Nano and Microstructural Design of Advanced Materials

NAN0 AND MICROSTRUCTURAL DESIGN OF ADVANCED MATERIALS A Commemorative Volume on Professor G. Thomas’ Seventieth Birthday

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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

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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

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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: 9 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 1

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 1 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.of India 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 0. 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 1 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, 2 books, numerous book chapters. Selected Publications 1. “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. 2. “Nd Rich Nd-Fe-B Tailored for Maximum Coercivity,” Er. Girt, Kannan M. Krishnan, G. Thomas, C. J. Echer and Z. Altounian, Mat. Res. SOC.Symp. Proc. 577, Michael Coey etal., eds. Warrendale, PA: The Materials Research Society, 1999, pp. 247-252. 3. “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, 0. B. Pedersen and G. Winther, eds., Ris# National Laboratory, Roskilde, Denmark, 1999, pp. 505-521. 4. “Origin of Giant Magnetoresistance in Conventional AlNiCo, Magnets,” A. Hiitten, G. Reiss, W. Saikaly and G. Thomas,Actu Muteriuliu 49, 827-835 (2001). 5. “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).

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Curriculum vitae of Professor Thomas

Controlled Rolling Process for Dual Phase Steels and Applications to Rod, Wire, Sheet and Other Shapes (G. Thomas, J. H. Ahn, and N. J. Kim), U.S. Patent 4,619,714 (1986). Method of Forming High-Strength, Corrosion-Resistant Steel (G. Thomas, N. J. Kim, and R. Ramesh), U.S. Patent 4,671,827 (1987). Method of Producing a Dense Refractory Silicon Nitride (Si3N4) Compact with One or More Crystalline Intergranular Phases (G. Thomas, S. M. Johnson, and T. R. Dinger), U.S. Patent 4,830,800 (1989). High Energy Product Permanent Magnet Having Improved Intrinsic Coercivity and Method of Making Same (R. Ramesh and G. Thomas), U.S. Patent 4,968,347 (1990). Giant Magnetoresistive Heterogeneous Alloys and Method of Making Same (J. J. Bernardi, G. Thomas, and A. R. Huetten), U S . Patents 5,824,165 (1998) and 5,882,436 (1999).

Table of Contents

Preface

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Curriculum Vitae of Professor Thomas

Part 1: Characterization 3

Characterization: The Key to Materials

R. Gronsky

Nanochemical and Nanostructural Studies of the Brittle Failure of Alloys D.B. Williams,M. Watanabe, C. Li and V.J. Keast

11

Transmission Electron Microscopy Study of the Early-Stage Precipitates in Al-Mg-Si Alloys H.W. Zandbergen, J.H. Chen, C.D. Marioara and E. Olariu

23

Laser Surface Alloying of Carbon Steels with Tantalum, Silicon and Chromium J. Kusinski and A. Woldan

35

In-Situ TEM Observation of Alloying Process in Isolated Nanometer-Sized Particles H. Mori, J.-G. Lee and H. Yasuda

49

Characterization of MetaVGlass Interfaces in Bioactive Glass Coatings on Ti-6A1-4V and Co-Cr Alloys E. Saiz, S. Lopez-Esteban, S. Fujino, T. Oku, K. Suganuma and A.P. Tomsia

61

Development of Advanced Materials by Aqueous Metal Injection Molding S.K. Das, J.C. LaSulle, J.M. Goldenberg and J. Lu

69

Part 2: Functional Materials Microstructural Design of Nanomultilayers (From Steel to Magnetics) G.J. Kusinski and G. Thomas Effects of Topography on the Magnetic Properties of Nano-Structured Films Investigated with Lorentz Transmission Electron Microscopy J.Th.M. De Hosson and N.G. Chechenin

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Slip Induced Stress Amplification in Thin Ligaments

109

Materials, Structures and Applications of Some Advanced MEMS Devices Sungho Jin

117

X. Markenscogand V.A.Lubarda

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Table of contents

Microstructure-Property Evolution in Cold-Worked Equiatomic Fe-Pd During Isothermal Annealing a t 500 O A. Deshpande, A. Al-Ghaferi, H. Xu, H. Heinrich and J.M.K. Wiezorek

Part 3: Structural Materials Microstructure and Properties of In Situ Toughened Silicon Carbide L.C. De Jonghe, R.O. Ritchie and X.F. Zhang Microstructure Design of Advanced Materials Through Microelement Models: WC-Co Cermets and Their Novel Architectures K.S. Ravi Chandran and Z. Zak Fang

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The Ideal Strength of Iron D.M. Clatterbuck, D.C. Chrzan and J. W.Morris Jr.

173

Microstructure-Property Relationships of Nanostructured Al-Fe-Cr-Ti Alloys L. Shaw, H. Luo, J. Villegas and D. Miracle

191

Microstructural Dependence of Mechanical Properties in Bulk Metallic Glasses and Their Composites U. Ramamurty, R. Raghavan, J. Basu and S. Ranganathan

199

The Bottom-Up Approach to Materials by Design W.W. Gerberich, J.M. Jungk and W.M.Mook

21 1

The Onset of Twinning in Plastic Deformation and Martensitic Transformations M.A. Meyers, M.S. Schneider and 0. Voehringer

221

Crystal Imperfections Seen by X-Ray Diffraction Topography R.W.Armstrong

233

Synthetic Multi-Functional Materials by Design Using Metallic-Intermetallic Laminate (MIL) Composites K.S. Vecchio

243

Taylor Hardening in Five Power Law Creep of Metals and Class M Alloys M.E. Kassner and K. Kyle

255

Microstructural Design of 7x50 Aluminum Alloys for Fracture and Fatigue F.D.S. Marquis

273

Elastic Constants of Disordered Ternary Cubic Alloys C.S. Hartley

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Index

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PART 1: CHARACTERIZATION

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Nan0 and Microstructural Design of Advanced Materials M.A. Meyers, R.O. Ritchie and M. Sarikaya (Editors) 02003 Elsevier Ltd. All rights reserved.

CHARACTERIZATION: THE KEY TO MATERIALS R. Gronsky Department of Materials Science & Engineering, University of California Berkeley, California 94720-1760 USA

ABSTRACT His seventieth birthday offers this special occasion to recall the many seminal contributions made by Professor Gareth Thomas to the field of materials science and engineering. A brief reckoning of his career, his dedication to the development of electron microscopy techniques, his applications of high precision characterization methods to numerous engineering materials systems, and his successes as both researcher and educator are recounted here.

INTRODUCTION The development of advanced materials is guided by assessment at appropriate levels of resolution. This has always been the preferred protocol, and hallmark, of materials science and engineering. Our discipline seeks to understand all of the links connecting the synthesis and processing of materials with the evaluation of their properties, with their performance in engineering applications, and with their internal structure and composition. However, as modem engineering progresses towards increased complexity and reduced dimensionality, our discipline places ever higher demands on the diffraction, spectroscopy, and microscopy techniques used for microstructural analysis. There was a time when “pearlite” was an acceptable designation for a microstructural constituent associated with certain mechanical properties of steels. Thirty years ago, it became essential to know the composition of both the ferrite and the cementite in “pearlite,” including whether or not there were any gradients in carbon concentration at their contiguous interfaces. And as this manuscript is being written, hundreds of scientists around the world are struggling to sort out carbon nanotubes as single-walled or multi-walled, spiral or concentric, vacant or filled, with what species, at which specific locations. Consequently, the levels of resolution appropriate for contemporary materials science and engineering are those that reveal individual atomicpositions in the spatial domain, and individual atomic identities in the temporal or energy domain. It is now generally accepted that atomic level characterization is the essential key to materials, old and new. Today’s symposium highlights many of the triumphs of advanced materials development based upon this singular tenet of microstructural design, which has been championed by Professor Gareth Thomas throughout his long and illustrious career. It was just over thirty (30) years ago that I came to Berkeley to begin my graduate studies in Professor Thomas’s group, and I’m honored to offer this contribution in celebration of his seventieth (70th)birthday.

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R. Gronslcy

BACKGROUND Gareth Thomas was born on August 9, 1932. He completed his Bachelor of Science degree with First Class Honors in Metallurgy from the University of Wales, Cardiff, in 1952. Three years later, in 1955, he obtained his Ph.D. from the University of Cambridge, where he stayed through 1959 as an ICUSt. Catherine’s College Fellow. In 1960 he arrived in Berkeley as a Visiting Assistant Professor and joined the ladder rank faculty as an Assistant Professor in 1961. During his first year on the faculty, when other assistant professors seeking tenure were buried in labs or libraries struggling to solidify their academic careers, Professor Thomas chose instead to organize an international conference. Securing a prime location on the Berkeley campus, he hosted “The Impact of Transmission Electron Microscopy on Theories of the Strength of Metals” in 1961, providing an aggressive examination of the Orowan and Petch equations as well as new insights into the mechanisms of strengthening by finely dispersed (TEM-sized) obstacles. Many of the luminaries in the fledgling field of transmission electron microscopy were there (Figure l), taking note of both the ambition and the dedication their colleague Gareth Thomas, who would continue this tradition of global congresses to advance the practice of electron microscopy in applications to engineering materials throughout his career.

Figure 1: A few of the attendees at the 1961 Berkeley conference on the “Impact of TEM on Theories of the Strength of Metals.” L to R first row, R.B. Nicholson, M.J. Whelan, G . Thomas, J. Washbum; L to R second row, K. Melton, A. Kelly, G. Rothman, P.R. Swann.

Also during his first year on the faculty, Professor Thomas found time to draft and edit a complete textbook, Transmission Electron Microscopy of Metals, published by Wiley only one year later, in 1962. This treatise was the first of its kind, a practical, pedagogical, “hands-on” treatment of the transmission electron microscopy technique, annotated with instructions on how to prepare representative samples worthy of scientific investigation. It served generations of students for the next 17 years, until his second edition, co-authored with M.J. Goringe, was released in 1979. Thomas’s early emphasis on high-resolution microstructural characterization of metals was born of his notable successes during his time at Cambridge. One of the most perplexing problems of the day was the catastrophic failure of the Comet aircraft, prompting many investigations into the relationship between the microstructure and deformation behavior of aluminum-based alloys. Thomas’s work [ 1,2] showed quite clearly (Figure 2) the occurrence of a precipitate-free zone (PFZ) adjacent to grain boundaries, and a coarser precipitate distribution adjacent to the PFZ, when compared to the surrounding matrix. Implicating such inhomogeneities in microstructure as the likely cause for inhomogeneities in mechanical response, the path forward was revealed through microstructural design. Subsequent development of thermomechanical processing cycles to eliminate the formation of PFZs and their attendant problems was facilitated by electron microscopy, the only technique with sufficient spatial resolution to verify success. Professor Thomas developed similar processing methodologies to protect age-hardening alloys against stresscorrosion cracking (Figure 3), resulting in his first patent [3], also issued within a few short years of his debut on the faculty.

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Characterization: The key to materials

Figure 2: Heterogeneous precipitation and precipitate-free zones (PFZs) in AI-6Zn-3Mg, after reference [2].

BI

I

.s

n 3% r ; -

*li

Figure 3: Plot of average stress corrosion life (days) vs aging time (hours) for aluminum alloys subjected to step agmg process, after reference [3].

EARLY DEVELOPMENTS In his quest for precision during diffraction analysis, Professor Thomas became an early advocate for the technique of Kikuchi electron diffraction [4],which results from an inelastic scattering event that is subsequently elastically scattered. Thomas and co-workers released a series of publications in the 1960s explaining the method and demonstrating its superior advantages over conventional (spot) electron diffraction for precise determination of crystalline orientations. By painstakingly assembling photo collages combining hundreds of Kikuchi electron diffraction patterns, they also generated “Kikuchi maps” to assist investigators in navigating reciprocal space. Figure 4 shows one such map for the diamond cubic structure [ 5 ] , but others were published for both body-centered cubic [6] and hexagonal close-packed [7] structures. Diffraction also figured prominently in the analysis of spinodal decomposition, but there was no more convincing evidence of structural modulation that the images published by Thomas and co-workers [S], Figure 5(a). Coarsening of the spinodally-decomposed product resulted in a square wave compositional profile seen in Figure 5(b), which was much less obvious, and sometimes completely obscured, in diffraction results. Thomas was also first to point out that microstructures generated by spinodal decomposition were not

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R. Gronslcy

susceptible to the formation of detrimental PFZs, and he proposed employing spinodal decomposition where possible in alloy systems with known miscibility gaps as another method of intelligent microstructural design.

Figure 4. Kikuchi map of the diamond-cubic structure (silicon) after reference [ 5 ] The top pole is readily identified by its four-fold symmetry as 001, the bottom center pole is 113, representing an angular range of 25 2” East-west extremes are 102 and 012 poles, at 36 9” apart

Figure 5 : Spinodally decomposed Cu-Ni-Fe alloy showing (a) early stage and (b) later stage product resulting from aging within the temary miscibility gap. The light phase i s Cu rich, the dark phase, Ni-Fe rich.

Yet another method of microstructural analysis pioneered about this time was the application of phase contrast ‘‘lattice’’ imaging to directly assess the local lattice parameter in close-packed metallic alloys. The resolution performance of transmission electron microscopes was limited thirty years ago to approximately 0.25 nm, consequently a two-beam “sideband imaging method was the only feasible option for extracting phase contrast, generating images of a single spatial frequency. Figure 6 shows how the technique yielded the modulation wavelength in a spinodally decomposed Au-Ni alloy, the first such demonsbation of its type. Thomas and co-workers continued to apply lattice imaging to a range of spinodal and ordered alloys during the late 1970s, coupled to the development of subsidiary analytical techniques such as optical microdiffraction [9]. As specimen preparation procedures for non-metallic materials also improved in Thomas’s laboratories, phase contrast methods yielded new insights into novel polytypoid formation in the non-oxide ceramics. The example shown in Figure 7 documents the substructure of a beryllium silicon nitride, BesSi3Nl0, as alternating stacking sequences of three layers of BeSiN2 followed by two layers of Be3N2.

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Characterization: The key to materials

24t

12

0

30

60 I

90

*

120 i

20 40 60 DISTANCE (NO OF FRINGES)

Figure 6 Lattice image (top) and plot of d-spacing vs distance in a spinodally-decomposed Au-Ni alloy The “average” modulation wavelength IS 2.9 nm, after reference [9].

INNOVATIONS These successes with a growing number of applications of electron microscopy in materials engineering were clearly noticed by the scientific community at large. Consequently Professor Thomas chose to convene another gathering of participants in 1976 for the purpose of addressing what had become a burning question for him and many others: “Should the US support a National Center for Electron Microscopy?’ The question originated in the understanding that electron microscopy had taken on the earmarks of “big” science, requiring multi-million dollar investments in order to construct, maintain, and run the high voltage electron microscopes that exhibited superior performance at the time. Attendees included eighteen (18) from Berkeley, forty-one (41) from elsewhere in the US, and seven (7) from abroad, and at the end of the workshop, all concurred that the time was right to seek a national, shareable, user resource in the model of the photon beam lines and es that had recently been funded by the federal government. The original estimate for this facility was a modest $5M. In rapid succession, the Energy Research and Development Administration (later DOE) held two national Materials Sciences Overview meetings, the proceedings of which were published as ERDA 77-76-1 and ERDA 77-76-2 . In these reports, the Office of Basic Energy Sciences identified a “critical need” for state-of-the-art fa in transmission electron microscopy. Thomas and collaborators submitted their proposal that year, and the Atomic Resolution Microscope (ARM) became a line item in the FY 1980 Congressional Budget at $4.3M [ I l l . The ARM was installed in 1982 and sustained the best imaging

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R. Gronsky

performance of any transmission electron microscope in the world for the next decade. With a top operating voltage of 1 MeV, a biaxial tilt stage of*45’ range, and an instrumental resolution limit of 0.16 nm, it’s utility extended to many new materials engineering problems requinng microstructural assessment at the atomic level. Moreover, the technological innovations funded by the federal government dunng this project spawned a new generation of “medium voltage” instruments with enhanced performarxe and smaller footpnnt, so they could be placed in a “normal” laboratory setting, instead of the three-story silo architecture needed by the larger megavolt units.

Figure 7: Phase contrast image of Be9Si3NIo(left) and structural model (right) showing three layers of BeSiNl interspersed with two layers of Be,N2, after [lo].

One of the most widely publicized images from the ARM is shown in Figure 8, showing the atomic structure of the double-layer defect in the high Tc superconductor, YBCO.

Figure 8: Phase contrast image of YBa2Cu3O,.* (left) and structural model (right) showing double layer CuO defect running horizontally through center of micrograph, after [ 1 I]. Only cations are visible.

It is instructive to compare Figures 7 and 8 for their historical significance since they represent best practice in

“contemporary” transmission electron microscopy, published in the world’s premiere scientific journals, one decade apart. The legacy of innovation that has distinguished Professor Gareth Thomas’s career is clearly revealed in these images.

Characterization: The key to materials

9

LEGACY But Professor Thomas’s legacy extends well beyond his contributions to the field of electron microscopy. His innovations in the development of novel materials and processing procedures have resulted in a dozen patents. The first, described above, was issued for a process to enhance resistance to stress corrosion cracking in A1 alloys. Six more patents cover his development of new steels, some high-strength, some dual phase [14], and some corrosion-resistant. Another patent was granted for a method to produce dense refractory ceramics [15]. And his four most recent patents are for magnetic materials, to enhance intrinsic coercivity and to enhance their giant magnetoresistive (GMR) response [16]. Professor Thomas’s contributions to the scientific literature number over five hundred (500) and counting. Even more impressive than this number is the range of topics on which he’s written. Metals and alloys, ceramics, semiconductors, superconductors, magnetic materials, composite materials, polymeric materials, and even organic materials appear in his manuscripts, along with a widely varied range of electron microscopy, diffraction, and spectrometry methodologies used for their characterization. One of very few individuals to have been elected to membership in both the National Academy of Engineering (1982) and the National Academy of Sciences (1983), Professor Thomas’s recent awards include the Gold Medal from ASM International (2001), a Doctorate Honoris Causa from the University of Krakow, Poland (1999), election as an Honorary Member of the Japan Institute of Metals (1998), an Honorary D.Sc. from Lehigh University (1996), election as an Honorary Member of the Indian Institute of Metals (1996), election as an Honorary Member of the Korean Institute of Metals and Materials (1996), a Humboldt Senior Scientist Award (1996), and the highest award given by his home campus, the Berkeley Citation for Distinguished Achievement (1995). Professor Thomas’s dossier of service is equally rich. He devoted four years as Editor in Chief of Acta Materialia and Scripta Materialia, currently continuing as a Technical Director (1998-), another four years as President of the International Federation of Societies of Electron Microscopy, four years as a Member of the Board of Governors of Acta Metallurgica, Inc., another four years as Chairman of the Acta Metallurgical, Inc., Board of Governors, and four more years as a member of the TMS-AIME Board of Directors, among other appointments of lesser duration, such as his one year (1993) term as Director of the technology Transfer Center at the Hong Kong University of Science and Technology, and one year (1975) reign as President of the Electron Microscopy Society of America. As he engages his seventy-first year, Professor Thomas is enjoying his honorable emeritus status on the faculty after having supervised more than one hundred (100) students through the pursuit of their graduate degrees. He has taught thousands more, undergraduate, graduate, and post graduate, in lectures and seminars at home and abroad. But, as expected, Gareth Thomas is not “retired.” He currently holds the position of Vice President of Research and Development for MMFX Steel Corporation of America, returning to one of his favorite metallurgical pastimes: enhancing the performance of steel. In an aggressive campaign to extend the lifetime of rebar used in concrete construction, Thomas has claimed another success through clever microstructural design. By replacing the ferrite/carbide microstructure common to low carbon rebar-stock steels with a “dualphase” microstructure (ferrite/martensite, or austenite/martensite) through simple adjustments in processing, an astoundingly superior corrosion resistance has been demonstrated, with high payoff potential for applications in marine environments. There can be little doubt that Professor Thomas’s legacy will continue to live on through these and other advances made by materials characterization in the Thomas tradition.

R. Gronsky

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SUMMARY

Accomplished in science, accomplished in engineering, and accomplished in academia, Gareth Thomas has certainly made his mark on the historical record. It is also clear that he leaves all of us a timeless message. It first appeared in the preface to his textbook Transmission Electron Microscopy of Metals, dated 1961. “Over the last twenty-five years electron microscopy has become an increasingly popular technique for examining materials. ...The tremendous advantage of the transmission technique is, of course, that the results obtained are visual and therefore convincing.” Over the intervening forty-one years, the message has remained the same. Advancing the state of the art demands results that are both visual and convincing. Making the case for new and improved materials requires evidence that is both visual and convincing. And, as he continues to demonstrate so effectively, the execution of his successful brand of microstructural design is stunningly visual and convincing. Happy birthday to very visual and convincing guy! ACKNOWLEDGEMENTS

I shall always be grateful to Gareth Thomas for accepting me into his group during the early summer of 1972. Thanks to my colleagues Prof. M.A. Meyers, Prof. R.O. Ritchie, and Prof. M. Sarikaya for their kind invitation to contribute to this commemorative volume. Thanks also to the stalwart program managers at OBES in DOE and ERDA before them who recognized the wisdom of microstructural design and funded this nation’s effort in electron microscopy through all of these years. REFERENCES

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.

Thomas, G., and Nutting, J. (1959-60) J. Inst. Metals 88, 81. Nicholson, R.B., Thomas, G., andNutting, J. (1960) ActaMet. 8, 172. Thomas, G. (1964) “Process for Improving Strength and Corrosion Resistance of Aluminum Alloys,” U.S. Patent # 3,133,839. Kikuchi, S. (1928) Jupnn J. Phys. 5, 83. Levine, E., Bell, W.L., and Thomas, G. (1966) J. Appl. Phys. 37,2141. Okamoto, P.R., Levine, E., andThomas, G. (1967)J. Appl. Phys. 38,289. Okamoto, P.R., and Thomas, G. (1968) Phys. Stat. Sol. 25, 81. Butler, E.P., and Thomas, G. (1970) Acta Met. 18, 347. Sinclair, R., Gronsky, R., and Thomas, G. (1976) AcfuMet. 24,789. Shaw, T.M., and Thomas, G. (1978) Science 202,625. Gronsky, R., (1980) in 38th Annual Proc. Electron Microscopy SOC.Amer., G.W. Bailey (ed.), p 2. Gronsky, R., and Thomas, G. (1983) in 41st Annual Proc. Electron Microscopy SOC.Amer., G.W. Bailey (ed.), p. 310. Zandbergen, H., Wang, K., Gronsky, R., and Thomas, G. (1988) Nature 331,596. Thomas, G., and Nakagawa, A. (1 986) “High Strength, Low Carbon, Dual Phase Steel Rods and Wires and Process for Making Same,” U S . Patent # 4,613,385. Thomas, G., Johnson, S.M., and Dinger, T.R. (1989) “Method of Producing a Dense Refractory Silicon Nitride Compact with One or More Crystalline Intergranular Phases,” U.S. Patent # 4,830,800. Bemardi, J.J., Thomas, G., and Heutten, A.R. (1999) “Giant Magnetoresistive Heterogeneous Alloys and Method of Making Same.” U.S. Patent # 5,882,436.

Nan0 and Microstructural Design of Advanced Materials M.A. Meyers, R.O. Ritchie and M. Sarikaya (Editors) 02003 Published by Elsevier Ltd.

NANOCHEMICAL AND NANOSTRUCTURAL STUDIES OF THE BRITTLE FAILURE OF ALLOYS D.B. Williams’,M. Watanabe!, C. Li’ and V.J. Keast’ ‘Department of Materials Science and Engineering and The Materials Research Center, Lehigh University, Bethlehem PA 18015, USA ’Australian Key Centre for Microscopy and Microanalysis, Madsen Building University of Sydney, NSW 2006, Australia

ABSTRACT Controlling the brittle intergranular failure of metals and alloys requires understanding the structure and chemistry of grain boundaries at the nanometer level or below. Recent developments in the analytical electron microscope (AEM) permit such studies. It is now feasible to determine, in a single AEM specimen, the grain boundary chemistry (using X-ray mapping), crystallographic characteristics (using automated crystallographic analysis) and the localized bonding changes that may accompany segregation (using fine structure changes in the electron energy loss spectrum). Computerized mapping techniques permit such information to be gained from dozens of grain boundaries. Integration of this knowledge may permit the design of new alloys and new heat treatments to create materials inherently resistant to the brittle failure often caused by nanometer level grain boundary segregation of impurities and alloying elements.

INTRODUCTION Gareth Thomas is primarily responsible for the development of the transmission electron microscope (TEM) as the most versatile and integrated technique for the solution of materials problems. Throughout his long and distinguished career Gareth has always stressed the essential need to use the TEM as one of a range of techniques to solve the problem at hand, rather than selecting a problem simply to suit the TEM’s capabilities. Nevertheless, he has also pushed the development of the TEM to its fullest capabilities, particularly in the exploration of its high-resolution imaging limits, embodied in the Atomic Resolution Microscope at the National Center for Electron Microscopy at Berkeley. At Lehigh, we have taken a similar approach to attacking materials problems, but emphasized the analytical side of the TEM, particularly elemental analysis via X-ray and electron spectroscopy. So we can perhaps talk about “Microchemical Design of Advanced Materials” in this article, in line with the theme of this book. This paper will review our implementation of Gareth’s philosophy to the long-standingissue of brittle failure. Brittle failure of metals and alloys remains a serious limitation to the development of new technologies and the improvement of existing ones. The record of brittle failure studies starts in the 19‘h century [ l ] and has encompassed classic examples such as the Titanic’s rivets [2], the Boston Molasses Tank [3], the SS Schenectady Liberty Ship [4], the Hinckley Point power-generation turbine [5] and the United Airlines DClO

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crash at Sioux City [6] Despite such a long and painful history, the problem of bnttle failure remains as current as ever in its societal effects For example, during 2001, the space shuttle fleet was grounded twice, first by the discovery of cracking in the liquid hydrogen flow liners and second by beanng cracks in the crawlers that transport the shuttles to the launch site Similarly, the high-speed Amtrak Acela trams were pulled out of service following the discovery of cracks and breaks in brackets on the wheel sets of at least 8 of the 18 trains Brittle failure in metals takes many forms, e g hydrogen embrittlement [7,8], temper embrittlement [9], environmental degradation [ 101 and associated stress-corrosion cracking [ 111, fatigue failure [ 121, irradiationinduced embnttlement [ 131, liquid-metal embnttlement [ 141 and, more recently, such new phenomena as quench embnttlement [ 151 Two key factors transcend this diverse array of failure phenomena, namely the role of the grain boundary and segregation of undesirable elements to the boundary, as epitomized in Figure 1 There is a long history of research relating the structure of the grain boundary to vanous properties, including the tendency for segregation e g [ 16,171 Some studies have shown correlations between individual grain-boundary misonentation and the local chemistry, or related aspects such as grain-boundary precipitation [18,19] Such correlations have been few and have rarely been carried out on undisturbed (I e non-fractured) grain boundanes or on enough grain boundanes to permit any statistical correlation to be inferred In general it has not proven possible to relate directly the properties of grain boundanes to their structure While structure-property correlations are very strong at the structural extremes of coherent twins (C = 3 ) and random high-angle boundaries (C > -29), intermediate special boundaries (e g C = 5 , 7, 9 etc ) do not always correlate well with properties Part of the reason for this is undoubtedly that the grain-boundary structure is not the pure elemental construction that is commonly assumed, but is modified senously by local changes in the grain-boundary chemistry The analytical EM (AEM) is uniquely configured to study these phenomena because it combines high-resolution imaging, diffraction and nanometer-scale analysis of the same specimen at the same time, permitting correlation of the grain-boundary structure, misonentation, chemistry and bonding - all at the nanometer or sub-nanometer scale No other technique is so versatile at such a high resolution At Lehigh, we have been using the AEM to correlate the chemistry, structure and bonding of embnttled grain boundaries by a) performing quantitative analysis of nanometer-scale segregation to many grain boundanes using X-ray mapping (XRM) via energy dispersive spectrometry (EDS), b), for those same grain boundanes, determining their crystallographic misonentation via the latest computenzed diffraction techniques and c) relating the occurrence of segregation to changes in the atomic bonding at the grain boundary via electron energy-loss spectrometry (EELS) This paper gives an overview of the results of our integrated AEM studies in model embnttling systems such as Cu Bi, Cu-Sb and Fe-P We will first introduce bnefly the techniques used r

Figure 1: SEM images of the fracture surface of a) pure Cu and b) Cu doped with 20 ppm Bi

Nanochemical and nunostructural studies of the brittle failure of alloys

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EXPERIMENTAL TECHNIQUES X-ray Energy Dispersive Spectroscopy (XEDS) XEDS has been the most extensively used technique for measuring segregation in the AEM, starting with the pioneering studies of Dog and Flewitt [20], who first demonstrated that monolayer-level segregation was detectable in thin foils. Subsequent work has been performed, for example, by Wittig et al. [21,22], Brummauer et al. [10,11,13,23], Rtihle and co-workers [24-261 and the Lehigh group [27-301. Today, with a field emission gun scanning transmission electron microscope (FEG-STEM) the spatial resolution of XEDS can be < 2 nm and segregation can be quantified with a sensitivity approaching 0.01 monolayer [31]. In contrast with the more widespread surface- analysis techniques, in the AEM it is possible to study both brittle and ductile grain boundaries since the boundaries are contained within the thin foil and do not need to be fractured. It is of course, also possible to determine the grain boundary crystallography at the same time via routine TEM diffraction methods, as amplified in the following section. A common approach is to acquire a segregation profile by stepping the electron beam along a line perpendicular to the grain boundary. For equilibrium segregation, the width of this profile will be determined by the size of the electron probe. Two-dimensional X-ray mapping (XRM) of segregant distributions has, until recently, rarely been performed but the unique 300kV ultra-high vacuum, field emission gun VG HB 603 FEG STEM permits the acquisition of compositional maps at high spatial resolution (< 2 nm) and high sensitivity (< 0.1 monolayer) [31-331. XRM offers the advantage that any compositional variations along a grain boundary plane or other complex elemental distributions are easily observed. Many (>30) boundaries can be studied in a single smallgrained sample and it is now possible to directly relate the segregation to the grain-boundary crystallography (misorientationand plane) via computerized diffraction pattern indexing as discussed below.

Automated Crystallographyfor TEM (ACT) While significant progress has been made in XRM and related AEM methods, most studies of grain-boundary crystallography still use standard TEM methods of selected-area or convergent-beam diffraction (SAED or CBED) which are generally non-computerized, labor-intensive and rarely produce statistically valid data. Recently, however, there have been attempts to characterize grain orientations automatically in the TEM [34371. This was stimulated by the success of electron back-scatter diffraction (EBSD) in the scanning electron microscope (SEM) [38,39], which gives computerized orientation of hundreds or even thousands of grains, thus permitting full microtexture analysis and other applications [40-431. Much EBSD work has been done exploring the effects of grain-boundary misorientation (and thus local texture if sufficient grain boundaries are analyzed) on materials properties (e.g. see texts [42.43]). Unfortunately, EBSD cannot be combined with the study of grain-boundary chemistry, because it is not possible to measure grain-boundary chemistry in the SEM. Both the spatial resolution and analytical sensitivity of SEM-XEDS are too coarse [44] to detect and quantify monolayerlevel grain-boundary segregation. To overcome these limitations we have used ACT in which the beam is scanned across the specimen and, when it satisfies the Bragg condition for a given grain, the corresponding area in the dark-filed image appears bright. The intensity of each pixel is recorded as a fbction of beam tilt and rotation angle (i.e. a diMaction pattern). A grain-orientation map is constructed and the misorientation between adjacent grains is calculated from the diffraction patterns, as in the EBSD technique. Eleetron Energy Loss Spectroscopy (EELS) The ionization edges in the EEL spectrum are also used to identify and quantify segregating elements [45.46], although the technique has been less frequently applied than XEDS. However, the fine structure on the ionization edges (the energy-loss near-edge structure (ELNES)) contains information about the unoccupied density of states (DOS) and can thus probe the interatomic bonding which is possibly affected when segregants induce intergranular brittle failure or, conversely, induce ductile behavior in otherwise brittle materials (e.g. B segregation to grain boundaries in NijAI;). There have been several recent examples where ELNES has been used to elucidate such changes in the atomic bonding at grain boundaries produced by segregating elements [45,47-501. The reliability and interpretation of ELNES at grain boundaries remains controversial. The main

D.B. Williamset al.

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Figure 2: XRM of Bi segregation to grain boundaries in Cu a) localization of Bi to one grain boundary out of a complex intersection of multiple grain boundaries (see corresponding TEM bright field image in b) The grain boundary with Bi is a C=9 while all the others a e C=3 coherent or incoherent twins. In c) there are detectable differences in Bi level at the two different facets of the high angle grain boundary, indicating a role for the grain boundary plane in determining the degree of segregation The upper facet has 10 6 2 1 atoms/nm2while the lower facet has 12 4 + 1 3 atoms /nm2 In d) the map clearly reveals the presence of Bi segregation at a level of 0 8 Bi atomsinm' (reproduced from refs [3 11 by permission of Elsevier Science) expenmental difficulties are the limited spatial resolution and/or statistics It is anticipated that the introduction of sphencal-aberration correctors in STEMS [51] will increase current densities by and order of magnitude and ELNES of interfaces will become considerably more reliable (as indeed will XRM) RESULTS & DISCUSSION

XRM of Brittle Failure in Cu-Bi and Low-alloy Steels Using XRM it is possible to discern numerous aspects of the behavior of segregants that are not routinely accessible via more traditional point and line analyses As summanzed in Figure 2, it is possible to discern a), b) the absence of segregation on certain low-Z boundaries, c) differences in segregation levels between different facets and d) the detection of levels of segregation far below the monolayer level A monolayer in Cu approximates to 18 atoms/nm2 on the grain boundary so the presence of < 1 atom of Bi/nm2 as shown in Fig 2d would probably not cause bnttle failure and, therefore, would not be detected by classical surface-analysis techniques Perhaps the most intriguing result from the use of XlZM for the study of segregant distnbution on dozens of grain boundanes was the discovery that, in a highly embnttled system such as Cu-Bi, significant numbers ofthe grain boundanes exhibited NO detectable segregation [31] (see the histogram in Figure 3) This

-

Nanochemical and nunostructural studies of the brittle failure of alloys

Quenched Tempered

Stress relieved

15

embrittled

Detectabesegregation

1 1.5 x Detectable segregation 1 2.0 x Detectable segregation 1 Figure 3: A histogram of grain boundary coverage of Bi in Cu (atoms/nm2).-30% of the grain boundaries have no detectable Bi segregation. (One monolayer corresponds to -18 atoms/nm2. Reproduced from [31] by permission of Elsevier Science.

Figure 4: Pie charts showing the amount and degree of P and Ni segregation in a low-alloy steel The grain boundary segregation behavior vanes as a function of the heat treatment and the P is never present at all grain boundaries (courtesy A.J Papworth) Modified from [54].

result contradicts much of the common wisdom on the distnbution of Bi, which has traditionally been thought to be present on all grain boundanes in embnttled Cu (e g [52]) This conclusion anses probably because of the prevalence of surface analytical data (e g Auger Electron Spectroscopy (AES)) which, by its nature, pre-selects embnttled grain boundanes for analysis Parallel work [53] showed that minimum detection limits in the VG HB 603 field emission gun (FEG) AEM approached the single atom level in ideal conditions and that the detection limit for mapping of grain-boundary segregants was < 0 1 monolayers [31] So the absence of detectable grain-boundarysegregant was not a limitation of the AEM technique The distribution of P at grain boundaries in low-alloy steels was then studied to see if similar behavior occurred The evolution of grain-boundary segregation of a range of elements, subject to heat treatments that give rise to temper embnttlement was studied Typical results are summarized in Fig 4, which shows pie charts indicating changes in the amount (gray level) and degree (number of grain boundanes (30 per full pie chart)) of segregation dunng the heat treatments [54] The results indicate that, in t h s temper-embnttled condition (when the alloy shows 100% intergranular bnttle failure), P is present on some grain boundanes but it is neither present on all grain boundanes, nor is it the primary segregant In fact, both the amount and degree of P segregation has decreased from the pnor (more ductile) condition This fact in isolation strongly confirms the data from Cu-Bi in Fig 3, that bnttle matenals need not have 100% grain-boundary segregation for failure to occur, but also highlights the complexity of bnttle failure in multi-element systems So there is now corroborating evidence that embntthng species are not necessanly present at all grain boundanes Therefore, grain-boundarycharacteristics may play a greater role than hitherto believed 111 controlling the distnbution of Bi in Cu and P in steel CombinedXRMand ACT of Sb Segregation in Cu It is well known that grain boundary misorientation plays a role in segregation, accounting in part for the vanation from boundary to boundary [55] A widely accepted view is that high-angle grain boundaries are more accommodating than low-angle grain boundaries and strong segregants are present at all high-angle gram

D.B. Williamset al.

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(a) BF TEM ima!

(b) diffraction patterns (c) orientation map

I 400nm

H

Figure 5: (a) BF image in Cu-0.08 wt%Sb alloy. (b) Diffraction patterns reconstructed from the DF images (c) Reconstructed onentation map. boundanes In fcc materials, e g , segregation is suppressed only at C=3 (the most close-packed) grain boundanes (as shown in Figs 2b and c) A possible reason for our observed lack of segregation at other highangle gram boundanes in Cu-Bi and Fe-P is that crystallography plays an even more important role than hitherto suspected and some high-angle grain boundanes are inherently resistant to segregation, perhaps because of a low density of ledges, intnnsic dislocations, etc To prove this hypothesis will require measurement of nanometer-level chemistry and local misonentation from many gram boundanes and companson with segregation in controlled textures and misonentations However, to date, it has proven extremely challenging to measure both these charactenstics from significant numbers of grain boundanes in the same specimen In order to pursue the details of the relationship between the occurrence (or absence) of segregation and the gramboundary characteristics, it is necessary to map the segregation of an embrittling species at a range of grain boundanes whose misonentation is determined, e g via ACT Figure 5a is a TEM image of a Cu-0 08 wt% Sb alloy, analyzed by ACT The diffraction patterns and onentation map are shown in Figs 5 (b) and (c) and the onentation relationship between adjacent grains is shown in Table 1 XRM was performed on these grain boundanes and the Sb images are shown in Figure 6 Clearly the segregation varies, while Sb is detectable on most gain boundanes, it is not detectable on #3, 4,s and 10 (and it has been shown this is not simply due to factors such as tilt of the grain-boundary plane) Again the crucial point is that a major embnttling agent is not present on many grain boundanes, supporting our data from Cu-Bi and Fe-P From Table 1 only one grain boundary (#3) is close to a E=3 structure, the rest are random high-angle grain boundanes Thus it has been demonstrated via a combination of XRM and ACT that a significant fraction (> -30%) of highangle grain boundanes, in 3 different strongly-segregating systems, Cu-Bi, Fe-P and CuSb exhbit no detectable segregation Therefore, it is reasonable to conclude that alloys in which such segregant-free grain boundanes are more prevalent should show enhanced resistance to segregation and any associated bnttle failure One method by which an increased fraction of segregation-resistant grain boundanes could be produced is grainboundary engineenng (GBE) which produces textures with a majonty of low-C grain boundanes, Such grain boundanes would shifi the distnbution of gram-boundary chemistry m Figure 3 towards the left-hand end of the spectrum, thereby significantly reducing the number of gram boundanes to which segregation can occur The concept of selectively enhancing the number of low-C grain boundanes through GBE, in order to reduce embnttlement was first proposed by Watanabe [41] As well as the pioneering work of Watanabe, GBE has also been implemented by other groups including, e g Lehockey et a1 156 571 and Kumar et a1 [58 591 GBE has

Nanochemical and nunostructural studies of the brittle failure of alloys

17

Sk Nt%)

Figure 6: Sb composition maps. The segregation between different grain boundaries is clearly not homogeneous and several grain boundaries have no detectable segregation although they are high-angle grain boundaries. TABLE 1 Axidangle pairs calculated from the ACT results for the grain boundaries numbered in Fig. 6 Boundary 1 2 3 4 5

Angle-axis 52'@[-11 -5 61 45"@[4 -2 -31 59"@[8 9 -81 -60°@,[1 1-11 28'@[15-1 I ] 49"@[-7 -8 121

Boundary 6 7

Angle-axis 43"@[9 -8 51 47"@[-2 -1 -51

8

47'@[2 5 -11

9 10

29'@ 12 -3 -71 40"@[-17 1-61

revealed the strong effect of the dzstnbutzon of grain boundary structures on properties, including embnttlement, and shown how, via thermo-mechanical processing (TMP), it is possible to engineer the distnbution of low-C grain boundaries to improve greatly the mechanical and other (e g corrosion) properties Implicit in GBE is the concept that manipulating the gramn=boundary structure may result in manipulating the chemistry, given the long-understood relationship between the two Since GBE produces a large fraction of

D.B. Williams et al.

18

2=3 grain boundaries (which exhibit no segregation) the possibility that GBE techniques will produce an inherently segregation-resistanttexture are now ripe for study using a combination of XRM and ACT. Energy Loss Near-Edge Fine Structure (ELNES) Studies of Embrittled GBs In addition to the role of the boundary crystallography in governing segregation it is important to discern the role of the segregant when it reaches the boundary plane. As has been noted, while this article emphasizes the segregant's role in brittle failure, segregants can also act to improve the ductility of otherwise brittle materials such as B in Ni3Al. So the segregation itself is not a necessary prerequisite for brittle failure. Clearly the segregant must be changing the character of the bonding at the grain boundary to induce either brittle failure or, conversely, ductilization. To probe the bonding changes at the nanometer level is also possible in the AEM using energy-loss spectrometry fine structure studies. We have demonstrated a clear relationship between the presence of Bi at grain boundaries in Cu and a change in the ELNES. The presence of Bi changes the electronic structure of the Cu but only within <1 nm either side of the grain boundary [29] and a small increase in intensity at the Cu L23 edge onset is observed, as shown in Figure 7. While the change in the ELNES intensity is small, it is consistently reproducible and is not due to spectrometer misalignment, oxygen segregation or specimen thickness effects, all of which can produce changes in ELNES intensity [49]. The peak is not detected at C=3 coherent twins where no Bi segregates (see Figure 2). We originally calculated that this increase in ELNES intensity at the edge onset arises from hybridization between Bi-p and Cu-d states, creating empty d states above the Fermi level and a narrowing of the filled d states [31]. Recently, Muller [60] proposed that the extra intensity arises from a core-level shift induced by the narrowing of thefilled d states, which also explains the embrittling effect. This latter proposal is also consistent with our calculations and we now believe that this is perhaps the best explanation of both the experimental data and the calculations. Similar changes have been observed in Sbdoped Cu and S-doped N, both of which embrittle the Cu while Ag segregation, which has no effect on the Cu, produces no detectable change. In contrast, studies by Muller and co-workers [61] on the ductilizing effect of B in brittle Ni3Al reveal the reverse effects to that in Cu-B, Cu-Sb and Ni-S. The Ni L23 edge from grain boundaries with B segregation is similar to the Ni L23 edge from Ni in bulk Ni3A1, i.e., the ELNES intensity decreases with B additions. Muller et al. show how these changes relate to differences in hybridization of the Ni d states and also how bond energies can be estimated directly 920 930 940 950 960 from the EELS spectrum. This is consistent with a rule of thumb for alloys with a d shell Energy Loss (eV) more than half full, that the larger the increase in ELNES intensity, the weaker the Figure 7: Change in the Cu L23 ELNES between a Cu grain bond. boundary with Bi segregated to it and pure Cu. The slight increase in the ELNES can be interpreted in terms of a These data imply that changes in the Cu L23 change in the Cu bonding at the boundary. Reproduced from ELNES are not due simply to segregation, [27] by permission of Elsevier Science. but onlv to seeregation that causes embrittlement. A simple interpretation of the effect of Bi on the Cu bonding leads to the conclusion that a cosegregant at the GB, which has the opposite effect on the ELNES (i.e. depending on whose theory is correct, U

"

Nanochemical and nunostructural studies of the brittle failure of alloys

19

broadens the filled 3d states, reverses the core-level shift, or fills in the empty Cu 3d states, or reverses the transfer of charge to the Cu) should also result in the restoration of ductility. According to the work of Muller et al., already cited, B has just this effect in Ni3A1. While early work [62] indicates that Fe lowers the amount of Bi segregation, Fe was not detectable on the grain boundaries. More recent studies by Muthiah [63] show that P does not de-embrittle Cu-Bi, so no effective co-segregant has been found. However, no comparative study of co-segregation of B in Cu-Bi has been performed and this is also an area in which combined X R M and ELNES may produce a significant improvement in our knowledge of the role of grain-boundary chemistry controlling mechanical properties. The ability to nullify embrittling species by controlled additions of co-segregants would indeed be a major step on the way to scientific tailoring of grain boundary chemistry to control the mechanical properties of materials.

SUMMARY Analytical electron microscopy now permits the simultaneous mapping of the grain-boundary chemistry and grain boundary misorientation. Studies of dozens of grain boundaries in several systems indicate that embrittling segregants are absent at a significant fraction of high-angle grain boundaries, contradicting current theories. This opens the possibility of controlling brittle failure by developing segregant-resistant textures via GBE or some similar process. Alternatively, it has been shown that segregants cause embrittlement by slight changes in the local electronic structure of GBs. Such changes in electronic structure might be reversed by careful choice of co-segregating species. These two approaches offer novel methods for designing advanced materials that are inherently resistant to the age-old problem of brittle intergranular failures. In either case the process will be considerably less expensive than current methods which rely on removing the offending segregant by removing the undesired element($ from the alloys during processing.

ACKNOWLEDGEMENTS DBW and VJK acknowledge the financial support of the National Science Foundation through grant DMR 99072670. MW acknowledges the support of the Materials Research Center at Lehigh University.

REFERENCES 1 2 3 4 5 6 7

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10 11 12 13

Hampe, W.Z. (1874) Berg-Hutten u. Salinen-Wese 22,93. http://www.tms.or,~lpubs/iournals/JOM/~8Ol/Felkins-~8Ol .html ht~://www.civ.toronto.edu/f~stuffldisaster/boston.htni htto://web.mit.edulcourse/3/3.11 /www/vri/shin.pdf http://www.shuclint.com/tekbrefs/0407pefeat4.pdf http://www.cndc.iastate.edu/ncce/K12/aircrash.htm Gaudett, M.A. and Scully, J.R. (2000) Metall. Mat. Trans. A 31A, 81. Kolman, D.G. and Scully, J.R. (2000) Corrosion Science 42(11), 1863. Lalam, S.H., Bhadeshia H.K.D.H. and MacKay, D.J.C. (2000) Science and Technologyof Weldingand Joining 5,338. Bruemmer, S . (1999) Materials Science Forum 294-296, 75. Gertsman, V.Y. and Bruemmer, S.M. (2001) Acta mater. 49,1689. Gasem, Z.M. and Gangloff, R.P. (2000) Materials Science Forum 331-337, 1479. Bruemmer, S.M., Simonen, E.P., Scott, P.M., Andresen, P.L., Was, G.S. andNelson, J.L. (1999)J. Nucl. Mat. 274,299.

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D.B. Williamset al. Wynblatt, P. and Takashima, M. (2001) Interface Science 9, 265. Krauss, G. (2001) Metall. and Muter. Trans. A 32A, 861. Howe, J.M. (1997). Interfaces in Materials. Wiley, New York, NY. Sutton, A.P. and Ballufi, R.W. (1995). Interfaces in Crystalline Materials. Oxford University Press, Oxford, UK. Williams, D.B. and Edington, J.W. (1976) Acta metall. 24, 323. Michael, J.R. and Williams, D.B. (1986). In: Interface Migration and Control of Microstructure, pp. 7381, Pande, C.S., Smith, D.A., King A.H. and Walter, J. (Eds.). American Society for Metals, Metals Park, OH. Doig, P. andFlewitt, P.E.J., (1978)J. Microsc. 112, 257. Wittig, J., Sinclair, R. and Viswanathan, R. (1985) Scripta metall. 19, 111. Wittig, J., Bentley, J., Al-Sharab, J.F. and Evans N.D. (2001). In: Electron Microscopy and Analysis, 168, pp. 429-432, Institute of Physics, Bristol and Philadelphia. Brummauer, S.M. and Thomas, L.E. (2001) Surface and Interface Analysis 31, 571. Albers, A,, Mullejans, H. and Riihle, M. (1997) Ultramicroscopy 69, 105. Riihle, M., Gemming, T., Kienzle, 0. and Schweinfest, R. (1999). In: Electron Microscopy and Analysis, 161, pp.1-8, Institute of Physics, Bristol and Philadelphia. Schmidt, S., Sigle, W., Gust, W. and Riihle, M. (2002) Z. Metallk. 93, 428. Baumann, S.F. and Williams, D.B. (198)J. Microsc. 123,299. Michael, J.R. and Williams, D.B. (1984)Metall. Trans. 15A, 99. Bruley, J., Keast, V.J. and Williams, D.B. (1996)J. Phys. D. (Appl. Phys.) 29, 1730. Keast, V.J., Bruley, J., Rez, P., Maclaren, J.M. and Williams D.B. (1998) Acta mater. 46,481. Keast, V.J. and Williams, D.B. (1999) Acta mater. 47, 3999. Williams, D.B., Watanabe, M., Carpenter, D.T. and Barmak, K. (1998) Mikrochim. Acta S15 49. Cqenter, D.T., Watanabe, M., Barmak, K. and Williams D.B. (1999) Microsc. Microanal. 5,254. Jensen, D.J. (1997) Ultramicroscopy 67,25. Schwarzer, R.A. (1997) Ultramicroscopy 67, 19. Wright, S.I. and Dingley, D.J. (1998) Materials Science Forum 273-275,209. Dingley, D.J. (2000). In: Electron Backscatter Diffraction in Materials Science, pp. 1-18, Schwartz, A.J., Kumar, M. and Adams, B.L. (Eds.). Kluwer Academic Press, New York, NY. Adams, B.L., Wright, S.I. and Kunze, K. (1993) Metall. Trans. A A24, 819. Field, D.P. (1997) Ultramicroscopy 67, 1. Goyal, A., Specht, E.D., Wang, Z.L. and Kroeger, D.M. (1997) Ultramicroscopy 67,35. Watanabe, T. and Tsurekawa, S. (1997) Acta muter. 47,4171. Randle, V. (1996.) The Role of the Coincidence Site Lattice in Grain Boundary Engineering. Institute of Metals, London. Schwartz, A.J. Kumar, M. and Adams, B.L. (Eds.) (2000). Electron Bachcatter Diffraction in Materia1.s Science. Kluwer Academic Press, New York, N Y . Goldstein, J.I., Newbury, D.E., Echlin, P., Joy, D.C., Romig, Jr. A.D., Lyman, C.E., Fiori, C. and Lifshin, E. (1992). Scanning Electron Microscopy andX-ray Microanalysis. Plenum Press, New York, NY. Muller, D.A., Subramanian, S., Batson, P.E., Silcox, J. and Sass, S.L. (1996) Acta muter. 44, 1637. Bruley, J., Cho, J., Chan, H.M., Harmer, M.P. andRickman, J.M. (1999)J. Amer. Ceram. SOC.82,2865. Ozkaya, D., Yuan, J., Brown, L.M. and Flewitt, P.E.J. (1995)J Microsc. 180,300. Keast, V.J., Bruley, J., Rez, P., MacLaren, J.M. and Williams, D.B. (1998) ActaMater. 46, 481 Bruley, J., Keast, V.J. and Williams, D.B. (1999) Acta muter. 47,4009. Browning, N.D., Buban, J.P., Prouteau, C., Duscher, G. and Pennycook, S.J. (1999) Micron 3,425. Krivanek, O.L., Delby, N. and Lupini, A.R. (1999) Ultramicroscopy 78,l. Wolski, K., Laporte V., Marie, N. and Biscondi, M. (2001) Interface Science 9, 183. Watanabe, M. and Williams, D.B. (1999) Ultramicroscopy 78, 89.

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Williams, D.B., Watanabe, M., Papworth, A.J. and Li, J.C., (2002) Thin Solid Films (in press, publication expected 12/02). Briant, C.L. (1983) Actu metull. 31,257. Lehockey, E.M., Palumbo, G. and Lin, P. (1998) Scriptu muter. 39,353. Lehockey, E. M., Palumbo, G. and Lin, P. (1998) Metall. andMater. Trans. A, 29A, 3069. Kumar, M., Schwartz, A.J. and King, W.E. (2002) Actu muter. 50,2599. Kumar, M., King, W.E. and Schwartz, A.J. (2000) Acta muter. 48,2081. Muller, D.A. (1998) Phys. Rev. B58,5989. Johnson,W.C., Joshi, A. and Stein, D F. (1976) Metall. Trans. 7A, 949. Muthiah, R.C. (1995) Project Report to International Copper Assoc., University of Pennsylvania, Philadelphia, PA.

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Nan0 and Microstructural Design of Advanced Materials M.A. Meyers, R.O. Ritchie and M. Sarikaya (Editors) 02003 Published by Elsevier Ltd.

Transmission Electron Microscopy Study of the Early-Stage Precipitates in Al-Mg-Si Alloys H. W. Zandbergen, J. H. Chen, C. D. Marioara, and E. Olariu National Centre for HREM and Netherlands Institute for Metals Research, Delft University of Technology, Rotterdamseweg 137,2628 AL Delft, The Netherlands

ABSTRACT Early-stage precipitates in the Al-Si-Mg based 6xxx alloys include solute clusters, GP-zones (including the pre-p’ phase), the p” phase as well as the so called Q particles (if a small amount of Cu is added in the alloys). Using high-resolution transmission electron microscopy and quantitative electron diffraction, these precipitates are studied in details. The p” phase has a monoclinic structure with the composition MgSSih. The structure of thc pre-P” phase is quite similar to that of the p” phase but the atom positions are more close to that of the A1 lattice. It is pointed out that Al poorly-develops many of the structures of the precipitates, due to the presence of defects and substitutions of Mg and Si.

INTRODUCTION The precipitation behaviour in Al-Si-Mg system has been extensively studied. Although there are still disagreements on the sequence, structure, and chemistry of the metastable precipitate, it is generally accepted that the precipitation in this alloy system can be described as [ 1-21:

SSSS + Solute clusters -+ GP(1) (including pre-p”)

-+ GP(II)/p’ -+ p’ -+ p ,

where SSSS = Super Saturated Solid Solution. The latter two stages are over-aged conditions. If the alloy contains excess Si, the formation of more Si-rich phases will overlap with the above precipitation sequence. Small additions of copper to these alloys may introduce some additional phases, e.g., Q - AlsCu2MgsSi6, in the equilibrium condition [3], but the major ageing sequence is basically the one shown above. The maximum hardness in these alloys is obtained when the alloys contain a combination of Guinier Preston (GP-I) zones [4-51 with diameters of about 2.5 nm and larger needles of p’ [6-81 with a typical size of about 4 3 4 x 4 ~ 5 0nm3. The number density of both precipitates is high; for the p” needles a number density of 10 /pm is normal, corresponding to a volume fraction of only nearly 1%. The GP-I zones are assumed to be strongly enriched in Si and Mg and to have a structure very similar to that of the surrounding Al matrix, whereas the p’ phase has a different structure. The monoclinic unit cell of p’ is reported to have the cell dimensions a = 1.53(1) nm, b = 0.405 nm, c = 0.67(2) nm, p = 106(2)’. For a full understanding of the mechanisms of strength enhancement, knowledge of the structures of the various phases is essential. Because of the small size of the j3” precipitates, their low volume fraction and their occurrence in 24 orientations in the Al matrix conventional structure determination (for example by X-

23

24

H. W. Zandbergen et al.

ray and neutron diffraction) is not possible. Conventional high-resolution transmission electron microscopy (HREM) also does not provide sufficient detail to elucidate the structure. Therefore we applied two techniques: i) exit wave reconstruction from a through focus series of HREM images [9-111, which was used to construct a rough structure model and ii) a least-squares structure refinement [12-131 using electron diffraction data and taking dynamic diffraction fully into account. Dynamic diffraction occurs for electrons even in very thin crystals because the electron-matter interaction is very strong (about lo5 times larger than for X-rays). The dynamic diffraction results in changes in the relative intensities of the reflections as a function of the specimen thickness. Therefore kinematical diffraction, which is valid for almost all X-ray and neutron diffraction, cannot be applied. As shown in this paper the inclusion of dynamic scattering in the refinement procedure leads to much more reliable results in particular for specimen thickness above 10 nm. For the GP-I zones or other poorly-developed particles, however, the electron diffraction technique is difficult to apply. Hence through-focus exit-wavefunction reconstruction (TF-EWR) was employed to access the structural details of the ill-defined precipitates [ 14-161, which are technologically relevant. For example, these poorly-developed particles play a role in the fast increase in hardness of Al alloys for automotive body panel applications [17-221. Further more, to detect the solute clusters, which are fully coherent with the matrix, atom probe field-ion microscopy (APFIM) plays an important role [23, 1-21. MATERIALS AND EXPERIMENTALS DETAILS All Al alloys were prepared following a standard procedure including casting, hot rolling, cold rolling, homogenization, solution treatment at around 540”C, quenching to room temperature, natural ageing at room temperature, and final hardening ageing or annealing at temperatures between 150°C and 185°C. Three types of Al-Mg-Si alloys were investigated (i). For the structure determination of the p” phase we used an A1-0.5Mg-0.53Si (weight percent) alloy, hardening aged at 185°C for 5 hours. (ii). For the structure determination of the pre-P” phase (GP-I) we used an A1-0.6Mg-0.9Si alloy, hardening aged at 150OC for a time varying from 4 hours to 9 days. The annealing temperature, 150°C, falls in the temperature interval in which the p’ phase is still stable. (iii). For the structure analysis of poorly-developed GP-I zones and poorly-developed Q particles we used an A1-0.43Mg-1.2Si-0.15Cu alloy, aged at 180°C for 30 minutes. All these alloys contain small amounts of Mn and Fe. The HRTEM foils were prepared by electropolishing in a Tenupol-3 machine using an electrolyte consisting of 1/3 HNO3 in methanol. The samples were examined in a high resolution Philips CM30UTIFEG operating at 300 kV. Through-focus series of HREM images of precipitates were recorded for constructing exitwavefunctions [ 14-161. Electron nanodiffraction patterns of precipitates were taken for structure refinement using MSLS software [12-131. The through focus exit wave reconstruction uses the focus dependence of the image distortion by the electron microscope to correct for this distortion [lo]. A major advantage of the exit wave is that the information, which is delocalized in the HREM images resulting in a blurred image, is restored to its origin [lo-111. In addition to the advantage of the deblurring, the noise level of the exit wave is less than for a single image since 15-20 HREM images are used for the reconstruction. In the present work, the BriteEuram meeting software package written by Coene and Thust was used for the reconstruction. RESULTS AND DISCUSSIONS The P p h a s e

EDX element analysis of about 50 p’ precipitates indicates a Mg/Si atomic ratio of approximately 0.8. Some precipitates showed a considerable higher Mg/Si ratio. Such a higher ratio is in agreement with the presence

H. W. Zandbergen et al.

26

From Figure la a trial model for the structure refinement was obtained in the following way. From the coherency of the interface between the p’particle and the A1 matrix it was concluded that the Si and Mg atoms are located at or close to the y = 0 and y = 1/2 planes. From the unit cell volume it was concluded that the number of atoms in the unit cell is 22. Taking into account the Mg/Si ratio as determined by element analysis it follows that the composition is probably MgS Si,. Next, atoms were placed at the dark spots in the exit wave image. The darkest spots were assumed to be two Si atoms in different layers, being so close together in projection that they merge into one spot. The dark spot with the largest distances to the other black dots was assumed to be Mg, since Mg has a larger radius (0.155 nm) than Si (0.115 nm). The remaining Mg and Si atoms were assigned to the other black dots based on the radii of Mg and Si. This model was used as the starting model for the MSLS refinement using simultaneously 7 electron diffraction data sets along [OlO] or [OOl]. These data were collected from p” particles containing no defects, because the presence of defects results in streaking or extra peaks. Because the electron diffraction data were recorded from areas containing p” and the A1 matrix, the A1 reflections were omitted and with that about 10% of the p” reflections [12-131. The refinements were done in space groups C2/m, C2, Cm and C1, which were suggested by the systematically absent reflections [ 131. The refinements in the lower symmetric space groups did not lead to significantly better fits nor to different atom positions, indicating that the space group is C2/m. The resulting atomic parameters arc given in Table 1. The overall R-value after refinement was 3.1%. Table 2 lists the number of reflections, the refined crystal misorientation and the R-values of each diffraction pattern. TABLE 1 Atomic positional parameters and isotropic temperature factors, B, for MgsSi,, with a = 1.516(2) nm, b = 0.405 nm, c = 0.674(2) nm, p = 105.3(5)’ and space group C2/m X

Y

Z

B

Mg( 1)

0

Mg(2)

0.3459(8)

0

0

0.5(2)

0

0.21 7(1)

1.0(2)

Mg(3)

0.4299(10)

0

0.652(3)

0.8(2)

Si(1)

0.0565(7)

0

0.652(3)

1.1(2)

Si(2) Si(3)

0.1885(8)

0

0.224(2)

0.5(2)

0.617(2)

2.5(4)

I 0.2171(9) I

0

1

Table 2 also gives the R-values when only kinematical diffraction is taken into account [12-131. Obviously for the thicker specimen areas these R-values are much higher than those obtained by including dynamic diffraction. This indicates that even for a material like MgsSi, with only light elements the dynamic diffraction is very significant for small specimen thickness (about >10 nm). Consequently, it is important to include the dynamic scattering in the structure refinement. Moreover, the use of diffraction data from areas with different thickness adds substantially to the reliability of the structure refinement. A perfect p’atomic structure [ 131 overlapped on a simulated exit wave is shown in Figure 2. Figure 2 shows the amplitude of the exit wave, where the black dots represent the atomic positions. The p” can be derived from a FCC Al lattice by relatively small shifts of the atoms, except for one Mg atom (Mgl). The atoms 2,4, 6 and 8 atoms in Figure 3 (A1 replaced by Mg) are shifted inwards while the atoms 3 , 5 , 7 and 9 (replaced by Si) are shifted outwards. This change in atom positions forces the middle atom (Mgl) to change its height over 0.2 nm. These Mg( 1) Mg4Si4 clusters are distributed such that a monoclinic unit cell is formed.

