in the monograph by Anatychuk L.I. and Semenyuk V.A. [2]. Technologies have been developed for obtaining these materials by pressing, extrusion, zone melting and Czochralski methods. These materials have been used for the manufacturing of thermopiles whose properties are shown in Fig. 2. It is seen from the figure that when materials with programmable inhomogeneity are used, the maximum temperature drop in cooling thermopiles increases from 70 to 90 degrees, i.e. by 25%, and the coefficient of performance can increase several times. To reach such parameters with the homogeneous materials, one must create a material with a thermoelectric figure of merit Z=4,510"^ K"^ which for the moment is impossible. This example shows that the use of thermoelectric materials with programmable inhomogeneity is a new efficient trend of improving the quality of thermoelectACxlO",cm^

Number of ATxlO" cm'' sanipJc sections '

'

TV

FGM

«-type

{CdCL) L

Fig. 2. J - the increase in ^Tmax with Fig.l. Optimalfunctions of thermoelectric approximation to the optimalfunction; material inhomogeneity.n-type Bi2Te2jSeo.3 + 2 - the increase in the coefficient of per(0,09,,. O.OSJCdCh; formance zfor the optimal inhomogeneity; P'typeBiosSbi^sTes + 4% Te 8o is coefficient ofperformance of the homogeneous leg.

503 lie devices. Materials with programmable inhomogeneity can be also used to improve the efficiency of a generator. This idea is extremely popular with the Japanese investigators. Thus, in the paper by Nishida [3] it is suggested that a material with programmable inhomogeneity should be created on the basis ofPb-Te. The generally accepted name for these materials in Japan is functionally graded materials. In conformity with the paper [3], FGM is defined as the envelope by the maximums of Z at various temperatures and, accordingly, at various concentrations. Equivalently, for wider temperature ranges FGM is formed as the envelope by the maximums of Z for various materials suitable for each temperature level. In reality, to design FGM, use must be made of more accurate, hence more complicated methods. Let us consider them in more detail. The purpose of material design is to determine the distribution of impurity concentration along the leg where at the given temperature of hot and cold sides Th and Tc the maximum efficiency or maximum power is reached. Thus, we have a basically new approach to the optimization of thermoelectric material. Really, if before optimization served the purpose of number, today it results in the optimal function of impurity concentration as coordinate function. To determine this optimal function is a complicated task. Unlike finding the optimal concentration in the homogeneous material, experimental determination of the optimal function is a complicated and expensive task with a result which is apriori not very reliable. Really, for this experimental selection one must make a leg of individual source materials with various concentration values. The greater the number of such source materials and sections, the greater the chance of more accurate determination of the desired function. Naturally, here we must accept a limitation that we have to change a continuous concentration function for a step one. Combinations of these constituent samples are extremely numerous. Under these complicated experimental conditions it is advisable to pass fi*om a real experiment to a computer-made experiment, which in our opinion is more accurate and involves considerably less expenditures. Fig. 3 gives a physical model for the construction of a computer-made FGM design. This model includes an inhomogeneous leg of nand p-type of conduction, îW' 'AT;"" K gr^TriT, connected to electric and thermal circuits, external optimal electric load Ropt A L where electric power W is ^ 'a 10^

10^ '^

CO

HH

(D 0

'SCo D

U

0

)

CD

CO - J — I — I

10^

I

I

5

Q

I

10

C

00

'^

10"^

:

-ri—'

5

Temperature lOV T (K-^)

^

1

1 J_

10

Temperature 10^/ T

Fig. 1

I

I

I

(K~M

Fig. 2

Temperature dependence of the Hall coefficient and resistivity tensor components.

^300

_Q

1

'

1

f—

Temperature dependence of the magnetoresistivity tensor components.

I

Q^

QL

^^^ftM

"2001

0

o

-X^^

100

••

-^^

: lOiil : IQ33I

(T3

a.

CD O

e 0

H

CD CD

1

100

,

1

200

Temperature T

i_

1

300 (K)

100 200 300 Temperature T (K)

Fig. 3

Fig. 4

Temperature dependence of the thermoelectric power tensor components.

Temperature dependence of the parameters u,v,w and /? of the Six-Valley Model determined from the observed galvanomagnetic tensor components.

512 Figiire 2 shows the temperature dependence of the observed magnetoresistivity tensor components. The ratios among the observed components were approximately constant below 200 K, while a sUght change was observed in the ratio of p^^^^ to the other components above 200 K. The observed temperature dependence of the anisotropic thermoelectric power is shown in Fig.3. The anisotropy was negUgible below 200 K, while above 200 K the anisotropy increased with temperature. DISCUSSION In the six-valley model proposed by Drabble et al.[3-5], the equi-energy surface of a valley is expressed by

E = £"o +

(ankn^ +ank2i^ +^33^:33^ -{-lankiki)

(2)

,

2/wo

where E^ is the minimum energy of the valley, mo the rest mass of a free electron, k^ (/ = 1,2,3) the wave number vector components, and « „ , a^^, a^^ and a^ the configuration

factors of the equi-energy

surface.

In this model,

the

galvanomagnetic tensor components should satisfy the following relationships: A3 ^ Ai

(3a)

2v

1

—1

1

I

r—

P213

(w + z/v)(l + i/) 4z/v

(3b)

e u

(3c)

(l + «)' - 1

-0.5

bo C u(U

AiAiii _ (>«'-5«M' + 3tn' + t,t?) = -

(2r,+5)F(r,+3/2,»7) -fj l(2r,+3)Fir, + l/2,t})

where r, is the component of an anisotropic scattering parameter.

(8)

The value of

514 r^ can be calculated from the observed thermoelectric powers, substituting the estimated r? value into Eq.(8), The calculation results are shown in Fig.5. At low temperatures below 200 K, the anisotropy in the scattering parameter is negUgible and r^^r^^w -0.7, which is slightly smaller than that in the pure acoustic phonon scattering case (r = - l / 2 ) . It is concluded that the sUght difference is due to the optical phonon scattering, because the observed temperatiu'e range includes the Debye temperature of Bi2Te3 (165 K)[8] and ionic bonding exists between Bi and Te atoms[9]. In the high temperature range above 200 K, r, approaches t o - 1 / 2 , while r^ decreases with increasing temperature. It is known that the second conduction band exists 30 meV above the first conduction band[10]. From these facts, it is concluded that the effect of the optical mode is greater in the c-direction than that in the a-direction, and that the second band is more anisotropic than the fij*st band, which is consistent to the report that the anisotropy in thermoelectric power increases with increasing amount of dopant[2]. ACKNOWLEDGMENTS Thanks are due to Prof. Ohta of Keio University for his helpful discussions. REFERENCES [1] K. Uemura and LA. Nishida, Thermoelectric Semiconductor and Its AppUcations, Nikkan-Kogyou Shinbun , 1988 (in Japanese). [2] H.T. Kaibe, T. Okumura, M. Sakata, Y. Isoda and LA. Nishda, Proc. the 10th Int. Conf. Thermoelectrics, Cardiff, U.K.,p.35, 1991. [3] J.R. Drabble and R. Wolfe, Proc. Phys. Soc. London, 69 (1956) 1101. [4] J.R. Drabble, R.D. Groves and R. Wolfe, Proc. Phys. Soc. London, 71 (1958) 380. [5] J.R. Drabble, Proc. Phys. Soc. London, 72 (1958) 380. [6] M. Stordeur, Phys. Stat. Sol, (b), 98 (1980) 199. [7] V.A. Kutasov and L.N. Lukânova, Sov. Phys. SoUd State, 28 (1986) 502. [8] G.E. Shoemake, J.A. Rayne and R.W. Ure, Jr., Phys. Rev., 185 (1969) 1046. [9] D.R. Lovett, Semimetals & Narrow-Bandgap Semiconductors, Pion, London, p. 182, 1977. [10] R.B. MaUison and J.A. Rayne, Phys. Rev., 175 (1968) 1049.


515

Percolation design of graded composite of powder metallurgically prepared SiGe and PbTe R. Watanabe^, M. Miyajima", A. Kawasaki^ and H.Okamura^ a Department of Materials Processing, Faculty of Engineering, Tohoku University, Sendai 980-77, Japan b Graduate Student, Faculty of Engineering, Tohoku University, Sendai 980-77, Japan

The design and the powder metallurgical fabrication of functionally graded thermoelectric material have been studied with specific interest to enlarge the working temperature range and increase the figure of merit. The percolation control of the electrical resistivity of the composite phases has been taken into account in the design scheme of the graded composite. The materials combination of SiGe and PbTe was selected as a model system for the verification of the percolation concept. The measurements were carried out on the thermal conductivity, electrical resistivity and Seebeck coefficient, which are involved in the figure of merit, of non-graded composites, as well as of the monolithic SiGe and PbTe. 1. Introduction To enhance the performance of the thermoelectric generating device, it is important to enlarge the working temperature range of the device. Toward this goal, functionally graded thermoelectric material [1,2] has a great potential. As the figure of merit of thermoelectric materials has remarkable temperature dependence, we have to use several materials along the temperature gradient to achieve the best performance of thermoelectric conversion. We have two large problems on preparing such sturucture i.e. segment bonded sturucture [3]. The first problem is the residual thermal stress at the material interface. And the second problem is the electrical properties of the material interface. For the furst problem, recent progress in the field of stress relaxation type functionally graded material helps us very well, and the principle is utilizing multi phase composite material. On the other hand, for the second problem, it is not desireble to introduce complicated interface geometry, for example muti phase composite structure Unfortunately, there are not very many works in the field of composite thermoelectric material. One of the rare clear theoretical works by Bergman and Levy [4] tells us that any multi phase composite in which unclusions are dispersed in matrix phase shows smaller figure of merit. But, as they modeled, this calculation does not contain cotinuous microstructure networks, which appears very often in functionally graded materials. We would like to see the continuous network structure effect, i.e., percolation property [5-11] of composite thermoelectric material. The following section 2 describes basic numerical modeling of percolative mateials, and the section 3 describes on experimental study of SiGe / PbTe graded composite.

516 2. Percolation Model 2-1 Percolation on thermoelectric material Percolation phenomena is characterized by large scale transition of physical property as a function of composition. The characteristic composition at which the percolation transition occurs is called percolation point. Generally, high electrical resistivity material has rather small thermal conductivity. So we may hope in thermoelectric material composite, preparing composite with high and low electrical resistivity material, large thermal conductivity reduction, whereas keeping rather low electrical resistivity, as shown in Figure 1. These are the key concept of introducing percolation microstructure. 2-2 Microstructure and equivalent electric circuit model To model the microstructure and evaluate the thermoelectric properties, we used following simple equivalent electric circuit model shown in Figure 2. We considered the two phase composite as a cluster pararrel network circuit. Setting for each cluster the characteristic single phase physical property, and settle the material composition to the cluster number ratio, we can simulate the total thermopower of the system by Millman's theorem of d.c. circuit. Numerical results of this model at fixed temperature are shown in Figure 3. The figure of merit are shown as a function of SiGe / PbTe composition. Physical properties for each materials are from ref [2]. As shown in Figure 3, such microstructure that contains SiGe property, which is modeled as high thermal conductivity / low electrical resistivity phase, for large composition range, shows better thermoelectric property. For such materials, only the thermal conductivity is effectively reduced by containing PbTe phase. On the contrary, such microstructure that is dominated by PbTe property, which is modeled as low thermal conductivity / high electrical resistivity phase, which has rather small percolation point, shows smaller figure of mertis compared to the former material model.

!5- «

\

^ K

\^^

•fi| ^

x^

3

]

T3

a8 D

13 'B

p

N.

'0>. O'^

V3 *oo

i^

quality enhancement available ....

l / / j

^ Phase A percolation point, Pc Phase B Compositon of phase A / B composite

_ £ai/pi

a "" Zl/pi

Figure L Schematic diagram of percolation Figure 2. Schematic diagram of equivalent transition of transport property and its use on electrical circuit model of phase A/ B (suffix a andb) thermoelectric composite material. thermoelectric composite material.

517 2-3 Modeling graded two phase thermoelectric composite In the next step, we would like to consider using such composites to prepare graded thermoelectric material. In Fig.4, results of simple numerical evaluation are presented. These curves present the basic features of percolation designed graded thermoelectric composite, that is, we can bridge the valley of figure of merit of different thermoelectric materials, by controling the percolation point and the transition width ( here we used the form of well-known Fermi-Dirac distribution function to model the gradual percolation to let the transition complete one half at ther percolation point) via microstructure control. The model parameters in Figure 4, however, do not include the composite phase interface geometries, explicitly. This is not enough for practical designing of graded structure and to be considered in further step.

l.U

^ ^ 0.9 ' ^ ^

2l.50

1

h = 0.2 (a) Pc=70 (b) Pc=50 V (c) Pc=30

P c = 3 0 \ p c = 5 0 \ p c == 7 o \ 0.7

~ Z(PbTe) \

n^

1

0

\ 1

1

25 50 75 100 PbTe Phase Fraction, Vf / vol.%

Figure 3. Thermoelectric figure of merit of SiGe/PbTe composite numerical model.

A = 0.2 A = 2.0 (a) Pc=70 (d) Pc=70 (b) Pc=50 (e) Pc=50 (c) Pc=30 (f) Pc=30

I

o

4.50

r^^

1

Z(PbTe)

m \^ \ ycc) 1

11.00 h

^^^y

|Z(SiGe)

tL,

Z(SiGe)

2.00 h=1.0 (d) Pc=70 /^ (e) Pc=50 / 1 (f) Pc=30 /

fe^^^W

N •a

T = 900K

\

0.8

2.00

I

numerical model with percolation point Pc [vol.%] / ' ^ r \

4g

^ ^

, \ Z(PbTe)

0.50

1000 800 900 Temperature, 7 / K (1) thermal conductivity reduction and figure of merit of numerical model with percolation point Pc (vol.% PbTe), where :

700

/c=ph

PbTe + (l-ph)/CsiGe

0.50

700

800 900 1000 Temperature, 7 / K (2) percolation transition width and figure of merit of numerical model with percolation point Pc (vol.% PbTe), where : P =f' P PbTe + ( ! - " / ) • P SiGe / =1.0/(exp(Pc-p)/A+1.0)

Figure 4. Parametric consideration for the figure of merit of the numerical model of SiGe/ PbTe graded thermoelectric composite.

518 3. Fabricating SiGe/PbTe graded composite 3-1 Aim of experiment Altiiough die numerical evaluation shows die possible thermoelectric property enhancement, there are not any appropriate experimental data on thermoelectric properties of composite. The aim of the following experimental procedure and some results is to collect basic data for composite thermoelectric materials design. 3-2 Experimental procedure The experimental procedure so far we have tried is described in Figure 5. The starting non-dope powders were prepared by High Purity Chemicals Co. Ltd. The impurities for conduction type adjustment were added via mechanical alloying, using steel tumbler mill, in argon atmosphere.

Starting powder Si-20at%Ge, PbTe ( 3N) Prealloyed / non-doped

I

Doping (via mechanical alloying) SiGe: B(p-type), P(n-type) PbTe: Ag2Te(p-type), Pbl2(n-type) Powder blending SiGe-30,50,70vol%PbTe Die compaction 100 MPa CIP 200 MPa I HIP in vacuum glass capsule 1123K / Ih / 200 MPa (Argon)

3-3 Results The thermoelectric properties of doped and Evaluation sintered samples are presented in Table 1. The p \ room temp.( Van der Pauw) electrical resistivity of the composite made by AC : 2 9 3 -- 1073 K ( laser flash) those doped powders become very high, XRD, EPMA a \ room temp. compared to monolithic phases. So far, we consider the results to have been caused by Ge diffusion between SiGe/ PbTe interface. By EPMA analysis, 0.9-3.5at% of Ge were probed Figure 5 Possible procedure of fabricating in PbTe phase. After the experimental work monolithic SiGe, PbTe and also the graded by T.Abakumowa [12] such Ge atoms could thermoelectric composite. work as donor site in PbTe lattice. The thermal conductivity of the composites showed modest monotonous reduction with increase of second phase (PbTe) composition.

I

Table 1 Mechanically doped impurities and the thermoelectric properties of sintered monolithic SiGe and PbTe test samples used to prepare SiGe / PbTe composite.

thermoelectric properties

Seebeck coefficient ( fi VK'^) Electrical resistivity ( 0 cm) Carrier density (cm'^)

SiGe p-type

n-type

B 0.5at%

P 0.5at%

171 135 5.417E-3 3.407E-3 6.514E+19 1.372E+20

PbTe p-type Ag2Te 2.0 mol%

n-type Pbl2 2.0 mol%

59 156 3.136E-4 9.217E-4 1.504E+19 5.333E+19

519 4. Summary Application of percolation conduction model on thermoelectric composite material has been considered using simple numerical model. The possible thermoelectric property enhancement were illustrated on SiGe / PbTe composite and graded structure model. The model, however, does not include composite microstructure geometry explicitly, so far. The possible experimental procedure and some results were also described. With simple powder metallurgical experiments on preparing composite SiGe/PbTe mixed phase material, the following results were obtained : (1) The electrical resistivity of the composite made by those doped powders become very high, compared to monolithic phases. We consider the results to have been caused by Ge diffusion between SiGe/ PbTe interface. (2) The thermal conductivity of the SiGe/PbTe composite showed modest monotonous reduction with increase of second phase (PbTe) composition. Acknovpledgement This work is partly supported by a grant from the research project in the Science and Technology Agency of Japan on the Development of Functionally Graded Materials for Energy Conversion. Reference 1. G.D.Mahan, J. Appl. Phys.,70 (1991) 4551. 2. T.Hirano, L.W.Whitlow and M.Miyajima, Ceramic Transactions, Functionally Gradient Materials, Ed. by J.B.Holt, M.Koizumi, T.Hirai and Z.Munir, The American Ceramic Soc, 34 (1993) 23. 3. F.D.Rosi, J.P.Dismukes and E.F.Hockings, Elec. Eng., 79 (1961) 450. 4. D.J.Bergman and O.Levy, J. Appl. Phys., 70 (1991) 6821. 5. S.Kirkpatrick, Rev. Mod. Phys., 45 (1973) 574. 6. R.Landauer, AIP conference proc., No.40 (1978) 2. 7. J.P.Straley, J. Phys. D, 14 (1981) 2101. 8. D.Stauffer, Introduction to Percolation Theory, Taylor & Francis, (1985). 9. O.Levy and D.J.Bergman, J. Phys., A25 (1992) 1875. 10. F.Lux, J. Mat. Sci., 28 (1993) 285. 11. R.Watanabe, J.Takahashi and A.Kawasaki, 3rd Ind. Symp. on Structural and Functionally Gradient Materials, Lausanne, Ed.by B.Ilshner and N.Cherradi, Pressis polutechniques et universitaires romandes, (1995) 3. 12. T.A.Abakumowa, et al, Neorg Mater, 30 (1994) 1121.


521

Design of Multi-Functionally Graded Structure of Cylindrical RI Heat Source for Thermoelectric Conversion System S.Ainada% J.Terauchi^ and T.Senda^ ^Dep. of Mech. Eng., Gunma University, 1-5-1, Tenjin, Kiryu, Gunma, 376, JAPAN ^Ship Research Institute, 6-38-1, Arakawa, Mitaka, Tokyo, 181, JAPAN The graded structure with the multiple functions is required to construct a radioisotope (RI) heat source for a thermoelectric conversion system. The first function is to get the surface temperature of the heat source as possible as high and the other must have a radiation shielding function. This structure is a cylinder, composed of RI-SrTiOg as a heat source and BN as a radiation shielding material. The composite Rl-cylinder must be designed to maxmize the surface temperature and to minimize the radiation intensity. It is presented that an optimum graded distribution of RI-SrTiOg exists to satisfy two distinct requirements. 1. INTRODUCTION Substitute energy developments are indispensable problem in our generation. As one of those candidates, RI thermoelectric conversion system is noticed [1,2]. This system is based on Seebeck effect which transforms temperature difference into voltage difference directly. In order to increase the efficiency of RI thermoelectric conversion system, not only a development of high efficient thermoelectric conversion materials but also a Rl-heat source structure must be done. The Rl-heat source must satisfy two requirements, those are an effective radiation shielding property and keeping the operating temperature below the melting point of heat-source material. Under these conditions, the surface temperature of Rl-heat source must be increased as high as possible. As Rl-heat source, we selected SrTiOg, a chemical compound of Sr-90 extrated from the waste nuclear fuel, and boron notride (BN) which controls to generate bremsstrahlung r -ray. Assuming that the RI heat source

522 is constructed from a cylinder mixed SrTiOg and BN, its optimum multi-functionally graded structure is studied to satisfy two distinct requirements, high surface temperature of the heat-source and low dose^, which leads to an efficient thermoelectric conversion system. 2. ANALYTIC METHOD 2.1. Temperature analysis The steady state heat conduction equation with heat source in cylindrical coordinate system is given by 1 d>. dT

1 dT d^T g(r) ^ + —5- + -2l2 = o (1) A, dr dr r dr dr X where T is temperature, r is radius, A is the temperature-dependent thermal conductivity and g is the heat generation rate. The estimated formula of the thermal conductivity of the composite material is given by Maxwell-Eucken formula [3]. +

2.2. r -ray shielding analysis Sr-90 is /3 -decay and its daughter nucleus Y-90 is also /3 -decay. Since jS -ray interacts with the coulomb field of the atomic nucleus, it radiates the secondary radiation, called bremsstrahlung [4,5]. Radiated r -ray has a continuous energy spectrum (0.11 '^ 2.09 MeV). The radiation shielding analysis is focused on the bremsstrahlung r -ray in this study. Assuming that the radiation source is an area radiation one accumulating of point isotropic sources, the distrbution of radiation energy is approximated by mono-energy (1 MeV). It is also assuming that there is no buildup (B=l). Putting the gamma-ray evaluating point P on the distance 30 cm from the central axis of the Rl-cylinder, the r -ray dose is calculated by •SB 2 exp(-i;|iiti)rdrde

(2)

where (f) is the r -ray flux at the point P, r is the distance from the point of radiation source to the point P, S is the r - r a y strength, B is the buildup factor, p. is the r -ray attenuation coefficient, t is the thickness of the shield. 2.3. Analytic model We selected a hollow cylindrical model. The base structure consists of two-layers of SrTiO, 100% and BN 100% as shown in Fig.l. This structure has a power 50 kW

523

with the heat generation rate of RI-SrTiOg 2.3 W/cm^ Let us look for the graded structure to optimize two functions high surface temperature and low dose based on the base structure. The composition distribution is represented by a modified probability density function based on un-symmetric T distribution function [6].

f{r) = r(a + l)Z?^ ^ { - r + 0.0l(r2-ri)ci}'exp

-r + 0.0l(r2-ri)q (3)

where F is the F function, r is radius, r^ the inner sufiface and r^ the outer surface radius. l{f(r)>l,f(r) equals to 1. Eq.(3) is defined as the graded composition distribution function. This function is not only symmetrical, but also r e p r e s e n t s various distributions by changing parameters (a,b,c^c^) as shown in Fig.2. In this study, focusing the parameter a of four parameters, and we call it the gradient parameter. We analyze the temperature and the radiation dose by changing the graFig.l Base structure (two-layer dient parameter. hollow cylindrical structure). 2.4. Evaluation method Let the temperature performance index r) ^ be defined by eq.(4) to estimate an improvement of the temperature performance. "^^

T^-T,

(4)

where Tând T^ are the surface temperature of the graded and the base structure, T^ is the melting point of Rl-cylinder (2313 K). Next, the r -ray shielding performance index 77 is defined by eq.(5) to estimate an improvement of the radiation shielding performance. Tly=l-*/K

(5)

where (t> and (f) ^ are the r -ray flux of the graded and the base structure. Let us introduce the integrated performance index 77 . defined by eq.(6) to estimate by combined i] ^ and 77 ^ . r|i = a-r|T+(l-a)-r|^ where a is the weight coeficient.

(6)

524 3. RESULTS AND DISCUSSIONS Fig.3 shows the rerationship between the temperature and the r -ray performance index r? ^, 7? ^ and the gradient parameter a. Generally, moving the distribution of SrTiOg to outside, the temperature performance increases. Oppositely, moving the distribution of SrTiOg to inside, the r -ray shielding performance increases. There is a trade-off relation between them. Accordingly, it is not enough only one-functional design of the graded structure for the Rl-heat souce. The graded structure of the Rl-heat souce must be designed by integrating two distinct functions. Assuming that the optimum design demands n =0, the optimum gradient parameter lead to a=2.2, and the temperature performance index n ^=0.39. It shows that the temperature performance is raised 39 % as compared with the base structure to make the graded structure, which means that the surface temperature increment increases 500 K. Its optimum graded structure and temperature distribution are shown in Fig.4 and Fig.5. According to these figures, the optimized structure leads to the gentle temperature gradient and higher surface temperature. In case of changing the weight coefficient a which specifies a weight of temperature and dose in the design, the integrated performance index curves are shown in Fig.6. The gradient parameter a which gives the maximum value of each curve corresponds to the optimum gradient parameter a^^^. Fig.6 shows that there is the optimum gradient parameter which obeys the specification of the design, and it exists the optimum graded structure. The relationship between the weight coefficient a and the optimum gradient parameter a^^^ is shown in Fig.7. It was shown that a^ ^ is smaller as a is larger which corresponds to the design weighted on the

Temperature performance index TJ

0.5 0.0

r ''i

0.01(r^-rj)c^ ^2

Radius, r Fig.2 Graded Structures (a=0.1, 1.0, 2.0, 3.0).

1

2 3 4 5 Gradient parametera, a

Fig.3 Variations of temperature and r - r a y shielding performance index (b=4, c^: =86).

525 2500 |Meltingpoint(2313K)

^ 100^ ^ c o

Base structure

80-

1 60Co

E

40

S

20

CO

structure

^ 2000 4 I— 1500

Optimum graded structure

Base structure

I 1000 E" ^

500 4

OH

04 10

25

15

0

Radius, r / cm

10

15

20

25

Radius, r / cm

Fig.5 Temperature distributions of base structure and optimum graded structure (a=2.2, b=4, Cj=86).

Fig.4 SrTiOg volume fractins of base s t r u c t u r e a n d o p t i m u m graded structure (a=2.2, b=4, c^=86).

surface temperature. That is to say, the design puts emphasis on the temperature performance, as the distribution of RI-SrTiOg moves to outside. The temperature gradient becomes smaller because the SrTiOg layer with low thermal conductivity can be thin to keep a constant volume as the layer moves to outside. At the same time, the r -ray shielding performance deteriorates because the radiation source moves to outside and the shielding layer is thinner. Deciding the weight coefficient a to satisfy the requirement, we can get the optimum graded structure for each a as shown in Fig. 8. Compared with the temperature performance, the radiation shielding performance was not improved in this study whose analytic model is two-ingredient system of SrTiOg and BN. Its maximum value is + 7 ^ 8 % . The reason is why BN can control producing the bremsstrahlung r -ray, because it is light material, but cannot shield ?r"~ 1 . 0

§• 4

0=0.9

I 0.5 03

S 0.04 c

//x\

CO

1-o.s

rr/\\

2.-1.0

j

^^^"^

2 4T

^Q3

0)

\ a=0.1"; E iE o. O

? -1.5 \ = -2.04 0

O

i 1

i 2

1

i

3

4

5

Gradient parameter, a

Fig.6 Integrated performance index curves ( a =0.1, 0.3, 0.5, 0.7, 0.9).

0

0.2 0.4 0.6 0.8 1.0 Weight coefficient, a Fig.7 Relationship between optimum gradient parameter aopt and weight coefficient Of . 0.0

526 radiated r -ray. It is expected that the radiation shielding performance may be considerably improved by two phase shielding. The first shielding must be done by a light material like BN located at the radiation souce in order to restraint producing the b r e m s s t r a h l u n g r -ray, and t h e second shielding by a heavy material (ex:Pb,W,etc.) located at the outer layer in order to shield radiated r -ray. The design of multi-ingredient graded structure is a future problem.

uu-

"•'^ôc=0.1

80-

(x=0.5"'"->i pa=0.3

600=0.7

4020-

cx=0.9

oJ

— 1 —

5

""'

— r"^*^*****!^— 10 15 20 Radius, r / cm

'"i"

Fig.8 Optimum graded structures ( a = 0 . 1 , 0.3, 0.5, 0.7, 0.9).

4. CONCLUSIONS We got the following conclusions. 1) Since there is a trade-off relation between the temperature performance and the r -ray shielding one, the optimum graded design of only one function is not enough. 2) Assuming that the optimum design demands 7? =0, the surface temperature increment increases 500 K, the temperature peraformance could improve 39%. 3) Moving the distribution of RI-SrTiOg to outside, the temperature performance increases. Oppositely moving, the r -ray shielding performance increases. 4) The graded distribution of the Rl-cylinder is effective for a high performance of the heat source. REFERENCES 1. K.Uemura and I. Nishida, Thermoelectric Semiconductor and Application, NIKKAN KOGYO SHIBUN, (1988), 13, (in Japanese). 2. The Science and Technology Agency, The Development Project of High Efficient Thermoelectric Conversion System by Using Functionally Graded Materials: Survey Report, The Society of Non-traditional Technology, (1993),(in Japanese). 3. A.Maezono, Ceramics, 29, (1994), 421, (in Japanese). 4. J.R.Lamrash, Atomic Nucleus Engineering Guide, SACHI-SHOBOU, (1982), 42, (in Japanese). 5. A.Ohashi et al., Procd. Functionally Graded Material 0.7 showed p-type conduction while those of y < 0.7 showed n-type conduction. This result is quite different from the results of typical bismuth telluride based materials which is made by melt process[8]. All n-type samples had 1.5 low Hall mobilities around 100 cmWs r) I (Bi2Te3Vy(Sb2T%)^ therefore only p-type compositions are "E 1.0 in selected to further study on thermoelectric 0 9>\ 0.5 properties. = P-type ^ ^ 0 ^ Figure 3 , 4 and 5 are temperature ^W 0 -_ c : n-type © dependence of Seebeck coefficient , the -0 0.5 1 @ i resistivity and the thermal conductivity as a S CO 1.0 — 0 M function of composition. All the samples 0 lo @ here are of p-type composition. The lines in • 11 1.5 0 0.2 0.4 0.6 0.8 1 Figure 3 and 4 vary in order of composition Composition y y and clearly each peak of line shift to higher temperature range as composition y ^-^^^^ 2. Carrier density - composition 1

1

1

'

1

•

1

1

1

I

1

1

1

1

1

1

1

1

L

536 4.0

300 y=0.8

, o o •-' u o o ,

> =1 250 c0 .2 200

y=o.8o

3.0 • ««• •

0.825

• #o

o

^nDnn°Bi|B! h

o0 ^ 150

0.875 ^ Q O

.

• •

ii"

I I I I I t I I I I I I I I I I I I I I

350

400

450

350

Seebeck coefficient

1

D C

•D

o o

1.3

/

[ L

0.875 \

r

0.9

L

/

1.2

L

- •- '

o 0

.-•''

«

K

t

r °"^ 8 2 5 r

f

0.8 h /

0.6

^•^ /

^^^

500

/

^^ 0.875

^

„

\— 0.7

/•/

^

Ft 0 . 8 2 5 " ^ • ^ - / - . -

1.1 k

^

" ° ^Q _ - c r / ^

h

[-

0.9

//°

"^

450

Figure 4. Temperature dependence of resistivity

1.5

^

400

Temperature /

Figure 3. Temperature dependence of

>

i l " " 0.9

I I I I I I I I I I I I I I I I I I I I I

300

500

Temperature / K

1.4 ^

iB iB

0

100 300 I

Bi

0.875g|

•I 10

0.9

0.825»**

2.0

.1 I I I I I I I I I I I I I I I I I I I I I I I I I I I I

35

"

E

v30

-"^ CD

25

> "D

•• 1

CO

"o

• • •

20

. °—» •

15

y=0.825

y=0.9

y=0.8

Figure 7. Bithmus and antimony content measured by EDX.

15 10

o

Upper

20

E %

o Q.

•+-•

O

30

D forward : • reversed 25

10

5

5

0

Q.

"3 O

I I I I I I I I I I I I I I I I I I I I I Igfif^.

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Current / A Figure 8. V-I and P-I characteristic of FGM sample.

538 4.CONCLUSIONS In this paper preparation and characterization of compositionally graded thermoelectric element were discussed. The sample preparation was successfully performed by using PIES / hot-press method and the figure of merit showed a maximum value of ZT= 0.88 for y = 0.825 at 340K. The figure of merit Z J showed a strong dependence on its composition and design and preparation of compositionally graded sample was successfully performed. Output characteristic of the FGM sample was measured under practical operating condition , AT=200K. The electrical output for forward temperature gradient was 6% higher than that for reverse one. This asymmetry for forward and reverse temperature gradient seems to stem from functionally graded structure of the sample. REFERENCES l.T.Caillat et.al., Mat. Res. Soc. Symp. Proc. Vol. 234 (1991), 189. 2.T.0hta et.al., The 8th Proc. Int. Conf on Thermoelectrics , Nancy , (1989), 7. 3.T.0hta et.al., The 13th Proc. Int. Conf on Thermoelectrics , Kansas City , (1994), 267. 4.T.0hta et.al., The 14th Proc. Int. Conf on Thermoelectrics , St. Petersburg , (1995), 24. 5.T. Caillat et.al., The 11th Proc. Int. Conf on Thermoelectrics , Arlington , (1992), 240. 6.T.0hta et.al., The 11th Proc. Int. Conf on Thermoelectrics , Arlington , (1992), 74. 7.B.A. Cook et.al., The 9th Proc. Int. Conf on Thermoelectrics , Pasadena , (1990), 234. 8.J. Shim et.al., The 9th Proc. Int. Conf on Thermoelectrics , Pasadena, (1990), 27.


