NAN0 AND MICROSTRUCTURAL DESIGN OF ADVANCED MATERIALS A Commemorative Volume on Professor G Thomas’ Seventieth Birthday Elsevier Internet Homepage: http://www.elsevier.com ScienceDirect Homepage: http://www.sciencedirect.com To contact the Publisher Elsevier welcomes enquiries concerning publishing proposals: book, journal special issues, conference proceedings, etc All formats and media can be considered Should you have a publishing proposal you wish to discuss, please contact, without obligation, the publisher responsible for Elsevier’s material science programme: David Sleeman Publishing Editor Elsevier Ltd The Boulevard, Langford Lane Kidlington, Oxford OX5 lGB, UK Phone: +44 1865 843265 Fax: +44 1865 843920 E.mai1: d.sleeman@elsevier.com General enquiries, including placing orders, should be directed to Elsevier’s Regional Sales Offices - please access the Elsevier homepage for full contact details (homepage details at the top of this page) NAN0 AND MICROSTRUCTURAL DESIGN OF ADVANCED MATERIALS A Commemorative Volume on Professor G Thomas’ Seventieth Birthday Edited by M.A MEYERS University of California, San Diego, USA R.O RITCHIE University of California, Berkeley, USA and M SARIKAYA University of Washington, USA 2003 ELSEVIER Amsterdam - Boston - Heidelberg - London - New York - Oxford Paris - San Diego - San Francisco - Singapore - Sydney - Tokyo ELSEVIER Ltd The Boulevard, Langford Lane Kidlington, Oxford OX5 lGB, UK 02003 Elsevier Ltd All rights reserved This work is protected under copyright by Elsevier, and the following terms and conditions apply to its use: Photocopying Single photocopies of single chapters may be made for personal use as allowed by national copyright laws Permission of the Publisher and payment of a fee is required for all other photocopying, including multiple or systematic copying, copying for advertising or promotional purposes, resale, and all f o r m of document delivery Special rates are available for educational 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contained in the material herein Because of rapid advances in the medical sciences, in particular, independent verification of diagnoses and drug dosages should be made First edition 2003 Library of Congress Cataloging in Publication Data A catalog record from the Library of Congress has been applied for British Library Cataloguing in Publication Data A catalogue record from the British Library has been applied for ISBN: 0-08-044373-7 @ The paper used in this publication meets the requirements of ANSUNIS0 239.48-1992 (Permanence of Paper) Printed in The Netherlands Preface The importance of the nanoscale effects has been recognized in materials research for over fifty years The understanding and control of the nanostructure has been, to a large extent, made possible by new atomistic analysis and characterization methods Transmission electron microscopy revolutionized the investigation of materials This volume focuses on the effective use of advanced analysis and characterization methods for the design of materials The nanostructural and microstructural design for a set of targeted mechanicaVfunctiona1properties has become a recognized field in Materials Science and Engineering This book contains a series of authoritative and up-to-date articles by a group of experts and leaders in this field It is based on a three-day symposium held at the joint TMS-ASM meeting in Columbus, Ohio The book is comprised of three parts: Characterization, Functional Materials, and Structural Materials The book is dedicated to Gareth Thomas who has pioneered this approach to materials science and engineering area over a wide range of materials problems and applications Professor Thomas’ lifetime in research has been devoted to understanding the fundamentals of structure-property relations in materials for which he has also pioneered the development and applications of electron microscopy and microanalysis He established the first laboratory for high voltage electron microscopy, at the Lawrence Berkeley National Laboratory His research has contributed to the development and nano/microstructural tailoring of materials from steels and aluminum alloys, to high temperature and functional ceramics and magnetic materials, for specific property performances, and has resulted in a dozen patents Professor Thomas