Transmission electron microscopy study of the early-stage precipitates in Al-Mg-Si alloys

21

TABLE 2

Data on the diffraction sets used for the refinement of Mg,Si, listed in Table 1. The kinematical R-values are obtained after refinement of only the scale factors keeping all other parameters fixed and using occupancies of only 1% [I21 zone

number

refined

obs. refl. thickness

crystal misorientation x

Y

2

R-value (%) MSLS

kinematic

[OlO]

50

6.7(5)

8.3

0

-2.3

3.0

3.7

[OlOl

56

15.9(6)

2.6

0

-1.8

4.1

8.3

[OlO]

43

16.1(8)

-1.7

0

0.3

0.7

12.4

[OlO]

50

17.2(6)

-5

0

-1

1.4

21.6

roioi

54

22.2~)

-5.9

0

2.5

5.3

37.3

[OOl]

72

3.7(3)

-3.9

4.5

0

4.1

4.5

[OOl]

52

4.9(6)

3.6

-1.9

0

6.8

9.3

m--

-7

0 Mg z=O, 0 Mg z=1/2 0

Alz=O,

0 Alz=1/2

Si z=O,

0

Si z=1/2

Figure 2: A perfect p’ atomic structure overlapped on a simulated exit wave The p r e - p or GP-Z zones

Conventional TEM reveals a high density of very fine precipitates formed in the very beginning of the precipitation process, as shown in Figure 3. The precipitates are needles oriented along <100>Al, like the p’ phase.

H. W.Zundbergen et al.

28

I

m

.---Y

W 8

P . .

e

Figure 3: Bright field images of samples with different annealing time: (a) 4 hours, (b) 11 hours (c) 2 days and (d) 9 days. All images are taken along the A1 zone axis, as well as Selected Area Diffraction Patterns from: (e) a 4-hours -sample and (0 2-days-sample. The volume fraction of particles (estimated from the number of particles and their average dimensions) is 0.5%-1.6%. Although the samples with short ageing time have a twice as high particle density they show a lower hardening effect. This indicates that the precipitates in these samples are more coherent with the matrix. This is in agreement with the fact that the diffuse streaks in the SADPs are less pronounced and more diffuse in the 4-hours and 11-hours aged specimens (Figure 3). If all Mg and Si atoms from the SSSS form p” (MgsSih), then the volume fraction of precipitates must be 1.3%. Because our data suggest that this value could be exceeded it is very likely that A1 is a constituent of the precipitates. In exit waves of p” in [OlO] orientation the dominant image feature is a black dot (the Mgl atom) successively surrounded by a white and a black oval around it (see Figure 2). This image feature looks like an ‘eye’. In [OlO] orientation the p” structure image is composed with these ‘eyes’ linked together by Si-Si bonds. Reconstructed exit waves of the samples aged at 150°C for 11 hours or 9 days are shown in Figures 4 and 5 . As in Figure 2 the amplitude of the exit wave is shown in these figures, such that black dots represent atomic positions. The reconstructed exit waves also show eye-like image features although less pronounced than in the exit wave for p”.

Transmission electron microscopy study of the early-stage precipitates in Al-Mg-Sialloys

29

Figure 5: Two exit waves of particles of the 11 days aged sample imaged along 4 0 0 2 Al

The particle in Figure 5a is composed of 1.5 x 3 p’ unit cells [13], and it has interatomic distances being in good agreement with literature data. Because of this we conclude that after annealing at 15OOC for 9 days the precipitates have a p’ structure despite their small size. In contrast, the particles in the 1I-hour specimen must have a different atomic arrangement, based on a detailed analysis on these images. The analysis of the interatomic distance [ 141, leads to two structural models for the two particles of the 11-hour aged specimen, as shown in Figures 6 and 7. It is very probable that the A1 content varies in the different precipitates in particular in the 11-hour aged sample. For example the particle in Figures 5a and 6 is more coherent with the matrix than that of Figures 5b and 7 and therefore it may contain more A1 as this fits better with the interatomic distances observed. If this is the case, some of the Si atoms around the Mg(1) atom might be replaced with Al. However, we did not substitute Si atoms by A1 in Figures 6 and 7, because this might also vary along the viewing direction.

H. W.Zandbergen et al.

30

Averaged interatomic distances: 1-2=1-6=271pm; 1-4=1-8=282pm; 1-3=1-7=288pm; 1-5=1-9=287pm; 5-10=270pm Unit cell:

a=1,457nm, b=0.40nm, c=0.683nm, p=104.9”

O M g

OW

Al z=O,

0 Al

0

Si z=O, 0 Si

Figure 6: Atomic structural model proposed for the particle in Figure 5 (left) for the 1Ih sample Averaged interatomic distances: 1-2=1-6=255pm; 1-4= 1-8=276pm; 1-3=1-7=302pm; 1-5=1-9=297pm; 5-10=272pm Unit cell: a=1.478nm, b=0.405nm, c=0.674nm, !3=106.8’

.Ms

Ow

.A1

z=O.

0 A1

0 Si z=O.

o Si

Figure 7: Atomic structural model proposed for the particle in Figure 5a for the 1ih sample Thepoorly-developedpre-p” or highly coherent GP-I zones We have seen that when the age hardening time is getting short, the hardening precipitate structures formed can be deviated far from the standard p’, as presented in Figure 1. In general, the precipitates formed in the very early stage have poorly developed crystal structures, which are more coherent with the Al matrix. These structures have to be studied because of their significance to automotive industry, where a quick paint bake response of the A1 alloys is required. Here we will show some different forms of the poorly developed or highly coherent GP-I zones, which appear upon a 30-minute hardening age at about 180’C. Figure 8 shows a highly coherent GP-I zone formed in half an hour of age hardening after a very short natural ageing. The interesting points of this precipitate are the following: (i). It still has a P”-like monoclinic unit cell with a = .460nm, b = 0.405nm, c = 0.653nm, and P = 105.4’. (ii). It is highly coherent with the Al matrix with [loo] p // [270]~1,[OlO] p // [001]AI, and [001] p // [ ? i O ] A l .

Transmission electron microscopy study of the early-stage precipitates in Al-Mg-Si alloys

31

Since the structure is more coherent with the A1 matrix, as compared with the p” phase, there should be more A1 atoms remained in the structure, as discussed in the previous section. Since these particles are poorly-developed in terms of crystal structure, both through-focus exitwavefunction reconstruction and image simulation are needed, in order to determine their atomic structures.

Figure 8: A highly coherent p-like monoclinic GP-I zone Thepoorly-developed Q particles

Figure 9 is a typical high-resolution image of another type of poorly-developed precipitates with a lath shape. Owing to the fact that these precipitates are poorly-developed in one of the three dimensions, the periodic arrangement of alloy elements in the particles cannot be seen clearly in the images. By combining the high-resolution images with their diffiactograms (Fourier transform of the image), we can deduce that these particles take ( 5 1 0 ) as ~ their ~ habit planes. They grow rapidly along the directions parallel to the habit planes, but their development along the directions perpendicular to their habit planes is very much restricted. According to the characteristic crystallographic relations between these particles and the matrix, they can be identified as the precursors of the Q phase (e.g., Weatherly et al. 2000 [3]). However, we should mention that the Q particles are not found everywhere in the matrix. It is also found that when a Burgers circle is drawn around such a particle in HRTEM images, the circle is not closed, indicating a dislocation as the nucleation site of the Q particle.

Figure 9: Poorly-developed Q particles (a and c images) with the diffractogram of a image in the middle

32

H. W. Zandbergen et al.

Again for such ill-defined Q particles, diffraction techniques are not suited to determine the atomic structural details of these clusters. Atomic imaging with ultra-high resolution is therefore needed to fulfill the tasks. Further work is on the way to investigate the atomic structures of such ill-defined precipitates, in order to fully understanding their forming mechanisms in the A1 matrix. CONCLUSIONS Using high-resolution transmission electron microscopy and quantitative electron diffraction, we have studied a number of the early-stage precipitates in the Al-Si-Mg based 6xxx alloys, including different GPzones (the pre-p’ phase), the p” phase as well as the so called Q-phase particles (if a small amount of Cu is added in the alloys). From the obtained results, we can draw the following conclusions: In the structure refinement of the p’(MgsSib) dynamic diffraction was fully taken into account, (i) allowing the accurate elucidation of an unknown structure, in particular by using data sets from various orientations and thicknesses. Since the crystal misorientation is also refined, a mistilt can be used to enhance the resolution in certain directions in diffraction space. The results from the MSLS refinement are more reliable than those from the TF-EWR (and HREM), because the diffraction information extends about twice as far (0.14 nm for TF-EWR versus 0.07 nm for electron diffraction). The structure of MgSSi6is very likely to be correct given the low R-values obtained. TF-EWR is a powerful tool for accessing the atomic structural details of nano-scale precipitates, (ii) especially those studied here. It can provide a good starting model for a further structural refinement based on microdiffraction data sets taken from the small precipitate crystals. Moreover when precipitates to be studied become very small (a few nanometers in size) or ill-defined in terms of their crystalline structures, TF-EWR is a usehl method for the structure determination. GP-I zones may have different structures depending on the temperatures and ageing times used, (iii) but our study indicates that all these structures have a close relation with the standard monoclinic structure of the p” phase. In general, GP-I zones are more coherent with the A1 matrix, indicating A1 atoms are incorporated in their structures. We have proposed two atomic models for GP-I zones. Incomplete Q-phase particles appear around dislocation sites even for a short annealing time (30 (iv) minutes). To study these poorly-developed precipitates, advanced HREM techniques with ultra-high resolution, e.g., TF-EWR, must be applied in association with image (exit-wavefunction) simulation. ACKNOWLEDGEMENTS This research was carried out under project number MC4.98047 in the Framework of the Strategic Research program of the Netherlands Institute for Metals Research in the Netherlands (www.nimr.nl). Dr. L. Zhuang (Corus R & D, The Netherlands) is appreciated for providing some of the samples. REFERENCES 1. Murayama, M. and Hono, K., Pre-precipitate clusters and precipitation processes in Al-Mg-Si alloys, Acta Mater. 47 (1998), 1537-1548. 2. Edwards, G . A,, Stiller, K., Dunlop, G . L. and Couper, M. J., The precipitation sequence in Al-Mg-Si alloys, Acta Mater. 46 (1998), 3893-3904. 3. G . C. Weatherly, A.Perovic, N. K. Mukhopadhyay, D. J. Lloyd and D. D. Perovic, The precipitation of the Q phase in an AA6111 alloy, Metall. Mater. Trans. A (2001), 213-218. 4. A. H. Geislet and J. K. Hill, Acta Cryst. 1,238 (1948). 5 . G. Thomas, The ageing Characteristics of Aluminium Alloys: Electron transmission study of Al-Mg-Si alloys, J. Inst. Met. 90 (1961), 57-62. 6. L. Zhen, W.D. Fei, S.B. Kang, H.W. Kim: Journal ofMuterial Science, Precipitation behavior of Al-MgSi alloys with high silicon content, 32 (1997), 1895-1902.

Transmission electron microscopy study of the early-stage precipitates in Al-Mg-Sialloys

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7. M. Takeda, F. Ohkubo, T. Shirai, K. Fukui: Journal of Materials Science, Stability of metastable phases

and microstructures in the ageing process of Al-Mg-Si ternary alloys, 33 (1998), 2385-2390. 8. S. J. Andersen, Quantification of the MgzSi p" and p' phases in AlMgSi alloys by transmission electron microscopy, Metallurgical and Materials Transactions A , 26 (1995), 1931-1938. 9. D. Van Dyck and M. Op De Beeck, Proc. 12th Int. congress on Electron Microscopy, p.26 San Francisco Press, Seatle (1992). 10. Coene, W., Janssen, G., Op De Beeck, M. and Van Dyck, D., Phase retrieval through focus variation for ultra-resolution in field-emission transmission electron microscopy, Phys. Rev. Lett. 69 (1992), 37433146. 11. C.L. Jia and A. Thust, Investigation of atomic displacements at a 1 3 { 1111 twin boundary in BaTi03 by means of phase-retrieval electron microscopy, Phys. Rev. Lett. 82 (1999), 5052-5055. 12. H.W. Zandbergen, S.J. Andersen and J. Jansen, "Structure determination of MgsSis particles in A1 by dynamic electron diffraction studies", Science Vol. 277 (1997), 1221-1225. 13. S.J. Andersen, H.W. Zandbergen and J. Jansen et al., "The crystal structure of the p" phase in Al-Mg-Si alloys", Acta Mater. Vol. 46 (1998), 3283-3298. 14. Marioara, C. D., Andersen, S. J., Jansen, J. and Zandbergen, H. W., Atomic model for GP-zones in a 6082 Al-Mg-Si system, Acta Mater. 49 (2001) 321-328. 15. J. H. Chen, K. Urban, B. Kabius, M. Lentzen, J. Jansen and H. W. Zandbergen, Atomic imaging in aberration-corrected HRTEM with application to A1 alloys, Microsc. Microanal. 8 (Suppl. 2) (2002), 46 8-469. 16. J.H. Chen and H.W. Zandbergen, Atomic imaging of solute clusters in Al alloys, Proc. of thel5th Int. Congr. for Electron Microscopy, Durban (2002), vol. I, 71 1-712. 17. L. Zhuang, J.E. Janse, P. De Smet, J.H. Chen and H.W. Zandbergen, Natural Ageing Effect on the Bake Hardening Response in Al-Si-Mg Alloys, Proc. of the 2001TMS Annual Meeting: Automotive Alloys, pp. 77-91, (New Orleans, Louisiana, USA). 18. J. Bottema, C. Lahaye, R. Baartman, L Zhuang and P. De Smet, "Recent development in AA6016-T4 aluminium type body sheet product", SAE International Congress and Exposition, 1998, SAE Paper No. 981007. 19. J.D. Bryant, "The effects of pre-ageing treatments on formability and paint bake response", Automotive alloys 11, Ed. by S.K. Das, TMS'97, 19-36. 20. H. Uchida and H. Yoshida, "Improvement in paint bake response of an Al-Mg-Si alloy by reversion", Aluminium and Magnesium for Automotive Applications, Ed. by J.D. Bryant and D. White, TMS Publ. (1996), 97- 104. 21. M. Saga, Y.Sasaki, M. Kikuchi, Y. Zhu and M. Matsu, "Effect of pre-ageing temperature on the behaviour in the early stage of ageing at high temperature for Al-Mg-Si alloy", ICAA-5, Mater. Sci. Forum, Vols. 2 17-222 (1996), 82 1-826. 22. L. Zhuang, R. de Haan, J. Bottema, C.T.W. Lahaye and P. De Smet, "Improvement in bake hardening response of Al-Si-Mg alloys", ICAA-7, Mater. Sci. Forum, Vols. 331-337 (2000), 1309-1314. 23. P. Ringer and K. Hono, "Microstructural evolution and age hardening in aluminium alloys: atom probe field-ion microscopy and transmission electron microscopy studies", Materials Characterization 44 (2000), 101-131.

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Nan0 and Microstructural Design of Advanced Materials M.A. Meyers, R.O. Ritchie and M. Sarikaya (Editors) 02003 Elsevier Ltd. All rights reserved.

LASER SURFACE ALLOYING OF CARBON STEELS WITH TANTALUM, SILICON AND CHROMIUM J. Kusinski and A. Woldan

Faculty of Metallurgy and Materials Science, University of Mining and Metallurgy, 30 Mickiewicza Ave., 30 059 Krakow, Poland

ABSTRACT The paper presents results of laser alloying that use laser beam in order to change the surface layer properties by changing its chemical composition and microstructure. The microstructure, chemical and phase composition and selected properties (microhardness, wear resistance) of the carbon steel laser alloyed with tantalum, silicon and chromium, were investigated. The surface alloyed zones varied in microstructure, depth, width and Ta, Si and Cr contents which depends on the thickness of pre-coated powder layer, binder type in the powder slurry and the process parameters (laser power and scanning velocity). The electron microprobe analysis of the alloyed layer showed that higher alloying element content in the melted zone resulted from the thicker pre-coated layer, lower laser power as well as higher scanning velocity Scanning electron microscopy examinations revealed that dendritic structure of the melted zone becomes evident when an organic binder was used as one of the slurry components. It was also found that the higher alloying element content in the alloyed zone resulted in lower weight loss during wear tests. Wear resistance analysis showed in general that the lowest weight loss of the surface alloyed samples was obtained for the thicker chromium pre-coated layer and for higher laser power used during the process of laser alloying.

INTRODUCTION There exists an increased demand for more producible and infallible tools and machinery components. Destruction process of such elements depends not only on the exploitation conditions but also on the hardness, wear, and fatigue and on the erosive and corrosive resistance of the surface layer. Generally speaking, materials should show a high resistance to different kinds of degradation. Wear of materials, which may be caused by adhesion or abrasion, is a surface or sub-surface phenomenon and can be reduced by modification of its surface layer [1,2]. Because wear and corrosion cost the economy many millions of dollars per year products with enhanced surfaces (i.e. friction, wear and corrosion resistance) are required [I]. The steels and cast irons used for high resistance to wear applications are usually composed of expensive alloying elements such as: Cr, Si, Ni, Co, Mo, Ta, Ti, V, or W. The high cost of using these materials for production of machinery components and tools are the main disadvantage. Since the durability of tools and machinery components depends strongly on the properties of the surface layer, this has led to the development and practical application of new technologies in the field of surface engineering. It can be noticed that the old surface technologies (e.g. thermochemical treatment, arc and induction hardening) are being replaced by new, energy saving, ecological and easily automated technologies (e.g. ion-assisted coatings, ion implantation, thermal spraying, as well as electron and laser beam treatments) [ 1,2]. Not all of these methods involve hardening of the surface layer. The change of the

35

J. Kusinski and A. Woldun

36

surface layer properties can also be obtained by changing its microstructure and/or chemical composition. Laser surface melting found many practical applications, as a method of formation of rapidly resolidified surface layers with many advantageous properties. Indeed, laser melting can harden alloys that cannot be hardened so effectively by laser transformation hardening. Application of the laser beam in materials processing lead also to the development of techniques changing chemical composition of the material surface layer, e.g. lasers cladding and laser alloying [3-61. Laser alloying of the material surface layer with selective elements, allows for modification of the properties of inexpensive products, instead of using very expensive highly alloyed materials [1,3-61. The potential of surface alloying to reduce consumption of expensive alloying elements is both strategically and commercially significant. The principal aim of the application of laser alloying technique in materials surface processing is to improve their properties due to formation of hard, homogenous and ultrafine structure of the surface layer by changing its chemical composition. Metallurgical changes that occur in the laser-modified layer are in the form of grain refinement, supersaturated solid solutions, and fine dispersions of particles. These can contribute to the hardening and strengthening of the surface layer. This technique is more and more popular, as there are several different ways to introduce alloymg elements into the thin surface layer melted by the laser beam [2-5,8]: direct injection into the melt pool at time of the treatment (powder, wire, gas); pre-placed adherent coatings deposited prior to laser treatment (electroplating, diffusion coating, thermal spraying, sputtering, etc.); pre-placed non-adherent coatings (foils, pastes, powder slurries). Recent results [2-71 showed that laser surface alloying of carbon inexpensive steels and cast iron with Cr, Si or C can convert microstructure and properties of the surface layer into ones characteristic of highly alloyed steels. Also, laser alloying of metallic substrates with alloying compounds, such as: W-Co-Cr-V, Ni-Cr-B-Si or Ni-Cr-Al-Fe [2-71, has been demonstrated as an effective method that modifies their surface layer properties significantly. To date, a variety of surface coatings have been easily achieved by using this noncontact and clean method [7]. One of the main interests in the surface alloying of Fe-base substrates is the production of a stainless steel surface equivalent [2]. Indeed, by laser alloying of iron or ordinary carbon steels, it is possible to obtain surface layers possessing chemical composition, microstructure and properties matching those of stainless, as well as tool, steels. After such treatment, alloyed surface layers, rich in alloying elements show higher hardness, better fatigue resistance, as well as better tribological properties and corrosion resistance than the substrate. Surface engineering of soft materials such as low carbon steels and other non-ferrous materials pose difficult problems. A main limitation is the lack of load bearing capacity of the substrate to support a thin surface layer whose hardness and other mechanical and physical properties are much different from its substrate. A solution to this problem is to strengthen the substrate by thermal treatment. The aim of this research was to study microstructure, chemistry and wear properties of carbon steels after laser surface alloying with tantalum, silicon and chromium.

EXPERIMENTAL PROCEDURE The composition of investigated carbon steel is given in Table 1. The samples were available in the form of TABLE 1. NOMINAL CHEMICAL COMPOSITION OF EXAMINED CARBON STEEL

C I M n / Si 0.17 0.55 0.21

I

I

1 I

Chemical composition [wt %] P I S I Cr Ni 0.006 0.006 0.08 0.13

I

1

1 I

I I

Mo 0.04

I I

Cu 0.19

1 1

A1 0.028

10 mm thick, 26 mm wide and 300 mm long slabs. Before laser alloying the specimens were pre-coated with Cr, Ta and Sic powder slurries. The organic and inorganic components were used as binders during predeposition of these powder slurries on the sample surface. The thickness of the pre-coated layers was in the range of 0.08 - 0.40 mm (see Figure 1).

Laser surjuce alloying of carbon steels with tantalum, silicon and chromium

31

Figure I: Schematic showing the laser alloyng process

The Photon Sources VFA 2500 C02 CW laser of nominal power of 2 5 kW was used for laser alloyng The laser power (P) was varied from 1 35 to 2 18 kW and the process speed (V) from 12 to 20 m d s Such a laser treatment permitted to achieve different melt depths combined with a reasonably smooth surface without cracks The laser alloying was performed under an argon atmosphere (see scheme in Figure 1) Optical (OM), scanning electron (SEM) and transmission electron microscopes (TEM), microprobe (EDS), X-ray diffractometry, microhardness and wear resistance measurements have all been applied to analyze microstructure, chemical and phase composition as well as a hardness of the laser alloyed surface layer TEM examinations were carried out on thin foil specimens obtained from - 0 5 mm slices cut parallel to the heated surface and carefully polished down to about 0 05 mm The 3 mm discs were punched from these slices and mechanically dimpled and polished using a Gatan dimple After dimpling, all discs were electolytically polished using a Tenupol jet electro polisher and a 95% acetic acid + 5% perchlonc acid electrolyte The polishing conditions were as follows T = 16 - 17"C, U = 25 V TEM examinations were performed using the JEOL lOOCX electron microscopy operated at lOOkV

RESULTS AND DISCUSSION Alloying with tantalum Figures 2a and b are the typical optical microscopy images showing the microstructure of Ta alloyed samples. The surface layer consisted of well-defined two zones: the zone that was laser melted and alloyed (LAZ) with Ta, and the heat affected zone (HAZ). The influence of the laser output power, the pre-

Figure. 2: Optical microscopy micrographs showing the microstructure of the alloyed samples in crossection; (a) - Ta + inorganic binder, g = 0.16 mm; V = 12 m d s ; P = 1.35 kW, (b) - Ta + organic binder, g = 0.16 mm; V = 20 mm/s; P = 1.8 kW.

38

J. Kusinski and A. Woldun

deposited layer thickness and the scanning velocity on the dimensions and the microstructure of the lasermelted layer was evident With increased scanning velocity, the laser beam-sample interaction time decreases and less laser energy is absorbed by irradiated matenal The same was observed with decreased output power Indeed, the size of the laser alloyed ( L a ) and heat affected zones (HAZ) decreased, too In such case, the laser beam melts only the pre-deposited layer of Ta and a limited thin layer of the base material As a result, the melted zone was rich in Ta The SEM microscopy examinations found a dendntic structure of the alloyed zone when an organic binder was used, while the structure has typically martensitic when inorganic binder was used for powder pre-deposition (Figures 3a and b) Two areas were well defined in the heat-affected zone The first one near the alloyed zone where during the laser treatment the matenal reachcd the austcnite rangc (betwccn sohdus and Az), contained martensite, and the second one near the matrix, where the material was heated to the A, - A3 range, contained ferrite and martensite (formed in the areas where the pearlite colonies were present before laser treatment) Samples covered with Ta and the organic binder showed higher hardness after laser alloymg than the samples covered using inorganic binder (Figures 4a and b) The electron microprobe analysis of the laser alloyed layer showed a higher tantalum content for a thicker original Ta coating as well as a slower scanning velocity (Figure 5 )

Figure 3: SEM images showing the details of the laser alloyed zone; (a) - Ta + inorganic binder and @) - Ta + organic binder

o

160

320

480

640

Distance from the surface [um]

Figure 4: The microhardness profiles of the surface layers after alloying with different conditions; (A) - Ta

+ organic binder, (B) - Ta + inorganic binder; g = 0.16 mm; a - V = 12 mm/s, P = 1.8 mmls, b - V = 12 mm/s,P=2.4 kW,c- V=20mm/s, P = 1.35 kW, d - V = 1 2 m m / s , P = 1.35 kW.

Laser surjuce alloying of carbon steels with tantalum, silicon and chromium

t.

39

Alloyed

F e - lo4

m

> P

-E

-

Mstnr

x /n

Ta

E

- 10'

I

I

Distance from the surface

-

Figure 5: Microanalysis showing the linear distribution of Fe and Ta in the crossection of laser alloyed layer; Ta + inorganic binder; g = 0.16 mm; V = 12 mmfs, P = 2.4 kW.

Alloying with silicon The SEM microphotographs in Figure 6a and b show the cross-section of the surface layer after laser alloying with chromium, when using following parameters: P = 2.18 kW, V = 20 m d s , g = 0.39 mm. The laser-affected layer is composed of two zones: laser alloyed zone (LAZ) and the heat-affected zone (HAZ). The macrostructure of the LAZ consisted of three well defined areas: an area where the planar crystals grow epitaxially on the partially remelted matrix grains (about 20 pm thick layer containing large martensitic needles, see Figure 6b), an area of columnar crystals (central part of alloyed zone) and an area of mixed dendritic/columnar crystals near the surface. These were the ferrite and austenite - crystals transforming after crystallization to martensite during rapid cooling of the material to room temperature. Indeed, the internal structure of the former austenite crystals consisted of martensite and retained austenite. The martensitic structure vaned in the needle sizes (Figure 7). The martensitic needles formed during the beginning stages of martensitic (y 3 a') transformation were very large, crossing several prior austenite crystals. Needles appearing in the later stages of martensitic transformation were fine. Their size was limited by the coarse martensite needles (Figures 7 and 8a) or austenite/ferrite interfaces (Figure 6b).

50 pm Figure 6: SEM micrographs showing. (a) - the microstructure of the laser alloyed and heat affected zones and (b) at the boundary of the laser alloyed and heat affected zones, (P = 2 18 kW, V = 20 mm/s, g = 0 39 mm).

-

40

J. Kusinski and A. Woldun

Figure 7: SEM micrograph showing acicular martensite in the laser alloyed zone with silicon, (P = 2 18 kW, V = 20 m d s , g = 0 39 mm)

Figure 8: TEM bright - field micrographs showing martensitic structure in the silicon laser alloyed zone; (a) - acicular martensite and @) - layer of retained austenite present between two martensite plates.

Figur ! 9: TEM micrographs: (a) - bright field; (b) - dark field images and related electrc n diffraction pattern taken from the laser-alloyed zone.

Laser surjuce alloying of carbon steels with tantalum, silicon and chromium

41

Such structure is characterized by a relatively high hardness level ranging from 700 - 1600 pHV, depending on quantity of silicon in the alloyed layer [8] The TEM microscopy studies revealed that there were three structural components acicular martensite, femte and retained austenite in the LA2 As was already mentioned, femte and austenite crystals were formed during crystallization of the silicon rich laser melted zone Microprobe analysis showed that silicon distnbution in that zone was not uniform The highest Si quantity was measured in the central areas of the alloyed zone (about 6 5% of Si), whereas, near the surface and near the bottom of the alloyed zone Si concentration was = 4% [8] Ihe I b M examinations did not show presence of SIC powder particles It seems that SIC dissolved completely in the melted pool Figure 8b shows a thick plate of retained austenite present between two martensitic needles Presence of retained austenite was confirmed by SAD patterns Figures 9 are the bright (9a) and dark field (9b) images presenting, interlath, thin films of retained austenite Alloying with chromium Similar to the case of laser alloying with tantalum and silicon, the influence of laser output power and scanning velocity on dimensions and microstructure of the chromium laser-alloyed layer (LML) was

Figure 10: a) - Optical image of the crosssection of the surface alloyed layer and SEM images of b) - the laser-alloyed zone (LAZ) and c) - the heat affected zone (HAZ), laser surface alloying with chromium using non-organic binder in the slurry

evident With increased scanning velocity, the laser beam-sarnple interaction time decreases and less laser energy is absorbed by irradiated matenal The same was observed with decreased output power Indeed, the size of the laser-alloyed (LAZ) and heat-affected zones (HAZ) decreased too In such case, the laser beam melts only the pre-deposited layer of Cr and a limited, thin layer of the base material As a result, the melted zone was highly enriched with chromium and carbon (in the case of using an organic binder in the slurry) The OM and SEM micrographs in rigure 10 show typical cross-section of the surface layer after laser alloying Lath martensitic structure, coarser than that observed in the heat-affected zone, was characteristic for the matenal alloyed with chromium (for pre-deposited chromium layer with non-organic binder) Figures 11 a - c are the microprobe line scans showing chromium distribution in the laser-alloyed layers The analysis was done for samples laser treated at constant g = 0 13 mm and V = 12 mmis, and with variable laser power (a) - P = 1 35 kW, (b) - P = 1 5 kW and (c) - P = 1 8 The depth of the substrate melted layer increase with the laser power, hence, for the same scanning velocity and the same thickness of the pre-deposited chromium powder layer, the alloyed zone was thicker and contained less chromium The dendritic structure of the melted zone was again evident when an organic binder was used (Figures 12a and b) The chemical compositions in the dendritic and the interdendritic regions at the middle part of the

J. Kusinski and A. Woldun

42

melted zone were analyzed by EDS. The average Cr content in the interdendritic regions was found to be higher than that in the dendrite center (the dendrite center - 8.22 wt% Cr; interdendritic regions -

LAZ

-of

Zi

0

Distance [pml

-+-+ 400

0

200

Distance [pm]

400

Distance [pm]

Figure 11: Microprobe line scannes showing chromium distribution in the laser alloyed layers; for constant: g = 0.13 mm and V = 12 m d s , and for variable laser power: (a) - P = 1.35 kW, (b) P = 1.5 kW and (c) - P = 1.8

Figure 12: SEM images of the sample alloyed with chromium using an organic binder: (a) - the central area of the laser-alloyed zone (LAZ) and @) at the boundary of laser-alloyed and hcat-affected (HAZ) zones. ~

10 08 wt% Cr, for the thickness of the pre-coated layer g = 0 26 rnm, V = 20 mm/s, P = 1 5 kW) The crystallization of the LAZ starts with planar epitaxial growth (Figure 12b) and, after 3 pm, changes to cellular and dendritic The cell dimensions were about 2 pm, corresponding to an approximate cooling rate The dispersion of the crystals and orientation in the laser alloyed zone depended on the of lo5 Ks direction of heat transfer and solidification velocity The TEM analysis showed that rapid cooling after solidification resulted in transformation of austenite to martensite, mainly lath martensite (Figures I0 and 14) However, regions of acicular martenslte were evident inside some cells - those containing higher carbon and chromium content (Figure 13, for 0 13 mm Cr pre-coated layer) This trend in martensite

'

Laser surjuce alloying of carbon steels with tantalum, silicon and chromium

43

formation is associated with the known reduction in M, with increasing Cr content, an effect enhanced by the extended solid solubility of Cr in austenite with rapid solidification The TEM analysis elucidated that martensite laths are separated by a thin film of retained austenite (see dark- field image in Figure 14b) Presence of plate-like &-carbidesin large martensite laths gives evidence that the process of auto-tempering occurs in the laser-alloyed layer This effect is due to the reversal of heat transfer from the warm substrate to the cold surface through the laser-alloyed layer In contrast, fully martensitic structure was observed in the laser-melted zone in case when uncoated samples were laser treated The microhardness within the laser-melted zone was constant for each analyzed layer, apart from fluctuations in the level of Cr due to microstructural heterogeneities The increase in hardness of the laser-melted zone wlth increased Cr content (Figure 15) was evident due to the presence of martensite and M7C3 carbides in the structure The high I

' I "

1

Figure 13: TEM micrograph showing microstructure in the chromium laseralloyed zone in low carbon steel; g = 0.13 mm, V = 12 mm/s and P = 1.5 kW.

Figure 14: TEM micrographs showing microstructure in the chromium laser-alloyed zone in low carbon steel: (a) -bright field; (b) - dark field images and related electron diffraction. hardness (1 720 pHV65) of the laser-alloyed zone (maximal for the thickness of the pre-deposited coating, g = 0.39 mm) may be attributed to the microcrystalline scale of the cell structure and to the extended solid solubility of the Cr in the matrix. In the heat-affected zone, hardness of 740 pHV65 (for samples heated with laser power, P = 1.8 kW) was measured, as is shown in Figure 15. The lowest hardness (650 pHV65) of the HAZ corresponded to a deeper melted zone and can be explained by the reduction in quench rate In order to examine wear resistance, various specimens were tested and their weight-losses were measured periodically. Figure 16 shows the weight loss for the various specimens Wear resistance analysis showed in general that the lowest weight loss was obtained for the thicker chromium pre-coated layer and for

44

J. Kusinski and A. Woldun

+V +V

=20 m,%; P -1.35 kW

=20m,k; P =1.5 kW

Figure 15: Microhardness of the laser alloyed layer of low carbon steel samples pre-coated with chromium-organic binder mixture.

Figure 16: Diagram shows wear resistance of the conventionally hardened low carbon steel and laser-alloyed layers with chromium: g = 0.13 mm and V = 12 m d s - constant, and variable laser power: P = 1.35, 1.5 and 1.8 kW.

higher laser power used during the process. It seems that alloying element content plays an important role in abrasive wear.The laser alloyed samples, having high chromium content in the surface alloyed zone, exhibit much better wear properties than those of the laser treated matrix (low carbon steel). Laser alloying of high carbon steel (1.25 wt% C) with chromium, under the same conditions as during the alloying process of low carbon steel formed different structures and properties of the chromium-alloyed layer. Optical microscopy examinations (Figures 17a and b) show structural inhomogeneity, which is due to the presence of well visible vortexes. The vortexes appear when the fluxes of Cr and C, that are present in the liquid material due to the convectional heat transfer that accompanies laser melting, are rapidly frozen during rapid cooling after. The cellular and dendritic crystals form in such chromium alloyed layers in high carbon steel (see Figures 18a and b). The measured cell size was in the range of 2 - 5 pm. Internal structure consisted of martensite and austenite (Figures 18b and 19). The inter-cell areas consisted of M7C3 and Mz3Cs (M = Cr, Fe) primary carbides precipitated during solidification due to segregation of carbon and chromium to the cell boundaries. Presence of martensite, M7C3, M23C6 carbides and retained austenite in the laser-alloyed zone was confirmed by XRD analysis (Figure 20). Such fine structure composed of martensite, M7C3, M& carbides and retained austenite, permitted to get relatively high hardness (1 8001900 pHV) in the alloyed zone (Figure 21) and good wear resistance (see Figure 22).

Laser surjuce alloying of carbon steels with tantalum, silicon and chromium

45

Figure 17: Optical images showing microstructure of the high carbon steel surface layer after laser alloying with chromium, (a) - P = 1 kW, (b) - P = 1,5 kW and V = 20 mm/s and g = 0.17 mm = const.

Figure 18: SEM images show microstructure in the central area of the high carbon steel surface layer after laser alloying with chromium; Cr powder mixed with an organic binder; P = 1,5 kW and V = 20 mm/s and g = 0.17 mm, (b) -magnified image of (a).

J. Kusinski and A. Woldun

46

Figure 19: TEM bright - field images showing microstructure of the chromium laser alloyed zone of high carbon steel; Cr powder mixed with an organic binder; P = 1.5 kW and V = 20 mm/s and g = 0 17 mrn; (b) - magnified image of (a)

548 7 I

M-martensite A-austenite

.-s E

v1

c,

E

n

0. ou

Figure 20: X-Ray diffraction pattern of chromium laser alloyed zone of high carbon steel.

41

Laser surjuce alloying of carbon steels with tantalum, silicon and chromium

I

2500

kw

+PP=l -P=1,35

lcJv

- a- P = 1 , 5 W

I

0

zoo

0

400

600

DistancehPm the surface [urn]

so0

Figure 21: Microhardness of the laser alloyed layer of high carbon steel samples pre-coated with chromium-organic binder mixture. 6 ,

I

El Matrix

a g = 0,17 mm, V = 12 rnm/s mg = 0,17 mm, V = 20 mmls

g = 0,37 mm, V = 12 mmls H g = 0,37 mm, V = 20 mmls

,

-

~~

_____

Figure 22: Diagram showing wear resistance of the conventionally hardened high carbon steel and laser-alloyed layers with chromium: g = 0.17 and 0.37 mm and V = 12 and 20 mmis, P = 1.5 kW - constant.

SUMMARY The structure of the LAZ depends on its chemical compOsition (Ta, Si or Cr contents). In all studied cases, two characteristic zones were distinguished in the laser processed material: laser alloyed zone (LAZ) of the resolidified matenal, Cr, Si or Ta nch, heat affected zone (HAZ) of the solid state hardened material. In addition, two areas were well defined in the heat-affected zone. The first one, near the alloyed zone, where during the laser treatment the material reached the austenite range (between solidus and A3), contained coarse martensite; and a second one, near the matrix, where the material was heated to the A, - A3 range, contained femte and martensite (formed in the areas where the pearlite colonies were present before

J. Kusinski and A. Woldun

48

laser treatment). The presence of cellular solidification structure in LAZ containing high carbon and alloying elements contents may be a consequence of solute segregation, which is determined by the shape of the solidus and liquidus of the constitution diagrams and cooling rate [6-81. The highest level of alloying elements in LAZ was reached when thick predeposited layers were remelted with substrate during laser treatment with high scanning velocity. Examinations showed that the microstructure and Ta, Si and Cr contents in the laser alloyed layer depends on the thickness of predeposited layers and treatment parameters, both influencing the S,/S, ratio (where S, and S, are the crossection areas of laser melted pre-deposited powder layer and the matrix, respectively). Studies by X-ray microprobe analysis indicated that the alloying occurs only in the laser melted zone. The tantalum, silicon and chromium contents varied from the cell boundaries and cell centers. However, inside the cells a fairly uniform composition was achieved in the case of all elements. The alloying elements content measured in the HAZ were at the same level as in the untreated matrix. Higher hardness was found in the alloyed layers containing average or higher contents of Ta, Si and Cr. Hence, it seems that solid solution hardening is less effective than transformation and precipitation hardening. Transmission electron microscopy examinations revealed that in the case of chromium alloying, the microstructures of LAZ are composed of lath martensite (frequently internally twinned) with some amount of plate-like E-carbide precipitates (present in large martensite laths) and retained austenite. In the laser chromium alloyed zones containing more carbon and chromium (characteristic for treatments when an organic binder was used for pre-deposition of powder layer on the sample surface) pnmarly M7C3 and M23C6 carbides in the cell boundaries were present. In the alloyed zones containing more Cr and high carbon content the martensite, austenite, carbides and 6 femte were present in the structure. Indeed, the hardness level of these zones, rich in Cr and C, was lower than that of the zones with martensitic structure containing less Cr and high carbon content. Research shows that, laser surface alloyed layers rich of silicon on the carbon steel can be easy produced with S i c powder. Acicular martensite, ferrite and austenite were identified in the laser-alloyed zones containing high C and Si concentrations, while lath martensite and retained austenite were identified in the zones containing low C and Si contents. Wear resistance analysis showed, in general, that the lowest weight loss of the surface alloyed samples was obtained for the thicker chromium pre-coated layer and for higher laser power used during the process of laser alloying. ACKNOWLEDGMENTS

The Faculty of Metallurgy and Materials Science, University of Mining and Metallurgy supported this work under grant No. 11. I 1.110.249. REFERENCES

1. Rickerby D.S., Matthews A. (1991) Advanced Surface Coatings: a Handbook of Suvfuce Engineering. Blackie & Son Limited, Glasgow. 2. Dahotre N. B. (1998) Laser in Suvface Engineering, Emptek Inc., Ontario. 3. Steen W.M. (1991) Laser Material Processing, Springer Verlag, Berlin. 4. Draper C.W. (1982) Journal of Metals, 34,6, p.16. 5. Draper C.W., Patoe J.M. (1985) Int. Met.Rev. 30,2, p.85. 6. Singh J.( 1994) Journal of Materials Science, 29, p. 5232. 7. Steen W.M. (1985) Metals and Materials 12, p. 730. 8. Kusinski J. (2000) Lasers - an Application in Materials Engineering, Akapit, Krakow.

Nan0 and Microstructural Design of Advanced Materials M.A. Meyers, R.O. Ritchie and M. Sarikaya (Editors) 02003 Elsevier Ltd. All rights reserved.

IN-SITU TEM OBSERVATION OF ALLOYING PROCESS IN ISOLATED NANOMETER-SIZED PARTICLES H. Mori'. J-G. Lee' and H. Yasuda' 'Research Center for Ultra-High Voltage Electron Microscopy, Osaka University, Yamadaoka, Suita, Osaka 565-087 1, Japan 'Department of Mechanical Engineering, Kobe University, Rokkodai, Nada, Kobe 657-8501, Japan

ABSTRACT Alloy phase formation in nanometer-sized particles has been studied as a function of the particle size by in-situ transmission electron microscopy, using particles in the Sn-Bi and In-Sn systems. When the size of particles is larger than about 10 nm in diameter, essentially similar phase equilibrium has been observed in both particles and bulk materials in either system. When the size of particles is approximately lOnm o r below, however, the finite size effect has become significant. In particles in the Sn-Bi system, a thermodynamically stable, fluid amorphous phase has been formed even at room temperature (RT). Namely, an amorphous phase which goes to melt without crystallization upon heating and solidifies into an amorphous solid with no traces of crystallization upon cooling, has been formed. The Gibbs free energy of the fluid amorphous phase is then supposed t o be lower than that of a crystalline counterpart(s) at least at temperature near and above room temperature. This is a situation never happens in bulk materials. In particles in the In-Sn system, a liquid phase has been formed even at room temperature. It is emphasized here that neither the fluid amorphous phase in the former system nor the liquid phase in the latter system is the equilibrium phase at RT in bulk materials. These phases can be present at RT as phases more stable than the crystalline counterpart(s) only when the size of the system is in the nanometer range. INTRODUCTION In recent years, much attention has been focused o n small particles in the size range from a few to several nanometers. This is because these nanometer-sized particles often exhibit structures and properties that a r e different from those of the corresponding bulk materials [ 1,2]. For example, with regard to structures, it is well known that the stable structure of indium undergoes a change

49

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H. Mori, J.-G. Lee and H. Yasudu

from bct for bulk to fcc when the size of particles is reduced down to several n m [3]. Also, it is well established that such phase transition temperatures as a melting point are significantly reduced with decreasing size of particles [4,5,6].Most of these studies are concerned with nanometer-sized pure substances, and in the related experiments temperature (T) and size (d) of particles were employed as experimental parameters. O n the other hand, studies o n nanometer-sized alloy particles, examined as a function of temperature (T), size (d), and composition (C), are quite limited [7-lo]. For example, studies o n the phase transformation in nanometer-sized alloy systems are rare [ I l l . The lack of studies o n nanometer-sized alloy particles is mainly due to the fact that it was rather difficult to control and measure the three experimental parameters, temperature (T), size (d), and composition (C), at the same time in a particle. However, recent remarkable progress in transmission electron microscopy (TEM) enables us to study not only the structure but also the chemical composition of an isolated nanometer-sized target material at a fixed temperature. Namely, with the use of this technique it now becomes possible t o examine the alloy phase formation in isolated nanometer-sized particles as a function of temperature (T), size (d), and composition (C) of the system [12]. This situation would open a wide, unexplored research field on the structure stability of nanometer-sized condensed matter in two- (or multi-) component systems. In fact, quite recently it was found with this technique that a unique amorphous phase that goes to melt without crystallization upon heating and solidifies into an amorphous solid with n o traces of crystallization upon cooling [lo], which has never been observed in bulk materials, does appear in isolated Au-Sn alloy particles when the size of particle is smaller than about 7 n m [lo]. The observation is of interest because the amorphous phase appearing in nanometer-sized alloy particles may provide an effective means for investigating the liquid-to-glass transition, the elucidation of which at an atomic level is one of the outstanding problems in modern condensed-matter physics [ 131. In the present work, in an attempt to have a better understanding of factors controlling the phase equilibrium in nanometer-sized systems, a series of in situ TEM experiments were carried out on alloy phase formation in isolated nanometer-sized particles in the Sn-Bi and In-Sn systems.

EXPERIMENTAL PROCEDURES Preparation of nanometer-sized alloy particles was carried out using a double-source evaporator installed in the specimen chamber of a Hitachi H-800 type 200kV transmission electron microscope (TEM). The evaporator consisted of two spiral-shaped tungsten filaments. The distance between the filaments and a supporting film (substrate) for particles was approximately 100mm. An amorphous carbon film was used as the supporting film, and was mounted on a molybdenum grid. Using this evaporator, tin (or indium) was first evaporated from one filament heated by the Joule effect onto the supporting film kept at ambient temperature, and nanometer-sized tin (or indium) particles were produced on the film. Next, bismuth (or tin) was evaporated from the other filament onto the same film kept at ambient temperature. Alloy phase formation in the nanometer-sized particles associated with bismuth (or tin) deposition was studied

In-situ TEM observation of alloying process in isolated nanometer-sized particles

51

by both bright-field image (BFI) and selected area electron diffraction pattern (SAED). The microscope was equipped with a turbo-molecular pumping system t o achieve a base pressure of around 5 X 1 0 ' Pa in the specimen chamber. The electron flux used was approximately 1.5 X 102" e * m z s'.

-

A series of alloy formation experiments were additionally carried out i n a 200kV high resolution electron microscope (HREM) of Hitachi HF-2000 type, using a unique side-entry holder equipped with a double-source evaporator at the tip. T h e experiments were performed to study the atomistic structure of alloy phases formed A photograph of t h e holder used in the present experiment is shown in Fig.1. Figure I ( a) and (b) show a low-magnificatlon photograph of the holder and a high-magnification photograph of the part enclosed with a square i n Fig.1 (a), respectively. It essentially consisted of three spiral-shaped tungsten filaments, t h e middle filament of which was attached with a flake of graphite used as a supporting substrate Prior to experiments, the flake of graphite was baked at 1073 K for 6 0 s to get a cleaned surface of graphite. After being baked, the graphite substrate was cooled down to room temperature T h e preparation of nanometer-sized alloy particles was carried out in a similar way as that mentioned above. In this holder, the temperature rise of substrate during evaporation was estimated to he below 10 K. The base pres5ui-e of this electron microscope was below 5 X 10 Pa. For in situ H R E M observation of alloying process, a television Lamera and video tape recorder (VTR) system was employed. T h e chemical composition o f individual particles on the substrate was analyzed by energy-dispersive X-ray spectroscopy (EDS).

'

Figure 1: Side-entry holder equipped with a double source evaporator at the tip. (a) A whole view, (b) High-magnification photograph of the part enclosed with a square in (a).

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H. Mori, J.-G. Lee and H. Yasudu

RESULTS The Sn-Bi system A typical example of alloying process of bismuth atoms into tin particles examined by a conventional transmission electron microscope (Hitachi H-800 type TEM) is shown in Fig 2 [ 141 Figure 2 (a) and (a’) show a BFI of as-produced tin particles on an amorphous carbon film and the corresponding SAED, iespectively The mean diameter of tin particles is approximately 6 nm. The Debye-Scherrer rings can consistently be indexed as those of pure B -Sn with a tetragonal structuie with lattice constants of a=O 581 n m and b=0.318 n m The structure is the same a s that of bulk [j -Sn Figure 2 (b) and (b’) show a BFI of particles after bismuth deposition and the Lorresponding S A E D , respectively The particle size increased from 6 nm to 10 nm by bismuth deposition The size increment partially came from the coalescence among particles. It was revealed by electron probe micioanalysis (EPMA) that particles shown in Fig.2 (b) contained, on average, about 60 at % Bi It should be noted here that n o interfaces weie recognized i n the interior of individual particles in Fig.2 (b) and only halos appeared in the S A E D (Fig 2 (b’)) This fact indicates that when bismuth atoms were vapor-deposited and came in contact with tin particles they dissolved quickly into tin particles to form either amorphous or liquid Sn-Bi alloy particles. To examine the atomic structure of the noncrystalline alloy particles as shown in Fig 2 (b), a series of in situ alloying experiments were carried out i n the HREM. The results will be shown later in Fig.3 Figure 2 (c) and (c’) shows a BFI of particles after additional deposition of both bismuth and tin and the corresponding SAED, respectively. T h e mean particle size incieased to approximately 20 n m In this additional deposition, the amounts of bismuth and tin deposited were controlled so that t h e composition of particles was kept constant at about 60 at. % Bi, i e , at the s a m e composition as that in Fig 2 ( b ) . It is evident i n F i g 2 (c) that there appeared definite

Figure 2. Alloy phase formation in nanometer sized particles i n the Sn-Bi system at room temperatuie. (a) BFI of as-produced tin particles on an amorphous carbon film, and (a’) t h e coiresponding SAED. (b) BFI of particles after bismuth deposition, and (b‘) the corresponding SAED. Particles shown in (b) contained, o n average, about 60 at. % Bi. (c) BFI of particles after additional deposition of both bismuth and tin, and (c’) the corresponding SAED. In this additional deposition, the amounts of bismuth and tin deposited were so controlled that the composition of particles remained unchanged as compared to that of particles shown in (b).

In-situ TEM observation of alloying process in isolated nanometer-sized particles

53

Figure 3: A sequence from a video recording of the alloying process of bismuth into a nanometer-sized tin particle. A crystalline-to-amorphous transition took place during deposition of bismuth onto the tin particle kept at room temperature (compare Fig. (b) with (c)). interfaces (arrowed) within individual particles. The Debye-Scherrer rings in the SAED can consistently be indexed as those of tin superimposed with those of bismuth. All these observations in Fig.2 (c) and (c’) indicate that in approximately 20 nm-sized particles of a Sn-60 at. % Bi alloy, each isolated particle was composed of two phases (i.e., tin and bismuth), which is the same phase equilibrium at RT in the bulk alloy of the same composition. Thus, I t seems safe to conclude the following from Fig.2. When the size of particles of a Sn-60 at. % Bi alloy is approximately 20 nm or above, a mixture of tin and blsmuth is the equilibrium microstructure at RT as in the case of bulk materials, but when the size of particles is approximately 1 0 nm or below, such a noncrystalline phase as shown in Fig.2 (b) and (b’) appears as the stable phase. This fact clearly indicates a strong finite size effect on the phase equilibrium in the binary alloy system. Figure 3 shows a typical sequence of alloying process of bismuth into a nanometer-sized tin particle as observed by HREM [14]. This observation was carried out to see whether such a noncrystalline phase as shown in Fig.2 (b) and (b’) was in an amorphous state or in a liquid state. The images were reproduced from the videotape. Figure 3 (a) shows an as-produced pure tin particle on a graphite substrate. The 0.291 nm-spaced fringes seen in this particle is the (020) lattice fringes of [j -Sn. Figure 3 (b) shows the same particle after bismuth deposition. The particle increased from 5 nm to 6 nm in diameter by bismuth deposition, but remained being a single crystal, indicating a solid solution is formed in the particle. With continued deposition of bismuth, the structure of the particle changed from crystalline to amorphous, as shown in Fig.3 (c). Namely, granular contrast, which is often called the “salt-pepper contrast” and is characteristic of an amorphous structure, appeared in the particle after bismuth deposition (Fig.3 (c)), instead of the lattice fringes characteristic of a crystalline solid solution (Fig.3 (b)). This fact indicates that a crystalline-to-amorphous (C+A) transition was induced in the tin particle by alloying of bismuth. The particle increased to 9 nm in diameter, and EDS analysis of the particle revealed that it contained 70 at. % Bi. One point to be noted here is the observation that the bright and dark spots in the granular image changed in position and intensity with time during observation. This is in sharp contrast to the feature of images obtained from the conventional amorphous material, in which these spots remain unchanged with time. An example of such fluctuation in granular contrast is shown in Fig.4 [14], photographs in which were reproduced from the videotape. Figures 4 (a) to (d) show sequential micrographs of one particle taken at a time interval of looms, keeping the objective lens excitation constant. The particle depicted in

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H. Mori, J.-G. Lee and H. Yasudu

Figure 4: In situ observation of fluid amorphous formed in a 9-nm-sized Sn-Bi alloy particle. Sequential micrographs (a) to (d) were taken at a time interval of 100 ms. It is shown that bright and dark spots in the granular contrast in the particle changed in position and intensity with time whereas such lattice fringes in the graphite substrate as those encircled, remained fixed. This fluctuation in the granular contrast reflects a high atomic mobility in the particle. Fig 4 is the same as in Fig.3 (c). It is evident from Fig.4 that the bright and dark spots in the granular contrast exhibited continuous changes in position and intensity with timc whcrcas lattice fringes i n the graphite substrate remained fixed with time (for example, refer to such fringes as enclosed with a circle). This fluctuation in the granular contrast reflects fluctuation of the electron-optical phase shift, which comes from the fluctuation of local mass-thickness Therefore, the observed fluctuation in granular contrast provides evidence for the high atomic mobility enough to induce the mass-thickness variation in the nanometer-sized particle in a time interval less than 100 ms In other words, such high atomic mobility is responsible for the fluid amorphous structure observed in the particle in Fig.4. In an attempt to study the thermal stability of the fluid amorphous structure, annealing experiments were carried out. Figure 5 shows a sequence from a video recording of the melting and the subsequent solidification of a Sn-40 at. % Bi alloy particle heated and subsequently cooled in-situ i n the HREM [14] Figure 5 (a) shows an as-produced alloy particle at RT with a fluid amorphous structure, sitting on a flake of graphite (bottom). With increasing temperature, the time frequency ot tluctuation in the granular contrast became high, suggesting an enhanced atomic mobility (Fig.5 (b)) With continued heating, the particle eventually melted, and in the molten state there appeared only a quite uniform contrast typical of a liquid state (Fig.5 (c)). It is noted that prior to the melting no traces of crystallization were observed Upon cooling to room temperature, the liquid particle solidified again into the fluid amorphous phase, as illustrated in Fig 5 (d) N o traces of crystallization were again recognized prior to the solidification It is evident from Fig.5 that the fluid amorphous phase possesses a high phase stability so that upon

Figure 5: A sequence from a video recording of the melting and subsequent solidification of a ,911-40 at. % Bi alloy particle heated and subsequently cooled in situ in a HREM.

In-situ TEM observation of alloying process in isolated nanometer-sized particles

55

heating it melts without prior crystallization and upon cooling the melt solidifies directly into the amoiphous phase. This fact indicates that at least at temperatures near and above room temperature the Gibbs free energy of the fluid amorphous phase is lower than that of a crystalline counterpart(s) and in this context the amorphous phase 15 thermodynamically more stable than a crystalline phaTe(T), which is not the case for conventional amorphous alloys in bulk. Namely, in the case of conventional bulk materials, the Gibbs free energy of an amorphous phase is higher than that of a crystalline counterpart(s) and therefore crystallization always takes place once the atomic mobility in the amoiphous phase becomes high. It can be said that the thermodynamically stable, fluid amorphous phase observed here is an alloy phase characteristic to materials in the nanometer range. The In-Sn system A typical example of alloying behavior of tin atoms into indium particles is shown in Fig 6 [15]. Figure 6 (a) and (a’) show a bright-field image (BFI) of as-produced indium particles on a

supporting film and the corresponding selected area electron diffraction pattern (SAED), respectively The mean diameter of indium particles is approximately 7 nm The Debye-Scherrer rings in the SAED can consistently be indexed as those of a crystal with the face-centered cubic (fcc) structure with a lattice constant of a=0.471 nm (i.e , fcc pure indium). Figure 6 (b) and (b’) show a BFI of particles after tin deposition and the corresponding SAED, respectively. These photographs were taken immediately after tin deposition, that is, in less than 20 s after the tin-atom beam was turned off The particle size increased from approximately 7 nm to 16 nm in the mean diameter, as seen from a comparison of Fig.6 (a) with (b) Electron probe microanalysis (EPMA) of the same sample shown in Fig 6 (b) revealed that the material on the supporting film contained, on the whole, about 70 at. % Sn One point to be noted here is the fact that a distinct heterointerface is present in individual particles (as indicated with arrows in Fig 6 (b)) This fact suggests that individual particles are composed of two phases. The Debye-Scherrer rings shown in Fig 6 (b’) can consistently be indexed as those o f In?Sn (which has a tetragonal structure

Figure 6 Alloying behavior of tin atoms into indium particles at ambient temperature (a) BFI of as-pioduced indium particles on an amorphous carbon film, and (a’) the corresponding SAED (b) BFI of particles after depositing tin atoms, and (b’) the corresponding SAED. The mean Tize of particles in (b) was 16nm in diameter. The chemical composition of the particles was evaluated to be approximately Sn-30 at. % In.