539

Microstructure and thermoelectric properties of p-type Bio.5Sb1.5Te3 fabricated by hot pressing Doo-Myun Lee, Jun-Ho Seo, Kyeongsoon Park^, Ichiro Shiota^, Chi-Hwan Lee Dept. of Metallurgical Engineering, Inha University, Inchon 402-751, Korea ^Dept. of Materials Engineering, Chung-ju National Univ., Chungbuk 380-702, Korea Dept. of Chemical Engineering, Kogakuin National University, Tokyo 192, Japan The p-type Bio.5Sb1.5Te3 compound doped with 4.0 wt% Te was fabricated by the hot pressing at the temperature range 380 to 440 °C under 200 MPa in Ar. The microstructure and thermoelectric properties of the compound were investigated. Optical microscopy, scanning electron microscopy, and X-ray diffraction were used to examine the microstructure. The microstructure was relatively dense. The density was increased with increasing the pressing temperature. The grains were preferentially oriented through the hot pressing and also the degree of preferred orientation was increased with the pressing temperature. It was also found that the figure of merit was increased with increasing the hot pressing temperature. The highest figure of merit (2.69 x 10"'^/K) was obtained at 420 °C. 1. INTRODUCTION Bi2Te3-based compounds are well known to be good thermoelectric materials for the applications near room temperature. The crystal structure of Bi2Te3 at room temperature is rhombohedral (a=0.438 nm and c=3.049 nm) [1]. This crystal is composed of atomic layers in the order of Te/iSi/Te/Te/ Bi/Te/Bi/Te/Te/ along the c-axis. The Te/Te layers are considered to be weakly bound with van der Waals forces [2]. The crystal has distinct cleavage planes perpendicular to the c-axis. Owing to the cleavage feature, the crystal has low mechanical properties and poor ability in micro-processing for fabricating the miniature thermoelectric modules and is inappropriate for mass production of thermoelectric modules. Many attempts were made by sintering to fabricate miniature modules without cleavage. However, sintering technique is not effective because the figure of merit of sintered compounds is lower than that of single crystals. In this work, we fabricated the p-type Te-doped Bio.5Sb1.5Te3 compound by the hot pressing and then investigated the microstructure and thermoelectric properties of the compound. 2. EXPERIMENTAL PROCEDURE To fabricate the p-type Bio.5Sb1.5Te3 compound doped with excess 4.0 wt% Te, the starting powders with >99.99 % purity were mixed. The powders mixture was placed into Si02 tube with 25 mm diameter and 330 mm length. Then, the tube was evacuated below 10" torr and sealed. The powders

540

mixture was heated at 700 °C. The melt in the tube was stirred under a frequency of 5 times/min at 700 °C for 6 hours using a rocking furnace to make a homogeneous melt without segregation. The tube containing the melt was cooled in furnace. The solidified ingot was crushed into fine flakes using AI2O3 bowl. The resulting flakes were ball milled for 12 hours and then sieved to prepare powders with 45-74 fm size. To remove the oxygen developed during the crushing and ball milling, the resulting powders were reduced in hydrogen atmosphere at 380 °C for 4 hours. The powders were compacted by the hot pressing at the temperature range 380-440 °C at steps of 20 "C under 200 MPa in Ar to produce the billets with 30 mm diameter and 6 mm length. The density of the hot-pressed compound was measured by pycnometer (Micrometric Co.). The compound for optical microscopy was etched with a solution of HN03*H20=1:1. The preferred orientation of grains was investigated by X-ray diffraction (XRD). The thermoelectric properties were measured at room temperature along the direction perpendicular to the pressing direction. The samples with dimensions of 2 x 2 x 1 5 min and of 4 x 4 x 4 mm were cut out of the compound for the measurements of Seebeck coefficient a and thermal conductivity /c and of the electrical resistivity p, respectively. Then, their surfaces were polished with a series of SiC polishing papers of up to #2000 and further polished on a polishing cloth impregnated with AI2O3 powders of 0.3 //m size. To measure the Seebeck coefficient a, heat was applied to the sample which was placed between the two Cu discs. The thermoelectric electromotive force (E) was measured upon applying small temperature difference ( J T < 2 "O between the both ends of the sample. The Seebeck coefficient a of the compound was determined from the E / J T . The electrical resistivity p of the compound was measured by the four-probe technique. The repeat measurement was made rapidly with a duration smaller than one second to prevent errors due to the Peltier effect [3]. The thermal conductivity K was measured by the static comparative method [3] using a transparent Si02 ( K =1.36 W/Km at room temperature) as a standard sample in 5 x 1 0 torr. 3. RESULTS AND DISCUSSION 3.1 Microstructure It was found that the p-type compound was relatively dense. The density was increased with increasing the pressing temperature because of the porosity decrease. The decrease results from an improvement in the bonding between the powders. We could not fabricate successfully the compound at 440 °C because of the local melting of the powders. The melt was identified as Te used as a dopant. Fig. 1 shows the optical microstructures along the longitudinal and transverse directions for the compound hot pressed at 420 °C. The dark areas shown in Fig. 1 correspond to the pores. The porosity present in the compound was decreased with the pressing temperature. To investigate the orientational change of grains depending on the pressing temperature, XRD analyses from the perpendicular and parallel sections to the hot pressing direction were made. Fig. 2 (a) and (b) show the XRD patterns obtained from the perpendicular and parallel sections, respectively, for the compounds hot pressed at 380, 400, and 420 °C. The intensity of the (0 0 15) and (0 0 18) planes from the perpendicular section is much stronger than that from the parallel section and is increased with increasing the pressing temperature. Also, the intensity of (0 0 6) plane is only observed at the perpendicular section. The (0 0 6), (0 0 15), and (0 0 18) planes are perpendicular to the c-axis. This indicates that the grains are preferentially oriented through the hot pressing and also the degree of preferred orientation

541

Fig. 1. Optical micro structures along the (a) longitudinal and (b) transverse directions for the compound hot pressed at 420°C

liT 380 X)

o o!2 OO

N

lii*iiiiiiiA

400*0 c

I LuJjJLaXjJ 42013

JJ\.J„ 20

30

XiiiU^^ 40

2e (DegrM)

20

30

40

26 (D«grM)

Fig. 2. XRD patterns obtained from the (a) perpendicular and (b) parallel sections to the hot pressing direction for the compounds hot pressed at 380, 400, and 420 °C is increased with the pressing temperature. It is thus expected that the thermoelectric properties will be improved with increasing the temperature owing to the increase in density and preferred orientation. It has previously been reported that the preferred orientation of grains in unidirectionally solidified materials is observed and the growing direction is perpendicular to the c-axis.

542 3.2 Thermoelectric properties Fig. 3 shows the carrier concentration nc and mobiUty ju as a function of the pressing temperature. With increasing the pressing temperature, the carrier concentration and mobility of the compound are decreased and increased, respectively. The increase in mobility results from the porosity decrease. The variation of Seebeck coefficient a with hot pressing temperature is shown in Fig. 4. As the temperature is increased, the Seebeck coefficient is slightly increased because of the

> CM

E b

Hot Pressing Temperature (ic)

Fig. 3. Carrier concentration nc and mobility // as a function of the hot pressing temperature.

decrease in carrier concentration. The relationship between the a and nc can be expressed as follows- a ~ r-ln nc, where r is the scattering factor [4]. The variation of electrical resistivity

300

250

>

200 h

150

380

400

420

Hot Pressing Temperature ("C)

Fig. 4. Variation of Seebeck coefficient a with hot pressing temperature.

380

400

420

Hot Pressing Temperature Cc)

Fig. 5. Variation of electrical resistivity p with hot pressing temperature.

p with hot pressing temperature is shown in Fig. 5. As the hot pressing temperature is increased, the electrical resistivity of the compound is decreased. The electrical resistivity can be expressed as the following relationship: p=l/nce/jt. As a consequence, two competing factors, carrier concentration and mobility, determine the electrical resistivity. Therefore, it seems that the decrease in electrical resistivity with increasing the pressing temperature would result from a significant increase in mobility and a slight decrease in carrier concentration. Fig. 6 shows a plot of thermal conductivity K VS. hot pressing temperature. The thermal conductivity is increased with the pressing temperature probably because of the density increase. Fig. 7 shows the figure of merit Z of the compound hot pressed at various hot pressing temperatures. The figure of

543

merit is increased with the pressing temperature because of the decrease m porosity and increase in preferred orientation. The compound hot pressed at 420 °C shows the highest figure of merit (Z-2.69X10 /K).

380

400

420

Hot Pressing Temperature ("c)

Fig. 6. Relationship between the thermal conductivity K and hot pressing temperature.

380

400

420

Hot Pressing Temperature (x;)

Fig. 7. Figure of merit Z of the compounds hot pressed at various hot pressing temperatures.

4. CONCLUSIONS The hot pressed p-type doped with 4.0 wt% Te Bio.5Sb1.5Te3 compound was found to be densified up to 99.0 % of theoretical density. The hot pressmg gave rise to a preferred orientation of grains and also the degree of preferred orientation was increased with increasing the pressmg temperature. It was also found that the figure of merit was increased with mcreasmg the pressing temperature due to the porosity decrease and the preferred orientation increase. The compound fabricated at 420 °C showed the highest figure of merit (2.69x10 7K).

REFERENCES 1. R. W. G. Wyckoff, Crystal Structure Vol. 2, Interscience Publishers, New York 1964 2. J. R. Weise and L. Muller, J. Phys. Chem. Solid, 15 (I960) 13 ^^^.^ .^ 3 A Goudot, P. M. ScWicklin, and J. G. Stockholn, 5th ICTEC (1984) 49. A K Uemura and I. Nishida, Thermoelectric Semiconductors and Their Application, Nikkan-Kogyo Shinbun Press, Tokyo, Japan, 1988.



545

Microstructural and thermoelectric properties of hot-extruded p - t y p e Bio.5Sb1.5Te3 Jun-Ho Seo, Doo-Myun Lee, Kyeongsoon Park^, Jong-Hoon Kim^, Isao A. Nishida"^, Chi-Hwan Lee Dept. of Metallurgical Engineering, Inha University, Inchon 402-751, Korea ^Dept. of Materials Engineering, Chung-ju National Univ., Chungbuk 380-702, Korea Korea Academy of Industrial Technology, Shiheung 429-450, Korea ^National Research Institute for Metals, Tsukuba 305, Japan The p-type Bio.5Sb1.5Te3 compound doped with 4.0 wt% Te was fabricated by the hot extrusion at the temperature range of 300-510 °C under an extrusion ratio of 201 and a ram speed of 5 cm/min. The microstructure of the compound was investigated by scanning electron microscopy and X-ray diffraction. The microstructure was highly dense and fine-grained (~1.0 fim). The hot extrusion gave rise to a preferred orientation of grains. With increasing the extrusion temperature, the bending strength and figure of merit were increased due to the porosity decrease. The highest bending strength (92 MPa) and figure of merit (2.94xiO'7K) were obtained at 440 °C. It is proposed that the hot extrusion reduced a grain size and increased a density, resulting in an improvement in bending strength and figure of merit. 1. INTRODUCTION Bismuth telluride (Bi2Te3) compound has been used as thermoelectric cooling and heating materials, since it has a high figure of merit (2.5xlO~/K 3.0 X10' /K) at room temperature and can be fabricated easily and chiefly. Many workers have reported on the fabrication and thermoelectric properties for the compound. The compound has a rhombohedral structure (a=0.438 nm and c=3.049 nm) and belongs to space group R3m. The electrical and mechanical properties are higher along the two equilivalent directions parallel to the (001) cleavage planes than the c-axis [1, 2]. Since the compound has the easy cleavage planes, it has difficulty for the mass production of small thermoelectric modules. The grain refinement and mechanical properties improvement may avoid the easy cleavage features. In this work, we attempted to refine the grains and to improve the mechanical properties by means of the hot extrusion. 2. EXPERIMENTAL To fabricate the p-type Bio.5Sb1.5Te3 doped with excess 4.0 wt% Te, the starting powders with >99.99 % purity were mixed. The powders were

546 compacted by the hot pressing at 420 "C and 200 MPa in Ar to produce the billets with 30 mm diameter and 60 mm length. Subsequently, the compacted billets were hot extruded at the temperature range 300-510 °C at steps of 70 "C under an extrusion ratio of 20:1 and a ram speed of 5 cm/min. The density of the compound was measured by pycnometer (Micrometric Co.). The preferred orientation of grains for the compound was investigated by X-ray diffraction (XRD). The mechanical properties were measured at room temperature under a crosshead speed of 0.5 mm/min by three-point bending in accordance with ASTM D790 using a universial testing machine. The thermoelectric properties were measured at room temperature along the direction parallel to the extrusion direction. The samples with dimensions of 2 X2X15 mm and of 4 x 4 x 4 mm were cut out of the compound for the measurements of Seebeck coefficient a and thermal conductivity K and of the electrical resistivity p , respectively. Then, their surfaces were polished with a series of SiC polishing papers of up to #2000 and further polished on a polishing cloth impregnated with AI2O3 powders of 0.3 pm size. 3. RESUTLS AND DISCUSSION 3.1 Microstructure and mechanical properties At the hot extrusion temperatures of 300-440 °C, we obtained good extruded bars without any defects such as tearing, orange peel, and blister. However, hot cracks were developed during the hot extrusion at 510 "C. This would result from the local melting due to the heat formed by the friction between the billets and die. The relative density of the compound was increased with increasing the extrusion temperature. This increase occurs due to the decrease in the porosity because of an improvement in the bonding between the powders. The highest relative density was obtained at 440 °C and its value was 99.6 % of theoretical density. The XRD patterns obtained from the compound hot extruded at 440 °C are shown in Fig. 1. Fig. 1(a) and (b) in (a) show the XRD patterns obtained from a. 1 the perpendicular and parallel sections to the hot extrusion direction, respectively. The intensity of (0 0 6), (0 0 15), and (0 0 18) planes, which are perpendicular to the c-axis, is only observed at the parallel section. (b) This indicates that the hot extrusion gave rise to a preferred orientation of s 0 grains. The bending strength was 0 ^ & increased with increasing the extrusion 0 e temperature. The increase in bending strength results from the porosity 50 60 decrease. The bending strength of the 2 e (Degree) compound hot extruded at 440 °C was 92 MPa. The fractograph of the compound hot extruded at 440 °C is shown in Fig. 2. The fractograph Fig. 1. XRD patterns obtained from transgranular cleavage the (a) perpendicular and (b) parallel represents sections to the hot extrusion. features. The fracture path follows transgranular cleavage planes. The

UJiii

547

,^>f\c-',*.

•yft.

iGjLOB

orientation change from grain to grain was also found. The grain size estimated from this fractograph is ~ 1.0 fM. We believe that the hot extruded compound with high strength and small grain size leads to an improvement in the bonding strength between the thermoelectric materials and metal electrode during soldering for the fabrication of thermoelectric modules and leads to a good ability in micro-processing for fabricating the miniature thermocouples for the semiconductor devices.

Fig. 2. Fractograph of the compound hot extruded at 440 °C.

3.2 Thermoelectric properties Fig. 3 shows the carrier concentration Uc and mobility // as a function of the hot extrusion temperature. As the hot extrusion temperature is increased, the charge carrier concentration is decreased and the mobility is significantly increased. The significant increase in mobility occurs due to the porosity decrease. The variation of Seebeck coefficient a with hot extrusion temperature is shown in Fig. 4. This figure represents that the Seebeck coefficient is increased with increasing the extrusion temperature because of the decrease in 300 370 440 Hot Extrusion Temperature (Tc) carrier concentration. The relationship between the a and nc can be expressed as follows^ a ~ r-ln nc, where r is the scattering factor [4]. Fig. 3. Carrier concentration HC and The values of a for the compound hot mobility /u as a function of the extruded at 300 and 440 t are 145.8 hot extrusion temperature. and 231.1 //V/K, respectively. The relationship between the electrical resistivity p and hot extrusion temperature is shown in Fig. 5. As the hot extrusion temperature is increased, the electrical resistivity was decreased. This is because with increasing temperature, the scattering of carriers is decreased due to the decrease in porosity and thus the mobility is increased. The value of p for the compound extruded at 440 °C is 1.85x10"^ Qm.

548

250

^% 6h

^"^^^

200

^ >=1 Q

150

•

X

100 1 300

370

440

300

Hot Extrusion Temperature ("C)

Fig. 4 Variation of Seebeck coefficient a witii hot extrusion temperature.

370

440

Hot Extrusion Temperature (ic)

Fig. 5. Relationship between the electrical resistivity p and hot extrusion temperature.

Fig. 6 shows plots of thermal conductivity K VS. hot extrusion temperature. The thermal conductivity is increased with increasing the temperature. The increase in thermal conductivity would be strongly affected by the decrease in porosity. Fig. 7 shows the figure of merit Z of the compound hot extruded at various hot extrusion temperatures. The figure of merit is increased with the extrusion temperature due to the decrease in porosity. The compound hot extruded at 440 "C shows the highest value of Z (Z=2.94xl0"^/K).

1.2

•

•

1.0

?

0.8

i^

0.6

Jff

0.4

•

0.2 0.0

1

300

370

1

440


Fig. 6. Relationship between the thermal conductivity K and hot extrusion temperature.

300

370


Fig. 7. Figure of merit Z of the compound hot extruded at various hot extrusion temperatures.

549 4. CONCLUSIONS It was found that the microstructure of p-type Bio.5Sb1.5Te3 compound doped with 4.0 wt% Te was highly dense and fine-grained ( — 1.0 jm). The grains were preferentially oriented through the hot extrusion. The bending strength and figure of merit were increased with increasing the extrusion temperature because of the porosity decrease. The bending strength and figure of merit of the compound hot extruded at 440 °C are 92 MPa and 2.94xiO'^/K, respectively. We believe that the hot extrusion provides enhanced bending strength and figure of merit and is thus a very useful technique for the fabrication of thermoelectric materials. REFERENCES 1. 2. 3. 4.

Y. M. Yim and F. D. Rosi, Solid State Electronics, 15 (1972) 1121. D. M. Rowe, Applied Energy, 24 (1986) 139. A. Goudot, P. M. Schlicklin, and J. G. Stockholn, 5th ICTEC, (1984) 49. K. Uemura and I. Nishida, Thermoelectric Semiconductors and Their Application, Nikkan-Kogyo Shinbun Press, Tokyo, Japan, 1988.



551

Effect of Dopants on Thermoelectric Properties and Anisotropics for Unidirectionally Solidified n-BiiTca N.Abe', H.Kohri\ I.Shiota', and I.A.Nishida' 'Department of Chemical Engineering, Kogakuin University, 2665-1 Nakano-machi, Hachioji-city, Tokyo, 192, Japan ''Institute for Materials Research, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai-city, Miyagi, 980-77, Japan TSfational Research Institute for Metals, 1-2-1 Sengen, Tsukuba-city, Ibaraki, 305, Japan

It is wellknown that thermoelectric properties of n-type Bi2Te3 compounds are affected by dopants. In this work, we used HgBr2, Hgl2, SbBrs and Sbis as the dopants. As a resuh, electrical resistivity p of specimens doped with Sb compounds showed a drop of about 18% as compared with Hg compounds. Thermal conductivity K of specimens doped with bromide showed a drop of about 6% as compared with iodine. The figure of merit Z of specimen doped with Sbis showed the greatest value of 3.88 X lO'^K"^ in these specimens. On the other hands, Bi2Te3 compounds have large anisotropy in the thermoelectric properties because of its crystal asymmetry of R3m.

In this work, anisotropics in hall

coefficient Ru and p of specimens doped with Hg compounds showed about 1.3 times as compared with Sb compounds.

1. INTRODUCTION The Bi2Te3 compound is the most excellent material for thermoelectric cooling materials at around room temperature, and has been widely used in the precise temperature control machines etc. The compound has a layered rhombohedral structure. Then the compound has strong anisotropics on mechanical and thermoelectric properties. The properties vertical to the direction of c-axis are better than parallel[l]. Anisotropy of

552

galvanomagnetism has been investigated by Drabble et al. to deduce expressions for anisotropic galvanomagnetic parameters on the basis of the six-valley model[2][3]. The resistivity along the c-axis is greater than vertical direction to the c-axis, and the hall coefficient measured with a magnetic field in the c-axis is less than that with a magnetic field vertical to the c-axis. HgBr2 has been empirically doped in the practically used n-type Bi2Te3 compounds. Recently, Kaibe et al. reported that Sbis is more effective than HgBr2 as the dopant in sintered n-type Bi2Te2.85Seo.15 [4]. But it is not confirmed which element was effective to improve the figure of merit. In this work, HgBr2, Hgl2, SbBrs and Sbis were used as the dopants. These dopants consist of combination Hg or Sb and Br or I. Each dopant was added in the unidirectionally solidified n-type Bi2Te3 to form a n-type compound. The effects of each element were determined by the combination of the observed values of four specimens. Anisotropics in the unidirectionally solidified n-type Bi2Te3 was also investigated.

2. EXPERIMENTAL PROCEDURE 2.1. Preparation of the specimens Bi and Te of normal purity 99.999% were used as the starting materials. Firstly, an ingot of Bi2Te3 without dopant was fabricated. Proper ratio of Bi and Te were weighed and the mixture of the powder was sealed in a quartz glass tube with 460mmHg Ar. The tubes was stirred sufficiently by using a rocking furnace at 923K, and the melt was unidirectionally solidified by using the Bridgman method with a cooling rate of 2mmh'^ under a temperature gradient of 5Kmm'\ The Rn of the ingot was measured to determine the carrier concentration. Dopant is required to form an n-type Bi2Te3 as Bi2Te3 is p-type. HgBr2, Hgt, SbBr3 or Sbl3 was mixed in the powder which was obtained by pulverizing the ingot. Amount of dopants were determined to adjust the electron concentration of 1.0 X lO^^m"^ at room temperature under the hypothesis that a halogen atom and a Sb atom give an electron and a hole, respectively. The n-type Bi2Te3 doped with each dopant was prepared by same process described above. The obtained n-type Bi2Te3 consisted of a few large crystals, which is very like a single crystal. The ingot consisted of several large crystal grains growing in the direction of soUdification. 2.2. Measurements of thermoelectric properties A sample of 1 X 2 X 7mm\ as shown infig.1 (a) (b), was taken out of the largest grain

553 which consists of a single crystal to measure p and Ru. Temperature dependence of p and Ru were also measured over the temperature range from 80 to 500K where the highest performance can be expected. A specimen of 4 X 4 X 4mm^, as shown infig.1 (c) (d) lower, was also cut out, which is also single crystal. Then the Seebeck coefficient a and K of the specimen were also measured at room temperature by the static comparative method, as shown in fig.2. Afiasedquartz block of the same size as the specimen was used for the standard material of the K. /?l,i^H

1

P//Ifn // Pressure (lOg/cm^)

Heater Thermo couple Specimen 1

Specimen 2 Copper Plate (c)

(d)

Fig. 1 Measurements of thermoelectric properties Subscript of p, Ru, a, and K : direction of measurements to c-axis

Fig. 2 Measurements of K and a

3. RESULTS AND DISCUSSION 3.1.Thermoelectric properties The carrier concentration n^ vertical to the c-axis of each specimen at room temperature were shown in table 1. It was observed that the n^ of each specimen were about 1 X lO^^m"^ equal to expected n^. The temperature dependence of p and Ru in the direction vertical to c-axis of each specimen are shown in fig. 3. The Ru of each specimen shows a same value over the observed temperature range because of the same n^. The Ru of each specimen decreased suddenly at the temperature range more than about 300K. Therefore it is obviously that it

554 Table 1 Thermoelectric properties (at R.T) Ru a [IQ-^Q m] [IQ-VCÎ riQ"'mV^s-^] [lO^^m'^] [ptVK'^] [WK'^m'^]

Dopant

[IQ-'K'^]

HgBr2

7.13

2.74

3.84

0.98

-210

1.78

3.44

Hgl2

6.79

2.49

3.67

1.07

-216

1.90

3.61

SbBrs

5.92

2.64

4.46

1.01

-205

1.99

3.57

Sbis

5.46

2.68

4.91

1.00

-212

2.12

3.88

begins to be influenced by intrinsic range around 300K. The p of each specimen increased with increasing temperature up to about 400K, and decreased suddenly at the temperature range over 400K. It is found that the p of specimens with iodide are less than those of specimens with bromide. It is also found that the p of specimens with Sb compounds are less than those with Hg compounds. The temperature dependence of hall mobility \i vertical to c-axis of each specimen is shown in fig.4. The \x of each specimen decreased with increasing temperature over the observed temperature. The [x of specimens with Sb compounds are larger than those of specimens with Hg compounds over the observed temperature range. This phenomena can be considered as follows; Hg ion traps more electrons than Sb ion as reported that Bi2Te3 compounds are the same crystal structure as Bi2Se3 compounds, and Hg atom acts as acceptor in Bi2Se3 compounds[5]. Moreover, Sb atom influences Bi2Te3 directly, and ionic bond become weaker by doping with Sb compounds[6].

t

1

1

1

1

1

1

^m^

1

1

îs

I

1

%i

1

1

.

10-

i '• 1 1 1

0

i 0 0:HgBr2 • :Hgl2 0:SbBr3 • :Sbl3

[ ^

^>*

4 \

IQ-^h

r

4> 1

1

1

1

1

110

; -

CM

E

•k«1 1

0:HgBr2

a:

• •:Hgl2

2:* €>';^

1 1 10" 10 103/T[K-^] Fig.3 Temperature dependence of Resistivity and Hall coefficient

5

-

> 10-5 Q-

^*

1 91

1

1

• 2*

IQ-^b f O

10

1

i

l

l

O o • O

^

0:SbBr3 10" - • : S b l 3 '

•

1

1

1

9 _ • 1

200 400 T[K] Fig.4 Temperature dependence of Hall mobility

555

The a, K and Z vertical to c-axis of each specimens at room temperature are shown in table 1. The a becomes smaller by doping with Sb compounds. The K of specimens with bromide are smaller than those with iodine. It is considered as follows; the ion radius of bromine is smaller than that of iodine and shows a tendency to exist substitutionally in the Bi2Te3 lattice, and the Kiattice which is the lattice component of the K becomes smaller. The K of specimens with Hg compounds are also smaller than those with Sb compounds. It might be caused by weak ionic bond due to doping with Sb compounds as described above. The Keiectron wMch is the Carrier component of the K become larger. Therefore the Z of each specimen doped with iodine or Sb compounds are larger than those of specimens doped with bromide or Hg compounds. The Z of specimen doped with Sbis is the largest, 3.88 X 10'^K'\ because of very high \x. It is obviously shown that Sbis is the most excellent as the dopant.

3.2.Anisotropies The temperature dependence of p and Ru vertical and parallel to c-axis of each specimen are shown in Fig. 5. Anisotropic coefficients of p and Ru of specimens with Hg compounds are about 2.5 and 2.7 at room temperature, respectively. Anisotropic coefficients of p and Ru of specimens with Sb compounds are about 2.1 and 1.9 at room temperature, respectively. From these results, it is found that anisotropics of specimens with Hg compounds are larger than those with Sb compounds. The anisotropic coefficients of a was only 1.1 in both cases of the specimens doped with Hg or Sb dopants,as shown in table 2.

—

1

i—

1

1

1

1

1

10"

'*

1

• ;o'

1 J

10-

8 " -4 E G

iio-

1

1

1

1

5

t

1

1

• . 1

1

, ,10 10^/T[K-^] (a)HgBr2 and SbBr3

1

1

1

1

1

1

i^B" • • • • • • • • A ^ ^ ^ i ^ ^ 412^^

U m

•

6

a

^

1

10-

•^H

: ^ '

o

' ^ ^

CJ

10-

—

1

1

•

1

•

A

A

1

-

10-

• A

^ ^ ^ ' -ho -4 E a D Hgi2 J-: Hgl2// •A Sbl3 ±•

D

^m^ - 10X :

•• ••

1

. ^ A A A A A A AA A

0:HgBr2 -L; • :HgBr2// 0:SbBr3 -L • :SbBr3// _

o ^ 10-

1

10-

- 10

- o

1

* *

RH

110-^ r 0

10-

1

• ^ e 8 6 o a ^8 5 e. ^

•

u

1

^

• Sbl3// _

10-

;

' % > • • ; . .

• • : « « a -iio1 1 1 1 ^

1

103/T[K-^j

10

(b)Hgl2 and Sbl3

Fig.5 Temperature dependence of Resistivity and Hall coefficient

556 Table 2 Anisotropies of a (at R.T) Dopant HgBr2 Hgl2 SbBrs Sbl3

-210 -216 -205 -212

a//

a i /a//

-191 -200 -183 -194

1.10 1.08 1.12 1.09

4.CONCLUTION n-type Bi2Te3 were doped with HgBr2, Hgl2, SbBrs or Sbls. The carrier concentration n^ of each specimen was highly controlled, and was 1 X lO'^^m"^ at room temperature. The p of a specimen doped with Sbis showed the minimum value, 5.46 X 10'^ Q m. The a became larger by doping with Hg compounds. The K of specimen doped with HgBr2 was the minimum value, 1.78WK"^m'\ The anisotropies of specimens with Hg compounds were larger than those with Sb compounds. The Z of specimen doped with Sbis is the largest, 3.88 X 10"^K'\ because of very high \i. It is obviously shown that Sbis is the most excellent as the dopant.

ACKNOWLEDGMENT We express our appreciation to supporting by Science and Technology Agency.

REFERENCES 1. K.Uemura and I.A.Nishida, Thermoelectric Semiconductor and its appliciations, Nikkan Kogyo Shinbun, LTD., 1983 2. Teledyne Energy System, Gas Fueled Thermoelectric Generators -Engineering and application Manual, TELAN/DECAP, August, 1983 3. S.W.Petric, Opt. Eng. 26, 965(1987) 4. H.Kaibe, "The Studies on the Thermoelectric Properties for Semiconducting Bi2Te3 Compounds", Thesis, 1989 5. Wessenstein. J., Horak. J., Tiehy. L., Vasko. A., :Cryst. Lattice Defects 8 (1980) 223 6. J.Sugihara,Electric Structure and Thermoelectric Properties of Bi2Te3, the Collected Papers of TEC'96,1996


557

Thermoelectric Properties of Arc-melted Silicon Borides Lidong Chen, Takashi Goto, Toshio Hirai Institute for Materials Research, Tohoku University, Katahira 2-1-1, Aoba-ku, Sendai 980-77, Japan

ABSTRACT Silicon borides were prepared by arc melting in a boron content range from 80 to 94mol%. As-melted specimens consisted of SiBn and free silicon. After heat treatment at 1500-1673K, SiB4 formed near the SiBn-Si boundary due to the solid reaction between free silicon and SiBn, and as the result SiBn-SiB4 composites were obtained. The SiBn-SiB4 composites showed larger electrical conductivity and smaller thermal conductivity than the as-melted silicon borides, which leads to an improvement of thermoelectric figure of merit.

1. INTRODUCTION The efficiency of thermoelectric power generation is in proportion to hot junction temperature and the temperature drop between hot- and cold-junctions [1]. Recently, in order to achieve a high conversion efficiency, a new concept called functionally graded thermoelectric material was proposed, in which several types of materials will be joined by graded structure so a broader range of temperature is expected to be covered practically than that is when a homogeneous material is used [2-3]. At present, Bi2Te3, PbTe and SiGe are generally considered practical materials for thermoelctric power generation in the low (about 300 to 500K), medium (about 500 to 800K) and high (about 800 to HOOK) temperature ranges, respectively. Unfortunately, no applicable material has been discovered for the ultrahigh temperature range over HOOK, though some candidate materials have been studied for the past three decades [4-9]. Boron-rich silicon boride is one of the candidate materials for ultra-high temperature thermoelectric conversion because of its moderate Seebeck coefficient (a) and small thermal conductivity (K) at high temperatures over lOOOK [1, 4-6]. In the Si-B binary system, there are many types of compounds such as SiB4 (rhombohedral), SiB6 (orthorhombic) and SiBn (hexagonal, n=15-49) [10-12]. Among them, SiB4 has a low thermal conductivity and high electrical conductivity (a) but a low Seebeck coefficient [13]. On the other hand, SiB6 and SiBn have a large Seebeck coefficient and a low thermal conductivity but a moderately low electrical conductivity. The authors have reported the synthesis and thermoelectric properties of arc-melted silicon borides [14]. As-melted sihcon borides in the boron content range of 80 to 94mol% consisted

558 of SiBn and free silicon, in which the free silicon dispersed in a network structure when boron content is below 90mol%. The existence of free silicon made both the electrical conductivity and thermal conductivity increase, so it did not improve the thermoelectric figure of merits {Z=a^c/K). If the composite of SiBn-SiB4 with SiB4 dispersed in network can be obtained, the decrease of the thermal conductivity accompanied with increase of the electrical conductivity will be expected, and so the thermoelctric figure of merit would be increased. Silicon borides such as SiB6 and SiBn can be synthesized by hot pressing [4], plasma activated sintering [14], arc melting [14] and chemical vapour deposition (CVD) [15]. In the cases of sintering including hot pressing and plasma activated sintering, a high sintering temperature over 1800K is needed. Unfortunately, SiB4 decomposes in 1500-1673K due to its metastability [10, 12, 16-17]. Therefore, SiBn-SiB4 composite is difficult to be synthesized by a sintering method. In the present research, we tried to prepare SiBn-SiB4 composites using arc melting combined with sequent heat-treatment process. In this paper, we report the microstructure changes after heat-treatment and their effects on the thermal conductivity and electrical conductivity.

2. EXPERIMENTAL The mixtures of silicon and boron powder in a boron content range of 80 to 94mol% were pressed into disk-shaped pellets (10 mm thickness and 20 mm diameter) and then arc-melted in an argon atmosphere. The arc-melted samples were then heat-treated in argon atmosphere at temperatures of 1400 to 1700K. The phase composition of the resulted specimens was identified by X-ray diffraction (XRD). Rod-like pieces (3x3x15mm) and disk-shaped pieces (2mm thickness and 10mm diameter) were cut out for the electrical conductivity measurement and the thermal conductivity measurement, respectively. Microstructure and phase distribution were observed by a scanning electron microscopy equipped with EPMA (JEOL: JXA-8621MX). Electrical conductivity was measured using a D.C. four-probe method. Thermal conductivity was measured using a laser-flash technique. All the measurements were performed in the temperature range of 300 to 1200 K.

3. RESULTS AND DISCUSSION Figure 1 shows a typical X-ray diffraction pattern of as-melted silicon boride containing 90mol% boron. In the present boron content range (80 to 94mol%), all the arc-melted specimens consisted of SiBn and free silicon. Figure 2 shows the changes of free silicon content with the boron content in the raw material. The content of free silicon decreased from about 30 to 3vol% as the boron content in raw material increased from 80 to 94mol%. The lattice parameter (a) of

20

25

30

35

26, CuKa / degree Figure 1. X-ray diffraction pattern of an arc-melted silicon boride (B=90mol%).

559 the free silicon was 0.5415nm, which was smaller than the JCPD value (0.543 Inm) [18]. It was reported that the lattice constant of silicon changes from 0.5431 to 5412nm as boron dissolves in silicon up to 3mol%, and the solubility limit of boron in silicon is generally considered about 3mol% [11, 19-20]. Therefore, the free silicon in the melted silicon boride could be almost saturated with boron. We reported that the free silicon phase is inter-connected to form a network structure when B=80-90mol%, while it dispersed isolatedly when B>90mol% [14]. And the Seebeck coefficients is almost independent of phase composition and changes from 100 to 300 jlVK' as the measuring temperature up to HOOK [14]. Figure 3 shows the changes of X-ray diffraction pattern of the melted sample containing 90mol% boron after heat-treatment. Only trace amount of SiB4 formed after annealing at 1538K for 5hr (Fig.3(a)). When the annealing time was 40hr at the same temperature, SiB6 phase appeared but without much change in SiB4 amount (Fig.3(b)). After annealing at 1673K for 0.5hr, moderate amount of SiB4 formed without formation of SiB6 phase (Fig.3(c)). However, after annealing at the same temperature for 2hr, SiB6 appeared and the amount of SiB4 decreased (Fig.3(d)). In the annealing temperatures between 1500 to :3 1673K, SiB4 formed at first, and then SiB6 appeared while the SiB4 amount got decreasing. When the annealing temperature was below 1473K, no new phase appeared even if annealing time is 40hr. And when (c) annealing temperature was over 1680K,

'o

(d) r

I

15

0 75

80

85

Boron content

90

•

14-

20

•

•

.

.

I

25

.

.

•

•

I

I

30

I

I

I

35

29, CuKa / degree 95

/ mol%

Figure 2. Relationship between free silicon content in arc-melted silicon borides and boron content in raw materials.

Figure 3. X-ray diffraction patterns of arcmelted silicon boride (B=90mol%) after heat-treatment. The heat-treatment conditions are: (a) 1538K, 5hr; (b) 1538K, 40hr; (c) 1673K, 0.5hr; (d) 1673K, 2hr.

560

Figure 4. Microstructures of arc-melted silicon boride (B=90mol%). (a) as-melted; (b) after heat-treatment at 1673K for 0.5hr. The A, B and C parts are SiBn, free-Si and SiB4, respectively. only SiB6 formed as the new phase when the annealing time is even lOmin. In general, SiB4 can be prepared in the form of mixtures with SiB6 and/or silicon by melting silicon and boron powder mixtures or heating the mixture powder at temperatures between 1500 and 1673K [12, 16-17, 21], though there is one report that the pure SiB4 was synthesized by heating the stoichiometric mixture at 1473K for about three weeks [16]. It is generally known that, when the mixture powder of silicon and boron are heated at 1500 to 1673K, SiB4 forms at first, and then it slowly decomposes into SiB6 and silicon [10, 12, 16-17]. SiB4 is stable below 1473K. The present experimental results agreed with those reports. The free silicon in the arc-melted silicon borides can be partially changed into SiB4 due to the solid reaction between silicon and SiBn through heat-treatment process by a proper annealing temperature and annealing time. Figure 4 shows the microstructures of the specimen containing 90mol% boron before and after annealing at 1673K for 0.5hr. In Fig.4(a) of the as-melted sample, the EPMA

104

oooc^° °OooOO0OO

000000°

^••••MM**

o

••••••••••••

^ ^ A M A A A A A Â^^'

AAAA

o B=88mol%, B=88mol%, B=90mol%, B=90mol%,

S 103 0.5

1.0

as-melted heat-treated as-melted heat-treated

1.5

X-1

/

2.0

2.5

10-3 K-1

Figure 5. Temperature dependence of electrical conductivity of arc-melted silicon borides before and after heattreatment at 1673K for 0.5hr.