is a pioneer and world leader in the applications of electron microscopy to materials in general Following his Ph.D at Cambridge in 1955, as an ICI Fellow, he resolved the problem of intergranular embrittlement in the AVZn/Mg high strength alloys which failed in the three Comet aircraft crashes and became identified with Prof Jack Nutting as the “PFZ’ -precipitate-free-zones, condition, now in wide general use to describe grainboundary morphologies leading to intergranular corrosion and mechanical failure This work prompted Dr Kent van Horne of Alcoa to invite him to spend the summer of 1959 in their research labs at New Kensington, Pa From there and after a trans-USA lecture tour he was invited in 1960 to join the Berkeley faculty, (becoming a full professor in 1966), where he started a major research program within the newly formed “Inorganic Materials Research Division” of the (now) Lawrence Berkeley National Laboratory It was there, after nine years’ effort, that he founded the National Center for Electron Microscopy, which opened in 1982 and which he directed until he resigned in 1993, to spend 1.5 years helping establish the University of Science & Technology in Hong Kong There he also set up and directed the Technology Transfer Centre He returned to Berkeley in 1994 to continue teaching and research, and in his career has over 100 graduates With his students and colleagues he has over 500 publications, several books, including the first text on Electron Microscopy ofMetals (1962), and in 1979 -with M.J Goringe, a widely used referenced text- Transmission Electron Microscopy of Materials which was also translated into Russian and Chinese His academic career in Berkeley has included administrative services as Associate Dean, Graduate Division, Assistant and Acting Vice-Chancellor-Academic Affairs, in the turbulent years of student unrest (1966-72) He was the Chair faculty of the College of Engineering (1972/73), and Senior Faculty Scientist, LBNL-DOE, which sponsored most of his research V Vi Preface funding In 1995 he received the Berkeley Citation for “Distinguished Achievement” at UC Berkeley Professor Thomas was Associate Director, Institute for Mechanics and Materials, UC San Diego, from 1993 to 1996 In this capacity, he formulated new research directions and stimulated research at the interface of Mechanics and Materials He is currently Professor in the Graduate School, UC Berkeley, Professor-on-Recall, UC San Diego, and VP R&D of a new company, MMFX Technologies, founded in 1999, to utilize steels for improved corrosion resistant concrete reinforcement In the USA the infrastructure repair costs are in the trillion dollar range In 2002 the company received the Pankow award (American Inst of Civil Engineers) for innovation in Engineering, based on Prof Thomas’ patents on nano microcomposite steels Professor Thomas has also played an important role in promoting the profession He was president of the Electron Microscopy Society of the US in 1974, and in 1974 he became Secretary General of the International Societies for Electron Microscopy for an unprecedented 12 years, and was president in 1986-90 He lectured extensively in foreign countries and helped promote microscopy and materials in developing countries, also serving as advisor in China, Taiwan, Korea, Singapore, Poland, Mexico, et al He also served on many committees of the ASM and TMS, and the National Research Council After reorganizing the editorial structure of Acta and Scripta Metallurgica (now Materialia), when in 1995 he took over as Editor-in-chief, he became Technical Director, Acta Mat Inc 1998 until April 2002 He was Chairman of the Board in 1982/84 In recognition of his many achievements, Professor Thomas has received numerous honors and awards, including, besides his Sc.D.