56

H. Mori, J.-G. Lee and H. Yasudu

belonging to the space-group 14/mmm with lattice constants of a=0.346 nm and c = 0 . 4 7 ~nm) superimposed on those of InSn4 (which has a hexagonal structure belonging to the space-group P6/mmm with lattice constants ot a=O 72" nm and c=0.299 nm) These two phases are nothing but the conjugate phases predicted from the bulk equilibrium phase diagram [16] All these observations indicate that when tin atoms were vapor-deposited onto 7 nm-sized indium pai ticles, rapid spontaneous alloying of tin atom5 into indium particles took place and a5 a result a mixture of two phases, one was InqSn and the other InSn4, foimed within each particle The formation of the two-phase mixture in individual particles is in agreement with alloy phase formation expected from the phase diagram for the bulk. The above ohservdtion is consistent with a recent iesult that when t h e size of particles is larger than about 10 nm essentially similar phase equilibrium was observed both in paiticles and bulk materials in the Au-Sn binary system [17] Therefore, it seems safe to consider that the finite size effect on the phase stability in alloy particles is rather small when the size of particles is larger than approximately 10 nm. An example of alloying behavior of tin atoms into relatively small indium particles is presented in Fig.7 LlS]. F i g u r e 7 (a) and ( a ' ) s h o w a B F I of as-produced i n d i u m particles a n d t h e corresponding SAED, respectively. The mean diameter or indium particles is approximately S nni. The Dehye-Scherrer rings in the S A E D can again be indexed as those of fcc pure indium. Figure 7 (h) and ( b ' ) show a BFI of particles after tin deposition and the corresponding S A E D , respectively. The particle size has increased from approximately 5 nm lo 10 n m in the mean diameter, as seen from a comparison of Fig.7 (a) with (h). It should he noted here that no interfaces are recognized i n the interior of individual particles in Fig.7 (b), in conlrast to the observation depicted in Fig.6 (b). In t h e S A E D (Fig.7 (h')), halos are recognized. This fact indicates that vapor-deposited tin atoms c a m e in contact with indium particles and dissolved quickly into the particles to form eilher amorphous o r liquid In-Sn alloy particles. The formation of a noncrystalline phase is consistent with the observation that n o interfaces are present within individual particles (Fig.7 (h)). EPMA of the same sample shown in Fig.7 (h) revealed that the material on the supporting film contained, on the whole, about 7 0 at. 76 Sn. The stable phases in the In-70 at. % S n bulk alloy at room temperature are InlSn and InSn4. as mentioned before. Accordingly, it can be said that in In-70

Figure 7: Alloying behavior of tin atoms into indium particles at ambient temperature. (a) BFI of

as-produced indium particles o n an amorphous carbon film, and (a') the corresponding SAED. (h) BFI of particles after depositing tin atoms, and ( h ' ) the corresponding SAED. The mean size of particles in (b) was lOnm in diameter. The chemical composition of the particles was evaluated to be approximately Sn-30 at. % In.

In-situ TEM obyewation of alloying process in isolated nanometer-sized particles

51

I

Figure 8: In situ observation of alloying process of indium atoms into an approximately 5.2 nm-sized tin particle. A crystalline-to-liquid (C-L) transition took place during deposition of indium onto the nanometer-sized tin particle kept at room temperature (compare Fig(b) with (d)). The three numbers inserted in each micrograph indicate the time in units of minutes, seconds, and one-sixtieth seconds. at. % Sn alloy particles of approximately 10 nm in the mean diameter, stable phases in the corresponding bulk material are not realized. A series of in situ alloying experiments were carried out in a HREM to investigate whether the structure of alloy particles shown in Fig.7 (b) is amorphous or liquid. Figure 8 is a typical sequence of alloying process in an approximately 5 . 2 nm-sized particle. Figure 8 (a) shows an as-produced, pure tin particle on a graphite substrate. The 0.291 nm-spaced fringes seen in this particles is the (020) lattice fringes of il -Sn. The same particle after indium deposition is shown in Fig.8 (b). The particle remains being a single crystal, indicating a solid solution is formed in the particle. The diameter of the particle has increased from approximately 5.2 nm (Fig.8 (a)) to 6.7 nm (Fig.8 (b)) during indium deposition. The indium concentration in the solid solution estimated from the size increment is approximately 53 at. % In. With continued deposition of indium, the particle underwent a crystalline-to-liquid (C-L) transition, as shown in Figs.8 (c) and (d). Namely, all the lattice fringes in the particle disappeared abruptly and there appeared only a uniform contrast typical of the liquid state (Fig.8 (d)). The time interval between Fig.8 (b) and (d) is 1/15 s, indicating that the C+L transition took place very quickly.

In an attempt to confirm that such droplets as the one shown in Fig.8 (d) are not a solid amorphous phase but a liquid phase, a series of detailed HREM observations on alloy droplets were carried out. An example of the results is depicted in Fig.9 [15]. Figure 9 (a) shows an as-produced alloy particle. The particle is in a crystalline state and therefore in a state of a solid solution. The 0.292 nm-spaced fringes seen in the particle can consistently be assigned as the (020) lattice fringes of the solid solution with the B -Sn structure, while the 0.278 nm-spaced fringes as the (101) lattice fringes. It is noted that the foimation of facets can be clearly recognized on the surface of the particle. With continued deposition of indium, all the lattice fringes abruptly disappeared and at the same time the shape of the particle changed from faceted, polygonal to round. semispherical, ds seen in Fig.9 (b). It is worthy o f note that no salt-pepper contrast characteristic of a solid amorphous phase is present in the particle in Fig.9 (b). It is also worth noting in Fig.9 (b) that the Fresnel ring ( m o w e d ) appears almost symmetrically around the particle, which indicates that astigmatism is satisfactorlly corrected and therefore the absence of any contrast features does not come from such an extrinsic factor as the astigmatism but is of i n t r i n s i c n a t u r e Fig.9 ( c ) s h o w s t h e s a m e f i e l d as in F i g . 9 ( b ) but t a k e n in a c o n d i t i o n

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H. Mori, J.-G. Lee and H. Yasudu

Figure 9: A series of HREM observations on an alloy droplet. (a) HREM of an asproduced, crystalline alloy particle, ( b ) HREM of the same particle after a melting transition, ( c ) the same field as in (b) but taken in a condition underfocused by an additional amount of 20 nm. underfocused by an additional amount of 20 nm. The fact that Fig.9 (c) was taken in a further underfocused condition compared to Fig.9 (b) can be confirmed from the observation that the width of the Fresnel maximum (the bright band double-arrowed) along the edge of the graphite substrate is large in Fig.9 (c) than in Fig.9 (b). It is evident that again no salt-pepper contrast can be observed in the particle in this varied defocus condition. All these observations clearly indicate that the droplet shown in Figs.9 (b) and 9 (c) is not a solid amorphous phase but a liquid phase. The results shown in Fig.9 indicate that such a droplet as in Fig.8 (d) is in the liquid state. The indium concentration in the liquid droplet in Fig.8 (d), estimated from the size difference between the particle shown in Fig.8 (a) and that in Fig.8 (d), is approximately 5 5 at. % In. Therefore, it can be said that the stable phase of approximately 5.2 nm-sized Sn-55 at. 70 In alloy particles at room temperature is liquid, and this is in sharp contrast with the equilibrium phase(s) in bulk materials (i.e., a two phase mixture of In3Sn and InSn4). Through the HREM observations shown in Fig.8 and 9, i t is verified that the structure of such alloy particles as depicted in Fig.7 (b) is not amorphous but liquid. One point to be noted here is the fact that the formation of liquid phase is in disagreement with a previous result that an amorphous phase was formed in alloy particles in the In-Sn system when the size of particles were less than approximately 20 nm [8]. The reasons for the disagreement are not clear at this moment, but it is worth noting that in the previous report [8] the formation of the amorphous phase was concluded only from the SAED showing diffuse rings and no complementary HREM study was done to draw the conclusion. So, there may be a possibility that the diffuse rings observed in the previous study came from not an amorphous but a liquid phase.

CONCLUDING REMARKS As shown in the preceding section, the finite size effect on alloy phase formation is not so strong when the size of particles I S larger than approximately 10 nm. In particles in the Sn-Bi system, a two-phase microstructure composed of tin and bismuth was formed at near eutectic compositions, whereas in those in the In-Sn system a two-phase microstructure composed of ln$n and InSn4 was formed. In both systems, the formation of the two-phase mixture is in agreement with alloy phase formation expected from the phase diagram for the hulk.

In-situ TEM observation of alloying process in isolated nanometer-sized particles

59

When the size of particles is approximately lOnm o r below, however, the finite size effect becomes significant. In particles in the Sn-Bi system, a thermodynamically stable, fluid amorphous phase was formed even at room temperature (RT). Here, the wording of “thermodynamically stable amorphous phase” comes from the fact that upon heating it went to melt without crystallization and upon cooling it solidified into an amorphous solid with n o traces of crystallization. T h e Gibbs free energy of the fluid amorphous phase is then supposed to be lower than that of a crystalline counterpart(s) at least at temperature near and above room temperature. This is a situation never happens in bulk materials. S u c h a situation is considered to be realized by q u i t e large suppression of the eutectic temperature, Teu, down to a temperature even below the glass transition temperature, Tg (i.e., T p T e u ) . This is a phenomenon induced by the system-size reduction down to a several-nm range [18]. In case the three temperatures, Teu, Tg, and RT (where the observation is carried out) lie in such an order as RT-Tg>Teu in nanometer-sized particles in the Sn-Bi system, it is then postulated that a crystalline-to-fluid amorphous (C+fluid A ) phase transition would be induced by simply adding solute atoms ( i x . , Bi atoms) onto nanometer-sized crystalline particles of a pure substance of tin. This postulation is in agreement with what is observed in the present work. In particles in the In-Sn system, the liquid phase was formed even at room temperature. The glass transition temperature, Tg, in this In-Sn system is supposed to be lower than that in the Sn-Bi system, since the liquidus line in the former system locates always below that in t h e latter system in the bulk phase diagrams. In case the three temperatures, Teu, Tg, and RT lie in such an order as RT>Tg>Teu in nanometer-sized particles in the In-Sn system, it is then postulated that a crystalline-to-liquid (C+L) phase transition would be induced by simply adding solute atoms (i.e., In atoms) onto nanometer-sized crystalline particles of a pure substance of tin. This postulation is again in agreement with what is observed in the present work. It is of interest to note here that in nanometer-sized particles in the Au-Sn system where the three temperatures lie in such an order a s Tg>RT>Teu, a crystalline-to-amorphous (C-A) phase transition has been induced by simply adding tin atoms onto nanometer-sized crystalline particles of a pure substance of gold [17]. Based upon the discussions, it seems that although different types of transitions are observed in particular systems ( i x . , C + A in the Au-Sn system, C+fluid A in the Sn-Bi system, and C + L in the Sn-In system), all the behaviors are consistently explained in terms of the relative position among Tg, RT, and Teu in the systems, and that these observations provide concrete evidence for the formation of a thermodynamically stable amorphous phase in nanometer-sized alloy particles over a temperature range from Tg to Teu.

ACKNOWLEDGEMENTS A part of this work was supported by “Nanotechnology Support Project” of the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan.

H. Mori, J.-G. Lee and H. Yasudu

60

REFERENCES

I.

2. 3. 4. 5.

6. 7. 8. 9. 10. 11.

12. 13. 14. 15.

16. 17. 18.

Andres, R. P., Averback, R. S . , Brown, W. L., Brus, L. E., GoddardIII, W. A., Kaldor, A,, Louie, S . G., Moscovits, M., Peercy, P. S . , Riley, S . J., Siegel, R. W., Spaepen, F. and Wang, Y. (1987) J . Mater. Res. 4, 704. Halperin, W. P. (1986) Rev. Modern Phys. 58, 533. Yokozeki, A. and Stein, G. (1978) J . Appl. Phys. 49, 2224. Sambles, J. R. (1971) Proc. R . SOC.Lond. A 324,339. Buffat, Ph. and Borel, J-P. (1976) Phys. Rev. A 13, 2287. Allen, G. L., Bayles, R. A., Gile, W. W. and Jesser, W. A. (1986) Thin Solid Films 144, 297. Palatnik, L. S. and Boiko, B. T. (1961) Phys. Met. Metallogr. 11, 119. Allen, G. L. and Jesser, W. A. (1984) J . Cryst. Growth 70, 546. Jesser, W. A . , Shiflet, G. J., Allen, G. L. and Crawford, J. L. (1999) Mater. Res. Innovations 2,211. Mori, H. and Yasuda, H. (2001) Scripta muter. 44, 1987. Asaka, K., Tadaki, T. and Hirotsu, Y. (2000) Philos. Mag. A 82(3), 463. Yasuda, H. and Mori, H . (2002) J . Crystal. Growth 237-239, 234. Stillinger, F. H . (1995) Science 269, 1935. Lee, J. G., Mori, H. and Yasuda, H. (2002) Phys. Rev. B 66, 012105. Lee, J . G., Mori, H. and Yasuda, H. (2002) Phys. Rev. B 65, 132106. Binary Alloy Phase Diagrams, edited by Massalski, T. B. et a l . (American Society for Metals, Metals Park, OH, 1986). Yasuda, H., Mitsuishi, K. and Mori, H. (2001) Phys. Rev. B 64, 094101. Lee, J. G. (2003) Diploma Thesis, Osaka University.

Nan0 and Microstructural Design of Advanced Materials M.A. Meyers, R.O. Ritchie and M. Sarikaya (Editors) 02003 Elsevier Ltd. All rights reserved.

CHARACTERIZATION OF METAL/GLASS INTERFACES IN BIOACTIVE GLASS COATINGS ON Ti-6A1-4V AND Co-Cr ALLOYS E. Saiz,' S. Lopez-Esteban,' S. Fujino,' T. Oku,' K. Suganuma3and A. P. Tomsia' 'Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA 2KyushuUniversity, Kasuga-shi, Fukuoka 816-8580, Japan 'Institute of Scientific and Industrial Research, Osaka University, Osaka 567-0047, Japan

ABSTRACT Coating metallic-based implants with bioactive materials promotes joining between the prostheses and the bone as well as increases long-term implant stability. In the present work, the interface between different alloys (Ti-6AI-4V and Co-Cr) and bioactive silicate glass coatings, prepared using a simple enameling technique, is analyzed at the nanolevel. Transmission electron microscopy and associated chemical analysis of the glassialloy interface show the formation of thin Ti& or CrO, reaction layers (-150 nm thick). These nanostructured interfaces facilitate the formation of a stable joint between the glass coating and the alloys.

INTRODUCTION Nowadays, biomaterials such as Ti or Co-Cr alloys are widely used in orthopedic and dental implants. However, their long-term effectiveness needs improvement [ 1-41, In particular, metallic implants have a variety of shortcomings related to their affixation, and in many cases, failures are caused by poor adhesion of the implant to the tissue or bone. A commonly used strategy to improve osseointegration is to coat the alloys with a bioactive material that will accelerate the stabilization of the implant and extend its duration. The fabrication of coatings for medical applications involves a compromise between adhesion, mechanical stability, and bioactivity, but coatings that satisfy all these requirements are extremely difficult to develop. For example, the most commonly used coating, plasma-sprayed hydroxyapatite (HA) [5, 61, shows several problems associated with its low crystallinity and adhesion that result in poor stability. Clearly, new coatings for implant materials are needed. Recently, we have developed a simple enameling technique to fabricate bioactive glass coatings on Ti- and Cr-based alloys. Using silicate glasses, it has been possible to fabricate coatings with a thickness ranging between 25 pm and 150 pm, which showed good adhesion to the metal and formed HA crystals on their surface during in vitro testing in simulated body fluid (SBF) [7-91. In order to design and control the interface between the glasses and the alloys, we must understand their bonding mechanism, which requires analysis of the interfacial microstructure at the nanoscopic scale. The purpose of the present work is to analyze the glassialloy interface formed during enameling. To understand the nature of the interfaces that showed optimum adhesion, microstructural analysis was carried out by transmission electron microscopy (TEM), a powerful method for structural analysis of advanced materials at the nanoscale [lo, 111. These studies will provide a guideline for designing and controlling the interfaces between metals and bioactive glass coatings that can be used in future prosthetic implants.

61

E. Suiz et al.

62

EXPERIMENTAL PROCEDURES Silicate glasses in the system Si02-Na20-K20-CaO-MgO-P~0~ were prepared using a standard procedure described in detail elsewhere [7-91. The composition and properties of the glasses used in this study are shown in Table 1. The thermal expansion (a)and softening temperature (T,) were measured in a calibrated dilatometer with an alumina holder and push rod, using glass bars 25 mm long. Glass 6P50 was used to coat Co-Cr-based alloys, whereas glasses 6P57 and 6P64 were used to coat Ti-based alloys. These glasses have thermal expansions similar to the alloys. In that way, the generation of large thermal stresses during fabrication is avoided. To manufacture the coatings, the glass was milled in a planetary agate mill, and a suspension of the glass powder (particle size < 20 pm) in ethanol was deposited on flat metallic substrates -10 mm x 10 mm x 1 mm (Ti, Ti6A14V or Vitallium@,a Co-Cr alloy), which had been previously polished with diamonds (1 pm particle size) and cleaned in acetone and ethanol. Additionally, suspensions of the glass powders in ethanol with a 75 wt% solid content were used to coat cylindrical Ti6A14V samples (1 mm radius, 10 mm long) and titanium internal hexagonal cylinder dental implants (3.3 mm diameter and 10 mm length from 3iiimplant innovation) by dip coating, using a coating speed of 1,000 mndmin. The coatings on Ti-based alloys were annealed at temperatures ranging between 800°C to 820°C for 0 to 30 s in air, whereas the coatings on Co-Cr were fired at 750°C for 30 s. The adhesion between the coating and the alloy was qualitatively evaluated using Vickers indentations on the coating surfaces and polished cross sections in air, with loads up to 6.2 kg. TABLE 1 GLASSCOMPOSITIONS (w%) AND PROPERTIES

'Measured between 200400 "C Samples for TEM were prepared by cutting cross sections of the glass/alloy interface. The sections were ground to a thickness of -100 pm with emery paper, and then fixed into a Cu mesh with a 3 mm diameter. The disks were polished with a dimple grinder (Gatan, Model 656) to a less than 20 km thickness, and milled by argon ion milling. TEM observations were performed with a 1,250 kV electron microscope (ARM-1250 kV) having a point-to-point resolution of 0.12 nm, and a FEI TECNAI 20 electron microscope operated at 200 kV. Chemical analysis of the interface was performed using electron probe microanalysis (EPMA). In the elemental line analysis, the focused incident beam (-4 nm in diameter) was positioned across the glass/alloy interface, and an x-ray spectrum was acquired for 1 s at each position.

RESULTS AND DISCUSSION After firing, the coatings exhibited good adhesion to the alloys. In indentations performed at the coating surfaces and the glasdmetal interfaces on polished cross sections, cracks did not propagate along the interface, but rather tended to be driven into the glass (Figure 1).

Characterization of metal/gluss intefaces in bioactive glass coatings

63

Ti6A14V

1

I

'

%

Figure 1. Vickers indentations at the glass 6P57/Ti6A14V (1.2 kg) and 6P50Ko-Cr (0.6 kg) interfaces performed in ambient air. The cracks were driven towards the glass, and the coating did not delaminate A TEM image of the 6P57iTi6A14V interface annealed at 800°C for 30 s is shown in Figure 2. An

interfacial titanium silicide (TiS&) layer, -150 nm thick, can be observed. The Ti& layer is divided into two regions: a continuous nanocrystalline layer in contact with the alloy and, on top of it, a zone with isolated Ti5Si3nanoparticles dispersed in the glass. The appearance of isolated particles on the TEM image can also result from the growth of elongated silicide grains, or dendrites, from the continuous layer into the glass. Consequently, they may appear as isolated particles (in the TEM samples) wherever the dendrite intersects the cross section. On the other hand, a thin (-150 nm) continuous CrOx layer can be observed at the interface between the Co-Cr alloy and the 6P50 coating (Figure 3). Figure 4 shows the Ti5Si3/alloy and TisSi3/glass interfaces. The lattice fringes of Ti (100) and TisSi3 { 121) are visible. See Figure 2 (a). A good lattice match exists between them, which can help in obtaining good adhesion. The glass/TisSij interface is shown in Figure 2(b). The size of the particles is in the range of -20 nm, and Ti& lattice fringes can be observed-{120}, { O l O } and (012). Following the experimental observations, the evolution of the glassimetal interfacial nanostructure can be summarized as follows. During heating, gas easily diffuses through the porous deposited glass coating, and a thin oxide layer forms on the surface of the metal. Thin-film x-ray diffraction showed the presence of an oxide layer on substrates annealed at temperatures below the glass softening point (550°C-650°C) [8]. At temperatures higher than the softening point of the glass, the glass layer sinters and flows. The inner glasdmetal interface becomes sealed from the external atmosphere, and the glass dissolves the oxide layer and starts to react with the substrate. TEM showed the formation of a -150 nm silicide or oxide layer after annealing. Coatings fired under these conditions did not delaminate during the indentation tests of adhesion [7, 81. TisSi3 and CrOx were also detected by x-ray diffraction and scanning electron microscopy in samples annealed at higher temperatures for longer times [8]. According to the previous discussion, the main reactions (formation of TisSi3 on Ti-based alloys, and formation of chromium oxide on Co-Cr alloys) can be written as:

8 Ti + 3 SiOz {glass} -+Ti5Si3 + 3 Ti02 {glass} 5 Ti + 3 SiOz -+TisSij + 3 0

2

?

(1)

(2)

Cr + 3/2 Na2O + 112 Cr203 + 3Na(g) ?

(3)

Cr + 1/2Si02 + CrO + li2Si

(4)

E. Suiz et al

64

6P57

A

=!

m .0 cn c 8 r v

0

200 400 Distance (nm)

Figure 2. TEM image of the cross section of a 6P57 Figure 3. TEM image and associated line glass coating on Ti6A14V annealed at 800°C for 30 s. analysis of the interface between glass 6P50 and a Co-Cr alloy after firing at 750°C for 30 s. If reactions (2) and (3) take place, the liberation of gas would form the bubbles observed in the overreacted samples [8,91 The bubbles and the thick, brittle interfacial reaction layers result in weak coatings with poor adhesion to the metal As an example, Figure 5 summarizes the evolution of the Ti6A14V16P57 interface during heating In conventional enameling theory, it is proposed that in order to achieve optimum glassimetal bonding, the glass should be saturated with the lowest valence oxide of the metal, without the presence of interfacial layers In this way, according to the theory, a transition region will form between the metallic bonding of the substrate and the ionocovalent bonding of the glass, providing a “continuity of electronic structure” that will result in good adhesion [12] However, the lack of characterization of enamel interfaces at the nanolevel precludes a complete confirmation of this theory More recent analysis of metalioxide interfaces tries to explain bonding in terms of fundamental contributions of image (electrostatic) forces and localized atomic bonding [13] In this work, optimum adhesion had been achieved through the formation of nanostructured interfacial layers For the coatings on Ti6A14V, the bond between the thin sihcide layer and the metal can be helped in part by the good lattice matching Also, if Ti5S13 dendrites grow into the glass, they can provide some mechanical interlocking that can contribute to the adhesion Consequently, control of the interfacial reactions at the nanolevel is a key fabrication step, and care must be taken to prevent excessive reaction, which can result in loss of adhesion due to the formation of a thick interfacial layer accompanied by bubbles in the glass

Characterization of metal/glass intefaces in bioactive glass coatings

65

Figure 4. High-resolution TEM image of (a) the Ti~Sij/Ti6A14Vinterface, and (b) the 6P57iTi~Si3interface formed after annealing at 800°C for 30 s. The optimum firing temperature is related to the temperature at which the glass softens and flows. The higher the softening point, the higher the temperature of the glass to flow, and higher processing temperatures are needed. For example, 6P68 coatings should be fired at 800°C in order to achieve the optimum adhesion, whereas, for the same firing times, 6P64 should be fired at 820°C.

Temoerature

o i', Ti-GAI4V Tc637 "C

I

Ti,Si, 150 nm

Ti,Si,

Ti-6AI-4Y

800"C,30seconds Optimum conditions

I

7

Gas bubbles

850 "C

Figure 5. Schematic illustration of the Ti6A14V/6P57 interface evolution during firing. Using the conditions described in the experimental section, it was possible to use dip coating to prepare -100 pm thick coatings on Ti dental implants with good adhesion to the alloy (Figure 6). During preparation of the ethanol-based slurries for dip coating, additional organics such as dispersants were not used in order to avoid additional problems related to burning of the organic materials (such as the formation of bubbles that cannot be eliminated in the short firing times required for Ti-based alloys). The firing conditions are similar to those used for the preparation of coatings on flat Ti6A14V substrates.

E. Suiz et al.

66

Figure 6. Original and coated titanium internal hexagonal cylinder dental implants. The -100 pm thick coating has been prepared using the enameling technique described in this work. SUMMARY The interfacial structure between Ti and Co-Cr alloys and bioactive glass coatings prepared using an enameling technique was investigated by TEM In coatings fired under the optimum conditions, reaction between the SiOz in the glass and Ti or Cr resulted in the formation of nanostructured interfacial layers (-150 nm thick) at the glass/alloy interface and optimum adhesion Control of the interfacial reactions between the glass and the alloys at the nanolevel was crucial.

ACKNOWLEDGMENTS The authors would like to acknowledge Prof K Hiraga and Mr B. Aoyagi for allowing us to use the ARM1250 kV microscope, and Drs S Hata and K Kaneko for TEM assistance. S Fujino wishes to thank the Japanese Ministry of Education, Culture and Science for a Young Researcher's Fellowship given to him in 2000, by the National Program of FelIowships for Young Researchers in Foreign Countnes S LopezEsteban was partly supported by a Fulbright Grant, and wishes to thank the Spanish Ministry of Education, Culture and Sports for financial sponsorship This work is supported by the Center of Excellence Project in the Institute of Scientific and Industnal Research, Osaka University, and the National Institutes of Health/ National Institute of Dental Research, Grant lROlDEll289, at Lawrence Berkeley National Laboratory

REFERENCES 1 2

3 4

NIH Technology Assessment Conference on "Improving Medical Implants Performance through Retrieval Information Challenges and Opportunities" January 10-12,2000 Bzomaterials and Medical Implant Science Present and Future Perspectives A National Institutes of Health Workshop, October 16-17, 1995, Summary Report Bzomzmetzcs,Tissue Engineering and Biomaterzals, Nahonal Institute of Dental Research Workshop, September 24-26, 1996 Annual Meeting of the Amencan Academy of Orthopedic Surgeons 1999 Anaheim, California u.n n aaos coni

Characterization of metal/glass inter$aces in bioactive glass coatings

5. 6. 7. 8. 9. 10. 11. 12. 13.

61

Chae, J. C., Collier, J. P., Mayor, M. B., Surprenant, V. A. and Dauphinais, L. A. J. Biomed. Mat. Res. (1992) 26, 93. Tisdel, C. L., Goldberg, V. M., Pam, J. A,, Bensusan, J. S., Staikoff, L. S. and Stevenson, S. Journal of Bone and Joint Surgery American Volume(1 994) 16, 159. Gomez-Vega, J. M., Saiz, E., Tomsia, A. P., Oku, T., Suganuma, K., Marshall, G. W. and Marshall, S. J. Advanced Materials (2000) 12,894. Gomez-Vega, J. M., Saiz, E. and Tomsia, A. P. J. Biomed. Mat. Res, (1999) 46, 549. Pazo, A,, Saiz, E. and Tomsia, A. P. Acta Mater. (1998) 46,2551. Oku, T. and Nakajima, S. Surf Sci. (1998) 407, L647. Oku, T. and Nakajima, S. J. Mat. Res. (1998) 13, 1136. Pask, J. A. Ceram. Bull. (1987) 66, 1587. Finnis, M. W.J. Phys.: Cond. Mat. (1996) 8, 5811.

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Nan0 and Microstructural Design of Advanced Materials M.A. Meyers, R.O. Ritchie and M. Sarikaya (Editors) 02003 Elsevier Ltd. All rights reserved.

DEVELOPMENT OF ADVANCED MATERIALS BY AQUEOUS METAL INJECTION MOLDING

S. K. Das I , J.C. LaSalle

', J. M. Goldenberg ' and J. Lu2

Polymer Technologies Inc., Clifton, NJ 07013 Honeywell International, Tempe, AZ 85285

ABSTRACT

Metal Injection Molding (MIM) is a well known technique for the cost effective production of complex multidimensional components. In general, such components are small, less than 25 grams, and often made in high production volumes. They are employed in a variety of industry sectors, for example, automotive and firearms. Application to aerospace industry has been limited due to demanding specifications, relatively low production runs, and difficulty in working with relatively advanced materials such as nickel-based superalloys. The development of a water based agar metal injection molding binder has allowed us to mold and sinter large superalloy components with mechanical properties exceeding those of investment cast superalloys. Tensile and fatigue properties of nickel-based superalloy IN718 exceed cast properties and meet aerospace specifications. INTRODUCTION

Traditional applications for metal injection molding (MIM) have been small (<25 gram) net shape parts exhibiting design and economic benefits over wrought or cast components. The traditional MIM process consists essentially of injection molding of metal powderhinder feedstock into a cavity to produce a net shape green part. The binder is then removed and the component is then sintered to full density. The process is shown schematically in Figure 1 . The firearm, medical and electronics industries are traditional users of MIM components with the firearm industry historically being a prime producer. Advances in binder systems and instrumentation for injection molding and sintering equipment are resulting in a dramatic expansion of MIM into new components and markets. Recently, Honeywell [1,2] developed

69

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S.K. Das et al.

Figure 1: Schematic of metal injection molding process using the aqueous based agar binder a new binder system for MIM that is an agar based aqueous binder. It eliminates the need for separate debinding and environmental liabilities associated with the debinding step. The result is cycle time reduction and cost savings compared with polymeric binders. The aqueous binder also molds at significantly lower pressures than traditional MIM feedstocks. As a result, longer thinwalled components can be molded as comparedwith traditionalMIM feedstocks. The low molding pressures also allow the use of soft epoxy/polymerictooling fabricated by rapid prototyping equipment. New component development times are thus shortened. Additionally,it offers the ability to produce large, thick parts more commensurate with those produced by investment casting. Net shape stainlesssteels components as large as 2 kg have been molded and sintered using the aqueous binder system. The advantages of the aqueous binder system are summarized in Table I. As a result of these advantages, the aqueous binder system is dramatically expanding the application of MIM to automotive, industrial, consumer, and aerospace components by moving MIM into parts traditionally manufactured by investment casting or wrought plus machining, Figure 2. Polymer Technologies is a licensee of the aqueous based agar binder and is now producing MIM parts on a commercial basis.

DESCRIPTION OF THE AGAR BASED AQUEOUS BINDER Traditional MIM binders are based on wax or polymeric systems that require the binder to be removed in a separate debind step, often taking many tens of hours. This debind step often requires acids or other noxious chemicals which present an environmental penalty and add significant process time. The aqueous binder is based on agar, a polysaccharidederived fiom seaweed used as a common food additive. It is hydrophilic, readily absorbing water. Metal powder is mixed with the water, agar and minor additionsto form feedstock pellets that can be easily fed into conventional plastic injection molding equipment. The metal powder

Development of advanced materials by aqueous metal injection molding

71

employed is typically under about 20 micrometers and is made by gas or water atomization. Compounding into feedstock is done by twin screw extrusion at rates 200 to 1,000 1bs.k. TABLE I COMPARISON OF AQUEOUS BINDER SYSTEM WITH TRADITIONALMIM SYSTEMS

I

Limitations of Todays Wax-Based Powder Injection Molding Systems

Benefits of Aqueous Based Agar Binder/ Molding System

+ Binder content - 10-20 Wt.%

+ Binder content - 2-3 Wt.%

+ Debindmg times - many hoddays

+ No separate debinding step required (Thick parts may require use of a 400 C/lhr hold BS part of sintering cycle)

+ Extra Steps - Special Operations

+ Water is the fluidizingagent - 8 wt. YO

(Powder pacWs0lvent extraction/bumout)

(evaporates &r molding leaving intergranularpores

+ Part Thickness < 1/4”

(for furepowdersyielding skong products)

+ No part thickness lhitations

+ Brittle as-molded part

(determines drying time)

+ Stiff but elastic as-molded part

+ Typical tolerance control to +/- 0.3%

+ Typical tolerance control to +/- 0.3%

+ Environmental Concern

(Explosive. toxicoutgas products or solvent requiring disposal)

+ No Environmental Concerns

i

8

lo*

‘S 104

s

a

E

a

Machining 103

Low

1 Medium

Investment casting

High

Complexity Figure 2: Schematic of market shift made available by the aqueous based agar binder

S.K. Das et al.

12

Typical metal solids loading of the feedstock is near 91wt% (61vol%), with approximately 2% agar and the balance consisting of water. The feedstock is relatively fluid at 85"C, having the consistency of toothpaste, Figure 3, and is thus easily injection molded into a net shape mold in a manner similar to plastic injection molding. Primary differencesare lower molding temperaturesand pressures. Upon cooling in the mold to near room temperature, the now molded feedstockdrops below its gelationtemperature, setting into a greenpart and allowing it to be removed. Cycle times are on the order of half a minute, depending on part size.

t

E

4 1

Figure 3 :Schematic of viscosity behavior of aqueous based agar binder

After approximately 1 hour in ambient air,the green part will have dried and is now ready to be sintered. No separate debind step is required as is necessary for traditional MIM feedstocks. Rather, a dwell time of approximately 1 hour is incorporated into the beginning of the sintering cycle. This step pyrolizes the binder, allowing the carbon to be removed during the sinteringcycle which is typically done in hydrogen or vacuum dependingon alloy. Sintering temperatures in the range of 1300-1400°Care typically employed for stainless steel alloys. Total debindinglsintering time is on the order of 14 hours using a large commercial batch furnace. Depending on part size, part loading quantities on the order of a thousand can be sintered in such furnaces, keeping per part sintering costs low.

MECHANICAL PROPERTIES 1 7-4 PH Stainless steel Many of the applications require demanding mechanical properties and dimensional tolerances. Figure 4 lists the average tensile properties of the stainless steel alloy 17-4PH,

14

S.K. Das et al.

Figure 5: Core and near surfme areas of 17-4 PH showing uniform formation of martensite Nkkel-Based Superalloy Inconel 718 One of the earliest nickel based superalloys developed is IN718. It is a precipitation hardened alloy strengthened by the y” phase, Ni3Nb, but it also has a host of competing phases which can form. IN718 is attractive for aerospace application because it has good high temperature oxidation resistance and strength to 650°C as well as good ductility and toughness. These positive service attributes,however, are a debit with respect to traditional forming techniques such as casting and machining, adding cost to complex shape components. Tensile properties are shown graphically in Figures 6a-d, which compare properties of Tensile Strength

0.2% Yield Strength

200

150

180

140

160

;; 130

‘

140

120

120

110

100

100

Figure: 6a Comparison of Ultimate Tensile Strength

Figure: 6b Comparison of Yield Strength

Development of advanced materials by aqueous metal injection molding

Elongation

15

Reduction of Area

25 20

s

15 10 5

0

Figure: 6c Comparison of Tensile Elongation

Figure: 6d Comparison of Tensile Reduction of Area

conventional cast, conventionalwrought, MIM and HIPed MIM components. In these figures, cast and wrought show specification minimum while MJM shows minimum and maximum values on the bars. Investment casting properties are the target of MIM components, since many of the aerospace components are conventionally cast and machined.HIPingof the MIM test bars to 111density does improve the tensile properties, as would be expected. It was found that the HIPed bars had superior ductility compared with wroughtproduct, although wrought had higher strength. Most notable, however, is that both the unHIPed and W e d tensile properties of the MIM IN718 easily surpassed the cast IN718 in both strength and ductility. High cycle fatigue properties were performed using an R= -1 (tensiodcompression)and k=l (smooth bar). The results are shown in Figure 7. Again, both the unHIPed and HIPed MIM IN718 surpassed the cast test bars, even when the cast bars were HIPed. Surprisingly, the UnHIPed MIM fatigue bars were comparable to wrought processed IN718 while the HIPed MIM bars exceeded wrought values. The superior properties are most likely a result of the refined grain structure observed in the MIM components

16

S.K. Das et al.

I10

m

B

m

m

m

m W

m 4

a rn

103

104

105

106

Cycles to Failure

107

108

Figure 7: High Cycle Fatigue IN718

AEROSPACE COMPONENT EXAMPLE Metal injectionmolding was thus explored as an alternative forming method for an aerospace flow body in alloy IN718. The flow body, essentially a butterfly valve housing, is extremely large by conventionalMIM standards,having an 8.8cm inner diameterand weighing approximately 1600grams. By formingthe thin wall ofthe body byMIh4 to the required final part thickness, significantlyless machining is required compared to a conventional cast machining blank, which must be cast thick to fully fill the part. The water based agar binder (1) was employed to utilize its low flow stress as well as its rapid and clean debind attributes. Before building a tool for such a large and novel MIM part, it was useful to mold and sinter a smaller prototype. Fortunately, prototype tool of a 7 cm ID tool existed for experimentation in plastic. Parts were successfullymolded and sintered, producing a sintered component 6.7cm ID. Excellent roundness was maintained during sintering through the use of proprietary setters. Before cutting a tool for the larger component, it was also desirable to employ mold flow simulation to explore gating options. Figure 8 shows the mold flow analysis applied to parameters commensuratewith the water based agar feedstock on the 8.8 cm ID flow body housing. After establishinga baseline by prototypingthe smaller flow body and performing simulation, a tool was cut and parts were molded and sintered. Water based agar feedstock of alloy IN718 was molded by Polymer Technologies, Inc. using an 350 ton Van Dorn Injection molding machine. Nominal chemistry of the alloy powder is 52.5Ni-18.5Fe-18.5Cr-5.1Nb-3Mo-0.9Ti-O.5Al-O.04C. Sintering was performed in batch sintering fiunaces, both Elnik and AVS. Proprietary setters were employed in a near net shape part requiring only minor finishingmachining. The green and sintered (8.8 cm ID) flow body are shown in Figure 9.The wall thickness of the green parts was typically 3 mm, filling a circumference of approximately 60 cm.

Hot Isostatic Pressing (HIP) was performed on one set of material to obtain full density and mechanical properties required by the aerospace industry. Solutionizingwas performed at 970°C for 30 minutes followed

I1

Development of advunced materials by aqueous metal injection molding

by a rapid gas cool. Aging was performed at 720°C for 8 hrs ramped down at a 4OoC/Hrrate to 620°C for an 8 hr hold, followed by an air cool to room temperature.

M

.

Figure 8: Moldflow analysis simulating time distribution as a function of different gating.

Figure 9: Green and sintered IN718 aerospace flow body housing

Densitiesof the test bars, as measured by Archimedes,are approximately99%. Carbon and oxygen values are 0.2 and 0.2wt??,respectively. It is noted that carbon for the cast and wrought alloys is nominallyO.O4wt%. An optical micrographs of sintered+heat treated material is shown in Figure 10. A refined microstructure is observed with equiaxed grains approximately20 micrometers. Some second phase precipitates are present, which are most likely carbides resulting from the carbon level.

‘IOUNO3 WNOISN3JUIa

PART 2: FUNCTIONAL MATERIALS

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Nan0 and Microstructural Design of Advanced Materials M.A. Meyers, R.O. Ritchie and M. Sarikaya (Editors) 02003 Elsevier Ltd. All rights reserved.

MICROSTRUCTURAL DESIGN OF NANOMULTILAYERS (FROM STEEL TO MAGNETICS) Greg Jan Kusinski and Gareth Thomas MMFX Technologies Corporation Irvine, CA 92612, USA

ABSTRACT The development of high-tech materials requires functional, multicomponent microstructures including multilayers, designed, processed and controlled at the micron and nanometer levels. It is now quite well recognized that to optimize and design materials for specified properties, materials are best utilized as composites. The nature of the components, their structures, morphologies and interfacial characteristics are most important. In particular, multilayered nano-structures are attractive for mechanical and many functional properties (e.g. magnetic). In order to understand the properties of any such multilayered system, and hence to be able to design pre-determined sets of properties, it is necessary to h o w their structure. For this reason, characterization of physical, chemical, and magnetic structures at relevant length scales is of particular importance. In this paper, attention is drawn to multilayered retained austenite/martensite (yret/MS) steels and multilayered Co/Pt films for high density magnetic recording.

INTRODUCTION Materials Science and engineering is concerned with understanding the relationships between processing, microstructure, and properties. With this understanding it is now possible to manipulate the microstructure down to the nano size, so as to achieve a set of defined properties. Since it is normally impossible to obtain such sets of properties in a monotonic monolayer, it is necessary to design the needed properties via composites within which the multilayer becomes an attractive morphology, and one in which control of the interfacial structure and bonding can be achieved. Clearly, the ability to characterize such nano materials requires advanced imaging and probe methods, within which high resolution (now at the atomic level), is essential. The results given in this paper, have involved detailed applications of electron microscopy, diffraction and microanalyses [ 1,2]. There are size limits that must be considered. Often no recognizable structures can be resolved when layer thicknesses are about 4 0 8, [3] and nano sized components do not necessarily have the same crystal structure as in bulk. Crystal structure determination is non-trivial and atomic imaging for real space analysis is becoming a viable approach [4]. Also as the dimensions of the components in the multilayers, approach nano scale and below, there is a marked increase in surface to volume ratios. Thus unique properties would be logically expected in such small scale composites

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In this paper we present results to show the microstructural similarity of nano composite structures in “traditional matenals” such as steels (to improve the mechanical and corrosion properties) and in the currently developing vertical magnetic recording materials for improving the information storage capacityof magnetic recording materials. The following abbreviations will be used through out this paper: Transmission Electron Microscopy (TEM); Bright Field imaging in TEM (BF); Dark Field imaging in TEM (DF); Selected Area Diffraction (SAD ); High Resolution Transmission Electron Microscopy (HRTEM); Multilayer (ML); Perpendicular Magnetic Anisotropy (PMA); martensite (Ms), austenite (y) martensite start transformation temperature (TMs),growth temperature (TG),Co layer thickness (tco),coercivity Hc.

NANO-LAYER MICROSTRUCTURES Steels-microcomposite martensite The austenite + martensite reaction in steels produces two main types of transformation products:- twinned plates when the transformation occurs at low temperatures (below about 250C), and packets of dislocated laths at higher temperatures (above about 320C). Figure 1 shows a schematic of the multilayer structure that is desired for improved properties. Crystallographic analysis, see Figure 2, shows that the orientation relationship is that of the Kurdjumov-Sachs (WS) with { 11l}y habits. Thus there is a maximum of four martensitic packets of laths per prior austenite grains. Notice also that the microstructure is designed to be free from precipitates such as carbides, carbonitrides etc. The basis for this is to greatly reduce the formation of microgalvanic cells between particles and ferritic matrix, which is necessary to improve corrosion resistance, especially in saline solutions. The current steels used in construction are generally femteipearlite mixtures such as in ASTM A615 steels, which are unsatisfactory for good corrosion resistance (see [5]).

Microcomposite Steels, Packet Lath Martensite

(Dislocated lath martensite enveloped by stable retained austenite films)

1 - Untransformed Nan0 Sheets of retained

BOUNDARIES WITHOUT CARBIDES

2 -Dislocated Laths

Figure 1 . Schematic of Microcomposite steels.

Microstructural design of nanomultilayers

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Figure 2 shows an actual example of the multilayered austenite/martensite compostie -note the scale of the multilayer structure in the packet. Many investigations have been carried out on martensitic steels, but it was not until 1973 that the microcomposite nature of packet martensite was elucidated [6-81. The microstructure can be rationalized in terms of the temperature dependence of the resolved shear stresses for slip vs. twinning-the latter being preferred at low temperatures [S]. Twinned martensites are relatively brittle, and are generally to be avoided in designing for toughness at high strength levels [9,10]. However since the relationship between composition and martensite start transformation temperature (TMs) is quite well known, it is possible to design a packet multilayer martensitic steel by choosing compositions which keep TMSabove about 320°C [S]. This restricts the %C to be usually below about 0.35 wt%. Typical alloys include the Fe/Cr/Mn/C and Fe/Si/C systems [7-lo]. A model to explain the multilayer martensite/austenite composite has been published recently and is illustrated in Figure 3 [l 11. The multilayer composite contains the tough work-hardened laths of martensite linked coherently (with the Kurdjumov-Sachs WS orientation relation) to the untransformed, ductile austenite, giving a packet of alternating layers of austenite (-50 atoms wide) and dislocated martensite laths. Unlike pearlitichainitic microstructures, there are no carbides or other particles, and the high strength, high toughness derives from this microstructure. A variant would be dual/triple phase steels (DFM) in which the packets are mixed with ferrite. In all these alloys, the key to attractive properties is in maintaining the multilayer austenitemartensite composites in the packets by keeping TMSabove -320"C, and cooling fasl enough lo avoid nonmartensitic products. Such microstructures offer a range of attractive properties [ 12-14], and some examples are summarized below and in Figure 4, which compares some properties of the multilayered steels with commercial ASTM A615 steel (ferrite - pearlite).

Figure 2: Transmission electron micrographs showing the interlath retained austenite. (a) Bright field image - packet lath martensite. (b) Corresponding dark field image formed with fil y reflection -thin films of retained austenite reverse contrast. (c) SAD pattern showing K-S relationship of martensite and austenite and hence, coherent interfaces. DF image @) was formed with iil y reflection.

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Martensite dislocations

Solute ennched stabilized austenite

Figure 3: Schematic to illustrate the transformation of austenite (y) to martensite (Ms) and the stabilization of untransformed austenite between martensite laths. (a) “entrapment” of stabilized untransformed austenite between laths in the martensite packets, (b) “Final State”, Martensite and austenite layers not to scale. (b) Fatigue (rebar samples) 140

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Figure 4: (a) The tensile properties of Microcomposite steels compared to ASTM A615-ferrite pearlite steel, (b) the superior fatigue properties compared to A615, (c) superior DBTT and low temperature Charpy toughness, (c) corrosion samples after several weeks in 3% chloride. Note the A615 steel is almost totally destroyed by corrosion.

Microstructural design of nanomultilayers

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Some properties (A) Variable strength may be designed by varying the %C in the laths since this is a linear relationship, or in DFM steels by varying the % packets+femte. Note there is no strict yield point, Figure 4(a), in the stressstrain curves from such structures since the laths are already rich in dislocations, and so the steel is already in the plastic condition. Typically the 0.2% offset in the stress-strain curve is taken as the “yield stress”, and the high tensile to yield ratios (1.5 or more), indicate excellent cold formability, e.g. for sheets (autos), wire and strands. This microstructure and its coherency allows plastic relaxation ahead of cracks, giving Klc values > 100 ksiJns [&lo]. (B) The multilayered structure contains no precipitates (carbides etc.) and hence there are few microgalvanic corrosion pitting centers. Thus there is a considerable gain in corrosion resistance especially in saline conditions. These benefits are now being utilized in new and repaired infrastructures in which corrosion limits the lifetime of steel in concrete structures (See the web site: [ 5 ] ) . It is an astounding fact that infrastructure repair costs are estimated to be approximately 4 trillions $ over the next decade. ColPt MAGNETIC MULTILAYERS Basis The realization in the past decade or so that many important magnetic properties are microstructure sensitive has led to rapid developments in the field of magnetic devices, involving atomically engineered thin films, nanostructures and multilayers. In these composites the structure of the interfaces between dissimilar materials or/and at the grain boundaries governs the novel properties (e.g. perpendicular magnetic anisotropy, giant magnetic resistance, etc.) [ 151. In particular, magnetic multilayers (MLs) composed of modulated ferromagnetic-nonmagnetic layers such as Copt MLs [ 16,171 with large perpendicular magnetic anisotropy (PMA) and high coercivity have recently been proposed as future magnetic media in Terabit/in* magnetic recording systems [18]. In addition, recent interest in Co/Pt was sparked by the discovery that the magnetic properties can he locally modified by ion-beam irradiation [ 19,201. Characterization of the microstructure and the magnetic domain structure in such films is important from a technological as well as a fundamental perspective [21-231. In this paper, the influence of growth temperature and multilayer thickness on the structure and magnetic properties of Co/Pt MLs are discussed. Other parameters which affect the magnetic performance of the MLs include magnetic patterning by ion irradiation which allows the separation of the vertical and in-plane magnetization. Further details can be found elsewhere [21,24-261. Microstructural characterization For the specific experiments discussed here, Co/Pt multilayers with representative structure: / 20 nm Pt seed / Nx(t nm Co/l nm Pt) / 1 nm Pt cap layer /, were fabricated by electron beam evaporation using a Torr base pressure deposition system [27,28]. Figure 5 shows a plan-view, bright field Transmission Electron Microscopy (TEM) image and Selected Area Diffraction (SAD) patterns of a Co/Pt multilayer grown at 250°C. The fine structure visible in some of the grains is attributed to Moirk fringes caused by the small lattice mismatch between Co and Pt. The plan-view SAD pattern shows the typical ring spacing associated with polycrystalline face-centered cubic fee) Pt except for ring splitting due to the presence of highly strained Co layers, which will be addressed later. The intensity distribution of the rings indicates a strong <111> texture with only some grains oriented randomly and contributing to the (1 11) and (002) ring intensities.

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Figure 5: (a) Plan-view TEM micrograph and (b) SAD pattern of a lOx(3 8, Co / 10 A Pt) multilayer grown at TG= 25O”C, (c) SAD with 30” sample tilt showing arcing of the rings. One of the questions to be resolved by careful characterization is whether the multilayers are alloyed or not, i.e. are the Co/Pt “pure” components. Careful examination of the SAD patterns revealed that all of the rings associated with thefcc structure were split, with separation Ag increasing with the diffraction vector g. For each doublet, the inner ring corresponding to a larger real space parameter is always more intense and the outer ring is weaker. This implies two distinctive lattice parameters through the thickness of the Copt multilayer stack. Figure 6 shows (a) the SAD pattern for the discussed Co/Pt multilayer and simulated ring diffraction patterns of (b) Ptf,, and Co Pt3, (c) Ptf,, and Cohcp,(d) Ptf,, and Cof,,. On all patterns, triangles label Pt rings: (11 l), (200), (220), (1 13) and (222). By comparing the simulated SADs to the experimental data shown in Figure 6 , it is clear that the layers must be “pure” Co-Pt both fcc. No evidence for alloying or ordered compound formation was detected. However, the ratio of the equilibrium Cofccto Ptf,, spacing in the simulated pattern is not correct. As shown, any two Co and Pt rings on the recorded diffraction pattern, for example Co(220) and Pt(220), are much closer to each other than on the simulated pattern (d). This implies that the Co layers are strained. Figure 6 (e) and shows simulated diffraction rings as a function of increasing tensile strain of the Co layers, with image (f) showing a good match. Hence, Starting from the seed Pt layer, the Pt(ll1) layers are stacked according to the equilibriumfcc stacking sequence observed in bulk Pt. The Co layers, which, in bulk are hcp, follow thefcc stacking sequence of underlaying Pt.

(a

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Figure 6: SAD pattern for the Co/Pt multilayer and simulated plan-view diffraction patterns for (b) Ptpc and Copt,, (c) PtP, and Cq,,,, and (d) Ptfccand Cof,, tnaiigles label Pt rings. (e) and (0 Simulated plan-view diffraction patterns of Ptrccand Cotccat various strains: (e)qo= 3.65 A, u= +2.85%, acJap, = 0.92 and (f) ac0= 3 85 A, u= +8.45%, aco/ap,= 0.98 Numbers label rings. 1) Pt(lll), 2) Co(1 ll), 3) Pt(002), 4) C0(002), 5) Pt(022), 6) C0(022), 7) Pt(l13), 8) Pt(222), 9) Co(113), 10) C0(222), (see text).

Figure 7 shows a lattice image with fcc multilayers stacking and good coherency across the CoiPt interfaces Ihis (1 11) stacking further implies a small volume anisotropy of Co Thus the perpendicular easy axis of magnetization is attributed to the interface anisotropy and in particular to strain contributions [29] d(,,,,,, - 2 265

A, d(,,,,c o =

2 047 A

Figure 7: Cross-sectional micrograph of a IOx(3 8, Co and 10 8, Pt) multilayer grown at T,

= 250°C.

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Analysis of the multilayers as a function ofgrowth temperature The microstructural evolution of multilayers as a function of growth temperature (TG)is presented in Figure 8, which shows plan-view BF images, SAD patterns and DF-hollow cone images obtained using (111) rings, (1 11)DF, of ML's grown at T, = 190"C, T, = 250°C and T, = 390°C. As depicted in the BF images, Figure 8(a), (e) and (i), all of the investigated samples were polycrystalline. The average grain size was found to increase with increasing T,. As discussed above the SAD patterns, Figure 8(d), (h) and (1) showed typical ring spacing associated with the polycrystalline fcc Pt structure. For all samples, a strong out-of-plane 4 11> texture was measured, as seen from very weak (111) and (002) rings and an intense (022) ring. Only some grains oriented randomly contributed to (1 11) and (002) rings. The SAD patterns from larger areas showed a uniform intensity distribution around all rings, indicating random in-plane orientation and only out-of-plane <111> texture.

Figure 8: Plan-view BF TEM images, SAD patterns and (1 1 1)DF images of the Copt ML's grown at TG= 190°C, TG= 250°C and TG= 390oC, displayed in rows. All SAD'S were collected with a 5 pm aperture ~41.

The (1 1I)DF images, Figure 8(b), ( f ) and (d), show the same areas as the respective BF images and display only the grains without the - 4 1 1> texture. Figure 8(c), (g) and (k) are lower magnification images showing the distribution of such grains. As presented, samples grown at the low temperature of 190"C, @) and (c), had a large number of grains lacking the < l l 1 > texture. The distribution of such grains was very uniform. With increasing T,, the number of such misoriented grains decreased. For the T, = 250°C sample, ( f ) and

Microstructural design of nanomultilayers

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(g), the majority of misoriented grains were smaller than the average grain size, although a few, large misoriented grains were also found. For samples grown at 390°C, a good < l l 1 > texture was observed, with only very few grains lacking the <111> texture, as shown in (i) and (k). Moreover, such misoriented grains were much smaller than the <111> textured grains. Hence, as clearly shown by the set of (1 1l)DF images the <111> texture was found to improve with an increase in sample growth temperature. For samples grown at TGup to 300°C, all diffraction rings were split, indicating two distinctive lattice parameters for the Co and Pt layers, as discussed above. For samples grown at TG= 390°C above a critical transition temperature, T,,,,, the ring splitting attributed to the two separate Pt and Co parameters was not detectable, indicating a continuous gradient in lattice parameter between that of strained Co and that of Pt.

Structure as a function of Co thickness

The structure of Co/Pt multilayers was also investigated as a function of Co layer thickness (b).In agreement with previously published data [30], it was found that the stacking sequence in the Co layers changes with increasing Co thickness. At 0.2 nm - 0.6 nm Co thickness, the (Co/Pt) multilayer structure showed fcc stacking with 2.2 8, layer spacing. When the Co thickness increased beyond -0.6 nm, hcp stacking faults (SF) were observed and their density increased with increasing Co layer thickness. Above approximately tco = 15 A,the Co layer stacking is mainly hcp. Co/Pt multilayers with Co layer thickness below approximately 6 A were uniform and relatively defect free. The only indication of the Co vs. Pt layer in the HRTEM image was a slightly higher intensity in the Co layer due to preferential thinning of the Co layer during specimen preparation by ion-milling and a lower atomic number contrast. This intensity variation had a periodicity of the analyzed multilayers. With increasing tco, roughening of the MLs was observed, with increased number of defects (Figure 9). As shown, the measured intensity is much higher within the Co layer; however, the precise location of the CoiPt interface is not known. The (1 11) stacking sequence in some of the locations isfcc, (same vertical atom position for every third layer, ABCABC), but some hcp stacking (same vertical atom position for every second layer, ABAB) is also seen.

Figure 9: Cross-section HRTEM image of (1 11) 15 A, Co layer in the C o p t multilayer.

G.J. Kusinski and G. Thomas

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Magnetic properties In addition to affecting the grain size and the <111> texture, TG is also known to influence the magnetic properties, such as coercivity (Hc). Magnetic hysteresis loops of the Co/Pt multilayers grown at different growth temperatures are shown in Figure 10. As shown, the perpendicular HC of the C o p t ML's was found to increase with increasing TG [27,24]. The coercivity increases by almost a factor of two on increasing the TG from 200°C to 300°C. However, when TG is increased beyond a critical transition temperature, Tc,it, a decrease in perpendicular coercivity is observed, and the HC for samples grown at 390°C is reduced to 5.8 kOe. A further increase in multilayer growth temperature results in loss of perpendicular anisotropy.

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Figure 10: Mgnetic hysteresis vs. multilayer growth temperature. (a) TG= 19OoC,(b) Tc = 250°C, (c) TG= 300°C and (d) TG= 390°C. These results show that the magnetic properties of such multilayer films depend on microstructure. With an increase in Tc up to a certain critical temperature, Tcrit, an increase in grain size and an improved <111> texture were found, both contributing to an increase in Hc. For ML's grown at TG = 390°C > Tait, a decrease in HC was measured, and small magnetically decoupled domains were observed. The size of these domains was similar to the grain size. This correlates well with Co depletion at the column grain boundaries and with the diffuse Co/Pt interfaces, measured as one set of Co-Pt rings. Such diffuse interfaces are known to reduce the PMA and, hence, reduce H,. Also with increasing Co layer thickness, a decrease in H, was observed. The coercivity is therefore a function of both the microstructure (grain size and texture) and interface quality, which is strongly influenced by Tc. Thus the magnetic properties can be engineered by appropriate choice of growth parameters and multilayer repetition. CONCLUSIONS

In this brief review we have shown that controlled multilayer structures provide superior properties such as mechanical and corrosion in austeniticllath martensitic steels, and magnetic properties in Co/Pt multilayers.