561 study revealed that, the black area (A) is SiBn and bright area (B) is free silicon. In Fig.4(b) of the annealed sample, the black area (A), bright area (B) and the gray area (C) are SiBn, free Si and SiB4, respectively. The free silicon phase inter-connected to form a network structure in the as-melted specimen. After annealing, the free silicon and SiBn reacted near the boundary to form SiB4, and as the result, the silicon network changed into SiB4 network though some silicon still remained within SiB4 mainly at the cross points of the network. Figure 5 shows the temperature dependence of electrical conductivity (a) of arc-melted silicon borides before and after annealing. The larger the free silicon amount, the greater the a values. After annealing at 1673K for 0.5hr, the a values increased about 30-60% for all the specimens. Particularly, the a values of the specimen containing 88mol% boron almost agreed with those of CVD-SiB4 [13]. Figure 6 shows the temperature dependence of thermal conductivity (K) of arc-melted silicon borides before and after annealing. The larger the free silicon amount, the greater the K values. After annealing at 1673K for 0.5hr, K values decreased about 20-30% for all the specimens. They changed from 8 to 6WK-im-^ when measuring temperature increased from room temperature to HOOK, which almost agreed with those of the SiB4 [13, 17] and SiBn [6, 14]. The composite of SiBn-SiB4 showed the greater electrical conductivity and smaller thermal conductivity than the as-melted silicon borides. These changes contribute to the improvement of the thermoelectric property.

4. CONCLUSION 12.0

Silicon borides were prepared by arc melting in argon atmosphere using silicon and boron powders in a boron content range from 80 to 94mol%. The as-melted specimens consisted of SiBn and free silicon. The contents of free silicon decreased from 30 to 3vol% as the boron content in raw material increased from 80 to 94mol%. The free silicon phase interconnected to form a network structure when B=80-90mol%. The as-melted specimens were heattreated in argon at temperatures of 1400 to 1700K. Below 1473K, no phase changes occurred by annealing for 40hr. In the anneahng temperatures of 1500 to 1673K, SiB4 formed at first due to the solid reaction between free silicon and SiBn near the S i B n - S i boundary, and then SiB6 appeared after a longer annealing time due to the d e c o m p o s i n g reaction of SiB4. Through annealing at 1673K for 0.5hr,

•: ii.oH1 r

^ ^

10.0

•

A :

•••••

•---..

' ^^^x ****• N

7.0

as-melted heat-treated as-melted heat-treated

\

••.. 9.0

B=88mol%, B=88mol%, B=90mol%, B=90mol%,

°: A:

6.0 H 5.0 '. 400

i

1

1

600

1

800

Temperature

1

1

1000

1

1200

/ K

Figure 6. Temperature dependence of thermal conductivity of arc-melted silicon borides before and after heat-treatment at 1673Kfor0.5hr.

562 SiBn-SiB4 composites, in which SiB4 is inter-connected into network, were obtained. The SiBn-SiB4 composites showed larger electrical conductivity and smaller thermal conductivity than the as-melted specimens, which leads to an improvement of thermoelectric figure of merit.

ACKNOWLEDGEMENTS We thank Mr. Y. Murakami of IMR, Tohoku University for helping EPMA analysis. This research was supported in part by the Grant-in-Aid for Scientific Research from the Ministry of Education, Science and Culture, under contact nos. NP0701 and (B)06453081, also supported by the Special Coordination Funds for Promoting Science and Technology from the Science and Technology Agency of Japan.

REFERENCES 1. C. Wood, Materials Research Society Symposia Proceedings, Vol 97, Ed. by D. Emin, T. L. Aselage and C. Wood (Materials Research Society, Pittsburgh, 1987), p.335. 2. T. Hirano, L. W. Whitlow, M. Miyajima, Ceramic Transactions, Vol.34, Ed. by J. B. Holt, M. Koizumi, T. Hirai and Z. A. Munir (Amer. Ceram. Soc, Westerville, Ohio, 1993), p.23. 3.1. A. Nishida, Material Technology, 14 (1996) 9. 4. C. Wood, D. Emin, R. S. Frigelson and I. D. R. Mackinnon, Materials Research Society Symposia Proceedings, Vol 97, Ed. by D. Emin, T. L. Aselage and C. Wood (Materials Research Society, Pittsburgh, 1987), p.33. 5. B. Armas and C. Combescure, J. Less-Conmion Met., 47 (1976) 135. 6. J. M. Darolles, T. Lepetre and J. M. Dusseau, Phys. Stat. Sol. (a), 58 (1980) K71. 7. O. A. Golikova and I. M. Rudnik, USSR Neorg. Mater., 14(1978)17. 8. T. L. Aselage: Modern Perspectives on Thermoelectrics and Related Materials, Ed. by D. D. Allred, S. B. Vining and G. A. Slack (Materials Research Society, Pittsburgh, 1991), p.l45. 9. T. Goto, E. Ito, M. Mukaida and T. Hirai, J. Jpn Soc. Powder & Powder Metallurgy, 43(1996)311. 10. R. W. Olesinski and G. J. Abbaschian, Bull. Alloy Phase Diagrams, 5 (1984) 478. 11. B. Armas, G. Male and D. Salanoubat, J. Less-Common Met., 82 (1981) 245. 12. H. R Rizzo, B. C. Weber and M. A. Schwarz, J. Amer. Ceram. Soc, 43 (1960) 497. 13. M. Mukaida, T. Goto and T. Hirai, Mater. & Manufacturing Processes, 7 (1992) 625. 14. L. Chen, T. Goto, J. Li, M. Niino and T. Hirai, Trans. lEE Jpn, 116-A (1996) 248. 15. M. Mukaida, T. Goto and T. Hirai, J. Mater. Sci. 27 (1992) 255. 16. C. Brosset, B. Magnusson, Nature, 187 (1960) 54. 17. R. S. Feigelson and W. D. Kingery, Ceram. Bull., 42 (1963) 688. 18. JCPD card. File No. 27-1402 (1977). 19. G. V. Samsonov and V M. Sleptsov, Russ. J. Inorg. Chem., 8 (1963) 1047. 20. J. Hesse, Z. Metallkd., 59 (1968) 499. 21. H. Moissan and A. Stock, Compt. Rend., 131 (1900) 139.


563

Graded thermoelectric materials by plasma spray forming Jiirgen Schilz"*, Eckhard Miiller", Wolfgang A. Kaysser'', Gregor Langer^, Erich Lugscheider^, Giinter Schiller^, Rudolf Henne^ "German Aerospace Research Establishment (DLR), Institute of Materials Research, D-51140 Koln, Germany Âachen, University of Technology, Materials Science Institute Jiilicher Str. 342, D-52056 Aachen, Germany ^German Aerospace Research Establishment (DLR), Inst, for Technical Thermodynamics, D-70503 Stuttgart, Germany Plasma spraying is a consolidation process for powders with the additional capability of a composition control of the spray formed structures. The paper reports on the first steps to adapt this method to the production of functionally graded thermoelectric materials with a locally maximized figure of merit. Iron disilicide (FeSi2) was used to test the performance of the technique on thermoelectric material. It was found that plasma spray forming is applicable to produce dense materials with thermoelectric properties comparable to hot pressed ones. Problems were however found with the thermal stability of the microstructure. Final goal is the employment of plasma spraying to form compositionally graded materials of the Mg2(Si,Ge,Sn) system. Here we report on the preparation and thermoelectric transport properties of Si-rich quasibinary Mg2(Si,Ge) and Mg2(Si,Sn) mixed crystals by mechanical alloying. 1. I N T R O D U C T I O N Thermoelectric (TE) generators have shown their reliability in space applications and there are already a number of efforts to bring TE generation of electricity into terrestrial commercial use. Requirement, however, are lower investment costs for the modules and simultaneously higher conversion efficiencies. In terms of costs it is indispensible to develop manufacturing processes for TE devices, which not only consolidate the powders in automized procedures, but also have the potential of lateral shape forming and composition control of the material. This would not only give the possibility to form complete elements or modules in a single manufacturing step, but also to prepare functionally adapted TE devices which show a higher figure of merit [1]. Here, we introduce plasma spraying as a forming process with the required capabilities. As first T E material to be bulk solidified by plasma spraying, we have chosen iron disilicide (FeSi2) [2]. Due to its well known properties, the processing of FeSi2 allows a valuation of

564

,

•

Al-doped PS FeSij

Co-doped PS FeSi,

i 2

I 1 ^ 20

40

60

Tempertime at 800°C in h

Figure 1. Scanning electron micrograph of SPS formed Al-doped FeSi2 perpendicular to the growth direction. 1: FeSi2 + 0.7at% Al, 2: FeSi2 + 1.4at% Al, 3,4: FeSia + 1.8at% Al, 5: FeSi, 6: Oxide.

Figure 2. Room temperature thermal conductivity values of SPS formed FeSi2 as a function of heat treatment time at 800° C.

the novel method's applicability. The results of the experiments are presented in the next section. Additionally, the first outcomes of the production of graded electrical contact junctions are reported. Final goal, however, is the preparation of compositionally graded materials made of Mg2(Si,Ge,Sn) crystals. The preparation of the powders by mechanical alloying and their properties after hot pressing is topic of the third section. The high reactivity of the Mg is the main difficulty which has to be overcome. For the preparational route the problems have been solved. The next step will be the transfer to the plasma spray process. 2. P L A S M A S P R A Y F O R M I N G Plasma spraying (PS) is a technology that has been widely used for coating both metals and ceramics [3]. In the present case, however, the spraying process is applied with the aim to form bulk material. Therefore we name the method plasma spray forming. 2.1. P l a s m a spray experiments on iron disilicide As first material to test PS forming of thermoelectric materials, we used gas atomized, Co- and Al-doped, FeSi2 powders [4]. The powder batch was sieved into two fractions. The powders with the larger mean particle diameter of 70 /im were successfully deposited by plasma spraying in ambient air (air plasma spraying, APS) or with an argon shroud which aggravates oxidation (shrouded plasma spraying, SPS). The targets were made of unalloyed conventional steel or of Ti-6A1-4V. PS powers between 20 and 30 kW with pure argon as plasma gas, or with hydrogen or helium additions were employed. Spraying distances were chosen from 70 down to 30 mm. The smaller distance made finer lateral structures of about 10 mm possible, but also led to a lower deposition rate. The scan velocity was varied by one order of magnitude between 16 and 160 m m per minute. With

565 a powder feeding rate of about 30 g per minute the typical layer thickness per scan reached 0.1 mm. When employing so-called vacuum plasma spraying (VPS), i.e. spraying in a closed chamber operated below atmospheric pressure filled with 200 mbar inert argon gas, only the use of the finer powder fraction with mean particle diameters of 20 //m resulted in a suffient melting and deposition rate in the high velocity plasma jet. However, though the spraying distance was larger in the present case, the layer thickness per scan did not exceed 0.02 mm. 2.2. Metallographic characterization For APS and SPS, the chosen spray parameters were appropriate to produce FeSi2 bulk material up to a thickness of 10 mm with a relative density of at least 92%. The mechanical strength was almost identical to that of hot pressed material and thus there were no problems in cutting and machining samples to be tested. In the case of VPS, however, the maximum sample thickness achieved did not reach much above 1 mm, but its relative density approached the high value of 98%, which is comparable to that of hot pressed FeSi2. A scanning electron microscopy picture of SPS FeSi2 (cf. Fig. 1), which is taken perpendicular to the growth direction, shows the main features of an as sprayed structure. Striking are the microcacks which develop in the splat bond regions. A similar microstructure has been observed in PS mullite [6]. These regions also contain oxides, which were found in all types of PS FeSi2. Up to now not explainable is the result that a chemical analysis of oxides in VPS FeSi2 gives much higher values than those found in SPS and hot pressed material (cf. Table 1). The PS FeSi2 in its as-sprayed state was mostly in its metallic a-phase, and had therefore to undergo a temper process of about 1 h between 700 and SOO^'C to obtain the desired semiconducting /?-phase [5]. 2.3. T h e r m o e l e c t r i c transport properties The thermoelectric properties of the plasma spray formed iron disilicide might be influenced by a possible change in material composition due to the high temperatures, and the highly disordered structure. From the three thermoelectric parameters, Seebeck coefficient S, electrical conductivity a, and thermal conductivity /c, the thermal conductivity is most sensitive to the microstructure. From Fig. 2, which shows a plot of room temperature thermal conductivity of SPS FeSi2 vs. heat treatment time at lOOO^C, it can be seen that there is obviously a change in microstructure due to the thermal treatment. At the beginning, the thermal conductivity is extremely low which is probably due to the large number of microcracks in the bond regions of the flats. Tempering induces an annealing process which lets K rise eventually reaching the value of hot pressed FeSi2. VPS FeSi2 does not exhibit such a large change in thermal conductivity. From the beginning, the material is more dense and /c quite large. Table 1 lists AC-values of SPS and VPS FeSi2 which were measured after a 2 h heat treatment at 800°C (i.e. the time required to induce the a to ^ transition) and after a certain temper time at 800°C. It can be seen that in both cases the thermal conductivity of hot pressed FeSi2 is approached. APS FeSi2 shows an extremely low electrical conductivity of only 15 (Ocm)"^ (Co-

566

30

^x . 0 *,

0.5 h 1.5 h 2.5 h 72 h

E

^ to

20

300

400

500

600

TIKI

Figure 3. Electrical conductivity of SPS formed Co-doped n-type FeSi2 after different heat treatment durations at 800° C.

Figure 4. Graded junction between FeSi2 (bottom) and an iron based alloy (top). The height of the picture represents 2 mm.

doped). The a-values of SPS material are somewhat higher (cf. Fig. 3), but still a factor 5 lower compared to hot pressed material. Only VPS FeSi2 exhibits acceptable values around 65 (Ocm)"^. Interesting is the fact, that the electrical conductivity does not show any significant depence on the aging process by which the thermal conductivity is influenced so dramatically. Fig. 3 shows, that even after 72 h of heat treatment at 800°C on an Co-doped SPS sample, the cr-values are almost constant. The same behaviour is valid for the thermopower S (cf. Table 1). 5-values for PS FeSi2 are higher than those of hot pressed material - especially for the VPS material - which is obviously due to a dopant loss during the spraying process.

Table 1 Comparison of hot pressed and plasma spray formed Co-doped FeSi2. Hot pressed SPS VPS "as sprayed" 50h at 800°C "as sprayed" 50h 22 a (1/ncm) Too 22 65 180 S (/.V/K) 165 190 180 1 • 10^1 n (cm~^) 2 • 10^1 ; • lO^*" 4.9 1.5 K (W/Km) 3.4 4.9 5.5 4.7 6.8 Z (10-VK) 1.6 0.17 0.7 0.15 O2 (wt%) Room temperature values.

at 800°C 190 4.5 5.2

2.4. G r a d e d j u n c t i o n Fig 4 shows a graded junction between the semiconducting FeSia and an iron-based alloy. Purpose is the formation of a metaUic surface on which electrical contacts can

567

100-

Mg2Sio,,Ge„3

80v>

J

Hall-mobility — o — Preparation as usual — • — Oxide-free preparation

> rTeoE o £40-

MgjSiogSrioi

20-

MgzSioeSnoz Mg;SySno3

/ . ^

J J _ôoo

/

"

•

()

J -^

'

o ^

\

050

100

Mg2Sio6Sno4

Figure 5. Layered Mg2(Si,Ge,Sn) ingot prepared by hot pressing.

/

/ // /

=L

]

/ / /

150

200

250

300

TinK

Figure 6. Hall mobility of two mechanically alloyed, hot pressed Mg2Si samples.

be soldered with a low melting point, ductile solder. Such a contact can release stresses. Gradient formation was achieved by simultaneously feeding FeSi2 and Fe into the plasma gas jet, and stepwise varying their relative fraction. From the however, it can be seen that the mixing of the powders was not complete which in a quasi-layer structure. In spite of this, the contact is mechanically stable.

thermal powders picture, resulted

3. S Y N T H E S I S A N D P R O P E R T I E S OF Mg2(Si,Ge,Sn) The Mg2(Si,Ge,Sn) mixed crystal system shows wide ranges of solid solubility and the compounds have been proposed to be good candidates for high-Z TE-materials [8,9]. Additionally, the material system offers the possibility to form compositionally graded elements. In the present project, in order to obtain the materials in the required powder form, the compound is prepared by a mechanical alloying process in a planetary ball mill Retsch PM4000DLR [10,11]. Up to now the method succeeded in synthesizing Si-rich quasibinary Mg2(Si,Ge) and Mg2(Si,Sn). Consolidation occured by hot uniaxial pressing. Layered structures were prepared by pressing stacks of powders having different compositions (cf. Fig. 5 for example). During the preparation process it became evident that a paramount parameter governing the thermoelectric properties is the oxide contents in the material. Figs. 6 shows mobility curves of two mechanically alloyed Mg2Si. The powders were prepared in the same way with n-hexane as oxygen free milhng fluid, but in the "oxide-free" preparation route, the powder was not dried in an argon atmosphere, but, still wet, filled into the pressing die. The room temperature mobiUty of such prepared material appeared to be a factor of three higher. Thus it is important to avoid any oxidation during the whole milling and consolidation procedure — a fact which has to be considered when transferring the consolidation into the plasma spray technology.

568 4.

CONCLUSIONS

Our experiments found that the employed Co- and Al-doped gas atomized iron disilicide powders exhibit a good spray ability in case of APS and SPS deposition. For VPS, the deposition rate has to be improved. Plasma spray formed layers have to undergo a postdeposition annealing process in order to obtain the semiconducting ^-phase. Regarding thermoelectric properties, the Seebeck-coefficient is comparable to hot pressed FeSi2 and the thermal conductivity is found to be lowered. However, the electrical conductivity was lowered as well, which in the case of APS and SPS material led to a lower Z-value. On the other hand, VPS FeSi2 showed an electrical conductivity high enough to compete with conventionally hot pressed material. The PS FeSi2 is not thermally stable. An aging process occurs, which may be due to recrystalHsation and/or microcrack annealing. Interesting is the fact, that the aging process seems to affect only the thermal diffusivity (conductivity), whereas the electrical conductivity and the thermopower remain unchanged. Quasibinary solid solutions of Mg2(Si,Ge) and Mg2(Si,Sn) could be prepared by mechanical alloying. By consequently avoiding the formation of oxides, the room temperature electron mobility values could be raised to 100 cm^/Vs. The obtained values indicate that the material is indeed a good candidate for future high efficient TE-material. However, due to its high reactivity, the maximum working temperature may be limited to 500° C. This work was supported by the Deutsche Forschungsgemeinschaft (DFG), Schwerpunktprogramm Gradientenwerkstoffe. REFERENCES 1. T. Hirano, L.W. Whitlow, M. Miyajima, in: Ceramic Transactions, Functionally Gradient Materials, ed. by J.B. Holt, M. Koizumi, T. Hirai, Z.A. Munir, The Amsterdam Ceramic Soc. 34 (1993) 23. 2. R.M. Ware, D.J. McNeill, Proc. lEE 111 (1964) 178. 3. R.W. Smith, R. Novak, pmi 23 (1991). 4. U. Stohrer, U. Taibon, E. Gross, U. Birkholz, Proc. IX Int. Conf. on Thermoelectrics, Pasadena CA, (1990) 242. 5. J. Schilz, M. Riffel, R. Mathesius, G. Schiller, R. Henne, R.W. Smith, Proc. of the XV Int. Conf. on Thermoelectrics (ICT'96), Pasadena, USA (1996). 6. W. Braue, G. Paul, R. Pleger, H. Schneider, J. Decker, J. Eur. Ceram. Soc. 16 (1995) 85. 7. H.E. Eaton, J.R. Linsey, R.B. Dinwiddle, In: Thermal conductivity 22, Ed. T.W. Wong, Technomic (1994) p. 289. 8. R.J. LaBotz, D.R. Mason, D.F. O'Kane, J. Electrochem. Soc. 110 (1963) 127. 9. R.J. LaBotz, D.R. Mason, D.F. O'Kane, Proc. of the XII Int. Conf. on Thermoelectrics (ICT'93), Yokohama, Japan (1993). 10. M. Riffel, J. Schilz, Proc. of the XV Int. Conf. on Thermoelectrics (ICT'96), Pasadena, USA (1996). 11. J. Schilz, K. Pixius, W. Amend, M. Plate, H.-J. Meyer, Proc. of the XIII Int. Conf. on Thermoelectrics (ICT'94), Kansas City MO, USA, AIP Conf. Proc. 316 (1995) 71.


569

Preparation of PbTe-FGM by Joining Melt-grown Materials M. Orihashi ^, Y. Noda ^, L. -D. Chen ^, Y. -S. Kang ^, A. Moro ^ and T. Hirai ^ ^ Institute for Materials Research, Tohoku University, Katahira, 2-1-1, Aoba-ku, Sendai, Miyagi 980-77, Japan " Faculty of Engineering, Tohoku University, Aramaki Aoba, Aoba-ku, Sendai, Miyagi 980-77, Japan ^ National Aerospace Laboratory, Kakuda Research Center, Koganezawa 1, Kimigaya Kakuda, Miyagi 981-15, Japan The 2-stage carrier concentration FGM of PbTe were prepared by plasma activated sintering (PAS) using the discs cut from melt-grown PbTe ingots. The component materials of PbTe ingots were prepared by the Bridgman method after the direct melting of the constituent elements (Pb and Te) and 2000 or 4000 molppm Pbl2 as a n-type dopant. The PAS conditions were as follows; in vacuum, pressure of 30 MPa, temperature at 1050-1100 K, and current of 600 A and voltage of 25 V. The powder of either of the component materials was adopted as joining reagent of the discs. The thermoelectric characterization of the FGM was made in the temperature range from 300 to 700 K. The electrical conductivity of the FGM at 300 K was almost intermediate between those of the components, while the thermoelectric power corresponded to that of the component with high carrier concentration at high temperature side. The thermoelectric power for the FGM was almost intermediate between those for the components. At T>650 K, the electrical figure of merit for the FGM was larger than that for the components. 1. INTRODUCTION PbTe is among the best materials used in construction of thermoelectric generators working at intermediate temperature region (450-840 K). Since the maximum figure of merit (Z) shifts in wide temperature range depending upon carrier concentration, the carrier concentration FGM of PbTe is expected to attain high efficiency of thermoelectric energy conversion.

570 Plasma-activated sintering (abbreviated as PAS) has been developed in the preparation of a variety of functionally graded materials (FGM)[1], where the powder particle surface are activated by plasma leading to an accelerated reaction or sintering. The PAS has lately been applied to the thermoelectric materials such as SiGe and PbTe[2,3]. In the present study, we prepared the stepwise carrier concentration FGM of n-type PbTe by using PAS. 2. EXPERIMENTAL 2.1 Preparation of PbTe-FGM The PbTe ingots as the source material were prepared by the Bridgman method after the direct melting of constituent elements of Pb and Te (nominal purity of 99.9999%). The weighed amount of the elements in the stoichiometric composition (Pb/Te=l) was vacuum sealed in a quartz ampule (10 mm ID and 120 mm length) with 2000 or 4000 molppm Pbl2 as the source of n-type dopant of iodine. The growth condition was as follows; the maximum heating temperature of 1223 K, the temperature gradient of about 1200 K/m at melting point, and growth rate of 4 mm/hr. The PAS was performed in a carbon die with 11 mm ID. The n-type 2-stage FGM was prepared by direct PAS of the two discs (^2 mm thickness X 10 mm diameter) cut from the 2000 and 4000 molppm Pbl2 doped ingots, where the powder from the 4000 molppm Pbl2 doped ingots was placed between the discs as the binder. The PAS condition was; in a vacuum of about 10 Pa under the condition of load of 30 MPa, and pulse current of 600 A at 25 V with 6 Hz for 90 s, followed by the heating at 810 K for 540 s. 2.2 Measurement of thermoelectric properties The thermoelectric properties were measured at 300 K for the FGM and its component layers separated from the FGM. The electrical conductivity (cx) and Hall coefficient (JR^) were measured by the 6-probe method for the FGM and by the van der Pauw configuration for the components cut from the FGM using Pt-wire electrodes. The carrier concentration (n) and Hall mobility ( A H ) ^^^^ calculated using the equation n=lleRY{ (e: electric charge) and /^jj=/?H cr, respectively. The thermoelectric power ( a ) at 300 K was estimated from the linear relationship between thermoelectromotive force (EMF) and temperature difference within 5 K. The thermoelectric properties of the FGM and its components were measured in Ar atmosphere in the temperature region from 300 to 700 K. The sample size was ^^3 X 3 X 8 mm^. On the thermoelectric power measurement, the components of high and low carrier

571 concentration were arranged to high and low temperatures, respectively, and thermoelectromotive force was measured at the temperature difference within 20 K between the hot and cold ends. The temperature was monitored by using Pt-13%Rh thermocouples and the additional Pt electrodes were adopted for the EMF measurement. For the conductivity measurement, the Pt wires of the thermocouples were served as the current lead and the additional electrodes as the potential lead. 3. RESULTS AND DISCUSSION Table 1 lists the thermoelectric properties of two stage n-type FGM and its components at 300 K. The data for the components (1) and (2) of the FGM corresponded to those for the melt-grown PbTe single crystals doped with 2000 and 4000 molppm Pbl2 respectively[4]. This indicates that PAS can produce a high quality material. The a value for the FGM was almost intermediate between those for the components and never became lower than those of the components[5], while thermoelectrical power, carrier concentration and Hall mobility seem to represent those for either component. Fig. 1 shows the potential profile near the joint boundary in the FGM. The abrupt potential change was found within a width of about 0.5 mm, which is also reported for the SiGeFGM[2]. Since the potential gradient corresponds to an increase of resistivity at the joint interface, the interface resistivity must be minimized by optimizing the sintering in the further studies in order to attain high efficiency of energy conversion. Fig. 2 shows the temperature dependence of CT for the FGM and the components. The (7 value of all the samples monotonously decreased with an increase of temperature, indicating that the samples are the typical degenerated semiconductors. The <J value for the FGM was almost intermediate between those for the components and never become lower than those of the components in spite of the existing interface resistivity. At Jb>500 K, the O value for FGM was larger than that for the components. Fig. 3 shows the temperature dependence of a for the FGM and the components. The a Table 1 Thermoelectric properties of the two stage n-type FGM of PbTe at 300K layer n-FGM(l+2) Component (1) (2)

Pbl2 (molppm) 2000 4000

a

n

(Q-V^)

(mV^s'l)

4.1X1024*

1.0X10^

1.5X10-1*

(V-K-1) -1.0X10-4

4.2X10^4 4.9X10^5

7.6 XIO^ 1.9X10^

1.1X10-1 2.4X10-2

-2.4X10-4 -1.1X10-4

Data obtained by 6-probe Hall measurement.

572

T

^S ^^ a

0.08 0.06 boOOmolppm Pblj

|

1

T"•~T

^.lO'

'>

"^^'^^Qj..

Z

0.04

'^^^^^^fej^

s -8 |10^ r

0 0.02

:

0 1 1 • A 2 1 ^ FGM|

\

4000molppm Pblj

1

Â'^'^ÂAA^VtoiA^^S^ [Hjgiijr'|fc^

^**i»M^^H|

"""^^

S r

at300K I=20mV

^

1 2 3 4 Position ,x /mm Fig.l Plots of electrical potential versus position near at the boundary joined between 2000 and 4000 molppm Pbl2doped PbTe in the two-stage FGM

u

103

- 1

1

1

1

1

200

300 400 500 600700600 Temperature, T/K Fig.2 Temperature dependence of electrical conductivity for 2-stage FGM of PbTe shown with those for component (1) and (2) with different electron concentration listed in Table 1 ^

10-^

1—I—]—1—r

r\w 2FGM ^ 10-2 b

^°

I 10-^1

I

300

400

500

600

700

Temperature, T/K Fig.3 Temperature dependence of thermoelectric power for 2-stage FGM of PbTe shown with those for component (1) and (2) with different electron concentration listed in Table 1

10-^

300

400 500 600 700 Temperature, T/K Fig.4 Temperature dependence of electrical figure of merit a ^ a for 2-stage FGM of PbTe with those for component (1) and (2) with different electron concentration listed in Table 1

value for the component (1) linearly increased up to near 600K and then took a maximum of 3.2 X lO""^ V-K"^ while the maximum for (2) was 2.1 X 10""^ V-K"^ at about 630 K. The curve for the FGM was almost intermediate between those for the components. Fig. 4 shows the temperature dependence of the electric figure of merit (or power factor, O) for the FGM and the components. With an increase of temperature, the a^ a value for the component (1) monotonously decreased with an increase of temperature, while that of (2) increased. In the measured temperature range, the a^ cr value for the component (2) was

573 lower-lying than that for (1). At J>650 K, the a^ a value for the FGM was found to exceed that for the components. However, the increase of efficiency for the FGM in the present study did not enhance the power factor in low temperature region. The large difference in carrier concentration between components (1) and (2) may degrade the thermoelectric properties of the FGM under the temperature difference within 20 K. Therefore, it is concluded that the difference in carrier concentration must be kept small between the adjacent component materials in a stepwise FGM in order to attain high efficiency, which leads to a FGM with well-designed continuous carrier concentration profile. 4. Acknowledgment The authors wish to thank Mr. K.Horasawa (Tohoku University) for manufacturing the glass equipments. REFERENCES 1. T. Hirai: Materials Science and Technology, A Comprehensive Treatment, ed. R. W. Cahn, P. Hassen and E. J. Kramer, Chapter 20 Functional Gradient Materials, VCH Verlag. (Weinheim), (1996), 293 2. K. Takahashi, T. Masuda, T. Mochimaru and T. Noguchi: Froc, FGM symp. (FGM95), (1995), 123. 3. M. Miyajima, K. Fujii and T. Hirano: Froc XII Int. Conf. Thermoelectrics (X II-ICT), Yokohama, (1993), 272. 4. Y. Noda, M. Orihashi and I. A. Nishida: Trans. lEE of Japan, 116-A (1996), 242. 5. Y. Noda, M. Orihashi H. T. Kaibe, Y. Imai, I. Shiota and I. A. Nishida: Froc. Int. Conf. Thermoelectrics (ICT96), Pasadena, (1996), in print. 6. Yu. I. Ravich, B. A. Efimova and I. A. Smimov: Semiconducting Lead Chalcogenides, Prenum Press, New York, (1970).



575

Improvement and thermal stability of thermoelectric properties for n-type segmented PbTe S. Yoneda^, H.T.Kaibe^, T. Okumura^, Y. Shinohaxa^, Y. Imai^, LA. Nishida^, T. Mochimaru^ K. Takahashi^ T. Noguchi^ and I. Shiota^ ^Department of Electronics and Information Engineering, Tokyo Metropolitan Universisty, 1-1, Minami-Ohsawa, Hachioji-shi, Tokyo, 192-03, Japan ^National Research Institute for Metals, 1-2-1, Sengen, Tsukuba-shi, Ibaraki, 305, Japan ^Vacuum Metallurgical Co., Ltd., 516 Yokota, Yamatake-cho, Yamatake-gun, Chiba, 289-12, Japan ^Kogakuin University, 2665-1 Nakano-cho, Hachioji-shi, Tokyo, 192, Japan The resistivities p of the n-type melt-grown and plasma activated sintered PbTe were measured as a function of temperature during heating and cooling cycles to progressively higher temperatures until 903 K in Ar atmosphere. The hysterisis of the temperature dependence of p appeared for both specimens after heated at 703 K, which indicates that the change of thermoelectric properties occurs during the operation as a thermoelectric generator. This phenomena was more remarkable for the sintered specimen than that for the melt-grown one. However, X-ray analyses did not detected the evidence such as the apperance of the secondary phase or oxidation. The each specimen prepared by meltgrown and plasma activated sintering was also annealed in an evacuated quartz tube at 793 K for 8.64x10^ s (24 h). p and the carrier concentrations for both specimens were almost unchanged after annealing. Then, it is pointed out that a PbTe thermoelectric generator is required to be used in a closed evacuated container in order to prevent the change of the thermoelectric properties during operation. 1. INTRODUCTION The n-type PbTe as a thermoelctric material whose carrier concentration n is controlled to have around 3.0 x 10^^ m~^ is commonly used in the temperature range of a hot side electrodes between 600 and 950 K.[l] The thermoelectric figure of merit Z has a maximum value of 1.4 X 10"^ K~^ at 700 K and the dimensionless thermoelectric figure of merit ZT attains to almost unity. Then, PbTe and its solid solutions are utilized such as a solar thermoelectric generator (STG) and a radioisotope thermoelectric generator (RTG).[1,2] Z of the n-type PbTe with a single and homogeneous carrier concentration has a maximum value Zmax at an optimum temperature T^pt and decreases rapidly with temperature higher than T(ypt. Topt and Zmax are the functions of n. Then, Topt shifts to the higher temperature side and Zmax decreases with increasing in n. When n varies from 5 x 10^^

576 to 7 X 10^^ m"^, Zjnax holds its value between 1.7 x 10"^ and 1.2 x 10"^ K"^ in the wide temperature range between 400 and 800 K. Then, the average figure of merit in an operation temperature range is expected to be improved to 1.5 times larger than that of a conventional homogeneous material with a single carrier concentration. [1] Imai et al. showed the evidence of the improvement in thermoelectric performance by using the hot-pressed n-type PbTe with a 3-stage carrier concentrations. [3] However, in order to form the FGM structure and to attach the metal electrodes such as Fe and other alloys the PbTe materials are needed to be heated up to around 1000 K during the diffusion bonding and hot pressing. [4] Then, it is possible to be caused the change of the thermoelectric properties and it becomes important and serious problems for designing the thermoelements used for a generator and for reliablity of the PbTe thermomodules.[5,6] The purposes of this study are to clarify the mechanism of the change of the thermoelectric properties for n-type melt-grown and sintered PbTe and to establish the methods and techniques for prevention of the change of the thermoelectrc properties. Then, the resistivities were measured during a series of heating and cooling cycles for the n-type melt-grown and sintered PbTe. X-ray analyses were carried out to examine the identification of the mother phase, precipitation of the second phase and oxidation. The annealing effects for n-type sintered and melt grown PbTe evacuated in quartz tubes were also examined. 2. EXPERIMENTAL P R O C E D U R E 2.1. Preparation of n-type melt-grown PbTe Pb and Te with purity of 99.999 % were individually weighed out corresponding to the stoichiometry. They were loaded into an evacuated quartz tube whose size was 50 mm in diameter and 300 mm in length together with 0.5 wt% Pbl2 as n-type dopant. The tube was sealed off under a pressure of I x 10"^ Pa. The melt was stirred sufficiently for 7.2 x 10^ s (2 h) at 1273 K and then it was cooled down along 2.8x10"^ K/s (10 K/h) with holding a temperature gradient of 0.8 K/mm. The obtained n-type melt-grown PbTe ingot was 50 mm in diameter and 30 mm in length. Hereafter, this ingot is named as Ingot 1. Parallelepiped specimens for resistivity p and Hall coefficient Ra were cut out of the top and bottom portions of Ingot 1. The measurements of p and Ru were carried out by d.c. method. Ru was measured with an applied magnetic field of 0.33 T. The p were 2.16x10"^ fi m at the top portion of Ingotl and 2.41x10"^ fi m at bottom one, which indicates that Ingotl was fairly homogeneous in respect of chemical composition and carrier concentration. Another ingot was prepared by the same process with the equal amount of Pb, Te and Pbl2 to those of Ingot 1. It was sealed off again under a pressure of 1x10"^ Pa in a quartz tube consisting of the two cylindrical parts with 16 and 50mm in diameter respectively and with a conical shaped end whose tip angle was 60^ as shown in Fig. 2 of reference 3. The melting and solidification were carried out the same process as the case of Ingot 1. The obtained ingot was 16 mm in diameter and 130 mm in length. The ingot is named as Ingot 2. The conduction type of whole region of Ingot 2 was n-type, while n was decreased along the growth direction from 2.1x10^^ to 2.8x10^^ m~^. X-ray powder diffraction analyses using Cu-Ko; (40kV-50mA) confirmed that both Ingot 1 and 2 consist of a single phase of PbTe.