-Cambridge University in 1969: Honorary Doctorates from Lehigh (1996) and Krakow (1999); The Acta Materialia Gold Medal (2003), The ASM Gold Medal (200 l), Sauveur Achievement Award (ASM- 199l), Honorary Professor, Beijing University of Sci & Technology (1958), Honorary Memberships in Foreign Materials societies (Japan, Korea, India, etc.), E.O Lawrence Award (US Dept of Energy-l978), Rosenhain Medal (The Metals Soc-UK-1977), Guggenheim Fellow (1972), von Humboldt Senior Scientist awards (1996 & 1981), the I-R Award (R&D Magazine-1987), Sorby Award, (IMS- 1987) and the Distinguished Scientist Award (EMSA-1980) He received the Bradley Stoughton Teaching Award (ASM) in 1956, and the Grossman (ASM), and Curtis-Mcgraw (ASEE) research awards in 1966 He is a Fellow of numerous scientific societies In recognition of these achievements, Professor Thomas was elected to both the National Academy of Sciences (1983) and the National Academy of Engineering (1982) Professor Thomas, born in South Wales, UK, is also a former rugby and cricket player (member, MCC), enjoys skiing and grand opera The editors thank the speakers at the symposium and the authors of the scholarly contributions presented in this volume A special gratitude is expressed to Prof S Suresh for having enabled the publication of this volume by Elsevier All royalties from the sale of this book are being donated to the TMS/AIME and ASM societies for the establishment of an award recognizing excellence in Mechanical Behavior of Materials November, 2003 Curriculum Vitae of Professor Thomas Date and Place of Birth: August 1932, Maesteg, Glamorgan, U.K Academic Qualifications B.Sc with First Class Honors in Metallurgy, University of Wales (Cardiff), 1952 Ph.D University of Cambridge, 1955; Sc.D University of Cambridge, 1969 Career Details 1956-59 ICI and St Catharine’s College Fellow, University of Cambridge 1960 Visiting Assistant Professor, University of California, Berkeley 1961-Present University of California, Berkeley: Full Professor (1966); Associate Dean, Graduate Division (1968-69); Assistant to the Chancellor (1969-72); Acting Vice Chancellor, Academic Affairs (1971-72); Chairman, Faculty of the College of Engineering (1972-73); Senior Faculty Scientist, Materials Sciences Division, Lawrence Berkeley Laboratory; Founder and Scientific Director, National Center for Electron Microscopy, Lawrence Berkeley Laboratory (198 1-93); on special leave as Director, Technology Transfer Centre, Hong Kong University of Science and Technology, Kowloon, Hong Kong (1993-94); Professor in the Graduate School, University of California, Berkeley (1995-present) Awards and Honors 2003 2003 200 Silver Medal in honor of Prof C S Barrett, ASM Intl Rocky Mountain Chapter Acta Materialia Gold Medal First Albany Int Distinguished Lecture in Mat Sci & Eng (RPI) Vii Curriculum vitae of Professor Thomas Viii 200 1999 1998 1996 1996 1996 1996 1995 1994 1994 1991 1987 1987 1987 1985 1983 1983 1982 1981 1980 1979 1978 1977 1976 1976 1973 1971-72 1966 1966 1965 1964 1953 American Society for Materials International, Gold Medallist Doctorate honoris causa, University of Krakbw, Poland Honorary Member, Japan Institute of Materials Honorary D.Sc., Lehigh University, Bethlehem, PA, USA, 1996 Honorary Member, Indian Institute of Metals Honorary Member, Korean Institute of Metals and Materials Alexander von Humboldt Senior Scientist Award, IFW, Dresden, Germany The Berkeley Citation for Distinguished Achievement, U C Berkeley Honorary Member, Mat Res SOC India of Medal of Academy of Mining and Metallurgy, Polish Acad of Sciences, Krakow Albert Sauveur Achievement Award (ASM International) I-R 100 Award, Research and Development Magazine Elected, Fellow, Univ Wales, Cardiff, UK Henry Clifton Sorby Award, International Metallographic Society Honorary Professorship-Beijing University of Science & Technology Confucius Memorial Teaching Award, Republic of China (Taiwan) Elected to the National Academy of Sciences, U.S.A Elected to the National Academy of Engineering, U.S.A Alexander von Humboldt Senior Scientist Award, Max Planck Institute, Stuttgart EMSA Distinguished Scientist Award for Physical Sciences Fellow, Metallurgical Society of AIME Ernest Lawrence Award (US Department of Energy) The Rosenhain Medal (The Metals Society, U.K.) Fellow, Royal Microscopical Society, U.K Fellow, American Society for Metals Visiting Professor at Nagoya University, Japan Society for Promotion of Science Guggenheim Fellow; Visiting Fellow, Clare Hall, Cambridge University Curtis-McGraw Research Award (American Society for Engineering Education) Grossman Publication Award (American Society for Metals) for paper “Structure and Strength of Ausformed Steels”, Trans ASM, 58,563 (1965) Bradley Stoughton Teaching Award, American Society for Metals Miller Research Professor, UC Berkeley National Undergraduate