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ACKNOWLEDGEMENTS Work at NCEM/LBNL was supported by the U.S. Department of Energy under Contract No. DE-AC0376SF00098. The authors acknowledge contributions from K.M. Krishnan, E.C. Nelson and G. Denbeaux of Lawrence Berkeley National Laboratory and B.D. Terris, C.T. Rettner, A. Kellock and J.E.E. Bagglin of IBM Almaden Research Center.

REFERENCES 1.

2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.

17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30.

Williams, D.B. and Carter, C.B. (1996). Transmission electron microscopy: a textbookfor materials science. Plenum Press, New York and London. Thomas, G. (1998). In: Boundaries and Interfaces in Materials: The David A. Smith Symposium, pp. 3-17, Pond, R.C., Clark, W.A.T., King, A.H. and Williams, D.B. (Eds). The Minerals, Metals and Materials Society, Warrendale. Walton, C.C., Thomas, G. and Cortright, J.B. (1998), ActaMaterialia, 46,3767. Thomas, G. (1999). In: 20th Ris0 Int. '1 Symposium on Materials Science, pp. 505-521, www.mmfxsteel.com Krauss, G. and Marder, A.R. (1971), Metallurgical Transactions A , 2,2243. McMahon, J.A. and Thomas, G. (1973). In: 3rd Int'l Conference on the Strength of Metals and Alloys, pp. 180-184, LBL-1490 Thomas, G. (1973), Iron and Steel International, 46,451. Thomas, G. (1978), Metallurgical Transactions A , 9A, 439. Rao, B.V.N. and Thomas, G. (1980), Metallurgical Transactions A , 11A, 441. Thomas, G . and Kusinski, G. (2000). In: ASMHeat Treat Conference, An International Symposium in Honor of Professor George Krauss, pp. 515-518, Koo, J.Y., Young, M.J. and Thomas, G. (1980), Metallurgical Transactions A , 11A, 852. Kim, N.J. and Thomas, G. (1981), Metallurgical Transactions A, 12A, 483. Kusinski, G. and Thomas, G. (1999). In: Proceedings of 1st Int. Con$ on Automotive Heat Treating, pp. 17-25, ASM International Ultrathin Magnetic Structures I: an introduction to the electronic, magnetic, and structural properties, edited by Bland, J.A.C. and Heinrich, B., Springer-Verlag,Berlin, Heidelberg (1994) Carcia, P.F. (1988), Journal ofApplied Physics, 63, 5066. Weller, D., Farrow, R.F.C., Marks, R.F., Harp, G.R., Notarys, H. and Gorman, G. (1993), Materials Research Society Symposium Proceedings, 313, 791. Wood, R. (2000), IEEE Transactions on Magnetics, 36,36. Chappert, C., Bernas, H., Ferre, J., Kottler, V., Jamet, J.-P., Chen, Y . ,Cambril, E., Devolder, T., Rousseaux, F., Mathet, V. and Launois, H. (1998), Science, 280, 1919. Weller, D., Baglin, J.E.E., Kellock, A.J., Hannibal, K.A., Toney, M.F., Kusinski, G.J., Lang, S., Folks, L., Best, M.E. and Terris, B.D. (2000), Journal OfAppliedPhysics, 87, 5768. Kusinski, G.J., Krishnan, K.M., Denbeaux, G., Thomas, G., Weller, D. and Terris, B.D. (2001), Applied Physics Letters, 79, 221 1. Thomas, G. and Hutten, A. (1997), NanoStructuredMateriab, 9, 271. Denbeaux, G., Fischer, P., Kusinski, G., Gros, M.L., Pearson, A. and Attwood, D. (2001), IEEE Transactions on Magnetics, 37,2764. Kusinski, G.J., Thomas, G., Denbeaux, G., Krishnan, K.M. and Terris, B.D. (2002), Journal of Applied Physics, 91, 7541. Kusinski, G.J. and Thomas, G. (2002), Microscopy and Microanalysis, 8, 319. Kusinski, G.J., Krishnan, K.M., Denbeaux, G. and Thomas, G. (in press), Scripta Materialia, Weller, D., Folks, L., Best, M., Fullerton, E.E., Terris, B.D., Kusinski, G.J., Krishnan, K.M. and Thomas, G. (2001), Journal of Applied Physics, 89, 7525. Kusinski, G.J. (2001). Ph.D. Thesis, University of California, Berkeley. Zhang, B., Krishnan, K.M., Lee, C.H. andFarrow, R.F.C. (1993), Journal OfAppliedPhysics, 73, 6198. Li, Z.G., Carcia, P.F. and Cheng, Y. (1993), Journal OfAppliedPhysics, 73, 2433.

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Nan0 and Microstructural Design of Advanced Materials M.A. Meyers, R.O. Ritchie and M. Sarikaya (Editors) 02003 Elsevier Ltd. All rights reserved.

EFFECTS OF TOPOGRAPHY ON THE MAGNETIC PROPERTIES OF NANO-STRUCTURED FILMS INVESTIGATED WITH LORENTZ TRANSMISSION ELECTRON MICROSCOPY Jeff Th.M. De Hosson and Nicolai G. Chechenin 'Department of Applied Physics, Materials Science Centre and Netherlands Institute for Metals Research, University of Groningen, Nijenborgh 4,9747 AG Groningen, The Netherlands. Skobeltsyn Institute of Nuclear Physics, Moscow State University, 118899 Moscow, Russian Federation.

ABSTRACT This paper concentrates on a detailed analysis of Lorentz transmission electron microscopy (LTEM) observations in the study of the magnetic properties of soft magnetic films. The nano-crystalline (Fe99Zrl)l-,NX, films have been prepared by DC magnetron reactive sputtering with a thickness between 50 and 1000 nm. The grain size decreased monotonically with N content from typically 100nm in the case of N-free films to less than 10 nm for films containing 8 at% N. Besides ripple fringes in the LTEM image that are commonly observed in nanocrystalline soft magnetic films also a dotted contrast apears along the ripple fringes. A theory of LTEM images for films with 1D- and 2D periodical topographies in combination with the micro-magnetic oscillations of the magnetization is presented. The theory predicts the 2D-pattern in LTEM in agreement with experimental observations. We show that in contrast to the traditional point of view not only the direction of the magnetization vector in nano-crystalline films makes a correlated small-angle wiggling but also the magnitude of the magnetization modulus fluctuates. LTEM studies were performed using JEOL 201 OF transmission electron microscope equipped with a post-column energy filter that provides an additional magnification of around 20 at the plane of the CCD camera with respect to the maximal attainable magnification by using a low field objective minilens.

INTRODUCTION In the early sixties of last century Gareth Thomas stood on the threshold of the development of transmission electron microscopy [ 11 and indisputably he became an inspiring and enthusiastic world leader in the application of this technique to solve materials problems. Only a few of us have pioneered so much in the structure-property relationship and in so many different areas of materials science. His research covered an extraordinarily broad range of topics, but it was and still is, characterized by a deep penetration into each subject to provide a thorough understanding. His seminal work stimulated hundreds of investigations over the last 40 years, clarifying structural aspects and thereby permitting analysis of the structural properties. Through these studies our understanding of the relationship between microstructure and property became more satisfactory and new concepts have been developed further. Besides structural properties Gareth Thomas showed great interest in the application of transmission electron microscopy to the field of functional materials. For instance he focused on a connection between the microstructure of various nano-structured alloys and the Giant Magneto-Resistive (GMR) properties [2,3] that also stimulated later our own scientific work [4,5]. Along these lines of his own interests this contribution concentrates on the application of transmission electron microscopy to functional materials, such as ultra-soft magnetic films for high-frequency inductors, to reveal the structure-property relationship. There exists an increasing demand for further miniaturization in portable appliances (e.g. mobile phones, palmtops), that is to say in communication tools. To this end the use of

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high-frequencies (e.g. 10-1000 MHz) in combination with thin magnetic materials is desirable. The use of magnetic films allows the integration of transformers and inductors into silicon 1C circuitry. Soft-magneticfilms are also widely used in modem electromagnetic devices as a high-frequency (>I00 MHz) field-amplifying component, e.g. in read-write heads for magnetic disk memories for computers and as a magnetic shielding material, e.g. in turners. The main requirements for the film material are: a high saturation magnetization, combined with a low coercivity and a small but finite anisotropy field. In addition the material should have a reasonably high specific electrical resistivity to reduce eddy currents, and also appropriate mechanical properties. To obtain the desired properties (low coercivity, little strain and very small magnetostriction) the use materials with grain size of the order of 10 nm nanometers, like nano-crystalline iron, becomes attractive [6]. Knowledge of local magnetic properties is essential for the development of new magnetic nano-sized materials. One of technique that is suitable for the measurement of local magnetic structures is Lorentz-Fresnel (or defocused) imaging mode of transmission electron microscopy. This rather classical TEM technique [7,8] has several outstanding advantages: uncomplicated application to various parts of thin foil, possibility of dynamical studies and good spatial resolution. Nevertheless, to obtain quantitative information from Lorentz micrographs is relatively difficult due to an in-direct link between image contrast and spatial variation of magnetic induction, which is problematic in regions of abrupt magnetization changes [9]. In this paper the possibility of a quantitative analysis of the magnetic properties of nano-crystalline iron using transmission electron microscopy is presented. The goal is to delineate a more quantitative way to obtain information of the magnetic induction and local magnetization. In particular the latter physical quantities affect the functional properties of ultra-soft magnetic materials for high-frequency inductors. One of the magnetic features that can provide quantitative magnetic information are the so-called magnetization or magnetic ripples, caused by local variation of magnetic induction that deviate from the mean magnetization direction [lo]. Besides Lorentz Fresnel (LTEM) also (off-axis) electron holographic modes can be used to analyze the magnetic structures [ 1I , 12,13,14,15]. For quite some time it is known that in polycrystalline and in nanocrystalline soft magnetic films with an induced uni-axial anisotropy, the direction of the magnetization wiggles around the easy axis producing a socalled micromagnetic ripple (see for example [lo] and references therein). The local variation of the magnetic field in a thin film influences the out-of-focus image in the transmission electron microscopy (TEM) via variation of the Lorentz force that acts perpendicular to directions of the electron beam and to the magnetic induction. Consequently, in Lorentz transmission electron microscopy (LTEM) the quasi-periodic oscillation of the transversal component of the local magnetization leads to almost parallel (1D) fringes in under- or overfocused images. From the spacing between the fringes the wavelength and the amplitude of the angular spread of the magnetization direction can be estimated using a simplified relation [I61 0.059-

C

Bt3,

where & is in degrees, B represents the magnetic induction in Tesla, f and Ax are the thickness of the film and the periodicity of the ripple structure (in micrometers), respectively. C = 2AUZo is the contrast of the LTEM image, where l o is the average intensity and AZ is the rms variation of the intensity due to ripples. This relation follows from both a classical approach of the LTEM imaging of micromagnetic ripple developed by Fuller and Hale [8] and a diffraction approach developed by Wohlleben [17], based on the theory of Aharonov and Bohm [18]. In both approaches the film is assumed to be flat and only the transversal component of the magnetization oscillates in the longitudinal direction. Often more complicated, e.g. bending or branching, Fresnel patterns are observed around magnetic domain walls, film edges, or for films with grain sizes larger than -50 nm [8,10,16,17]. The influences of the grain size and inhomogenieties on the periodicity and dispersion angle of the magnetization have been discussed in a number of papers [ 10,16,19,20]. Several of the studies has come to a quantitative analysis of Fresnel images of more realistic micromagnetic structure than proposed in [17], e.g. for a review reference is made to [21]. Here we focus on the analysis of an interesting complication of the Fresnel image, namely the variation of the contrast along the ripple fringes, which is visible in many LTEM micrographs, e.g. [17,22,23] but this has so far not been discussed in great detail. As an interpretation of this 2D contrast we suggest a model where the micromagnetic oscillations of the magnetization compete with oscillations due to topography of the film. Note

Effects of topography on the magnetic properties of nano-structured filmr

95

that the fluctuations or variations discussed here are only related to space modulations either of magnetization in the film or of intensity in the LTEM image. Any time dependence is neglected.

EXPERIMENTAL OBSERVATIONS Nano-crystalline Fe-Zr-N films have been prepared by DC magnetron reactive sputtering with a thickness between 50 and 1000nm. The presence of zirconium is to catch the nitrogen in the iron matrix. Iron was chosen because it is easy to prepare and cheaper than other soft magnetic materials, e.g. cobalt. The nitrogen is added to get a small (nano-sized) grain size. Pure (99.96 at%) Fe sheets partially covered with Zr wires were used as targets. The N and Zr contents were controlled by varying the sputter power andor the ArlN2 gas mixture. A 64 k N m magnetic field was applied in the plane of the samples during deposition to induce uni-axial anisotropy of up to 1.6 kA/m. More details on the film deposition can be found in [6,20]. The films have been deposited on a glass or silicon substrates at several temperatures between room temperature and 200 "C. The DC-sputtered samples were deposited on either a silicon substrate covered by a polymer, which was removed in acetone after sputtering, or on a silicon substrate covered by a Si3N4 layer. The former samples were extracted on copper TEM-grids for support, while the latter samples kept their substrate because the layers were very thin. The deposition conditions were chosen to obtain a composition (FessZrl)l.,N, ,where the concentration of nitrogen was in the range x I 2 5 at%. The best films as far as nano-size dimensions are concerned have been obtained for 8 at%<x<20 at%. The nitrogen concentration has been measured with Elastic Recoil Detection technique, Neutron Depth Profiling methods and compared with shifts in the XRD pattern. Standard 8 - 28 XRD scans showed that up to x=10 at% as sputtered films were bcc-phase materials with a strong (110) fiber texture. The grain size estimated from the width of the (110) peak decreased monotonically with N content from typically 100 nm in the case of N-free films to less than 10 nm for films containing 8 at%. The specimens were examined with a JEOL 201 OF 200 kV transmission electron microscope equipped with a post column energy filter (GIF 2000 Gatan Imaging Filter, with a resolution of 1024~1024pixels),which provides an additional magnification around 20 at the plane of CCD camera with respect to the maximal attainable magnification by using the objective minilens (magnification: 6 103).Grain size determination was done with several tilting experiments using an ACT: Automated Crystallography for the TEM, from TSWEDAX and a Gatan dual-view CCD camera. A single-tilt specimen holder and a double-tilt heating specimen holder were used. The images are acquired and edited using DigitalMicrograph (DM) 3.3 and 3.4 on both Apple Macintosh and Microsoft Windows PCs. Furthermore an additional script package for DM was used: the NCEM Package Image that was developed at the national center at Lawrence-Berkeley National Laboratory-USA. XRD as well as conventional TEM and selected area diffraction (SAD) reveal a 2-30 nm size of crystallites after various tilting experiments for most of the investigated sputter deposited films and in the diffraction pattern the allowed reflections for the bcc structure were found (1 10,200,211). No signs of F e 8 or Fe16N2 were detected in XRD. The average measured grain size is approximately 34 nm as shown in Figure 1. The grain size distribution is rather broad, even for sputtered films. Indeed one should be careful with this analysis when the film thickness is much larger than the grain size. The information of more grains on top of each other may cause the ACT to measure an incorrect grain size and a different orientation distribution. It should be stressed that the grain size distribution depends on the exact condition of the deposition process, i.e. on the nitrogen concentration. There are many defects in individual grains. With in-situ annealing till 25OoCthe grain size distribution becomes sharper and this phenomenon is related to the crystallization of the inter-granular amorphous-like phase. Figure 2 shows a cross-tie wall imaged with LTEM. Because the magnetization is perpendicular to the magnetic ripple structure within the magnetic domains, magnetic induction vectors can be drawn in the image(s). The magnetic ripples are characterized by the mean wavelength and the mean angle of deviation of the local magnetization variation. These could be scrutinized by a careful analysis of the Lorentz images in Fourier space. The procedure of image analysis is as follows and has been displayed in Figure 3. First an image containing homogeneous ripples is acquired. To determine the ripple wavelength the rotational average of the modulus of the fast Fourier transform (FIT) is calculated (Figure 3 B and 3 C). If a line profile from the center of the image is taken the wavelength can be determined. This is done by looking at the first order maximum (indicated by a vertical line in Figure 3 D). Using the distance between this peak and the central peak the average ripple wavelength can be calculated [24].

J.Th.M. De Hosson and N.G. Chechenin

96

t.

681 890116 1 1 2 1 3 8 2 5 3 3 3 8 U 2 5 7 7 7 5 4 G f a Durm(a Inn1

c) Figure 1: a) Nano-crystalline iron and b) SA diffraction pattern of nano-crystalline Fe94N~Zrl c) grain size distribution

Figure 2: LTEM observations: a) Cross-tie wall with alternating circular and cross Bloch ; b) LTEM image for a tilt angle of 2.8', with the tilt axis parallel to the easy axis.

A. Lorentr micrograph of magnetic ripples

B, FFT of

C.Rotaoonal average of

image 4

FFT of Lorenn image

E. Band pass mask on FFT of Lorena image

D. Lineprofile (fmm centre) of rotational average of FFT of Lorentz image

F. Rotational profile in band passed area

Figure 3: Schematic description of the quantification method

Effects of topography on the magnetic properties of nano-structured filmr

97

The deviation angle of the ripple spectrum can also be found by calculating the modulus of the FFT [23]. The FFT contains two triangular shapes, from which the mean deviation angle can be obtained (Figure 3). A band pass mask is applied on the FFT at the distance from the origin where the first order maximum lies. Then a rotational profile is taken within this filtered FIT. Then, the ratio between the peak width (indicated by the rectangular shape in Figure 3F) and the entire profile determines the angle. The peak width is determined by looking at the maximum intensity and by finding the points where the intensity falls to 5542 (-70%) of the maximum intensity. As revealed by atomic force microscopy (AFM) the films with Cu and with polymer substrates had often a roughness with a height variation up to 10 nm and a quasi-periodicity in the roughness of 100-200nm, in contrast to the films deposited directly on the Si, which were atomically smooth. An example of an LTEM image with a ripple structure is depicted in Figure 4. The thickness of the film was about 70 nm. The film deposited on a Cu substrate has a granular or hillock type of roughness with an rms amplitude of o = 5 nm, with the base of the hills between 100-200 nm and with the distance between hills around 200 nm as revealed by AFM scans depicted in Figure 5. The in-focus bright-field TEM image in Figure 6 shows a variation of contrast that is not due to finite grain size: the diffraction pattern in the inset in Figure 6 indicates that the film is in an amorphous state. The contrast of the LTEM digital micrograph in Figure 4 was analyzed taking linear scans at various places and in different directions within the image. A linear scan perpendicular to the ripple fringes (T-profiles) shows a quasi-periodic arrangement of the fringes, Figure 4b-d, with a wavelength h, = 0.22f0.02 km and a contrast of C = 0.5fo.1, see Table 1. This type of fringes corresponds to the wiggling of the magnetization vector, perpendicular to the easy axis, called here the transverse component of magnetization (TCM). With B =,uOMs =1.7 T, t = 70 nm Eq. (1) gives the amplitude of the wiggling angle ~ 1 . 2 ’or the amplitude of the TCM ,&AMoY = ,uOM& = 1.03x10”Ci(tAx) = 36 mT. In addition, the intensity of the image is rather inhomogeneous along the ripple direction, seen as a dotted contrast in Figure 4a, and demonstrated in the longitudinal scan (L-profile) in Figure 4 , e . This variation cannot be explained by longitudinal oscillations of the TCM, but requires a variation of the magnetization along the main direction, i.e. an oscillation of longitudinal component of magnetization (LCM). The periodicity of this mode is in between A, = 0.11-0.12 pm, the contrast C = 0.3-0.4, Table 1. If we write analogously to Eq. 1 for the oscillation of the LCM

then ,&AMoX = 41 -43 mT, which is only slightly higher than the amplitude of the transversal oscillation obtained before. In the next section we analyze a possible influence of the topography of the film on the LTEM contrast.

Scan TI T2 L1 L2

A,I*m 0.24 0.23 0.11 0.12

C 0.57 0.55 0.30 0.34

MAM, mT 36 36 41 43

PIO,820, degrees 1.2 1.2 8.9 9.1

zmax,nm 2.7 3.0

J.Th.M. De Hosson and N.G. Chechenin

98

wn

vm

Figure 4: a) LTEM image of micro-magnetic ripple; b) intensity profile in the transverse direction T1; c) intensity profile along the ripple in the longitudinal direction L1; d) intensity profile in the transverse direction T2; e) intensity profile along the ripple in the longitudinal direction L2.

Figure 5: AFM image of the (Fe99Zrl)l.,NX sputtered film deposited on a Cu substrate

Effects of topography on the magnetic properties of nano-structured films

99

Figure 6: Bright field TEM image and diffraction pattern.

THEORETICAL ANALYSIS A. Fresnel contrast of LTEM image. Following the theory of Aharanov and Bohm [ 181the phase shift between two points of the image is determined by the magnetic flux through the area within lines connecting the corresponding points on the upper and lower surfaces of the films and the trajectories of electrons passing these points, see e.g. [8,17]. If one of the points is at the origin of the coordinates we write for the phase shift

where @” = h/2e = 2.06.10 l5 Wb = 2.06 mT p 2 i s the magnetic flux quantum, e is the electron charge, h is Planck’s constant, t is the film thickness, B(r,t) is the local magnetic induction and dS is an element of the area, bounded by the two electron trajectories in consideration, and represented by the vector oriented along the normal to this element. For a uniform thickness Eq. (3) can be rewritten as

The intensity of the diffracted beam at the plane of LTEM image can be evaluated using the Fourier transforms technique, e.g. [25]: ~ ( x : y =IjjF(k~,k,)T(k,,k,)exp(i(k,x’+k,y?dk~dk, > 1’

where T(k,, ky) is a transfer function and

(5)

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J.Th.M. De Hosson and N.G. Chechenin

is the Fourier transform of the exit electron wave function. Assuming that a plane electron wave exp(ik0z) enters the film, where k0=27r/& and & is the electron wave length (& = 2.5 pm for the 200 keV-electrons), and only the phase is modified by the magnetic film, the z-dependent part of thef(x,y) can be omitted in Eqs.(5,6), and then

Neglecting effects of the aperture and of the spherical aberration in the Fresnel mode of LTEM the transfer function in Eq.(5) can be written as [26]

where Az is a defocus value (- for overfocus, + for underfocus). A nonzero value of dz makes the ripple image observable. In this case Eq.(5) can be represented in the form of a convolution betweenf(x,y) in Eq.(6) and the Fourier transform of T(kx,ky),which gives

It should be emphasized that the theoretical analysis presented here is restricted to the case of uniform thickness and no external stray fields.

B. Effect of the micromagnetic ripple and 2D-topography of thefilm on LTEM pattern

A first contribution to the modulated magnetic induction, entering Eqs. (3,4), stems from the wiggling of the magnetization around the easy axis (EA), taken to be the x-axis. In the simplest approximation we have BY=&AMy(x)=,@Moys i n ( 2 n ~ / A , ~ )

(10)

The variation dMy(x)is the longitudinal oscillations of the TCM. A transversal fluctuation of dMy(y)was shown to be energetically unfavorable [ 10,161because it costs exchange energy. Therefore, oscillations of dMy in y- nor in z-directions do not appear in flat homogeneous films. The wiggling induces an internal stray field oriented parallel and antiparallel to the main magnetization direction. The magnitude of the stray field can be easily estimated as mst,,x -w$ Bi c o s ( 4 n ~/ 1 (11) Recently we have shown [20] that the internal stray field can strongly affect the FMR width and high frequency properties of the ultra-soft magnetic films. The presence of this stray field induces a small oscillation in the magnitude of the Lorentz force, acting perpendicular to the magnetization direction on electrons moving in the z-direction. As a second source of the magnetic induction variation we consider the contribution due to a 2D topography of the film. We consider a thin film deposited on a rough substrate with a two-dimensional periodical variation of roughness. The thickness of the film is constant and is smaller than the wavelength of the topography modulations. Due to demagnetizing effects the magnetization vector will follow the film zmodulation, so that projection of the magnetic induction will be

B,, = &M cosp,

&M(l-

8,’ / 2)

Effects of topography on the magnetic properties of nano-structured films

101

where the angle & = dz/dx describes the 2D-surface modulation in the x-direction with an amplitude &O and periodicities A2, and & in x- and y-directions, respectively. At this step we assume that the angle follows a periodic dependence on n- and y- coordinates in the form of:

which corresponds to the film surface modulation

shown in Figure 7 as a contour plot. In Eq. (1 4), zmx =&,I&J2n and for an rms amplitude of the substrate roughness of about 5 nm, zmar = 0, and a periodicity of 200 nm, the modulation angle amplitude is &O = 9’. Integrating Eq. (4), with Eqs. (10-12) we obtain

q ( x ,y ) =

{a (I

2nx

Q,

2n

- cos -)

4ZY 2 . 2 2n.X y 4, . 4ny +npf0ycos - y + p,, sin (-)[---sin 14x Ax 2 8n 4,

}

(15)

JlX

-6.4

-6.1

i

6.a

okx

Figure 7: Topography of the surface in the 2D-calculation Integration of Eq. (9) with Eq. (13) for the phase shift is not difficult but rather tedious. Assuming small values of S,, and S, and skipping all intermediate steps we arrive at the final intensity as a sum of five terms: I ( x ’ , y ’ ) = x Z n ,with

102

J.Th.M. De Hosson and N.G. Chechenin

where k = np&ftl@o,S, = ,&MtA,,P,012@o, S, = ~ t A ~ , & ~ l 2 @ 1 . It follows from Eqs. (16) that the intensity of the LTEM image varies in both x- and y-directions, responding to the modes of magnetic oscillations of TCM and LCM Eqs. (10)-(12). The second term, Iz, corresponds to the longitudinal oscillations of the TCM, Eq. (10). It gives a phase contrast for the fringes oriented perpendicular to the main magnetization vector. The period of these fringes is the same as for the micromagnetic ripple Eq.(lO). From Eq. (16) the predicted contrast of the ripple image is

The maximum contrast occurs when the defocusing conditions correspond to a situation where the sin term in Eq. (17) equals unity, leading to

This relation is just the same as Eq. (2) used before [ 16,201. The last contribution in Eqs. (16) corresponds to a variation of the magnetization due to the topography and gives a periodic contrast in bothx- and y-directions, i.e. a 2D-contrast similar to that observed in Figure 4. The wavelength of the intensity variation in the image is two times shorter than the wavelength of topography modulation, Eq. (13). The maximum contrast is

The third term I3 is due to stray field variation. It gives a contrast in the x-direction and no oscillating contrast in the y-direction, similar to the fourth term I,, which is due to the main, non-oscillating component of magnetization. Both these terms originate from the phase component with a linear dependence on the ycoordinate in Eq. (15), which appears after integration in Eq. (4) over dy’ of the x’-component ofB (which does not oscillate in the y’-direction). Removing non-oscillating terms, linear in y, Eq. (15) can be simplified to a form 2nx 1 2nx . 4ny p(x,y) = S , ( 1 - c o s - - ) - - ~ , s i n ~ ( - ) s i n ~ ix 8 4 Y 4Y

Taking only the first order terms in S, and S,, the intensity consists of three contributions:

Effects of topography on the magnetic properties of nano-structured films

103

The f i s t two are the same as I,, 12 , and the third one is similar to 15 in Eq (16). An example of the contour map of the intensity in Figure 8 illustrates the 2D type of the contrast calculated using Eq. (21). The parameters for the plot were chosen close to those for the film in Figure 4 t = 0.07 m, A,x = 0.2 pm, Azx= ?Q = 0.1 pn, zmlu= 5 nm, p&i = 1.5 T, B l 0 = lo, dz = 0.5 mm. The relations for the maximum contrast, Eqs. (17) to (19), are valid also for Eq. (21). Using the experimental data derived from Figure 4, C = 0 . 2 , s = 0.1 and t, p&i,listed above, from Eq. (19) we can obtain zmox= 3 nm, which is smaller than the rms amplitude of roughness of substrate and film surfaces, Figure 5. Evidently one of the reasons for such discrepancy is that the real topography differs from the simple periodical oscillations, Eq. (13), we used in the model calculations. A second reason could be a deviation of demagnetizing factor from one, resulting in smaller effective oscillations of Bx2,Eq. (12). Further, the linear approximation (1.e. weak phase object) may not be safely applicable with the high contrast values over the entire range 1

Y 0.5

0

-0.5

0

-0.5

0.5

x

1

Figure 8: Contour map of the LTEM image intensity according to Eq.( 19).The x and y coordinates are in micrometer. C. ID-wavefilm topography A 2D- contrast in LTEM can also be induced by a ID-wave-like film topography, e.g. such as described by z = z,,

sin(2lrx”i

(22)

as is illustrated by Figure 9. We suppose that x” -axis deviates by an angle y from x-axis (EA) in the xyplane.

104

J.Th.M. De Hosson and N.G. Chechenin

-0.4 -0.2

0

0.2

0.4 X

Figure 9: 1D-wave topography Since x” = xcos y + ysin y the tilt angle of the magnetization direction in the xz-plane with respect to thexy-plane is

A=-&= dz z,,,

2n

-cosycos

:[

-(xcos

1

y + ysin y >

Neglecting non-oscillating terms linear in y the phase shift is 2nx S, q ( x , y) = Sx(l - cos -) +-sin[ .1, 8siny

2n(xcosy+sin ysin y)

4

]-&sin(8siny

2nxcos y

4

1

(25)

Four major terms determine the intensity contrast in this case:

It follows from these equations and Figure 10 that the compromise between the micromagnetic (12) and topography (13 and 1 4 ) oscillations depends not only on the combination of the micromagnetic and topography

Effectsof topography on the mugnetzcpropertzes of nu?io-structuredfi~~?~

105

parameters but It also critically depends on the tilt angle?. When the topography wave vector IS parallel to the EA, PO, then there is no y-oscillations, but at y >O the topography component can be even more pronounced than the micromagnetlc component and could lead to fringes whlch are oriented perpendlcular to the topography wave vector as illustrated in Figure 10. Consequently for this reason one must be careful in asslgnlng the direction of the m a n magnetlzation.

-0.5

0 1

Y 0 .s

-0J

-0 J

0

Figure 10: a) Calculated LTEM contrast for the ID-wave topography with a wave vector that deviates by an angle y of 30' form the EA; b) calculated LTEM contrast for the 1 D-wave topography with a wave vector that devlates by an angle of 30' form the EA; c) calculated LTEM contrast for the 1D-wave topography with a wave vector that deviates by an angle of 90' form the EA.

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J.Th.M. De Hosson and N.G. Chechenin

DISCUSSION Deviations of thin film interfaces from flatness may have a substantial effect on their physical properties, e.g. magnetic coercive field, demagnetizing field, giant magetoresistance and domain walls [27, 28, 29, 301. Recently the effects of roughness on magnetic properties have been examined describing the roughness in terms of a self-affine fractal scaling but these studies are focused on the theoretical description rather than on an experimental validation. The purpose of this paper is to promote transmission electron microscopy not only as a tool for observing structural defects at the highest possible resolution but to employ the technique for measuring the effect of topology on physical properties as well. In this way the linkage between structural information and functional properties can be made. We emphasize that the 2D LTEM patterns considered here refer to the dotted contrast along the ripple fringes and not to two-dimensional features due to a bending, crossing, or branching of the fringes itself, as considered elsewhere, e.g. [25,26]. With this bending-crossing-branching the Fresnel images are always 2D patterns. The micromagnetic oscillation of magnetization in nanocrystalline materials is driven by the coupling volume of the exchange interaction. Estimations [16] show that the longitudinal size of the coupling volume (along the EA) according to Hoffmann [lo] is of the order of the ripple wavelength and orders of magnitude smaller than the transversal sizes of the coupling volume (perpendicular to the EA) 1251. (We agree with [25] that quantitative estimates based on Hoffmann theory should be taken with precaution). With the dotted contrast the wavelength ratio is reversed: the periodicity of dotted contrast is usually smaller than that for micromagnetic ripple. This supports the idea that transversal oscillations of TCM cannot be considered as a possible source of the dotted contrast reported here. As a matter of course our simulated images Figures 8,lO are rather idealized. If we include for example terms with higher orders of S, , S, the images become more complicated but resemble more the experimental ones. In this paper we do not pursue the goal to reproduce fully the experimental images, but to find analytical relations between selected features of the LTEM images and the magnetic features so as to find the physical reason. We have demonstrated that the model of TCM plus topography oscillations developed here predicts reasonable values for parameters of both the ripple fringes and dotted contrast. Relating our analysis to the values of the contrast we eliminate the problem caused in another approach [3 11, in which an out-of-focus image is divided by the in-focused image. In our case one obtains the contrast value from neighboring peaks of intensity in a single out-of-focus image. Nevertheless it may produce problems in the analysis of emulsion micrographs due to a possible non-linearity of emulsion contrast with respect to the recorded electron density. It is also evident from simulations and Eqs. (15), (20) and (25) that variation of the intensity in ydirection occurs not only at maximum intensity in x-direction, but at all possible x-values. This is also in agreement with experimental observations. Dotted contrast appears on the top of the fringes only because of an intensity threshold to demonstrate the image contrast. Similar variations of intensity exist in any scan between the ripple fringes.

CONCLUSIONS We have shown that in addition to the quasi-periodic ripple structure of the Fresnel contrast caused by an oscillation of the magnetization around the easy axis, there exists a dotted contrast along the ripple fringes. This type of contrast can be simulated within a model of image comprising the oscillations of magnetization around easy direction and a wavy topological structure; the former mode gives periodical ripples with the wave vector parallel to the easy axis, whereas the latter one gives the dotted contrast along the ripple fringes. The observed and simulated contrast of both longitudinal and transversal modes of the ripple is in reasonable agreement for the case of significant ripple structure. It is also shown that at a large surface roughness the LTEM ripple fringes can follow the direction of the topography oscillations and not the micromagnetic ripple what can cause considerable mistakes in interpretation of LTEM patterns. However, in most practical cases the topologyinduced contrast is negligible, because it is proportional to the square of the amplitude of the angle variation, & ,: which is usually small enough.

Effectsof topography on the magnetic properties of nano-structured films

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ACKNOWLEDGEMENTS Thanks are due to Professor Gareth Thomas for his stimulus provided over the years to the microscopy research in our Department of Applied Physics at the University of Groningen, the Netherlands. The work is part of the research program of the Priority Program on Materials of the Netherlands Organization of Research (NWO- The Hague) and supported by the Netherlands Foundation for Technical Sciences and the Netherlands Institute for Metals Research. Discussions with Tomas Vystavel, Daan Hein Alsem, Toni Chezan, Bart Kooi, George Palasantzas and Dik Boerma are gratefully acknowledged. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28.

Thomas,G. and Goringe, M.J. (1979) Transmission Electron Microscopy of Materials. Wiley, New York. Berkowitz, A.E., Mitchell, J.R., Carey, M.J., Young, A.P., Zhang, S., Spada, F.E., Parker, F.T., Hutten, A., Thomas, G. (1992) Phys. Rev. Lett. 68, 3745. Hutten, A,, Bemardi, J., Friedrichs, S., Thomas, G. (1995) Scripta Metull. 33, 1647. Vrenken, H., Kooi, B.J., De Hosson, J.Th.M. (2001)J. Appl. Phys. 89,3381. Kooi, B.J., Vystavel, T.,De Hosson, J.Th.M. (2001)J. Nanoscience and Nanotechnology 1,65. A.R. Chezan (2002).PhD Thesis, University of Groningen, The Netherlands. Grundy, P.J., Tebble, R.S. (1968)Advances in Physics 17: p. 153. Fuller, H.W., Hale, M.E. (1960)J. Appl. Phys. 31,238. De Graef, M. (2000). In: Experimental Methods in the Physical Sciences, Volume36: Magnetic Imaging and its Applications to Materials, Chapter 2, pp.27, M. De Graef and Y. Zhu (Eds), Chapter 2, pp.27. Academic Press, New York. Hoffmann, H. (1964)J. Appl. Phys. 35,1790. McCartney, M.R., Dunin-Borkowski, R.E., Smith,D.J. (2000).In: Experimental Methods in the Physical Sciences, Volume36: Magnetic Imaging and its Applications to Materials, Chapter 4, pp.111, M. De Graef and Y. Zhu (Eds). Academic Press, New York. Cowley, J. ( 1 992)Ultramicroscopy 41,335. Midgley, P.A.(2001) Micron 32,167. Tonomura, A. (1999).Electron Holography. Berlin, Germany: Springer Series in Optical Sciences. De Hosson, J.Th.M., Chechenin, N.G., Alsem, D.H., Vystavel, T., Kooi B.J., Chezan, A.R., Boerma, D.O. (2002) Microscopy and Microanalysis 8,274. Chechenin,N.G., Chezan,A.R., Craus, C.B.,Vystavel,T.,Boerma,D.O.,DeHosson, J.Th.M.,Niesen.L. (2002)J. Magn. Magn. Muter. 180,242. Wohlleben, D. (1967)J.Appl.Phys.38,3341. Aharanov, Y., Bohm D. (1958) Phys. Rev. 115,485. Hoffmann, H. (2000) Thin Solid Films 373 ,107. Chezan , A.R., Craus, C.B., Chechenin, N.G., Niesen, L., Boerma, D.O. (2002)Phys. Stat. Sol (a) 189, 833 De Graef, M. and Zhu Y. (2001)ExperimentalMethods in Physical Sciences, Magnetic imaging and its applications to materials, volume 36, Academic Press, New York. Aitchison, R.P., Chapman, J.N., Gehanno, V., Weir, L.S., Schenfein, M.R., McVitie, S., Marty, A. (2001)J. Magn. Magn. Muter. 223, 138 Gillies, M.F., Chapman, J.N., Kools,.J.C.S. (1995)J. Magn. andMugneticMaterials 140-144:,721. Henmann, M., Zweck, J., Hoffmann, H.(1994) ICEM13, p.245. Jeong, IS., Walser, R.M. (1988)IEEE TransMugn. 24, 1725. Chapman,J.N. (1984)J. Phys. D:Appl. Phys. 17,623. Zhao, Y-P., Wang G-C. and Lu T.M., (2000) ExperimentalMethods in the Physical Sciences, Vol. 37, Academic Press, New York. Palasantzas, G., Zhao, Y-P., Wang, G-C., Lu T-M., Bamas, J., De Hosson ,J.Th.M. (2000)Phys. Rev. B

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Nan0 and Microstructural Design of Advanced Materials M.A. Meyers, R.O. Ritchie and M. Sarikaya (Editors) 02003 Elsevier Ltd. All rights reserved.

SLIP INDUCED STRESS AMPLIFICATION IN THIN LIGAMENTS X. Markenscoff and V. A. Lubarda Department of Mechanical and Aerospace Engineering University of California, San Diego; La Jolla, CA 92093-041 1, USA

ABSTRACT The solution for a screw or edge dislocation in a multiply connected solid containing two cavities is not unique, but depends on the selected cut used to impose the displacement discontinuity and to create the dislocation. The Peach-Koehler force and the location of the equilibrium dislocation position is determined for screw dislocation in the ligament. The dislocation induced stress amplification in the ligament between two approaching cavities of equal or unequal sizes is then derived.

INTRODUCTION The stress fields and dislocation forces for a screw or edge dislocation in a multiply connected region depend on the cut used to create a dislocation, and if the connectivity of the region is n, there are as many possible solutions (Lubarda [l]). A screw dislocation between two cavities in an infinite medium is considered in this paper. By using the method of image dislocations, three different solutions are derived depending on the cut used to impose a displacement discontinuity and create a dislocation. The slip induced stress amplification in a ligament between two approaching cavities is then calculated, thereby extending the earlier studies by Markenscoff [2], and Wu and Markenscoff [3]. It is shown that in a ligament of small thickness d, the shear stress amplifies at the order of d-'lz.

SCREW DISLOCATION BETWEEN TWO CAVITIES A screw dislocation between two cavities in an infinite medium is shown in Fig. 1. The radii of the cavities are R1 and R z ,and their distance is c. Two infinite sets of image dislocations are required to achieve the traction free conditions on the surfaces of both cavities. One set of image dislocations is entirely within the region of the first cavity, and the other is entirely within the region of the second

109

110

X. Murkenscoff and V.A.Luburdu

Figure 1: Screw dislocation between two cavities in an infinite medium. Image dislocations pile-up at two conjugate points at distance x1 and z2 from the centers of the cavities. cavity. The stresses are obtained by superposition as [4] Y

+ y2

-

Y

(x - u2n-1)2 + y2

+ (x -xc +c + + y2 - (x xc +c + bzn-i + yz -

a2n

azn)2

-

-

bzn-1)2

I>

’

where p is the shear modulus, and b, is the Burgers vector of the dislocation. The recursive formulas

apply for n = 1 , 2 , 3 , .. . , with a1 = RT/a, and bl = R;/(c - u ) . As n goes to infinity, the image dislocations in the first cavity pile up at the distance x1 from its center, while image dislocations in

Slip induced stress amplification in thin ligaments

111

4.0

3.0

-3.0/ -4.0

,J,

,

,

,

,

,

,

,

-

,

____

;

I

/

-5.0

_,,

,

,

Cut 2

cm 3

I ;

-6.0

1 1

1.0

1.1

1.2

1.3

1.4

am 1.5

1.6

1.7

1.8

1.8

,I

Figure 2: The variation of the dislocation force (scaled by pb2/27rR1) as the dislocation moves along horizontal direction between the two cavities in an infinite medium. the second cavity pile up at the distance 2 2 from the center of the second cavity. The two points are conjugate to each other with respect to both cavities, and are thus specified by c - x 2 = - ,R: 51

This gives 21

=

1 ( c~ C; 2c

-

+ RI - Ri) ,

where C:

= [c2 - (Ri

c-x1=-

R,2 x2

52

1

= - (c' - C;

+ R2)'] [c2

2c

-

+ R;

(R1- R z ) ~. ]

-

R;) ,

(6) (7)

The contributions from the pairs of positive and negative image dislocations are summed in Eqs. (1) and ( 2 ) ,which ensures the convergence of the series, and implies a displacement discontinuity along the cut

from a to infinity. If Rz = 0.5R1 and c = 2.5R1,for example, we find that dislocation is at an unstable equilibrium position for a E 1.535R1. The variation of the dislocation force, as the dislocation moves between the two cavities, is shown by a solid curve in Fig. 2.

SOLUTIONS FOR DIFFERENT DISCONTINUITY CUTS The previously derived solution is associated with a displacement discontinuity along the cut from the point a to infinity. One such cut is shown in Fig. 3a. Two other solutions are, however, possible since the considered region is triply connected. One solution corresponds to a displacement discontinuity along the cut from a to the surface of one cavity, and the other is associated with the cut from a to the surface of another cavity (Fig. 3b,c). To obtain these two solutions and to relate them to the solution derived in the previous section, we need to solve two auxiliary problems. The first is the problem of an infinite body with two cavities, and a displacement discontinuity imposed along the cut from one cavity

X. Murkenscoff and V.A.Luburdu

112

Figure 3: Three different ways of creating the screw dislocation by imposing a displacement discontinuity along the three indicated cuts. to the other. The solution is obtained by placing two opposite dislocations at two points conjugate with respect to both cavities (Fig. 4a). The second problem is the problem of an infinite body with two cavities and a displacement discontinuity imposed along the cut from a point on one cavity to infinity (Fig. 4b). In the latter case we need to consider two infinite sets of image dislocations, situated in the region of each cavity. These are created by starting with two alike dislocations at the centers of each cavity, and proceeding with a built-up of image dislocations at the conjugate points with respect to the boundary of each cavity. A sequence of negative and positive image dislocations within the first cavity pile up at the distance z1from the center of the cavity, while a sequence of negative and positive dislocations in the second cavity pile up at the distance z2 from the center of that cavity. After enough image dislocations is introduced to cancel the traction on both boundaries, we end with equal number of positive and negative dislocations in the first cavity, and with one more positive than negative dislocation in the second cavity. This ensures a displacement discontinuity from the point on the surface of the second cavity to infinity, and provides the solution of the second auxiliary problem. The stresses are, therefore, given by

cJzz

=

2

-${ [

Y

(z - B,)2

+ (z - C + Yb,)2 + y2] -

+ y2

2

N-l

-

Y

(z - a,)2

Y

+

+ y2

(z - c + A , ) ~ y2

Slip induced stress amplification in thin ligaments

113

’f

’f

Figure 4: Image dislocations required to solve the problem in which a displacement discontinuity is imposed: (a) along the cut between the two cavities, and (b) along the cut from the surface of one cavity to infinity.

x - B, (X - B,)2

+ y2

-

x - a,

(x - a,)2

N-1

+ y2

x-c+~, x-c+A, ’ ( x - c b,)2 +y’]- n=l (x - c + A,)2 + y2

I

+

}’

for large N . The conrdinates R-,‘ define nemtive and nnsitive .-.sufficientlv - _.. -. .. .._ ,.. ._ -. - .._ - - -- - n- and _______the distances of _ _ the ____ ___ 0---- ---- r-----__,I

I___

I__ -___I_____

image dislocations in the region of the first cavity from its center, while A, and b, are the corresponding distances of the image dislocations in the second cavity from its center. They are defined by the recursive formulas b,=-, R; a, = R: c - b, ’ c - a,-l ~

RZ

R2

bl lL2 B, = A, = (11) C-B,’ c - An_l ’ which apply for n = 2,3,4,. . . . For n = 1, we have a1 = R l f c , A1 = R;/c, and bl = B1 = 0. ~

Numerical evaluations reveal that the convergence is reached with only few terms included, typically N = 5 or 6. The solid and dashed curves in Fig. 5 show the variation of the shear stress czy(x,0) along the x axis, corresponding to imposed displacement discontinuities along the cuts from Fig. 4. The remaining (dotted) curve in Fig. 5 is obtained as the sum of the values corresponding to solid and dashed curves, and represents the shear stress associated with a cut from the first cavity to infinity. The solution for the dislocation between two cavities in the case when a displacement discontinuity is imposed as in Fig. 3b is obtained by subtracting from the solution of the problem in Fig. 3a the

X. Murkenscoff and V.A.Luburdu

114

2.0

1.o

bb

0.0

-1.0

-2.0

-3.0 -3.0

-2.0

1.0

0.0

1.0

x/R.

2.0

3.0

4.0

I

5.0

Figure 5: The variation of the shear stress (scaled by pb,/27rR1) along the x axis, corresponding to imposed displacement discontinuity along the two cuts shown in Fig. 4. The dotted curve is the sum of the values from the solid and dashed curves, and corresponds to the cut from the first cavity to infinity. Linear segments span across the region of cavities and should be discarded. stress distribution corresponding to the cut shown in Fig. 4b. Thus, we subtract from Eqs. (1) and (2) the stresses defined by Eqs. (8) and (9). The variation of the corresponding dislocation force with a dislocation position between two cavities is shown by a dashed curve in Fig. 2. The results are for

Rz = 0.5R1 and c = 2.5R1. Dislocation is in an unstable equilibrium for a M 1.220R1.This is smaller than the equilibrium distance in the previous case because the closest added image dislocation to the left is positive, and to the right negative, so that they exert a force on the positive dislocation directed toward the second cavity.

Finally, by subtracting from the last solution the solution associated with a cut shown in Fig. 4a, i.e., by subtracting the stress field of two opposite dislocations at x1 and x2 from the centers of respective cavities, we obtain the solution for a dislocation between the cavities created by a displacement discontinuity along the cut shown in Fig. 3c. The variation of the dislocation force in this case is shown by a dotted curve in Fig. 2. Dislocation is in an unstable equilibrium for a z 1.695R1. This is greater than the equilibrium distance for the cut from Fig. 3b because the added negative dislocation to the left and positive to the right exert a force on the positive dislocation between two cavities directed toward the left cavity.

SLIP INDUCED STRESS AMPLIFICATION IN THIN LIGAMENTS The problem depicted in Fig. 4a can be used to derive an analytical solution for the slip induced stress amplification in thin ligaments. A comprehensive analysis of stress amplification in vanishingly small geometries due to remote stress or thermal loading was given by Markenscoff [3]. Let d be a thickness

Slip induced stress amplification in thin ligaments

of the ligament, so that c = (I

115

+ P + OR1,

where The shear stress r ( x )= ozy(x,0) across the ligament is

The image dislocations needed to impose a displacement discontinuity across the ligament are approximately located at the distances

from the centers of respective cavities. The terms that are proportional to higher order exponents of the small ratio = d/R1are neglected in Eq. (15). It readily follows that the shear stresses at the end points of the ligament are

c

(T)

r l = r ( R 1 ) = iPbZ 7RI 1 + P

1'2c-

(1 + - - () 1 P 2 l+p

1

c) This establishes the (-'I2 order of singularity in the region of thin ligament between two cavities in an infinite solid, produced by the relative sliding of two faces of the ligament along the cut between two end points of the ligament. We retained the term proportional to in Eq. (16) to quantify the difference in the shear stresses at the end points of the ligament between the cavities of unequal sizes. If the cavities are identical ( R , = R2 = R ) ,we obtain in the limit

c

51

= x2 = (1 -
(17)

and

Two numerical examples reveal the following. First, suppose that R1 = 30b,, R2 = lob,, and d = 2b,. The image dislocations are approximately located at x1 = 25b, and x 2 = 4.98bZ, while the shear stresses at the end points of the ligament are rl = 0 . 0 5 8 9 ~and r2 = 0 . 0 6 2 5 ~ .The shear stress r2 is about 6% greater than 7-1. In the second case, consider two equal cavities of radius R = lob, at a distance d = b,. The image dislocations are located at z1= x2 = 7.34b,, while the shear stresses

X. Murkenscoff and V.A.Luburdu

116

are T~ = r2 = 0 . 1 ~ If . the cavities were at a distance d = lob,, the shear stresses would have been 71 = rz = 0 . 0 3 6 ~ .This is calculated from the exact results

and

In the limit of infinitely distant cavities the stress 71 approaches the value pbZ/2.irRcorresponding to a single dislocation at the origin. An analysis of the slip induced stress amplification in thin ligaments associated with other geometries is presented by Lubarda and Markenscoff [4].

REFERENCES 1. 2. 3. 4. 5.

Lubarda, V.A. (1999). J. Elasticity 52,289. Markenscoff, X. (1996). Comput. Mech. 19,77.

6.

Wu, L. and Markenscoff, X. (1997). J. Mech. Phys. Solids 45,2033. Lubarda, V.A. and Markenscoff, X. (2003). J. Matel: Sci. Engng., to appear. Seeger, A. (1955). In Handbuch der Physik, VW1: Crystal Physics I, pp. 383-665, S. Flugge (Ed). Springer-Verlag, Berlin. Nabarro, F.R.N. (1967). Theory of Crystal Dislocations, Oxford Univ. Press, Oxford.

7.

Hirth, J.P. and Lothe, J. (1982). Theory ofDisZocations (2nd ed). John Wiley, New York.

Nan0 and Microstructural Design of Advanced Materials M.A. Meyers, R.O. Ritchie and M. Sarikaya (Editors) 02003 Published by Elsevier Ltd.

MATERIALS, STRUCTURES AND APPLICATIONS OF SOME ADVANCED MEMS DEVICES Sungho Jin University of California, San Diego, 9500 Gilman Dr., La Jolla, CA 92093-0411

ABSTRACT Since the famous lectures by Richard Feynman, “There is Plenty Room at the Bottom” in 1959 and “Infinitesimal Machinery” in 1983, the drive toward nano- and micro- materials and devices has been one of the most fascinating scientific and technological goals. The MEMS technology owes much of its base to modem silicon fabrication and lithography processes. While the design and fabrication of standard MEMS devices can relatively easily be accomplished through available MEMS foundries, differential advantages such as new functionalities and improved reliability may more readily be obtained by incorporating newladvanced materials, for example, nano materials or active functional materials. In this presentation, some unique approaches related to the advanced materials, design of MEMS structures and potential applications of electron-emitting MEMS will be discussed. Careful considerations of physical and materials structure and properties are needed to ensure high performance of the devices. The R&D and applications of the MEMS devices offer exciting and challenging opportunities for materials scientists.

INTRODUCTION The interesting and unique characteristics of carbon nanotubes come mostly due to their nanoscale geometry of elongated tube shape. While substantial progress has been made in the growth of nanotubes, the management of key nanotube geometries such as the diameter, height, inter-nanotube spacing, alignment, etc. and the processing to optimize them are yet to be fully understood and controlled. Currently, a promising source of electrons in vacuum microelectronic devices is field emission apparatus which releases electrons into vacuum from suitable cathode materials. These devices include flat panel displays, klystrons and traveling wave tubes used as effecient microwave power amplifiers, ion guns, electron beam lithography, high energy accelerators, free electron lasers, and electron microscopes and microprobes. A typical field emission device consists of a cathode including one or more of field emitter tips and an anode spaced from the cathode. A voltage applied between the anode and cathode induces the emission o i electrons towards the anode. In a triode type configuration, a gate electrode is added near the cathode to facilitate the extraction of the electrons.

117

118

Sungho Jin

Carbon nanotubes [ l ] have recently emerged as promising field emitters that can emit very large current densities at relatively low electric fields [2 - 51. The carbon nanotubes are composed of cylindrically arranged graphitic sheets with diameters in the range of 130 nm and lengthldiameter aspect ratios greater than 1,000. Of particular interest is the capability of nanotube emitters to stably deliver very high emission currents, as individual nanotubes can emit up to 1 micro ampere [3] and nanotube layers can generate current densities in excess of 4 Nc m2 [4,5]. Carbon nanotubes are a stable form of carbon which exhibits high mechanical strengths and chemical stability as well as a very high aspect ratio (>1,000) and small tip radii of curvature (-1 0 nm). These geometric characteristics provide a tremendous local concentration of applied electric field, which makes carbon nanotubes very attractive as electron field emitters as relatively low and practical voltages can be applied to induce significant electron emission. There are three important geometric issues that influence the behavior and performance of carbon nanotubes for field emission applications. They are i) the alignment perpendicular to the substrate surface, ii) the density of nanotube packing, and iii) the diameter of nanotubes. CVD nanotube growth methodologies need to be adjusted to optimize the nanotube configurations. We report here a novel method for fabricating fully integrated, on-chip, vacuum microtriodes using carbon nanotubes as field emitters via silicon micromachining of MEMS (Micro-Electro-Mechanical Systems) device fabrication.

EXPERIMENTAL PROCEDURES Our new microtriodes were fabricated using a three-layer polysilicon micromaching process on a silicon nitride coated silicon substrate [6]. The triode structure was chosen because, despite its simple device geometry, its characterization can be easily parameterized and its behavior can provide important insight to the design and performance of more sophisticated devices. The triode here is a drastically miniaturized, micrometer-scale version of a conventional vacuum triode, consisting of a cathode, a grid, and an anode. Each electrode here is made of a hinged polysilicon panel that can be rotated and locked into position. Well-aligned carbon nanotubes were selectively grown on the cathode regions by first depositing a thin, nanotube-nucleating catalyst layer of iron (50 A) through a shadow mask, and then growing the nanotubes in a microwave plasma of ammonidacetylene mixture at 750°C at a growth rate of about 10 micrometers per minute. The microwave plasma-enhanced CVD system was operated with a 2.45 GHz, 5 KW microwave power supply and inductively heated substrate stage [7,8].

Materials, structures and applications of some advanced MEMS devices

119

RESULTS AND DISCUSSION As is well known, the birth of modem communications industry was instigated by the development of gridded vacuum tube amplifiers [9]. These vacuum devices made broadcast radios and television possibles. The vacuum tubes generally suffered from various limitations, all related to the use of thermionic cathodes, which typically had to be heated to above 800°C for electron emission to occur. In low power applications (lo GHz) and low control voltage (50-100 V) operation. In beam forming tubes, density modulation of electron beams by the grid through gated emission thus becomes possible so that a long beam interaction section is no longer required, and the tubes can be shortened substantially. A cold cathode vacuum tube amplifier system is 'thus attractive to the commercial wireless communications industry, as the highly efficient and miniaturized vacuum devices can help move the amplifier electronics to the tower tops of antennas. They are also especially valuable for

Sungho Jin

120

space operation where radiation is strong, available power and space is limited, and heat can only be dissipated by radiation. Over the years, there have been considerable efforts spent in building cold cathode microwave power tube amplifiers [11,12]. All devices have been based on Spindt-type field emitter array cathodes that were used as the electron source for triodes, klystrodes and traveling wave tubes (TWT). TWT devices operating at 10 GHz with molybdenum field emitter arrays emitting at current densities of 50 A/cm2 for a period of 5000 hours (at 1% duty cycle) have been demonstrated [13]. However, density modulation at microwave frequencies through gated emission has proven to be difficult due to inadequate emission stability and reliability of the FEA cathodes. As a result, continuous operation of beam tube devices has not been possible, and no practically useful triodes have been reported. If effecient and reliable cold-cathode vacuum tube amplifiers can be fabricated, and also miniaturized into microscale, on-chip integrated devices, then they could become the amplifier of choice for many applications, not necessarily limited to communications area. Carbon nanotubes, which have recently emerged as promising field emitters that can emit large current densities at relatively low electric fields, in combination with a micromachining concept, can provide a possibility for such efficient amplifiers as described below.

Nanotubes

Cathode

Poly-Si

Gate

Anode

Figure 1. Assembly of on-chip micro vacuum tube. Shown in Fig. 1 is a schematic illustration of the process used for fabricating the carbon nanotube based MEMS microwave amplifier structure. Silicon micromaching process

Materials, structures and applications of some advanced MEMS devices

121

generated a flat substrate containing three panels, the cathode, the gate, and the anode, as illustrated in Fig. l(a). All three panels are connected to the silicon substrate by hinges and springs. The gate panel is made to contain many apertures for electrons to pass through and accelerate toward the anode. On the cathode surface, vertically aligned carbon nanotubes are deposited by CVD processing. The three panels are then raised to the vertical position, Fig. 1(b), so that they are placed in a parallel configuration relative to each other. The carbon nanotubes nucleate from metal catalyst islands of Co or Fe. A thin layer (e.g., 2-5 nm thick) of such a metal is deposited on a desired silicon substrate (for example, on the cathode panel only in Fig. l(a)) by sputtering or evaporation. On heating to the CVD deposition temperature of 700 - 800"C, the layer naturally and conveniently breaks up into islands and forms a multiplicity of nucleating sites for carbon nanotubes as illustrated schematically in Fig. 2 (left). For better control of nanotube size and distribution, a more intentional arrangement of nucleation sites is desirable, for example, by patterning the Co or Fe layer prior to the CVD process. This produces a finer and further spaced apart nanotube configuration as illustrated in Fig. 2 (right). Such a refined nanotube arrangement is being pursued and the results from such an improved structure will be reported in future publications. Spaced-apart field emitter arrangement such as illustrated in Fig. 3(c) or (d) are in principle better than the structures of Fig. 3(a) or (b) because of electric field concentration possible in more isolated sharp emitters.

Thick Crowded C N T Planar / catalyst (Co, Fe)

(a) L

Substrate

(b) O n heating

I

P a rt ic u late

/'

T h n Separated C N T

(a)

r I

, , ,

Subdivided catalyst

I

(b) On heating

CNT

Figure 2. Growth of carbon nanotubes on catalyst metal islands formed by heating a thin film (left) and those formed by patterning of the metal layer (right).