577 2.2. Preparation of n-type sintered PbTe Each portion of 20, 60 and 96 mm from a growing tip was cut out of Ingot 2. They corresponded to those with p of 2.84x10"^, 5.68x10"^, 9.46x10"^ fim and with n of 2.0x10^^, 1.0x10^^, 0.6x10^^ m~^, respectively They were used as starting materials for the plasma activated sintered PbTe. Each starting material was ground into a fine powder with an average particle size of 42.5/im under 106 /xm. The plasma activated sintering was carried out using a carbon dice in an atomosphere of Ar+5 %H2. Then sintering pressure was 4x10^ Pa and the temperature of the dice was controlled to be kept constant between 684 and 709 K during each sintering. The obtained sintered specimens were the pellets with 15 mm in diameter and 3 mm in thichness.The apparent density of each specimen was larger than 99 %. Each pellet prepared from the portions of 20, 60 and 96 mm of Ingot 2 is named as p-1, p-2 and p-3, respectively. The p-1 was ground into a fine powder again and then sinter process under the same condition as mentioned above was carried out, since the cracks were observed in it. X-ray powder diffraction analyses confirmed that all the pellets were in single phase state of PbTe. Each pellet was cut into the parallelepiped specimens with a dimensions of 1x2x5 mm^ for the measurements of the resistivity p and the Hall coefficient RH2.3. Measurement of hysteretic temperature dependence of resistivity p during a series of heating cind cooling cycles to progressively higher temperatures Each parallelepiped specimen that was cut out of Ingot 1 and p-2 was set on an AI2O3 plate binding with Pt wire in a stainless stem with a dimension of 26 mm in diameter and 650 mm in length. Pt wire with 50 /xm in diameter was attached to the specimen as electrodes. The stainless stem was evacuated under a pressure of lxlO~^ Pa and then it was filled with pressure of 1x10^ Pa of Ar gas. The resistivities p were measured as a function of temperature during heating and cooling cycles. The heating was carried out with a rate of 2.5x10"^ K/s (90 K/h) and holding was for 3.6x10^ s (Ih) and cooling was with rate of 4.2x10"^ K/s (150 K/h). The holding temperatures were raised to progressively higher temperatures at intervals of lOOK from 423 to 903 K. The temperature of specimes were measured using the R-type thermocouples with 76 /xm in diameter which were put under an AI2O3 plate. The specimens cut out of the Ingot 1 and p-2 are named as h-m and h-p, respectively. After h-m and h-p were heated up to 903 K, they were identified by the means of the X-ray powder diffraction. 2.4. Annealing of the n-type melt-grown and the sintered PbTe Each parallelepiped specimen cut out of Ingot 1 and p-2 was sealed off under a pressure of lxlO~^ Pa in an evacuated quartz tube with a dimension of 11 mm in diameter and 70 mm in length. They were annealed at 793 K for 8.64 x 10^ s (24 h). The annealed specimens of Ingot 1 and p-2 are named as a-m and a-p, respectively, p and RH of a-m and a-p were measured at room temperature. 3. RESULTS AND DISCUSSION The resistivities piw at room temperature for p-1, p-2 and p-3 were 1.42x10"^, 1.03x10"^ and 1.04x10"^ Qm, respsctively.The carrier concentrations npT estimated from the Hall coefficients for p-1, p-2 and p-3 were 3.22x10^^, 1.83x10^^ and 1.69x10^^ m-^ respectively

578

2 2.5 XQÎT (1/K) Figure 1. Temperature dependence of resistivity p measured during a series of heating and cooling cycles to progressively higher temperatures for the n-type melt-grown PbTe in Ar atmosphere (h-m). Max. Temperature of each cycle from 1 to 6 are 423, 503, 603, 703, 803 and 903 K, respectively.

2

2.5

3

3.5

10^/r (i/K) Figure 2. Temperature dependence of resistivity p for the n-type plasma activated sintered PbTe in Ar atmosphere (h-p) under the same heating and cooling cycles as ones for h-m. The measurement could not be carried out during coohng from 903 K because of the crack occurrence.

PUT and URT were higer and lower respectively comparing with those for the corresponding portions of Ingot 2 as the starting material. The Hall mobility ^H calculated from PRT and UJIT were less than 10~^m^/(Vs) which is two orders less than those of Ingot 2. This is mainly due to the evaporation of Pbl2 as dopant when the electric current flew directly through the powder materials and when temperature of the portion at which the particles contact each other was raised. It was also reported that p after being powdered and pressed for the n-type PbTe doped with PbBr2 considerably increased. [7] The Hall mobihty pin for the n-type hot pressed Pbo.95Sno.05Te doped with Pbl2 was decreased and the temperature dependence of fin changed drastically comparing with those of the melt grown one. [8] Then, it can be considered that powdering and sintering process forms the potential barrier at the grain boundaries and that the additional scattering mechanism besides due to the lattice vibration, ionized impurity and interaction of poin defect is introduced. [7,9,10] Fig.l is the temperature dependences of the resistivity p during a series of heating and cooling cycles to progressively higher temperature for h-m. The resistivity PRT of the as-grown one at room temperature is 2.35x10"^ Qia and was almost unchanged after heated up to 603 K. However, after heated at 703 K, PRT decreased to 2.26x10"^ Hm after heated at 803 K and finally decreased to 1.91 x 10~^ Hm after 903 K. The carrier concentration URT of the as-grown one estimated from the Hall coefficient was 1.82 x 10^^ m~^ and increased to 2.44 x 10^^ m~^ after heated up to 903 K. It is considered that those are due to the deviation of the stoichiometry caused by the evaporation of the Te with a comparatively high vapor pressure from the surface of the specimen. [11-13] Fig.2 is the temperature dependence of the resistivity p during a series of heating and

579 Table 1 PUT and nj^ for the melt-grown (a-m) and plasma activated sintered (a-p) specimens annealed in the evaquated quartz at 793 K for 8.64x10^ s. Pj^To (Hm)

a-m a-p

2.11 X 10-^ 9.36 X 10-^

PRT (^m)

URTQ (m~^)

TIBT

(m~^)

2.06 x 10"^ 8.85 x 10"^

2.92 x 10^^ 2.06 x 10^^

3.21 x 10^^ 2.19 x 10^^

PRTO and rijirpQ are the values before annealig.

cooling cycles to progressively higher temperature for h-p. ppj^ of the as-pressed one was 1.03x10"^ d m . p had a hysteretic temperature dependence after heated up to 703 K similar to that in a case of h-m. PRT decreased to 1.89x10"^ Dm after heated to 803 K. Both h-m and h-p had hysteretic temperature dependence of the resistivity after heated up to 703 K. However, the decreasing ratio was larger for the h-p comparing with the case of h-m, which indicates that the volume of the grain boundaries in the specimen relates closely to the decreasing of p. However, the mass decreasing was negligible small and X-ray analysis detected no evidences of the precipitation of the secondary phase nor oxidation. Then, it can be pointed out that the more precise and accurate structural and compositional analysis are required in order to clarify the mechanism of the decreasing of the resistivity. Table 1 summarizes the results for a-m and a-p. The change after annealing were less slight comparing with those for h-m and h-p. Then, It is found that using lead telluride as thermoelectric material in an encapsulated container is promisingly useful to prevent the changes of the thermoelectric properties. However, since it was also reported that p for the n-type sintered PbTe decreased one order of magnitude after annealed at 1073 K for 1.12x10^ s (310 h), the more detailed investigations concerning the other factors such as operation temperature, container volume, species and pressure of ambient gas are needed. [7] 4. C O N C L U S I O N The resistivities p for the n-type melt-grown and the plasma activated sintered PbTe were measured as functions of temperature in the heating and cooling cycles to progressively higher temperature up to 903 K. The irreversible phenomena in the temperature dependence of p occured and p decreased for the both specimens after heated up to 703 K. The phenomena was more remarkable for the sintered specimen than for the melt grown one, which indicates the correlation of the volume of the grain boundaries. However, the evidences of the precipitation of the second phase nor oxidation could not be detected. The changes of the thermoelectric properties for both specimens evacuated in the quartz tubes were less slight comparing with those in the cases of heating and cooling cycle. Then, it can be concluded that to use PbTe as thermoelectric material in an encapsulated container is promisingly useful to prevent the changes of the thermoelectric properties.

580 5. ACKNOWLEDGMENT The authors wish to thank Prof. T. Kojima and Dr. I.J. Ohsugi of Salesian Polytechnic for their collaboration in X-ray analyses. This work was supprted by a Grant-in Aid for Physics and Chemistry of the Functionally Graded Materials from the Education, Science and Culture. REFERENCES 1. LA. Nishida, Materia Japan, 35 (1996) 943, in Japanese. 2. K. Uemura and LA. Nishida, Thermoelectric Semiconductors and their applications (in Japanese), Nikkan-Kogyo Shinbun-sya, 1988. 3. Y. Imai, Y. Shinohara, LA. Nishida, H.T. Kaibe, K. Sato, H. Kohri and L Shiota, in Proceedings of FGM'95, Tokyo, 1995, edited by L Shiota, pp.101-106. 4. M. Weinstein and A.L Mlavsky, Rev.Sci.Instr., 33 (1962) 1119. 5. E.H. Putley, Proc.Phys.Soc.London, 68 (1954) 22. 6. J. RxDsenzweig, J. Zhang and U. Birkholz, phys. stat. sol. (a)83 (1984) 357. 7. R. Breschi, A. Olivi, A. Camanzi and V. Fano, J. Mater. Sci., 15 (1980) 918. 8. H.T. Kaibe, S. Yoneda, Y. Shimazaki, T. Okumura, Y. Imai, LA. Nishida and I. Shiota, Journal of Advanced Science, 7 (1995) 157. 9. J. Yoshino, in Proceedings of FGM'94, Tokyo, 1994, edited by I.Shiota, pp.223-228. 10. J. Yoshino, in Proceedings of FGM'95, Tokyo, 1995, edited by I.Shiota, pp.66-64. 11. LB. Cadoff and E. Miller, Thermoelectric Materials and Devices, (Reinhold Publishing Corporation, New York, 1960), pp.149. 12. R.F. Brebrick and R.S. AUgaier, J. Chem. Phys., 32 (1960) 1826. 13. Vacuum Handbook, (ULVAC Co., Ltd.,1989 edited by S. Yoshikawa) pp.133.


581

Preparation and thermoelectric properties of IrSba M. Koshigoe', I. Shiota^, Y. Shinohara^ , Y. Imai'', I. A .Nishida*' ^ Department of Chemical Engineering Kogakuin Univ., 2665-1 Nakano-cho , Hachioji-city , Tokyo 192, Japan ^ National Research Institute for Metals ,1-2-1 Sengen , Tsukuba-city , Ibaraki 305 , Japan An attempt is made to fabricate IrSbs compound and Iri.xCoxSb3(X=0.12) solid solution by the liquid-solid phase sintering and hot-pressing techniques. The compound and solid solution were found to be single phase of IrSbs and Iro.88Coo.i2Sb3 by X-ray diffractometry, respectively. The electrical resistivity and Hall coefficient were measured in the temperature range from 80K to room temperature. The hot-pressed IrSbs and Iro.gsCoo.nSbs were p-type degenerated semiconductors with hole concentration of 9.53 and 6.80 X lO^'^/m^, respectively. The cobalt atoms act as donors in the solid solution. The hole mobilities for both of the hotpressed materials (IrSbs and Iro.88Coo.i2Sb3) were larger than for the liquid-solid phase sintered and hot-pressed materials. A high thermal stability was obtained in hot-pressed IrSbs. 1. INTRODUCTION The maximum figure of merit of thermoelectric materials is obtained at a characteristic temperature Tc. Tc of BiaTes, PbTe and SiGe alloy are around room temperature, 500K and lOOOK, respectively. Tc can be controlled by the carrier concentrations, compositions and textures in a thermoelectric material. Thermoelectric materials with a functionally graded structure have been investigated in a project supported by Science and Technology Agency of Japanese Government since 1993. In the project, high efficient thermoelectric materials in the low, intermediate and high temperature ranges are produced by forming graded carrier concentrations in Bi2Te3, PbTe and SiGe, respectively. Besides forming graded carrier concentrations, attempts have also been made to join these materials to form a stepwise graded structure parallel to the heat flow. Combining these two methods it should be possible to expand the utilization temperature range from 300K to 1300K [1] which is much larger

582 than monolithic thermoelectric materials. PbTe is a typical thermoelectric material for the intermediate temperatures and shows a high figure of merit for the temperature rangefrom400K up to approximately 800K according to the carrier concentration. However, PbTe is unstable above TOOK because of a compositional change due to the high vapor pressure of Te. IrSbs compound is an interesting thermoelectric material in the intermediate temperature range. This material is expected to have better thermal stability at high temperatures than that of PbTe, because of its higher melting point and lower vapor pressure of Sb. The IrSbs compound and the solid solution of the isostructural compound have high carrier mobilities, low electrical resistivities, moderate Seebeck coefficients and moderate thermal conductivities [2]. IrSbs belongs to a large family of compounds with the skutterudite crystal structure. This structure is composed of a cubic lattice and the unit cell contains 8 of the AB3 group lattices[3].

t

2000

20

10

Weight percent Sb 30 40 50 60 70 80 90 100 — ^ - ^ — 1

\'

i
materials and their service temperature. Figure 1 is a schematic diagram of the TEC unit. For the application at vy/y/ ZZZZZZ2^h high temperature about 1000 °C, SiGe alloys are believed to P n be suitable for TEC cell. The /'-type of SiGe cell is Cell Cell r. connected to the «-type of SiGe cell with electrode [1]. r-EZZZZa EZZZZ3-1 Obviously, the materials used as an electrode should satisfy Cooling the requirements on the low electrical resistivity, high heat \ Load h conductivity as well as the good corrosion and oxidation resistance at high temperature. Our former research work Fig. 1 A schematic diagram of [2,3] has developed an electrode material in MoSi2/Al203/Ni the TEC unit. system, which not only exhibited good electrical properties but also excellent mechanical properties because of the strong surface compressive stress introduced by the symmetrically graded structure. However, the electrode was failed to be jointed with SiGe TEC cell due to the considerable mismatch of the thermal expansion between the MoSi2 and SiGe alloys. Further development of electrode materials is required for the efficient and reliable operation of thermoelectric power generators. The researches in this paper try to suggest a new process to fabricate the electrode of TEC unit with TEC cell in one step based upon the concept of functionally graded materials (FGMs). For this purpose, MoSi2, undoped Si and SiGe were selected as raw materials to design the (Si-MoSi2)/SiGe thermoelectric conversion unit. Preliminary experimental and theoretical analyses were carried out on the material design and evaluation of mechanical and electrical properties.

600 2. EXPERIMENTAL The raw materials used in this work were MoSi2 powder, undoped Si and SioygGeoii powders. Their nominal sizes were 1.09 jxm, 20 |Lim and 30 jim respectively. The powders in pre-determined volume fraction were mixed together by AI2O3 ball milling for over 48 hours, then dried in a vacuum furnace. The green compacts were pre-pressed under 200 MPa using CIP before HIP sintering. X-ray residual stress determination was performed on the surface of the samples prepared by HIP sintering. The measured residual stress was compared with the results calculated by the finite element method (FEM). The electrical resistivity was measured by the four probes method on the slices cut from the cylinder samples. In order to inspect the thermal stability, the samples were annealed at 900 °C for 24 hour in vacuum. The microstructure on the section was observed by scanning electron microscope. 3. DESIGN AND FABRICATION OF (Si-MoSi2)/SiGe TEC UNITS In this work, the TEC unit was imagined as a structure as shown in Figure 2. SiGe alloys possessing excellent thermoelectric properties were used as the TEC material at high temperature. The silicon has good thermal conductivity (1.5 Wcm'^deg'^ at 0 °C) and low thermal expansion coefficient (2.5x10"^ deg'^ at 0 °C); MoSi2 has low electrical resistivity (2x10"^ Q c m at room temperature). The composites of the both were expected to be an excellent electrode material with high thermal and electrical conductivity at high temperature. The electrical conductivity of (Si-MoSi2) composites would be dependent on the volume of MoSi2 in the Si matrix. Increasing the ratio of MoSi2 to Si can effectively reduce the electrical resistivity of (Si-MoSi2), however, the addition of MoSi2 will enhance the mismatch of

al E S F G M e l e c t r o d e ^ 0(2

06

SiGe TEC cell

^SiOe

E F G M electrode strode Z 3 a2 //A al w/ / / / / / / Fig.2 Structure of the sample.

250 200

L

•

n=0.6

^

r

n=1.0

Z^

150

L

0

100 1 1 50

A n=1.6

^Â

AO# AO»

W3

A

0

r>^

< -100 r

SiGe 1 , . . , 1. . , . -150 1 2 3 4 Distance away from axis (mm)

(a)

0.0

FGM 1 1 1 1 1

2.5 5.0 7.5 Distance away from center (mm)

(b)

Fig. 3 Residual stress distribution with different n values (a) radial stress, (b) axial stress.

601 thermal expansion between the SiGe and (Si-MoSi2), which may lead to crack of the sample during cooling from sintering temperature to room temperature. In order to satisfy the requirement on the fabrication process, it is necessary to understand the behavior of the residual stress produced in the process of sample preparation. Figure 3 shows the preanalysis results on the thermal residual stress with FEM method assuming the composition distributing function, f{x) = (x/ dy, where x is the distance from the end of the sample, and d is the thickness of the FGM layer. It can be seen that the maximum radial stress, which is in the surface layer, decreases while the maximum axial stress, which is on the cylinder surface, increases with the n value rising. Therefore, in the case of the sample D, the n value of 1.0 was taken to design the graded structure, but in order to introduce a compressive stress into the surface layer, relatively lower thermal expansion material was employed for the surface layer. The samples with four kinds of structures were listed in the Table 1. Table 1 The structures and composition of the samples used in the present study (vol%) Number

B

C

D

First layer

Si

Si+15MoSi2 Si+20MoSi2

Second layer

Si+30SiGe

/

Si+20MoSi2+40SiGe Si+30MoSi2

Third layer

Si+70SiGe

/

/

Si+20MoSi2+40SiGe

Central layer

SiGe

SiGe

SiGe

SiGe

Si+15MoSi2

The samples were fabricated by HIPing method. The green compact was sealed into a borosilicate glass container with BN powder bed in vacuum, then placed into a graphite crucible [4]. HIP sintering was performed at 1250 °C which is lower than the melting temperature, 1268 °C while applying an Argon pressure of 100 MPa. The SiGe sample sintered in the same process gave a density of 3.06 g/cm^ which is 99.6% of the theoretical density, 3.07 g/cm^. Figure 4 illustrates the microstructures in the vicinity of interfaces for the sample D. The interfaces between every two neighboring layers were well bonded, and the microstructures were distributed uniformly along the radial direction.

Fig. 4 Microstructures in the vicinity of every interfaces for sample D.

602 4. THERMAL RESffiUAL STRESS The residual stress often leads to the failure of HIP sintering. It should be controlled to be lower than the strength of the material. In this study, FEM method was used to analyze the stress distribution of every kind of samples supposing a temperature drop of 1250 °C. Four-node elastic axisymmetric element was employed. Material parameters used in the calculation are listed in the Table 2. In the case of sample D, the coefficients of thermal expansion were controlled as an arrangement of «/< aj> as >asiGe, the radial stress would be in a state of compression/tension/tension/ compression, as shown in Figure 6(a). The maximum tensile stress, about 150 MPa, existed in the second layer. The stress near the interface of electrode/ SiGe was relaxed effectively. The compressive stresses on the surfaces for all values of x-ray measurement.

(a)

Table 2 Physical properties used in FEM analysis of residual stress a(xlO-^) ^ ( G P a )

Materials (vol%)

V

199 0.22 4.18 210 0.22 4.55 234 0.23 5.31 205 0.22 4.75 150 0.22 3.27 Sio.78Greo.22 a. thermal expansion; E\ Young's modules; v: Poisson's ratio Si+15MoSi2 Si+20MoSi2 Si+30MoSi2 Si+20MoSi2+40SiGe

Table 3 Residual stress on the surface of samples Sample A B C D Residual stress measured (MPa)

-40

Residual stress calculated (MPa)

17

-33

-130

35

-47

-144

the samples are listed in the Table 3 with the

(b)

Fig. 6 The contour map of the residual stress in the sample D; (a) radial stress, (b) axial stress

603 The axial stress in the sample is showed in Figure 6(b). It can be seen that the maximum tensile stress in the direction of axis occurred on the cylinder surface near the electrode/SiGe interface. It often caused samples to crack in the SiGe alloy, and should be controlled lower than the strength of SiGe (about 170 MPa [5]). 5. ELECTRICAL RESISTIVITY AND THERMAL STABILITY Figure 7 shows the experimental results of the electrical resistivity before and after annealing for four kinds of samples. Obviously, the electrical resistivity of the electrode was strongly dependant on the volume of MoSi2 in Si matrix. In the case of MoSi2 free, the electrical resistivity of electrode was about 1.5x10'^ Q c m as shown in Figure 7(a). However it decreased sharply from 1.7x10"^, 4.0x10'^ to 1.0x10'^ Qcm while the volume fraction of MoSi2 increased in the order of 15 (Figure 7(b)), 20 (Figure 7(c)) to 30% (Figure 7(d)). This 0.40

0.10

I

[ (b)i

I 11'111111 I

I'

Samj)le B

0.08 o

S 0.06 i a

I 0.04

i I

%

0.02

5 10 Distance (mm)

15

0.00

I I I I I I I I I M I I I I t I I I I I I I I I I I I I

5 10 Distance (mm)

15

5 10 Distance (mm)

15

0.50 I

0.20

5 10 Distance (mm)

15

Fig. 7 Electrical resistivity of the samples, • before annealing; O after annealing at 900 °C for 24 hours.

604 phenomenon can be attributed to the compositional and microstructural changes of the SiMoSi2 composites. The microstructure observation indicated that it was not enough for MoSi2 to be adjacent each other in (Si+15vol%MoSi2) composite, as shown in Figure 8(a). For 30 vol% MoSi2, however, the MoSi2 was completely connected each other to form good conductor as seen in Figure 8(b).

Fig. 8 Microstructures of Si+15vol%MoSi2 (a) and Si+30vol%MoSi2 (b). Thermal stability is highly important to ensure high efficiency and long life of the TEC unit with graded structure. The measurements of electrical resistivity after heat treatment were illustrated in Figure 7 as well. These results identified that there were no evidently effects on electrical resistivity after a 1-day thermal exposure at 900 °C. In this study, the electrical resistivity of undoped Si and SiGe was much lower than standard undoped Si and SiGe, the diffusion of B might be responsible for it because the green compact was surrounded by the BN powder in the process of sintering. CONCLUSION It is expected that one-step sintering process of SiGe and electrode can substitute for jointing of the both, and the mechanical properties can be significantly improved by the design using the concept of FGMs. The addition of MoSi2 into the Si matrix can reduce the resistivity and control the thermal expansion mismatch between Si and SiGe. The resistivity measurement is a useftil way to examine the thermal stability of the graded composition and microstructure. REFERENCES 1.1. Nishida, Ceramics Japan, 21(1986) 516 2. Y.S. Kang, Y.Miyamoto, Y.Muraoka and O.Yamaguchi, J.Soc.Mat.Sci.Japan, 44(1995) 705 3. Y. Miyamoto et al., Proc. Int. Symp. on FGMs at the Annual Meeting of Am. Ceram. Soc, Indianapolis, April, 1996, in press 4. Y. Miyamoto, J. S. Lin and K. Tanihata, Proc. of Composite & Advanced Ceamics Materials and Structures, Jan. 7-11, 1996, Flolida. 5. R. A. Lefever, G. L. McVay and R. J. Baughman, Mat. Res. Bull., 9(1974) 863


605

Temperature Dependence of the Porosity Controlled SiC/B4C+PSS Thermoelectric Properties K. Kato, A. Aruga, Y. Okamoto, J. Morimoto and T. Miyakawa Department of Materials Science and Engineering, National Defense Academy, 1-10-20, Hashirimizu, Yokosuka, Kanagawa, Japan, 239

In the previous paper, it was reported that the thermoelectric properties of SiC/B^C system could be controlled by the addition of PSS at room temperature. In this report, the porous structure of these samples were confirmed by using SEM, and the measurements were carried out on the temperature dependence of the thermoelectric properties from room temperature up to 600 V (the thermal conductivity up to 300 °C ). The figure of merit of the sample (B^C: 2.0 wt.% + PSS: 5.0 wt. %) is estimated about 2 X10'^ K^^ around 600 V.

1. INTRODUCTION The thermoelectric semiconductor converts directly thermal energy into electric one. It can generate electric power even when the temperature difference between the heat source and atmosphere is much smaller compared with the one needed in conventional thermal power generation. The figure of merit Z, which is one of the measure for the thermoelectric energy conversion, is defined by the following equation: Z=aV/0 /c, where a , p and K is Seebeck coefficient, electrical resistivity and thermal conductivity, respectively. One of the criterion for the practical thermoelectric materials is that the value of figure of merit exceeds 10'^ K"\ Usually, it is difficult to increase a and at the same time decrease p and /c , because these parameters depend not only on the carrier concentration, carrier mobility, scattering mechanism in the crystal grains, but also on many factors such as grain size, microstructure of grain boundaries. At room temperature, Bi^-TCj is one of the practical thermoelectric semiconductors with its

606 large figure of merit. However, thefigureof merit of this system decreases with temperature [1]. SiC is chemically stable and it has the high mechanical strength even in high temperature region. These characteristics are essential features for the high temperature applications. At the present stage of our study, the figure of merit of the sample (SiC + 20 wt. % B^C) is 8 X10"^ K"^ at 600 V [2]. This is still 1000 times smaller than the value of practical materials, and leaves a room for improvement. PSS (polysilastylene) is one of the sintering additives in this system. Excess PSS evaporates during the sintering process and pores remain in the sample [3]. We have reported that the thermal conductivity at room temperature could be controlled by the amount of pores in this system [4]. In this paper, we report on the results of the SEM(Scanning Electron Micrograph) observation for the cross sections and also of the measurements for the temperature dependence of the thermoelectric characteristics of porosity controlled SiC + B^C 2.0wt.% samples. We also discuss temperature dependence of these parameters in the light of microscopic structure of the system. 2. EXPERIMENT and RESULT 2 . 1 . Sample preparation Sample preparation procedure is the same as described in our previous papers [2,4]. yS -SiC (average particle size 0.15 // m and BET surface area 19.5m^/g, Mitsui Toatsu Co., Ltd.), B^C (average particle size 0.7 // m, Denki Kagaku Kogyo Co., Ltd.) and PSS were the starting materials. Slurries were made from mixed powder of SiC, 2.0wt.% B^C and 0.5'-"^25 wt.% PSS in polyethylene jars with nylon coated iron balls. The mixing agent is xylene. After mixing for 20 hours and passing through 75 // m mesh sieve, these slurries were dried. The dried mixture were granulated using 500 ju m mesh sieve and pressed into 20 mm 0 x 4 mm pellet at 2 X 10^ N/m^ Then the pellets were sealed into an evacuated rubber tube and then pressed isostatically at 2 X 10^ N/m^. Each pellet was covered with the same compositional powder to prevent the change in composition and it was placed into a carbon crucible. The samples are pre-sintered to evaporate PSS at 1000 X^ for 60 miu. in an atmosphere of 1.0 atm. Ar gas flow. After furnace cooling, the sintering procedure was carried out in a furnace with a RF induction heater. First, the furnace was heated up to 1000 °C ata rate of 20 degree/min. in vacuum, then Ar gas was introduced up to 1.0 atm. Then the temperature was raised to sintering temperature (2100 *C) at a rate of 10 degree/min., the sample was kept at this temperature for 2 hours and cooled naturally down to room temperature. Sintered materials were cut into rectangular shaped specimens of 3 X 4 X S'ÎO mm^ in dimensions for measurement of the themioelectric properties.

607 2.2 Sample structure The large X-ray diffraction peaks could be assigned to SiC and B^C. These peaks show that dominant structure in our SiC is 6H-SiC. The small additional peaks were found which could not be identified to the composite materials of Si, B and /or C. Figure 1 shows the PSS concentration dependence of the density. The sample with the PSS concentration of 0.5wt.% is the most dense one in all samples in this work. The sample density then decreases when PSS concentration exceeds 0.5 wt.% . The thermal conductivity of the sample also decreases with sample density.

,90 •35 80 c u •o

.S 701

£ 60 10

20

30

PSS concentration (wt.%) Figure 1. Initially added PSS concentration dependence of sample density and thermal conductivity. The right side ordinate (closed circle) indicates thermal conductivity measured at room temperature. The left side ordinate (open circle) indicates sample density and packing density.

SEM observations were made on the surface and cross section of the samples. One can see pores in the sample which seems to be induced by the evaporation of PSS during the sintering process. Figure 2-a is the SEM observation of the surface of the sample with PSS concentration of 0.5 wt.% sample. Pores with diameters around 1 nm can be seen. Figure 2-b is the SEM

20 /im Figure 2-a. SEM observation of the surface of 0.5 wt.% PSS concentration sample.

20 /im Figure 2-b. SEM observation of the surface of 25 wt.% PSS concentration sample.

608 observation of the surface of 25 wt.% PSS concentration sample. The size of pores increases. 2.3 Temperature dependence of the Thermoelectric properties Figure 3 shows the temperature dependence of the electrical resistivity with the PSS concentration as a parameter. The current-voltage characteristics of the sample obeys Ohm's law. The values of the electrical resistivity around 600 V is reduced by a factor of 100--1000 times compared to the values at room temperature. Figure 4 shows the temperature dependence of tiie tiiermal conductivity of die samples also with PSS concentration as a parameter. They are measured by the PPE method, proposed in the previous reports [2,4,5]. The unstable tiiermal contact at higher temperatures of tiie sample to thermocouple in our experimental system limits the range of the thermal conductivity measurements under 300 "C. The thermal conductivities of tiie samples witii 0.5, 5.0 and 10 wt.% PSS concentration decrease with increasing temperature. Hie thermal conductivities of PSS concentration 15 and 25 wt. % samples slowly increase with temperature above 150 *C. Figure 5 shows the temperature dependence of the Seebeck coefficient. The data are obtained by the conventional DC metiiod. The Seebeck coefficient of all the samples increases with temperature monotonously. The rate of increase, however, is not large. Figure 6 shows the temperature dependence of the figure of merit. In this calculation of tiie figure of merit, the interpolated values of the Seebeck coefficient a and the electrical resistivity

120 r

10

O A D

D

e 0 a 10

PSS 0.5 wt.% 1 PSS 5.0 wt.% PSS 10 wt.% PSS 15 wt.% PSS 25 wt.% 1

+ D

X

B 100

.2 10 C/S

s

+% A

A

^°

1

A

+

1

X

[ 9

O

^

o

+D

X

HQ

40 r

>
150

PSS 0.5 wt.% PSS 5.0 wt.% PSS 10 wt.% PSS 15 wt.% PSS 25 wt.%

o A • + 1 X

4»-

S r 1 lOO

^

•g

+ CD o

u

1

'A

50

^ 0

D

® O O '-^

GP

nl

•

,

L -

.

1

200 400 Temperature (°C)

.

600

Figure 5. Temperature dependence of Seebeck coefficient.

200 400 Temperature (°C)

600

Figure 6. Temperature dependence of figure of merit.

p are used from room temperature to around 600 °C. The values of the thermal conductivity /c are also interpolated ones using polynomials under 300 °C, Above 300 "C, we have assumed that the thermal conductivity stays constant. The values of the figure of merit of all samples increase with temperature monotonously. Around 600X), 5.0 wt.% PSS initially added PSS concentration sample represents the largest figure of merit (2 X10"^ K"^) in this work. 3. DISCUSSION We discuss on the miaoscopic structure of our samples, in reference to the result of thermal conductivity measurements. A K. Collins et al. have reported that grain size of their poly crystal line sample could be estimated from the temperature dependence of low temperature thermal conductivity [6] with peak at around 200 K. They obtained values from several to 10 fi m. The grain sizes in our samples are smaller than these value from SEM observations. Although the temperature of our measurement is higher the phonon scattering on the grain and pore boundaries may still be important. Our samples can be classified into two groups according to the temperature dependence of thermal conductivity /c, Group 1: K decreases with increasing temperature. Group 2 : /c increases slightly with increasing temperature above 150 "C.

610 Samples with 0.5, 5.0 and 10 wt.% PSS and almost all samples in our previous paper [2] belong to group 1. Samples with 15 and 25 wt. % PSS belong to group 2. Acx:ording to Litovsky et a/.'s classification, group 1 and group 2 samples seems to correspond to structure with "dense grain boundaries" or "microcracks", and "porous grain boundaries with microcracks", respectively. It seems that excess PSS causes changes in the microstructure of samples in addition to the reduction in sample density. For the high temperature applications group 1 samples are preferable. 4. CONCLUSION We found that the addition of PSS has three effects. First (--0.5 wt.%) it acts as the sintering additive and increases density of the sample. Then the density and also the thermal conductivity K decreases ^parently because of pores introduced by evaporating PSS. (0.5--10 wt.%). In these concentration range, K decreases with temperature. At still higher PSS concentrations, they seem to cause some change in microstructure of grain boundaries and the temperature dependence of the sample becomes unfavorable for high temperature applications. From these results, one may infer that the optimum PSS concentration (with 2.0% B^C) is about 5 wt.% under conditions of our present work. Ai this concentration we could find Z=2 X10"^ K"^ at 600 °C. Tliis is somewhat lower but very close our best record in which the improvement of the electrical resistivity was the main theme. Acknowledgement The authors are largely indebted to Mr. M. Furuta for assistance and Prof. S. Fujimoto for discussion. References 1. K. Uemura and I. Nishida, in Netsudenhandotai to sono oyo (Thermoelectric Semiconductor and its Application) (Nikkan Kogyo, Tokyo, 1988), 33-38. 2. Y. Okamoto, A Aruga, K. Shioi, J. Morimoto, T. Miyakawa, and S. Fujimoto, Proc. 12th. Int. Conf. on Thermoelectr., Yokohama, edited by K. Matuura, 184, (1993). 3. K. Sugamuma, G. Sasaki, T. Fujita, M. Okumura, A Nakazawa and K. Niihara, J. Jpn. Soc. Powder and Powder Metallurgy, 38, 62 (1991) . 4. Y Okamoto, K. Tanaka, A Aruga, F. Furuta, J. Morimoto, T. Miyakawa,and S. Fujimoto, AIP Conf. Proc, 316, 62 (1994). 5. H. Wada, M. Watanabe, J. Morimoto, and T. Nfiyakawa, J. Mater. Res. 6, 1711 (1991). 6. A K. Collins, M. A Pickering and R. L. Taylor, J. i^pl. Phys. 68, 6510 (1990). 7. Efim Ya. Litovsky and Michael Shapiro, J. Am. Ceram. Soc, 75, 3425 (1992).


611

Preparation of B^C-B System Composites adding PSS and their Thermoelectric Properties A. Aruga, K Tsuneyoshi, Y. Okamoto and J. Morimoto Department of Materials Science and Engineering, National Defense Academy, 1-10-20 Hashirimizu, Yokosuka, Kanagawa 239, Japan B4C-B quasi-binary composites were prepared at 1950 °, 2100 ° and 2250 °C by pressxireless sintering in argon atmosphere using commercially manufactured B4C and amorphous B powders adding 0.5 wt.% polysilastyrene (PSS). As B9C possesses higher thermoelectric property as p-type semiconductors applied at high temperature, in this study we focused upon the lattice constant, density, electric resistivity, thermal conductivity, and Seebeck coefficient. These values as a fiinction of carbon concentration added on preparation over range 7'^20 at.% at room temperature were addressed. Also figure of merit (Z) of specimens were calculated. X-ray powder diffraction (XRD) revealed that the phase of specimens were mainly B]^2(C' Si, B)3 and a little carbon. Si was detected by energy disparsion Xray spectrometer (EDX), but SiC did not appear on XRD, though Si and C elements were due to a pyrolysis of PSS. Namely, isostructure substitution occurred at a site of C in B4C. Sintering density is less than 70 % that of B4C, especially lower in the range of 7'^9 at.% C owing to excess B. SEM observation showed a lot of opening pores, but particles were binded and grain growth occurred at higher temperature. The values of thermal diflfusivity were from 3 to 13 m^/s. Specific heat of samples was almost all 1.0 J/gK Then thermal conductivities of these composites were at a range of 4'^23 W/mK Electric resistivity (7 X lO'^'ê X10'^ Qm) tended to increase with increasing C content, while Seebeck coefficient (0.30^0.38 mV/K) showed opposite tendency. Consequently, the largest Z value of these B4C-B composites was about 2.4 X10"^ K'^ at room temperature. So it is estimated that this value of Z is between BgC and B4C, although near to B4C, and the value of ZT at 1000 °C will be predicted over 0.06.