Student Prize, Institute of Metals (London) Professional Activities 19981995-98 1992 1991-95 1986-90 1974-86 1991-94 1987-88 1982-85 1985-90 Managing Director, Acta Metallurgica, Inc Board of Governors Editor in Chief, Acta Materialia and Scripta Materialia Founder Member, Editorial Board, NanoStructured Materials (Elsevier) Vice President, International Federation of Societies for Electron Microscopy President, International Federation of Societies for Electron Microscopy Secretary General, International Federation of Societies for Electron Microscopy Reappointed, Member, Board of Governors Acta Metallurgica, Inc Member, US Department of Energy E 0.Lawrence Award Selection Committee Chairman, Acta Metallurgica, Inc Board of Governors Member, Acta Metallnrgica, Inc Board of Governors Curriculum vitae of Professor Thomas ix 1978-8 1975 1972-73 1961-present TMS-AIME Board of Directors President, Electron Microscopy Society of America UC Convenio Program Visiting Professor, University of Chile, Santiago, Chile Served on many national and international committees including National Research Council (USA), International Federation of Electron Microscopy Societies, EMSA, ASM, TMS, University of California, editorial boards, etc Served on science and technology boards (Taiwan, Singapore, Korea, South Africa and Mexico) as materials advisor Publications Over 550 papers, books, numerous book chapters Selected Publications “Structure-Property Relations: Impact on Electron Microscopy,” in Mechanics and Materials: Fundamentals and Linkages, Marc A Meyers, Ronald W Armstrong and Helmut Kirchner, eds New York: J Wiley & Sons, 1999, pp 99-121; LBNL 40317 “Nd Rich Nd-Fe-B Tailored for Maximum Coercivity,” Er Girt, Kannan M Krishnan, Symp Proc 577, Michael Coey G Thomas, C J Echer and Z Altounian, Mat Res SOC etal., eds Warrendale, PA: The Materials Research Society, 1999, pp 247-252 “Some Relaxation Processes in Nanostructures and Diffusion Gradients in Functional Materials,” G Thomas, in Deformation-Induced Microstructures: Analysis and Relation to Properties (Proc 20th Ris# International Symposium on Mat Sci.,), J B Bilde-S#rensen, J V Carstensen, N Hansen, D Juul Jensen, T Leffers, W Pantleon, B Pedersen and G Winther, eds., Ris# National Laboratory, Roskilde, Denmark, 1999, pp 505-521 “Origin of Giant Magnetoresistance in Conventional AlNiCo, Magnets,” A Hiitten, G Reiss, W Saikaly and G Thomas,Actu Muteriuliu 49, 827-835 (2001) “Novel Joining of Dissimilar Ceramics in the Si3N4-Al2O3 System Using Polytypoid Functional Gradients,” Caroline S Lee, Xiao Feng Zhang and Gareth Thomas, Acta Materialia vo1.49,3767-3773, & 3775-3780 (2001) See web-site (below) for more details: Internet: http://www.mse.berkeley.edu/faculty/thomas/thomas.html Patents Process for Improving Stress-Corrosion Resistance of Age-Hardenable Alloys, U.S Patent 3,133,839 (1964) High Strength, High Ductility Low Carbon Steel (J Koo and G Thomas), U.S Patent 4,067,756 (1978) High Strength, Tough Alloy Steels (G Thomas andB V N Rao), U.S Patent4,170,497 (1979) Method of Making High Strength, Tough Alloy Steels (G Thomas and B V N Rao), U.S Patent 4,170,499 (1979) High Strength, Low Carbon, Dual Phase Steel Rods and Wires and Process for Making Same (G Thomas and A Nakagawa) U.S Patent 4,613,385 (1986) 290 C.S Hurtley MPF is a three-parameter function, this procedure makes the constant term in the polynomial a function of the other three coefficients A similar process can be applied to express the polynomial potential in terms of other mathematical forms as long as there are only three adjustable parameters The Virtual Potential In order to develop expressions for the composition dependence of the elastic constants of an alloy it is necessary to construct a potential for the alloy based on the potentials for like and unlike atomic pairs Consider a single-phase alloy single crystal to be a virtual crystal in which the mean interatomic spacing and virtual pair potential are obtained by a quasi-chemical approach using the potentials of like and unlike pairs In the quasi-chemical approximation [12], the internal potential energy of a random solid solution is expressed as a sum over interatomic potentials of the several types of pairs in the alloy, weighted by the probability of existence of each pair In an alloy of M components a