Sungho Jin

122

Field-Concentrating Nanotube Configuration

Substrate

Substrate

Figure 3. Carbon nanotube growth with varying degree of inter-nanotube spacing. Such a lateral configuration of Fig. l(b) obtained by MEMS fabrication is in contrast to the conventional, horizontally arranged structures based on field emitter arrays [ 11,121 or metal nanopillar cathodes [ 14,151. Our approach offers greater flexibility in designing sophisticated microwave devices and circuitries, employs simpler and more precise fabrication processes, and produces completely integrated structures. The technique combines high-performance nanomaterials with MEMS-based solid state fabrication technology to produce miniaturized vacuum tube devices in an on-chip form, which could have important and far-reaching scientific and technological implications. Shown in Fig. 4 as an SEM micrograph is the actual device of miniaturized, on-chip, vacuum microwave amplifier structure obtained by combining the MEMS and the nano technology. The structure here was assembled under a microscope using a mechanical microprobe. Various self-assembly techniques could be used to achieve better manufacturability for future devices. The carbon nanotubes grown here are multi-walled and highly oriented, with diameters ranging from 20 - 50 nm. Their length was determined by controlling the growth time, which, in turn, controlled the spacing between the cathode and grid (and hence the emission field). From this device, we obtained a dc power gain of 16 dB by operating the carbon nanotube cathodes at a record emission current density of 16 Alcm2. The cutoff frequency for such devices is currently at 216 MHz. With improved designs and optimized materials, we expect to achieve cutoff frequencies in excess of 20 GHz in future devices. To our knowledge, this is the first demonstration of incorporating carbon nanotube field emitters in a MEMS design to create power-amplifying vacuum devices on silicon [ 5 ] . The inset in Fig. 4 shows a magnified view of the cathode region. The nanotubes were typically patterned on the cathode according to the grid geometry in order to minimize the

Materials, structures and applications of some advanced MEMS devices

123

intercepted grid current. The aligned and patterned nanotubes point toward the apertures in the grid structure.

Aligned and Patterned Nanotubes

Figure 4. Scanning electron microscopy (SEM) micrograph of a completely assembled vacuum microtriode.

The dc characteristics of the triodes was evaluated by measuring how the anode current (Ia) changes as a function of both the grid voltage (V,) and the anode voltage (V& These measurements were performed at room temperature within a vacuum chamber with a base pressure of lo-* torr. A triode is the vacuum equivalent of a field effect transistor, in which electrons are emitted from the cathode into vacuum, and a grid (or gate) electrode varies the electric field between the cathode and grid to control the emission current. Some of the electrons pass through apertures in the grid, accelerate towards the anode, and are collected to give a current through the device. The devices can have substantial current gain (I&) if the grid intercepts only a small fraction of the emitted current. As this grid-controlled current goes to the anode and passes through external loads, it can produce a voltage larger than the control voltage at the grid, resulting in a voltage gain

Sungho Jin

124

(AV,/AV,). Therefore, if the device geometry is designed correctly, this can yield an overall power gain. 30

'

2.0

. 1.5 . 1.0 a, 10 U 0

2

0 3

- 0.5

5 0

80

100

140

120

160

180

200

- 0.0

Grid Voltage (V)

25

U, = 200 V

10 MQ load line 20

3W 4-l

F

15

U, = 190 U

10

U, = 180 U

L

5

U,

= 160 U

U,= 1 4 Q U 0

U,=QU

0

100

200

300

400

500

Anode Voltage (V) Figure 5. (a) Grid current, anode current and transconductance vs gnd voltage with the anode voltage held at 1OOV. (b) Anode current vs anode voltage at various grid voltages. The lOMR load line indicates the voltage gain that can be achieved by this device.

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In the data of Fig. 5(a), the variation of grid current (I,), anode current (Ia), and transconductance (g,,,=61a/6V,) with grid voltage, while the anode voltage was held at 100 V, is shown. It is observed that the grid and anode currents increase exponentially with the grid voltage, as is expected from the Fowler-Nordheim emission tunneling theory 11161. Under reverse bias conditions, no current was observed until electric breakdown of the silicon nitride layer occurred at approximately 200 V. The plateau in the Fowler-Nordheim plot, shown in the inset in Fig. 5(a), is associated with the desorption of adsorbates present at the nanotube tips, as described in detail elsewhere [3,17]. The grid and anode currents were observed to follow each other closely, with a current gain (IJI,) of roughly 3 for this particular device tested but varying between 1-10 from device to device. The anode current was plotted only up to 28 pA in the figure; however, the maximum currents we have measured so far were I, = 100 pA and I, = 50 pA, meaning a total emission current of 150 pA from the cathode. This corresponds to a peak emission current density (Jpeak) generated by the cathode (effective emission area of nanotubes = 9x(lOxlO) pm2) of 16 A/cm2, exceeding the previously published record emission current density from carbon nanotubes [4]. The MEMS microtriode device was operated continuously without degradation for 24 hours at a current density of approximately 2 A/cm2 (I, = 12 PA). It was also found that the microtriode device remained robust while running at an elevated pressure of tom. Considering that field emitter arrays typically have to be operated at a vacuum under 10-9 ton: to achieve lifetimes of even a few minutes [7], the data from the microtride represents a significant improvement. This impressive behavior of our microtriodes may be attributable to the excellent chemical and mechanical properties of carbon nanotubes. The use of small-area (-pm’) cathodes in our microtriodes also contributes to the emitter stability by reducing the impact of extreme emission non-uniformity (i.e. hot spots) that is frequently encountered and often unavoidable in large-area (e.g. -mm2 and larger) cathodes [ 17-19].

As shown in Fig. 5(a), the transconductance of the microtriode is low, about 1.3 pS at the anode current of 28 pA. It should be correspondingly much higher at the maximum anode current level of 100 pA that we observed. On a normalized basis with respect to the emission area, our number (0.15 S/cm2)is about half of but potentially much better (at higher current levels) than the thermionic triode (0.3 S/cm2) [ 101. If normalized to the emission current, our number (0.05 S/A) is comparable or even better than Spindt cathode-based structures (-0.03 S/A). While it is clearly important to have a high transconductance for successful high frequency device operation, such a high transconductance is desirably achieved at relatively low emission currents and voltages in order to reduce the probability of emitter failure due to overheating or arcing and to minimize the heat dissipation at the anode. Because the fields required for emission from nanotubes are typically low [20], our nanotube based triode structure is likely to perform well in this regard.

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Shown in Fig. 5(b) is the characteristic curves measured at the anode. It is observed that an electric breakdown occurrs across the thin silicon nitride layer on the Si substrate at voltages above 200V. To circumvent this problem, an external metallic anode was brought into close proximity to the original polysilicon anode, and data at voltages above 200 V were subsequently collected. The internal anode resistance (Ra=6V,/6I,), measured in the linear region above anode voltages of 200 V, was approximately 100 MQ. Also included in the figure is a 10 MQ load line. Operating at the point of V, = 325 V and I, = 16 pA, a peak-to-peak voltage swing of 10 V on the grid induces a peak-to-peak anode voltage change of 75 V, resulting in a voltage gain of 17.5 dB. Assuming that the load resistance (R1) is equal to the internal anode resistance (Ra), we can conveniently calculate the power gain by GPO,, = ?4 (AIa/AIg)g,,,Ra. Using a current gain (I,/&) of 10, a transconductance (g,) of 1.2 pS, and an anode (and load) resistance (R, and RI) of 100 MQ, we obtain a power gain of 18 dB. Because of the breakdown of the silicon nitride layer, the total output power at the integrated anode is currently limited in the range of 110 mW. Assuming that these devices will eventually be built on a better substrate with a much larger breakdown voltage, we expect that an output power of 100 mW (100 pA at 1000 V) per device is obtainable. In a distributed amplifier system (which can be easily designed and fabricated through MEMS), this would require only 100 devices to generate 10 watts of power. Normalized to a linear dimension of the anode, this kind of power level would be comparable to state-of-the-art GaAs HBT (heterojunction bipolar transistor) and GaN HEMT (high electron mobility transistor) devices that typically generate 4 W per millimeter gate length [21].

SUMMARY It is demonstrated, for the first time, that a completely integrated, laterally built, MEMS triode incorporating carbon nanotube field emitters can be constructed. Such a device can provide a powerful, on-chip, power-amplifying capability. The fact that the MEMS structure and materials withstood the high temperature nanotube growth processing and the device demonstrated impressive dc power gain is encouraging enough for us to further explore device structures that are more compatible with high frequency operation. Additional improvements in nanotube configuration and distribution are likely to further improve the performance of the MEMS based vacuum microtriode type devices.

ACKNOWLEDGMENTS The author wishes to thank Drs. W. Zhu, C. Bower, D. Shalom, D. Lopez, and P. L. Gammel of Agere Systems and Dr. G. P. Kochanski of Bell Laboratories, New Jersey for collaborations and helpful discussions.

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REFERENCES

1. Ijima, S (1991), Nature, 354, 56. 2. de Heer, W. A., Chatelain, A., and Ugarte, D. (1995), Science 270, 1178 (1995). 3. Dean, K. A. and Chalamala, B. R. (2000), Appl. Phys. Lett., 76,375. 4. Zhu, W., Bower, C., Zhou, O., Kochanski, G., and Jin, S. (1999), Appl. Phys. Lett., 75, 873. 5. Bower, C., Zhu, W., Shalom, D., Lopez, D., Chen, L. H., Gammel, P. L., and Jin, S. (2002), Appl. Phys. Lett., 80, 3820. 6. http://wn~w.meinsrus.com: The Design Handbook of MUMPS (Multi-User MEMS Processes), Cronos Integrated Microsystems, a JDSU Company, Research Triangle Park, North Carolina, 2000. 7. Bower, C., Zhu, W., Jin, S., and Zhou, 0. (2000), Appl. Phys. Lett., 77, 830. 8. Bower, C., Zhu, W., Werder, D. J., Jin, S., and Zhou, 0. (2000), Appl. Phys. Lett., 77, 2767. 9. Gilmour, A. S. Jr., Microwave Tubes (1986), Artech House. 10. Morton, J. A. and Ryder, R. M. (1950), Bell System Tech. J. 29,496. 11. Brodie, I. and Spindt, C. A. (1979), Appl. Surf. Sci., 2, 149. 12. Neidert, R. E., Phillips, P. M., Smith, S. T., and Spindt, C. A. (1991), IEEE Trans. Electron Devices, 38, 661. 13. Makishima, H., Imura, H., Takahashi, M., Fukui, H. and Okamoto, A. (1997), Proc. 10'' Int. Conf. Vacuum Microelectronics, Kyongju, Korea, p. 194. 14. Takemura, H., Yomihari, Y., Furutake, N., Matsuno, F., Yoshiki, M., Takada, N., Okamoto, A. and Miyano, S. (1997), Tech. Digest ofIEDM, p. 709. 15. Driskill-Smith, A. A. G., Hasko, D. G,. and Ahmed, H. (1999), Appl. Phys. Lett., 75, 2845. 16. Fowler, R. H., and Nordheim, L. (1928), Proc. R. Soc. London, Ser. A , 119, 173. 17. Zhu, W., Bower, C., and Jin, S. (2001), Solid State Electronics, 45,921. 18. Nilsson, L., Groening, O., Emmenegger, C., Kuettel, O., Schaller, E., Schlapbach, L., Kind, H., Bonard, J. M., and Kern, K. (2000), Appl. Phys. Lett., 76,2071. 19. Andrienko, I., Cimmino, A., Hoxley, D., Prawer, S., and Kalish, R. (2000), Appl. Phys. Lett., 77, 1221. 20. Zhu, W., Baumann, P. K., and Bower, C. A., (2001), Chapter 6 in Vacuum Microelectronics, edited by Zhu, W., John Wiley and Sons, p. 247. 21. Hadaway, R., Surridge, R., Greshishchev, Y., Schvan, P., Voinigescu, S., and MacElwee, T. (1999), GaAs Mantech Digest of Papers.

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Nan0 and Microstructural Design of Advanced Materials M.A. Meyers, R.O. Ritchie and M. Sarikaya (Editors) 02003 Elsevier Ltd. All rights reserved.

MICROSTRUCTURE-PROPERTY EVOLUTION IN COLD-WORKED EQUIATOMIC FE-PD DURING ISOTHERMAL ANNEALING AT 50OOC A. Deshpande, A. Al-Ghaferi, H. Xu, H. Heinrich' and J.M.K. Wiezorek Department of Materials Science and Engineering, University of Pittsburgh, 3700 O'Hara Street, 848 Benedum Hall, Pittsburgh, PA 15261, USA; ' on sabbatical leave from ETH Zurich, Institute of Applied Physics, CH-8093 Zurich, Switzerland;

ABSTRACT In this work the evolution of magnetic properties and microstructure in cold-deformed equiatomic Fe-Pd during isothermal annealing at 500°C has been studied, The magnetic age hardening behavior has been determined using a vibrating sample magnetometer. The microstructures have been characterized by a combination of X-ray diffraction and scanning and transmission electron microscopy experiments. During annealing of the cold-deformed Fe-Pd concomitant recrystallization and ordering produces a complex microstructure that exhibits enhanced coercivity relative to conventionally processed material. The maximum coerciviy observed here was associated with a partially recrystallized or combined reaction transformed microstructure. The magnetic age hardening behavior of the combined reaciton processed fePd has been attributed to a grain size hardening effect. The experimentally observed microstructural evolution of the cold-deformed Fe-Pd during annealing has been rationalized in terms of the competition between the combined reaction mode, which is associated with the discontinuous mode of ordering, and the continuous ordering transformation. The release of the stored strain energy during annealing of the colddeformed Fe-Pd appears to accelerate the kinetics of a discontinuous ordering mode with respect to those of the usually dominant continuous ordering mode.

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INTRODUCTION At room temperature Fe-Pd alloys of near equiatomic composition form a stable tetragonal L1,-ordered intermetallic phase, y,-FePd, that exhibits high uniaxial magnetocrystalline anisotropy with an “easy” caxis, large theoretical B-H products and good mechanical and corrosion properties. This combination of properties renders the FePd based L1,-intermetallics very attractive for a range of permanent magnet and thin film applications [ 11. However, while the intrinsic properties of the intermetallic y,-phase are comparable to those of rare-earth magnets, the technical magnetic properties reported for conventionally processed FePd based alloys are disappointingly low [2, 31. This indicates that the technical properties of the FePd alloys are very sensitive to microstructure. Hence, property optimization relies on the development of a basic knowledge of the evolution of microstructure and defect structure during processing. In conventionally processed FePd based alloys, the L1,-ordered phase forms upon cooling below the order-transition temperature via a thermodynamically first-order type order-disorder transformation from the disordered high-temperature solid solution, the y-(Fe,Pd) phase with Al(FCC) structure [3,4]. During conventional processing a continuous ordering reaction involves the nucleation of coherent precipitates of the tetragonal y,-phase throughout the grains of the disordered y-matrix followed by growth [3, 41. As the ordered precipitates grow, the attendant transformation strains are relaxed by the formation of self-accommodating arrays of dodecahedrally conjugated twins, i.e. the polytwin structure characteristic of the L1,-ordered FePd alloys develops [3-51. It has been shown [3] that the surprisingly low technical magnetic properties of these alloys are associated with the presence of the polytwin structure. In fact, more recent studies [6, 71 reported thermomechanical processing schemes that resulted in FePd based alloys with improved hard magnetic properties by successfully suppressing the formation of the polytwin structure. These processing schemes involved the annealing of alloys that had been cold-rolled in the disordered state at temperatures below the ordering temperature in order to induce transformation of the microstructure by a combined reaction of concomitant recrystallization of the cold-deformed state and ordering, y(FCC) => y,(Ll,). The combined reaction (CR) transformed alloys exhibit significantly more heterogeneous microstructures than conventionally processed FePd alloys, which is expected to alter the magnetic hysteresis behavior. It has been proposed [7] that the increased coercivity of the CR transformed alloys relative to the conventionally processed FePd alloys originates from a combination of a domain wall drag effect resulting from the reduced grain size (grain size hardening) and domain wall pinning by planar faults [7]. The intriguing interplay of recrystallization processes, which are driven by the stored energy of cold-work, and the ordering processes, which, interestingly, have been shown to include both continuous and discontinuous mechanisms [6], promises the potential to generate new microstructural morphologies in intermetallic FePd alloys with enhanced technical magnetic properties. However, in order to optimize properties intelligently a better basic understanding of processing-microstructure-property relationships for CR transformed FePd alloys has to be developed. To date, microstructural studies of CR transformed microstructures have been rather limited and only included results from transmission electron microscopy (TEM) [6, 71. Hence, here a systematic investigation the microstructure-property evolution during annealing of Fe-Pd alloy after cold-deformation by equal-channel angular pressing (ECAP) has been undertaken. The advantages of using ECAP for the cold-deformation prior to annealing are the preservation of the cross-sectional dimension and the controlled accumulation of very large amounts of total effective strain larger than 1.0 [8]. The latter enables the exploration of a wider range of driving forces for recrystallization than is attainable with cold-rolling for instance and expands the matrix of processing

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parameters. The evolution of properties and microstructure is observed by experimental studies using magnetic hysteresis measurements together with a combination of microstructural characterization methods of x-ray diffraction (XRD), scanning electron microscopy (SEM) and TEM. The combination of complementary methods of XRD, SEM and TEM enables a more complete microstructural characterization of the transforming Fe-Pd alloys that bridges the length scales from mesoscopic to nanoscopic. In his paper preliminary results regarding the evolution of microstructure and magnetic properties of equiatomic FePd that has been cold-deformed by a single pass of ECAP during isothermal annealing at 500°C are reported. Implications for structure-property relationships and the mechanisms of microstructural transformation of cold-deformed Fe-Pd during isothermal annealing are discussed.

EXPERIMENTAL PROCEDURE The equiatomic Fe-Pd alloy used in this study has been prepared from high-purity elemental starting materials using vacuum arc melting in an atmosphere of purified argon gas. Sections from the as-cast buttons have been cold-rolled to about 50% reduction in thickness, followed by a homogenization treatment at 950°C (1223K) for 6 hours (21.6ks) and quenching into ice-brine. In the as-quenched state the material consisted of grains of the disordered FCC y-(Fe,Pd) solid solution with an average diameter of approximately 130 pm. Billets of the as-quenched material 36mm long with square cross-sections of 6x6 mm2 have been cold-deformed at room temperature by a single ECAP-pass, 120" inner-die angle. Isothermal anneals after ECAP have been performed for up to 50 hours (180ks) at 500°C (773K), well below the critical ordering temperature TC=650"C(923K), in order to induce the combined reaction of concomitant recrystallization and ordering. The evolution of the magnetic properties was then documented as a function of annealing time using a vibrating sample magnetometer (VSM) producing a maximum field of 15 kOe at room temperature. The evolution of the microstructure as a function of annealing time has been studied by XRD, SEM and TEM using a Philips X'pert XR-diffractometer, a field-emission gun equipped Philips XL30 SEM and a Jeol 2000 FX TEM, respectively. Thin foils for TEM have been prepared by twin-jet electropolishing using an electrolyte of 82% acetic acid, 9% perchloric acid and 9% ethanol, all by volume, at approximately 0°C (273K) and 30 V.

RESULTS Figure 1 shows SEM micrographs obtained in the backscatter electron mode (BSE) of the microstructure of the Fe-Pd material in the as-quenched and as-deformed states respectively. The contrast observed is not associated with differences in elemental composition but rather purely due to differences in crystallographic orientation. The compositional homogeneity of the nominally equiatomic material has been confirmed by energy dispersive X-ray spectroscopy (EDS) of selected as-cast and as-quenched specimens. In Figure l a grains, including many annealing twins, can be distinguished for the as-quenched state. The average grain size after homogenization and quenching has been determined by computerassisted image analysis as approximately (130?5)p. After ECAP the microstructure consisted of heavily deformed grains that exhibited deformation bands at various length scales, i.e. shear, micro- and transition bands. The local rotations of the crystal lattice resulted in fairly rapid orientation changes and a mosaic

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Figure 1: SEM BSE micrographs of a) as-quenched Fe-Pd, scale marker 200pm, and b) as-deformed Fe-Pd, scale marker 50 pm.

b

Figure 2: a) TEM bright-field multi-beam micrograph of the dense dislocation cell-structure in a grain in the Fe-Pd after ECAP and b) SADP of the grain with beam approximately parallel to [loo]. Note the diffuse L1,-structure superlattice spots and spot splitting.

structure or cell structure inside a given deformed grain, which is reflected by the much more complex contrast in SEM BSE micrographs (e g Figure lb). The TEM micrograph in Figure 2 presents a typical example of the dense defect structure developed in the deformed grains. Using diffraction contrast images the dislocation density, pdlal=,has been estimated as pdlrloc = 10” - 10”cm ’. The accompanying selected area diffraction pattern (SADP) in Figure 2b clearly indicates the presence of a mosaic structure associated with the frequent small orientation changes across the dense dislocation walls between cells of lower dislocation density (Figure 2a). The matrix of the as-deformed material has the FCC crystal structure of the disordered y-phase and diffuse intensities for superlattice spots (e g. 110) in SADP’s indicate the presence of L1,-type either short-range order (SRO) or of very small (< 2nm) coherent precipitates of L1,-ordered orientation variants (Figure 2b) VSM experiments have been performed with the material prior to and after annealing to monitor the development of the magnetic age hardening curve. Some representative data collected from the VSM runs is collated in Table 1. The coercivity, H,, of the as-quenched disordered y-(Fe,Pd) solid solution was 27 Oe.

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The deformation induced during the single ECAP pass enhanced the coercivity to 37 Oe. During annealing the coercivity, H,, increases from a minimal value of the as-deformed state (37 Oe) to a maximum (523 Oe) after 12 hours of annealing at 5 0 0 ° C (673K) before decreasing again at longer annealing times to a lower value (349 Oe) (Table 1). Interestingly, coercivities of about 180 to 350 Oe have been reported previously [6, 71 for undeformed L1,-ordered FePd after long-time annealing at 5 0 0 " C , which had developed polytwin microstructures typical of the continuous ordering reaction. The type of magnetic age hardening behavior documented in Table 1 is consistent with previous studies [6, 71, which included a different mode of cold-deformation and different annealing temperatures. Thus this behavior appears to be characteristic of cold-deformed FePd during annealing at T
TABLE 1 COERCIVITY,

H,,

VERSUS TIME OF ANNEALING AT 5 0 0 ° C .

A Q AND A D IN 0 HOURS OF TIME OF ANNEALING REFER TO THE AS-QUENCHED STATE AND THE AS-DEFORMED STATE, RESPECTIVELY.

Time[hours] H, [ O ~ I

I

I

O(AQ) 27

I I

O(AD) 37

I I

1.5 239

1 I

3 261

I I

5 442

I I

12 523

I I

24 349

XRD experiments have been performed in order to monitor the changes of the lattice parameters during annealing. The { 113) and (1311 diffraction peaks have been used to determine changes in the (c/a)-ratioor tetragonality as a function of annealing time at 500°C as summarized in Table 2. For annealing times of less than 3 hours the quality, peak width and signal-to-noise ratio, of the XRD signal was insufficient to determine with confidence apparent changes in the prominent lattice parameters. This lack of useful XRD data for the shorter annealing times can presumably be attributed to the small sample size, the small fraction of ordered material and the small size of the ordered domains or grains. The data collated in Table 2 indicates that the (c/a)-ratio decreases from unity prior to annealing towards the equilibrium value of 0.966 within 24 hours and remains constant thereafter. Hence, it appears reasonable to conclude that, while significant LI,-type the long-range order (LRO) certainly develops within the first 5 hours of annealing at 500"C, the maximum LRO parameter is attained only after between 12 to 24 hours of isothermal annealing.

TABLE 2 TETRAGONALITY VERSUS TIME OF ANNEALING AT 500°C: TIME [HOURS]

5

12

24

50

1.154

1.157

1.157

1.157

1.135

1.130

1.128

1.128

n 911

n 968

n 966

n 966

{ 131) PLANE SPACING [A] [113) PLANE SPACING [A] TETRAGONALITY (c/a\

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SEM and TEM investigations of the annealed samples have been conducted in order to document the microstructural evolution during isothermal annealing of the cold-deformed Fe-Pd. TEM allows detailed local probing of structural, morphological and compositional changes on a nanoscopic to microscopic scale ( = l o to 10’ pm). Compared to TEM, SEM studies can provide information on the microstructural evolution for much larger fields of view and also at the larger length scales, namely from the sub-micron scale to the meso-scale (=lo-’ to lo3 pm). Hence, by combining SEM and TEM complementing data sets regarding the microstructural evolution during annealing of the cold-deformed Fe-Pd could be obtained across the relevant length scales. Figure 3 and Figure 4 present SEM BSE micrographs representative of the pertinent features of the microstructural changes observed during isothermal annealing at 500°C. Even at the shortest annealing times (1 hour) small (<5pm), morphologically irregular grains of the L1 ,-ordered y,phase emerged initially at grain boundaries (GB’s) between the large (=130pm) deformed grains and somewhat later also at transition and micro-bands within the deformed grains (Figure 3). These new grains are the product of the nucleation and growth processes of the combined reaction of concomitant recrystallization and ordering and are referred to in the following as the recrystallized (Rex) grains or combined reaction product (CRP) grains. Conversely, the grains of the deformed material that do not transform by the combined reaction are referred to in the following as unrecrystallized (Unrex). Figure 3a shows a typical example of the morphology after 3 hours of annealing. The CRP grains (Rex in Fig. 3a) formed heterogeneously preferentially at or near GB’s between the unrecrystallized deformed grains (Unrex 1 to Unrex 3 in Fig. 3a). Figure 3b depicts an example of the microstructre after 5 hours of annealing. Now a significant fraction of CRP grains is also present at micro-bands within an unrecrystallized grain in addition to CRP grains at GB’s. During up to 12 hours of annealing this process of heterogeneous nucleation of CRP grains at GB’s and deformation bands and their growth into the surrounding unrecrystallized volume continued. Figure 3d depicts a typical example of CRP grains at transition bands, which separate regions of differently oriented deformed crystal with shear bands. Planar faults, akin to stacking faults or microtwins, are discernible in the largest of the CRP grains in the annealed FePd (e.g. Figure 3a and 3d). Furthermore, the population of CRP grains consists of a very large number of grains with sizes of less than 1.0 I”and very few large grains up to about 10 pm in size (e.g. Figure 3c and 3d). Comparison of Figures 3a-c clearly indicates qualitatively that the volume fraction transformed by the combined reaction, the recrystallized fraction, increases with annealing time up to 12 hours. Computer assisted image analyses of SEM micrographs covering fields of view of approximately 500pm by 500pm for each annealing state have been used to determine the recrsytallized area fraction. Accordingly, the fraction recrystallized increased from = 2%, = 12% and ~ 3 6 % after 3 hours, 5 hours and 12 hours after 24 hours annealing. Hence, recrystallization remained annealing, respectively, to a maximum of ~ 4 5 % incomplete even after 24 hours annealing. Figure 4 presents SEM micrographs of the microstructures typical of annealing for 12 hours and 24 hours at 500°C. While the microstructural morphology, namely heterogeneously distributed, irregularly shaped, small CRP grains and a majority volume fraction of unrecrystallized grains, remained essentially the same up to 12 hours of annealing (Figures 3 and 4 4 , a significantly different microstructure emerged after 24 hours of annealing at 500°C (Figure 4b). After 24 hours of annealing the microstructure appears to be more homogeneous, since the heterogeneously distributed small CRP grains that decorated GB’s between and deformation bands within unrecrystallized grains are no longer observed (Figure 4b). Instead, many much larger recrystallized grains (Rex in Figure 4b), that contain tell-tale annealing twins, and unrecrystallized grains (Unrex in Figure 4b) constitute the

Y

a

4

ij

c

F E

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w

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1

Figure 4: SEM BSE micrographs of the microstructures after a) 12 hours and b) 24 hours of annealing. TEM studies have been performed to determine in detail the local microstructural changes in the unrecrystallized and the recrystallized grams in the cold-deformed Fe-Pd during the isothermal annealing at 500°C The TEM micrographs in Figure 5 have been obtained from unrecrystallized grains i n FePd samples after annealing at 500°C for 5 hours and 24 hours, respectively The complex contrast exhibited by the unrecrystallized grains (Figure 5) is characteristic of the nucleation and growth processes associated with t h e continuous ordering reaction [3] Strain contrast features of lenticular or nearly lamellar morphology align approximately parallel to the traces of dodecahedral planes, namely the directions [l-111 and [l-1-11 marked in the lower magnification bright field micrograph of Figure 5a The superlattice dark field micrograph in Figure 5b shows the same region as in Figure 5a at higher magnification and reveals in bright contrast very small (5 1Onm) coherent precipitates of one of the three orientation variants of the L1,ordered phase that emerge within the FCC matrix Under the influence of the attendant transformation strain variant selection occurs locally during growth and the small coherent L1,-precipitates coalesce to form larger ordered domains aligned parallel to traces of dodecahedral planes [e g 31 These observations are consistent with the emergence of an incipient polytwin structure I n the unrecrystallized grains during annealing of the cold-deformed Fe-Pd [3, 41 The continued ordering and coarsening of these aligned ordered domains during continued isothermal annealing at 500°C produces a fairly well developed polytwin structure i n the unrecrystallized grains after 24 hours (Figure 5c) The accompanying [OOI] zone axis SADP inset in Figure 5c exhibits eight superlattice spots surrounding the central spot, which indicates the presence of all three possible orientation variants of the tetragonal ordered phase in the unrecrystallized gram Effects of the internal strains associated with the defect structure introduced by cold-deformation are still detectable in SADP's after 24 hours of annealing at 500°C i n the unrecrystallized grains (inset in Figure 5c) Hence, during isothermal annealing of the cold-deformed Fe-Pd at 500°C the unrecrystallized grains transform from heavily deformed FCC y-(Fe,Pd) to Ll,,-ordered y,-FePd with a polytwinned morphology via the continuous ordering reaction that is characteristically observed for the undeformed material [4-71 Figure 6 presents an example multi-beam bright field TEM micrograph of the early stages of growth of CRP grains (marked A, B and C in Figure 6) after heterogeneous nucleation at a grain boundary between two unrecrystallized grains i n a sample of the deformed Fe-Pd after10 hours annealing. The bright field

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137

a

C

Figure 5: Example TEM micrographs depicting the evolution of L1,-type LRO in the unrecrystallized region. a) Bright field, g=002, off 11 101, b) corresponding dark field with g=OOl, both for 5 hours annealing at 5OO'C. Traces of dodecahedra1 planes parallel to [l-1 I] and [l-1-11 are marked in a). c) multi-beam bright field, beam direction = [OOl], inset SADP, for 24 hours annealing at 500°C. TEM micrograph of Figure 7a depicts i n more detail the CRP grain marked A in the overview presented i n Figure 6 The small CRP grain is essentially free of defects and diffraction experiments in the TEM confirmed it to have the ordered L1,-structure of y,-FePd The segment of GB between the CRP grain and

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the upper unrecrystallized gram (Unrex 1 i n Figure 6) contains numerous interfacial defects, most of which presumably are dislocations Microdiffraction patterns (pDP's) obtained from the regions marked X, Y and Z i n Figure 7a are shown in Figures 7b, 7c and 7d, respectively The pDP's indicate that regions X and Y exhibit similar orientations off [110] with only a small misorientation (< 3 " ) relative to each other (Figure 7b and 7c) Hence, the short segment of GB between the CRP grain (A i n Figure 6) and the upper unrecystallized grain (Unrex 1 in Figure 6) is consistent with a segment of low-angle GB (LAGB) The pDP obtained from the lower unrecrystallized grain (Unrex 2 in Figure 6 and label Z in Figure 7a) indicates a much larger misorientation with respect to the CRP grain (compare Figures 7b and 7d) Therefore, the GB segments between the CRP grain and the lower unrecrytallized grain appear to be consistent with highangle GB's (HAGB's) These observations are quite typical for the CRP grams that heterogeneously nucleated at GB's

25 t

I

t

Figure 6: Multi-beam bright field TEM micrograph depicting an example of new LI,-ordered CRP grains, near letters A, B, C, at a grain boundary between two unrecrystallized grains, marked Unrex 1 and Unrex 2, in the cold-deformed Fe-Pd after 10 hours of annealing at 500°C DISCUSSION The increase i n the maximum magnetic hardness, e g coercivity, attainable during annealing of cold-rolled Fe-Pd has been attributed to changes in microstructural morphology associated with the transformation of the cold-deformed, disordered material by the combined solid state reaction of concomitant recrystallization and ordering [6, 71 Here the magnetic age hardening behavior and microstructural evolution of equiatomic Fe-Pd cold-deformed by a single ECAP pass dunng isothermal annealing at 500°C has been determined experimentally In the initial stages of annealing the coercivity increases monotonically to a maximum (523 Oe) followed by a decrease to values typically exhibited by polytwinned L1,-FePd (349 Oe) (Table 1) This behavior is consistent with previous work 171 The XRD data (Table 2 ) indicated that the vgnificant increase i n coercivity from the initially very low value associated with the as-

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139

.-

Figure 7: Details of the new LI,-ordered grain marked A in Figure 7. a) Bright field TEM, g=-l1-1, off [I lo], b) low camera length SADP from the new grain at X in a), c) SADP from unrecrystallized grain 1 at Y in a), p l 1 - 3 off [110], and d) SADP from unrecrystallized grain 2 at 2 in a), g is of type (111) and beam direction is far off [I 101. deformed state (37 Oe) to the maximum value (523 Oe) correlates with the development of significant fractions of the ordered tetragonal L1,-structure The SEM and TEM observations (Figures 3 to 7) are consistent with the LRO evolution documented by the XRD data (Table 2) However, the subsequent decrease in coercivity to about 350 Oe cannot be attributed to the LRO parameter alone, which, as would be expected, continues to increase to the equilibrium value at 500°C with annealing time (Table 2). Similarly, the fraction recrystallized increased monotonically with annealing time to a maximum of about 45% after 24 hours (e.g Figures 3 and 4) Thus, the charactenstic magnetic age hardening behavior of colddeformed Fe-Pd (TabIe 1) cannot be attributed solely to the evolution of LRO and/or the evolution of the fraction recrystallized Furthermore, recrystallization remained incomplete, even after 24 hours of annealing The microstructure responsible for the maximum coercivity (523 Oe after 12 hours annealing at 500°C) contained about 64% of unrecrystallized volume and only 36% of recrystallized or combined reaction transformed volume (e g Figures 3 and 4). The former consists of the LI,-ordered phase with nearly the equilibrium LRO parameter and exhibits an incipient polytwin structure after annealing for 5 hours or more (Table 2 and Figure 5) The latter is comprised of heterogeneously distributed, perfectly L1,ordered and nearly defect-free, monolithic CRP grains with maximum grain sizes of less than = 10 pm and average grain size of about l p m (e g. Figures 3 and 4) It has been proposed [7] that the increased coercivities of combined reaction transformed FePd alloy3 originates from a superposition of magnetic hardening by a greatly reduced grain size (grain size hardening) and by pinning of magnetic domain walls by planar defects According to Klemmer et al [7] the grain size hardening contribution to the coercivity enhancement, AHD, in the combined reaction transformed FePd can be given approximately by AHD= 6 (y /DM,) Here fi is a geometrical term with a value between 1 to 5, y is the domain wall energy (17 ergkm’), M, is the saturation magnetization (1 100 emukm’) and D is the grain size [7] Considering the range for 6 and a grain size of 1 pm, the approximate upper and lower bounds of AH, are estimated as about 155 Oe to 775 Oe. For grain sizes of 30pm or larger the grain size hardening effect becomes negligible (I e for 80 pm AH, = 2 Oe to 10 Oe) After 24 hour? annealing at 500°C the fraction recrystallized increased to a

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maximum of = 45%, i.e. recrystallization was incomplete, and the CRP-grains increased dramatically in size to = 80pm (e.g. Figure 4). Hence, it appears reasonable to conclude that the significant grain growth in the fraction of CRP grains documented here for the first time (e.g. Figures 3 and 4) is responsible for the observed drop in coercivity for annealing times in excess of 12 hours (Table 1). Conversely, the coercivity increase in the first 12 hours of annealing may be attributed chiefly to the monotonic increase in the volume fraction of CRP grains with an average size of approximately 1 pm (Figures 3 to 7). Of course, an additional contribution to the coercivity increase over the first 12 hours of annealing is associated with the increases in LRO from the transformation of the unrecrystallized grains by the continuous ordering reaction. At longer annealing times the development and coarsening of the polytwin structure should further reduce the coercivity of the material. In conclusion, a grain size hardening effect as proposed in [7] appears to be most suitable to rationalize the magnetic hardening behavior observed here. The SEM and TEM observations of the microstructural evolution of the CR transformed fraction in the FePd alloys are very similar to those reported for the early stages of annealing of cold-deformed FCC metals with low stacking fault energy [9-111. For instance, the large strain energy gradients present at deformation (shear, micro- and transition) bands and at large angle GB's in the cold-deformed microstructure appear to enhance the probability for the formation of the essentially strain-free CRP grains (Figure 3), just as in recrystallization of disordered metals. Furthermore, small CRP grains growing at GB's between unrecrystallized grains exhibit an approximate orientation relationship with one of the unrecrystallized grains, with which they share a segment of LAGB (Figures 6 and 7). The CRP grains grow predominantly into the other unrecrystallized grain, with which they share HAGB's, while growth into the unrecrystallized grains with which they share a LAGB is negligible (Figures 6 and 7). Based on the TEM observations (Figures 6 and 7) it is tempting to propose that the formation of stable embryonic CRP grains can occur by processes similar to a bulge mechanism for recrystallized grains in disordered metals [lo, 121. Thus, the recrystallization front or more precisely the CR transformation front propagates by migration of HAGB's. Therefore, mechanisms similar to those proposed for stacking fault and microtwin formation at the migrating HAGB's during the recrystallization of cold-deformed FCC metals with low stacking fault energy [13, 141 appear to be suitable to explain the origin of the planar defects observed in the larger ordered CRP grains. The usual definition of recrystallization is the formation and migration of HAGB's driven by the stored strain energy of cold-deformation [e.g 111. During the CR transformation in equiatomic Fe-Pd HAGB's form and migrate. Hence, in this sense the CR is similar to recrystallization of disordered metals and alloys. However, the change in crystal structure facilitated by the CR is usually not a feature of concern in recrystallization of disordered metals and alloys. It is interesting to note that the ordering transformation in equiatomic Fe-Pd can be achieved by both the usually kinetically dominant continuous ordering mode and/or by a discontinuous ordering mode, akin to a massive transformation 114, 151. Indeed, during isothermal transformation of undeformed Fe-Pd at sufficiently low temperatures a limited volume transformed by the discontinuous mode of ordering has been observed [6]. Therefore, an important effect of cold-deformation on the ordering transformation of equiatomic Fe-Pd appears to be the acceleration of the kinetics of the discontinuous mode with respect to those of the continuous mode of ordering. Hence, it is likely that the experimentally observed accelerated ordering kinetics in cold-deformed equiatomic Fe-Pd relative to the undeformed material [16-181 can be attributed to the CR mode of transformation. The driving force for the CR mode is a combination of the difference in Gibbs free energy of the ordering reaction, y(FCC) => y,(Llo), and the stored strain energy of cold-deformation. This driving

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force diminishes with increasing time during annealing mainly because the continuous mode of ordering is operative in the unrecrystallized volume and to a lesser degree because recovery processes lower the stored energy of cold-deformation. Thus, once the LRO parameter reaches the equilibrium value the recrystallization process or the CR transformation essentially comes to a halt. Then the annealing phenomenon of grain growth becomes significant in the CR transformed fraction of the material. This scenario is consistent with the experimental results presented here.

SUMMARY AND CONCLUSION 1)

2) 3) 4)

Isothermal annealing of the cold-deformed FePd at 500°C produces complex, hetcrogencous microstructures that exhibit significantly enhancd coercivities with respect to conventionally processed FePd with the polytwin structure. For the processing condition utilized here, the maximum coercivity (523 Oe) is associated with a partially recrystallized (=36%) microstructure of fully ordered y,-FePd with the L1,-structure. The magnetic age hardening behavior of the combined reaction transformed FePd observed here has been attributed to a grain size hardening effect. The observed microstructural evolution during annealing of the cold-deformed FePd has been rationalized in terms of the competition between the combined reaction, which may be considered as a discontinuous ordering mode with kinetics enhanced by the stored energy of cold-deformation, and the continuous ordering mode.

ACKNOWLEDGEMENTS The authors gratefully acknowledge support for this work from the National Science Foundation, DMRMetals (NSF-0094213), with Dr. K. L. Murty as program manager. One of the authors (HH) also gratefully acknowledges support from the Department of Materials Science and Engineering, University of Pittsburgh, during his sabbatical stay in Pittsburgh during the summer 2002.

REFERENCES 1. 2. 3. 4. 5. 6.

Weller, D., and Moser, A. (1999) IEEE Trans. Magn. 35,4423. Magat, L.M., Yermolenko, AS., Ivanova, G.V., Makarova, G.M., and Shur, YAS. (1968) Fiz. Metal. Metalloved. 26,511. Zhang, B., Lelovic, M., and Soffa, W.A. (1991) Scripta met. mat. 25, 1577. Khachaturyan, A.G. (1983) In: Theory of Structural Transformations in Solids”, p. 368, John Wiley & Sons, New York. Yanar, C., Wiezorek, J.M.K., and Soffa, W.A. (2000) In: Phase Transformations and Evolution of Microstructure in Materials, pp. 39-54, Turchi, P. et a1 (Eds).TMS, Warrendale. Klemmer, T., and Soffa, W.A. (1994). In: Solid-Solid Phase Transformations, pp. 969-974, Johnson, W.C., Howe, J.M., Laughlin, D.E., and Soffa, W.S. (Eds). TMS, Warrendale.

142 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18.

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Klemmer, T., Hoydick, D., Okumura, H., Zahng, B., and Soffa, W.A. (1995) Scripta met. mat. 33, 1793. Segal, V.M. (1999) Mat. Sci. Eng. A 271, 322. Berger, A,, Willbrandt, P.-J., Emst, F., Klement, U., and Haasen, P. (1988) Progr. Mat. Sci. ??, 1. Willbrandt, P.-J., and Haasen, P. (1980) Z. Metallkde 273. Doherty, R.D., Hughes, D.A., Humphreys, F.J., Jonas, J.J., Jensen, D.J., Kassner, M.E., King, W.E., McNelley, T.R., McQueen, H.J., and Rollett, A.D. (1997) Mat. Sci. Eng. A 238, 219. Reed-Hill, R.E., and Abbaschian, R. (1992) In: Physical Metallurgy Principle, p 247, PWS Pub. Co., Boston. Gleiter, H. (1969) Acta met. 12,1421. Yanar, C., Radmilovic, V., Soffa, W.A., and Wiezorek, J.M.K. (2001) Intermetallics 9, 949. Yanar, C.,Wiezorek, J.M.K., Radmilovic, V., and Soffa, W.A., (2002) Met. Mat. Trans A 33, 2413. Greenberg, B.A., Volkov, A.Y., Kruglikov, N.A., Rodionova, L.A., Grokhovskaya, L.G., Gushchin, G.M., and Sakhanskaya, I.N. (2002) Phys. Met. Metallog. 92,167. Kulovits, A. (2002) Diploma thesis, University of Vienna. Peiler, W. (2002) priv. comm. at MRS Fall Mtg, Boston.

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PART 3: STRUCTURAL MATERIALS

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Nan0 and Microstructural Design of Advanced Materials M.A. Meyers, R.O. Ritchie and M. Sarikaya (Editors) Published by Elsevier Ltd.

MICROSTRUCTURE AND PROPERTIES OF IN SITU TOUGHENED SILICON CARBIDE Lutgard C. De Jonghe

R. 0. Ritchie

and Xiao Feng Zhang

'

' Materials Sciences Division, Lawrence Berkeley National Laboratory, University of California, Berkeley, CA 94720, USA Department of Materials Science and Engineering, University of California, Berkeley, CA 94720, USA

ABSTRACT A silicon carbide with a fracture toughness as high as 9.1 MPa.ml' has been developed by hot pressing pSic powder with aluminum, boron, and carbon additions (ABC-Sic). Central in this material development has been systematic transmission electron microscopy (TEM) and mechanical characterizations. In particular, atomic-resolution electron microscopy and nanoprobe composition quantification were combined in analyzing grain boundary structure and nanoscale structural features. Elongated Sic grains with 1 nmwide amorphous intergranular films were believed to be responsible for the in situ toughening of this material, specifically by mechanisms of crack deflection and grain bridging. Two methods were found to be effective in modifying microstructure and optimizing mechanical performance. First, prescribed postannealing treatments at temperatures between 1100 and 15OO0Cwere found to cause full crystallization of the amorphous intergranular films and to introduce uniformly dispersed nanoprecipitates within Sic matrix grains; in addition, lattice diffusion of aluminum at elevated temperatures was seen to alter grain boundary composition. Second, adjusting the nominal content of sintering additives was also observed to change the grain morphology, the grain boundary structure, and the phase composition of the ABC-Sic. In this regard, the roles of individual additives in developing microstructure were identified; this was demonstrated to be critical in optimizing the mechanical properties, including fracture toughness and fatigue resistance at ambient and elevated temperatures, flexural strength, wear resistance, and creep resistance. INTRODUCTION Silicon carbide (Sic) offers many intrinsic advantages as a structural ceramic, including a high melting temperature, low density, high elastic modulus and hardness, excellent wear resistance, and low creep rates at elevated temperatures. This remarkable combination of features make Sic one of the most promising advanced structural ceramic materials for a variety of advanced engineering technologies. An imperative in these structural applicationsis high fracture toughness, which for commercially available Sic is typically on the order of 3 MPa.m'", well below that of grain-elongated Si3N4 and yttria-stabilized ZrOz, for example. This low toughness clearly limits its utility. The toughening of ceramic materials can best be induced by crack bridging mechanisms (i.e., extrinsic toughening by crack-tip shielding), which can result from crack paths bridged by unbroken reinforcement fibers in composite ceramics (ex situ toughening) [l-31, or by self-reinforcement from elongated grains in monolithic ceramics (in situ toughening) [4]. The latter approach was exploited in the present work by hot pressing Sic with Al, B and C additives (ABC-Sic [ 5 ] ) . Two strategies, specifically post-annealing heat treatments and changes in the additive content, were used to optimize the microstructure.

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In this paper, we review the microstructure and mechanical properties of in situ toughened Sic. In particular, atomic-resolution TEM in conjunction with nanoprobe chemical analyses were employed to determine the structure and chemistty of the grain boundaries. Such atomic-scale characterization was correlated with materials processing and mechanical testing with the objective of optimizing the structural performance of ABC-Sic.

It is perhaps fitting that this work is presented in a symposium dedicated to the career of Professor Gareth Thomas, who was a pioneer in the development of materials through the use of transmission electron microscopy and intelligent microstructure design - this paper is dedicated to him in recognition of his leading contributionsto this field of materials science [e.g., [6,7]].

EXPERIMENTAL PROCEDURES Submicron P-SiC powder was mixed with 3 w P ? aluminum metal powder, 0.6 wt% boron, and 2 wt% carbon sintering. The slurry was stir dried, sieved, and uniaxially pressed at 35 MPa. The green bodies were hot pressed at 50 MPa at 190OOC for 1 hr in an Ar atmosphere. The final product, which was produced as 99% dense (3.18 g/cm3),4 mm thick and 38 mm diameter disks of polycrystalline Sic, was compromise of predominantly 4H and 6H a-Sic phases, with a minor fraction of 3C p-Sic. Some as-hot-pressed ABCSic samples were further annealed in a tungsten mesh furnace under flowing Ar, at temperatures between 1000 and 15OO0C, for times typically ranging from 72 to 168 hr. Structural and mechanical characterizations were performed for both as-hot-pressed and annealed samples. Structural and chemical analyses were carried out in a 200 kV Philips CM200 transmission electron microscope equipped with a windowless detector and corresponding X-ray energy-dispersive spectroscopy (EDS) system. A spatial-difference methodology was developed to determine the concentration of the impurities in the Sic grain boundaries using a nanoprobe with a diameter varied between 3 and 20 nm [8,9]. Indentation hardness, four-point bending strength, creep resistance, abrasive wear properties, R-curve fracture toughness, and cyclic fatigue-crack growth behavior at ambient and elevated temperatures were all evaluated for ABC-Sic. Experimental procedures for each of these mechanical property assessments are described in detail in the respective references quoted in this paper.

RESULTS General Aspects Some typical mechanical properties for as-processed ABC-Sic are summarized in Table 1. Of particular note is the fracture toughness, which has been measured to be as high as 7 to 9 MPa.m’”; this is the highest 4,value recorded for Sic to date.

Sample

ABC-Sic

4-Point Bending Strength (MPa)

691+12

Hardness* (GPa)

561f13

Fracture Toughness (MPa.mIn)

6.8-9.1 (iO.4)

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Using X-ray diffraction, 70 vol.% of the hot-pressed structure was identified as hexagonal 4H-Sic and the remaining 30% as cubic 3C-Sic. TEM studies revealed that the 3C-to4H phase transformation, which is presumed to have occurred during hot pressing, promoted anisotropic grain growth [lo], resulting in high area density of plate-like, elongated S ic grains (Figure la); the length and width of these grains ranged from 3 to 11 pm and 1 to 3 pm, respectively, with an aspect ratio for 90 % of them between 2 and 5. Interlocking between the elongated Sic grains was often observed, as shown in Figure lb. Equiaxed 3CSic grains with a submicron size were also found in ABC-Sic. It is believed that the unusually high toughness of ABC-Sic results from a combination of crack deflection and principally frictional and elastic bridging by the elongated Sic grains in the wake of the crack tip [5,11]. To optimize this toughening mechanism, an understanding of the grain boundary properties and structure is crucial; consequently, extensive TEM studies were focused on this feature of the microstructure.

Figure 1: (a) Bright-field TEM images showing elongated Sic grains in ABC-Sic. (b) Two elongated grains are interlocked

Figure 2: (a) High-resolution electron micrograph showing a typical intergranular film between two Si c matrix grains. An amorphous structure is observed with a width of about 1 nm. (b) Distribution of amorphous grain boundary widths determined by high-resolution electron microscopy. The grain boundary width ranges from 0.75 nm to 2.75 nm, with a mean of about 1 nm. Figure 2a shows a high-rcsolution TEM image of a typical grain boundary area in as-pressed ABC-Sic. An amorphous intergranular film is seen between two adjacent Sic grains, about 1 nm in width. Using highresolution electron microscopy, the statistical width of these films was determined; results are shown in Figure 2b. Specifically, the amorphous grain boundary films range in width from about 0.75 to 2.75 nm, with a mean of -1 nm. This width is consistent with the values found in other ceramic materials [12,13], and with theoretical explanations developed by Clarke [14]. In some particularly wide films (e.g. -2.75 nm), nanoscale crystallites were recognizable, indicating local ordering in the glassy films. Earlier work on Sic sintered with boron and carbon showed a solid-phase sintering procedure with no grain boundary films being formed [ 15,161. The formation of the current films was due to liquid-phase sintering promoted by the A1 additives. The liquid phase allowed for densification of the Sic at temperatures roughly 200°C lower than Al-free compositions, i.e., at -1900°C instead of -2100°C. The amorphous intergranular films provide the preferred crack path, which is an essential element for the development of crack bridging and hence toughening in ABC-Sic.

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Nanoprobe EDS analyses revealed that the grain boundary films contained substantial Al, 0, Si, and C. The oxygen came mainly from the SO2 surface oxidation of the Sic starting powder, and is one of the features responsible for difference in the behavior of different starting powders. Boron was below the detectability limit at the grain boundaries and in the interior of the Sic grains. In fact, boron was largely involved in forming A1&C7 secondary phases. Other secondary phases identified in ABC-SIC include A120C-Sic, mullite, A1203, A14C3, A1404C,and Al-0-C-B crystalline phases. These secondary phases were submicron in dimension and were present as triple-junction particles [8,17]. A1 in solution in the Sic matrix grains was also detected. Similar to Sic studied here, A1 and 0 concentrations in grain boundaries and their effects on Si3N4 phase transformation were reported by Goto and Thomas [ 181. Effects of Post-annealing The most significant phenomenon that we observed in the efforts of modifying microstructure of ABC-Sic was crystallization of amorphous intergranular films in post-annealing. While no significant change in the overall, large-scale microstructure was recognized, annealing at 1000°C for only 5-30 hours was sufficient to transform about half number of the amorphous grain boundary films into more ordered structures. Apparently, 1000°C was about the threshold temperature for activation of grain boundary diffusion. Annealing at higher temperatures for prolonged hours fully crystallized the intergranular films [8]. For example, whereas about 90% of the grain boundaries were amorphous in as-hot-pressed samples, 86% of the intergranular films in the annealed material were found to be crystalline. Figure 3a shows a highresolution TEM image of a grain boundary film crystallized after annealing at 1200°C for 500 hrs. In this image, the crystallized grain boundary film is not readily distinguishable because the grain boundary phase was strictly epitaxial with the 6H-Sic grain on the left-hand side. However, corresponding EDS detected substantial AI-0-Si-C segregations between the two Sic grains, confirming the existence of the boundary phase. An enlarged image from the framed area is shown in Figure 3b for closer inspection. The two adjacent Sic grains in this image show very different orientations. Due to a large deviation from the [l 1 201 type zone-axes, only (0004) lattice fringes, with the lattice spacing of 0.25 nm, could be resolved for the 4H-Sic grain on the upper-right side, while a two-dimensional [llZO] zone-axis lattice can be recognized in the 6H-Sic grain on the other side of the grain boundary. Under the imaging conditions for Figure 3, the black dots in the image correspond to cationic columns along the incident electron beam direction. Some black dots in the 6H-Sic grain were marked with black circles. The zigzag stacking of the dots correspond to the ...ABCACBABCACB... hexagonal structure of the 6H-Sic. The closest layer spacing along the c-direction is 0.25 nm.

Figure 3: (a) High-resolution electron microscopy image for a grain boundary area in ABC-Sic annealed at 12OO0Cfor 500 hrs. Amorphous intergranular film is crystallized. (b) Enlarged image from the framed area in (a). Atomic stacking in 6H-Sic grain on the bottom-left side is marked by black circles. 2Hwurtzite atomic stacking in grain boundary film (GB) are marked by white circles. Note the epitaxial orientation relationships between the grain boundary film and the 6H-Sic matrix grain.

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The grain boundary layer outlined in Figure 3b can be distinguished by the abrupt change in the atomic arrangement. Some lattice points in the boundary region are marked with white circles. The projection distance between adjacent lattice dots in the grain boundary layers is very close to that in the neighboring 6H-Sic grain, and the characteristic zigzag lattice arrangement is also apparent in the boundary layer. These observations would suggest a grain boundary film structure similar to 6H-Sic. However, instead of the ...ABCACBABCACB.. . periodic stacking for every six layers in the 6H-type structure, the stacking period in the grain boundary phase contains only two layers in one period, resulting in ...ABABAB... stacking with an 0.5 nm repeat length, within a grain boundary width of about 1.25 nm. In conjunction with the quantitative analysis of the grain boundary composition and computer image simulations, we concluded that one of the intergranular crystalline phases was aluminosilicate with a AIzOC-SiC solid solution composition and a 2H-wurtzite structure (hexagonal unit cell, a = 3.1 8, c = 5.0 A) [8,19]. The crystallized structure usually has an epitaxial structural relationship with Si c matrix grains when the (0001) habit plane is available. As shown in Figure 3, the typical grain boundary width after crystallization remains about 1 nm.

To further study the crystallization process in intergranular films at elevated temperatures, an ABC-Sic sample was heated in situ in a 300 kV JEOL 3010 transmission electron microscope equipped with a hot stage. Figure 4 shows high-resolution images €or the same intergranular film before and after in sifu heating, respectively. The amorphous film prior to heating crystallized discretely after 25 hrs at 1200°C, as indicated by arrowheads in Figure 4b. The crystallization tended to proceed epitaxially on the (0001) plane of the adjacent 6H-Sic matrix grain, with a 2H-wurtzite structure similar to that observed in ex situ annealed Sic samples. No discemable features could be identified as potential preferential sites for nucleation at the SiCifilm interface. Presumably, local compositional fluctuations in the intergranular films serve as nucleation sites.

Figure 4: (a) High-resolution image of an amorphous intergranular film in as-hot-pressed ABC-Sic. (b) The same film as in (a) but after in situ heating in a transmission electron microscope at 1200°C for 25 hrs. Arrowheads indicate the discrete, crystallized boundary segments. Another significant consequence of the thermal treatment was coherent nano-precipitation within Si c matrix grains, as seen in Figure 5a. Although Figure 5a was taken from a sample annealed at 14OO0C,the plate-like nanoprecipitates first formed at 130OOC. The precipitates were uniform in size and shape, and dispersed within the Sic matrix grains. The projected dimension of the precipitates after 1300°C annealing is -4 x 1 nmz with a volumetric number density of 5x1OzZ/m3. The precipitates coarsened with annealing temperature, accompanied by decrease in the number density. Detailed high-resolution electron microscopy characterization and nanoprobe EDS analysis determined an AlbCs-based structure and composition for the nanoprecipitates [20]. A comparison between 6H-Sic and A14C3 structures projected along the [OOOl] direction is shown in Figure 5b. The similarity between the two structures caused coherent precipitation with the (0001) habit planes. The formation and coarsening of the precipitates at 1300 to 1600°C was a

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150

consequence of lattice-diffusion-controlled classic nucleation and growth [20]. The diffusion of Al-rich species through Sic lattice starting at 130OoCresulted in At-enrichment in grain boundary films, as revealed by EDS.

Figure 5: (a) A14C3-based nanoprecipitate formed in a 6H-Sic grain annealed at 1400'C. The viewing directions are marked. (b) Atomic models for 6H-Sic and Al&3 projected along the [OOOl] direction. The similarity between the two structures can be seen.

The A1 content in intergranular films as a function of annealing temperature was analyzed with EDS. The results are plotted in Figure 6. It is apparent that Al solution in Sic grains decreased at llOO°C and especially above 1300'C, consistent with TEM observations that Al solutions formed nano recipitates &) changed exsolved from the Sic lattice. Not surprisingly, the A1 site density in the grain boundaries (NAI as well upon annealing. Below 12OO0C,the composition of intergranular films was virtually invariant, even while the intergranular films crystallized. The N*yB value was doubled at 1300°C, which can be readily correlated with diffusion of the Al-rich chemical species into the grain boundary films. The Al content in intergranular films after annealing at 1300°C is in agreement with All lSi0 @ c , a solid solution between 2Hwurtzite AlzOC and Sic [19]. At even higher annealing temperatures up to 16OO0C, N A ? ~changed marginally taking the standard deviation into account.

- . ; i

0

.

.

.

.

.

.

.

.