1. INTRODUCTION Boron carbide is very hard, refi-actory solids (m.p.>2400 °C). And its thermoelectric properties are unconventional in high temperature range above

612 700 °C; that is, low electric resistivity, high Seebeck coefficient, and low thermal conductivity [1]. So it is useful material as a p-type semiconductor applied for thermoelectric power conversion at high temperature. Nuclear properties such as high cross-section and resistance to irradiation are also grateful for neutron absorption (^^B). These are attractive especially for radioisotope fueled thermoelectric generator in space. Nonetheless, boron carbide does solemnly not utilize as thermoelectric devices except for thermocouple of B^C/C. Boron carbide is easily oxidized in air above 500° C [2], and react with rare metal such as Pt and Pd [1], which is used as an electrode. However, these are only technical problems. It would use for thermoelectric devices if it were highly efficient, a low cost one and easy to make it. Therefore, we first focused on a low cost and an easy making. Starting materials selected are commercially manufactured B^C and amorphous B powders. And selected process is usual pressureless sintering. Generally, boron carbides were prepared from boron and carbon atoms by hot pressing (HP), because it is said that pressureless sintering is very difficult against covalent material such as B4C. But our selections are cheaper than HP, chemical vapor deposition (CVD) [3], and other processes [4], We did not get B9C powder commercially manufactured. So our trial is to react B4C with B so as to obtain BgC ceramics in consideration of following; the single phase regime of boron carbides extendsfi:-omnear 9-20 at.% [5], and sintering is promoted at lower temperatures by introducing free carbon or other impurities [6]. In addition, one of our attention is to make machinable ceramics [7]. Polysilastyrene (PSS) is adopted as a binder, which acts to bind B4C particles, and produces porous ceramics so that it improve the electric properties and thermal conductivity affected by the density while maintaining the physical properties of B^C.

2. EXPERIMENTAL The starting materials used in this experiment were B4C (average particle size of 0.7 Jim, Grade: #1200, Denki Kagaku Kogyo, Japan), amorphous B powder (average particle size of 0.1 jim, Rare Metallic, Japan), and polysilastyrene (Grade: PSS-100, Nippon Soda, Japan) as a binder. After mixing above B4C and O-'S.S mol B with 0.5 wt.% PSS in xylene solution, the green bodies were prepared by same manner described in a previous report [8]. First, the green bodies were slowly treated up to 1000 ° C in a flowing argon atmosphere for pyrolysis of PSS. Then each preheated body covered with each powder of similar composition in each graphite crucible were sintered at 1950 °, 2100 °, or 2250 °C for 2 hrs in an argon atmosphere. The specimens with dimensions of 3.0 X 4.0 X10 mm^ for the electrical transport measurements were cut out from the sintered bodies. Samples were cleaned in ultrasonically agitated baths of acetone and ethanol.

613 The microstructure of the specimens were examined by a scanning electron microscope (SEM; model S-2100, Hitachi, Japan) and simultaneously elements were analysed by using the energy dispersion X-ray spectrometer (EDX; model 3700-2000S, Horiba, Japan). Also B4C-B composites were identified using an Xray diffractometer (XRD; Rint 2500, Rigaku, Japan) equipped a graphite monochromator and precise lattice parameters were corrected with internal standard of Si (NBS, 640B). Electrical resistivity measurement adopted conventional four probes method. Seebeck coefficient was measured by the standard DC method. Thermal conductivity K, was calculated fi-om density, specific heat, and thermal diffusivity. Specific heat measurement was carried out by use of a differential scanning calorimeter (DSC; model 8230, Rigaku, Japan) compared with a standard material of a -AI2O3. The values of thermal diffusivity obtainedfiôma differential phase analysis of photo-pyroelectric signal (AL-A 6 analysis) [9]. All measurements were done at room temperature.

3. RESULTS AND DISCUSSION Figure 1 shows the XRD profiles for B4C+6.5B (B^Q 5C) composites adding 0.5 wt.% PSS sintered at various temperature. And hexagonal lattice parameters of a and c for B4C-B sintered bodies added 0.5 wt.% PSS are given in Fig. 2, compared with a starting material of B4C. XRD analysis shows that some sintered bodies included a little amount of amorphous or crystallized carbon, but there was no SiC. Then all lattice parameters were slightly greater than these of B4C as raw material. 2250°C These revealed that a little amoxuit of added Si, which arisesfi:-omp3a'olysis of ,XJ PSS and which in all specimens was detected by use of EDX, was incorporated 2100°C into the B4C lattice. Furthermore, the lattice parameters slightly increased with increase in content of added B, though extension of the lattice upon incorporation 1950°C of Si and B suggested thatSi and B atoms -li vL JUJ substituted for C site. Fig. 3 shows SEM 20 30 40 50 photographs of cutting surfaces for Cu Ka 2 /9 ( deg.) B4C+5B ceramics sintered at various

Li

temperature. And density of B4C-B ceramics was plotted out in Fig. 4. Relative density is less than 70 % theoretical density

u

Fig. 1. XRD profiles of B4C+6.5B composites sintered at various temperature.

614

[•

• • 1 "

• 1 • ' '

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1.

I r

, 5.615J-L a>

t fit^^fi

i

, . . . 1

- - • — 1950°C —e—2100°C --5^2250t • raw mat.

•1

j

i

5.611

.^^-.^ -> 5.605

6

8

10

12

14

16

18

20

C content initially added (at.%)

22

C content initially added (at.9

Fig. 2. Hexagonal lattice parameters (a and c) of sintered B4C-B composites as a -. function of initial C content. 1 Jim

(a) (b) (c) Fig. 3. Scanning electron micrographs of the cutting surfaces of the B4C+5B composites sintered at (a) 1950 °C, (b) 2100 °C, and (c) 2250 °C. 1.8 of B4C, especially lower (about 50 %) in the range ofl'^d at.% C owing to excess ^ 1.7 B, which prevented sintering. SEM observation showed a lot of opening pores, 1.5 h i T /r^^^^^~^^^ but particles were binded and grain growth 'JA 1.4 r // --•—1950°C occurred at higher temperature. That is, C j —e—2100t ^^-î* Q 1.3 7*^|p* —^^ 2250°C these composites are porous ones and ,_^2 1.2 component is mainly B^g^^, Si, B)3 [10], a 6 8 10 12 14 16 18 20 22 little amount of carbon and excess Concentration (at.%) amorphous B. Roughly speaking, these are Fig. 4. Density of B4C-B ceramics close to B4C ceramics. sintered at various temperature. Figure 5 shows electrical resistivity p measured at room temperature as a function of C concentration initially added. The p of B4C-B ceramics tended to increase with increasing carbon content. This tendency is opposite with other reports [1]. For almost all specimens prepared in this study are similar to B4C except for a little substitution of C to B and Si. And . . 1

1 .

615

B 40 LI I I I I I I I I I I I I I I j I I I I I I I I I I I I I I 35

-•—1950^: -e—2100°C ^5r- 2250°C

30 25 20 15 10 OS

8

10

12

14

16

18

20


Fig. 5. Electric resistivity as a function of initially added C content.

22

B u H

5 0

' ' • • • ' ' • ' ' • • * ' • • • ' • • • ' • • •

8

10

12

14

16

18

20

22

C concentration (at.%)

Fig. 6. Thermal conductivity as a function of initially added C content.

in a view of sintering temperature, it is insufficient for sintering at 1950 °C, especially for B4C. But its values sintered at 2250 °C are about 1.4X lO"^ Qm, which is good agreement with other reports [1], and minimum value of 6 X10"^ Q m for B4C+8B ceramics sintered at 2250 °C is lower than that of the recent report [11]. This proves that B4C particles were successfully binded with each other by use of B and PSS (see Fig. 3), and yet the physical properties of sintered bodies remain such as low electric resistivity even though porous ones. Thermal conductivity K of samples, is easily deducible by simple arithmetic from data of the density (see Fig. 4), specific heat and thermal diflfusivity, graphs out in Fig. 6. Among them, specific heat of all samples was 1.06 ±0.07 J/gK, which is good agreement with general values, on the groiinds that its value of B^C and B is similar to each other. The values of thermal diffiisivity were from 3 X10"^ to 1.3 X10"^ m^/s. Higher sintering temperature rises, lower the values of thermal diffusivity tend. The K of these composites were at a range of 4 ^ 2 3 W/mK The tendency was similar to that of thermal diffusivity. And all samples sintered at 2250 °C were with low thermal conductivity. The Seebeck coefficient a and figure of merit Z for B4C-B ceramics as a function of C content are given in Fig. 7 and Fig. 8, respectively. The a was always positive, and its absolute value increases with increasing carbon content except for B4C+5B. a (0.30-^0.38 mV/K), whose maxima was observed at 20 at.% C (B4C) sintered at 2250 °C, showed opposite tendency of electric resistivity (7 X lO'^^-êx 10"^ Qm), whose minimum was at B4C+8B sample fired at 2250°C. Though the figure of merit Z is evaluated from electrical resistivity, thermal conductivity and Seebeck coefficient, the Z values showed maximimi of 2.4 X 10'^ K'l at B4C+8B composite fired at 2250 °C. Therefore, the electric resistivity affects more than the Seebeck coefficient. This material in analogy with SiC is good in high temperature range but not in low one. So in practical use it needs to combine other effective materials in low and middle temperature range for a high performance device.

616

8

^

10

12

14

16

18

20

22


Fig. 7. Seebeck coefficient as a function of initially added C content.

6

8

10

12

14

16

18

20

22


Fig. 8. Figure ofmerit as a function of initially added C content.

4. CONCLUSION The largest Z value of these B4C-B composites added PSS was about 2.4 X10"^ K"^ at room temperature. So it is estimated that this value of Z is between BgC and B4C, although near to B^C, and the value of ZT at 1000 ''C will be predicted over 0.06. It will be obtained a good result if we have get B9C powder with a little B, adding more PSS (about 2 wt.%), and some other additives will be able to improve the electric resistivity.

REFERENCES T. L. Aselage and D. Emin, "CRC Handbook of Thermoelectrics", Ed. by D. M. Rowe, CRC Press, New York (1995) 373. D.-H. Riu, R. Choi and H.-E Kim, J. Mat. Sci., 30 (1995) 3897. K Koumoto, T. Seki, C. H. Pai and H. Yanagida, J. Coram. Soc. Jpn., 100 (1992) 853. T. L. Aselage, D. Emin, G. A. Samara, D. R. Tllant, S. B. Van Deusen, M. O. Eatough and S. M. Johnson, Phys. Rev., B48 (1993) 11759. M.Bouchacourt and F. Thevevot, J. Less-Common M e t , 82 (1981) 219. F. Thevenot, J. Eur. Coram. Soc, 6 (1990) 205. K Suganuma, G. Sasaki, T. Fujita, M. Okumura, A. Nakazawa and K Niihawa, Funtai oyobi Funmatsu Yakin, 38 (1991) 62. Y. Okamoto, A. Aruga, H. Tashiro, J. Morimoto, T. Myakawa and S. Fujimoto, Proc. 14th Inter. Conf. Thermoelec, Ed. by A. F. loffe, Phys.-Tech. Institute, St. Petersburg (1995) 269. H. Wada, Y. Okamoto and T. Miyakawa, J. Mat. Res., 6 (1991) 1711. 9. 10. File of X-ray powder diffraction standards of American Society for Test and Materials. Inorganic Compounds; BJL2(C, Si, B)3, 19-178. 11. T. Goto,J. Li and T. Hirai, Funtai oyobi Fxmmatsu Yakin, 43 (1996) 306.


617

Joint of n-type PbTe with Different Carrier Concentration and its Thermoelectric Properties Y.Imai, Y.Shinohara, I.A.Nishida, M.Okamoto, Y.Isoda, T.Ohkoshi, T.Fujii, I.Shiota' and H.T.Kaibe^ National Research Institute for Metals, STA, Ibaraki 305, Japan '"Kogakuin University, Tokyo 192, Japan ^'Tokyo Metropolitan University, Tokyo 192-03, Japan ABSTRACT The experimental examination and investigation have been carried out on the jointed ntype PbTe ingot and the sintered n-type PbTe compact with 3 layers of graded electron concentrations n^s to develope a higher efficient thermoelectric material. The jointed ingot composed of materials with /^7e=0.18 and 4.5Xio^Vm'' was prerared by difBasion jointing apparatus. No jointing boundary was confirmed by the opitical micro structure observation. Both the electrical resistivity p and Seebeck coefficient a of the jointed ingot were strongly affected by the lower part of ^ZeÔ. 18 X 10^Vm' at lower temperature and by the higher part of nc=4.5 X lO^Vm^ at higher temperature. The sintered compact with 3 layers of ne= 3.51, 2.60 and 2.26 X lO^Vm^ was prepared by the hot-pressing technique. It was found that the graded structure of rie can perform a 7% higher effective maximum power than the homogeneous structure at a temperature difference of 280K. 1. INTRODUCTION The lead telluride compound systems are typical thermoelectric materials in an intermediate temperature region, and had been developed as space power generating materials in the 1960's[l,2]. Currently, the thermoelectric generators with the combustion heat source of LNG and LPG come into the market as self-supporting electric sources on the earth[l,2]. The figure of merit Z for thermoelectric materials with a homogeneous composition generally shows a maximum value at a certain temperature Topt and rapidly decreases above and below ôpt [1-3]. As shown in Figure 1, the Topt can be changed higher or lower by higher or lower carrier concentration in the material, respectively[4]. Theftmctionallygraded material(FGM), which have a slope of carrier concentration in the heat flow direction, can have a higher Z in a wider temperature range(a broken line in Figure 1). As a part of the national project in Japan,

618 highly efficient thermoelectric materials have been recently studied in Bi2Te3, PbTe and Si-Ge alloy systems with graded structures of carrier concentration, crystal grain size, composition, etc[4,5]. The present study was to examine the thermoelectric properties of jointed ntype PbTe with different electron concentrations n^s. The 3-layered FGM of sintered PbTe with graded n^ was also prepared by hot pressing technique, and the performance of the FGM was discussed to attain high energy conversion efficiency. 2. EXPERIMENTAL PROCEDURE

Temperature Distribution Low ^ — High I

1

11

JJ[

IV

V

Electron concentration FGM

300 400 500 600 700 800 Temperature(K)

900 1000

Figure 1 Temperature dependences of figure of merits

The mixture of weighed amounts of for n-type PbTe with various electron concentrations. Pb and Te in a stoichiometric composition of Pb/Te=l was vacuum sealed in quartz tubes with dopant of Pbt. The purity of raw materials was 99.999%, and the «e was controlled by the amount of Pbt in the range from 0.2 to 1.2wt%. The mixture was mehed at 1300K and solidified at the cooling rate of 30K/h by the rocking furnace to obtain homogeneous ingots. The rocking cycle was IHz, and the slope of temperature given to quarts tubes was 0.5K/mm. The PbTe ingots with different n^ of 0.18 and 4.5 X lO^Vm^ were cut and subsequently jointed by the difiRision jointing apparatus to form the jointed PbTe specimens. The jointing was under 1.4Pa at 1073K for 30min in an argon atmosphere. PbTe ingots with n,=3.5, 2.5 and 2.0X lO^Vm' were crashed to pieces and shifted to obtain the starting powders of 74-124 A^ m in particle size. The powders with n,=3.5, 2.5 and 2.0 X 10^Vm'' were stacked one by one in a carbon die and subsequently hot pressed to form the 3-layered FGM specimen of sintered PbTe with graded n^. The hot pressing was at 1 lOOK for 30min under 3.3MPa in an argon atmosphere. The dimension of FGM was 10 ^ X 6^mm' and each layer was 2mm in thickness. The measurement of thermoelectric properties employed the DC method with high speed and high resolution[2] to remove fully errors occurring by Peltier effect. The thermoelectromotive force EQ was measured as a function of temperature difference A 7 at both ends of a specimen. The thermoelectric power a was obtained from a slope of Eo-A Jcurve and expressed as an absolute value.

619 Tabic 1

Conduction paramcrtcrs of solidified n-lypc PbTc and jointed electron concentrations.

doped Pbl2 wtSli

0.2 1.2 0.2/1.2

Rfl

ne

u-

lO-'^xDiVC 33.88 1.40

lO^Vm^ 0.184 4.459

mVV-S 0.190 0.064

P

lO'^xfim 17.74 2.20 7.33

material with two kinds of

3. RESULTS AND DISCUSSIONS 3.1. Joint of Solidified Ingot The electrical conduction parameters at room temperature for solidified ingots with «e=0.18 and 4.5 X 10^Vm^ and their jointed material are shown in Table 1. for ingots with «e=0.18 and 4.5XlO^Vm^ were 0.2 and 1.2wt%.

The amount of P b t

The jointed material is

refered to as 0.2/1.2wt%Pbl2 in tables and figures afterwards. No jointing boundary was confirmed by the opitical micro structure observation, and the joint was satisfactory.

The

resistivity p of the jointed material is smaller than an average value(14.4jiQm) of ingots, although the length of 0.2wt%Pbl2 part from the jointed face is 3.7 times larger than that of 1.2wt%Pbl2 part.

Yoneda e/.a/.[5] have reported that p of the solidified n-type PbTe is

decreased to 15 and 50% by annealing at 703 and 803K for Ih in an argon atmosphere, respectively.

The ingots were jointed at

1073K for 30min in an argon atmosphere, 10'

resulting that the p of the jointed material is 50%

lower

than

soHdified ingots.

an average value

of

Figure 2 shows the

CJ X

temperature dependence of p for the ingots and the jointed material.

The p of the ingot

1.2wt%)Pbl2 increases

with

increasing temperature monotonously.

This

doped

with

10^

o:0.2wi%Pbl2 A:1.2wt%Pbl2 o:0.2/1.2wt%Pbl2

tendency reveals that the heavily doped ingot is a degenerated semiconductor.

On the

contrary, the ingot doped with 0.2wt%Pbl2 and the jointed material show maximum values at high temperatures, and the jointed material has the maximum at an higher temperature.

As resuhs, it was found that p

of the jointed material is affected by the part

10^

_i

I

1.5 2 2.5 3 3.5 Reciprocal of temperature (IO'VK)

Figure 2 Temperature dependences of resistiviteis for solidified n-typc PbTe doped with 0.2 and l.2wt%Pbl2 and jointed material.

620 with lower n^ at lower temperature and by 0| ~1 I I I I I I I I T" the part with higher n^ at higher 1.2wt%Pbl2 temperature. Figure 3 shows the temperature dependence of a obtained from Eo-/^T curves for the ingots and the jointed material. In the measurement of the jointed material, the length of 0.2wt%Pbl2 part is 1.5 times larger than that of 1.2wt% Pbl2 part. The 0.2 and -350 _J I I I I I I I I L_ 300 400 500 600 700 800 1.2wt%Pbl2 parts were set up at a heat Temperature (K) sink of 300K and a heater to obtain AT", Figure 3 Temperature dependences of Ihermoelectric respectively. The |a| of the ingot doped properties for solidified n-type PbTe doped with 0.2 with 0.2wt%Pbl2 increases with increasing and 1.2\M%Pbl2 and jointed material. temperature and shows a maximum value near 600K, while the |a| of the ingot doped with 1.2wt%Pbl2 and the jointed material increase with increasing temperature lineally and also the latter is larger than the former. It is difficult to judge whether the joint of thermoelectric materials may improve the maximum output power from the above results, because the ratios of (the length of 0.2wt%Pbl2 part) to (the length of 1.2wt%Pbl2 part) for the jointed material are different on the measurements of a and p. However, it is clarified that both the temperature dependences of a and p for the jointed material are affected by the higher and lower n^ parts at higher and lower temperatures, respectively. 3.2. Sintered PbTe FGM The thermoelectric properties at room temperature of the sintered PbTe FGM with different n^s and of the high(a), intermediate(Z?) and low n^ (c) layers composed FGM were shown in Table 2. The high n^ (a)- layer gives an optimum Z to the homogeneous PbTe as reported Stavitskaya[5], and the n^ is not changed from the starting solidified ingot. However, «eS of (by and (c)-layers are higher than those of the starting ingots, and the lower n^ layer has a higher increasing ratio of «e by sintering. The a and p of FGM are -85.0^V/K and 3.95piQm, respectively. The a is close to the average a value of (a)-, (b)- and (c)-layers, while the p is even larger. Takahashi et.al{6'\ have reported that the Si-Ge alloy FGM with 3 steps of different n^ has higher electrical resistance at jointed faces. The phenomenon of increasing p for the PbTe FGM is not clear yet, but it is likely that the jointed faces of the FGM cause increase of p.

621 Tabic 2

layer

(a) (b) (c) FGM

Thermoelectric properties of 3-layered FGM of PbTc with different electron concentrations and of layers composed FGM at room temperature.

a(/zV/K) -67.1 -72.3 -88.6 -85.0

p(Qin)

RHCIDVC)

/7e(1025/Di3)

2.54x10-6 2.81x10-6 3.34x10-6 3.95x10-6

1.78x10-'' 2.30x10-'' 2.75x10-7

3.51 2.60 2.26

XieCmVVs) 7.00x10-2 8.18x10-2 8.22x10-2

a2a(ff/K2m) 1.77x10-3 1.86x10-3 2.34x10-3

Figure 4 shows the temperature dependence of p for the sintered PbTe FGM and for (a)-, (by and (c)-layers shown in Table 2. All ps increase with increasing temperature, and they have typical variations for the degenerated semiconductor. However, the increasing ratio of p for the FGM is smaller than those of (a)-, (b)- and (c)-layers. p of the FGM is strongly affected by the lower n^ layer at lower temperature and by the higher n^ layer at higher temperature as same as the jointed material in § 3.1. Figure 5 and Figure 6 also show the temperature dependences of |a| and electrical figure of merit aâ, respectively. All measured specimes have maximum values for aâ. The temperature corresponding to a maximum a}a for each layer increases with increasing n^. The aô of the FGM is lower than those of all layers below 500K because of the increased p, while is higher above 63OK. This result confirms the graded structure of A?e is effective to higher thermoelectric performance. Figure 7 shows the relationship between the effective maximum power Pmax and AT for the sintered PbTe FGM and for (a)-, (b)- and (c)-layers at cold edge temperature T^ of 500K. 10^ • :FGM 0:a-layer A:b-layer D:c-layer

X

• :FGM 0:a-layer A:b-Iayer D:c-layer

b^

>a

^ 10^

10'

1.0

1.5

2.0

2.5

3.0

3.5

Reciprocal of temperature (10"VK) Figure 4 Temperature dependences of resistivities for n-type PbTe FGM and for high(a)-, intermediate(/))and low electron concentration(c)-layers in FGM.

300

400 500 600 700 800 Temperature (K)

Figure 5 Temperature dependences of thermoelectric powers for n-type PbTe FGM and for high(«)-, intermediate(Z))- and low electron concentration(c)-layeri: in FGM,

622 The Pmax of FGM at Ar=280K is 150Wm/m^ and is about 7% larger than that of (a)-layer whose Pmax IS largest in all layers. This value shows the electric power reaches 25kW/m if the operation temperature range from 500 to 780K is given to the FGM with 6mm of thickness. From these results, it is concluded that the highly efficient n-type PbTe FGM can be performed by the optimum control of electron concentration graded structure.

300 400 500 600

700

800

Temperature (K) Figure 6 Temperature dependences of electrical figure of merits for n-type PbTe FGM and for high(o)-, intermediate(6)- and low electron concentrations(c)-layers in FGM.

50

100 150 200 250 300

Temperature difference AT (K) Figure 7 Effective maximum powers for n-type PbTe FGM and for high (a)-, intermediate (b)- and low electron concentrations(c)-layers in FGM at cold edge temperature Tc of 500K.

REFERENCES 1. D.M.Rowe and C.M.Bhandari, Modern Thermoelectrics, Holt, Rinehart and Winston, London, 1983. 2. K.Uemura and I. A.Nishida, Thermoelectric Semiconductors and Their Applications, Nikkan-Kogyou Shinbun-Sha, Tokyo, 1988. (in Japanese) 3. LB.Cardoff and E.Miler, Thermoelectric Materials and Devices, Reinhold Publishing Co., New York, 1960. 4. I. A.Nishida, Proc. Japan-Russia-Ukraine Int'l. Workshop on Energy Conv. Mater.(RNCOM'95), (1985)1. 5. S.Yoneda, H.T.Kaibe, Y.Imai, Y.Shinohara, I.A.Nishida, T.Mochimaru, K.Takahashi and T.Noguchi, J. Advan. Sci., (1996). to be pubiUshed. 6. K.Takahashi, T.masuda, T.Mochimaru and T.Noguchi, Proc. FGM Domestic Sympo. (FGM'95), Tokyo, (1995)123. (in Japanese)


623

Effects of plasma treatment on thermoelectric properties of Si8oGe2o sintered alloys K. Kishimoto^, Y. Nagamoto^, T. KoyanagP, and K. Matsubara^ ^Department of Electrical and Electronic Engineering, Yamaguchi University, 2557, Tokiwadai, Ube 755, Japan. •^Department of Electronics and Computer Science, Science University of Tokyo in Yamaguchi, 1-1-1, Daigakudori, Onoda 756, Japan.

A microstructure control at grain boundaries of SiGe sintered alloys has been attempted to improve their thermoelectric figure-of-merit. SiGe raw micrograins were exposed to GeH4-plasmas to be coated with Ge layers, and then were sintered. Results of the microstructure analysis suggested that the plasma-treated alloys had Ge-rich layers around grain boundaries. In these alloys, a reduction of the thermal conductivity and increases in the electrical conductivity and the Seebeck coefficient were observed. This favorable change of the thermoelectric properties may be associated with the microstructure modification around grain boundaries. 1. I N T R O D U C T I O N Silicon germanium is one of the most well-known and efficient thermoelectric materials [1]. So far, many efforts on silicon germanium[2-4] have been devoted to improve its thermoelectric figure-of-merit Z = S^GJK^ where *S, c, and K is the Seebeck coefficient, the electrical conductivity, and the thermal conductivity, respectively. In previous papers [5,6], we reported that the thermoelectric properties of sintered iron disilicides were improved by the microstructure control around grain boundaries using the plasma processing. Iron disilicide micrograins were exposed to rf plasmas of reactive gases, such as O2, SiH4, or GeH4, and then were sintered. It was found that the obtained sintered alloys had a larger electrical conductivity and a lower thermal conductivity than untreated alloys due to modification of grain boundaries. In this paper, we investigate effects of GeH4-plasma treatment on the microstructure and the thermoelectric properties of Si8oGe2o sintered alloys. 2. E X P E R I M E N T A L Si8oGe2o micrograins of 1 to 10 /xm in size were obtained by milling arc-melted SiGe

624 102 E

0.18

-—> O) (D •o

0.16

JZ •o

^

*r

CO

X

0.14

50 100 150 Treatment time (min)

200

Fig.l. Dependence of the increase in Ge concentration by the plasma treatment and half width of SiGe(lll) XRD peak on the treatment time.

o C/)

>, >

10^

r

•C^

o3 T3 C

\^ %. \ %. ^^.

treatment time • : 0 min O: 20 min 0\ 60 min A: 180 min

10^

o o

.^

a

•c 10o CD LU

10-'

SisoGego 1

,

^^ 1

,

1

iooo/r(K-^) Fig.2. Temperature dependence of the electrical conductivity of GeH4-plasmartreated SiGe sintered alloys.

ingots. The micrograins were exposed to an rf-plasma. The processing apparatus was reported previously[5]. The treatment was made under the following conditions: processing gas 5 % GeH4 diluted with Ar of 132 ml/min; rf-power 200 W; total pressure 0.4 Torr; processing time 0 to 3 h; micrograin amount 15 g. The treated micrograins were sintered by the hot-pressing under the following conditions: vacuum pressure 10~^ Torr; sintering temperature 1473 K; pressing pressure 32 MPa; pressing time 3 h. For comparison, untreated Si8oGe2o sintered alloys were prepared without treating the micrograins in an rf-plasma. The sintering conditions were same as those of the plasma-treated alloy. The microstructure of the samples was examined by the x-ray diffraction (XRD), the scanning electron microscope (SEM), and the electron probe microanalysis (EPMA). The electrical conductivity and Seebeck coefficient were measured from 300 to 1200 K. The thermal conductivity was measured by the laser-flash method at room temperature. 3. R E S U L T S A N D D I S C U S S I O N The Ge concentration of SiGe sintered alloys measured by EPMA increased with increasing the treatment time. This result indicated that a thickness of Ge coating layer on micrograins by the GeH4-plasma treatment increased with the treatment time. In XRD patterns of the GeH4-plasma-treated sample, Ge crystalline peaks were hardly observed, indicating that a part of Ge might diffuse into the grains while sintering. Ge concentration of the sintered alloys was obtained by XRD peak position of SiGe(lll)[7]. Figure 1 shows increases in the Ge concentration by the plasma treatment measured by EPMA and XRD. The half widths of XRD peaks of S i G e ( l l l ) are also plotted in the figure. The increase in Ge concentration obtained by EPMA are larger than that obtained by XRD. A difference between the two values increases with increasing the

625 1.0

0.036

0.6 —

0.8

^

> E "c

2.5 and y>2,5 where the value of a was saturated and the value of p increased further. Not only the value of a of the Fe098Si2.5CO0.02 film but also the value of p were higher than those of the

637 ordinary sintered Feo.98Si2.oCoo.02, while the Feo.92Si2.5Mno.08 film corresponded to the ordinary sintered Feo.97Si2.oMno.03 material [4] because of evaporation of Mn. A lack of Si is supposed to be caused by selective oxidation of Si [6] and evaporation rate of Si is larger than that of Fe. But these causes are not sufficiently related to above results. Molar ratio of Mn and Co in each film were evaluated by the EPMA analysis and found to be 0.03 and 0.02, respectively. The dispersion in the direction of thickness and diffusion in the insulator were observed in the case of Mn as shown in figure 6.

0

^

Cu - Ka

e) (0

'c 13

d)

_^ ^__^^____

i^Jv.^-^^

0

j8 - FeSi

A

a - Fe Si

•

e - FeSi Si

T

^

2

2

5

c) .

CO

c

b)

_c

AJ

_J/

A

.

*

a) 1

20

1

30

1

_iit___

1

40

50

60

2(9/deg Figure 5. Result of XRD analysis of the Feo98SiyCoo.o2film. a) y=2.0; as melted, b) y=2.0; as annealed, c) y=2.2; as annealed, d) y=2.4; as annealed, e) y=2.6; as annealed.

a) SEM image b) the image of Mn -Ka 0.1 mm Figure 6. Cross sectional photos of SEM image and image of Mn-Ka of the Feo.92Si25Mno.08 films. 1; metal sheet, 2; insulator, 3; thermoelectric film. 3.2. Thermoelectric sensing device The device was shown in figure 7. The size was 40 (W) x 60 (L)x 0.9 (T) and the weight was about 5 g. The electrical output of the device loaded an LED (Stanley Co., Inc., BR5334S) was evaluated with a gas flame as shown with figure 8. The value of E increased steeply reacting to a gas flame and decreased gradually after the temperature of the device was saturated by the gas flame within 30 seconds. The value of i^ decreased steeply accompanying the change of the value oiE and gradually after the value oiE was saturated. The temperatures of hot junction and cold junction were saturated at approximately 890 K and 350 K, respectively. As the value oiE reached 1.5 V within 5 seconds, the device lighted the LED. The maximum output was nearly 3 mW.

638 The resistivity of the hot junction was extremely high because of the difference in the melting temperature between Feo.92Si2.5Mno.08 material and Feo.98Si25Coo.02 one. As the former material melt earlier than the latter, the former material penetrated into the latter in the sintering process through the hot junction by the capillary effect. Fortunately the resistivity of the hot junction decreased by the hot junction being heated as the device was operated. For the cold junction, it was better to connect them electrically by soldering or using electrical conductive adhesive to avoid the defect described above. The thick film shrunk during the sintering process and expanded during annealing process. Though these factors arose the warping of the device, the degree of warping was adjustable by dimensions of the film and thickness of the substrate. Therefore the device could be finally flattened. > —.

E: open circuit

UJ

o E

/ Figure 7. The view of the heat sensing device. 4.

Figure 8. The thermoelectric properties of the heat sensing device. The LED begins lighting up above £"=1.5 V.

CONCLUSIONS

The heat sensing device with the thermoelectric thick film laid on insulated metal sheet was investigated. The device well responds to a heat source and generated enough power to drive an LED. The thick films were made from the thermoelectric iron disilicide materials whose compositions were Feo.92Si25Mno.08 and Feo98Si25Coo.o2 for p type and n type, respectively. It was found that melting was effective to decrease the porosity of the film and to increase mechanical strength of the device. It was also found that, by adding Si more than stoichiometric composition of the j^FeSi2, the residual f-FeSi phase could be minimized and thermoelectric property of the film could be maximized as much as that of ordinary sintered iron disilicide material. REFERENCES 1 2 3 4 5

D. M. Rowe, Proc. 12th ICT (1993) 429. H. lizuka, T. Yamazaki, M. Komabayashi, Proc. 12th ICT (1993) 295. T. Kojima, N. Hiroyama, M. Sakata, J. Materials Science Soc. Japan 28 (1991) 252. T. Kojima, M. Okamoto, I. A. Nishida, Proc. ICTEC, Arlington, March, (1984) 56. I. Isoda, K. Masumoto, T. Kojima, I. A. Nishida, K. Tanaka, Abstracts of Japan Institute of Metals, April, (1985) 175. 6 K. Herz, M. Powalla, Appl. Surf. Sci. 91 (1995) 87.


639

Recent Developments in Oxygenated Thermionic Converters *. J.-L. Desplat Rasor Assoc. Inc., 5670 Stewart Ave., Fremont, CA 94358, USA Addition and control of oxygen in thermionic converters is the key to achieving high efficiencies and power densities. Converters with collectors containing cesium oxide, and with cesium oxide vapor circulation have shown barrier indices near 1.9eV. A new method, based on sputtering and readsorption for measuring the vapor pressures of both cesium and oxygen-bearing species in research converters was developed, hi addition, the vapor phase in research devices operating under similar conditions was sampled by time-of-flight mass spectrometry: vapor pressures of CS2O around 1x10"^ Torr were detected in Cs pressures around 1 Torr. These CS2O pressures were consistent with those obtained using the readsorption technique.

1. INTRODUCTION Parametric studies have shown that, in order to achieve high efficiencies and power densities at realistic spacings and emitter temperatures, it is necessary to have a high emitter bare work function O^Q at or above 5.2eV and a barrier index Vg at or below 2 eV. One approach successfully implemented in the past was to incorporate oxygen in the collector layer by subliming molybdenum in an oxygen atmosphere [l]. Extensive performance mapping of such converters has shown that the release of oxygen is increased as the collector temperature is raised, resulting in higher O^Q [2]. This linkage however restricts the range of collector temperatures available to design thermionic nuclear reactors by establishing a constraint on the rejection temperature. Rasor Associates therefore initiated a research program with the DOE to test other approaches and in the process gain some insights about controlling the oxygen addition. This paper is mostly a summary of a report available from the DOE [3l

2. NEW APPROACHES IN OXYGENATED CONVERTERS 2.1.Cesium oxide loading in collectors The mechanism by which the sublimed oxygen-containing Mo collector leads to better performances is not well understood. It is commonly assumed that Cs reduces the molybdenum oxide formed during the sublimation, the resulting volatile CS2O then dissociating on the emitter surface. To bypass the molybdenum oxide reduction step, the first approach tried was to load commercial "cesium oxide" (composition close to that of CSO2) in hollow collectors. * This research was sponsored by the U.S. Department of Energy

640 Figure 1 shows two versions of such converters assembled around a planar variable-spacing research converter body built by ThermoTrex: one was fitted with a collector whose cavity contained - 0.6g of CsO^ , the other had a porous W disc in which CsQ had soaked in after melting, hi both cases cesium vapor was supplied by an outside liquid reservoir.

COLLECTOR BASE-

Figure 1. Two versions of planar converters with CsO^ - loaded collectors. After extensive activation both designs achieved good performance: OgQ-^ 5.5eV and Vg at 5A/cm^ < 2eV. (see Figure 3 below for some JV curves). However given the complexity and expense associated with variable-spacing research converters, a new test vehicle was designed to allow faster iterations: Builtfi"omdemountable standard UHV components, it featured a 7cm stainless steel cube to which variousflange-mountedelectrodes and instrumented ports could be attached, hence its name - the "cube" converter. 2.2. Development of a vapor circulation source Early tests in the cube consisted of investigating the performance of fixed-spacing planar converters in which a pool of liquid Cs was gradually oxidized. However cesium oxide migration out of the reservoir was observed, against the temperature gradient, leading to a segregation of the oxide in a hotter region of the converter. To confine the oxide to the reservoir a technique already used with molten alkali salts was adopted [4]: a porous platinum disc, resulting fi'om partial sintering of platinum black, was placed in the reservoir. Figure 2 shows the cube with its OXYGEN DETECTOR electrodes, the reservoir with the Pt pellet, and the newly developed oxygen detector (see section 3.). The emitter was a W layer CVDed fi-om WClg, the collector polycrystalline Mo, the spacing ~0.6mm. Cesium POROUS Pt PELLET could be distilled in measurable amounts into the reservoir. Two such converters with similar Pt pellets exhibited very good performance without activation Figure 2. "Cube" converter. : Both achieved barrier indices below

641 2 eV and O^Q above 5.5eV. Figure 3 shows that the performance of the first one was nearly identical to that of the converter with the CsO^ - containing collector. Figure 4 shows that the second one had a Vg of 1.91eV at the beginning which later settled at 1.97eV, during a limited life test. \ \ VB = 2.0« V I

>vM8k

l

"

^

TcyBE=710K Tcup'VAR.