virtual pair potential can be defined as: where ppvrepresents the probability of the pair consisting of an atom of type p and one of type v, and qyPV) is are the pair potential for the pv pair Both pPvand qPV) symmetric in p and v The probability of a randomly chosen atomic site being occupied by an atom of species v is cv, where c is the atomic fraction of that species For a disordered alloy having no short-range order the mean number of atoms of species p in the nth neighbor shell is z(")c;) where the coordination number of the nth neighbor shell is z(") and the concentration of species p in the same shell is c:) Then the probability of finding an atom of species p in the nthneighbor shell is c' For such an alloy the probability of finding a vp pair with ; one atom at the origin and the other in the nthneighbor shell is: where':n is the number of atoms of species p in the nth neighbor shell Then equation ( ) gives for the virtual potential of a disordered, single-phase binary alloy of species A and B: where the suffixes indicate the type of pair to which the potential applies Writing the potential for each component pair as a cubic polynomial in the form of equation (4), inserting into equation (7) and collecting coefficients of like powers of r reveals that each in equation (4) depends on composition according to equation (7) with the appropriate coefficient substituted for the corresponding 'p(lrv) It is important to note that this quadratic composition dependence applies to the coefficients of the cubic polynomial, but not necessarily to the parameters appearing in other mathematical forms of the potential [3] To determine the alloy ASFCs from equation (2), it is necessary to evaluate the virtual potential at appropriate values of the first and second neighbor distances For this purpose, the mean nearest neighbor distance in the alloy can be expressed in terms of the corresponding spacings of the like and unlike pairs Elastic constants of disordered ternary cubic alloys 29 present in the alloy [13,14] The mean nearest neighbor distance in the disordered binary alloy considered above is where the r,, refer to spacings of various kinds of atomic pairs in the alloy, which are assumed to be constant throughout the composition range of interest The mean spacings of more distant neighbors are calculated from the geometry of the lattice In the spirit of the quasi-chemical approximation, we assume that the nearest neighbor distances of atomic pairs depend only on the atomic species, but not otherwise on the surroundings of the pair Elastic Constants and Axisymmetric Force Constants Both face-centered (FCC) and body-centered cubic (BCC) crystals are characterized by a lattice parameter, a,, which is also the distance from an atom at the origin to its six, second neighbors, which lie along directions The twelve nearest neighbors in FCC lie at a distance a0/d2 from the origin along > directions, while the eight nearest neighbors in BCC are a0d3/2 from the origin along -4 directions The 11> relationship between single crystal elastic constants, referred to cube axes and expressed in reduced Voigt notation, and the first and second neighbor ASFCs can be expressed where the order of the neighbor is indicated by the suffix on the ASFC and M is a X matrix that depends on the crystal structure Values of M for both FCC and BCC crystals are given in reference [3] In order to relate the ASFCs to the virtual potential, it is necessary to evaluate derivatives at mean neighbor distances appropriate to the alloy composition These can be obtained by determining like and unlike pair spacings from data on the composition dependence of the lattice parameters in the phase field of interest using a least-squares tit to equation (S), which can then be employed to calculate the nearest neighbor spacing for any composition of interest in the single-phase field Composition Dependence of Elastic Constants The definitions of ASFC in terms of the virtual potential using equations (2) and (4) and the composition dependence of the pair spacings, equation (S), can be used to solve for the coefficients of the virtual potential in terms of experimentally determined elastic constants of alloy single crystals and their mean interatomic spacings Equation (9) leads to: for the coefficients of the polynomial form of the