.-

200 400 600 800 1000 1200 1400 1600 1800 Anneallng Temperature ( O C )

0

Figure 6: Plots of EDS-determined Al site density in grain boundary films @A?*) (AVSiC, wt??)as a function of annealing temperature.

and in Sic matrix grains

The structural evolutions in intergranular films during thermal treatment demonstrated a profound influence on mechanical properties. It was found that the high strength, cyclic fatigue resistance, and particularly the fracture toughness of A3C-Sic at ambient temperature were not severely compromised at elevated temperatures. For example, the fatigue-crack growth properties up to 130OoC were essentially identical to those at 25OC. Figure 7 illustrates the variation in fatigue-crack growth rates, du/dN, with applied stressintensity range, AK, at a load ratio (minimum to maximum load) of R = 0.1 for ABC-Sic under different test conditions. It can be seen that at both 2% and 13OO0C,crack-growth rates display a marked sensitivity to the stress intensity but little effect is from change of loading frequency over the range 3 to 1000 Hz [21-231. Mechanistically, the lack of a frequency effect in ABC-Sic is expected as crack advance occurs via predominantly intergranular cracking ahead of the tip, as shown in Figure 8. Grain bridging in the crack

Microstructure and properties of in situ toughened silicon carbide

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wake is a common feature. However, the absence of a frequency effect at elevated temperatures is surprising, particularly since comparable materials, such as Si3N4, A1203 and silicide-matrix ceramics, show a marked sensitivity to frequency at above 1000°C [24-281. In these later materials, softening of the intergranular films, grain boundary cavitation and viscous-phase bridging are common. In contrast, TEM studies of regions in the immediate vicinity of the crack tip in ABC-Sic (e.g. Figure 8) provided direct confirmation of fracture mechanisms which were similar at ambient and elevated temperatures, with no evidence for grain boundary cavitation (creep) damage or viscous-phase bridging at temperatures as high as 1300°C. We conclude that the unique high-temperature mechanical characteristics of ABC-Sic appear to be a result of the thermal-induced crystallization of intergranular glassy films. vZ25Hz. R=0.1 1 0 25% o 850°C A 1200°C 0 13OO0C F 3 H z . R=0.1 U 850°C 6 A 1200’C % 1300°C F25Hz. R=0.5 @ @ 1300°C

i

8

2 3 4 5 6 stress intensity Range, AK (MPam”‘)

Figure 7: Cyclic fatigue-crack growth rates, da/dN, in ABC-SIC as a function of the applied stress-intensity range, AK,for the tests conducted at temperatures between 25 and 13OO0C,load ratio R = 0.1, and frequencies between 3 and 1000 Hz.

Figure 8: TEM images of the intergranular crack profiles at the crack tip region in ABC-Sic at 1300°C under (a) cyclic loading (25 Hz, R = O.l), and (b) static loading. Arrows indicate the general direction of crack propagation. No evidence of viscous grain boundary layers or creep damage. The structural evolutions in grain boundary and matrix grains at elevated temperatures also benefit other mechanical properties of ABC-Sic. For example, the steady-state creep rate at high temperature of 1500°C was still impressively low (5 x 10-9/sat 100 MPa), and the creep rates at 120OoC in ABC-Sic was about three orders of magnitude slower than in single-crystal Ni-base superalloy tested under the same conditions [29]. In addition, 80% strength loss at 1300°C was restored by post-annealing [20]. Abrasive wear resistance was improved as well by formation of nanoprecipitates and by structural and compositional changes in grain boundaries after annealing [30]. These structural and mechanical characterization results demonstrate that the prescribed annealing is an effective way in tuning the microstructure and in turn optimizing the mechanical properties of ABC-Sic.

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Effects of Additive Content Parallel to the post-annealing, another effort in tailoring microstructure and mechanical properties of ABCSic was in adjusting the nominal contents of the Al, B, and C sintering additives. A series of samples were prepared by changing content of one of the three additives. For example, the A1 content was 3 w f ?in most ABC-Sic samples. This was then increased to 4 np to 7 wt%, while boron and carbon contents remained at 0.6 and 2 wt%, respectively. The samples were referred to as 3ABC-, 4ABC, up to 7ABC-SiC, according to the weight percentage of the A1 content. Structural characterizations showed that A1 variations between 3 and 7 wt% did not reduce the densification of Sic samples under the same processing conditions. However, changing the A1 content did alter the microstructure, as illustrated in Figure 9 (only images for the 3ABC5ABC-, and 7ABC-Sic are shown). Although all samples were composed of plate-like, elongated Sic grains and equiaxed Sic grains, the size, aspect ratio and area density of the elongated grains varied significantly with increasing A1 content. The length of the elongated grains was found to be at a maximum in the 5ABC-Sic, with the aspect ratio increasing almost linearly up to 6 wt% Al. Compared to 3ABC-SiC, the aspect ratios in the 4ABC- to the 7ABC-Sic are much higher, but the area density of these elongated grains continuously decreases. A distinct bimodal grain distribution is seen in the 5ABC-Sic, with elongated a-Sic grains and submicron-sized equiaxed p-Sic grains [3 11.

Figure 9: Morphologies of the 3ABC-, 5ABC-, and 7ABC-Sic are shown in images in (a) to (c), respectively. Note the significant changes in dimension and area density of the elongated Sic grains. Note also the bimodal grain systems with 5ABC-Sic.

Samples 3ABC-Sic 4ABC-Sic

I

Phase and Volume Fraction 70% 4H 30% 3 c 19% 6H, 23% 4H 58% 3 c 67% 3C 24% 6H 76% 3C 20% 6H

Toughness Hardness* (GPa) 6.8fO.3 24.1

4-Point Bending Strength (MPa) 691f12

I

561k13

(MPa.ml’*)

I

6.3f0.7

480f30

8.9f0.4

598f34

3.2f0.2

533f58

3.9f0.4

I

23.9

*Vickers indentation, Load = 10 kg. E = 430 GPa (for calculation). Changing of the A1 content by 1 wt% not only caused a considerable change in the grain morphology, but also induced different degrees of 3C-to-4H and/or 6H-to-4H Sic phase conversion during hot-pressing. Xray diffraction spectra were collected from polished surfaces of the 3ABC- to 7ABC-Sic samples and from the starting powder for comparison. The spectra were matched with standard 3C-, 4H-, 6H-, and 15R-Sic phase spectra; results are summarized in Table 2. It was found that the 3 wt% A1 addition in the 3ABC-Sic was sufficient to transform all of the 20% preexisting 6H-phase seeds in 3C-dominanted starting powder

Microstructure and properties of in situ toughened silicon carbide

153

into 4H-SiC, with more than 50% of the p-3C transforming into a-4H phase as well. However, a 1 wt% higher A1 content resulted in a completely different phase composition by retarding the 3C-to-4H transformation. Further increases in A1 monotonically decreased the extent of the 3C-to-4H transformation, and apparently inhibited the preexisting 6H phase to be transformed into 4H. These results imply that the 3C-to-4H transformation was mainly promoted by boron and carbon, and the transformation was retarded when boron and carbon were compensated by increasing the A1 content. The experimental data also suggest close relationships between the phase composition and grain morphology, which would be expected if the pto-a transformation promotes the grain elongation [ 101.

In addition to the grain morphology, a factor that may have a determining influence on mechanical properties of dense, polycrystalline ceramic materials is the grain boundary structure and composition, as noted above. High-resolution TEM showed that about 90% of the intergranular films examined in the 3ABC-Sic processed an amorphous structure. In contrast, this fraction dropped to about 50% in the 5ABCSic, and all grain boundary films examined in the 7ABC-Sic were crystalline in structure. Quantitative EDS analyses indicated that increasing the nominal A1 content enhanced A1 concentration in the intergranular films, as well as in the Sic grains bulk, but the concentrations saturated in 5ABC-Sic. More than 5 wt?? A1 resulted in precipitation of excessive free Al, as observed in the 6ABC-and 7ABC-Sic. It should be pointed out that crystalline grain boundaries were prevalent in as-hot-pressed SABC-, to 7ABCSic without any post-treatment. It is thus plausible that enhanced A1 facilitates formation of crystalline intergranular films. These changes in microstructure can be expected to affect mechanical properties. Table 2 lists various mechanical properties for the sample series. The mechanical data illustrate the tradeoff mechanical performance which is often encountered in developing advanced ceramic materials. While the highest strength was obtained in the 3ABC-SiC, the hardness was at maximum for the 6ABC-Sic. As for toughness, it is clear that 5 wt% A1 resulted in the best toughness whereas 6 wt?? or higher A1 additions significantly degraded the toughness so that the materials became extremely brittle. Cyclic fatigue tests revealed that the 3ABC- and particularly the 5ABC-Sic displayed excellent crack-growth resistance at both ambient (25T) and elevated (1300'C) temperatures. Again, the crack propagation in both 3ABC- and 5ABC-Sic was intergranular, and crack bridging was observed in the crack wake. No evidence of viscous grain boundary layers and creep damage, in the form of grain-boundary cavitation, was seen at temperatures up to 13OO0C. The substantially enhanced toughness in the SABC-Sic was associated with extensive crack bridging from both interlocking grains, as in 3ABC-SiC, and uncracked ligaments, which only occurred in 5ABC-Sic. No toughening by crack bridging was apparent in 7ABC-SiC, concomitant with a transition from intergranular to transgranular fracture [32]. Similar to the aluminum concentration variations, changes in boron and carbon contents also alter the microstructure and phase composition. Typical results are shown in Figure 10. In this case, the A1 content was fixed at 6 wt%, while either the B or the C concentrations were changed. The phase composition determined by X-ray diffraction is noted in each image. It is clear that at fixed A1 (6 wt??)and B(0.6 wt%) contents, 1 wt?hadditional carbon promoted the formation of more elongated grains and enhanced the 3Cto-4H transformation (most of the 6H phase should originate from starting powder). This effect of carbon on 3C-to-4H transformation was also reported before by Sakai et al [33]. Growth of the equiaxed grains was found to be limited. With the A1 and C contents kept constant, increasing the boron content from 0.6 wt?? to 0.9 wt% largely increased the number density of elongated grains, but reduced their aspect ratio. In addition, boron promoted the 3C-to-4H and 6H-to-4H phase transformations more effectively than carbon. The positive effect of boron on the 6H-to-4H transformation is consistent with the previous observations of Huang et a1 [34].

-

L.C. De Jonghe, R.O. Rztchie and X.F. Zhang

154

6 Wt% A1

0 6 wt% Boron

0.9 wt% Boron

2wt%C

1 3wt%C

Figure 10: Microstructural changes with fixed A1 (6 wPh) and adjusted boron or carbon contents. Phase compositions are marked in each image. Effects of boron and carbon additions in changing microstructure and phase composition are clear. The systematic processing and characterizations of a series of ABC-Sic described above also allowed for the determination of the roles of Al, B, and C additives in developing the microstructures of silicon carbide. The observed effects may be summarized as follows: in terms of developing phase composition, boron is more effective in promoting the p-to-a phase transformations than carbon. Aluminum retards the p-to-a phase transformation,but promotes the 6H-to-4H transformation. As for the developing grain morphology, aluminum and carbon both promote anisotropic grain growth, whereas boron tends to coarsen the volume fraction, but reduce the aspect ratio, of the elongated grains. It should be noted that during processing, the combined roles of the Al, B and C additives often override their individual roles. For example, B and C together favor of the P-to-a phase transformation associated with grain elongation; however, the final microstructure does not necessarily have strongly elongated grains as B and C have opposite effects on anisotropic grain growth. Actually, the B:C ratio determines the final grain configuration. Aluminum has a different effect: when the B:C ratio favors the anisotropic grain growth, Al-rich liquid phase accelerates such growth so that the aspect ratio is hrther increased. However, if the AI:B and AI:C ratios are reduced, less liquid phases are expected to be present after the Al-B-C reactions so that the effects of A1 are diminished. Further experiments have indicated that even at constant A1:B:C ratios, a change in total amount of additives can still alter the grain configuration and phase composition significantly. This emphasizes the fact that the optimization of the mechanical properties of many structural ceramics such as ABC-Sic is a strong function of the absolute and relative amounts of the sintering additives.

SUMMARY ABC-Sic ceramics with unprecedented toughness values as high as 9 MPa.m'" have been developed by hot pressing @-Sicpowder with additions of Al, B and C. Such high fracture toughnesses were attributed to an in situ toughening mechanism primarily involving crack bridging by interlocked and elongated Sic grains. The anisotropic growth of Sic grains, which promoted such toughening, was the result of the liquid-phase sintering in which A1 additives acted to form a liquid phase. The existence of this liquid phase also lowered the sintering temperature to 190OoC. The toughening mechanism also requires intergranular cracking which was aided by the presence of amorphous intergranular films (typically 1 nm in width) in the grain boundaries of the as-processed ABC-Sic. Two effective methods for modifying the grain boundary structure and chemistry, as well as the overall microstructure, were investigated using post-processing annealing and adjustments in the nominal contents of sintering additives. Prescribed post-annealing treatments at higher than 1OOO°C were found to activate grain boundary diffusion and consequently caused the crystallization of most of the glassy intergranular films (not simply the

Microstructure and properties of in situ toughened silicon carbide

155

“pockets” at the grain boundary triple points). This led to superior high temperature strength, creep and fatigue properties at elevated temperatures with no evidence of creep damage in the form of grain boundary cavitation until temperatures above 14OO0C were reached. Using atomic-resolution electron microscopy and quantitative nanoprobe EDS, one of the crystallized intergranular structures was identified as 2H-wurtzite ahminosilicate. Heating at 13OO0C or higher also resulted in uniformly dispersed nanoprecipitates as a result of lattice diffusion. In addition, the lattice diffusion almost doubled the segregation of A1 into the intergranular films. It is believed that this significant microstructural evolution, which occurs during postannealing and is not characteristically observed in other advanced ceramics such as Si3N4, and A1203, is the origin of the many outstanding mechanical property attributes of ABC-Sic at elevated temperatures. These include high resistance to crack growth at temperatures between ambient and 13OO0C,far superior steadystate creep resistance than in single-crystal Ni-base superalloys, enhanced resistance to abrasive wear, and high-temperature strength loss recovery. Changing the nominal contents of the sintering additives, Al, or B, or C, was also used as an effective means to modify the microstructure. In particular, the area density and dimensions of the elongated Sic grains, their phase composition, and the grain boundary structure were all found to be sensitive to small variations in additive content. Using this approach, a series of materials processing with systematic changes in sintering atom additions were used to develop optimal microstructures for ABC-Sic. Compositions with superior fracture toughness, or creep properties or abrasive wear resistance were all defined. Such methods, in conjunction with prescribed post-annealing heat treatments, permit the tailoring of microstructures in ABC-Sic to achieve and optimize a wide range of mechanical properties in a highly controlled manner. ACKNOWLEDGMENTS

This work was supported by the Director, Office of Science, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering of the U.S. Department of Energy under Contract No. DE-AC0376SF0098. Part of this work was made possible through the use of the National Center for Electron Microscopy facility at the Lawrence Berkeley National Laboratory. Thanks are due to Da Chen, Mark E. Sixta, Qing Yang, Rong Yuan, Jay J. Kruzic, and Rowland Cannon for their assistance and discussion in this work. REFERENCES

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.

Faber, K.T. and Evans, A.G. (1983) Acta Metall. 31,565. Faber, K.T. and Evans, A.G. (1983) Acta Metall. 31,577. Becher, P.F. (1991)J. Am. Ceram. Soc., 74,255. Becher, P.F., Sun, E.Y., Plucknett, K.P., Alexander, K.B., Husueh, C.-H., Lin, H.-T., Waters, S.B. and Westmoreland, C.G. (1998) J. Am. Ceram. Soc. 81,2821. Cao, J.J., MoberlyChan, W.J., De Jonghe, L.C., Gilbert, C.J. and. Ritchie, R.O. (1996)J. Am. Ceram. Soc. 79,461. Thomas, G. (1994) Ultramicroscopy 54,145. Thomas, G. (1996) J. Euro. Ceram. Soc. 16,323. Zhang, X.F., Sixta, M.E. and De Jonghe, L.C. (2000) J. Am. Cerum. Soc. 83,2813. Zhang, X.F., Yang, Q., De Jonghe, L.C. and Zhang, Z. (2002) J. Microsc. 207,58. MoberlyChan, W.J., Cao, J.J., Gilbert, C.J., Ritchie, R.O. and De Jonghe, L.C. (1998), In: Ceramic Microstructure: Control at the Atomic Level, pp. 177-190,Tomsia A.P. and Glaeser A. (Eds). New York Plenum Press. Gilbert, C.J., Cao, J.J., De Jonghe, L.C. and Ritchie, R.O. (1997) J. Am. Cerum. Soc. 80,2253. Kleebe, H.-J., Cinibulk, M.K., Cannon, R.M. andRuhle, M. (1993)J. Am. Ceram. Soc. 76, 1969. Chiang, Y.-M., Silverman, L.A., French, R.H. and Cannon, R.M. (1994) J. Am. Ceram. Soc., 77, 1143. Clarke, D.R. (1987) J. Am. Ceram. SOC.70, 15.

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Hamminger, R., Grathwohl, G. and Thummler, F. (1983) J. Muter. Sci. 18,3154. Lane, J. E., Carter, C.H. and Davis, R. F. (1988)J. Am. Cerum. Soc., 71,281. Zhang, X.F., Sixta, M.E. and De Jonghe, L.C. (2001) J. Am. Cerum. SOC.84,813. Goto, Y. and Thomas, G. (1995) J. Muter. Sci. 30,2194. Cutler, I.B., Miller, P.D., Rafaniello, W., Park, H.K., Thompson, D.P. and Jack, K.H. (1978) Nature 275,434. Zhang, X.F., Sixta, M.E. and De Jonghe, L.C. (2001) J. Muter. Sci. 36,5447. Chen, D., Gilbert, C.J., Zhang, X.F. and Ritchie, R.O. (2000) Actu Muter, 48,659. Chen, D., Zhang, X.F. and Ritchie, R.O. (2000) J. Am. Cerum. SOC.83,2079. Chen, D., Sixta, M.E., Zhang, X.F., De Jonghe, L.C. and Ritchie, R.O. (2000) Actu Muter. 48,4599. Hansson, T., Miyashita, Y. and Mutoh, Y. (1996), In: Fracture Mechanics of Ceramics, Vol. 12, pp. 187-201, Bradt R.C. (Ed). Plenum Press, New York. Zhang, Y.H. and Edwards, L. (1998)Muter. Sci. Eng. A256, 144. Edwards, L. and Suresh, S. (1992) J. Muter. Sci. 27,5181. Liu S.Y., Chen, I.W. andTien, T.Y. (1994)J. Am. Cerum. SOC.77, 137. Ramamurty, U., Kim, A.S., Suresh, S. (1993) J. Am. Cerurn. SOC.76, 1953. Sixta, M.E., Zhang, X.F. and De Jonghe, L.C. (2001) J. Am. Cerum. SOC.84,2022. Zhang, X.F., Lee, G.Y., Chen, D., Ritchie, R.O. and De Jonghe, L.C. (2003) J. Am. Ceram. Soc., in press. Zhang, X.F., Yang, Q. and De Jonghe, L.C. (2003) Actu Muter.,in press. Yuan, R., Kruzic, J. J., Zhang, X. F., De Jonghe, L. C. and Ritchie, R. 0. (2003) Actu Muter., in review. Sakai, T. and Aikawa, T. (1988) J. Am. Cerum. SOC.71, C-7. Huang, J.-L., Hurford, A.C., Cutler, R.A. and Virkar, A.V. (1986) J. Muter. Sci. Lett. 21, 1448.

Nano and Microstructural Design of Advanced Materials M.A. Meyers, R.O. Ritche and M. Sarikaya (Editors) 02003 Elsevier Ltd. All rights reserved.

MICROSTRUCTURE DESIGN OF ADVANCED MATERIALS THROUGH MICROELEMENT MODELS: WC-COCERMETS AND THEIR NOVEL ARCHITECTURES K. S. Ravi Chandran’ and Z. Zak Fang Department of Metallurgical Engineering 135 South 1460 East, Room 412, The University of Utah, Salt Lake City, UT 841 12

ABSTRACT Design and development of advanced materials for superior strength and toughness is a perpetual effort in meeting the material needs for demanding applications. The WC-Co cermet is one of the truly advanced materials, due to its unique combination of properties. Although such cermets are widely used, further improvements require a good mechanistic understanding of the microstructural aspects that govem the mechanical properties. The broad goal of this research is to establish such a mechanistic basis that enables a sound explanation of their excellent properties. The origins of the unique mechanical properties of traditional and novel cermets are closely examined using some microstructure-based models. It is shown that the superior properties arise as a result of the spatial arrangement of WC grains within Co, the strength and stiffness of W C and the constrained plastic deformation behavior of ductile Co layer binding the WC grains. It is also shown that the high toughness of “functional” cermets with hierarchical microstructures can be understood on the basis of the microstructure-based mechanistic models. The microstructure-based models illustrate the key aspects in traditional WC-Co microstructures that make them unique as well as the pathways for designing advanced composites materials following the architecture of WC-Co cermets.

INTRODUCTION WC-Co cermets as a class are one of the truly advanced materials, with their processing, microstructure and mechanical properties having been optimized through several decades of research and development. Cermets such as WC-Co, WC-Ni and WC-Tic-Co are successfully produced commercially with a high degree of control and reliability in mechanical properties [l-51. Owing to the large industrial demands, their continued development is an active area of research [6-101. It may, to some extent, be surprising to note that although empirical correlations between microstructural parameters and properties exist, a complete mechanistic basis for their superior mechanical properties is yet to be developed. The WC-Co microstructure is made of angular and hard WC grains that are nearly completely surrounded by ductile Co binder formed either by liquid phase sintering (LPS) of WCiCo under vacuum or by LPS followed by a low pressure hot isostatic pressing (sinter-HIP). Figure 1 illustrates typical microstructures of WC-Co at two different volume fractions of Co. When a comparison is made between several hard materials listed in Table 1, the general superiority of WC-Co is clearly evident: the possession of high elastic modulus, high hardness and flexure strength and acceptable toughness that is unique to WC-Co cermets. The objective of this study is to demonstrate the micromechanisms behind the unique properties of WC-Co cermets by using the approach termed, ‘microelement-modeling’ that captures the effects of the relevant microstructural parameters on properties. Idealized geometrical models consisting of microelements and ’ Author for correspondence, ernail r.i\icu.inincsiuIi cdu. Ph 1-801-581-7197. Fax I-801-581-4937

157

K.S. Ruvz Chundran and Z. Zak Fang

158

simple relationships of stress and strain from the mechanics of materials have been employed for this purpose The goal IS to develop simple yet reasonably accurate analytical models that allow insight into the aspects of the microstructural factors pertaining to WC and Co that lead to the superior properties This work also illustrates the fracture toughness characteristics of hierarchically structured “functional” WC-Co cermets through modeling It is shown that the present modeling approach is very effective in illustrating the microstructural effects on strength, creep resistance and fracture toughness of WC-Co cermets and their derivatives The approach may be useful in designing the microstructures of advanced materials, in general

WC-G%Co

wc-1O%Co

Figure 1: Microstructures of WC-Co cermets

MICROELEMENT MODELS OF WC-CO

In WC-Co cermets, the microstructure morphology can be idealized as WC grains enveloped by Co binder forming a nearly continuous matnx In such an arrangement, the ductile Co binder sandwiched between strong and stiff WC grains is in a physically constrained state during deformation and any modeling attempt should capture this aspect accurately and consistently In this work, the WC-Co microstn~cture idealized as a periodic arrangement of cubic WC inclusions in a continuous Co matrix as illustrated in Fig 2(a) Fig 2(b) illustrates the three dimensional geometry of the WC-Co unit cell. This unit cell can be thought of built upon the parallel and series arrangements of WC and Co phases, identified generally as A and B in Figures 3(a) and (b) The modeling approach basically involves first dividing the unit cell into such parallel and senes microelements and deducing the composlte behavior from the behavior of the elements It is first essential to determine the appropnate volume fractions of the microelements at different levels of division The division of the WC-Co unit cell can be done as illustrated in Figure 3(a-d) First, the two microelements of volume fractions V3 (WC) and V4 (Co) in Fig 3(d) add up in senes to form a composite, which in turn forms an effective microelement of volume fraction V1 (WC+Co) in Fig 3(c) Then, microelements of volume fractions V2 (Co) and V1 in Fig 3(c) add up in a parallel arrangement to complete the unit cell Hence, if the deformation behavior of parallel and series loading arrangements of WC and Co

WC-Cocermets and their novel architectures

159

are known, the macroscopic properties of the unit cell and hence the cermet can be derived using the appropriate volume fractions of the microelements at different levels.

Figure 2: Schematics of the idealized unit cell of the WC-Co microstructure

4 A co

Figure 3: Schematics of the division of WC-Co unit cell into microelements; (a) the parallel arrangement, (b) the series arrangement, (c) the parallel arrangement of microelements 1 and 2, and (d) the series arrangement of microelements 3 and 4. First, from geometric considerations of Figure 2(b), a microstructure parameter “c” can be defined in terms of the bulk volume fraction of Co, V, e o , as.

This definition allows the determination of volume fractions of the microelements as:

v,=

volume of element 1 1 volume of the unit cell (1 + c)’

v, =

volume of element 2 volume of the unit cell

v, = volume of element 3

volume ofelement 1

v4 =

-

1--

1 (1 + c)’

- 1

(1 + c)

volume of element 4 c -volume ofelement 1 (1 + c )

160

K.S. Ravi Chandran and Z. Zak Fang

It is to be noted that VI, V2, V3 and V4 are defined such that VI+V2=1 and V3+V4=1 to enable consistent division of microelements at different levels. The applicable mechanics of materials equations for the parallel arrangement of a two phase material, with the loading parallel to the interface are

E,, = EAVA+ EBVR

(3)

where Ell is the elastic modulus, EA and Eg are the modulus of phases A and B respectively, oapp is the applied stress, OA and CSB are the average stresses in A and B, respectively, cappis the composite strain and EA and EB are the average strains in phases A and B. respectively. VA and VB are the volume fractions of the respective phases. A similar set of equations for the series arrangement of phases A and B are

where E,, is the elastic modulus of the series composite loaded with the applied stress normal to the interface. Equations (3) through (8) along with equation (2) were used to determine the elastic modulus of WC-Co cermets and the results have been published elsewhere [l 13. Here we focus on the determination of the strength and creep resistance of the WC-Co cermets.

STRENGTH OF WC-COCERMETS In order to determine the strength of WC-Co cermets incorporating the constitutive properties of WC and Co, the plastic deformation behavior of the unit cell needs to be constructed. The deformation behavior of Co matrix can be represented in the Ludwik form as m=Eco~e

for the elastic part

d =K,,(E~)"

for the plastic part

with the total strain in the plastic regime being given by E = + .sP where E,,, 8 and B are the elastic modulus of Co, elastic strain and plastic strain in Co, respectively. K,, and n are constants of power law fit to the plastic part of the stress-strain curve of Co. Since the WC grains are much stiffer and harder than Co, to a first approximation, they can be considered to be rigid and the elastic strain contribution from microelement 3 is neglected leading to c3= 0 . The calculation of elastic stress-strain characteristics of WCCo cermet is straightforward and this is discussed elsewhere [12]. With the WC-Co unit cell deforming in the plastic regime, the following relationships can be written for the microelements 1, 3 and 4:

WC-Cocermets and their novel architectures

161

where & I , EZ, ~3 and 6 4 are the average plastic strains in the respective microelements. The superscript “p” is omitted hereafter for brevity CT{and C T ~ are the A ow stresses in microelements 1 and 2 resulting from the strain compatibility and the partitioning of the applied stress between microelements 1 and 2 according to the relation:

Simplification of the set of equations (1 1) leads to

At this stage, the physical constraint of Co deforming between WC grams should be considered. In the microelement scheme, this means that the plastic deformation of microelement 4 will be influenced by the constraint of rigid WC particles forming microelement 3, located above and below microelement 4 in the actual cermet. As the raho (hc,,/dwc) of thickness of Co in the microelement 4, ‘hc:, to the size of WC forming element 3, Idw:, decreases, the constraint expenenced by the Co matrix during plastic deformation would increase [13,14]. Murray [15] noted that through this effect the in-situ flow stress of Co is several times higher than that is observed in the bulk Co specimen It was suggested that the theoretical shear strength of Co is influenced by the presence of WC particle boundaries limiting the mean-free-path of shear deformation in Co as illustrated in Figure 4(a). To accurately represent the WC-Co plastic deformation behavior, this constraint effect should be incorporated in the model

Figure 4: (a) Schematic o f a ductile layer deforming under rigid WC grains [ 151 and (b) the normalized flow stress as a function of d/h as predicted by the plasticity solutions of Unksov [16]. One way to introduce the constrained deformation of Co is to modify the expression for in equation (13) to give a lower effective plastic strain for a given stress (in this case, 5,)acting on this element (see ref 12 for details):

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162

Equation (15) is an approximation for the constrained deformation of Co, based on the analogy of Co deforming between WC grains to that of a ductile metal layer deforming between two rigid platens, as illustrated in Figure 4(b). Since there should be strain compatibility between microelements 1 and 2 , ~ & ~= : ,E, ,, = E~ and from equations (1 1) and (14)

From equations (12), (14) and (16) the plastic strain in the cermet is given by

The flow stress of Co is related to the plastic strain in Co as

Combining the equations (17) and (18), the normalized flow stress of the WC-Co cermet is given by

A

9

8

21

f

17

L,

v

Eqn. (19)

tn tn

13

5

9

zE ii

E x p t . Data (0.02 e p ) E x p t . Data (0.002 e p )

-a

-.Bm

5

z

1

E

0

0.2

0.4

0.6

0.8

1

W C V o l u m e Fraction, V p

Figure 5 : Comparison of the predictions from equation (19) with the experimental data of flow stress of WC-Co cermets normalized with the flow stress of Co. The experimental data is from: H. Doi, Elastic and Plastic Properties of WC-Co Composite Alloys, Freund Publishing Inc., Israel, 1974 Figure 5 illustrates the comparison of the normalized flow stress of the WC-Co cermet as a function of the volume fraction of WC. Both the predictions according to the microelement model (lines) for different strain hardening exponents of Co as well as the experimental data on compression strength of a variety of cermets are presented. The increase in flow stress, or alternatively the strength, comes from the fact that as WC

WC-Cocermets and their novel architectures

163

content increases, the extensive plastic deformation must be generated in the Co binder, especially the constrained region of Co present in the form of microelement 4. Equation (19) captures most of the dominant microstructural parameters that determine the strength of WCCo cermets, including, the size of WC grains, d,,, the thickness of the Co binder h,,, the volume fraction of Co, Vf,,, and the strain hardening behavior of Co, n, as well as the geometric constraint effect due to WC grains through the parameter For a given volume fraction of WC grains, increasing the constraint by manipulating the ratio h,,/d,, or the strain hardening characteristics of Co should lead to stronger WC-Co cermets. In particular, exceptionally high strength levels can be achieved if the WC volume fraction is increased as much as possible while ensuring a continuous layer of Co around WC grains throughout the microstructure. It is worth noting that the above conclusions are general and can be applied to any hard particle-ductile matrix composite system to achieve very high strength levels.

CREEP DEFORMATION BEHAVIOR OF WC-CO While a large fraction of commercial interest is in near-room-temperature applications of WC-Co, there are also research and developmental efforts [ 17, 181 in the area of high temperature deformation resistance in order to extend the temperature range of application of WC-Co cermets. Therefore, it is also of interest to examine the high temperature or creep deformation characteristics of WC-Co cermets. The microelement model for the creeping cermet can be devised following the same approach outlined in the previous section. The essential difference is that the strain rate takes the place of strain in the microelements. The strain rate compatibility between microelements 1 and 2 is expressed as

Since the WC grains can be considered as rigid and non-creeping due to its excellent strength retention at high temperature, the only constitutive relationship that is relevant here is that of the Co matrix:

where k,, and ncoare the constants characterizing the steady-state creep behavior of bulk Co. The complete details as well as extensive comparisons with the experimental data on several composites are published elsewhere [19]. The steady-state creep rates of WC-Co cermets can be derived as

The creep rate of the cermet, normalized with respect to that of Co is then expressed as

+=kcol E CO

r (1+ c)"

1

1"co

q 5 c +(1+c)2 o ( -1 y f l c o

K.S. Ravi Chandran and Z. Zak Fang

164

Figures 6(a) and (b) illustrate the predicted normalized creep rates as a function of the volume fraction of rigid particles or second phase, in the general sense. In Figure 6(a) the effect of not including versus including &o in equation (23) is illustrated. It can be seen that without the constraint (i$co=l), there is virtually no difference between the creep rates of composites having matrices of with different creep exponents. In contrast, when the constraint factor, i$,, is included in the model, the effects of matrix creep exponents are differentiated. The predicted data are also in good agreement with the numerical results obtained by the self-consistent method, as illustrated in Figure 6(b), attesting to the reliability of the microelement modeling approach. For detailed comparisons involving other composite systems, ref. 19 may be consulted.

W

Unit cell model

E

...--.... Self-consistent Model

-

.WU

0

0.4

0.2

0.6

1

0.8

Vf of Second Phase, V

(a) (b) Figure 6: The predicted creep rates from the microelement model (equation (23)). (a) illustration of the effect of the WC grain constraint on Co and @) comparison with the data from a numerical model 0

,

--

,

,

,

/

,

-CO(8Oo"C) - - w c - c o (WC V( =o 81)

~

,

,

,

,

0

. I

,

.

,

co (8OOT)

I

I

I

,

I

I

,

w c - c o (WC V f =o 9)

0

-

T=800"C -12

"

1

"

2

1

'

"

3

Log Stress, MPa

'

:...

-

"

4

-12

"

1

'

I

2

"

"

3

T=800"C '

"

4

Log Stress, MPa

(a) (b) Figure 7: Comparisons of the predictions from equation (22) with the experimental data on steady state creep of WC-Co cermets Figures 7(a) and (b) illustrate the predicted steady-state creep rates compared with the experimental creep data of WC-Co cermets. The reasonable agreement is quite encouraging, given the idealizations employed in the microelement modeling. It is to be noted that according to the model, the creep exponent of WC-Co

WC-Cocermets and their novel architectures

165

cermet (equation (22)) is necessarily the same as that of Co. This is the result of the geometrical arrangement of Co as continuous matrix material nearly surrounding every WC grain in the cermet by a complex term that microstructure. The effect of WC grains is to modify the proportionality factor, to, includes most of the microstructural parameters, d,,, h,,, Vtca and $ca as in equation (22). As can be seen from Figure 7, the effect of WC grains is to decrease the value of proportionality factor, k, leading to a downward shift in the steady-state creep curve, relative to that of Co. FRACTURE TOUGHNESS OF WC-COCERMETS

Modeling of fracture toughness of WC-Co cermets is not only useful in developing an understanding of the microstructural factors that control the resistance to fracture, but also enables designing better cermets to mitigate cracking. This is of particular importance in cermets as a class, since the major constituent, WC, is nearly completely brittle and the cermet applications involve severe loading conditions, often leading to chipping. Fracture in WC-Co systems has been found [2,4,14] to occur mainly by the ductile rupture of Co through void nucleation and coalescence. Other fracture modes such as fracture along WC-Co interface and WCWC grain boundary decohesion as well as cleavage across WC grains were also noted [20,21]. These mechanisms occur especially at low volume fractions of Co binder in the composite at which the contiguity of WC grains begins to increase. The effect of the contiguity of WC skeleton on fracture toughness has also been demonstrated [22]. In a fracture toughness experiment, in a given crack plane, the crack propagation is easy along the relatively weak WC-WC boundaries and final fracture is primarily controlled by the area fraction of WC grains and Co regions intact across the crack plane ahead of the tip. Many studies have confirmed that the plastic deformation at the crack tip is restricted to a single binder layer in the crack plane located immediately ahead of the crack tip. Since the WC grains are nominally elastic under load, the deformation of Co at the crack tip will be highly constrained. Although there are a few fracture toughness models such as that developed by Nakamura and Gurland [23], these models do not explicitly consider this constraint effect in terms of microstructural parameters. More recently, a simple model to predict the fracture toughness of WC-Co cermets, incorporating the microstructural parameters was developed by one of the authors [24]. In that study, the total fracture energy of the WC-Co cermet is taken as the sum of the weighted fracture energies of WC and Co:

where Gwc is the critical strain energy release rate of WC phase and Vf, oeff,co and hco are respectively the volume fraction, the in-situ flow stress and the thickness of the Co phase. The parameter p represents the extent of plastic stretch of Co before fracture and is usually between 1 and 2. The first term accounts for the energy due to fracture along WC while the second incorporates the resistance arising from the plastic rupture of the ductile Co. Recalling

oeff,co

Kc,w,co

=

=

+

EW,,,

0.3(k)]

(1 - v/ )&,wc(l,2

(26)

where &,WCCO, Ewcco and vwcco are respectively the cermet fracture toughness, modulus and Poisson's ratio, and &.wc, Ewc and vwc are the fracture toughness, modulus and Poisson's ratio of WC respectively.

K.S. Ravi Chandran and Z. Zak Fang

166

It can be seen that knowing Oeff,co, from equation (25), in addition to the properties and sizes of WC and Co phases, fracture toughness of the WC-Co cermet can be estimated. Equation (26) is not only considerably simpler, but also provides a direct correlation of fracture toughness to the microstructure parameters of the cermet.

rfiin

5

-

”

s

50

40

(II

Y

6

30

u)

0

9 C

c

20

0

0

10 20 30 40 50 M e a s u r e d Toughness, K c , e x p ,(MParn”2)

Figure 8: Comparison of the fracture toughness of WC-Co cermets calculated from equation (26) with the experimental data. The experimental data include over 100 data points from diverse studies, a listing of which may be found in ref. 24. The calculated fracture toughness according to equation (26) for a variety of WC-Co cermets reported in literature is plotted as a function of the experimentally measured fracture toughness data in Figure 8. An average value of 850 MPa for the bulk flow stress of Co in equation (25) and a value of p=2 in equation (26) were for these calculations. A study [25] confirms that the bulk flow stress of the Co may vary from 700 MPa to about 1100 MPa depending on the degree of dissolution of W and C as well as the nature and distribution of carbide precipitates in Co. Since the amount of W and C in solution would depend on a number of processing parameters such as that in hot pressing and heat treatment, the use of a more accurate value for the Co flow stress is not possible. Nevertheless, a reasonable agreement between the measured and the calculated toughness values, with only a few data points falling outside the +lo% confidence level, can be seen. The experimental data is from WC-Co microstructures having a wide variation of WC particle diameter from 0.66 pm to 7.8 pm and the mean free path in binder varying from 0.04 pm to 1.9 pm. The volume fraction of Co varied from 0.05 to 0.4 in these cermets. These represent a reasonably wide variation in the microstructural conditions of WC-Co cermets. Therefore, equation (26) may be taken as a fairly accurate representation of fracture toughness of WC-Co cermet class as a whole and may be used as a predictive tool in the microstructure design of two-phase cermets in general. DESIGNING CERMETS SUPERIOR TO WC-CO

Although WC-Co cermets occupy the largest share of tool applications, there have been considerable efforts in designing cermets with other hard materials and binders, but with a microstructural architecture similar to that of WC-Co. Noteworthy in this regard are the systems containing TaC or T i c or TiBz or A1203 as the hard component and Co, Ni, Fe or Cr as the binder component. With the increased availability of synthetic diamond, Co bonded diamond, with or without WC additions, has also become one of the contenders. It is of interest to examine where the level of fracture toughness that can be achieved in these cermet combinations lie relative to the WC-Co system. Equation (26) was used to calculate the fracture toughness values for the systems listed in Table 2 using the constitutive data also listed in the table. In the calculations, a hard particle size, d = 3 Fm and a binder volume fraction, Vf = 0.1 were assumed.

WC-Cocermets and their novel architectures

167

The calculated fracture toughness data is interesting for two reasons. First, all of the systems based on carbides and borides of Ti or Ta offer fracture toughness levels lower than that of WC-Co. Secondly, only the fracture toughness diamond-Co system was higher than that of the WC-Co system. The fracture toughness of the cermet is also influenced by the elastic modulus of the brittle phase, in addition to the volume fraction and properties of the binder. In fact, in table 2, the fracture toughness can be seen to increase in general with an increase in the modulus of the hard phase. This, although may seem to be unusual, is entirely consistent with fracture mechanics principles. The fracture toughness, K, is related to the critical strain energy released for an infinitesimal increase in crack length, G,, during unstable fracture as K,

=JG,E

and

where ys is the surface energy of the solid. The surface energy is indirectly related to the atomic cohesion in solids. It is known that the elastic modulus of solids in general increases with an increase in the melting point. The increase in melting point is generally thought to arise from an increased cohesion between in solids. Therefore, it is not unreasonable to expect that in principle, the surface energy should also be higher in a solid having a high stiffness, although this interesting aspect needs to be verified. Thus, the effect of increased elastic modulus should work to increase the fracture toughness directly through equation (27) and indirectly through equation (28).

TABLE 2. Calculated fracture toughness levels for different cermet systems

L

"

'

"

"

'

"

"

"

'

"

'

"

'

J

14

E

2

12

y'-

10

a

E

4

u

2

Single crystal

5

E

0

diamond

N ~ C

SIC (CVD)

...... .._..._..-

_....' ._.. ._..

. . .

I 0

I

200

.

.

.

,

.

400

:

.

,

.

600

.

Elastic Modulus (GPa)

.

I

800

.

.

.

\

L

.

.

1000

Figure 9: Fracture toughness of ceramics as a function of elastic modulus

i

168

K.S. Ruvz Chundran and Z. Zak Fang

In order to venfy the above hypothesis, the experimental fracture toughness data of a wide variety of ceramics are plotted as a function of elastic modulus in Figure 9 A reasonable correlation is obvious, with the fracture toughness increasing with an increase in elastic modulus Figure 9 may explain why only the diamond-Co system is supenor to WC-Co in terms of the calculated fracture toughness In equation (26), both the higher fracture toughness of diamond, together with its high value of modulus around 1000 MPa contribute to the increased value of the calculated toughness It also implies another remarkable fact to design cermets with fracture toughness levels higher than WC-Co, one should resort to hard constituents having elastic moduli higher than that of WC, with all other vanables in the cermet system being invariant HlERARCHlCALLY STRUCTURED “FUNCTIONAL” WC-COCERMETS In the past few years, a new approach that involves hierarchical structuring of microstructure constituents is used to design WC-Co cermets Figure 10 illustrates a “double cemented tungsten carbide (DC carbide)”, consisting of WC-Co granules (usually containing a very low cobalt content) embedded in a matnx of ductile Co Figure 11 illustrates an idealized schematic of this class of microstmctures This unique microstructure is functionally designed to boost the fracture toughness of the materiaIs without comprising its wear resistance Figure 12 illustrates the combination of superior toughness and abrasive wear resistance in the DC carbide The hierarchically structured DC carbide provides another degree of freedom that is not available in conventional WC-Co cermets One of the consequences of equation (26) is the fact that the fracture toughness of conventional WC-Co is derived nearly equally from WC as well as Co phases If the fracture resistance of WC can be increased by replacing it with a tougher WC-Co granule, the properties of DC carbide can then be augmented Additionally, the sizes of WC grains in the granules are much finer than that in the equivalent WC-Co cermet The contributions of the WC-Co granules to the overall properties of the DC carbide are two fold First, when compared to conventional WC-Co cermets, the fracture energy of the hard component in DC carbide, i e the term G,, in equation (24), is significantly higher The higher fracture energy of the hard component particles Contribute to increasing not only the overall fracture toughness, but also the micro-chipping resistance, which in turn is manifested in the form of good overall abrasive wear resistance Secondly, the WC-Co granules in DC carbide resist the tendency of being dug-out in an abrasive wear environment. Therefore, the excellent wear resistance of WC-Co can be preserved even though a significantly larger amount of Co is present in this matenal, relative to the conventional WC-Co cermet

Figure 10: Microstructures of a hierarchically structured “functional” WC-Co cermet. The microstructure contains a total of 27 wt. % Co. The fracture toughness of hierarchically structured DC carbide can be modeled using the same approach described in the previous section. This requires calculating first the fracture toughness of WC-Co granules, & grr according to equation (26) as:

WC-Cocermets and their novel architectures

169

50

WC grains Co matrix

-

*€

z

z

'x

40

30

8

-

-

-

2

a

u.

10

.

I

1 xv -1.

rconventlonal W C C O

;*

A DC Carbtde ( - 3 0 0 i t 7 5 urn)

= D C Carbide (-75 rrn)

The fracture toughness of the DC carbide, &,Dc, can then be calculated as:

where Eoc is the elastic modulus of the DC carbide, V; is the volume fraction of Co in the matrix (not including the Co in granules) surrounding the granules, and cr>,co is the flow stress of Co in the matrix, hz,, is the thickness Co matrix and p=2. The

g&,co can

be expressed as

where oi,coand d,, are the unconstrained (bulk) flow stress of the Co matrix surrounding the WC-Co granules and the granule size The microstructures of two types of hierarchically structured DC carbides made in a recent study [26] are illustrated in Figures 13 and 14. Microstructures of DC carbides with a constant WC-Co granule size, but with a varying volume fraction of the matrix Co, are presented in Figure 13. Microstructures of DC carbides

K.S. Ruvz Chundran and Z. Zak Fang

170

1

having constant a volume fraction of Co in the matrix as well as in the WC-Co granules, but with varying sizes of granules are presented in Figure 14

I I

I.

Figure 13: Microstructures of hierarchically structured DC carbide cermets with varying Co volume fraction and constant WC-Co granule size. The matrix Co volume fractions from left to right are: lo%, 20% and 30%. In the granules, the WC grain size is 3 pm and the Co volume fraction is 10%.

Figure 14: Microstructures of hierarchically structured DC carbide cermets with constant Co volume fraction (30%) in the matrix and varying WC-Co granule size. The average granule sizes from left to right are. 130 pm, 90 pm and 60 pm. The size of WC grains in the granules is 3 pm,

35 -

c

,

30 -

-Eqn. (WC-1O%Co Granule) -- Eqn. (WC-l8%Co Granule) Eqn. (WC-25YoCo Granule) A Expt. (WC-iO%Co Granule) 0 Expt. (WC-l8%Co Granule) Expt (WC-25%Co Granule)

lo'? 5 -

O?