\ \ \ \ \ \ \

N

\ ^

Tc=670K

I

V s^9k fe 15

Tg« 1800K

'"••

516k

— PL E-4 HE T-4R

" ^

XAV'^ 02

0.4

0.6

0.8

::.225^^

1.0

0.4

ELECTRODE VOLTAGE(V)

Figure 3. JV curves for two converters: HET4R with CsO^ -collector, PUE4 with Pt pellet reservoir.

0.6

0.8

VOLTAGE. V

Figure 4. JV curves during a short life test of PUE5 with Pt pellet reservoir (no further change from 600h to lOOOh).

EXTERNAL VAPOR FtOW

Figure 5. Processes assumed to be occurring in DECOR. These data together with visual observations of the reservoir and SEM examinations of the sintered Pt lead to a description of the cesium-loaded Pt pellet as a "dynamic equilibrium cesium oxygen reservoir" (acronym: DECOR) capable of generating pressures of Cs and oxygen-bearing

642 species and circulating them throughout the converter. A brief summary of this model follows: 1. Due to its large specific area the sintered Pt contains a significant amount of adsorbed oxygen. Cesium addition results in the formation of a dilute Cs/0 solution. 2. The internal structure of the Pt pellet is bi-porous, consisting of a continuous web of small pores,filledwith a Cs/0 liquid, around which large interconnected pores carry a Cs/0 vapor. 3. This bi-porous structure under a heat flux (e.g. from the electrodes) generates internal liquid and vapor flows [5], and extemal flows as well. Figure 5 shows the resulting concept. 4. The thermal gradient within the pellet generates composition gradients in the liquid and vapor. 5. Chemical equilibrium establishes the local Cs/0 liquid and vapor composition. 6. The oxygen concentration in the extemal vapor is determined by the temperature and composition of the liquid at the hot end of DECOR. 7. Thermochemical calculations suggest that the material holding the Pt pellet is involved in determining the steady state oxygen content of the liquid film at the cold end of the pellet.

3. OXYGEN PRESSURE MEASUREMENT 3.1 Basic Method The technique consists first of removing the adsorbed oxygen layer through in-situ sputtering by Cs"*" ions generated during a voltage sweep of the emitter current, and then to monitor the rate of oxygen readsorption through its effect on the emission. As oxygen is readsorbed on the emitter, the Cs coverage also rises concurrently, resulting in a rise in emitted current. The relationship between the current rise and the "equivalent" oxygen pressure was derived by Ned Rasor [3] under the following assumptions: •small oxygen coverage, GQ 14

14

1.2

1.2 I

1.01—I—i—t1.0 1.2 1.4

1.6

1.8

TC/TR

(c) W O X

2.0

2.2

2.4

1.0 1.0

—I

1.2

1

1

1.4

I

L_

1.6

1.8

TC/TR

(d) TaO X

Fig.4 Work function of metal oxide in Cs vapour

2.0

2.2

2.4

651 temperature range. Then the AgO x was intentionally heated up to 620 °C for 3hrs,and the NbO X up to 745 °C for 3hrs respectively. After heating, 0 c (mi n) of AgO x increased by O.leV, i.e. 1.25 -^ 1.35eV. The 0 c cmi n) of NbO x did not change at all. 3.2 Power generation tests of the W-AgO x thermionc converter Output J-V curves of the thermionic converter with T R below 515K are shown in Fig.5 and Fig.6. The open curcuit voltage of Fig.5 was lower than the one of Fig.6. The reason was guessed to be a very slight short-circuit between the collector and the emitter . Therefore, after that , both J-V curves of the collector - emitter (C-E) and the collector guard - emitter (CG-E) were taken. A noticeable point of Fig.5 and Fig.6 is that the forward saturation current J f o r in the unignited mode was very large , being inconsistent with the theory. (Refer an appendix.) For instance, J for of electron rich ( /3 < 1, /3 means " ion richness ratio"), diffusion conditions (d/ A e-n > 1, A e n means " electron -Cs atom mean free path") under the unignited mode operation, is estimated to be not greater than 0.4A/cm ^ as shown J f o r in Table 2. The value of J f o r of the experiment greatly exceeded 0.4A/cm ^ . J-V curves at T E = 1300 °C are shown in Fig.7, Fig.8, and those at T E = 1350 °C in Fig.9, Fig.10, respectively. The J-V curve of T R =553K in Fig.7 should be noteworthy because the curve has barrier index V B = 1.5V. Although it is not clearly shown in Fig.7, all curves in Fig.7 ignited in 2nd quadrant. They were measured at the phase of half sinusoidal wave of applied voltage from the minus peak toward the plus peak, i.e. from unignited toward ignited mode. Therefore all curves in Fig.7 were in unignited mode opration. Again it is noteworthy J f o r in unignited mode operation is veiy large. In Table 2 are shown the converter parameters calculated on the curve of T R = 5 5 3 K in Fig.7, when the Richardson current J R from the emitter supposed to be J R =10A/cm ^ . The value of ion richness ratio /5 =4.44 X 10 ~ means the electron rich condition and nevertheless the very large forward current was obtained in Fig.7. This is not explainable . Except this point there was not any contradiction in Fig.7. The value of 0 c in Table 2 was calulated by Fig.4 (a), and the 0 c value was far from the minimum value of 0 c because of higher T c . Therefore if the collector temperature could be lowered to the value of minimum 0 c , the output J-V curve could be greatly improved. In fact there are high levels of back emission current from the collector as clearly shown in Fig.7 ^ Fig. 10. The J-V curves in Fig.8 ^ Fig. 10 can be explained as the same way as in Fig.7, and barrier index V B = 1.7V was obtained in these Figures. In Fig. 11 is shown the maximum output power with regard to the emitter temperature. The maximum power of 3.9W/cm " , 0.6 V, 6.5Aycm ' were obtained on the J-V curve of CG-E, at T E = 1 5 8 3 K . 3.3 Future study An image of a FGM collector for a thermionic converter is shown in Fig. 12. The distinctive feature of the FGM collector is that the metal oxide materials with the compositionally graded structure is coated on the metal substrate by sputtering method. At the same time the electric insulation materials with the small columnar shape are placed uniformly dispersed on the collector to hold the gap of 10 jLL m between the emitter and the

652 lOOOi

Em'W.Col'AgOx TE = 1580K Tc = 978K d = 0.3mm (CG)

-0.5

Fig.5

0.0

0.5

1.0

-0.5

1.5

Output Voltage, V (V) J-V curve of T E = 1 5 6 5 K

0.0

0.5

1.0

1.5

Output Voltage, V (V) Fig.6 J-V curve of T E = 1 5 8 0 K Em'W.Col'AgOx TE = 1583K Tc = 1075K d = 0.3mm (CG)

20V, 7y

-0.5

0.0

0.5

1.0

1.5

-0.5

2.0

0.0

0.5

1.0

1.5

Output Voltage, V (V)

Output Voltage, V (V) Fig.8

Fig.7 J-V curve of T E = 1 5 7 8 K

J-V curve of T E =1583K

24 ...

;r20

20 ^ o 16

\

\ (

523K-\^n

' ' ' \

1

:.i2

Em'W.Col'AgOx 1 TE » 1625K Tc = 1098 K d = 0.1mm (C)

2.0V 1.7V

543K \533K \

\

\

L 553K^M| ,

r 533l^.

0

-4

\

O^^ ^

t^ n o

Em'W.Col'AgOx 1 TE = 1623 K Tf = l ? | 6 K d » 0.3mm ICG)

M

\

8h

VVB=I.5V

\

^

20V1-7V : T ; •

\

£

^^"•~~-^-oL [ T R = 513K

553K\

1 1 1 1 1 1 1 1 1 1 1 i_i 1 1 1 1 1 1 1 ' ^ ' ' 1 ' ' ' '

-0.5

0.0

0.5

1.0

1.5

Output Voltage, V (V) Fig. 10 J-V curve of T E = 1623K

2.0

653 Table 2 Estimated parameters of J-V curve of Fig.7 T E

Tc

1578K

1074K

01

TR

553K

2.35eV

l.OSTorr 1.40x10 ' N / m

d/ A 4.44.X10

3.5x10

^ mm

1.48eV

2.8

lOA/cm '

9.02x10 " ' A / c m '

Tc/T

0 E- 0 (

1.94

0.87eV

0.37A/cm

0 E is estimated, supposing J R =10A/cm -

D:C

—

o:CG

Q_ 4

0^ Q

\h 3h h

0

D

0 D D

80

o a.

I

collector. A higher efficiency of the thermionic converter operating in unignited mode can be expected by developing the FGM collector.

0 0

L_

L1 1 1 1 1 1400 1500 1600

1

1 . 1 . 1700 1800

1900

Emitter Temp. , TE ( K ) Fig. 11 Maximun output power density of the converter Insulator Oxide graded layer Metal substrate-^

- F G M layer 1^^Metal substrato Fig. 12

Image of FGM collector

4. Conclusion 1) Fabrication of metal oxide collectors The sample electrodes of metal oxides for a thermionic converter collector were fabricated by RF sputtering method in Ar + O 2 gas mixture. Refractory metals of W, Mo, Nb, Ta and also Ag were chosen as target materials of the RF sputtering apparatus. The oxygen partial pressure was intentionally set at stoichiometrically oxygen short levels so as to make the metal partially oxydized and dispersed into the metal matrix of the sputter coated layer. The sample electrodes consist of the functionally graded materials (FGM), the composition changing from the metal to the metal oxide by controlling the oxygen partial pressure of sputtering. The sputter -coated layer showed sound, no peeling off and good adhesion. 2) Work function in cesium vapour The work function values of these sample electrodes were measured by immersing them into the cesium plasma.

654 The lowest work function values 0 c (mi n) of four kinds of metal oxides were as follows. AgOx:1.25eV, NbO x :1.38eV, WO x :1.42eV, TaO x :1.43eV. The AgO x was intentionally heated up to 620 °C for 3hrs, and the NbO x up to 745 °C for 3hrs respectively, in order to obtain data on the high temperature endurance capability. After heating them, 0 c (mi n) of AgO x increased by O.leV, i.e. 1.25 ^ 1.35eV. The 0 c (mi n) of NbO X did not change at all. The materials of AgO x and NbO x made by sputtering were judged to be promising for a thermionic collector. 3) Power generation test The research thermionic converter, with the poly-W emitter, the AgO x collector, interelectrode spacing 0.1mm, was fabricated and power generation tested. The maximun output power was obtained in the unignited mode operation. The maximum power, 3.9W/cm ^ , 0.6V, 6.5A/cm ^ was obtained between the collector guard and the emitter at T E = 1 5 8 3 K . The barrier index V B = 1 . 5 V was obtained between the collector and the emitter at T E =1578K, T C =1074K, d=0.1mm, under the unignited mode operation. 4) Subjects to be solved In the experiment the forward saturation current density J f o r under the electron rich and diffusion conditions of the unignited mode, was 20 times larger than the value expected by the theory. This inexplicable results should be examined by another experiment. Also, what extent the V B could be reduced by T c optimization and what the maximum endurance temperature of the AgO x collector could be, should be examined further. 5) Future study The FGM metal oxide collector which has the integrated spacers and can hold 10 ILL m interelectrode spacing is proposed for the realization of the micro-gap thermionic converter. APPENDIX; The forward saturation current J f o r

under the electron-rich, diffusion conditions of unignited mode

(5 )

Operation is expressed by the equation J for

=

(2 A e - n

n 0 V 1 )/(3d)

(1)

n o = 4(J R J c /v 1 V 2 )

equihbriun density determined by emission currents

V 1 =(8kT E / ;r m)

electron average thermal velocity

V 2 =(8kT E / TT M)

Cs ion average thermal velocity

J R : electron emission current of Richardson eq. J c : ion emission currents of Saha-Langmuir eq.

/I e - n : electron-Cs atom mean free path d : interelectrode spacing

REFERENCES: 1) I.Langmuir, K.H.Kingdom: Phys. Rev. 23, p. 112 (1924). 2) R.Fukuda et al :7th Functionally Graded Materials Symposium(FGM'93), pubhshed by the Fomm of FGM Society, p.211,Tokyo, Nov. 1-2,(1993). 3) R.Fukuda et al : 29th Inter. Energy Conv. Eng. Conf.,Monterey, CA. U.S.A., p. 1041,(1994). 4) R.Fukuda et al :8th Functionally Graded Materials Symposium(FGM'95), pubhshed by the Fomm of FGM Society, p.l61,Tokyo, Oct. 12-13,(1995). 5) P.Stakhanov, et al: Plasma Thermal Emission Energy Conversion, cliapter IE , pl57, machine aided trans, version (1969).


655

Thermionic Properties and Thermal StabiHty of Emitter with a (0001) Oriented Rhenium Layer and Graded Structure M. Katoh", R. Fukuda*" and T. Igarashi' "Tokyo Tungsten Co., Ltd., 2 Iwasekoshi-machi, Toyama-shi, Toyama 931, Japan ^lectrotechnical Laboratory, 1-1-4 Umezono, Tsukuba-shi, Ibaraki 305, Japan Rhenium exhibits excellent thermionic electron emission characteristics in a cesium plasma converter. Chemical-vapor-deposited rhenium with a preferred (0001) orientation should have advantages over polycrystalline rhenium with respect to thermionic emission. Rhenium layers with (OOOl)-oriented three-dimensional surfaces have been successfully deposited on molybdenum substrates. The work function of rhenium emitters was estimated to be 4.9 eV from the results of power generation tests. The maximum power of a thermionic energy converter incorporating a rhenium emitter is 2.0 W/cm^ when the temperature of the emitter is 1800 K, that of the molybdenum collector is 990 K and that of the cesium reservoir is 561 K. The composition and surface morphology of the rhenium layer may change as molybdenum from the substrate diffuses into the rhenium layer at high operating temperatures. In order to improve the thermal stabiUty of the rhenium layers at elevated temperatures, tungsten layers were inserted between the rhenium layers and the molybdenum substrates to form graded composition interfaces. The tungsten layers prevented excessive diffusion of molybdenum into the rhenium layers. 1 . Introduction Thermionic energy conversion is a power generation method which can be used to convert thermal energy into electric energy directly. A thermionic energy converter is a nonmechanical device that has high reliability. Research has been carried out on thermionic energy converters for use in space and ocean environments. On thermionic energy conversion, electrons are emitted from a hot electrode and collected using an electrode at a lower temperature. These electrodes are usually separated by a distance of 0.5 mm or less. The electrons condense at the collector and return to the emitter via the electrical load, thereby delivering electrical work. The limitation of the output current density due to the space charge is prevented by enclosing cesium vapor between the electrodes, because of the low ionization energy of cesium. Due to the adsorption of cesium ions, the work function of the electrodes decreases with decreasing electrode temperature (T^ ) and increasing cesium reservoir temperature (Tj^) [1]. The work function of the electrodes is maintained at the Optimum value by controUing the operating conditions.

656 The emitter for the thermionic energy converter is required to have not only excellent thermionic emission characteristics but also hot strength, good workability and bondability with adjacent component materials. Surface-coated emitters are unique in that they possess the thermionic emission characteristics of the overlayer and the mechanical characteristics of the substrate. On the other hand, it is necessary to fabricate an overlayer, which has good thermal stability, for a surface-coated emitter, because the overlayer easily generates damage at the interface between the overlayer and the substrate during heating and cooling due to the thermal stress which results from the difference between the thermal expansion coefficients of the overlayer and the substrate, and the diffusion of substrate constituents to the emitter surface under high temperature operation. Therefore, it is necessary to fabricate a diffusion prevention layer, which suppresses chemical diffusion between the overlayer and the substrate, and results in a composition gradient at the interface, which reduces the thermal stress. Due to the composition gradient at the interface, the formation of a concentration gradient is suppressed, and the thermal stabiHty is improved. In this work, the work function of a (0001) preferred orientation rhenium layer, the thermionic power generation characteristics under conditions in which this layer operates as an emitter and the thermal stability of the interface between the rhenium layer and the substrate are described. 2 . Experimental 2.1. The formation of a rhenium thermionic emission layer and a tungsten diffusion prevention layer Rhenium layers with (0001) preferred orientation were fabricated on molybdenum substrates by chemical vapor deposition (CVD). Molybdenum has light weight, high thermal conductivity and good workability compared to other refractory metals. A schematic drawing of the CVD apparatus is shown in Figure 1. Rhenium base powder was reacted with the chlorine gas at 1070-^ 1170 K, resulting in the formation of ReCls gas. This gas decomposed on the substrate, which was thermally heated to 1400-^ 1520 K, and thus rhenium was deposited. The ReCls generation reaction and the thermal decomposition reaction are represented as 5

Re

— a.

ReCL

(1)

CL

(2)

2

ReCL

Re

heater

It was found that tungsten is an effective diffusion prevention layer, which improves the thermal stability of the rhenium layer by reducing the amount of chemical diffusion between the rhenium layer and the molybdenum substrate. The tungsten layer was deposited by reduction of WFg using hydrogen, at a substrate temperature of 900^1100 K, and a reaction pressure of 1.3 kPa.

induction coil

CZH Figure 1. Schematic diagram of the rhenium CVD apparatus.

657 2 . 2 . Observation of the rhenium layer surface morphology The surface morphology of the rhenium layers was observed using a scanning electron microscope (SEM), and the surface area was measured using an atomic force microscope (AFM). Using X-ray diffraction (XRD), the macroscopic crystal orientation was examined, and the (0001) crystal plane was identified from electron channeling patterns (ECP) [2]. 2 . 3 . Formation and observation of the composition gradient Diffusion was promoted by heating the samples in a vacuum of about 6.5 X 10" Pa at 2000 -^2300 K in order to form a composition gradient between the molybdenum substrate and the rhenium layer. The composition gradient was investigated using an electron probe microanalyzer (EPMA), 2 . 4 . Measurement of the work function and thermionic power generation characteristics A schematic diagram of the power generation test apparatus is shown in Figure 2. The emitter, which was a disc with a diameter of 16 mm and a thickness of 5 mm was joined using ruthenium-molybdenum braze to a support made of tantalum, and was placed facing the molybdenum collector at a distance of 400/^m. The emitter was heated to 1400-^ 1900 K by electron bombardment. Then the collector was cooled by radiative cooling to about 1000 K. By maintaining T^ at 400^570 K, the cesium ^Radiation fin ( C u ) vapor pressure (P^) was kept at 0.35~2.05 Pa. ^ Thermocouple hole An AC power source (100 V, 50 Hz) and X Collector guard ring ( M o ) a load were connected to the power generator, and the current-voltage characteristics were y / O ^ " ^ Spacer (AI2O3) measured using a digital oscilloscope. The Collector ( M o ) effective work functions were evaluated under Emitter (CYD-Re) conditions of P^^ = 0.8~ 13 Pa, for which there Temp, measurement hole is no volume ionization (unignited mode). The power generation characteristics were measured Emitter holder ( T a ) under conditions of P^^ = 1.1 X 10^ --" 2.6 X Heat choke ( T a ) 10^ Pa , i.e., the cesium was in the plasma state Filament guard ( Mo ) (ignited mode), in which an output current Filament ( W ) density more than ten times that for the unignited Figure 2. Schematic diagram of the mode is obtained. thermionic power generation test apparatus. 3 . Results and Discussion 3 . 1 . Evaluation o f the rhenium layer In Figure 3, an SEM image (a) and an AFM image (b) of the rhenium layer surface formed at a substrate temperature of 1520 K are shown. On the surface, (0001) facets, with the characteristic hexagonal structure of the most dense plane, are obseived. The surface area with (0001) orientation was estimated as 42%, and the surface area was increased by 13% due to the surface roughness. 3 . 2 . Fabrication of a gradient structure emitter Figure 4(a) shows the composition of a rhenium/molybdenum interface that was heated for 10 hours at 2300 K. At the rhenium/molybdenum interface, the thermal stabiUty is low, because a rhenium-molybdenum alloy layer over 200/i m thick is formed.

658 (b)

Figure 3. Surface morphology of an as-deposited CVD rhenium layer : (a) SEM image and (b)AFM image. The composition gradients of the rhenium/tungsten and tungsten/molybdenum interfaces formed by heating for 10 hours at 2300 K are shown in Figure 4(b). The samples have an intermediate tungsten layer between the rhenium layer and the molybdenum substrate. The rhenium-tungsten alloy layer is 40// m thick, i.e., about 1/5 of the thickness of the layer formed in the rhenium/molybdenum system. The tungsten-molybdenum alloy layer is 65 // m thick and the rhenium/tungsten/molybdenum structure is stable at high temperatures. Chemical diffusion is suppressed by the composition gradient at the interface at temperatures which are sufficiently higher than the operating temperature, and the thermal stability of the rhenium layer is improved. In Figure 5, the composition dependences of the average thermal expansion coefficients measured at 303-1073 K for the rhenium-tungsten alloy and at 293-1273 K for the tungstenmolybdenum alloy are shown. For the rhenium-tungsten system, the dependence is almost linear, including that for the ^-phase intermetallic compound, formed in the 30-^ 55 mass% tungsten composition range. The results indicate that the stress concentration can be reduced by the composition gradient, even if the (T-phase, which has low ductility, is formed. In the tungsten-molybdenum system, the thermal expansion coefficients change by about 13% in the composition range 0^^ 15 mass% molybdenum. However, for molybdenum compositions greater than 15 mass%, thermal stress concentration is unlikely to occur, since the change in the theimal expansion coefficients is small.

I

I

I

-I

r~

303-1073 K

o *

1

1

293-1273 K

\ \ . \. _l

I

I

I

I

L_

0 20 40 60 80 100 80 60 40 20 0 (Re) (W) (Mo) mass % W distance

Figure 4. Composition gradient at (a) Re/Mo and (b) Re/W/Mo interfaces.

Figure 5. Mean thermal expansion coefficients of W-Mo and Re-W systems.

659 Based on these results, a (0001) oriented rhenium thermionic emission layer ( 100/^ m ), and a tungsten diffusion prevention layer (500jum) were formed on a molybdenum substrate, and emitters with a composition gradient at each interface were produced. 3 . 3 . Evaluation of the power generation characteristics 3 . 3 . 1 . Evaluation of the work function The relationships between ^ g and 7^ / 7]^ for polycrystalline rhenium and CVD rhenium are shown in Figure 6. It has been reported that the work o A functions of (0001) single-crystal rhenium (^ ^Q^^^ ) 3.5 D and polycrystalline rhenium ( f ^^^y^) in vacuum are 5.5eV [3] and 4.6eV [4], respectively. Using the measured values of ^ ^ ^^^ the relationship between 7^/ TR and ^ ^ ^^^ various bare work function ((/> Q ) , reported by N. S. Rasor, ^ o ^^ ^^^ ^ ^ ^ rhenium emitter was evaluated as 4.9 eV.

1450-1500K 1500-1600K 1600-1700K

ô = 4.9eV

3.3.2. Evaluation of the power generation w characteristics 2.5 When P^ and the interelectrode gap (d) have 4.0 3.5 3.0 TE/TR values greater than a specified value (P^^ • d>20 mil • Torr), the cesium ionizes and forms a plasma, referred Figure 6. Comparison between the to as the ignited mode. In this ignited mode, an output work functions of polycrystalline current density more than ten times that for the and CVD rhenium emitters. unignited mode is obtained. The output currentvoltage characteristics obtained at Tg = 1800 K, T^ = 1000 K and T^ = 497 ~ 561 K are shown in Figure 7. The maximum output increases as the reservoir temperature increases. A maximum output of 2.0 W/cm^ was obtained at 7]^=561 K. The current-voltage characteristics for the above conditions were calculated using the standard computer model "TECMDL" [5] for the ignited mode, developed by J. B. MacVey et al. The current-voltage characteristics were calculated using the measured values of Tg, T^, T^, <j> E^ i> c and d. Although this result does not take into account time degradation, the experimental value for the output exceeded the calculated value. For a cesium plasma thermionic energy converter, there are six important parameters, T^ , ^ c ^R' ^ E ' i^ c ^^^ ^' ^s mentioned above. To improve the output of a thermionic energy converter, it is necessary to determine how these parameters affect the power output. The adjustment of Tg , T^ and T^ is necessary in order to produce appropriate power generation conditions. ^ ^ and j5 ^ of the materials have a significant effect. The interelectrode gap, d, is also an important parameter, since the output depends on it exponentially. E ^^ ^^ô an important factor, since it strongly affects the maximum output. The results calculated using the relationship between the work function and the maximum output of the emitter are shown in Figure 8. In this figure, T^ is optimized for the work function of each emitter. When the work function of the emitter is increased, the maximum output increases rapidly. If the area ratio of rhenium (0001) increases, then (f> ^ increases, and an improvement in the output is expected.

660

0.5 1.0 Output Voltage, V/ V

4.0 4.2 4.4 4.6 4.8 5.0 5.2 Emitter Work Function, ^ / eV

Figure 7. Current-voltage characteristics Figure 8. Calculated variation of maximum of CVD rhenium emitter. (Dotted Hne output with the work function of the emitter. indicates calculated value for T^ = 561 K.) 4 . Conclusion A gradient structure emitter, in which the molybdenum substrate is covered by a (0001) rhenium layer with a three-dimensional surface and an intermediate tungsten layer was fabricated, and the work function and thermionic power generation characteristics were evaluated. The following results were obtained. (1) The thermionic emission area was about 13% greater than that of a flat plane, and a (0001) preferred orientation rhenium layer with a three-dimensional surface and a work function of 4.9 eV in vacuum was obtained. (2) An intermediate tungsten layer was formed, which prevented thermal diffusion of the surface layer into the substrate, and improved the thermal stability of the surface layer. (3) A maximum output of 2.0 W/cm^ was obtained at T^ = 1800 K, T^ = 1000 K, T^ = 567 K a n d d = 400 //m. Acknowledgement This work was carried out as part of the second phase of the FGM R & D program for the development of direct energy conversion technology. This work was supported by the Science and Technology Agency of Japan. References 1. 2. 3. 4.

N. S. Rasor and C. Waner, J. Appl. Phys., 35 (1964) 2589. D. C. Joy, D. E. Newbury, D. L. Davidson, J. Appl. Phys., 53 (1982) R81. V. S. Fomenko, Zmissionne Svojstva Materialov, (1991) 59. Thermo Electron Corporation ed.: Thermionic Research Computation Aids, TE320-1-77, July (1976) 17. 5. J. B. McVey and N. S. Lasor : in Proceedings of the 27th Intersociety Energy Conversion Engineering Conference, SAE/P-92/259, Sandiego, CA, August 3-7, 1992.


661

Development of Efficient Thermionic Energy Converter T.Kato% K.Morimoto% K.Isogai^ M.Kato\ T.Fukushima^ R.Fukuda^ ^ Mitsui Engineering & Shipbuilding Co.,Ltd., Ichihara-shi, Chiba 290, Japan ^ Tokyo Tungsten Co.,Ltd., Toyama-shi, Toyama 931, Japan ^ National Research Institute for Metals, Tsukuba-shi, Ibaraki 305, Japan ^ Electrotechnical Laboratory, Tsukuba-shi, Ibaraki 305, Japan In the near future, thermionic energy converter will be a more promising device for space power generation. To this end, a solar heated thermionic energy converter has been developed by applying functionally graded materials (FGM) to the electrode. It is majorly composed of a W/Re-FGM emitter, a NbOx collector, and a TiC/Mo-FGM solar receiver. 1. DESIGN OF FGM-BASED CONVERTER 1.1. High Temperature Electrode High temperature electrode, called emitter, is made up of a refractory metal block with three circular parts, as shown in Fig. 1. The surface of upper disc is coated with a layer of TiC/Mo materials by a plasma spray method^^l The TiC surface has emissivity of approximately 0.9 and can be heated up to a temperature range of 1800 to 2000 [K] by solar concentration. Furthermore, such a FGM layer reduces the stress caused by difference of thermal expansion between TiC surface and Mo base. The surface of bottom disc is covered with a layer of ReAV materiales, which is formed through heat treatment after two step CVD coatings^^l The Re surface, having preferred orientations with (0001) plane, shows higher work function than a surface of conventional type. The FGM layer pre-coated with W prevents the diffusion at high temperature. Then both Mo discs are brazed to a middle block of Ta. 1.2. Low Temperature Electrode The structure of collector electrode at lower temperature is similar to the emitter one, but with two circular parts, as shown in Fig. 1. The surface of Mo disc opposite to the emitter is covered with NbOx (Niobium oxide) layer coated by a sputtering method^^l NbOx surface, which shows low work function in Cs vapor, can reduce the energy loss of electron condensing in to collector. This coated Mo disc is brazed to base block of Ta, similar to emitter.

662 1.3. Connections and Other Components Fig. 1 also shows that the emitter and the collector are connected by several units. To reduce the heat conduction loss, Ta tubes called heat-chokes are joined to the both electrodes. Ceramic seal rings are used to insulate the electrodes electrically. Two rings are arranged for Cs vapor tube inlet and electrical leads. Each unit is connected by a electron beam welding or a vacuum brazing method. Insulator pins, called ceramic spacers, are attachet on the collector to keep a constant interelectrode gap. Small crown parts are assembled inside the converter in order to block the radiative heat. 1.4. Converter for Laboratory Tests We have to prepare another type of converter for laboratory testing, shown in Fig. l(a dotted line). Such a converter has a long emitter block with three holes for thermocouples, instead of Mo disc. It can be heated by electron bombardment. The surface temperature of emitter, TE, is estimated from the temperature distribution of the emitter block.

1®J ?ctron-bombardment heat i ng

radiation 18 00

TiC/Mo graded Re/W graded emitter ceramic spacer radiation seal NbOx col lector ceramic seal

m

M

-^ electrical lead Cs vapor inlet Fig. 1 Cross-sectional view of eflBcient thermionic energy converter.

663

radiation seal vacuum chamber

ai r cool ing fin

fi lament

thermionic converter Cs vapor pipe

Fig. 2 Schematic of experimental apparatus.

2. EXPERIMENTAL APPARATUS An experimental measuring apparatus as shown in Fig. 2 consists of an electron bombardment heating system, an air cooling system, a vacuum system, and an electrical measuring system. By adding assistant alternating voltage to the electrodes, the corresponding output current density is measured, differently from a passive method. The way to estimate the surface temperature of collector, Tc, is the same as that of the emitter. The collector codling system has three holes to insert thermocouples along conductive heat flow. The pressure of Cs vapor filled in the interelectrode gap is controlled by the temperature of liquid Cs reservoir, TR. 3. EXPERIMENTAL RESULT AND DISCUSSION 3.1. J-V C h a r a c t e r i s t i c s The electron current density, JR, emitted from the electrode is given by a relationship^'*^

664

J R = AT^-exp

kTJ

[A/cm2

(1)

where A = 1 2 0 [A/cm^-K^] T = electrode temperature [K] (f) = electrode work function [eV] k = 8.62 X 10"^ [eV/K] : Boltzmann's constant Eq. (1) is called Richardson-Dushmann equation. JR never indicate output current density in itself, although it helps account for the converter performance. Large JR from Eq. (1) suggests that the converter generates a great deal of output power. Since the work function of the electrodes immersed in Cs vapor can be expressed as a ratio of TR to T, following three temperatures, TE, TC, TR, are important parameters, which will be presented later. A typical curve of current-voltage (J-V) characteristics and maximum output power (Pmax) are shown in Fig. 3. For three given temperatures, increasing the voltage up to 0.8 [V] results in a gradient decrease of the output current. In this region the converter is operated in an ignited mode, and a large number of ions a r e g e n e r a t e d by i n e l a s t i c collisions in the interelectrode gap, this leading to a plasma state. Pmax is usually obtained at large voltage of the ignited mode. Then there is a rapid current drop because of transition of the operating mode. In a voltage range from 0.9 to 1.0 [V], the converter is operated in the unignited mode without plasma. In this region the output current density is limited by electron space charge. J-V characteristics helps define the interelectrode phenomena such as electron and ion emission from electrodes, sheath height at the electrode surface, voltage loss in the plasma, and so on. But it Fig. 3 Typical J-V characteristics of the is difficult to discuss those converter with an electrode surface area phenomena in detail. In following of 3 [cm^], # depicts a Pmax point for, s e c t i o n , we d i s c u s s the V= 0.7519 [V] correlation between Pmax and J=10.4159 [A] some temperatures, apart from P= 7.9069 [W/cm^]. J-V characteristics.

665 3.2. Tc Effect on Pmax In the experimental converter of Fig. 1, collector surface covered by a NbOx layer serves as a reservoir of electronegative gas (oxygen-contained molecule), which reduces the emitter work function. Therefore Tc has a large effect on the converter performance. The dependence of Pmax on Tc is shown in Fig. 4. This indicates that an optimum value of Tc is found to be between 925 and 950 [K]. As Tc increases from 750 to 950 [K], Pmax increases monotonously because emitter work function is reduced by oxygen from the collector. But further increasing of Tc results in a reduction of Pmax because, broadly speaking, the electron emission from the collector can not be negligible. 3.3. TR Effect on Pmax The dependence of Pmax on TR is shown in Fig. 5. It is seen from this figure that higher TR seems to achieve larger Pmax. If TR was in excess of 610 [K], Pmax would reach a peak at a given TR. But a great deal of current density is not suitable for practical use. Table 1 shows experimental values of electrode voltage (Vmax), current density (Jmax) corresponding to Pmax, and controlled temperatures, which present the plotted data of Fig. 5. It is found that Vmax shows a large decrease with an increase of Jmax when TR rises ten degrees from 593 [K]. When Jmax is limited below 10 [A/cm^] to avoid a large voltage drop across the actual leads, Pmax has a value of about 8 [W/cm^]. 4, CONCLUSION To date an efficient thermionic energy converter has been developed and operated at various test conditions. It is concluded that the converter design, including a technical method of coating, welding, and brazing, has been successfully done because there observed no trouble through operating at high temperature. Typical output power density is 7.9 [W/cm^] at the emitter temperature of about 1800 [K]. It is pointed out that higher TE of 2000 [K], may be desirableto produce large Pmax. REFERENCES 1. T. Fukushima, S. Kuroda, and S. Kitahara, Proc. 8th Symp. on FGM, pp.167-170. The FGM Forum (1995). (in Japanese) 2. R. Igarashi, et al., ibid., pp.155-160. (in Japanese) 3. R. Fukuda, Y. Kasuga, and K. Kato, ibid., pp. 161-166. (in Japanese) 4. G. N. Hatsopoulos and E. P. Gyftopoulos, "Thermionic Energy Conversion, vol.2," The MIT Press (1973).

666 Table 1 Testdata-operating temperatures, output voltages and current densities.

h

1 Exp No

SI

h

Vmax [V]

[fe

Pmax [W/cn?]

3.0768 3.1142 3.2003 3.7666 4.8332 7.1485 15.0007 3.9472 4.5133 5.5754 7.0158 9.3982 I 11.3566 15.5721

1.6667 1.6437 1.6667 2.0140 2.6853 3.7730 6.3543

1 2 3 4 5 6 7

1851.2 1846.2 1849.8 1847.8 1846.2 1840.8 1818.6

1061.4 1056.7 1056.1 1062.2 1073.9 1088.5 1122.6

543.3 553.3 562.8 573.3 583.5 593.9 603.4

0.5417 0.5278 0.5208 0.5347 0.5556 0.5278 0.4236

8 9 10 11 12 13 14

1844.9 1844.5 1840.6 1835.2 1831.4 1826.0 1817.4

970.8 969.9 977.6 986.4 996.9 1000.7 1015.0

543.4 552.5 563.4 572.9 583.1 593.2 604.0

0.7917 0.7873 0.7847 0.7792 0.7129 0.7062 0.6197

TE ! Emitter temperature Tc ! Collector temperature TR ! Reservoir temperature 3. 5

1

•

.