virtual potential Values of N for FCC and BCC crystals are given in reference [3] It is understood that the elastic constants and nearest neighbor spacing apply to the same alloy composition Inserting the explicit composition dependence of the virtual potential C.S Hurtley 292 coefficients ofa binary alloy and inverting equation (10) leads to the expression i ; - C, for the explicit composition dependence of the elastic constants in terms of the polynomial coefficients and the mean nearest neighbor spacing corresponding to the composition, CA This procedure has been demonstrated for several binary alloys having both face-centered cubic and body-centered cubic lattices and varying types of solubility conditions [3,15] The procedure can easily be generalized to a multi-component, single-phase alloy by noting that for an M component alloy there are 3M(M+1)/2 independent Coefficients required to construct the polynomial potential and M(M+1)/2 independent pair spacings required for determination of the mean nearest neighbor distance These parameters can be determined from the lattice parameter and elastic constants of the pure components when they have the same crystal structure as the alloy in question Otherwise, it is necessary to obtain them from least squares fits to experimental data on elastic constants and lattice parameters of alloys in the single-phase field being studied This process is facilitated by expressing the pair probabilities, the pair spacings and the Coefficients of the polynomial potential as multidimensional vector quantities First, as define the M (M+1)/2 dimensional pair probability vector, P(M) P MM PM(M-I)P(M-I)M + where the elements of the matrix are the random probabilities of each type of pair The top M terms are the probabilities of pairs of like species, while the bottom M(M-1)/2 terms are the probabilities of unlike pairs In a similar manner, define the pair spacing vector, %MI, where the elements are the pair spacings of each type of pair in the alloy Then the mean nearest neighbor spacing of the alloy in terms of these vectors becomes where the superscript T indicates the transpose of the vector In a completely analogous manner, the coefficients of the polynomial virtual potential can be expressed as functions of composition Defining the vectors @{"' (i = 1,2,3) for the coefficients of the polynomial potential of the types of atomic pairs in the alloy permits writing the coefficients of the virtual potential as Elastic constants of disordered ternary cubic alloys 293 (14) is formed by stacking the transposes of the three vectors The X M(M+1)/2 matrix, extension of equation (1 1) to M components can be written Then the which, with equation (13), gives the composition dependence of the elastic constants of alloys explicitly in terms of composition using parameters that describe the spacing and polynomial potential coefficients of each type of pair APPLICATION TO A TERNARY ALLOY SYSTEM The procedure described in the previous section is illustrated in the following discussion by applying it to a calculation of the elastic constants of ternary alloys of copper, aluminium and nickel All three of the components have the face-centered cubic crystal structure in the pure form and, although there is not complete miscibility of all three components in the solid state, there is a considerable single-phase field adjacent to the copper-nickel binary system extending well into the copper-rich and nickel-rich comers [16] Lattice parameter data exist for binary alloys in sufficient quantity to determine the spacings of the like and unlike atomic pairs in the three binary systems using equation (13) [17] Virtual potentials in the polynomial format have been constructed from data on single elastic constants and lattice parameters of a sufficient number of binary alloys to construct a virtual potential for the temary system [3,15] in the form of equation (14) Values of the relevant pair spacings and polynomial pair potential coefficients are given in Table Table Pair Spacings and Polynomial Potential Coefficients The data in Table were used in Equation (15) with the value of N for face-centered cubic crystals, 1.414 4.121 -5.536 11.314 11.314 -11.314 36.728 22.607 -18.364 to obtain the room-temperature elastic constants of single crystals of ternary alloys in the range