--

~~~~~~~~~

'005

'

0'1

'0;5

'

Oh

Vf of Co Matrix

(a)

'025

'

01

0

= 75 MPa) .

Eqn. (Matrix

--Eqn

(Matrixnoco=IOOMPa)

Eqn (Matrix no

0

50

~~

100

= 200 MPa) 150

Granule Size, pm

(b)

Figure 15 Comparisons of the predicted and experimental fracture toughness data for the hierarchically structured DC carbide cermets, as a function of (a) the volume fraction of matnx Co and @) the WC-Co granule size The effect of volume fraction of matrix Co on the fracture toughness of DC carbides with a constant WC-Co granule size is illustrated in Figure 15(a) The points are from expenments and the lines are the predictions

WC-Cocermets and their novel architectures

171

from equation (30). In these calculations, the value of C T : , ~ ~was taken as 87 MPa, based on the agreement between the experimental data and the theoretical predictions as illustrated in Figure 15(b). The effect of WC-Co granule size on the fracture toughness at a constant matrix Co volume fraction is illustrated in Figure 15(b). In this figure, the data predicted using equation (30) for four different o,',,, values is illustrated. It appears that the reasonable value of oi,,that can result in a good agreement between the experiment and theory is between 75 and 100 MPa. This choice of strength for the matrix Co surrounding WC-Co granules is not unreasonable, since a powder processing route was employed in the making of DC carbide cermets.

CONCLUDING REMARKS The present study has shown that the key aspects of the microstructure design of WC-Co cermets and its mechanistic basis can be understood by modeling with microelements. The microelements seem to capture important microstructure details such as the WC particle size, thickness and volume fraction of the Co binder, the constrained deformation behavior of Co as well as the fracture characteristics of WC and Co. The following conclusions may be drawn. 1. The strength of WC-Co cermets is largely controlled by the volume fraction of WC and is supplemented by the constrained plastic deformation of Co between the rigid WC grains. The expected functional form of this strength can be predicted using the microelement model that consistently incorporated the local average stresses and strains as well as the physical constraint experienced by the ductile Co during plastic deformation. 2. The creep or high temperature deformation behavior of Co is controlled primarily by the deformation characteristics of Co. The steady-state creep exponent of WC-Co is necessarily the same as that of Co. The effect of WC content is to shift the creep curves down in proportion to the WC volume fraction. An accurate prediction of creep deformation behavior requires consideration of the constrained deformation behavior of Co.

3. Fracture toughness of WC-Co cermets can be predicted quite accurately by considering fracture processes in WC and Co and is determined by the fracture properties of both phases. A large share of fracture toughness is contributed by the WC itself. Further, the constrained deformation behavior of Co during fracture, where the in-situ flow stress is several times larger than that of bulk Co significantly affects the fracture toughness. This latter aspect is responsible for the increase in the cermet toughness with an increase in Co content. Decreasing the WC particle size and increasing the strength of Co by alloying would help to increase the fracture toughness further.

4. A surprising finding of this study is that for designing cermets with toughness levels beyond WC-Co requires the use of hard materials with stiffness and fracture toughness levels higher than that of WC. The diamond-Co system is particularly attractive in this regard.

5 . Hierarchically structured WC-Co cermets with fracture toughness levels higher than that of the traditional WC-Co cermets are possible. The fracture toughness levels of such novel cermets can be predicted reasonably well using two-level models that consistently incorporate the microstructure details at different levels. These models explain well the effects of granule size and the Co volume fraction on fracture toughness.

6. The microelement models, having been validated by the extensive experimental data on WC-Co, suggest pathways for designing advanced composites with high strength and creep resistance and with reasonable fracture toughness. The simplest is to have a high volume fraction of hard and stiff constituent completely surrounded by a ductile and binding phase with good interface strength between them. Further, following the hierarchically structured WC-Co cermet design, different binder types at different levels of the structure may be chosen to enhance the combination of properties.

K.S. Ravi Chandran and Z. Zak Fang

172

REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26.

Pickens J.R., and Gurland, J. (1978) Muter. Sci. Eng. 33, 135. Viswanatham, R.K., Sun, T.S., Drake, E. F. and Peck, J.A. (1981) J. Mat. Sci. 16,1029. Lindau, L. (1977). In: Proc. 4th Int. Con$ Fracture, Fracture 1977, 2,215. Sigl, L.S. and Fischmeister, H.F. (1988) Acta Metall. 36, 887. Ravichandran, K. S. (1994) Acta Metall. Muter. 42, 143. Fang, Z. and Easton, J.W. (1995) Int. J. Refractory Metals and HardMaterials 13, 297. Fang, Z., Lockwood, G. and Griffo, A. (1999) Metall. Mater. Trans. 30A, 3231. Sommer, M., Schubert, W. and Warbichler, P. (2002) Int. J. of Refractory Metals and Hard Materials 20,41. Kinoshita, S., Kobayahsi, M. and Hayashi, K. (2002) J. Jpn. Soc. of Powder and Powder Metallurgy 49, 299. Carroll, D.F. and Conner, C.L. (1997). In: Advances in Powder Metallurgy and Particulate Materials, Proceedings of the I997 International Conference on Powder Metallurgy and Particulate Materials 2, 12-61, Metal Powder Industries Federation, Princeton, NJ, USA Ravichandran, K.S. (1994) J. Am. Ceram. Soc. 77, 1178. Ravichandran, K.S. (1994) Acta Metall. Mater. 42, 1113. Drucker, D.C. (1964). In: High Strength Materials, Zackay, V.F. (Ed), John Wiley & Sons, Inc., New York, NY. Evans, A.G. and Hirth, J.P. (1992) Scr. Metall. Mater. 26, 1675. Murray, M.J. (1977) Proc. Roy. Soc. Lond. 356A, 483. Unksov, A.P. (1961) An Engineering Theory of Plasticity, Buttenvorths, London. Mari, D., Ammann, J.J., Benoit, W. and Bonjour, C. (1988). In: Mechanical and Physical Behaviour of Metallic and Ceramic Composites, Proceedings of the 9th Riso International Symposium on Metallurgy and Materials Science, Published by Riso National Laboratory, Roskilde, Denmark, 433. Lee, I.C. and Sakuma, T. (1997) Metall. Mater. Trans. 28A, 1843. Ravichandran K.S. and Seetharaman, V. (1993) Acta Metall. Mater. 41,3351 Hong J. and Gurland, J. (1981). In: Science of Hard Materials, p. 649, Viswanatham, R.K., Rowcliffe D. J. and Gurland, J. (Eds) Plenum Press, New York. Slesar, M., Dusza, J. and Parilak, L. (1986). In: Science ofHard Materials, p. 657, Almond, E.A., Brookes, C. A. and Warren, R. (Eds), Inst. Phy. Conf. Series No. 75, Adam Higler Ltd., Bristol, UK. Chermant, J.L. and Osterstock, F. (1976) J. Mat. Sci. 11, 1939. Nakamura, M. and Gurland, J. (1980) Metall. Trans. 11A, 141. Ravichandran, K. S. (1994) Acta Metall. Mater. 42, 143. Roebuck, B., Almond, E. A. and Cottenden, A.M., (1984) Muter. Sci. Eng. 66,179. Deng, X., Patterson, B. R., Chawla, K.K., Koopman, M. C, Fang, Z., Lockwood, G. and Griffo, G, (2001) Int. J. Refiactory Metals and Hard Materials 19, 547.

Nan0 and Microstructural Design of Advanced Materials M.A. Meyers, R.O. Ritchie and M. Sarikaya (Editors) 02003 Elsevier Ltd. All rights reserved.

THE IDEAL STRENGTH OF IRON D. M. Clatterbuck, D. C. Chrzan and J. W. Morris Jr. Department of Materials Science and Engineering, UC Berkeley and Materials Sciences Division, Lawrence Berkeley National Lab, Berkeley CA 94609 ABSTRACT

The ideal strength of a material can be defined as the stress that causes an infinite defect-free perfect crystal to become mechanically unstable. The ideal strength is of interest because it sets a firm upper bound on the mechanical strength the material can attain. It is also approached experimentally in situations where there are few mobile defects. The present paper is concerned with the ideal strength of iron. We specifically compute the ideal tensile strength of iron for tension along cool>, the weak direction, and the ideal shear strength for relaxed shear in the <111>{ 112) and 4 11>{110) systems. We also consider the influence of pressure on the strength. The computation is done ab initio using the Projector Augmented Wave Method within the framework of density functional theory and the generalized gradient approximation in order to account for the magnetism of the material. The fact that iron can have a high tensile strength is puzzling. Because Fe has a stable fcc phase (at least at moderate temperature) simple models suggest that it should be very weak in tension on . That it is not turns out to be due to the difference in magnetic character between the bcc and fcc phases, which has he consequence that iron behaves like a “typical” bcc metal in both its tensile and shear behavior. INTRODUCTION

For almost three millennia the element Fe and its alloys have provided the most commonly used structural metals, and remain the materials of choice for a large fraction of all engineering structures and devices. There are three basic reasons why this is true. First, Fe is common in the earth’s crust, and is relatively easy to extract from its ores. Second, Fe has reasonable inherent strength, and can be alloyed or processed so that it becomes even stronger. Third, Fe (or steel) is a very flexible material that can be made soft for forming, or hard for structural strength by fairly straightforward changes in the way it is processed. The strength of Fe is a prerequisite. If it did not lend itself to the creation of alloys that are “as strong as steel”, it would not be widely used. Advances in computational techniques and computing machines have recently made it possible to compute the ideal strength of a crystalline material - the stress that drives the crystal lattice itself unstable and sets an upper bound on the strength the material can possibly have [1,2]. When these techniques are applied to Fe, as was done for the first time in the work reported here [3,4], a couple of surprises emerge. First, Fe is not really all that strong. Second, it is surprising that Fe is as strong as it is. These statements can be based on a simple model that is derived from the dominant role of symmetry in determining the ideal strength, as is well established from first-principles calculations [2,5]. The energy of a deformed crystal depends on the six independent components 173

174

D.M. Clatterbuck, D.C. Chrzan and J.W. Morris Jr.

of the strain and is, hence, a 6-dimensional hypersurface in a 7-dimensional space. The local extrema and saddle points on this hypersurface almost always correspond to structures with high symmetry. The configurations of greatest interest are the saddle points on the energy surface that neighbor the initial state. For a given load geometry (stress state) the crystal deforms along a particular path on the strain-energy surface as the load is increased. The stress required to dnve the system is related to the local slope of the energy surface in the direction of travel. The ideal strength is determined by the steepest slope along the path between the initial state and the first saddle point. The steepest slope corresponds to the maximum stress; the crystal is elastically unstable as soon as the point of maximum stress is passed. To understand the ideal strength it is necessary to identify the relevant saddle point structures. Four such structures have been identified in studies of the ideal strengths of bcc metals: the fcc structure, the simple cubic (sc) structure, a body centered tetragonal (bct) structure, and a base centered orthorhombic structure [6-81. For example, relaxed shear of a bcc metal in the “easy” 4 1 1 > direction on the (112) or (110) plane generates a stress-free bct structure [8]. Because the <111>{112} shear system is not symmetric in the sign of the shear direction, it is also possible to move from a bcc structure to a base centered orthorhombic structure by shearing in the “hard” direction. Uniaxial tension in the 4 1 1 > direction takes a bcc structure to a sc structure [6,8], while cool> tension moves it from bcc either to fcc (the Bain transformation in Fig. 1 [2]) or to bct (the same stress-free bct structure encountered in shear [7]). The competition between the two possible paths that can be reached by 4 0 1 1 tension has the result that, while most bcc crystals (Mo, W) are governed by the instability associated with the fcc structure and, ideally, fail in cIeavage, at least one (Nb) becomes unstable with respect to evolution toward the bct saddle point and fails in shear [7].

Figure 1: The bcc crystal structure becomes the fcc structure after elongation along the direction. Ab initio total energy calculations of the ideal tensile strengths of unconstrained bcc metals show that they are weakest when pulled in a <001> direction [2] (unsurprisingly, {OOl} is the dominant cleavage plane in bcc metals). A constant volume tensile strain along <001> converts the bcc structure into fcc at an engineering strain of about 0.26 (the ’Bain strain‘, Fig. 1). Since both structures are unstressed by symmetry, the tensile stress must pass through at least one maximum along the transformation path. If we follow Orowon [9] in assuming a single extremum (the solid line in Fig. 2), and fit the stress-strain curve with a sinusoid that has the correct modulus at low strain, the ideal tensile strength is approximately

in good agreement with ab initio calculations (for example, om = 30 GPa = 0.072 E<100> for W [lo]). Since the modulus of Fe is significantly less than that of other transition metals, such as W, Mo and Ta, the upper bound on its strength is smaller as well.

The ideal strength of iron

0.00

0.10

0.20

Engineering Strain

0.30

0.00

175

0.10

0.20

Engineering Strain

0.30

Figure 2: The energy as a function of strain has an extremum at the fcc structure which can be a local maximum (solid line) or minimum (dotted line). Assuming sinusoidal form, the inflection point governing the ideal strength falls at a much lower strain in the latter case, and the ideal strength is significantly less. But a second problem intrudes when we extend this analysis to iron [3]. The fcc phase in Fe is known to have an energy only slightly above that of bcc and is at least metastable at low temperature. In fact, the thermomechanical treatments that are used to process structural steel (particularly including the many developed or explored by Gareth Thomas) rely on the ease of transforming it from bcc to fcc and back again. If we assume a metastable fcc phase connected by a continuous strain-energy curve (the dotted line in Fig. 2), the tensile instability intrudes at a much smaller strain, and the ideal strength should be only about 6 GPa (versus 12 GPa based on an unstable fcc). This number is too small to be credible. Since tensile stresses that are several times the yield strength are developed ahead of crack tips in elastic-plastic materials, steels with yield strengths much above 1 GPa would necessarily be brittle. In fact, steels with much larger yield strengths have high fracture toughness and considerable ductility. A possible resolution of this paradox is suggested by the work of Herper et al. [ 111. They computed the energies of Fe for various magnetic states and lattice strains. Their calculations suggest that the energy of ferromagnetic Fe increases monotonically if it is distorted toward an unstable, ferromagnetic fcc, which can be stabilized by transforming into a complex antiferromagnetic state. This has the consequence that the low energy antiferromagnetic fcc phase is a minimum rather than a saddle point on the strain-energy surface of Fe. While Herper, et al. [ 111 did not investigate the point (they had other interests), this suggests the possibility that ferromagnetic Fe may become mechanically unstable under 4 OO> tension before encountering the magnetic transition that converts it into the antiferromagnetic state that stabilizes fcc. If this is the case, Fe can have the mechanical behavior of a typical bcc metal, while still having a metastable fcc structure that is stabilized by a late magnetic transition. That is, it can be both strong and easy to process.

As we shall show below, this is the apparent explanation for the fact that Fe has both a useful tensile strength and an fcc phase that facilitates processing. Going further, we shall establish that Fe naturally fails in cleavage on (100) planes and compute its tensile and shear strengths. Finally, we consider how the strength of Fe is affected by superimposed hydrostatic stress as encountered, for example, at the tip of a sharp crack.

116

D.M. Clatterbuck, D.C. Chrzan and J.W. Morris Jr.

COMPUTATIONAL METHODS To compute the ideal strength of Fe we must include magnetic interactions. These are non-local, and considerably complicate the problem. In particular, the non-local magnetic interactions have the consequence that the local density approximation cannot be used. In fact, computations based on the local density approximation predict that the ground state of Fe should be a non-magnetic close packed structure rather than a bcc ferromagnet. The use of the generalized gradient approximation (GGA) has been shown to correct this problem [ 121. Full Potential Linearized Augmented Plane Wave (FLAPW) calculations which make no further approximations beyond the GGA (assuming convergence of the basis set, charge density representation and Brillouin Zone integration) are probably the most reliable [13]. Unfortunately, in order to efficiently relax the stresses orthogonal to the applied stress, the stresses on the unit cell must be directly computable, and there are no implementations of the FLAPW method known to us that can do this in a straightforward way. For this reason we selected the Projector Augmented Wave (PAW) method, originally developed by Blochl [ 141, for this work. PAW is an approximation to FLAPW that captures most of its important features and can be formulated to calculate local stresses by the Hellman-Feynman method. We also performed some calculations using the FLAPW method as a check on the accuracy of the results. The two methods are in reasonable agreement. The details of the computation are given in ref. [4]. The ideal strength was computed for uniaxial stress in tension or shear. The lattice vectors were incrementally deformed in the direction of the imposed stress, and at each step the structure was relaxed until the stresses orthogonal to the applied stress vanished, as indicated by those components of the Hellman-Feynman stresses being less than 0.15 GPa [15]. Because there is no unique measure of strain for a given finite deformation, we describe our deformations in terms of the engineering strain from the equilibrium structure. The initial set of lattice vectors ra (a=!,2,3) in an orthogonal coordinate system become the vectors ra' after homogeneous deformation by the transformation :r = rla + D, rJa . From this transformation, we define the strain to be e,=[D,,+DJ,]/2. As is customary, we redefine the shear strains to be yIJ=2elJfor i#j. While the engineering strain is convenient for describing the change in the lattice vectors from their original configuration, the Cauchy (true) stress cannot be calculated from the derivative of the free energy with respect to this strain measure. To compute the Cauchy stress we take the derivative of the free energy with respect to the incremental strain from a nearby reference state, yielding a stress that converges to the thermodynamic definition of the Cauchy stress in the limit of small incremental strain. It should be noted that the ideal strengths determined from these calculations are for quasi-static deformation at OK, and that other dynamic instabilities such as soft phonons may lower the ideal strength.

EQUILIBRIUM STRUCTURES We chose to compute the ideal strength with the Projector Augmented Wave (PAW) method because of its computational efficiency and its ability to treat lattice stress. To check the accuracy of the method, we computed the energy as a function of volume for several magnetic structures and compared the results to calculations done using the FLAPW method as well as

The ideal strength of iron

111

with available experimental data. The magnetic structures included the following: bcc ferromagnet (FM), fcc ferromagnet (FM), fcc antiferromagnet (AFM), fcc non-magnetic (NM). The results are plotted in Fig. 3. The results for the ferromagnetic bcc phase are tabulated in Table 1 .

%

a: E

I

45

-

40

.

35

.

30

-

25

.

+BCC-NM +BCC-FM +FCC-NM +-JFCC-FM -c- FCC-AFM * FCC-DAFM

20 .

60

P

64

68 72 76 80 Vdurneiatom (au')

84

88

Figure 3: The energy and magnetic moment per atom as functions of volume computed using the PAW method for Fe in the bcc (filled symbols) and fcc (open symbols) crystal structures for several magnetic states: (diamonds) non-magnetic (NM), (squares) ferromagnetic (FM), (circles) anti ferromagnetic (AFM), and (triangles) double period anti ferromagnetic (DAFM). The discontinuity in the fcc FM curve separates two distinct phases with different magnetic moments. In general the agreement between the two computational methods is good. Comparing the PAW and FLAPW methods, the equilibrium volumes of the various phases agree to within 1%. The elastic constants of the bcc FM phase agree to within 3% with the exception of c44, which has a discrepancy of 13%. Compared with experimental measurements of the bcc phase at 4 K, the PAW calculations predict a lattice parameter that is too small by 1% and elastic constants which are generally about 10% too large suggesting a slight over-binding (the only discrepancy being c44 which is 18% too small). From the computed elastic constants, the relaxed tensile modulus in the <001> direction, E<,00>= l/sll, is found to be about 29% too large, while the relaxed shear modulus in the 4 11> direction, G= 3c44(c1I-c12)/(4c44+c~ I - C I ,~is) about 18% too large.

D.M. Clatterbuck, D.C. Chrzan and J.W. Morris Jr.

178

In regards to the magnetic properties, both the PAW and FLAPW methods correctly predict that the ground state is the bcc ferromagnetic phase with a magnetic moment of 2.20 pg and 2.15 p~ respectively as compared to the experimental value of 2.22 pg [. Both sets of calculations also predict that the ferromagnetic fcc phase undergoes a pressure-induced, first order phase transformation at a volume of 76-77 au3/atom from a low-volume, low-moment phase to a highvolume, high-moment phase. The groundstate magnetic structure of fcc Fe has been debated on theoretical grounds extensively in the literature. While bulk fcc Fe is difficult to achieve experimentally at low temperature, there is some probative experimental data on the magnetic state of nearly pure Fe in the fcc crystal structure. It is possible to stabilize fcc Fe by growth as a thin epitaxial film or as small precipitates in a copper matrix. Tsunoda [17,18] found that small fcc precipitates in Cu that are almost pure Fe have a spiral spin density wave (SSDW) ground state. Knopfle et al. [19] have recently published calculations using the modified augmented spherical wave method that show good agreement with this experimental data. Their minimum energy fcc structure has a spiral vector of q=(0.15,0,1) with an energy which lies <1 mRy below the AFM phase and has a slightly larger equilibrium volume than the AFM phase. Due to the complexity involved in treating non-collinear magnetism, in the present work we have used collinear structures as approximate representations of the true magnetic ground state. Herper, Hoffmann, and Entel [ 1I] proposed using a collinear double period antiferromagnetic structure (DAFM) as an approximate to the non-collinear ground state in fcc Fe. In this structure the spins on (002) planes are oriented up-up-down-down. The energy as a function of volume of this structure is plotted in Figure 4 and we see that it is located <1 mRy below the AFM phase and has a similar equilibrium volume. The spiral spin density wave studied by Knopfle, et al. [ 191 has an energy only slightly below this. TABLE 1 Lattice parameters, volumes, relative energies and elastic constants from PAW and FLAPW calculations as well as experiment. All energies are relative to the FM bcc phase which is taken as 0. Experimental elastic constants at 4K are from [20] and the experimental lattice parameter extrapolated to 4 K is from Ref. [21]. PAW

FLAPW

PAW-FLAPW

Experiment (4K)

%Enor

PAW-Experiment %Error

bcc-FM V, (au3)

76.47

76.20

0.4%

78.94

-3.1% -1.1%

a0 (4

2.830

2.827

0.1%

2.86

0 (GPa)

194

196

-1.0%

174

11.5%

C I I (GPa)

286

289

-0.9%

245

16.9%

c12@Pa)

147

152

-3.43%

139

5.9%

c44 (GPa)

99

114

-12.8%

122

-18.5%

EclOO>

P a )

G
187

184

1.5

144

29.2%

77

78.9

-1.9%

65

18.4%

The ideal strength of iron

179

IDEAL STRENGTH IN TENSION We first consider the ideal strength in tension. Since previous calculations and symmetry arguments suggest <001> is the weakest direction in tension for bcc metals [2], we have focused on the ideal strength in this direction. Tetragonal versus orthorhom bic instability

There are two possible deformation paths for uniaxial tension in the <001> direction (Fig. 4). An infinitesimal strain in the Cool> direction distorts the crystal into a body centered tetragonal (bct) configuration. If we compute the deformation path under the constraint that the cell maintain tetragonal symmetry we obtain the results shown in Fig. 5. The energy reaches a local maximum at 28% strain in the fcc structure (c/a ratio = &, and then it reaches a local minimum at 42% strain in a stress-free bct structure with a c/a ratio of 1.66. The plot of tensile stress versus strain along this path has a maximum of 12.6 GPa at 15% strain. The maximum locates the elastic instability along the bcc-fcc (Bain) deformation path and corresponds, physically, to cleavage on the {OOl} plane.

,ao:

0

Bain Path 40 0'

0

bcl (black) fcc (while)

'pi3 0

0

0 -

bcc (black) fco (while) 0

bcc (black) bcl (black) ico (while) Orlhorhombic Path

Figure 4: The geometry of the Bain path and the orthorhombic instability. If tetragonal symmetry is maintained the Bain path is followed from the bcc structure to the fcc, which is equivalent to a bct structure with a c/a ratio of 62. If the tetragonal symmetry is broken the orthorhombic path is followed and a maximum energy is reached at a special bct structure that has a c/a ratio of 1.66. The orthorhombic path eventually produces a bcc cell that is rotated relative to the original bcc cell. The initial bct structure can also be treated as a special case of a face centered orthorhombic (fco) structure that is rotated by 45' (Fig. 4) and has a:b:c ratio of 62: 62:1, where we take the caxis to lie in the direction of the applied strain. If we preserve orthorhombic symmetry (which allows the tetragonal symmetry to be broken) the deformation is coincident with the Bain path up to a strain of -18%, but then diverges from it. The evolution of the ratios of the orthorhombic lattice parameters along the loading path is shown at the bottom of Fig. 5 and the geometric relationship between the special crystal structures is shown in Fig. 4. At a strain of 18% the crystal spontaneously develops an orthorhombic distortion. The energy reaches a maximum at 21% strain, then falls off into a local minimum at a strain of 42%. The energy maximum along the orthorhombic path occurs at the "special" bct structure with a c/a ratio of 1.66, and the energy

180

D.M. Clatterbuck, D.C. Chrzan and J.W. Morris Jr.

minimum is a bcc structure that is rotated relative to the initial bcc cell (see Fig. 4). If one refers the structure back to the bct structure with the deformation in the [OOI] direction, the orthorhombic instability corresponds to the elastic constant c66 vanishing, which causes the crystal to become unstable with respect to a shear. Although the crystal is pulled in tension this instability initiates a shear failure on the 4 11>( 112) system of the bcc crystal. The competition between tetragonal and orthorhombic instabilities in bcc crystals was first noted by Luo, et al. [7], who found that the tetragonal instability dominates in Mo (as in W) while the orthorhombic instability intrudes in Nb. The issue is physically important, since the tetragonal instability leads to failure in tension ((001) cleavage) while the orthorhombic instability leads to failure in shear 4-( 1l>{ 112) shear). Ferromagnetic Fe behaves like the conventional bcc metals, W and Mo. Its ideal strength in <001> tension, 12.6 GPa, is determined by the tetragonal instability and, hence, by cleavage on (001). In keeping with this result, Fe cleaves on (001) when tested at low temperature. We also computed the ideal tensile strength of Fe using the FLAPW method; however, in those calculations only tetragonal structures were considered. A slightly higher ideal strength, 14.2 GPa was found, which is consistent with the larger energy difference between the bcc FM and fcc FM structures found with the FLAPW method as compared to the PAW method. The energy difference may be due to the differences in the treatment of the GGA or errors introduced by the PAW potential. The conditions of stability developed by Morris and Krenn [xx] were tested at 14% strain to check for orthogonal instabilities. No orthogonal instabilities were found at that strain, consistent with the PAW calculations. However, the elastic constant c66 was found to be only -30 GPa, quite a bit smaller than in bcc Fe (114 GPa), which is an indication of the close proximity of the orthorhombic instability. Assuming a sinusoidal stress-strain curve that returns to zero at the actual strain needed to reach the fcc phase, 0.286, we have

o = omsin(ed0.286). (2) = 0.091E, Requiring that Hooke's law be satisfied for small strains: om = 0.286E<001>/n: where E<001, is Young's modulus for elongation in the <001> direction. Eq. 2 agrees well with the results calculated here: om/E=0.087 with the experimental value for E<001>,or o,lE=0.068 with the calculated value.

The ideal strength of iron

0

01

02 03 Engneering %an

.15

-20

C

0

01

0

01

05

04

05

04

05

"

02 03 Engheer~ngStrain

02

04

181

03

Engineering Strain

Figure 5 : (a) Energy and (b) stress as a function of applied tensile strain along cool>: (filled squares) Bain Path with tetragonal symmetry, (open square) orthorhombic path. (c) Ratios of the lattice parameters along the orthorhombic path: (filled diamond) ah,(filled triangle) d c , (filled circle) b/c. Numbers and open circles an (a) and (c) indicate special structures with high symmetry that are shown schematically in Figure 6. Magnetic instabilities

The results to this point have only considered ferromagnetic (FM) states; however, the fact that Fe has a metastable, antiferromagnetic fcc phase at low temperature suggests that it must become unstable with respect to magnetic transitions at large strains. We will now consider this possibility.

As discussed above, we approximate the magnetic structures of fcc Fe by collinear structures for computational simplicity. In addition, we used a scalar relativistic approximation that does not include the effects of spin-orbit coupling. However, our earlier calculations using the FLAPW method showed that this makes a negligible effect on the energy differences between various magnetic structures. In the actual calculation we fix the magnetic structure and relax the lattice into the required stress state. We then increment the strain to obtain the energy and stress as a function of the strain, relaxing the lattice at each step along the path. This entire process is then repeated for various magnetic structures.

D.M. Clatterbuck, D.C. Chrzan and J.W. Morris Jr.

182

Fig. 6 shows the calculated energy as a function of strain for Fe in the FM, AFM, DAFM and low-spin FM structures. We have studied both bct and fco structures and found that the AFM and LSFM structures remain tetragonal while the DAFM and FM structures undergo a transformation to the fco structure at different points along the loading path. The DAFM structure is preferred to FM Fe for strains above about -20%. This result suggests that the ideal strength is not compromised by magnetic instability since the structural instability ((001 } cleavage) occurs at about 15% strain, well before the magnetic transition intrudes. Thus, the ideal strength in <001> tension is -12.6 GPa and is set by a tensile elastic instability along the Bain path from bcc to fcc. The stability of fcc iron is made possible by a magnetic phase transition at larger strains that does not affect the ideal strength. 20

-E

16

$14E

2 P x

* BCTFM

12-

10-

p 80

6-

0

.

.

/

FCOFM ,,-:* BCTAFM ‘,a BCTDAFM *$’ FCODAFM .t BCT LSFM

;

P ~ ’

:a,

i

0.1

rn

* .*+<: ;(I. -. I..

*

a

0.2 0.3 Engineering Strain

*

-cA

0.4

Figure 6: Energy versus strain in the <001> direction for various magnetic structures: (solid square) bct-FM, (open square) fco-FM, (filled triangle) bct-DAFM, (open triangle) fco-DAFM, (filled circle) bct-AFM, (filled diamond) bct-LSFM. The fco-AFM and fco-LSFM structures follow paths identical to bct-AFM and bct-LSFM respectively and are not shown. A magnetic phase transformation is seen near 20% strain. Comparison with previous calculations and experiment

Several previous authors have studied the energy as function of tetragonality for Fe, but have not determined the ideal strength [ 11,221. Friak et al. [23] independently calculated the ideal tensile strength along the tetragonal loading path using the FLAF’W method and found a strength of 12.7 GPa, in good agreement with our results from the PAW method and slightly lower than our calculations using the FLAF’W method (14.2GPa). While the use of different GGA formulations in the three cases makes exact comparison difficult, the differences are within the error range for density functional methods. To our knowledge, the only attempt to measure the ideal tensile strength of Fe was by Brenner [24] who tested Fe whiskers in tension. He measured a value of -5GPa for tension in the c o o l > direction. While this value is considerably lower than the calculated ideal strength, the failure initiated at the surface and, therefore, does not represent bulk strength. The measured value of the strength in the <111> direction was 13GPa, but it is expected that the ideal strength of bcc metals in the 4 11> direction is significantly larger than in the cool> direction [2].

The ideal strength of iron

183

IDEAL STRENGTH IN SHEAR Shear strength of FM bcc Fe

We computed the ideal shear strength of Fe for two common slip systems: <111>{112) and 41I>{ 110). The energy and the stress are plotted as functions of the shear strain for the two systems in Fig. 7. We note that the ideal strength in the easy direction is very similar for the two slip systems, 7.2 GPa for 411>{ 112) and 7.8 GPa for <1 11>{110). The energy curves for the two systems also have the same maximum. These results, which are common in bcc metals, have their origin in the symmetry of the "saddle point" structures that govern the shear strength [7,10]. The saddle point structures for the two slip systems are identical. Moreover, the saddle point structure in shear is precisely the bct saddle point structure that governs the orthorhombic instability in tension. The convergence of the three strain paths to the same saddle point simply shows that the nearby saddle points on the energy hypersurface act as "attractors" to which the various deformations are drawn.

080

-060

040

-020

000

EngneeiingStain

020

040

-0 8 0

-OW

040

020

000

Engineering Stran

020

Figure 7: (a) Energy versus shear strain and (b) absolute value of the stress versus strain for (filled square) < I 1 I>{ 112) shear and (open square) 4 1 I>{ 110) shear.

Table 2 Summary of stresses and strains associated with instabilities and saddle points. The tensile strains are referred to a bct cell with the [OOI] axis along the z-axis. For <11 l>{ 112) shear, the reference structure is a base centered monoclinic cell with its 2-fold axis parallel to the x-axis, one orthogonal lattice vector parallel to the shear direction which coincides with the y-axis, and the other orthogonal lattice vector in the y-z plane. For 411>{110} shear, the reference structure is a triclinic cell with one lattice vector in the shear direction which coincides with the y-axis, the second lattice vector in the shear plane which coincides with the x-y plane, and third vector with some component in the z-direction.)

040

D.M. Clatterbuck, D.C. Chrzan and J.W. Morris Jr.

184



Tension



<111>{112}

Shear <112>{112)

tetragonal

orthorhombic

(hard)

(easy)

12.6

12.6

15.0

7.2

7.8

bct

bct

monoclinic

monoclinic

triclinic

< I l l > { 110)

-.042

-.049

,037

-.008

-.002

-.042

-.049

-0.26

-.006

-.001

,150

,176

,042

,028

.029

-.374

,140

,059 ,020 ,035

fcc

bct

-.091

-.070

-.091

-.070

,286

,209

bct

bct

,046

,004

-.014

-.03 1

-.016

-.015

,088

,044

,033

-.726

,288

,339

orthorhombic

,022 ,154

While the saddle point structure for the two slip systems is the same, the strain paths on the energy hypersurface are slightly different. This difference is responsible for the fact that the strain at which the bct structure occurs is slightly larger for the 4 1l>{ 110) system, and the ideal strengths for the two systems differ by -8%. The relaxation of the crystal lattice during strain is also distinctly different. A constant volume shear on the 4 1l>{ 112) system (with no relaxation in the slip plane) produces a body centered orthorhombic structure at a engineering shear strain of 33%. Allowing relaxation, the special bct structure is reached after a strain of 29% with a 4% expansion perpendicular to the slip plane, and relaxation strains in the slip plane of < 2% (see Fig. 8 and Table 2). On the other hand, a <111>{ 110) shear reaches the bct structure at 34% strain, but requires a significant relaxation in the slip plane, the largest component being a 15% shear. The reason for the differences between (112) and (110) shear lies in the fact that while both paths begin at bcc and end at the bct saddle-point structure, the very different applied stresses cause them to diverge from one another at intermediate strains and produce significantly different atomic configurations near the point of instability.

The ideal stvength of iron

185

Base Centered Monoclinic Cell

Base Centered Ort horhoinbic Figure 8: Geometry of the <111>{112} shear system. The base centered monoclinic cell is shown inside the initial bcc structure (left). A { 110) projection of the structure shows the how the monoclinic cell becomes a bct cell upon applying a -33% shear in the easy direction (top). A shear in the opposite (hard) direction generates a base centered orthorhombic structure after a shear strain of -66% (bottom). The monoclinic structure's two fold axis is pointed out of the page. Black atoms are those in the closest plane and the gray atoms are in the following plane of atoms.

As suggested by Frenkel [25], we model the ideal strength by assuming the that the stress-strain relation is sinusoidal with an amplitude z,,,and period 2 YB:

If we require that Hooke's law be satisfied for small strains, this implies that

where G<11p is the shear modulus in the < I l l > direction. (Note that the shear moduli are the same for both shear systems.) If we take YB to be 0.34, then Eq. 4 predicts z, = 0.1 ~ G < I I Our ~>. results give dimensionless strengths which are very close to this, for { 112) t,,,/G=O. 11 and for { 110 ) tm/G=O.12, where we have used the experimental value of G from Table 1. Using the calculated value of G < I I ~the , reduced strengths are 0.10 and 0.094 for shear on the { 112) and (1 10) planes respectively. The shear strength in the hard direction for the 4 11>{112) system is 15.0 GPa. It follows a path toward a different saddle point that is much higher in energy (see Figs. 7 and 8). The saddle point structure is base centered orthorhombic with an a:b:c ratio of 1: 1.06:1.77. This structure can also be pictured as a simple tetragonal structure with a c/a ratio of 2.42 that has undergone an (engineering) shear strain of 6% in the plane perpendicular to the unique axis. Figure 9 demonstrates the geometry and the fact that the strain needed to reach this saddle point is approximately twice that for shear in the easy direction.

186

D.M. Clatterbuck, D.C. Chrzan and J.W. Morris Jr.

To test the numerical accuracy of the PAW method, the energies of several structures along the 4 11>{112) "easy" shear path were also computed with the FLAPW technique. The energy differences were less than 0.2 mRy. While we have not confirmed that the stress states of these structures are uniaxial when computed with the FLAPW method, the close agreement in the energies along the deformation path suggests that the PAW method is quite accurate in this regime. Magnetic instabilities

We also investigated the possibility that finite shear strain would induce magnetic instabilities that would limit the shear strength. This was done by testing several different magnetic structures and relaxing the stresses, as in the ferromagnetic case. The energy was only computed at a few interesting points along the i l l 1>{112) loading path. The magnetic structures were chosen to mimic the DAFM structure used for the tensile strength calculations, but because the crystal is monoclinic along the loading path, there are several inequivalent ways of arranging the up and down spins in such a fashion. The 5 structures we studied are shown in Fig. 9. They include superlattices made up of one or two base centered monoclinic cells, with different arrangements of the up and down spins occupying the sites.

BCTDAFM 0

0

DAFM-x 0

DAM-Z

0

0

DAFM-Y

AFh4

DAFM-Y?

Figure 9: The magnetic structures used to describe complex magnetic ordering in <111>{ 112) shear. The structures are supercells made up of I or 2 body centered monoclinic cells whose 2fold axes are oriented out of the page. The bct-DAFM structure is shown for reference. 50-

-E 40 -; SO'

'

0

K

-6 2 0 ' P

W

10.

o i

A

-

0

FM o DAFMX

Y

.... . D

.. ..

.

o DAFMZ A DAFMY o DA-MY2

'6

.'. o

O

9.

__

x

AFM

". os, c m&..w-

... -.

0

I

The ideal strength of iron

187

Fig. 10 shows the energy as a function of strain for the relaxed structures. There is a magnetic transformation at -20% strain to the magnetic structure denoted DAFMX. However, this strain is beyond the point of elastic instability, so this transformation does not affect the ideal shear strength. The energy as a function of strain for the DAFMX structure was confirmed by FLAPW calculations using a method similar to that described above. We again note that we have only considered here a set of collinear structures which we hope approximate the ground state magnetic structure; however, the introduction of non-collinear magnetic ordering may further reduce the energy of some of these structures. IDEAL STRENGTH IN MULTIAXIAL LOADING The previous two sections have described the ideal strength of iron under simple loading configurations: uniaxial tension and pure shear. However, in many engineering applications the stress state experienced by a material is more complex. In this section we study the strength of iron for uniaxal tension in the [OOl] direction in combination with biaxial tension or compression in the (001) plane. The case of unbalanced triaxial tension is commonly encountered in front of a crack tip and is thus of practical importance. The ideal strength calculations were carried out in a manner similar to that used for uniaxial tension; however, in this case the structure is relaxed to achieve the multiaxial stress state desired. For triaxial tension the stress state was taken to be ol1=2022=2033 while for uniaxial tension plus biaxial compression the stress state was taken to be (TI]=- ( ~ 2 2 = - 0 3 3 . In practical terms, the desired stress state was said to be achieved when the Hellman-Feynman stresses obeyed the above equalities to within 0.1 GPa.

.

. . 'I' .

Tension

150

1 20t 10

7.5. 5.0.

25'

OodoO

. m

.: . . 'I' '

' t c

' a

c

e

0.05

0;O

0;5

020

0.25

. OiO

Engineering Strain

Figure 11: Stress as a function of strain for FM Fe under three different multiaxial loads: uniaxial tension plus biaxial compression (triangle), uniaxial tension (square), triaxial tension (diamond). In all cases the largest tensile stress is in the [OOl] direction. The large symbols with arrows indicate the location of tetragonal to orthorhombic instabilities. (The load configuration that includes biaxial compression was not tested for this type of instability.) The weak direction in tension for bcc metals is known to be the <001> direction, so we focus our attention on this orientation. Fig. 11 shows the stress as a function of engineering strain in the ~ 0 0 1 direction 2 for the three different stress states considered. We see that the application of a tensile stresses perpendicular to the primary tensile direction raises the ideal tensile strength while compressive stresses decrease the ideal strength. In conjunction with this we note that the

188

D.M. Clatterbuck, D.C. Chrzan and J.W. Morris Jr.

strain corresponding to the ideal strength is increased in the tensile case and decreased in the compressive case. These results are in contrast to the often held assumption that the tensile strength of a material should decrease in a triaxial stress state. However, the reason for this result becomes clear if one examines the effect of these stresses from the perspective of their associated strains. The application of a [OOl] tensile strain to a bcc metal causes the symmetry to be broken and the crystal structure becomes body centered tetragonal (bct). When the c/a ratio of the bct crystal is increased to $2 it becomes the fcc structure. Cubic symmetryrequires that the [OOl] tensile stress vanish for both the bcc and fcc structures (at least, if we ignore the magnetic effect, which is small). As such, these structures are symmetry-induced extrema (or saddle points) on the multidimensional energy-strain surface. We can model the stress-strain curve between the two energy extrema by a sinusoid as suggested by Orowon [ 9 ] : D = cm sin(e xiemax),

(5)

where omis the ideal strength, e is the engineering strain, and emaxis the engineering strain of the second stress-free structure. Requiring that the Hooke's law be obeyed at small strain, one finds that D m = emaxE/~, (6)

where E=1/sll is the Young's modulus in the <001> direction. Now consider the effect of the triaxial stress state on the bct structure. The addition of the orthogonal tensile stresses increases the length of the crystal in the [loo] and [OlO] directions. Because of this, a larger strain is needed in the [OOl] direction to reach the fcc structure, increasing emax.Given this, Eq. 6 implies that the ideal strength should be increased in tension. In a similar way, the addition of compressive stresses orthogonal to the tensile direction will have the opposite effect and decrease the strain needed to reach the fcc saddle point structure. In this analysis we have assumed that the stress-strain curve remains sinusoidal under multiaxial loads. An additional effect not explicitly included in Equation 6 is caused by the pressure dependence

of the Young's modulus. It would be possible for triaxial tensile stresses to lower the ideal tensile strength of a bcc metal if the additional stresses decreased the Young's modulus more than they increased the strain needed to reach the fcc structure. From the initial slopes in Fig. 11, we see that triaxial tensile stresses increases the Young's modulus in iron, which increases the ideal strength even more than if the Young's modulus were independent of pressure. This increase in the Young's modulus with pressure is consistent with the experimentally determined pressure dependence of the elastic constants [ 2 6 ] .

As discussed in above, the body centered tetragonal structure can become elastically unstable with respect to transformation to a face centered orthorhombic structure. For uniaxial tension in iron, this shear failure occurs at strains larger than the elastic instability associated with the

The ideal strength of iron

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tetragonal Bain path. We find that the triaxial stress state studied here increases the strain at which the tetragonal to orthorhombic transition occurs; however, the increase is less than the increase in the strain associated with the peak in the stress-strain curve (see Fig. 11). The effect is to cause the orthorhombic instability to occur closer to the maximum in the stress-strain curve of the tetragonal structure for triaxial tension. We have not studied the effect of pressure on the magnetic transformations that can occur along the Bain path. In the uniaxial case, the elastic instability occurs at smaller strains than these magnetic transitions and thus it dictates the ideal strength. To a first order we expect that the addition of orthogonal tensile stresses would enhance the stability of the ferromagnetic phase due to a narrowing of the bandwidth, while the addition of compressive stresses would tend to favor antiferromagnetic or non-spin polarized (paramagnetic) phases. This suggests that even under multiaxial loading the ideal strength is governed by the elastic instability rather than the magnetic instability; however, a more detailed study would be needed to verify this claim as it is not known whether the change in the strain associated with the magnetic phase transitions would be larger or smaller than the change in the strain associated with the elastic instability. CONCLUSIONS

Ab initio total energy calculations using the PAW method were used to calculate the ideal strength of iron in tension and shear. The ideal tensile strength in the <001> direction is 12.6 GPa and is associated with an elastic instability at 15% strain along the Bain path from bcc to fcc. At this strain the structure is stable with respect to both orthogonal elastic instabilities and magnetic instabilities. However, if it were possible to reach larger strains, both an elastic instability toward a face centered orthorhombic structure occurs and a magnetic instability from the bct FM to a DAFM magnetic structure would be encountered. The ideal shear strengths of the two shear systems, <111>{112} and <111>{110}, are 7.2GPa and 7.8 GPa respectively. The ideal shear strengths are very similar because they are determined by the same body-centered tetragonal "saddle point structure". (This bct "saddle-point structure" is also responsible for the orthorhombic instability in tension). Along the <11 l>{ 112) shear path, a magnetic instability toward a complex magnetic structure is found at -20% strain. Like the magnetic instabilities in tension, it does not compromise the ideal strength because it occurs at larger strains than the elastic instability in the ferromagnetic phase. The ideal tensile strength in the <001> direction is increased when one applies a biaxial tensile stress in the (001) plane while the strength is decreased when the additional stress is biaxial compression. This effect can be understood based on a simple crystallographic model. The triaxial stress state increases the strain needed to reach the fcc saddle point structure, which results in a higher strength. The tetragonal to orthorhombic instability is found to move closer to the peak in the stress strain curve, a result similar to what is found in Nb despite the fact that they undergo different failure modes under uniaxial tension. Despite its complex magnetic behavior and its metastable fcc phase, the ideal strength of Fe is governed by the same elastic instabilities that are found in typical bcc transition metals like W and Mo.

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ACKNOWLEDGEMENTS This work was supported by the Director, Office of Science, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering, of the U.S. Department of Energy under Contract No. DE-AC03-76SF00098. REFERENCES 1. A. Kelly and N. H. MacMillian (1986). Strong Solids. Clarendon Press, Oxford, 3rd ed. pp. 1-56. 2. J. W. Morris Jr., C. R. Krenn, D. Roundy, and Marvin L. Cohen (2000). In: Phase Transformations and Evolution in Materials. P. E. Turchi and A. Gonis (eds.). TMS, Warendale, PA., pp. 187-207. 3. D. M. Clatterbuck, D. C. Chrzan, and J. W. Morris Jr. (2002). Phil. Mug. Lett. 82, 141. 4. D. M. Clatterbuck, D. C. Chrzan, and J.W. Morris Jr. (2003). Actu Muteriulia, 51,2271. 5. M. Sob, L. G. Wang, and V. Vitek (1998). V. Kovove Muteriuly 36, 145. 6. M. Sob, L. G. Wang, and V. Vitek (1997). Mat. Sci. Eng. A 234-236, 1075. 7. W. Luo, D. Roundy, M. L. Cohen, and J. W. Morris Jr. (2002). Phys. Rev. B 66,094110. 8. F. Milstein and J. Marschall(l988). Phil. Mug. A 58, 365. 9. E. Orowon(1949). Rept. Prog. Phys. 12, 185. 10. D. Roundy, C. R. Krenn, Marvin L. Cohen, and J. W. Morris Jr. (2001). Phil. Mug. A 81, 1725. 11. H. C. Herper, E. Hoffman, and P. Entel(l999). Phys. Rev. B 60, 3839. 12. D. J. Singh, W. E. Pickett, and H. Krakauer (1991). Phys. Rev. B 43, 11628. 13. D. J. Singh (1994). Planewaves, Pseudopotentials and the LAPWMethod.Kluwer Academic, Boston 14. P. E. Blochl(l994). Phys. Rev. B 50, 17853. 15. D. Roundy, C. R. Krenn, Marvin L. Cohen, and J. W. Moms Jr. (1999). Phys. Rev. Lett. 82, 2713. 16. B. D. Cullity (1972). Introduction to Magnetic Materials. Addison-Wesley, Reading Mass., p 617 17. Y .Tsunoda (1989). J. Phys. Condens. Mutter 1, 10427. 18. Y. Tsunoda, Y. Nishioka, R. M. Nicklow (1996). J. Mugn. Mug. Mat. 128, 133. 19. K. Knopfle, L. M. Sandrastskii, and J. Kubler (2000). Phys. Rev. B 62, 5564. 20. M. Acet, H. Zahres, E. F. Wassermann, and W. Pepperhoff (1994). Phys. Rev. B 49,6012. 21. J. A. Rayne and B. S. Chandrasekhar (1961). Phys. Rev. 122, 1714. 22. L. Stixrude, R. E. Cohen, and D. J. Singh (1994). Phys. Rev. B 50,6442. 23. M. Friak, M. Sob, V. Vitek (2001). In: Proc. Znt. Con$ Juniormat 2001, Institute of Materials Engineering, Bmo University of Technology, Bmo, p. 117 24. S. S. Brenner (1956). J. Appl. Phys. 27, 1484. 25. J. Frenkel(l926). Z. Physik 7, 323. 26. F. Nelson (ed.) (1992). Landolt-Bornstein LBIIV29a -- Low Frequency Properties of Dielectric Crystals: Second and Higher Order Elastic Constants, Springer-Verlag, Berlin

Nan0 and Microstructural Design of Advanced Materials M.A. Meyers, R.O. Ritchie and M. Sarikaya (Editors) 02003 Elsevier Ltd. All rights reserved.

MICROSTRUCTURE-PROPERTY RELATIONSHIPS OF NANOSTRUCTURED Al-Fe-Cr-Ti ALLOYS L. Shawl, H. Luol, J. Vilegas' and D. Miracle' Department of Metallurgy and Materials Engineering University of Connecticut, Storrs, CT, USA Air Force Research Laboratory, Materials and Manufacturing Directorate Wright-PattersonAFB, OH, USA

ABSTRACT Nanostructured Al93Fe3TizCr2 alloys were prepared via mechanical alloying (MA), followed by extrusion to form bulk materials. The microstructure of the alloy was characterized using a variety of analytical instruments including X-ray diffraction (XRD), scanning electron microscopy (SEM) and transmission electron microscopy (TEM). Compression tests were conducted as a function of temperature ranging from 25 to 40OoC. It was found that the MA-processed A193Fe3Ti2Cr2 alloy had excellent compressive strength and ductility. High temperature strengths were especially impressive with the ratio of the ultimate strength to density equivalent to that of Ti-6Al-4V up to about 30OoC. The enhanced strength at both ambient and elevated temperatures was attributed to grain refinement, formation of supersaturated solid solutions, and presence of intermetallic precipitates. INTRODUCTION Aluminum alloys and their composites with greater strength at elevated temperatures are needed for applications in aerostructure, aeropropulsion and rocket propulsion. Current commercial alloys provide high strength at room temperature, but at 200 - 35OoCthe strength of these materials decreases rapidly. Consequently, other materials are used for high temperature load carrying applications with a resultant penalty of weight. Recent progresses in studies of bulk amorphous and nanostructured alloys have offered opportunities to improve the strength of aluminum alloys at both room and elevated temperatures. It has been shown that amorphous A1 alloys could possess high tensile strength coupled with good bending ductility [ 141. The strengths obtained from the amorphous A1 alloys are much higher than those of the best conventional coarse-grained A1 alloys. Furthermore, the primary crystallization of the amorphous A1 alloys could lead to a microstructure of a high density of A1 nanocrystals in an amorphous matrix that offers even higher strengths than those of the parent amorphous A1 alloys [5-lo]. When the primary crystallization is carried out to completion, the nanocrystalline A1 alloys still exhibit superior tensile strengths (e.g., 800 - 1000 MPa) that are much higher than those of the best conventional crystalline

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A1 alloys [lo]. A1 alloys with quasicrystalline phases (e.g., icosahedral structure) or a nanoscale mixture of quasicrystalline phases surrounded by a continuous fcc-A1 phase have also been shown to possess high tensile strengths ranging from 500 to 1300 MPa [5,11-131. In this study we have investigated the feasibility of making nanocrystalline A193Fe3TizCrz alloys via mechanical alloying (MA) starting from elemental powders, and examined the potential of the MAprocessed A193Fe3TizCrz alloy for high-temperature structural applications. A193Fe3Ti~Crzalloys have been chosen for investigation because Fe, Cr and Ti all have very low difisivity and equilibrium solubility in fcc-A1 (0.03 at.% Fe, > 0.01 at.% Cr, and > 0.2 at.% Ti) [14-171. Low difisivity and solubility are the basic requirements for preventing Ostwald ripening [181. Thus, Al93Fe3Ti~Cr2alloys are expected to have good microstructural stability at elevated temperatures and therefore superior high-temperature strengths. Al93Fe3TizCrz alloy has been prepared previously by Inoue, et al. [5] using the gas atomization approach followed by extrusion. They have indeed found that this alloy possesses superior high temperature strength. The reported ultimate tensile strength at 3OO0C is 360 MPa [5]. This high temperature strength compares very favorably against the current commercial Al alloys, most of which lose their useful strengths at temperatures above 25OoC (typically becoming lower than 200 MPa) [ 191. In contrast to the gas atomization approach, we have utilized the MA approach to prepare the nanostructured A193Fe3Ti~Cr2alloy. The potential advantage using MA over rapid quenching (i.e., gasatomization) to prepare nanocrystalline Al93Fe3TizCrz alloys is the possibility of making nanocrystalline A1 matrix composites with nano-reinforcements (i.e., nano/nano-A1 composites) through blending the elemental constituents of the metallic matrix or pre-alloyed metallic powder with insoluble nano-reinforcements such as nano-SiC particles. Nanohano-A1 composites are expected to have better microstructural stability and thus higher elevated temperature strengths than those exhibited by the corresponding nanocrystalline A1 alloys.

EXPERIMENTALPROCEDURES Crystalline elemental powders were used to prepare A1 alloys with a nominal composition of A193Fe3TizCr2. The aluminum powder had a purity of 99.5 wt% with a mean particle size of 70 pm, while the corresponding values for iron, chromium and titanium powders used were 99.0%, 98.5% and 99.5% as well as 50, 30 and 30 pm, respectively. The as-received aluminum powder was made via atomization, whereas the iron powder was manufactured via a vapor phase chemical decomposition process, the chromium powder via electrolytic plating and milling, and the titanium powder via the hydride technique followed by a dehydride process. Mechanical alloying was performed in a Szegvari attritor. The canister of the attritor was made of a stainless steel and the charge consisted of stainless steel balls with a diameter of 4.76 mm. A ball-topowder weight ratio of 20:l and a milling speed of 600 RPM with the milling duration of 30 hours were employed in all the experiments. During milling the canister was cooled using circulation water with a flow rate of about 770 mVmin throughout the process and an argon atmosphere was employed in all the experiments. To prevent excessive cold welding of A1 alloys, 1.2 wtYo stearic acid [CH3(CH2)&0OH] was added to the powder mixture as the process control agent. The MA-processed powder was used to make bulk materials via extrusion technique. Prior to extrusion, the MA-processed powder was containerized within a metal can and subjected to degassing which was carried out in a temperature ranging from 300 to 55OoC until the pressure of the can was reduced to lo-’ ton. The parameters controlled during extrusion included the included angle of the

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extrusion dies, extrusion temperature, extrusion ratio and strain rate. The extruded Al93Fe3Ti2Crz bulk material was used to prepare cylindrical compressive specimens 6-mm in diameter and 9-mm in height. Both ends of the compressive specimens were coated with MoS2 before tests and the strain rate sec-' for all the tests. All the compressive tests were displacement controlled and empolyed was terminated if the specimen did not fracture at -0.45 true strain. The test temperature investigated ranged from 25 to 40OoC. Powders received and milled as well as extruded bulk A1 alloys were analyzed using X-ray dimaction (Rigaku RU-200B series) with CuKa radiation. In addition to monitoring phase transformations, XRD was also used to measure the crystallite size and internal strains of fcc-Al. The detailed procedure for estimating the crystallite size and internal strain can be found elsewhere [20,21] and will not be repeated here. The microstructure of the extruded A1 alloy was examined using a field-emission SEM (Leica Cambridge Stereoscan 360FE) equipped with energy dispersive spectrometry (EDS). Analyses of the gain size, crystal structure and chemical composition within the microstructure of the Al alloy were also performed using a TEM (Philips CM200 FEG) operating at 200kV. In the TEM analysis, both bright and dark field image techniques coupled with selected area difhction (SAD), convergent beam electron d i M o n (CBED) and EDS with an electron beam of 3.5 nm were used to characterk the MAprocessed Al alloy. RESULTS AND DISCUSSION Figure 1 shows typical true stress-true strain curves of extruded A193Fe3Ti~Cr2alloys obtained from compressive tests with a strain rate of lo5 sec-*.The different stress-strain curves in Figure 1 are due to different extrusion ratios with Sample C having the largest extrusion ratio. For Sample A tested at 25'C, the specimen cracks laterally after a small compressive plastic strain (-0.02). The cracking is accompanied by a sudden drop in the stress, as shown in the stress-strain curve of 25'C in Figure l(a). As compression continues, more cracks form on the lateral surface of the specimen. Eventually the entire specimen breaks into pieces at the true compressive strain of -0.37, indicating that Sample A is quite brittle at 25OC. However, the ductility of Sample A improves as the test temperature increases. As shown in Figure l(a), Sample A does not form lateral cracks even after a true strain of -0.45 when the test temperature is 300'C. The ductility of Sample A at 200'C is between those exhibited at 25 and 300'C.

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Figure 1. Overleaf.

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Figure 1. True stress-true strain curves of the MA-processed A1 alloys obtained from compression tests with a strain rate of 10" sec-'. (a) Sample A, (b) Sample B and (c) Sample C have different extrusion ratios. Sample B is also brittle at 25OC; however, it appears to have better ductility than Sample A at 2OO0C because Sample B does not form any large lateral cracks and thus has no sudden drop in the entire stress-strain curve before the termination of the test. At both 300 and 4OO0C Sample B exhibits superior ductility because no lateral cracks are formed after a true compressive strain of -0.45. Sample C is ductile at both ambient and elevated temperatures, and therefore has great potential for structural applications. Note that although Samples A, B and C have different ductilities, their strengths are similar and appear to be only temperature dependent. At 25OC, their ultimate strengths are about 700 m a , while their corresponding values at 200 and 3OO0C are about 500 MPa and 300 MPa, respectively. At 4OO0C, Sample B has an ultimate strength of about 200 m a . These ultimate strengths compare very favorably against current commercial A1 alloys, most of which lose their useful strengths at temperatures above 25OoC [19]. Figure 2 compares the compressive strength of the MA-processed A193Fe3Ti2Crz alloy with the tensile strengths of two typical coarse-grained A1 alloys, one being 7075 A1 - one of the best A1 alloys for ambient temperature applications, and the other being 2219 - one of the best A1 alloys for

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high temperature applications. Included in Figure 2 are also the tensile strengths of the future aluminum alloys that have the ratio of the ultimate strength to density equivalent to that of Ti-6A1-4V alloy. It is clear from Figure 2 that the MA-processed Al93Fe3Ti2Cr2 alloy is much stronger than 7075 and 2219 alloys at both ambient and elevated tem eratures. Furthermore, for lightweight, high strength structural applications at temperatures below 300gC, the MA-processed A193Fe3Ti2Cr2 alloy competes very favorably against Ti-6A1-4V. K 700 I

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Figure 3. XRD patterns of Sample A and the A1~,33Fe3Ti&rz alloy before extrusion. Note that before extrusion the alloy contains only fcc-A1 solid solution with substantial peak broadening, suggesting nano-sized fcc-A1 grains. After extrusion, two additional phases, A16Fe and Al3Ti, have been detected.

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To understand the strength and ductility achieved in the MA-processed A193Fe3Ti2Cr~alloy, the microstructure and phases of the Al93Fe3Ti2Cr2 alloy have been investigated. Figure 3 shows the XRD pattern of Sample A. The XRD patterns of Samples B and C are identical to that of Sample A. Three phases have been identified from the XRD pattern of Sample A; these are fcc-A1 solid solution, A16Fe and Al3Ti. The TEM analysis reveals that the particle sizes of A16Fe and A13Ti intermetallic precipitates are similar to the grain size of fcc-Al, all of which range from 15 to less than 100 nm [21]. Shown in Figure 4 is the typical TEM bright-field image of the Alg3Fe3Ti~Cr~ alloy after extrusion, clearly indicating that the grain size of the MA-processed A193Fe3TizCrz alloy is below 100 nm.

Figure 4. TEM bright-field images of the MA-processed A193Fe3TizCr2 alloy after extrusion.

SEM images of Samples A, B and C are shown in Figure 5 . Note that the microstructures revealed via the SEM analysis are quite different for Samples A, B and C. A continuous oxide film is present at the prior powder particle boundaries (PPB) in Sample A, whereas the oxide film in Sample C has been completely broken down into discontinuous particles during extrusion. The situation for Sample B is in between Samples A and C, i.e., most of the oxide film at the PPB has been broken down, but not completely. Since Samples A, B and C have identical XRD and TEM results, it is reasonable to infer that the ductility of the MA-processed alloy exhibited in compression tests is mainly dictated by the status of the oxide film at the prior powder particle boundaries. Furthermore, the MA-processed A193Fe3TizCrz alloy is brittle when the oxide film is continuous at PPB, and is ductile when the oxide film is broken down into discontinuous particles. Based on XRD, TEM and SEM analyses, it can also be inferred that the superior ambient- and hightemperature strengths possessed by the MA-processed Al93Fe3Ti2C1-2alloy are due to a combined effect of (i) the retention of ultrafine fcc-A1 grains and (ii) the presence of nanoscale intermetallic precipitates. Detailed deformation mechanisms whereby these two factors control the strength are currently under investigation.

CONCLUDING REMARKS Promising mechanical properties (i.e., superior compressive strength and ductility) at both ambient and elevated temperatures have been achieved via mechanical alloying of A193Fe3TizCrz alloy, followed by

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extrusion. The superior high-temperature strength of the MA-processed Al93Fe3TizCrz alloy is derived from low difisivities of the alloying elements, the presence of nanoscale intermetallic precipitates, and the retention of ultrafine grains (fcc-A1 < 100 nm after extrusion). Mechanical properties, especially ductility, depend strongly on whether the oxide film at the prior powder particle boundary has been broken down or not. The MA-processed A193Fe3Ti~Cr2alloy is brittle when the oxide film is continuous at PPB, and is ductile when the oxide film is broken down into discontinuous particles during extrusion.

Figure 5. SEM images of the nanostructured A193Fe3Cr2Ti~alloy. (a) Sample A, (b) Sample B, and (c) Sample C correspond to those shown in Figure 1. Note that a continuous oxide film is present at the prior powder particle boundaries in Sample A, whereas this is not the case for Samples B and C. The white particles in Samples A, B and C are Cr-rich, Fe-rich or Ti-rich solid solutions [20].

Acknowledgements - The authors acknowledge the insightful discussion with Drs. Sheldon L. Semiatin, Oleg Senkov, Kevin Kendig and B.V. Radhakrishna Bhat at the Air Force Research Laboratory in a wide range of the topics regarding this work. The authors are also thankful to Tony Houston and Pat Fagin of UES, Inc. for help in mechanical testing and to the Materials Processing Lab of the Air Force Research Laboratory for performing extrusion. The first author, L. Shaw, would also like to thank the University of Connecticut for granting a sabbatical leave to conduct research at the

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Force Research Laboratory. The partial support from the Materials and Manufacturing Directorate of the Laboratory Director’s Fund of the Air Force Research Laboratory is greatly appreciated.

REFERENCES

1) Y. He, S. J. Poon and G. J. Shiflet, “Synthesis and Properties of Metallic Glasses That Contain Aluminum,” Science, 241,1640-1642 (1988). 2) A. Inoue, K. Ohtera, A.-P. Tsai and T. Masumoto, “New Amorphous Alloys with Good Ductility in Al-Y-M and A1-La-M (M=Fe, Co, Ni or Cu) Systems,” Jpn. J. Appl. Phys., 27 [3] L280-L282 (1988). 3) A. Inoue, K. Ohtera and T. Masumoto, “New Amorphous Al-Y, Al-La and Al-Ce Alloys Prepared by Melt Spinning,” Jpn. J. Appl. Phys., 27 [5] L736-L739 (1988). 4) G. J. Shiflet, Y. He and S. J. Poon, “Mechanical Properties of a New Class of Metallic Glasses Based on Aluminum,” J. Appl. Phys., 64 [12] 6863-6865 (1988). 5 ) A. Inoue and H. Kimura, “High-Strength Aluminum Alloys Containing Nanoquasicrystalline Particles,” Mater. Sci. Eng., A286 [l] 1-10 (2000). 6) A. Inoue and T. Masumoto, “Production and Properties of Light-Metal-Based Amorphous Alloys,” Mater. Sci. Eng., A133,6-9 (1991). 7) H. Chen, Y. He, G. Shiflet and S. J. Poon, “Mechanical Properties of Partially Crystallized Aluminum Based Metallic Glasses,” Scripta Metall. Mater., 25, 1421-1424 (1991). 8) A. Inoue, “Fabrication and Novel Properties of Nanostructured A1 Base Alloys,” Mater. Sci. Eng., A179-A180,57-61 (1994). 9) Z. C. Zhong, X. Y. Jiang and A. L. Greer, “Microstructure and Hardening of Al-Based Nanophase Composites,” Mater. Sci. Eng., A226-228, 531-535 (1997). 10)J. Q. Guo and K. Ohtera, “Microstructures and Mechanical Properties of Rapidly Solidified High Strength Al-Ni Based Alloys,” Acta Mater., 46 [l 11 3829-3838 (1998). 11)A. Inoue, “High-Strength Al-Based Alloys Consisting Mainly of Nanoscale Quasicrystalline or Amorphous Particles,” Mater. Sci. Forum, 235238,873-880 (1997). 12)A. Inoue, H. M. Kimura, K. Sasamori and T. Masumoto, “Microstructure and Mechanical Properties of Rapidly Solidified Al-Cr-Ce-M (M=Transition Metal) Alloys Containing High Volume Fraction of the Icosahedral Phase,” Mater. Trans., JIM, 36 [l] 6-15 (1995). 13)A. Inoue, H. Kimura, K. Sasamori and T. Masumoto, “High Mechanical Strength of Al-(V, Cr, Mn)-(Fe, Co, Ni) Quasicrystalline Alloys Prepared by Rapid Solidification,” Mater. Trans., JIM, 37 [6] 1287-1292 (1996). 14)U. R. Kattner, in Binarv Alloy Phase Diaaams, 2”d edition, T. B. Massalski, Eds., ASM International, Materials Park, OH, 1990, pp. 147-149. 15)J. L. Murray, in Binarv Allov Phase D i a m s , 2”d edition, T. B. Massalski, Eds., ASM International, Materials Park, OH, 1990, pp. 138-140. 16)J. L. Murray, in Binary Alloy Phase Diamams, 2”d edition, T. B. Massalski, Eds., ASM International, Materials Park, OH, 1990, pp. 225-227. 17) H. Mehrer (eds.), Diffusion in Solid Metals and Alloys, Landolt-Bornstein,New Series, Group 111, Volume 26 (Springer-Verlag,NY, 1990). 18) C. Wagner, “Theorie der Alterung Von Niederschlagen durch Unlosen (Ostwald-Reifund),” Z. Elektrochem., 65,581-591 (1961). 19)D. L. Erich, “Development of A Mechanically Alloyed Aluminum Alloy for 450-650’F Service,” AFML-TR-79-4210,(1980). 20)L. Shaw, M. Zawrah, J. Villegas, H. Luo and D. Miracle, “Effects of Process Control Agents on Mechanical Alloying of Nanostructured Aluminum Alloys,” Metall. Mater. Trans., in press. 21) L. Shaw, J. Villegas, H. Luo and D. Miracle, “Thermal Stability of Nanostructured A193Fe3Ti~Cr2 Alloys Prepared via Mechanical Alloying,” Acta Mater., in press.