1

,

•

Vmax ! Voltage at the maximum output power Jmax ! Current at the maximum output power Pmax ! Maximum output power 1

1

o •2.5

-

T A

1. 5

0

J

A

o j T ^ oH

750

I

1

5

1

Fig. 4 Dependence of output power on collector temperature. O: T E = 1 6 2 0 ± 1 0 , TR=573±1[K] • : TE=1620±10, TR=533±1[K] A: T E = 1 6 2 0 ± 1 0 , T R = 5 2 3 ± 1 [ K ]

-

12

~ -

S 4 _

11

A

• 10

J

"6

•9

-j

0,5

°?

J

°4

S 1

540

0, 7 J

•_

a>

1

800 850 900 950 1000 C o l l e c t o r T e m p e r a t u r e [K]

14

J

-•e f^ 2 _ =3 °i

l—

^T"

• „

tr>

=3

L.

' •13

^>^ 1

•^ 1 J

r •

e ^ " y - 8

*> 3

A

1'^,"

1

^' ^

V.

T

1 0.5

o

]

AA ^ -^ A •

r A

-

^

o

0 o XL

^loi irradiation

•

0

A

X

A

0

0

500 1000 1500 Emitter temp.TE[K] magnetic field (i)T,=400[K] (ii)t=450[K] X 0 (iii)Tg=TJK](Wall temp.) 0

(b)

Figure 5. The relation between the emitter temperature and the short circuit current with and without illumination and external magnetic field.

678 lo[A/cm^ 2r

Cs gas temp.Tg:400[K]

lo[A/cm^ 2\

(u)

Emitter temp.TE:1070[K]

Without irradiation

-3

2~^

-2 " -

loIA/cm"] 3

(c)

3^°^

With irradiation

-3 • -2 • -V"Ol

2

3Vo[V]

lo[A/cm^ 3r

(d)

Cs gas temp.Tg:443[K]

1

Emitter tempTg: 1280[K]

Without irradiation

T

0'

^VoM

1

• Without magnetic field,

With irradiation

-3

-2

-1

0"

;Vo[V]

-With magnetic field(Coii current:1,3,5[A])

Figure 6. The output characteristics of the themionic energy converter operated by the ignited mode. The experimental conditions are written in the figure. lo[A/cm2]

4. D I S C U S S I O N

With irradiation

0.3r

Cs gas temp.Tg:443[K] Emitter temp.TE:1280[K] 0.2

\ Coil current: '^\5[A] 0.1 .3[A]

Im. 0.1

0.2

yoM

0.3

Figure 7. The output characteristics of the thermoionic energy converter. The data shown in Fig.6(d) is enlarged.

The increase of output current in the unignited mode operation due to the illumination can be explained by the impovement of the space charge neutrahty a. As mentioned above, a is usually smaller than unity at the low emitter temperature so that most electrons emitted from the emitter cannot reach the collector. However, the illumination creates so many electrons and ions by photoionization that a approaches to unity [2]. Though the remarkable effect of illumination on the output current is observed at the operation of the low emitter temperature, the increase of a does not contribute to the increase of the output current at the higher emitter tem-

679 perature where the number of the positive ion produced by the contact ionization becomes larger than that of the electron. These features are clearly shown in Fig.5. As for the ignited mode operation, the increased electrons and ions in the space between both electrodes contibute to induce the breakdown because the probabiHty of collisional ionization is proportional to the electron and cesium atom density. Therefore, the larger output current will be obtained when the ignited mode operation will take place by increasing the cesium gas pressure and emitter temperature and by illuminating the intense light on the thermionic energy converter. REFERENCES l.W.Otto,Z.Naturf,22a(1967)1057. 2.M.Kando,H.Furukawa,M.Ichikawa and S.Yokoi,Proc.of 29th IECEC,Vol.2(1994)1067.



681

Hybrid Mode Concept of a Thermionic Converter with a FGM Structured Collector Mitsuo Iwase

Yoshihiko Hirai

Department of Electrical Engineering, Tokai University Kitakaname 1117, Hiratsuka-shi, Kanagawa 259-12, Japan

ABSTRACT A new hybrid mode concept of the thermionic energy converter was proposed. A number of papers deaUng with the hybrid mode have been published, but they mainly deal with the mechanism of the arc at the emitter. On the contrary, this paper proposes that the ball of fire at the collector can result in an hybrid mode. To that effect a FGM structured collector is considered to generate the new hybrid mode. In this study, the FGM structured collector was produced by means of the ion beam sputtering for mosaical target. The material distribution deposited on the substrate was detected by the X-ray photoelectron spectroscopy(XPS). Results of the XPS were recognized to be FGM structured collector.

INTRODUCTION 1989, a new idea was proposed by the study group resident in Sendai: to alter gradually the internal components or the microscopic organization of the materials with the objective of achieving arbitrary material properties. This is a epochal concept of material design named Functionally Graded Material (FGM).l) At the start, the techniques based on the concept of the FGM for realization of compositoin and structure gradients have succeeded in development of the wall materials for the space-plane that is needed to achieve relaxation of thermal stress. Subsequently to this success, FGM technology has been applied to many fields, because FGM technology, in its original sense, means providing a gradient in materials properties such.as electronic, chemical, optical, nuclear, and biological applications. 2) In this study, we have as its objective the improvement of the efficiency of thermionic energy converters. The electrical output characteristic of the converter shows two mode of operation, arc mode and unarc mode. Each mode have some merits and demerits. Therefore, hybrid mode is an ideal mode which makes use of the each mode merits. So, we applied the FGM technology to the development of the electrode materials needed for the hybrid mode. Usually, the hybrid mode has been realized by using the arc generation on the "emitter", such as a grooved type emitter. However, FGM technology makes it possible to realize the hybrid mode by using the ball of fire generated at the collector. We report on the new hybrid mode and on a FGM collector which could be used to generate it.

682

THEORY In order to discuss the I-V characteristic of thermionic converter, a schematic of such a characteristic curve(pc? < 20, /? < 1) is shown in Fig.l. The positions on the I-V curve have been useful in determining a inner potential distribution which can be a effective guide in developing the theory of the hybrid mode. During the negative resistance region ((3)-(4))on the I-V curve, the discharge has been observed to look as a "ball of fire".3) Motive diagrams for the negative resistance region on the I-V curve are shown in Fig.2. At (4) on the I-V curve, the ball has been observed to be positioned near the collector.

b a l l of

/"VT::L-Z

V\

ICA3

arc mode

' negative resistance region unaicmode^ v:

V,

nv]

Fig. 1 Schematics of the critical I-V curve (pd < 20, ^ < 1)

fir*

ball of f i r *

^4>z\

/

v/

4>z

FL( i )

V4=o Vi Vt

0

XQ

(b)

Fig. 2 Motive diagram for the negative resistance region of I-V curve. (a) corresponding to (4) of Fig. 1, (b) corresponding to (3) of Fig. 1 As soon as the current increases the ball moves toward the inter electrode space, as shown in Fig.2(a). At the point of (3) on the I-V curve, the ball has been observed to positioned near the emitter, as shown in Fig.2(b). Probe measurements indicate the existence of an accelerating electric field for electrons near the collector which leads to the formation of the ball. The mechanisms of the ball formation depend on the collector work function. If we prepare two kinds of collector work functions, then the lower forms the strong accelerating field, and the higher forms the weak field, as shown in Fig.3. The former operates as an arc mode, and the latter operates as an unarc mode.There are two modes together in the converter, so called hybrid mode.

683 This new hybrid mode model, however, can be realized very rarely. If we have various collector work functions the probability of the realization of the model increases. Thermionic converters usually use cesiated, refractory metal electrodes. The work functions of these surfaces are dependent on the electrode materials. Accordingly, the collector materials produced by FGM technology can have a spatially dependent work function. In other words, FGM technology makes it possible to realize the new hybrid mode.

I

pr*-are nodt

7^

^

Fig. 3 Motive diagram for the hybrid mode corresponding to the two kinds of work function of the collector.

EXPERIMENTAL The ion beam sputtering (IBS) system is used in the present experiment as shown in Fig.4. The chamber was pumped down to 8 X 10~^ Torr prior to the deposition using the cryopump. The ion source is the hotcathode type with an effective beam diameter of 30 mm. Argon gas was supplied into the ion source and the pressure in the sputtering chamber was set 1.6 x 10"'^ Torr during operation. The target was designed for FGM technology. Other operation conditions of IBS system are a,s follow : Ion energy 1.2 keV and current density 0.4 mA/cvn? . The deposition rate of Nb/Mo under those condition was about 17.0 A / min.

^

1). Beam Shutter ft Qineot Deast^ Kiisoc. 2).Neutiillz»r.

3).T«i9ct. 4). Sutatntc.

Fig.4 Schematic diagram of ion beam sputtering system.

RESULTS AND DISCUSSION By the IBS system, about 500 Athin film deposition, (Mo/Nb) was formed on the substrate (Inconel : 100 x 100mm)during about 30 min. As another, we picked up the test samples (Inconel : 10 x 10) which placed along the substrate at intervales of 10 mm. The detection of the MQ/NI deposited on the Inconel was executed by XPS. As seen on Fig.5, the presence of Mo is recognized by the peaks at 227.7 eV for 3^5/2 and 230.9 eV for 3^3/2. In the same way, the peaks at 202.7 eV for 3^5/2 and 205.4 eV for 3^3/2, identify A^^, as seen on Fig.6. Since the ratio of the peaks in the spectra at each point corresponds to the ratio of the concentrations of each material, we ploted them as a function of distance. As seen on Fig.7, the distribution of the components is fiat, when the target materials are placed like a symetrical mosaic. On the contrary, for the unsymetrical mosaic target.

684 as seen on Fig. 8, the distribution of the components has a gradient. The slope for Mo is about -0.6 %/cm, that of Ni is about +0.6 %/cm. Those values are very small, but they are FGM structured collectors. Mo 3d

Nb3d 1

10000

t'

3000 'w*

j\\iftVA/ \

8-

III

C

1000 230 Binding Energy (eV)

•

•

'

1

lA V /

.

'

240

1

,

200

i\ ]\

I

U

•u

ÂWNM/^^NV^

1

i

i.„ -1

i

1

H

1, , J

210 Binding Energy (eV)

1—J

220

100

uu Mo 0

0 b

"

0 0

0

^

Nb

X X

X

n —1

1

0 ^-

^

^^"iO X(cnn)

Target

Fig. 7 Distribution of the deposited atoms from the symmetrical target.

.Nb ou

30 o \ .

0

MoV ^ r* 0 ^ 700"

Target

1 J

Fig. 6 XPS Nb spectra at 3 locations on the substrate.

Fig. 5 XPS Mo spectra at 3 locations on the substrate.

•Mo-

1

V\,î,Mh\-f^*f*^ xi A^M\

'**-V*' 1 \

32000

220

'

2 0-

~^'' Nb," ^

v^ X t

X,

1

X.

1

1 20 1

X'lO

X(cm)

Fig. 8 Distribution of the deposited atoms from the unsymmetrical target.

685

SUMMARY In this study, we proposed a new hybrid mode model of the thermionic energy converter with a FGM structured collector. Based on the model, we have experimented to deposit graded Unearly molybdenum (Mo)and niobium {Nb) on the substrate considered as the collector. The results can be summarized as follows: 1. "The ball of fire" yielded on the collector is available for the hybrid mode. 2. This is not to say that the model realize usually. However, FGM technology makes it possoble to realize the hybrid mode easily. 3. In the present experiment, Ion Beam Sputtering system was used, in which we designed unsymetrical target for the FGM technology. 4. The existence of Mo on the substrate was recognized by the XPS peaks, at 227.7 eV for 3 (^5/2 and 230.9 eV for 3 ^3/2, and for, A^^ at 202.7 eV for 3 ^5/2 and 205.4 eV for 3 ^3/2-

5. Results of XPS for the samples versus distance showed concentration gradients of -0.6 %/cm for Mo and +0.6 %/cm for A^^,. Thus, we have obtained a FGM collector, whose cesiated effective work function can be predicted by the SIMCON code. 4),5)

ACKNOWLEDGMENT This paper is a part of results prepared as an account of the Government sponsored work; the Ministry of scientific and Technical Administration of Japan. The authors would like to thank Mr.Watanabe Noboru of the department of general study, and Mr.Azuma Shiro of the department of material development for their efforts in support of this study. Many thanks are also due to the chairman of the FGM - II project. Dr. Niino Masayuki, to the chief of the working group. Dr. Fukuda Ryuzo, and all of the member of FGM - II project for the useful advices.

REFERENCES 1) R. Watanabe : "Functionally Graded Material" committee of the FGM.(1993) 2) M. Koizumi and M. Niino : "Overview of FGM Research in Japan" MRS BULLETIN/JANUARY (1995) 19 3) J. M. Houston, etal : J. Appl. Phys. vol.38, (1967) 3425 4) D. R. Wilkins : AEC Research and Development Report, GESR - 2109 (1968) 5) N. S. Rasor and C. Warner : J, Appl. Phys. vol.35 (1964) 2589



687

THERMOELECTRICALLY MODULATEDE/NANOSCALE MULTILAYERED GRADIENT MATERIALS FOR APPLICATION IN THE ELECTROMAGNETIC GUN SYSTEMS M.A.OTOONI^, John F. ATKINSON^, and I.G.BROWN^, US Army Armament Research, Development and Engineering Center, Picatinny Arsenal, N.J. USA Science and Thechnology Center, Far—East Lawrence Berkeley Laboratory, University of California, Berkeley, CA ABSTRACT Analysis of fired rails from electromagnetic railguns indicates severe surface damage occurs due to high current arcing and tribological mismatch. We have explored the behavior of several nanoscale multilayered materials as possible routes to improve the thermomechanical properties of the rail and armature materials Structures investigated include (i) Ti—Co alloy on Ta—Cu alloy on die (diamond—like carbon) on stainless steel; (ii) Ti—Co alloy on Ta—Cu alloy on die on Cu, (iii) Ti—Co alloy on Ta—Cu on Cu; and (iv) Ti—Co on Ta—Cu alloy on Al. The alloys were all 50:50 at% and film thicknesses were in the range 400-1000 A. The films were formed using a repetitively pulsed vacuum arc plasma deposition method with substrate biasing- and IB AD—like techniques. The surfaces were characterized by scanning electron microscopy, transmission electron microscopy, Rutherford backscattering spectroscopy, optical microscopy, microhardness measurements, arc erosion resistance and scratch resistance tests. Preliminary results show improvement in the microhardness, arc erosion resistance and scratch resistance, most especially for the die—coated surfaces. This kind of multilayered approach to the fabrication of electromagnetic railgun and armature surfaces could be important for future advanced Electromagnetic EM Gun systems. l.INTRODUCnON Copper and aluminum have been used in the design of the electromagnetic (EM) rails and armatures. The primary reasons for selecting these materials are based on the high electrical and high heat conductivities of both metals. Recent data indicate that in addition to these two important properties, the creep behavior also plays an important role. This is particularly so when the EM gun is designed to function in the hypervelocity regime with repeated firing capabihty. Research on the materials behavior of copper railguns and aluminum armatures was initiated in the early 1980s

688 by several universities and centers where most of the EM gun research thus far has been conducted. Based on these efforts, the thermomechanical behavior of most elements and alloys materials used in EM system, such as Cu, Mo, W, and Al alloys, has been known for some time. Thermoionic and thermoelectric properties have also been investigated.

In addition, extensive data on the behavior of these materials have now become available through simulation, structural design studies, laboratory studies of materials commonly employed in various phases of the EM gun, theoretical results derived from application of the imposed electrodynamic conditions, fluid materials. These investigations have shown that the electromagnetic dynamics, and the characteristics of field tested launch package and electrodynamic properties of the railgun vary with time and space throughout the length of the gun barrel. From a structural design standpoint these variations, if true, give rise to severe electromagnetic and electromechanical responses which may be unattainable from materials currently used in EM Gun design. This is particularly true when singleelement materials are used, i.e., Cu for the radl or Al for the armature or sabot designs. In the light of these analyses, which are supported by many field demonstration results, there appears to be no adequate justification for using these materials in electromagnetic guns other than for their superior electrical and heat conductivities. These requirements are indeed necessary but insufficient for modem EM Gun systems. In view of the transient thermomechanical and electrodynamical functions of the rail and armature two avenues for improvement may be possible: (a) appUcation of advanced coating materials on railgun and armature where simulation results indicate application of coatings may prevent localized degradation due to localized melting, wear and spark erosions; and (b) a new design of the rail and launch package (armature and sabot) from a new class of synthesized materials whose properties are made to correspond to the transient fluid dynamics of the system. These new classes of materials are collectively known as gradient materials[l-4]. It is envisoned that future designs of improved EM systems will incorporate combinations of these two strategies for a significant enhancement in EM gun performance. We have synthesized and examined the behavior of several nanoscale multilayered materials that could provide possible routes to improved thermomechnical behavior of rail and armature materials. 2.EXPERIMENTAL PROCEDURE 2.1. Metallurgical Procedure Several nanoscale multilayered structures were prepared. These included (i) Ti—Co alloy on Ta—Cu alloy on dlc(diamond—like carbon) on stainless steel; (ii) Ti-Co alloy on Ta~Cu on die on Cu; (iii) Ti-Co aUoy on Ta-Cu on Cu; (iv) Ti-Co alloy on Ta-Cu alloy on Al. The alloys were all 50:50 at% and film thicknesses were in the range of 400—lOOOA. The specimens were plasma processed, and then evaluated by scratch testing, spark erosion testing, Rutherford Backscattering spectroscopy (RBS), scanning electron microscopy (SEM) , transmission electron microscopy(TEM), Reflection High Energy Electron Di&action, optical microscopy, and microhardness measurements. The plasma processing technique and other treatments employed in the preparation of the test specimens are briefly described below.

689 2.2.Plasma Processing Vacuum arc plasma discharges are intense sources of dense metal plasma, and can be used to deposit metal alloy thin films of various kind including both conventional alloys as weU as non—equilibrium alloys. In our approach, the basic plasma deposition process is combined with the ion bombardment; the method is environmentally friendly, highly efficient, can be scaled up to large size, and can synthesize films of a wide range of materials[5-9]. A metal plasma of the required species is formed by a vacuum arc plasma gun and directed towards the substrate with a moderate streaming energy, typically in order of 100 eV. At the same time, the substrate is repetitively pulsed biased to moderate negative voltage (typically a few hundred volts to a few tens of kilovolts), thereby accelerating a fraction of the incident ion flux and energetically bombarding the ions into the substrate and the previously—deposited film. This technique provides a means for precise control of the energy of the depositing plasma ions. At early—times high ion energy will be used as to atomically mix the film into the substrate, and a later—time, when the film is in the growth stage, lower energy ions bombardment is used to add an " ion assist" to the deposition - a process which is similar to an ion beam assisted deposition or DBAD technique. In this way the film is ion stitched to the substrate and has very strong adhesion, high density (void—free), good microstructur and excellent morphology (close to being atomically smooth). Using this plasma materials synthesis techniques four nanoscale multilayered specimens with different substrate materials have been prepared. Two of the specimens, one stainless steel and one copper, were coated with die (diamond-like carbon) prior to the plasma processing. Two other specimens, one 7075—T6 aluminum and one copper, were directly subjected to the plasma processing. Table 1 describes characteristic features of the samples. Table 1 The four nanoscale multilayered structures were produced as indicated. A. B. C. D.

Multilayered Multilayered Multilayered Multilayered

SS/dlc/Ta-Cu(50:50)/Ti-Co(50:50) Cu/dlc-/Ta-Cu(50:50)/Ti-Co(50:50) Al(7075-T6)/Ta-Cu(50:50)/Ti-Co(50:50) Cu/Ta-Cu(50:50)/Ti-Co(50:50)

To form the Ta—Co and Ti—Co films, vacuum arc cathodes were first fabricated by using pressed powders of 50:50 at% composition ratios. The plasma formed by the plasma gun has a composition that approximately reflects the composition of the cathode[10-13]. 2.3.Test Procedure Following surface processing, the test coupons were tested for relative improvement in their surface characteristics, and depth profiled. The characterization techniques included scratch testing, spark erosion testing, Rutherford Backscattering, scanning electron microscopy, optical microscopy, high resolution transmission electron microscopy, and reflection high energy electron diffraction microscopy. Scratch testing was done using a simple but accurate device in which a diamond probe was drawn across the surface at a

690 constant rate and constant loading. The scratch mark was of a length of a few mm. A region of the coupon was masked during the plasma processing of the surface so as to provide an unprocessed reference region. Spark erosion testing was performed using a specially made instrument in

which

a

single, highly—reproducible

spark

was formed

by

the

discharge

of

a 10 F capacitor at 3.5 kV though a precise gap in which the test surface was one of the electrodes. The spark craters so formed were then examined under an optical microscope. The measurements were carried out several times for both the scratch testing and the spark to insure consistency of the results. Elemental depth profiling was done with RBS using 1.8 MeV He ions. Scanning electron microscopy and cross—sectional transmission electron microscopy were employed in an effort to examine the nature of the several boundary layers of the multilayered structure. Reflection high energy electron diffraction technique was also employed to study the nature of the coated surfaces. 3.RESULTS AND

DISCUSSION

S.I.Scratch Tests Scratch test measurements indicated that die is a far more scratchresistant surface (i.e.,it is harder) than any of the metal surfaces used in the present work, as expected. It is possible that a more extensive testing progranni, perhaps scanning in diamond stylus loading, could reveal further differences between the different metal surfaces. This procedure wiU be attempted in the future and will be the presented in another paper at a later date. Several specimens were subjected to microhardness measurements. The microhardness values varied from 3365 to 3942±66 in the Hv scale. 3.2.Spark Erosion Tests Erosion craters from single discharges of the spark tester were formed on surfaces of all specimens of the multilayered materials. Figures 1—3 show spark tests and the photomicrographs of the damaged craters of the four specimens. The geometry of the craters on the die surface is quite different from that of the other surfaces. This effect could be attributed to different electrical conductivities of the surfaces, particularly because of the addition of Mo as dopant to make the die somewhat conductive. The depth of the craters on the die surface are also much shallower, indicating a much harder surface.

MO

\

^

MkV >

UW

^ ^

lOiloekO

rM 1 -^

1 T

^?

I v = ^

Figure 1 Schematic representation of the spark erosion apparatus

691

Figure 3 Optical photographs of spark erosion craters of the nanoscale Multilayer A after coating. Mag.lOOx

Figure 2 Optical photographs of spark erosion craters of the nanoscale Multilayer A before coating. Mag.lOOx

3.3.Rutherford Backscattering Spectroscopy RBS was used to measure the concentration and depth profiles of the implanted Ta in SS/dlc/Ta-Cu(50:50)/-Ti-Co, Cu/dlc/Ta-Cu(50:50)/Ti-Co, Al-Ta Cu (50:50)-Ti-Co, and Cu/Ta-Cu-(50:50)/Co-Ti surfaces. Depth profiles of several nanoscale multilayered specimens are shown in Figures 4 - 5 . As can be seen from these results, the Ta is implanted to a depth of about 150-170A from the surface. The composition is shown in atomic percent. While the presence of the implanted Ta ion has the effect of increasing the microhardness of the near-surface layer, the optimum values for the Ta implantation dose and energy for maximum hardening will need to be tested at a later stage. These specimens were Ta implanted to a dose of 4-4.5x10*^ cm ^ and energy range of 100 keV. Note that for these high doses, the applied implantation dose is not the same as the retained implantation dose because of the effect of surface sputtering including sputtering away of the previously implanted Ta. The deposited concentration of Ta ions varies in the range of 0.3—0.4 atomic fractions. 3.4.Electron Microscopy and Microanalysis A scanning electron micrograph showing the TaN on die on SS is shown in Figures 6(a,b). The micrograph indicates the nature of the interface to be r m 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 I M 1 1 1 1 1 1 t I t T T !T I1 1 1 1 1I I I1! 1-nq 2 #2 Tl/Co, Ta/Cu on Cu

: =- • •• ••• I

2

Li- 0.4

E o

oOoO^% o o

-• t c

• o • o

r.

o

oooooo

ho

* o

O O

..

O

••••A

•Oo^ • *ooO o • o • . o • .

Co Ti Ta Cu

i 1

-\ -. ij

• o •f

: ;

[h *^¥> p. , M i l l i » i » i # t T i 1111111111111111111 1 1 1 iTi^PtHî *M 200

(o)

400

600

800

1000

Depth (e15/cm2)

Figure 4 RBS graph from Multilayer B showing atomic fractions of the elements as a function of Depth

0.8

1 1 I I I 1 1 1 I I 11 1 1 1 1 1 1 M 1 r I i-rr111.. j i i ini -ir m i i- r

#2 Tl/Co, Ta/Cu on A17075

F 0.6 tr • L *

c .2

-•

I 0.4,P° 3

o E o < 0.2

• o

••**•. * °°o

• o

-

o

o

•

d

*•

•

• •

o

Co

q

Ti

H

Ta

d

Cu A J

•

q

L

•

J ^< ° •. % d dopants. The ^—x«o /' / similarity with the JM|x«0.6.^ shift in the diffusion ,.^r?r?^ KT F111 >»1 >>iin reflection spectra is 200 300 400 500 200 300 400 500 Waval6iH|Ui4s (the resonant peak positions are 75.5, 76.5 and 74 eV for Cu, CU2O and CuO, respectively [9-10] ), where we can easily distinguish the different Cu chemical states. SnO2(110)

SnO2(101)

Binding Energy ( eV )

Binding Energy ( eV )

Fig. 2 SRPES spectra from Sn02 surfaces from the (110) surface (I) and the (101) surface (II). (a) clean surface, (b) Cu-covered surface (0.7 monolayer), (c) the sample annealed to 500K in 1x10"^ mbar O2 for 20 min., and (d) the sample annealed to 600K in 1x10'^ mbar O9 for 20 min.

3,3 Conductivity measurements of CuO/Sn02 system Sn02 is practically an n-type semiconductor and CuO is a p-type semiconductor. They can be used to form a p-n junction to make a sensitive gas sensor [1]. To measure the conductivity of this system, gold was evaporated to the rear side of the Sn02 single crystal to achieve better ohmic contact. Then several monolayers of Cu was deposited in submonolayer steps to the front side. The cleanness of the surface was checked by AES until the impurity level was beyond the detection limit. The copper-covered Sn02 surface was at each step annealed in O2 at a pressure of 1x10"^ mbar. The temperature was increased in steps of 50 K, staying 20 min at each step, reaching finally 700K. After the first CuO layer was

711 formed, the deposition of Cu and oxidation was repeated until the CuO layer thickness finally reached 30 A. No LEED pattern appeared during the oxidation process of the copper side view overlayers and the substrate LEED was greatly attenuated even if the Cu coverage was only 0.2A. From an AES spectrum we know that the substrate Sn signal becomes smaller and smaller top view as the CuO layer becomes thicker. It is quite important also to increase the temperature in ^ steps since by increasing the temperature too fast the deposited Cu will shrink to form islands or evaporate before it has been oxidized, and that Fig.3 Schematic of sample with dewill make it difficult to form uniform layers of posited contacts CuO. After the growth of a 30A layer of CuO on SnO2(110) at which the Sn (MNN) intensity was greatly attenuated, a thick layer (thicker than aprox. 1 jam ) of gold islands was deposited through a mask onto the CuO surface. The size of the islands were 0.2mmx0.2mm in area and 0.2 mm separated from each other ( Fig.3 ). Then one electrode was moved to touch the gold in the front side of the sample while another electrode was permanent in contact to the rear side. The resistance measurement was through the p-n junction to which the oxygen diffused. All of the above work was carried out in ultra high vacuum. The resistance change of the CuO/SnO2(110) system vs O2 partial pressure at room temperature (RT) shows a resistance change of 3% as the pressure changes from 10"^ to 10'^ mbar. When the sample temperature is kept at 450K, the resistance changes about 50% when the O2 pressure is increased from 5x10'^ to 5x10"^ mbar. To make sure that this change is not due to the Sn02 substrate itself, the resistance change of the clean substrate Sn02 was measured at same temperature and same O2 pressure range as above. The change was now only 6%. It should be mentioned that for our model the sample electrode area was 0.04mm^ while the CuO layer was only 30A thick ( 3xlO"^mm). Most of the current originated directly from the part that was not exposed to O2. In a rough estimation, the area exposed to O2 is 0.2mmx4x30A=2.4x10"^ mm^, so the ratio of the area of exposed to and not 6

2

^

exposed to O2 is 2.4x10' :4xl0" =6x10' . Hence the quite large change in conductivity originates from only a very small exposed area. The conductivity change may be due, however, to a combined effect of oxygen interface diffusion and the presence of the heterojunction. 4. CONCLUSION Ultrathin films of Cu were PVD-deposited at RT onto model SnO2(110) and (101) crystal surfaces in ultrahigh vacuum. SRPES spectra show CU2O epitaxial layers were formed by using 1x10" mbar O2 pressure at the temperature of 500K to oxidize the Cu-covered Sn02 (110) and (101) surfaces. A CuO layer can be obtained at the temperature of 600K. The changes in electrical conductivity of the ultrathin sandwich-layer system was followed through in situ measurements of the changes of the current passing through this n-type and

712 p-type heteroj unction system as a function of the exposure of oxygen diffuses to the interface. The relatively large conductivity change was compared to the ratio of perimeter to area, and may be due to a combined interdiffusion and heteroj unction effect. By using an atomic-scale gradual way of synthesizing a CuO layer on top of a Sn02 crystal surface, we have joined two materials to a sensor with better functional properties. ACKNOWLEDGEMENT We are very grateful to G. Thornton and P. L. Wincott for providing the samples and to S. V. Christensen for assistance during the experiment.

REFERENCES 1. G. Sarala Devi, S. Manorama, and V. J. Rao, J. Eletrochem. Soc, 142 (1995) 2754. 2. S. Lenaerts, M. Honore, G. Huyberechts, J. Roggen, and G. Maes, Sensors and Actuators B, 18-19(1994)478. 3. G. Williams and G. S. V. Coles, Sensors and Actuators B, 15-16 (1993) 349. 4. G. L. Shen, R. Casanova, G. Thornton, and I. Colera, J. Phys: Condens. Matter, 3 (1991) S291. 5. E. De Fresart, J. Darville and J. M. Gilles, Surf. Sci., 126 (1983) 518. 6. Z. S. Li, Q. Guo, and P. J. Moller, Z. Phys. D, in press. 7. D. F. Cox, T. B. Fryberger and S. Semancik, Surf. Sci. 224 (1989) 121. 8. P. J. M0ller and M. C. Wu, Surf. Sci. 224 (1989) 265. 9. M. R. Thuler, R. L. Benbow, and Z. Hurych, Phys. Rev. B, 26 (1982) 669. 10. Z.-X. Shen, R. S. List, D. S. Dessau, F. Parmigiani, A. J. Arko, R. Bartlett, B. O. Wells, L Lindau and W. E. Spicer, Phys. Rev. B, 42 (1990) 8081.


713

Fabrication of Magnetic Functionally Graded Material by Martensitic Transformation Technique Yoshimi Watanabe % Yuzo Nakamura ^ and Yasuyoshi Fukui ^ ^ Department of Functional Machinery and Mechanics, Shinshu University, Ueda 386, Japan '' Department of Mechanical Engineering, Kagoshima University, Kagoshima 890, Japan Abstract It is known that the paramagnetic phase in an austenitic stainless steel, such as Fe-18Cr-8Ni, transforms into a ferromagnetic a '-martensite phase by plastic deformation at low temperature. The amount of saturation magnetization due to the martensitic transformation increases with increasing plastic strain. Thus, a manufacture of magnetically graded materials based on the concept may require the inhomogeneity of plastic deformation. In the present study, it is aimed to obtain a suitable gradient of the magnetization by introducing inhomogeneous deformation and to examine the relationship between the magnetization and applied plastic strain using Fe-18Cr-8Ni. A simple model to evaluate the distributions of strain and saturation magnetization is obtained in order to clarify the results mentioned here.

1. INTRODUCTION Functionally Graded Material (FGM) is known as a new material whose compositions and microstructures are varied continuously from place to place [1-3]. FGMs can be classified into composite and monolithic materials. FGMs made of composite materials are, however, not considered to be preferable from the viewpoint of material recycling, since it is difficult to separate the dispersion phases from the matrices. In contrast, monolithic FGMs have a possibility of the recycling or the recovering of their functions using very easy methods like melting or other heat treatments. Unfortunately, very few works have concerned with the monolithic FGMs. FGMs are applicable not only to the mechanical field but also to the electronic, chemical, optical, nuclear, biomedical and other fields [1-2]. However, most of the previous studies on FGMs have deah with those mechanical function but little attention have been focused on other functions and those applications. It is well known that paramagnetic phase in austenitic stainless steels, such as an Fe-18Cr-8Ni, transforms into ferromagnetic a ' martensite phase by plastic deformation at low temperature [4,5]. Since the amount of the deformation-induced martensite increases at a larger

714 strain, the saturation magnetization of the deformed austenitic stainless steel increases with increasing strain. Therefore gradually inhomogeneous deformation is considered to bring about the change of the saturation magnetization depending on local strain [6]. The idea is the origin to manufacture a magnetic FGM using an austenitic stainless steel. The method is named a martensitic transformation technique which controls the degree of the inhomogeneity of plastic deformation [7]. However, in the previous study [6], the saturation magnetization of the austenitic stainless steel before the deformation is not zero. This is because that the specimen was used without heat treatment. In the present study, therefore, it is aimed to obtain a suitable gradient of the magnetization using an annealed Fe-18Cr-8Ni alloy. If the relation between the amount of the deformation-induced martensite and the amount of plastic deformation be known, it would be easy to design the profile of the saturation magnetization by changing the local strain. A simple model to evaluate the distributions of strain and saturation magnetization is obtained in order to clarify the results mentioned in the present study. 2. EXPERIMENTAL PROCEDURE Three kinds of tensile specimens, hereafter called Type (A), (B) and (C) respectively, were machined from a 1 mm thick plate of SUS304 stainless steel. The chemical composition of the steel was: Cr; 18.06, Ni;8.47, C;0.04, Si;0.52 Mn;1.27, P;0.026, S;0.005, Cu;0.06, Mo;0.06, N;0.049, O;0.0039, all in mass pet. The shape and dimensions of the specimens are shown in Fig. 1. Type (A) specimen is a standard test piece with a uniform cross-sectional area in its reduced gauge section (Fig. la). In this type of test pieces, a uniform plastic strain is expected to be introduced, resulting in the corresponding saturation magnetization constantly distributed along tensile axis. In Type (B) and (C) specimens, the cross-sectional areas of their reduced gauge sections decrease linearly from the left shoulders of Fig. lb and Ic (designated "O") in a direction of tensile axis. The inclination angles, defined as the angles of specimen edges from tensile axis, are 1 degree for Type (B) and 3 degrees for Type (C), respectively. All specimens were solution -annealed at 1283 K for 3.6 ks in evacuated quartz capsules and then quenched in air. In this study, it is necessary to observe the distribution of plastic strain along tensile axis precisely.

JL

:^î'

40

Type (A) .Point 0

-I

3.P2 1

-i^

Type (B) .Point O

2.02

Type (C)

Figure 1 The dimensions of three types of specimens used for experiment. Specimen thickness is 1 mm. Type (A) specimen is a standard test piece which has an uniform cross-sectional area. Type (B) and Type (C) specimens have non -uniform cross-sectional areas. The inclination angles are 1 degree in the Type (B) specimen and 3 degrees in the Type (C) specimen, respectively.

715 The plastic strains are measured by means of point marking method. The markings with 1 mm interval in a direction of tensile axis were made by a micro-vickers hardness tester before tensile tests. Tensile tests were conducted at room temperature at a cross-head rate of 0.5 mm/min with an Instron-type testing machine. After the tensile deformation, the relative displacements between markings were measured under a precision machinery microscope, and the corresponding local strains in the direction of tensile axis were calculated. Then deformed specimens were cut into pieces of 1 mm width by a low speed cutter perpendicular to the tensile axis. The saturation magnetization of each piece was measured by magnetic balance at room temperature. 3. EXPERIMENTAL RESULTS AND DISCUSSION 3.1. Uniform Deformation in Type (A) Specimens A typical true stress-true strain curve of Type (A) specimens is shown in Fig. 2. The true strain is calculated from the displacement of cross-head. As can be seen, the fracture of the specimens occurs at a strain of about 0.5. Relation between true stress, a , and true strain, E , in uniformly deformed Type (A) specimen is given by the following Ludwik law, = a, . Ke"

(1)

where a o = 235 MPa, K = 1820 MPa and n = 0.917. Figure 3 shows the change in the saturation magnetization with strain in Type (A) specimens. It is clear that the saturation magnetization increases with increasing deformation (strain). This is because that the paramagnetic phase in austenitic stainless steels transforms into ferromagnetic a ' martensite phase by the plastic deformation. It is also found that the saturation

0.2 0.3 0.4 True Strain Figure 2 A typical true stress-true strain curve obtained by tensile deformation test of the Type (A) specimen. The presence of a strain of 0.5 causes the specimen to fracture.

0.2 0.3 0.4

0.6

True Strain Figure 3 The values of the saturation magnetization of Type (A) specimens as a function of tensile strain.

716 magnetization of a non-deformation specimen is zero. Relation between saturation magnetization, L (tesla), and true strain, E , is given by following equation. /

(2)

= 5.948^ - l.OOe^ + 0.498

3.2. Inhomogeneity of Plastic Deformation in Type (B) and (C) Specimens As shown above, the fracture of the specimens occurs at a strain of about 0.5. Therefore, the maximum local strain was limited to 0.35 in both Type (B) and (C) specimens. Figure 4 shows the change of the local strain in Type (B) and (C) specimens with distance from the point O of Fig. 1 in a direction of tensile axis. It is seen in the figure that the inhomogeneity of plastic deformation in Type (C) specimen is larger than that in Type (B) specimen. Moreover, as shown in the figure, the linear relationship between distance and the local strain is not observed, although the cross-sectional areas of their reduced gauge sections decrease linearly. The strain distributions of these specimens will be discussed later. 3.3. Magnetic Gradient in Type (B) and (C) Specimens Figure 5 shows the distributions of the saturation magnetization in Type (B) and (C) specimens. In Type (C) specimen, although the gradient of the saturation magnetization is produced between the distances of 30 mm and 50 mm, magnetic gradient is not observed at distances less than 30 mm. This implies that the inclination angle of 3 degrees is so large that the degree of inhomogeneity of plastic deformation is unsuitable for our purpose. In contrast to Type (C) specimen, the saturation magnetization is gradually distributed over the whole gauge length in Type (B) specimen. In this way, we can obtain a magnetic graded material with suitable gradient of the magnetization by the martensitic transformation technique.

0.5

0.5 0.4

1 0.3

• : Specimen (B) A : Specimen (C)

0.4

g tsa

0.2

1 • : Specimen

1 • : Specimen (C)

(B)

JT J/

T * ^ *

,

0.3

a 0.2

0.1 0

10 20 30 40 50 60 Distance / mm

Figure 4 The change of the local strain in Type (B) and (C) specimens with distance from the point O of Fig. 1 in a direction of tensile axis.

.2

0.1 0

0

A,

,

,

1

10 20 30 40 50 60 Distance / mm

Figure 5 The distributions of the saturation magnetization in Type (B) and (C) specimens.

717 3.4. Evaluation of the Distributions of Strain and Saturation Magnetization If the relation between the amount of the deformation-induced martensite and the amount of plastic deformation be known, it would be easy to design the profile of the saturation magnetization by changing the local strain. For this purpose, the following model is used Point 0 to evaluate the distributions of the plastic strain and saturation magnetization in wedge-shaped plates of SUS304. In iohomogeneously deformed specimens, the X-axis is taken in a direction of tensile axis as shown in Fig. 6. When the specimens are separated into 50 elements Fig. 6 The schematic representation of the along tensile axis, the cross-sectional area wedge-shaped specimen and reference axis, X-axis. a(x) is given as a function of jc.

a(x) = a, - (a,-a3^x(_)

(3)

where ao and aso are the areas at x=0 and x=50, respectively. If the area of the ith element changes from a, to a,' by tension, the plastic strain of the ith element is given by the following equation. (4) " t

At the same time, the plastic strain of the ith element follows the Ludwik law mentioned above. P/a. e, = [-

_0-|l/«

(5)

where F is a tensile load. The value of e is calculated iteratively with increasing the tensile load, P, by 1 MPa. The elongation of the ith element Ax, is given by the following equation. Ax, = (X, - x,.^)[cxp(8,) - 1]

(6)

Therefore, the distance from the point O to ith element after the tensile test, dt, is given by «/, = / - E Ax,

(7)

when we assume the gage length is 50 mm. Figure 7 shows distributions of the plastic strain calculated for Type (B) and Type (C) specimens. As seen in Fig. 7, the theoretical distributions fit in with the measured distributions for low strain levels. However, the calculated values are not in agreement with the experimental values at high strain levels. The lack of such coincidence at high strain levels is considered to be attributed to the contribution of strain associated with stress-induced martensite.

718 T

1

1

r-

Specimen (B) Specimen (C) //%^

a 0.3

1 ^

I

CO

: Specimen (B) : Specimen (C)

.0.4 O

0.3

0.2 "^0.1 o

10 20 30 40 50 60 70 Distance / mm Figure 7 Distributions of the plastic strain calculated for Type (B) and Type (C) specimens.

2 0 en

10

20 30 40 50 Distance / mm

60

70

Figure 8 The theoretical distributions of saturation magnetization in the wedge-shaped plates.

When Eq. (2) is substituted in the theoretical distributions of the plastic strain (Fig. 7), we obtain the theoretical distributions of saturation magnetization in the wedge-shaped plates as shown in Fig. 8. Although the calculated values differ from the measured ones at high strain levels, they are in good agreement with the experimental values at low strain levels. 3.5. Advantages of Martensitic Transformation Technique Several fabrication methods, which can produce the tailor-made distribution, are proposed. These methods are applications of the relatively new technology, and the fabrication facilities are expensive. In addition, it is difficult to obtain relatively large materials by these methods except for the centrifugal method [8-10]. On the contrary, as shown in this study, no special facility is required in the martensitic transfomiation technique. It is easy to obtain large materials by this technique. Moreover, since the deformation-induced martensite transforms into austenite when the deformed stainless steels are heated to temperatures of austenitic region, it is also easy to obtain virgin materials for FGMs. This may be one of the simplest methods to obtain virgin materials for FGMs. The magnetic FGM may be available as a position measuring device by combining it with a magnetic sensor. For instance, it can be used as a device that determines the focus point in an automatic focusing camera. REFERENCES 1. M. Koizumi and Y. T2ida,Kinzoku, 58,No4 (1988) 2. 2. M. Koizumi and K. Urabc Jetsu to Hagane, 75 (1989) 887. 3. T. Hirai and M. SsiS^ki, JSME InternationalJournal Series 1,34 (1991) 123. 4. R. Lagnemorg,^crfl Metall, 12 (1964) 823. 5. P.L. Mangonon, Jr and G. Thomas,Mem//. Trans., 1 (1970) 1587. 6. Y. Watanabe, Y. Nakamura, Y. Fukui and K. Nakanishi/. Mater, ScL Letters, 12 (1993) 326. 7. T. Hirai, "Functional Gradient Materials" (Materials Science and Technology, 17B), VCH, Germmany, (1996). 8. Y. Fukui JSME Int. J. Series lU 34, (1991) 144. 9. Y. Fukui, N. Yamanaka, Y. Watanabe and K. Nakanishi, J. Jpn. Soc. Heat Treat, 35 (1995) 11. 10. Y. Watanabe and Y. Fukui,/ Jpn. Inst. Light Metals, 46 (1996) 395.


719

Characterization of single-crystalline Cu/Nb multilayer films by ion beam analysis S. Yamamoto, H. Naramoto, B. Tsuchiya and Y. Aoki Dept. of Materials Development, Japan Atomic Energy Research Institute, 1233 Watanuki, Takasaki, Gunma, 370-12 Japan

Successful growth of Cu/Nb single crystal multilayer films on sapphire substrates with different orientations is reported based on the crystal symmetry characterization using the planar channeling technique. The difference in lattice structure and the big lattice mismatching was overcome by adjusting the substrate temperatures. The layered structure was prepared by using electron-beam evaporation under UHV condition. The typical thicknesses of Cu and Nb layers were in the range of 50 nm to 250 nm. The exact orientation relationship among Cu, Nb layers and sapphire substrate was determined through the mapping of planar channeled points at each layer of Nb, Cu and sapphire. The growth habit depends on the substrate orientations: Nb(110)/Cu(lll)/Nb(110) on sapphire (1120) and Nb (lOOyCu (100)/Nb (100) on sapphire (0112).

1. INTRODUCTION In modern technologies, materials are exposed to the severe conditions like high temperature, high pressure, low temperature and chemically reactive environment to exert their abilities effectively. The trials to improve the materials properties in bulky phases have been performed but for further improvements the surface modification with the graded nature will become important. This concept of the graded nature is also useful to design or to synthesize new materials with special function. The multi-layered structure with a certain periodicity, so called superlattice, can be assumed to be one of the graded materials controlled in nm scale. The superlattice with one dimensional crystal nature is useful to improve the reflectivity for soft X-rays but there appear another kind of problems to be solved. For the applications to soft X-ray mirrors it is critical to prepare multilayered structure with sharp interface in an atomic scale[l]. For that purpose, two kinds of layer unit, single-crystalhne or amorphous layers, are expected typically. In the present study, the efforts are described to prepare the single-crystalline layered structure with the sharp interface. In this context, Nb/Cu system which are immiscible even at higher temperature[2], is suitable for exploring a condition of multilayered structure growth with the sharp interface but might not be so for siagle crystal growth. It is

720 demonstrated that the single-crystalline multilayered structure composed of Nb and Cu on aAI2O3 is formed with the excellent crystal quality by controlling the substrate temperatures. The crystal quality was assessed by RBS/channeling technique[3]. 2. EXPERIMENTAL Nb and Nb/Cu multilayers were deposited on three kinds of major crystallographic planes, (1120) , (0001) and (0112) sapphire (a-AlaOa) substrates using the electron beam evaporation technique under UHV condition. All of sapphire substrates were pre-heated at 1500°C for 24 hours in air to eliminate the induced strain during polishing. This process is very important also for preparing the crystallographically stepped faces. During evaporation, the vacuum in a growth chamber was maintained around 5 x 10'^ torr after a long term evaporation to trap the residual gases with deposited Nb on the chamber wall. The thickness of each layer was monitored with quartz oscillators which were calibrated with Rutherford backscattering spectroscopy (RBS) measurements. The Nb and Cu fihns were deposited at the rate of about 0.2 nm/s onto the sapphire substrate kept at TSO'^C for Nb and less than 600°C for Cu. The typical thicknesses of Cu and Nb layers were in the range of 50 nm to 250 nm, respectively. At each step of evaporation, the surface structure was examined with low energy electron diffraction (LEED) technique. The surface structure of the top Cu layer was observed by SEM to check a possibility of columnar growth. The layered samples were analyzed with RBS/channehng method using 3 MV single stage accelerator at TIARA, JAERI/Takasaki. The analyzing beams of "^He ions with energy of 1.5 to 2.7 MeV were incident on samples. The size of the beam was about 1 mm in diameter and beam current was about 10 nA typically. Backscattered particles were detected by standard surface barrier detectors at 160® and 110° to the incident beam. 1500

n—I—I—r

1—I—I—r

T—I—I—r

2.0MeV '^He'^ RBS-C 6=110° Nb(110)/sapphire(1120) Thickness: 100 nm 1000

Random

>^ 500

O Al I

I

0.5

I

hmi^\

I

1

\

I

l\ I

I

I

L

1.5 Energy (MeV) Fig. 1. 2.0 MeV ^He RBS/channeling spectra from Nb(llO) epitaxial fihn on (1120) sapphire substrate. Thickness of Nb fOm is about 100 nm.

721 3. RESULTS AND DISCUSSION Fig. 1 illustrates the axial channeling results of 2.0 MeV "^He ions in single crystal Nb(llO) layer with 100 nm thickness on (1120) sapphire substrate. Xmin, the ratio between the random and the aligned yield at the fixed thin layer is an important parameter to characterize the crystal perfection. Judging from Xmin specified at the depth (~10 nm) just behind the surface peak at Nb layer, the crystal quality is ahnost the same as in a bulky Nb crystal at the corresponding depth. A comparison among the channeling data from Nb layers prepared under several different conditions shows that the quality of single crystal Nb films is dependent on the substrate temperature during evaporation. For the growth of high quality Nb single crystal layer it is needed to employ the high temperature condition. In this figure it is recognized that some amounts of disorder exist around the interface region between Nb layer and sapphire substrate, however, the interface is not mixed with each other under the present condition. At higher temperature there is a possibility to form a compound with Nb. The crystallographic analysis was examined by setting the energy windows of RBS spectra at Nb and Al component of sapphire. The orientation relationships obtained from planer channeling measurements were as follows: Nb(110)/sapphire(1120) Nb(lll)/sapphire(0001) Nb(100)/sapphire(0112). The same crystallographic relationship was observed based on TEM analysis in small area but this is the first time to examine the whole area of grown layer under the channeling condition. This kind of thin Nb layer is expected to show the different chemical and physical behaviors because clamping the atoms at surface and/or interface might induce the anisotropic nature even if Nb has the cubic nature originally. In Cu deposition on sapphire with the thickness of 100 nm, the epitaxial growth was not realized at the substrate temperature ranging from 200°C to 700°C. The structure of Cu layer tends to be highly textured perpendicular to the substrate with the increase of substrate temperature.

Fig. 2. SEM observation of Cu (50nm) deposited on Nb(110)/sapphire(1120) at different temperatures, .(a) 200°C,(b) 400°C, (c) 500°C.

722 Fig. 2 shows three kinds of SEM photographs on Cu layer deposited on Nb single crystal fikns on sapphire. An additional deposition of Cu on Nb layer has spent so much time to find out a suitable condition for the single crystal growth of Cu. The substrate temperature was changed from RT to 600 °C. Different from simple imagination, the best condition for single crystal growth with the smooth surface was around 200 °C. The SEM photographs here show that the higher substrate temperature induces the island growth, however, each island is connected coherently judging from the studies of channeling and LEED analyses. Fig. 3 is the LEED pattern from the top Cu(lll) layer on Nb(110)/sapphire(1120) taken with a conventional LEED/Auger spectrometer. As the first layer, Nb was deposited on sapphire substrate at 750 °C, and then the sample temperature was lowered down to 200 °C to assure the hetero-epitaxial growth of Cu layer. Here in this photograph one can see the formation of Cu single-crystalline layer with good quality but the present information is not good enough about the three dimensional packing of atoms. Fig. 4 illustrates RBS/channehng results of the same sample as in Fig. 3. Nb and Cu layers were deposited with the same thickness of 50 nm. By employing rather higher energy 2.7 MeV "^He"*" ions, the mass-resolution in the spectra has become good enough to judge the interface sharpness. The peak at the 2.2 MeV corresponds to the Nb layer, and the peak at 2.1 MeV to the top surface Cu layer. The orientation relationship among Cu layer, Nb layer and sapphire substrate was determined through the angular mapping of planer channeling. Curiously fee Cu(lll) matches with bcc Nb(llO) with the following relationship: Cu(lll)/Nb(110)/sapphire (1120) 1000

T — I — I — I — I — r — I — I — I — I — I — I — I — I — I — I — | -

2.7 MeV ^He^ RBS-C 6=160° 800 h

Nb

Cu(50nm)/Nb(71nm) on sapphire(1120) Cu

600

Random

.SJ 400

200

Aligned

1

Fig. 3. LEED pattern from the top Cu(lll) layer on Nb(110)/sapphire(1120) substrate.

1.5 2 Energy (MeV)

u 2.5

Fig. 4. 2.7 MeV^He RBS/channeling spectra from Cu(lll)/Nb(110) epitaxial fihn on (1120) sapphire substrate. Thickness of Cu and Nb layers are 50 nm and 71 nm, respectively.

723 The single crystal growth of Cu on Nb(100)/sapphire (0112) was also successful around 200 °C but at higher temperatures the columnar structure appeared. As a third choice, the Cu deposition on Nb(lll)/sapphire(0001) was made in the temperature range of 200 °C to 800 °C. In this case any single crystal growth was not found. Further deposition of Nb layer was examined on the top Cu layer at 200°C. The Nb deposition on sapphire at 200 °C resulted in the polycrystalline growth but Nb(llO) single crystal film was grown under the same condition. The crystallographic relationship between Cu and Nb layers can be explained by stacking the closest-packed planes of bcc Nb and fee Cu.

4. CONCLUSION As one of synthesizing techniques of functional materials with the graded nature, the effectiveness of molecular beam epitaxial growth technique was demonstrated in Cu/Nb single crystal multilayer films on sapphire substrate. The sharpness at the interface and the crystal quahty were assessed with RBS/channeling analysis. The orientation relationship among Nb layer, Cu layer and sapphire substrates was determined by mapping the planar points on the angular coordinate. The results obtained are Nb(110)/Cu(lll)/Nb(110)/aAl2O3(1120) andNb(100)/Cu(100)/Nb(100)/a-Al2O3(0li2) .

REFERENCES 1. T. W. Barbee Jr., Materials Research Society Bulletin/February(1990)37. 2. Ed. By T. B. Massalski(chief), H. Okamoto, P. R. Subramanian and L. Kacprzak, Binary Alloy Phase Diagrams 2nd edition vol. 2(ASM International, 1990). 3. For example; Ed. by J. R. Bird and J. S. Williams, Ion Beams for Materials Analysis (Academic Press, 1989). 4. D. M. Tricker and W. M. Stobbs, Phil. Mag. 71, 1037(1995). And Phil. Mag. 71, 1051(1995).



725

Enrichment of ^^Si by Infrared Laser Irradiation T.Tanaka", I.Shiota", H.Suzukib, and T.Noda^ ^Kogakuin University, 2665-1, Nakano-cho, Hachioji, Tokyo 192, Japan ^National Research Institute for Metals, 1-2-1, Sengen, Tsukuba, Ibaraki 305, Japan The enrichment of -^Si has been studied using isotope selective decomposition of Si2F6 by infrared pulse laser. ^^Si was enriched in the residual Si2F6 by the laser irradiation at 952-956 cm^ where Si2F6 containing ^sgi and ^"Si preferentially decomposed to SiF4. The ^^Si content increases with lowering the flow rate of Si2F6 and increasing the laser power. Especially the addition of inert gases such as He and Ar to the source gas accelerates the enrichment of ^^Si. Under the optimum condition, Si2F6 gas with a maximum ^^Si content of 99.72% could be continuously produced.

1. INTRODUCTION Materials of which compositions are isotopically controlled are expected to show improved physical and nuclear properties which can not be attained by usual combinations of elements 11]. Natural silicon is composed of three stable isotopes such as -^Si, -'^Si and ^"Si. If the purified -^Si is obtained, high thermal conductivity of silicon and its compounds is achievable because of suppressing isotope scattering against phonon conduction. In the present paper, effects of wavenumber and energy fluence of a laser, and gas pressure and flow rate of a reactant gas on the enrichment of ^^Si were examined using isotopic selective decomposition of Si2F6 under irradiation of a pulse CO2 laser. The effect of inert gas addition to the reactant on the concentration of '^"Si was also studied.

2. EXPERIMENTAL Hexafluorodisilane(Si2FG) with a purity better than 99%, which was prepared by fluorination of Si2CL> with ZnF2, was used as a source gas for silicon isotope separation. Figure 1 shows the schematic diagram of the experimental apparatus. The transversely excited atmospheric pressure CO2 pulse laser (LUMONICS TEA-841) was used as a light source. The laser beam was slightly converged by a ZnSe lens with a focal length of 1.5 m and introduced into a reaction cell. The reaction cell was a cylindrical stainless steel tube, 2000 mm long x 54.6 mm inner diameter, equipped with NaCl windows at both ends. The wavenumber of the laser was set

726 at 929.023-983.248 cm-i by adjusting the rear grating mirror. The laser pulse with 104 ns full width at half maximum was set at the fluence of 1.62-3.2 J. The beam size is 30 x 30mm in the front of the reaction cell and 6 x 7mm at the focal position which is the midpoint of the tube length. The flow rate and pressure of Si2FG were kept at 3.33-83.5 mm%(at standard state) and 3.34-798.0 Pa, respectively. The irradiation was performed with a repetition of 10 Hz at room temperature. Inert gases such as He, Ar and Kr were also introduced to the reaction tube with a flow rate of 1.67-167mm%. Si2F6 is decomposed by the laser irradiation to form SiFj. Both SiFj and residual Si2F6 were captured with a liquid nitrogen cold trap followed by dividing into the respective component with low temperature distillation. The isotope ratios of silicon were determined by using a quadrupole mass spectrometer (ANELVA AQA-360) from the relative ion intensities of isotope species.

NaCI Window

He.Ar.Kr Power j\ Detctor

To Vacuum

Cold Trap

Col l e c t i o n Cylinder

Fig. 1 Schematic drawing of the apparatus.

1050 1000 950 Wavenunnber (cm"^)

0^ 900

Fig.2 Infrared spectrum of Si2F6 and the laser emission lines

3. RESULTS AND DISCUSSION 3.1 Effect of wavenumber Figure 2 shows infrared spectrum of Si2FG and CO2 laser Hues in the wavenumber region of 900-1100 cm^. Si2F(; has a strong absorption peak at 990 cm^ due to antisymmetric stretching vibration of-^Si-F bond. It is considered that the absorption peaks of-'^Si and ^"Si exist at the lower wavenumber region[2]. CO2 laser has four branches of lOP, lOR, 9P and 9R in the infrared region. Since the emission lines in lOR and lOP branches of CO2 laser appear in the absorption region of Si2F(i, infrared multiple photon decomposition[3] of Si2F(} molecules including ^-^Si and ^*'Si occurs effectively by selecting appropriate wavenumber. The decomposition reaction[3] producing SiFi by the laser irradiation is assumed as Si2FG(gas) + nhv -> SiF,,(gas) + SiF2(solid) (1) A mixture of SiFi and residual Si2FG is easily separated into each component by

727 vacuum distillation utilizing a large difference in boiling point between these gases. Figure 3 shows the concentrations of 2«Si, ^^Si and ^"Si in the Si2F6 after the laser irradiation as a function of wavenumber. Other parameters such as energy fluence and repetition rate of the laser, and flow rate and pressure of Si2F6 were fixed. ^«Si, ^-î and ^"Si abundance in the natural Si are 3.1, 4.67 and 92.23 %, respectively. When the Si2F6 was irradiated at 945-955 cm-i, SiF4 containing large amounts of -^Si and '^"Si was produced. As a result, ^sSi was concentrate in the residual Si2FG. Especially at 956.205 cm-i, ^sSi content increased to 97% from the natural abundance of 92.23% On the other hand, at 975-980 cm-i which is close to the absoii^tion spectrum of ^^Si-F bond, Si2F6 with ^sSi is preferentially decomposed to SiFj. -^Si and ^'*Si concentrations increase in the Si2FG at this wavenumber range and reached 6 and 4.3% , respectively, at 983.305 cm^ while 28Si concentration was increased slightly in the SiF4. Energy Si2F6 flow rate Pressure

1.67J 16.7mm^/s 133Pa

Wavenumber Energy pressure

100j

28si

952.925cm~^ 3.14J 133Pa

"^^--^.^^^

'\-

^

./

- 2o

95! /

29Si

1° 'o

o

> ^^^^ 1

990

980 970 960 950 940 Wave number (cm"^)

930

Fig. 3 Si isotope concentrations in the residual Si2F6 as a function of w a v e n u m b e r .

iC>0-Oi—r

1

1

50

1

1

1

1

~

0

100

Si2F6 Flow Rate (mm^/s) Fig.4 Relation between Si isotope content as a function of t h e flow rate.

3.2 Effect of flow rate and pressure of Si2Fr> Figure 4 shows the relation between concentrations of ^^Si, ^^Si and ^''Si in the residual Si2F6 and the flow rate after irradiation at 952.925 cm-i where Si2FG with -•^Si and ^"Si is preferentially decomposed. The decomposition of Si2FG especially with --^Si proceeded with lowering the flow rate of the source gas. That is, -«Si content in the residual Si2FG increased with decreasing the flow rate and attained 99.65% at 3.34 mm3/s. The concentration of 28Si in the residual Si2F6 increased with the pressure of Si2FB and exceeded 99% at around 100-600Pa. Figure 5 shows the energy fluence dependence of isotope concentrations in the residual Si2FG. -«Si content increased with increasing energy. In the present study, higher energy than 1.62 J at 956.206 cm-i, which is the most suitable wavenumber as shown in fig.3, could not be obtained because of the limitation of the laser power as shown in figure 6.

728 3.3 Effect of inert gas addition to Si2FG Figure 7 shows the concentration change in silicon isotopes in the Si2F(5 with He gas flow rate after the irradiation at 956.206 cm-^ at 1.62 J. A di-astic increase in 28Si content was observed by the addition of He and the concentration reached 99% even though the flow rate of Si2F6 was 16.7 mm^/s. It became constant almost independently on the He flow rate above 33.4 mm%. As have seen in fig. 6 and 7, the increase in laser energy and the addition of He to the source gas are effective to increase the concentration of 2«Si in the residual Si2F6. Since the spectrum of the laser shows the maximum in the energy at around 940 cm-i of lOP branch as shown in fig.6. the laser beam with higher energies than 1.62 J can be emitted if the smaller wavenumber than 956 cm-i is selected. Wavenumber pressure Si2F6 flow rate

956.206cm~^ 133Pa 16.7mnn^/s

5.0

COj laser line

4.0 LIT

3.0

S 2.0 Q)

1.0

0.5

1 Energy (J)

0.0 990

1.5

980 970 960 950 940 Wavenumber, i^/cm"^

Fig.6 Relation between laser energy and wavenumber.

Fig.5 E n e r g y dependence of Si isotope concentration in t h e residual Si2F6. Si2F6 flow rate 16.7mm^/s , Wavenumber 956.206cm"^ Energy 1.62 J

100|

930

He flow rate 33.4mm^/s pressure 133Pa SigFs flow rate 16.7mm7s

95 c

42g

(D O C

C O

29Si

o O

O

>

\ 3°Si

>•

1

1

1

1

1

1

1 1 1 1 1 1 1 1

. . . . < ^do -

100 . He Flow Rate (mm7s)

Fig. 7 Relation between Si isotope concentrations a n d He flow r a t e .

956

954 . 952 Wave number (cm )

Fig.8 Si isotope concentrations a t a m a x i m u m laser energy.

Figure 8 shows the concentration of silicon isotopes in the residual Si2F(; after

729 the irradiation with a maximum power under the He flow as a function of wavenumber. Maximum concentration of ^^Si was obtained at 952.925 cm-i with a energy of 2.8IJ which is about 2 times higher than at 956.206 cm i. Under the constant energy, the concentration of ^^Si h a s a tendency to increase with increasing the wavenumber as seen in fig.3. However, the maximum power increases with decreasing the wavenumber. Then the irradiation condition showing the maximum concentration is the optimum for ^sSi with respect to the laser power and the wavenumber. Wavenumber Si2F6 flow rate 16.7mm^s"^ Inert gas flow rate 33.4mm^s"^

100

100|

R 98

o O

o O

954 , 952 Wave number (cm ') Fig.9 Effect of i n e r t gas addition on t h e Si isotope c o n c e n t r a t i o n s .

100 Ar Flow Rate (mm^/s)

956

Fig. 10 Si isotope c o n c e n t r a t i o n as a function of Ar flow r a t e .

Table 1 S e p a r a t i o n condition for m a x i m u m 28Si c o n c e n t r a t i o n . 952.925cm"' 7.47kJ/m' 931 Pa 8.35mm^s''' 83.5mmV^

Wavenumber Energy Pressure SigPeflow r a t e A r f l o w rate Natural SizFg

Si2F6

Product SiF4

2«Si=92.23% 2^Si=4.67% 3°Si=3.10%

''Si=99.72% '^Si=0.21% '°Si=0.07%

2«Si=81.63% 2^81= 5.3% ^°Si=13.07%

lO.Ocm^

0.15cm'

7.21cm'

Residual

93

9 4 9 5 9 6 9 7 9 8 99 1 0 0 28Si C o n c e n t r a t i o n i(%)

Fig. 11 Relation between yiel a n d 2«Si c o n c e n t r a t i o n in t h e r e s i d u a l Si2FG.

Figure 9 shows the comparison between inert gases on the -"Si concentration. He and Ar gases are more effective than Ki* to concentrate -"Si. The role of inert gas in the isotope selective decomposition of Si2F(; has not been clarified. One of the explanations is made by a mixing effect of the inert gas. The present reaction tube has a large inner diameter compared to the laser beam size

730 in the front position. Furthermore, the beam is focused to the smaller diameter. That means that the laser does not irradiate the whole volume inside the reaction tube. The addition of the inert gas is therefore considered to act as a mixer so that the Si2F6 in the reaction tube is efficiently irradiated. Among inert gases, Kx does not so effectively increase the concentration of ^^Si because the mean free path of Kr is about one ninth of He though the mass is about twenty times larger.

3.4 Optimum separation condition of ^sSi In order to obtain the high concentration of ^^Si, it is necessary to increase the laser power, to decrease the flow rate of Si2F6 and to add the inert gas. Figure 10 shows the ^^Si concentration change with Ar flow rate under the maximum laser energy at 952.925 cm-^ at the Si2F6 flow rate of 8.355 mm%. The concentration of ^^Si higher than 99.5% is constantly produced up to the Ar flow rate of around 100 mm^/s. Table 1 summarizes the optimum condition to continuously produce Si2F6 with a highest concentration of ^sSi in the present study. ^^Si was concentrated from 92.23 to 99.72% though the yield efficiency is only 1.5%. The yield decreases with increasing the concentration as seen in figure 11. If the ^^Si concentration of 99% is enough, the yield of above 10%o is easily attained.

4. CONCLUSION The isotope separation for ^^Si was made using the isotope selective decomposition of Si2F6 by infrared pulse laser. The followings are concluded: 1. High enrichment of ^sSi in the residual Si2F6 was observed by the laser irradiation at 952-956 cm^. 2. The concentration of ^sSi increases with lowering the flow rate of Si2F6 and increasing the laser power. 3. The addition of inert gases, especially He and Ar, to the source gas increases the concentration of ^^Si. 4. The Si2F6 gas with a maximum ^sgi concentration of 99.72% could be continuously produced. 5. The present result indicates the practical isotope separation for -"Si will be realized.

REFERENCES 1. T.Noda, Kinzoku 7(1993)32. 2. L.Halonen, J.Mol. Spectrosc. 120(1986)175. 3. H.Suzuki, H.Ai'aki and T.Noda, SiUcon Carbide and Related Materials, l O P P u b . Ltd, 1996, p i 103.


731

Adaptive and Functionally Graded Structure of Bamboo Shigeyasu Amada* and Naoyuki Shimizu** * Department of Mechanical Engineering, Gunma University, 1-5-1, Tenjin, Kiryu, Gunma, Japan 376 ** Mitsuba Electric Go. Ltd. 1-2681, Hirosawa, Kiryu, Gunma, Japan 376

Bamboo is a natural composite material reinforced by fibers called bundle sheaths, and also a functionally graded and hierarchical structural material. Bamboo grown on the slanted ground cannot grow straight up because it is subjected to a large bending moment due to its own weight. To avoid such a state, it will be bent toward the gravitational direction. This bent part must be reinforced in some way to support the upper portion of the bamboo, for example reinforced by reaction wood for the most of trees. This paper presents how bamboo reacts to such loading conditions. Typically, the cross-section of the bamboo culm changes from circular to elliptical shape which leads to a reduction of the stress generated by the bending moment. It is concluded that the shape of the reaction wood for bamboo is closely related to the loaded bending moment. 1. INTRODUCTION

Plants including bamboo hold a fundamental structure in common which constructs their organs on the ground. Especially, cells have a hard wall and cannot move by themselves. So, the possibility is to stack cells on top of each other like bricks for growing their body. Therefore, plants have adopted a system that segmentation is located on their top portion. They also have acquired an adaptability to their environments because they cannot move from their rooted position [1,2]. Plants have phototropism to grow toward the sun light and geotropism to support themselves for catching the sun light. Their shape and structure must be designed by a compromise of both these characteristics. Trees grown on the slanted ground develop reaction wood[3,4,5] at the bend part as shown in Fig. 1 to reinforce their trunk. There are two kinds of reaction wood, tensile for Gymnosperm and compression wood for Angiosperm. Bamboo is a natural fiber reinforced composite and functionally graded material[6,7,8]. It has

732

TENSION WOOD COMPRESSION WOOD

Fig. 1 Reaction wood been recognized that fibers in the culm cross-section distribute optimaUy under bending moment[6,9]. The graded structure of diameter, thickness and intemodal change of bamboo along the height such that surface stress becomes constant[10]. These two kinds of the graded structure are hierarchical[ll]. This paper presents the structure of the reaction wood of the bamboo grown on the slanted ground. The shape of the reaction wood is related to loading condition. Finally this plant shows an optimum structure to adapt to their environments. Z BAMBOO FOR MEASUREMENTS

Culm No.14

CulmNo.syi

^'''^ sNo.a XJf

Node No.14

Node No.O

(a) Bamboo forest

(b) Coordinate system Fig.2 Curved Bamboo

The studied bamboo is Mosou-bamboo (Phyllostachys eduhs Riv.) and 2 years old. A

733

sample bamboo in the bamboo forest is shown in Fig.2(a). Fig.2 (b) shows the curved, near root part of the bamboo. This curved bamboo is subjected to bending moment due to its own weight besides the environmental loads. The slope angle of the forest ground is about 22° from the horizontal plane and the straight part above the curved cuhn part is tilted by 11.5' from the vertical axis. Internodal is numbered in terms of the cuhn number n from the ground. Judging from Fifi:.2(b), the bend part finishes around the culm number n=14. E E^

n X TO

X

o o

Hb O

o (u) Culm No. 0

(b) Culm No. 1

' •

U-

z

0

2

4

4 • 4 # S

6

CULM NUMBER: n

Fig. 4 Profile of reaction growth ^

i

o ta TENSILE SIDE

o

(e) Culm No. 4

+ \

? ^f

CO

A

20

tc

D

m15 0) LU •z.

^

COMPRESSIVE SIDE

^10 X h-

_ 1

10 (g) Culm No. 6

i 15

(h) Culm No. 7

Fig. 3 Cross section of culm

CULM NUMBER : n Fig.5 Thickness of cross section

Fig. 3 shows the cross-sectional shapes of the bamboo cuhn from n=0 to 8. The upper side is in tensile and lower in compressive side under bending moment. The cross section of tiie bamboo cuhn grow to an elliptical shape in compressive side as well as tensile one. Assuming tiiat tiie straight bamboo culm has a circular cross section, tiie distance from its circular surface to tiie elliptical one is led by the adaptive growth and noted by H, in the tensile, H^ in the compressive side, respeaively. Fig.4 shows tiie changes of H^ and W^ witii respect to tiie cuhn number n. It is clearly

734

seen that the distribution of Hu is lager than Hg. This graph concludes that bamboo has both the properties of Gymnosperm and Angiosperm of trees although the larger reaction wood is developed in the compressive side. Fig. 5 shows the thickness change of the elliptical cross section with respect to culm number. Thickness \^ and t^ become larger than 1^, and \^ to reinforce the culm subjected to bending moment. 3. STRESS ANALYSIS OF CURVED CULM

#

: NON-ADAPTIVE BENDING

O

: ADAPTIVE

D

: TENSILE STRENGTH

STRESS

3ENDING STRESS

8[

D

]• n

D

D D D

D

D

D

D

Q.

150

6

•

• • • • • • •

• •

i> 100

4

O

o Z Q Z LU CQ

CQ

CO LU

cn 1.5

b

CO UJ

on 00

2.0

^CO ^-^

c]

b 00

ib

ZOO

10

2

Functionally Graded Materials 1996

Functionally Graded Materials 1996

Graded syzygies

Graded Syzygies

Graded Orders

Introduction to Surface Engineering and Functionally Engineered Materials (Wiley-Scrivener)

Graded ring theory

Methods of Graded Rings

Methods of Graded Rings

Bugs (ELT Graded Readers)

3D analysis of functionally graded material plates with complex shapes and various holes

Graded Lessons In English

Graded Ring Theory

IMIA 1996

Dominion (1996)

The Category of Graded Rings

Graded Ferroelectrics, Transpacitors And Transponents

Graded problems in computer science

'Одиссей' за 1996 год

Dilbert Collection 1996

Your Hate Mail Will Be Graded

Your Hate Mail Will Be Graded

«Если», 1996 № 04

Самолеты мира 1996 03

Dean Koontz - (1996) - Intensity

Modern Radio Science 1996

Financing the 1996 Election

«Если», 1996 № 01

Circuit Cellar (January 1996)

Капище (Чечня-1996)

Functionally Graded Materials 1996