Nan0 and Microstructural Design of Advanced Materials M.A. Meyers, R.O. Ritchie and M. Sarikaya (Editors) 02003 Elsevier Ltd. All rights reserved.

MICROSTRUCTURAL DEPENDENCE OF MECHANICAL PROPERTIES IN BULK METALLIC GLASSES AND THEIR COMPOSITES U. Ramamurty, R. Raghavan, J. Basu and S. Ranganathan Department of Metallurgy Indian Institute of Science, Bangalore - 560 012, INDIA

ABSTRACT Successful technological exploitation of a material requires a thorough understanding of the connection between its microstructure and properties. Introduction of metastability into a microstructure increases the number of choices that are available to a material designer. Bulk metallic glasses are a new class of metastable materials and offer fascinating possibilities. These glasses can be divided into two broad categories: metal-metal glasses and metal-metalloid glasses. A number of composites can be synthesized from bulk metallic glasses either by the addition of second phase particles or by controlled crystallization leading to a number of novel microstructures. These glasses upon crystallization give rise to nanocrystals, nanoquasicrystals and nano-scale phase separation. Due to the diverse crystallography and extremely fine size, the effect of the crystals on the mechanical behavior is also diverse. A glass deforms by the formation and propagation of localized shear bands leading to the early fracture at room temperature. Partial crystallization or introduction of second phase particles hinders the flow of shear bands leading to an increase in the toughness of the material. Beyond a certain level of crystallization the fracture behavior of the partially crystallized glass changes from shear-band dominated fracture to intergranular cleavage type fracture resulting in a precipitous drop in the fracture strength. As mechanical properties are very sensitive to the microstructure, precise control of microstructure is required in order to produce a material with reproducible properties. In this paper different microstructures derived from BMGs and their consequent influence on mechanical properties is discussed.

INTRODUCTION Understanding the connection between the microstructure of a given material and its properties is a major theme of materials research. Professor Gareth Thomas has made seminal contributions to this theme. Since equilibrium microstructures give rise to only a limited number of choices, tailoring microstructures through the purposeful introduction of metastability into the material is a widely explored option. Transformation toughened materials (be it in steels or ceramic systems), precipitation hardened alloys and refined microstructures are a few classical examples of the exploitation of such a concept. Terminal extension of the refinement concept leads to amorphous materials or glasses. Conversely, one can view metallic glasses as precursors giving rise to a plethora of microstructures upon heat treatment. Naturally, the microstructural

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evolution will depend on the path the metallic glass is subjected in the thermo-chrono-temporal space. The key to the successful utilization of this strategy is the understanding of the path dependency of the microstructure and the performance of it in terms of properties. While glasses in silicate and polymeric systems can be readily obtained due the sluggish crystallization kinetics inherent to them, synthesizing metallic glasses requires subjecting the molten alloy to severe degree of quenching (cooling rates of the order of lo6 Ws).Hence, most of the early research on the transformation and mechanical behavior of metallic glasses was confined to those that are subjected to rapid quenching. As the thickness of such specimens was in the micrometer range, their mechanical properties could not be evaluated in a rigorous fashion. The recent discovery of alloy systems that do not require rapid quenching facilitates the production of bulk metallic glasses (BMGs) [1,2,3]. Widely studied BMG systems include the Zr-, Pd-, Mg and La-base as well as Fe- and Ni- base alloys. While the BMGs as such have interesting properties and hence potential applications, they offer interesting additional possibilities, as devitrification of glasses can lead to crystals, structurally complex intermetallics and quasicrystals. Additionally, devitrification in many of these systems can lead to nanocrystals and nanoquasicrystals [4]. While the deformation of glasses is controlled by nondislocation mediated processes, crystal plasticity is governed by dislocations, while the plasticity of structurally complex intermetallics and quasicrystals is mediated by meta dislocations. When such diverse structures OCCLU together, the flow process in a devitrified alloy is expected to be complex and has begun to receive serious attention in recent years as such structures have improved mechanical properties as compared to the starting glassy matrix. In this paper, we shall make attempts to map the microstructural evolution due to annealing of BMGs and the resultant property changes, with emphasis on our own recent work. We shall highlight the richness of both the microstructures that result as well as the attendant development of beneficial properties. The mechanical property variation of such systems with annealing will be highlighted. This paper is organized in the following manner. In the next section, we shall briefly review the concepts involved in processing BMGs. The subsequent section I11 examines the development of microstructures. In section IV,the connection between microstructures and mechanical properties will be explored. We conclude this paper with a brief summary and identification of the outstanding issues.

SYNTHESIS OF BULK METALLIC GLASSES Since the discovery of metallic glasses in 1960 [ 5 ] , there has been a constant effort to produce glasses with lower cooling rate in the bulk form. The first success in this direction was in the early eighties, when Drehman et al. [6] produced millimeter size Pd-Ni-P glasses. The resurgence of interest in this field occurred when Inoue et al. [7] demonstrated that a bulk metallic glass could be cast in a copper mould by conventional casting technique. The BMG forming alloys have a large supercooled liquid region that can span over a temperature regime of 100K. Another attribute of BMG forming system that was realized very early is the multicomponent nature of the alloys. These two features make the alloys resistant to crystallization following the requirement for long range diffusion. Since then, a number of BMG forming alloy systems has been discovered among which Mg, Zr, Hf, Ti, Pd, La, Fe and Ni based alloys are important. Apart from conventional casting technique, BMGs can be synthesized by high pressure die casting, suction casting and unidirectional zone melting method. Solid state synthesis by mechanical alloyng can also yield bulk glasses after consolidation. In the Mg-based BMG forming alloy family most important is the Mg-Y-transition metal system in which Cu and Ni have been used extensively. Y can be replaced by rare earth metals including misch metal.

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Addition of Ag increases the glass forming ability of the Mg-based alloys [8]. The alloy design strategy for Ti, Zr and Hf based glasses follows a similar trend as these three elements appear in the same group in the periodic table and they are structurally and chemically very similar. Ti, Zr and Hf can form binary glasses with late transition metals like Cu and Ni over a wide composition range. Most widely studied systems in these alloys are along with A1 and a late transition metal such as Ni and Cu. Zr-Al-(CuiNi) bulk metallic glasses have a wide supercooled liquid region. There are a number of important quaternary Zr-based BMG forming systems among which Zr-Cu-Ni-A1 is important as it can be cast in the form of a 30 mm diameter rod. Addition of Ti, Hf, Pd, Pt, Au, Ag etc. introduces important attributes in the BMG so far their phase formation and microstructural evolution is concerned. The most important quinary Zr-based BMG forming alloy system is the Zr-Ti-Cu-Ni-Be alloy [9]. Be being a very small atom it provides a large atomic radii mismatch and it can go into the voids of the random packing of Zr, Ti, Cu and Ni resulting in a closer packing of atoms. It can be cast in the form of 14 mm diameter rod with a critical cooling rate of 0.9 - 1.2 Ks-'. BMGs in these alloy systems are highly processable above the glass transition temperature because of the large supercooled liquid region. La forms BMGs when alloyed with aluminum and transition metal. The first composition to be reported was La55A125Ni20. Addition of Cu and Co increases the glass forming ability and it can be cast in the form of a 9 mm diameter rod [lo]. Ni based quaternary and quinary alloys with early transition metal and late transition metal can also be cast in the form of 3 mm diameter rod [ l 11. In Mg, Zr, Ti, Hf, La and Ni based BMG forming systems glass forms because of the high negative heat of mixing and atomic radii mismatch between the metallic constituents. In these systems the metallic atoms play a major role in high glass forming ability of the alloys and hence these BMGs fall in the category of metal-metal glasses.

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Temperature, T f C ) Figurel: Dynamic DSC thermogam of as cast Pd40C~30Nil~P20 glass.

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Pd-based alloys have always attracted attention since the discovery of the BMGs. Pd forms glasses with transition metals and metalloid. Fluxing has proved to be useful in decreasing the cooling rate in this alloy system. Early studies on the Pd-based glasses were performed on Pd-Ni-P system. Partial replacement of Ni by Cu increases the glass forming ability and it can be cast in the form of a 40 mm diameter rod. This alloy has a supercooled liquid region spanning over 75 K and T,, equal to 0.71. Recently Nishiyama and Inoue [ 121 have further refined the composition in order to synthesize BMGs with the slowest possible cooling rate. They have identified the composition corresponding to the quaternary eutectic Pd42 5CujONi7 jP20, as the most favored one. Fe-based BMGs are younger members in the bulk glass forming alloy family. Fe forms glasses with Al, Ga along with minor addition of P, C, B, Si and Ge. Another class of Fe-based glasses form when alloyed with transition metals like Ni, Cu, Co, Zr, Nb along with B. In a recent development Inoue and Wang [13] have shown that the addition of a small amount of B to commercial cast iron makes it possible to cast glassy 0.5 mm diameter rods. In the Pd- and Fe-based BMGs high negative heat of mixing and atomic radii mismatch between metallic Fe and Pd with P, C, B, and Si leads to high glass forming ability. These glasses fall in the category of metal-metalloid glasses. BMGs show interesting thermal behavior, which can be divided into a number of regimes identified by temperature defined transitions. Those are glass transition temperature (T,), crystallisation onset temperature (Tx), melting temperature (Tm), liquidus temperature (TI).The reduced glass transition temperature, T, is the ratio of T, and T,. The dynamic scanning calorimetric thermogram recorded at 20 Kmin.' of a Pd40Cu3"Ni10PZ0 BMG is shown in Fig. 1 to illustrate some of these temperatures. In this alloy glass transition occurs at 570 K and it crystallizes in a single exothermic heat event showing its proximity to a deep eutectic. The temperature span between glass transition and crystallization onset temperature is called supercooled liquid region, which is 75 K for the Pd40Cu30Ni10P20 BMG.

MICROSTRUCTURAL DEVELOPMENT FROM BMGs

A number of composites can be synthesized from the BMG forming alloys by suitably selecting the processing conditions. Broadly, these composites can be classified into two groups as in-situ and ex-situ composites. The in-situ composites are produced by controlling the cooling rate during casting or by precipitation of crystalline phases during annealing subsequent to casting. On the other hand, reinforcement phases such as WC, TIC, Ta, steel fiber or particles can be added to the melt during conventional casting of BMGs to produce ex-situ composites containing dispersed crystalline second phases in the amorphous matrix [14]. While processing these, the shape, size and volume fraction of the second phase particles can be controlled externally in order to control the microstructure. It has been observed that the second phase particles do not act as the heterogeneous nucleation sites. Diffusion takes place at the interface of the second phase and the BMG matrix, which results in a composition shift at the interface. During melt processing it has been observed that some part of the second phase melts and reprecipitates at the interface during solidification. The addition of the second phase increases the melt viscosity, which, beyond a certain limit, affects the processability of the composite. Glass formation from a metallic liquid essentially involves kinetic suppression of nucleation and growth from the liquid state. If a metallic liquid is continuously cooled from the liquid state, then at the melting temperature a discontinuous transition of different physical properties like viscosity, density takes place. Then again the change becomes continuous. By application of nonequilibrium processing techniques nucleation and growth of solid phase at and below the melting temperature can be suppressed. In such cases, the physical properties of the liquid changes continuously up to the T, where it becomes configurationally frozen in order to transform to a glass. Processing parameters can be changed in a systematic manner in order to precipitate some crystalline phases in the glassy matrix directly during cooling. This results in a crystalline

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phase reinforced BMG composite This, in terms of CCT diagram, is as following For glass formation critical cooling rate is that which avoids the nose of the C curve One can choose a cooling rate that is slightly higher than the critical cooling rate but facilitates crystalline phase precipitation in the glassy matrix in a controlled manner Figure 2 represents an elcctron micrograph and electron diffraction pattern of a ZrCu-Ni-AI BMG forming alloy in which BCC Zr has precipitated in the amorphous matrix during casting i n a copper mould The precipitates are irregular in shape and their size ranges up to 200 nm In depth knowledge of the effcct of processing parametcrs on the nucleation and growth of the crystalline phases is required in order to control the size and the volume fraction of the prccipitates in the glassy matrix Crystallization of BMGs can give rise to a number of inicrostructures with variation in scale and morphology In order to technologically exploit BMGs as a precursor for microstructural design, selection of processing parameters e g temperature and time is very important Two distinct temperature regimes for studyng crystallization are those below and above T, The mechanism of crystallization as enunciatcd by Herold and Koster [ 151 explains different crystallization behavior observed in BMGs Crystallizition occurs in three different modes In primary crystallization, a crystalline phase that is different in composition from that of the amorphous phase is precipitated in the amorphous matrix In polymorphous crystalliration, a crystalline phase of composition similar to that of the matrix is precipitated and in eutectic crystallization, crystallization occurs through an eutectic reaction Though the above thcory can explain most o r the crystallization phenomena observed in metallic glasses, it suffers from two drawbacks First, it does not account for phase separation and second it cannot explain the nuclealion sequence In order to predict phasc formation and rationalize nucleation sequence “phase hierarchy maps” may be useful

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Figure 2 Transmission electron micrograph and electron diffraction pattern showing the presence of cubic Zr in Zr-Cu-Ni-A1 alloy precipitated during casting

Figure 3. Transmission electron micrograph and electron diffraction pattern showing the phase separation in a Cu-Ti-Zr glass heat treated in the supercooled liquid region.

In a number of alloy systems, phase separation can be observed when they are heat treated in the supercooled liquid region Excellent glass forming systems like Zr-Ti-Cu-Ni-Be [16] is known to phase separate Phase separation can also be seen in some Zr-based glasses where copper concentration is very high Figurc 3 represents transmission electron micrograph and electron diffraction pattern of a Cu-Ti-Zr glass, which phase separates when heat treated in the supercooled liquid region From the diffraction pattern, it can be deduced

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that, both the phases are in an amorphous state The difficulty in studying these systems is posed by the lack of thermodynamic data As the position of the alloy in the free energy composition diagram cannot be confirmed by regular thermodynamic calculations, it is difficult to determine whether it is a true spinodal or it is a phase separation dominated by nucleation Most of the BMG forming alloys precipitate nanocrystals upon crystallization Nanocrystals are distributed in the amorphous matrix at the initial stages of crystallization With the progress of crystallization, a considerable amount of gram growth and further precipitation of other crystalline phases can be observed As growth of these nanocrystals requires long-range diffusion, their growth IS kinetically hindered In this regard, the Johnson-Mehl-Avrami (JMA) model has received wide acceptance though the basic assumptions of JMA model are sometimes violated with respect to crystallization of amorphous alloys Kelton [17] has modified the model in this light Ranganathan and Heimandahl [18] have successfully applied JMA model in various glass forming systems under different growth conditions to predict the shape and growth dimensions of the precipitates Recent studies by Matsushita et a1 [19] have shown that growth behavior of quasicrystals from the amorphous phase is linear The resultant microstructure conforms to the nano-scale with diffcrent phases, crystallography, shape and size

Figure 4 Transmission electron micrograph and electron diffraction pattern showing nano-quasicrystallization in a Zr-Ti-Ni glass after heat treatment in the supercooled liquid region Ideally amorphous nature of an alloy I S characterized by the presence of a diffuse hump in the X-ray diffraction pattern. From such patterns, it is possible to calculate the radial distribution functions and deduce the atomic coordination. Unlike ceramic glasses, there exists no model based on networking of tetrahedra in BMGs By analogy, it has been postulated that a polyhedral structure exists in the glasses Out of the proposed theories, the most widely accepted model is that of Bernal deltahedra As the Bernal deltahedra cannot fill space, it is thought that metalloid atoms fill up the vacant spaces But, in metal-metal glasses the idea of the existence of Frank-Kasper polyhedra seems to be gaining more acceptance Crystallography of the phases precipitated at the initial stages of crystallization from BMGs gives a strong indication that polyhedra exist in BMGs The icosahedron is common to Bemal deltahedra and Frank Kasper polyhedrd Recently, a number of BMG forming alloy systems have been discovered, which precipitate nanoquasicrystals at the initial stages of crystallization In this regard, Zr-Ti-Cu-Ni-AI [20],Zr-Cu-Ni-Al(Pd, Pt, Au, Ag) [21], Zr-Ti-Ni are important systems Figure 4 represents the electron micrograph of a Zr-

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Ti-Ni amorphous alloy after heat treatment in the supercooled liquid region In the micrograph, spherical or polygonal precipitates can be seen and from the nano beam diffraction patterns, quasicrystalline nature of thc precipitate with icosahedral symmetry can be ascertained Most of the quasicrystalline phases so precipitated are metastable Zr-Ti-Ni is ail important system to study in this regard, as it precipitates stable icosahedrdl quasicrystalline phase This phase forms in a number of binary Zr and Hf alloys containing Pd and Pt [22] Oxygen plays an important role in precipitation and stabilization of this phase [23] A number of studies have reported that in Zr-Cu-Ni-A1 alloy [24] 0 5-1 5 at% oxygen stabilizes the quasicrystalline phase Beyond this limit, this phase gets destabilized A commonly observed phase where quasicrystalline phase IS destabili7ed is Ti2Ni [ 2 5 ] type phase, which has cF96 structure Though it has cubic symmetry, the phase has distorted icosahedral cluster in it Studies by Li et al [26] have shown that, icosahedrdl cluster is stdbilized in a BMG by the high ncgativc h a t of mixing and atomic radii mismatch in the alloy It has been observed that around 10% atomic radii mismatch stabilizes the forniation of icosahedral cluster These clusters act as seeds for quasicrystallization It has been postulated that, depending on composition, number o f seeds in the amorphous matrix can be controlled, which, in turn, is reflected on the size of the quasicrystalline precipitates

Figure 5 Transmission electron micrograph of micron-size crystals precipitated in a Pd-Cu-Ni-P BMG after heat treatment below the glass transition temperature

It I S seen from the above discussion that, most of the BMG forming alloys precipitate nanocrystals and quasicrystals upon crystallization giving rise to different novel microstructures It is possible to achieve s i x variation in different glass forming systeins While the heat treatment at or below the T, allows the glass to relax, prolonged heat treatment can lead to crystallization Figure 5 represents an electron micrograph of a Pd-Cu-Ni-P bulk metallic glass which has been heat treated below its T, Nearly micron sized crystals with a flower-like morphology can be seen in the amorphous matrix Some of the Fe-based metallic glasses, which contain metalloid, can give rise to micron size crystals upon crystallimtion In these BMGs crystallites si7e is fine at the initial stages of crystallization but with the increase in time the crystals grow to micron s u e due to the rapid growth rate

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206 MECHANICAL BEHAVIOR

Metallic glasses, in general, exhibit high stiffness (-100 GPa), high yeld strength (-2 GPa), large elastic strains (-2-3%), low strain hardening and negligible plastic strains in tesnion Figure 6 represents strength and elastic limit of different types of conventional materials along with BMGs and BMG composites It is seen that bulk glasses and its offspring have strength in the range of 1000-2500 MPa coupled with 2.3% of elastic strain In contrast, the conventional materials exhibit either high strength or high elastic limit but not both This is the most important combination in these kinds of matenals

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Figure 6: Comparative representation of fracture strength vs elastic strain of conventional materials with BMGs and BMG composites. BMGs show a drastic change in their mechanical behavior with temperature At ambient temperature, when a BMG is tested in tension, the stress-strain plot observed is linear up to fracture with negligible plasticity In compression, however, most BMGs behave in an elastic perfectly-plastic manner, with the ability to accommodate significant plastic strains Tensile fracture occurs by formation and unhindered flow of localized shear bands along the plane of maximum shear stress This behavior can be substantially improved by the introduction of second phase particles via partial crystallization or reinforcement as these acts as barriers to the propagation of the shear bands. Reinforcement of second phase particles can impart ductility and increase toughness of the materials [27] Introduction of second phase particles changes the fracture behavior of the BMG composites from shear-dominated fracture to fiber splitting and bucking of the second phase Fatigue crack growth behavior of BMGs is very similar to that of the crystalline counterpart but it has considerably lower fatigue limit than the crystalline alloys Above the T,, the mechanical behavior of the BMGs is drastically different Here, it deforms homogeneously and in a Newtonian viscous manner Above this temperature, superplastic forming ability of the alloy increases and it can be used for near net shape processing Mechanical behavior of the BMGs can be altered substantially by annealing below or above T, Annealing a La-based BMG below its T, leads to a decrease in impact fracture toughness though evidence of crystallization can not be seen under microscope [28] Nature of the fracture surface also changes substantially With the increase in the annealing time, propensity of shear band formation decreases and the

Microstructural dependence of mechanical properties in bulk metallic glasses

material becomes brittle This behavior associated increase in viscosity

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Figure 8 Normalized impact toughness and transition in fracture behavior with increasing amount of crystallinity in La-based BMG.

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Annealing above T, leads to crystallization Partial crystallization increases strength of the BMGs However, controlling the shape, size and volume fraction of precipitated phase is necessary to optimize the mechanical performance of such systems It is generally observed that up to 30 vol.% of crystallization in the amorphous matrix, the strength increases whereas beyond this limit, a precipitous drop in the fracture strength of the alloy is observed as exemplified in Fig 7 [29] Also, the fracture morphology changes, from ductile vein type fracture to brittle intergranular cleavage type fracture Figure 8 represents the fracture behavior of a BMG with increasing amount of crystallinity Commensurate with the change in fracture morphology, marked changes in other physical properties such as viscosity and elastic modulus of the partially crystallized alloys are also observed, Fig 9 [29] This type of transition is attributed to the attainment of percolation threshold and networking of the crystalline phases At lower amount of crystallization, deformation takes place by viscous shear deformation D u n g this deformation, a considerable rise in temperature can be seen, which results in localized melting of the amorphous phase Residual amorphous phase accommodates most of the plastic deformation through the formation of shear bands and acts as a crack shield With increase in crystallization, shear band and cleavage dominate the nature of fracture and at higher levels o f crystallization, intergranular cleavage type fracture takes place [30] This change in the fracture behavior can also be explained on the basis of the viscoelastic response time As viscosity of the material increases with annealing and with the increase in crystallization, charactenstic response times also increase As a result of this tendency of the amorphous and partially amorphous alloy towards vlscous deformation decreases under the condition of same strain rate

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Figure 9. Variation in viscosity and elastic modulus with crystallization for La-based BMG Hardness tests on these systems show evidence of plastic flow in the form of shear bands There is a drastic increase in hardness (and corresponding loss in ductility) upon heat treatment in the supercooled liquid region In the amorphous alloy shear bands can be seen around the indents and with the increase in annealing time and crystallization tendency for shear band formation decreases At large crystallizations, cracks emanate from the edges of the indent Indentation behavior of amorphous and partially crystallized Pd-NI-P

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and Zr-Cu-Ni-A1 BMG [31] has shown pile-ups at the edges of the indents. Examination of the subsurface deformation patterns (obtained using the bonded interface indentation technique) shows semicircular and radial shear bands at the interface. With increase in crystallinity density of semicircular shear bands decreases with a increase in radial shear bands. Cracks can be seen when the BMG is totally crystallized. In all the experiments constancy of the normalized deformed zone size can be seen. This observation proves the validity of the expanding cavity model and the pile-up at the edges substantiates the validity of the slip line field theory. Kim et al. [32] have reported the formation of nanocrystals by performing indentation tests on BMGs. The free volume theory is found to be very useful in explaining the mechanism of flow and fracture of metallic glasses. CONCLUDING REMARKS

Bulk metallic glasses are important materials, not only because of the unique combination of properties exhibited by them, but also because of the fact that they can be used as precursors for bulk nanocrystalline materials. From the limited studies conducted on the nanocrystalline materials, it can be concluded that their properties are better than those of bulk metallic glasses. The important point to note is that their properties are very sensitive to the microstructure. In order to precisely define a microstructure, the four basic parameters, i.e. phase, shape, size and volume fraction of precipitates are to be taken care of. While synthesizing ex situ composites, volume fraction, shape, size of the second phase particles can be controlled independently. In case of in situ composites, numerous choices exist. In-depth knowledge of phase selection sequence and selection of processing parameters is needed. There are a few studies in the growth behavior of the phases. In nanomaterials, interface to volume fraction is very large. The interface structure is the least studied and hence, understood in these systems. This, unless clearly understood, may lead to hindrance in our ability to design desired microstructures. While nanomaterials can be processed by powder compaction, their production using BMGs as precursors avoids problems (inherent to compaction) such as residual porosity and surface contamination. Nanocomposites can be considered to be more stable than their “parents” because the nanocrystals have very low grain growth rate and the residual amorphous phase becomes resistant to further crystallization. Mechanical behavior of the all these phases may be distinctly different and they should be treated separately. As has been observed from the mechanical behavior of BMGs and composites, they are highly sensitive to morphology and volume fraction of the precipitates. In order to design a microstructure with optimum and reproducible mechanical properties, proper understanding of the above parameters is needed. Thus, broadly speaking, the combination of amorphous regions and complex crystallites in the microstructure has the potential to revolutionize technological development. ACKNOWLEDGEMENTS

The authors would like to thank Profs. K. Chattopadhyay, V. Jayaram, B. S. Murty, and Drs. S. Banerjee, G. K. Dey and N. Nagendra for the fruitful interactions and discussions on various topics related to BMGs. They would also like to acknowledge the collaboration with Prof. A. Inoue and Drs. D. V. Louzguine and N. Nishiyaina of the Institute for Materials Research, Tohoku University, Sendai, Japan and Prof. Y . Li of National University of Singapore. Research funding from the Board of Research in Nuclear Sciences (DAEOIMMTISRGI105) is gratefully acknowledged.

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Nan0 and Microstructural Design of Advanced Materials M.A. Meyers, R.O. Ritchie and M. Sarikaya (Editors) 02003 Elsevier Ltd. All rights reserved.

THE BOTTOM-UP APPROACH TO MATERIALS BY DESIGN W.W. Gerberich, J.M. Jungk and W.M. Mook Department of Chemical Engineering and Materials Science University of Minnesota Minneapolis, MN 55455

ABSTRACT Bottom-up approach implies understanding the building blocks and then assembling them into a useful structure. For nanoparticle and multilayer composites used in aggressive loading environments, this requires an understanding of the length scales controlling the strength and toughness of the blocks. Here, we examine both nanospheres of silicon and thin films of Au in the 30 to 300 nm regime. With mechanical probing by nanoindentation we show that length scales can be defined by volume to surface ratio with connectivity to dislocation evolution. These can predict to first order the variations in hardness that may be initially high due to an indentation size effect but then later dislocation harden due to a back stress mechanism. For small nanospheres of Si, hardnesses in the 15-30 GPa regime are measured, while for very thin Au films the apparent hardness can vary from 2 to 6 GPa.

INTRODUCTION In 1964, nearly four decades ago, the Proceedings of the 2nd Berkeley International Materials Conference addressed “High-Strength Materials” [ 11. The seeds of “materials by design” were strongly evident in at least half the papers with Friedel [2], Zackay and Parker [2], Honeycombe, et al. [2], Thomas, et al. [2], Davies [2],Westbrook [2], and Drucker [2] all discussing how to improve hardness and strength by refining the microstructure. These top-down approaches were typified by Drucker’s discussion of size effects associated with going from the macroscale to the microscale. There he suggested that a large size effect should be apparent in a WC-Co composite with a dislocation density of 10’4/m2if the Co layers were decreased from 1 pm to 0.1 pm but not if one went from 10 pm to 1 pm. Present-day discussions are not so different, with the main change being that we are expanding the size effect paradigm to include the nanoscale. Also, it’s not the size scale effect so much, but what the length scales are and how one measures and physically describes them. In two ongoing studies on thin films and on nanoparticles we have measured the length scale and shown it to be characterized by a volume to surface ratio (V/S). If you can now relate the mechanical property of interest to this length scale, then from a bottom-up approach one would be poised to produce materials by design. We briefly describe

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W.W. Gerberich, J.M. Jungk and W.M. Mook

212

the theoretical basis for why V/Smight represent an appropriate length scale for the hardness of films and nanospheres. We then present two sets of hardness data on silicon nanospheres and Au thin films.

THEORETICAL BASIS We originally became interested in length scale effects through very shallow depth nanoindentation of single crystals [4]. Here, the volumes of plasticity were extremely small. The motivation was to evaluate the indentation size effect (ISE) at the nanometer scale using spherical diamond tips. Following a suggestion by Baskes and Horstemeyer [5],we considered carefully the effect of surfaces at these small volumes. For shallow depths we discovered that the volume to surface ratio was constant for four single crystals of Au, Al, W and Fe-3wt%Si oriented in the . This led to a V/Slength scale concept that could be used to predict the ISE. With &= VIS,it was shown that [4]

where o,, was the bulk yeld stress, 6, was the penetration depth or tip displacement, and R was the indenter tip radius. Using various tip radii, Eqn. 1 predicted hardness vs. penetration depth for these four single crystals. Later this approach was applied to thin films [6] and nanoparticles in the form of single crystal nanospheres [7]. While we described the length scale in a similar way, no detailed comparison of the resulting mechanical response for the different geometries was conducted. As illustrated in Fig. 1, we schematically interrogate a bulk single crystal, a thin film of thickness, h, or a nanosphere of diameter 2r,. The schematics roughly indicate the contact diameter, Za, to be the same in all three cases. For a length scale in terms of V/S,we take the surface of contact to be between the diamond tip and the deforming crystal except for the nanosphere which involves a top and bottom contact. Alternatively, since the whole surface of the nanosphere is deformed one might use the entire spherical surface. This leads to two possible interpretations of length scale from V/S giving the two choices noted in Fig. 1. For consistency we will use the contact radius, a , and its surface area to illustrate the point. In Fig. I , the plastic zone diameter is 2c for bulk crystal and film but 2r for the

I

I

v

2c3

S

3a2

V S

-

c2h a'

Figure 1: Schematic of length scales for a conical diamond probing a bulk single crystal, a thin film or a nanosphere. Here, 2a and 2c are contact and plastic zone diameters, h is the film thickness and r is the nanosphere radius.

The bottom-up approach to materials by design

213

nanosphere. Here we drop the subscript from r, because of constancy of volume. From previous studies it is known that cla 3 is fairly typical for many indentation conditions. Assume then that cia 3 for a 100 nm contact radius into a bulk single crystal, a 100 nm thick film or a 100 nm diameter nanosphere. The length scales corresponding to the V/Svalues indicated in Fig. 1 would be 1800 nm, 900 nm, and 8.33 nm, respectively. Not too surprising is the factor of two decrease from bulk to thin film. However, the two order of magnitude decrease for the nanosphere suggests a possible large change in behavior. One should be careful here as we are discussing single crystal behavior. The length scale appropriate to mechanical behavior for thin films may well be truncated by a nanocrystalline grain size length scale if these were sputter deposited for example. For small contacts this may not be too serious since the nanocrystalline grain size may approach the size of the plastic zone. It should be mentioned here that if the whole nanosphere surface were used, giving V/S= ri3, that the length scale would still only be 16.7 nm.

-

-

To assess the effect of these far-ranging length scales on mechanical behavior, we examine the variation in hardness as determined from monotonically increasing deformation of either a nanosphere or a thin film. While only two general results are examined in detail, the implications are considerable. EXPERIMENTAL PROCEDURES We choose not to present procedures in depth here but to direct the reader to several recent publications for the preparation of the single crystal nanosphere and the polycrystalline thin films used. Silicon single crystal nanospheres were grown by a hypersonic plasma particle deposition process [8]. These directed beams may be rastered to deposit lines of nanoparticles with relatively narrow particle size distributions in the range of 10 to 100 nm. With an atomic force microscopy based nanoindenter, these may then be measured as to their size and then deformed by crushing them between a sapphire substrate and a large radius diamond tip. For details see reference [7]. For determining hardness it is fairly simple since geometric contact areas can be used after plastic deformation. As will be shown, even silicon, with a brittle to ductile transition near 700°C in tension, deforms like a relatively ductile metal when compressing these nanospheres at room temperature. In a separate study of sputter deposited gold, fairly thin nanocrystalline films 30 nm thick were deposited onto silicon wafers. These were then nanoindented with a 1 pm diamond tip to a series of increasing depths. Contact radii were both measured and calculated while the plastic zone illustrated in Fig. 1 could be measured by AFM where the pile-up merges with the zero plane. See reference [9] for additional details. Length scales as determined from geometry, as in Fig. 1, were compared to thin film hardness as a function of depth. Results for the deformation of both nanospheres and thin films follow.

RESULTS AND DISCUSSION First consider the load-displacement response for a single nanosphere. In Fig. 2(a) we seen AFM height image of a 55 nm silicon nanosphere prior to deformation. It appears to be much wider since we are imaging the sphere with a very large 1 pm spherical diamond tip. Deconvolution shows this to be a 55 nm sphere as indicated by the height. The load displacement curve in Fig. 2(b) indicates considerable plastic deformation noting that a 27.5 nm displacement would be 50 percent strain taking the height to be the gage length. The unloading slope is quite steep with nearly all the displacement irreversible. Since the height was originally 55 nm and the apparent height of (55-50) 5 nm is too small, we conclude

W.W. Gerberich, J.M. Jungk and W.M. Mook

214

80 60

z a -50

0

1

40

2

3 80

Figure 2: Deformation of silicon nanospheres: (a) AFM cross-section of a 55 nm diameter nanosphere prior to deformation, (b) load-displacement curve for the particle in (a); (c) AFM crosssection of a 43 nm diameter nanosphere prior to deformation; (d) load-displacement curve for the particle in (c) that the silicon particle fractured with the tip sliding in between the vertical cavity formed by the two hemispheres moving laterally apart Since the large 1 pm diamond is still in contact with both halves, we simply overestimate the contact area and underestimate the hardness ( H A ) Given the shape of the curve, we believe this occurs in the vicinity of 6 = 25 nm A much more normal loading curve I S obtained for the smaller 43 nm sphere (see Fig 2(c)) and Fig 2(d) By determining the contact areas from the spherical geometry under load [7] we determined the hardness (Pha’) versus normalized displacement (6h) Note that the appropnate radius, Y, is for the nanosphere and not the diamond indenter since Y (( R. For the 55 nm diameter nanosphere data in Fig 3 we see that the hardness decreases continuously with increasing displacement. It immediately occurred to us that this was like an indentation size effect and employed the analysis that had worked well for shallow indentations of single crystals [4] For the initial deformation of the defect free single crystal nanosphere this IS a realistic expectation From the previous analysis, we found the appropriate length scale to be V/S and for a sphere this would be 4/3 xr3/4nr2or r/3 From Eqn 1 this would give the ISE [4] for a nanosphere to be

The bottom-up approach to materials by design

215

Analysis of length scales showing hardness versus normalized displacement for a 55 nm Figure silicon nanosphere. 113 with an appropriate yield strength for the deformation of the 55 nm particle. With o,, = 36 GPa, it is seen that this fits the initial portion of the loading curve at small displacements. The deviation near a Sir of 0.5 was initially thought to be associated with a dislocation back stress at a pile-up. The concept is that a dislocation pile-up as produced by prismatic punching at the sphereidiamond contact would provide a large back stress. Upon calculating this from Hirth and Loethe [ 101, we find this to be, HZ-

P a

n(1- v)x

-

-

P6 n(1- v)r

(3)

the latter resulting from the number of dislocations in the pile-up being 6ib. Using 66 GPa for the silicon shear modulus and a Poisson’s ratio of 0.218, this gives H 3 26.9 GPa 6/u. This intersects the ISE curve about where the data start deviating but the data do not follow the trend. Rather than the silicon particle hardening, we propose that it fractures. With the large release of dislocation loops, the local stress could exceed the fracture stress whereupon the particle halves split apart. This gives rise to extra displacement as the two halves slide apart. This resulted in the fairly large jump seen in Fig. 2@) near 20 nm. Beyond this the actual contact area would be less than experimentally determined from the measured displacement: This would result in the hardness data beyond the fracture region being clearly underestimated. A more realistic result was obtained for the 43 nm particle shown in Figs. 2(c) and = 36 GPa in Fig. 4(a). As is seen in 2(d). Hardness follows the ISE curve of Eqn. 2 using the same oYs Fig. 2(d), the load-displacement curve was much smoother with no displacement jumps. Even if the particle did fracture, it apparently stayed together. We did have to scale the contact area for S > r assuming a constancy of volume. This was accomplished by assuming a geometrical contact for displacements up to 6 = Y and then setting an equivalent right cylinder volume equal to the sphere volume for 6 > r. The same scaling had been used in Fig. 3. For the 43 nm nanosphere, we see in Fig.

216

W.W. Gerberich, J.M. Jungk and W.M. Mook

n

m

c. I

Figure 4: Analysis of length scales showing hardness vs. normalized displacement for a 43 nm silicon nanosphere: (a) analysis for increasing hardness at deeper depths utilizing a dislocation back stress; (b) analysis for increasing hardness using a volumeisurface length scale. 4(a) that the hardness goes through a minimum near the point where Eqs. 2 and 3 intersect. Here, we believe that the calculated hardnesses are more representative and similar to the hardness observations seen recently as produced by repetitive work hardening [ 7 ] . Taking a closer look at the phenomenology, we note that the hardness follows a dislocation back stress argument more closely at higher displacements in Fig. 4(a). In a future paper under preparation [ll], we show that a work per unit fracture area approach can lead to a length scale given by

es =

PBYs

(4)

2 2 0 n(1-v ) YS

where E and cry. are modulus and yield strength, ys is the surface energy and p'is a constant which depends on the character of the dislocation structure created, One might expect such an approach to be more appropriate where the plastic work involved with dislocation loop evolution become dominant at larger displacements. Here, we use the second ViSdescription of k', in Fig. 1 and note that a* 6r for the nanosphere, giving

-

Since the hardness is some multiple of the yield strength H - p " ~ , , , w e combine constants,

P = P')3"''

and obtain from Eq. (4)

The bottom-up approach to materials by design

0

(a)

2 s

217

5 0 I-lm

10 0

7 5

(b)

Figure 5: Indentation into a 300 nm Au film supported on a silicon substrate image, (b) mid-plane cross-section

(a) AFM height

Since this is determined from a work per unit surface area concept, i t is not surprising this mimics the Griffith criterion except now the length scale is that associated with the defonnation process With a single fitting constant of = 6, this fits the 43 nm sphere data well in Fig 4(b) for the latter deformation stages Here, we use Eq. (6) for hardness with f, defined by the last relationship in Eqn. 5 allowing H to be determined as a function of S/r While it is tempting to suggest that the measured hardness curve is a simple superposition of these two hardening mechanisms, this is premature and awaits further material studies Given this description of nanosphere deformation in terms of VIS length scales, we next turn to thin films where 300 nm Au films had been sputter deposited on Si A typical conical diamond with a 1 pm spherical tip produces relatively constrained plastic deformation in very thin films Such a result is shown in Fig 5 with the pile-up and plastic zone size indicated in the cross-sectional AFM profile From a series of such indentations to different depths, measurements of contact diameter and plastic 5

a=15

[

.

ah2

=-

a

m

u

Figure 6: Analysis of normalized plastic zone (cia) as a function of normalized contact ( d h ) fur determining a length scale, i?,, in 300 nm Au films.

218

W.W. Gerberich, J.M. Jungk and W.M. Mook

zone size indicated in Fig. 6 allowed a determination of the length scale. The data fit of cia vs. aih allowed a length scale, as defined by Fig. 1 for thin films, to be given by fj

ah a

=-

(7)

where h is the film thickness and a is the contact radius. As described elsewhere [6], this led to a fracture mechanics criteria for slow-crack growth representative of R-curve behavior. Here, for hardness we assume that initial deformation exhibits little if any ISE as these deposited Au films have a large inherent defect density. If the initial deformation is predominantly controlled by a dislocation back stress argument, then Eqn. 3 is appropriate as modified by the slip band length being the plastic zone size, c, and the fact that this is constrained plastic flow with H 3 9 , . With these modifications Eqn. 3 becomes HE-. 3P6 n(1- v)c

-

Comparing this to measured hardnesses in Fig. 7(a) gives a surprisingly good accountability of the hardness variations with increased normalized depth. This strongly suggests that the hardness of relatively ductile films on a rigid substrate need not take into consideration the strength contribution of the substrate as many composite approaches have suggested. In many ways this behavior is analogous to the silicon nanosphere being squeezed between two high stiffness, non-yielding platens. The hardening comes from the internal defect structure in the nanosphere. Similarly, the material trapped between the spherical diamond tip and the silicon substrate can harden due to the increased dislocation density being confined to decreasingly smaller spaces. It is significant that the plastic zone about the

The bottom-up approach to materials by design

219

indentation in those thin films increased as giving hardness proportional to 6”’from Eq. (8). Similarly, from Eqs. 5 and 6 it is seen that the hardness of the nanospheres would increase as Since the dislocation densities would increase in proportion to the displacement, this would give flow stress proportional to the square root of the dislocation density. This suggests a future area of investigation involving transmission electron microscopy. To assess whether our length scale argument held up for this thin film, we utilized the same Eqn. 6 with a tensile modulus of 80.8 GPa, a surface energy of 1.485 Jim’ and a Poisson’s ratio of 0.35 appropriate to gold. The length scale as given in Fig. 1 was used. For a reasonable fit as shown in Fig. 7(b), a considerably sharper increase in measured hardness with is observed than predicted by Eqn. 6. This may be partially a result of measurement difficulties for these extremely thin films but more likely a shortcoming of attempting to apply a model for single crystal thin films to nanocrystalline ones. The encouraging aspect is that for the data fit in Fig. 7(b), p was taken to be 15 whereas for the fit in Fig. 4(b) for the nanosphere it was 6. This difference could easily be the difference in constraint with the nanosphere exhibiting little and the thin film being fully constrained from the standpoint of contact mechanics. SUMMARY

This contribution purports to demonstrate the importance of length scales, their measurement, and their inclusion in design rules for materials performance. Here, we’ve emphasized two important aspects of volumeisurface and dislocation slip-band morphology in length scale interpretations. These are shown to be important in understanding the hardening mechanisms in both silicon nanospheres and thin gold films in the 30-300 nm regime. At very small increasing displacements into single crystal nanospheres, it is seen that hardness decreases with a (l/S)”’dependence. However, at larger displacements, it is seen that hardness can then increase with a(6)’” dependence due to dislocation hardening. The increase in film hardness with depth is predicted to give a similar(6)’” dependence when factoring in how the plastic zone increases with increasing depth of indentation. These length scales for nanospheres and thin films should eventually lead to design rules for incorporation into small volume structures. ACKNOWLEDGEMENTS

This work was supported by the National Science Foundation under grant DMI-0103 169 and an NSFIGERT program through grant DGE-0114372. One of us (JMJ) would like to acknowledge support of Seagate Technology through the MINT program at the University of Minnesota. REFERENCES 1.

V. F. Zackay, High Strength Materials (New York, NY: J. Wiley and Sons, Inc., 1965).

2.

J. Friedel, “High Strength Materials,” (ibid.), 1-11; V. F. Zackay and E.R. Parker, “Some Fundamental Considerations in Design of High-Strength Metallic Materials,” (ibid.), 130-166; R. N. K. Honeyconlbe, H. J. Harding and J. J. Irani, “Strengthening Mechanism in Ferritic and Austenitic Steels” (ibid.), 213-250; G. Thomas, D. Schmatz and W. Gerberich, “Structure and Strength of Some Ausformed Steels,” (ibid.), 251-326; G. L. Davies, “The Growth of Fiber

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W.W. Gerberich, J.M. Jungk and W.M. Mook

Structures from the Melt,” (ibid.), 603-650; J. H. Westbrook, “The Sources of Strength and Brittleness in Intermetallic Compounds,” (ibid.), 724-768; D.C. Drucker, “Engineering and Continuum Aspects of High Strength Materials,” (ibid.), 795-833. 3.

N. I. Tymiak, D. E. Kramer, D. F. Bahr and W. W. Gerberich, “Plastic Strain Gradients at Very Small Penetration Depths,” Acta Mater. 49 (2001), 1021-1034.

4.

W. W. Gerberich, N. I. Tymiak, J. C. Grunlan, M. F. Horstemeyer and M. I. Baskes, “Interpretations of Indentation Size Effects,” J. A ~ p lMech. . 62 (2002), 433-442.

5.

M. Baskes and M. Horstemeyer, private communication, Sandia National Labs, Livermore, CA (1999).

6.

W. W. Gerberich, J. M. Jungk, M. Li, A. A. Volinsky, J. W. Hoehn and K. Yoder, “Length Scales for the Fracture of Nano-structures,” Intern. J. of Fracture (2003), accepted.

7.

W. W. Gerberich, W. M. Mook, C.R. Perrey, C. B. Carter, M. I. Baskes, R. Mukherjee, A. Gidwani, J. Heberlein, P. H. McMurray and S. L. Girshick, “Superhard Silicon Nanospheres,” JMech. Phvs. Solids (2003), in press.

8.

F. DiFonzo, A. Gidwani, M. H. Fan, D. Neumann, D. J. Iordanoglu, J. V. R. Heberlein, P. H. McMuny, S. L. Girshick, N. Tymiak, W. W. Gerberich and N. P. Rao, Aml. Phvs. Lett. 77 (2000), 9 10-9 12.

9.

D. E. Kramer, H. Huang, M. Kriese, J. Robach, J. Nelson, A. Wright, D. Bahr and W. W. Gerberich, “Yield Strength Predictions from the Plastic Zone around Nanocontacts,” Acta Mater. 47 (1994), 333-343.

10.

J. P. Hirth and J. Loethe, Theory of Dislocations, 2nd ed. (New York, NY: John Wiley and Sons, 1982).

11.

J. M. Jungk, W. M. Mook and W. W. Gerberich, “Nanoindentation Length Scale Measures in Small Volumes,” in preparation.

Nan0 and Microstructural Design of Advanced Materials M.A. Meyers, R.O. Ritchie and M. Sarikaya (Editors) 02003 Elsevier Ltd. All rights reserved.

THE ONSET OF TWINNING IN PLASTIC DEFORMATION AND MARTENSITIC TRANSFORMATIONS Marc AndrB Meyers', Matthew S. Schneider', and Otmar Voehringer* 'University of California-San Diego, Dept. of MAE, La Jolla, CA 92093 USA 'University of Karlsruhe, Inst. for Matls. Research., Karlsruhe Germany

ABSTRACT A quantitative constitutive description for the criterion postulated by Thomas [l-31 for the morphology of martensitic transformations is presented. Thomas observed that the temperature and strain-rate sensitivities of slip are much higher than those for twinning, rendering twinning a favored deformation mechanism at low temperatures and high strain rates. Constitutive relationships for slip and twinning are presented and applied to the martensitic transformation in steels: the lath to plate morphology change that is observed with increasing carbon content is successfully predicted by calculations incorporating the two modes of deformation. The Hall-Petch coefficient, for the inclusion of grain size effects is two times larger for twinning than slip. A simple calculation of the strain rates during martensitic transformation is also provided. For FCC metals, the constitutive description for the slip-twinning transition incorporates the effects of material (stacking-fault energy, grain size, composition) as well as external (temperature, strain rate) parameters successfully. It can also applied to the shock compression regime, where the shock front thickness (and, consequently, strain rate) is related to the peak pressure by the Swegle-Grady relationship. Predictions are compared to seminal shock loading work by Johari and Thomas [4] and Nolder and Thomas [5] demonstrating that there is a threshold pressure for twinning in copper and nickel.

INTRODUCTION It was shown by Thomas [ 1-31 that slip and twinning are competing deformation mechanisms and that they have a profound effect on the mechanical properties of martensitic steels and FCC metals like copper and nickel. The schematic representation by Thomas [2] is shown in Figure 1. This plot, although qualitative, provides deep insight into the mechanical response of metals and alloys, which can deform by slip, twinning, or martensitic transformations. Figure 1 shows that slip has substantially higher temperature dependence than twinning; hence, slip and twinning domains are established. Martensitic transformations are displacive, virtually diffusionless transformations with the thermodynamics and kinetics governed by the transformation strains. In steels, the martensite structure undergoes a drastic morphological transition as the carbon content reaches the 0.6-1 .O weight percent region. Early German literature classified the two regions into Schiebung and Umklapp; the current nomenclature is lath and plate where the basic difference resides in the deformation mode: the transition from slipped (lath) to twinned (plate) martensite. Figure 2 shows the change in Ms as well as the two modes as a function of increasing carbon content [6].Figure 3 shows transmission electron micrographs of the two morphologies in different compositions of steel. This paper provides a quantitative description of the transition from

221

M.A. Meyers, M.S. Schneider and 0. Voehringer

222

lath to plate martensite by applying the Zerrilli-Armstrong constitutive equation. It is a straightforward method of predicting the threshold carbon concentration for the nucleation of plate martensite as a function of strain rate, temperature, and grain size.

\

\

?

n

1

MARTENSITE SUBSTRUCTURE DISLOCATED

TEMPERATURE

4

Figure 1: Variation of the stress for slip and twinning as a function of temperature. Composition variations are expected to affect the slip-twin cross-over as suggested by the arrows. (Adapted from Thomas [2]). 'F

P 600t"

4m1

-

t

0 0

LATH

-l2zi2L MIXED

PLATE

0.2

0.4

0.6

0.8

1.0

WEIGHT PERCENT CARBON

1.2

1.4

1.6

Figure 2: Variation of Ms temperature with carbon content; notice transition from lath (slipped) to plate (twinned) morphology; from Marder and Krauss[l 13.

The onset of twinning in plastic deformation and martensitic transformations

(c)

223

a,

Figure 3: (a) Twinned plates of martensite and residual austenite in Fe-33Cr- 01C; (b) Twinned and dislocated martensite in Fe-28Ni-OtC; (c) Twinned plates of martensite in Fe-8Cr-1C; from Thomas [3]. CALCULATIONAL PROCEDURE The calculations require constitutive equations for slip and twinning that have the appropriate temperature and strain rate dependencies. These equations were implemented by Meyers et al. [7,8] into a sliptwinning transition criterion and will only be briefly described herein By considering slip and twinning as competing mechanisms, and equating the appropriate constitutive equations, one obtains the critical condition:

where 05 and OT are the slip and twinning stresses, respectively. Constitutive Description of Slip There are numerous equations that successfully incorporate the strain, strain rate and temperature effects and predict the mechanical response over a broad range of external parameters. The Zerilli-Armstrong [9] equation is used here to describe the lath to plate transition in martensite. It is modified to incorporate the solid solution hardening effects induced by carbon additions. There are two different forms of the equation applicable to FCC and BCC metals. The barrier size is quite different: dislocation forest dislocations are considered the primary barriers for FCC materials, whereas the Peierls-Nabarro stress is the principal obstacle for BCC materials. These differences are responsible for higher strain rate and temperature sensitivity for the BCC structure. When iron-based alloys undergo the martensitic transformation, the FCC structure transforms to BCC or BCT. This newly created structure has to undergo a complex deformation to accommodate the Bain and lattice invariant strains. The ZerilliArmstrong equation for the BCC structure has the form:

M.A. Meyers, M.S. Schneider and 0. Voehringer

224

The variables are strain, E, strain rate, E and temperature, T. The coefficients C,, Ct, Cr, Ch, and C, arc experimentally obtained parameters. The parameters, their physical meanings and values chosen are for pure iron [ 9 ] :

1033 MPa 0.00698 0.000415 266 MPa 0.289

CS: Stress Constant Ct : Thermal Softening Constant Cr : Strain Rate Constant c h : Strain Hardening Constant Cn. Strain Hardening Constant

The terms og and oc represent the athermal components of stress, which have minimal strain rate and temperature dependence. The grain size term, og represents the grain-size dependence, which is represented by a Hall-Petch relationship: og = k,d

-112

(3) I12

where ks for low carbon steels is found to vary between 15-18 MPdmm [lo]. An average value of 16.5 112 , MPdmm is used in the calculations. Figure 4 shows the Hall-Petch plots for both slip and twinning. The value matches well with experimental data by Marder and Krauss [I 11.

I100

-

(Armstrong and Worthington)

900

Kt data for Fe-C (Magee, et al.; McRickard and Chow)

m

2 700

A

v

v) v)

W

0

0

0

’** 0

.b ’

0

0

0

500

H
300

100

0

10

20

30

40

50

d-”* (mm-’l2) Figure 4: Effect of grain size on stress for slip (k,) and twinning (k,)

The onset of twinning in plastic deformation and martensitic transformations

225

~ J Crepresents the contribution to strength due to the presence of solute atoms (in this case, carbon). It is observed that the flow stress at large concentrations of solute varies with the square root of carbon content [ 121:

(4)

oC=k [carbon]"

n is often given as 0.5 and for this case k is 450 MPa. For lower concentrations, Pickering and Gladman [ 131 use a linear fit to describe the solid solution hardening effect of carbon in austenite with a coefficient of 324 MPa/wt% carbon. Figure 5 shows the predicted stress-strain curves for different (a) grain sizes; (b) carbon contents; (c) strain rates; and (d) temperatures. The calculated curves agree well with experimentally-obtained curves.

1000

L====l STRAIN

STRAIN

(4

(b)

-z

-

W rn

v)

rrn

Frn

70 650

m a

r

rn

?rn

----us+zao

0

0.2

0.4 0.6 STRAIN

0.8

1

(d) Figure 5: Calculated stress-strain curves (assuming slip) for different: (a) grain sizes; (b) carbon contents (D=100 pm; strain rate=104 s-'); (c)strain rates; (d) temperatures above M,.

M.A. Meyers, M.S. Schneider and 0. Voehringer

226

Constitutive Equation for Twinning In these calculations, the twinning stress is assumed to be relatively independent of strain, temperature, and strain rate, in contrast to slip processes and therefore no work hardening effects are taken into account. Nevertheless, the grain-size dependence is much larger. Indeed, kT values are 2-4X greater than ks values. The following equation was used: (TT = (TO

+ kTd1/2

(5)

Armstrong and Worthington [ 141 report for Fe-3%Si: k~=66.3MPa/mm1/2. For low-carbon iron, McRickard and Chow [15] and Magee et al. [I61 report values of 45.5 MPdmm'". This latter value is used here. Figure 6 shows the experimental results by Magee et al. [16] as well as the best-fit plot for the effect of carbon on the twinning stress of steel: 0=662 MPa*[at%C]'

15*

(6)

460 44 0 h

m

420 400 380 360 340 320 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 A t % Carbon

Figure 6: Effect of interstitial carbon on the twinning stress of iron-carbon alloy (from Magee et al. [16]). The twinning stresses are extrapolated from this curve for higher concentrations of carbon. Figure 7 shows the predicted stress-strain curves for different (a) grain sizes and (b) carbon contents. Marfensitic Strains and Strain Rates: Figure 8 shows, in a schematic fashion, the growth of martensite lens. The material within the expanding lens is subjected to Bain and lattice invariant strains. During martensitic transformations, the strain rate can be approximated by:

f=S-" D

(7)

The onset of twinning in plastic deformation and martemitic transformations

221

where v is the growth velocity for the martensite lens, y is the transformation strain (y = 0.2) and D is the grain diameter. In Figure 8, two growth directions are indicated: longitudinal and transverse growth.

(4 (b) Figure 7: Room-temperature stress-strain curves assuming twinning for different grain sizes and carbon contents. Meyers [17] has analyzed the two modes and discusses the two velocities. The longitudinal growth velocity has been measured by Bunshah and Mehl [18] for Fe-Ni-C alloys; it was found to be equal to 1,OOds. Schoen and Owen [19] measured the lateral growth velocity for Fe-1ONi-C alloys with carbon contents between 0 and 0.010. The values varied from 0.01 to 1 m/s. Considering a range of velocities of 1-1000 d s , one obtains a range of strain rates:

i= 0 . 2 0 * v ~

D

1 - -(0.2 D

-9

200)

For a grain size of 100 pm (a reasonable value for Fe alloys), this provides the following range of strain rates: f 2x103 + 2x106s-* w

-

-

v

z

-

y-

-, ,

Figure 8: Schematic representation of growth of martensite lens with longitudinal (Vl)

M.A. Meyers, M.S. Schneider and 0. Voehringer

228

’‘

2

7 K

1:

a:

a

In

0.5

:

1

\

-&- 10 urn

’’

Wt% Carbon

Figure 9: Predicted carbon content for slip-twinning transition in martensitic transformation in steels with different grain sizes a function of carbon content; shear strain for martensitic transformation equal to 0.2.. In the calculations conducted and reported herein, a strain rate of lo3 s-’was assumed. It is interesting to notice that the strain rate along the mid-rib (region subjected to longitudinal growth) the strain rate is much higher. It is also observed that this region is more prone to twinning. Often, one observes martensite lenses with twinning along the mid-rib and dislocations in the latcral growth regions. The results of the computations are shown in Figure 9. Calculations were conducted for three grain sizes: 10, 100, and 1000 pm. For the 100pm grain size, the predicted transition from dislocated to twinned martensite is in excellent agreement with the observed results: 0.55 wt% C. For the other grain sizes, significant differences are observed. It would be interesting to verify whether the predictions of this simple model are corroborated by experiments: a reduction of grain size favors dislocated (plate) martensite. PREDICTED VALUES IN SHOCK COMPRESSION The procedure presented in this section [7,8] can be used to predict the critical pressure for twinning in shock compression experiments. The early experiments performed by Johari and Thomas [4] in Cu and Cu-A1 and Nolder and Thomas [5] in Ni demonstrated that there is a threshold pressure for twinning. It has been established by Murr [20] that this pressure is a function of stacking-fault energy for FCC metals. The application of this criterion to the shock front necessitates the knowledge of the strain rate. The strain rate at the shock front has been established by Swegle and Grady [21] to be:

P

=

k,i’14

(9)

The constitutive response of the copper monocrystal is represented by the modified mechanical threshold stress (MTS) expression below; the parameters are taken from Follansbee and Gray [22]. The MTS model and parameters are defined by Follansbee and Kocks [23]. A modified MTS equation is used, with values of p=1/2 and q= 3/2, respectively [24]. The value of go is 0.8 [25].

The onset of twinning in plastic deformation and martensitic transformations

229

We apply Eqn. (1) to Eqn. (lo), assuming a constant CTT. We find E‘ from Eqn. 10, which is inserted into Eqn (9). This provides a first estimate of the pressure, P, where f(6) is an experimentally obtained stress-strain relationship (polynomial expression). This pressure is then used to calculate the shock strain and temperature through the Rankine-Hugoniot relations. This procedure is iterative. Figure 8 shows the application of this method to copper. The plot shows how the initial temperature and grain size affect the threshold shock pressure. The calculated threshold pressure for a monocrystal (10 mm grain size) shocked fiom an initial temperature of 300 K is 17 GPa. This compares favorably with experimental results by De Angelis and Cohen [26]: 14 GPa. Recent laser compression experiments by Meyers et al. [27] yield a threshold stress in this range. Two transmission electron micrographs are shown in Figure 11: copper shocked at (a) 12 GPa (below the twinning threshold) and; (b) copper shocked at 40 GPa (above the twinning threshold).

20.0

19.5

2 19.0

0

$ 18.5

+T= 100 K +T= 200 K +T= 300 K -T= 400 K

\

01

m

20 18.0 E

2m 17.5 f!

if

17.0 16.5 16.0 0.001

o.or0

0.1 00

1 .ooo

10.000

Grain Size, mm

Figure 10: Calculated threshold stress for twinning in shock compression of monocrystalline copper (fiom Meyers et al. [S]).

M.A. Meyers, M.S. Schneider and 0. Voehringer

230

(4

(b)

Figure 11: Laser shocked monocrystalline copper at (a) 12 GPa (below the twinning threshold) and; (b) 4 GPa (above the twinning threshold. CONCLUSIONS

The slip-twinning transition criterion postulated by Thomas [ 1-31 and recently quantified by Mcyers ct al. [7,8] is applied to martensitic transformation. The constitutive response by slip is described by Zerilli-Armstrong equation with addition of interstitial strengthening term. A simple non-work hardening twinning equation was used. The model predicts change from lath to plate as carbon content exceeds 0.56 wt%. at a grain size of 100 pm. This is in agreement with experiments. It is interesting to notice that the predicted change in lath to plate morphology is dependent on the austenitic grain size. By the application of the Swegle-Grady relationship to the slip-twinning criterion, it is possible to extend the prediction to threshold pressure in shock compression. Johari and Thomas [5] observed a slip-twinning transition in shock compressed copper which was successfully calculated through the constitutive approach outlined here. It is therefore concluded that the Thomas criterion is successfully quantified. REFERENCES

Thomas, G (1965)ActuMet 13, 1211 Thomas, G (1971) Met Tranr 2,2373 Johari, 0 and Thomas, G (1965) Tranr ASM, 58,563 Johari, 0 and Thomas, G , (1964) Acfa Mat, 12, 1153 Nolder, and Thomas, G , (1 964) Acta Met 12, 227 Krauss, G (1 980) Pnnciples of Heat Treatment of Steel, ASM, Metals Park, OH, p 52 Meyers, M A . Voehringer. 0, and Chen, Y J , in 4dvnnces in Ttiinning, eds S Ankem and C S Pande, TMS, 1999, pp 43-66 8 Meyers. M A , Voehringer, 0 , and Lubarda, V , (200 I ) Acta Mut, 49,4025 9 Lerilh, F J , and Armstrong, R W , (1987)J Appl P b y .61, 1816 10 Pickermg, F B Comtitution and Propertley ofSteelr, hlaterialr Science and Technology 7, VCH Publishing, NY,1992 11 Marder, A R ,and Krauss, G ,Proc on the Strength ofMetaly and Alloyy, Vol 3, ASM. Metals Paik. OH, 1970, pp 822-823

1 2 3 4 5 6 7

The onset of twinning in plastic deformation and martensitic transformations

23 1

12. Pickering, F. B. Physical Metallurgy and the Design of Steels, Applied Science Publishers, Essex, England, 1978. 13. Pickering, F.B. and Gladman, T. (1963) T. Iron andSteel Inst. Spec. Rep. #81, 10. 14. Armstrong, R. W., and Worthington, P. J., (1974) in Metallurgical Effects at High Strain Rates, eds. R. Rohde, B. Butcher, J. Holland, and C. Kames. Plenum, NY, p. 41. 15. McRickard, S. B., and Chow, J. G. Y., (1965) Trans. AIME, 223, 147. 16. Magee, C.L., Hoffman, D.W. and Davies, R.G., (1971) Phil. Mag. 23, 1531. 17. Meyers, M. A., (1979) Acta Met., 28,757. 18. Bunshah, R. F., and Mehl, R. F., (1953) J. Metals, 5, 1251. 19. Schoen, F. J., and Owen, W. S., (1971) Met. Trans., 2,2431. 20. Murr, L. E., (1988) in Shock Waves in Condensed Matter, Eds. Schmidt, S. C. and Holmes, N. C., Elsevier, Amsterdam, pp. 315. 21. Swegle,W and Grady, D. E., (1983) J. Appl. Phys., 58,941. 22. Follansbee, P. S. and Gray 111, G. T., (1991) Matls. Sci. and Eng. 138,23. 23. Follansbee, P. S. and Kocks, U. F., (1988) Acta Met., 36, 81. 24. Follansbee, P.S., in Metallurgical Applications ofshock -Wave and High-Strain Rate Phenomena ed, L. E. Murr, K. P. Staudhammer, and M. A. Meyers, M. Dekker. 1986, pp.451. 25. Gray 111, G.T., in “Shock-Wave and High-Strain-Rate Phenomena in Materials”, eds. M.A. Meyers, L.E. Murr, and K.P. Staudhammer, M. Dekker, NY, 1992, pp. 899. 26. De Angelis, R.J, and Cohen, J. B. (1963) J. ofMetals, 15,681. 27. Meyers, M.A. Gregori, F., Kad, B., Schneider, M.S., Remington, B., Kalantar, D., Boehly, T., Ravichandran, G, and Wark, J. (2003) Acta Mat. 51, 1211.

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Nan0 and Microstructural Design of Advanced Materials M.A. Meyers, R.O. Ritchie and M. Sarikaya (Editors) Published by Elsevier Ltd.

CRYSTAL IMPERFECTIONS SEEN BY X-RAY DIFFRACTION TOPOGRAPHY R.W. Armstrong AFRL/MNME, 2306 Perimeter Road, Eglin Air Force Base, FL 32542-5910

Abstract

Internal lattice strains imaged via x-ray diffraction topography (XRDT) methods are presented for relatively low dislocation density, or dislocation-free, crystals, much as investigated for higher dislocation density materials by Professor Gareth Thomas and colleagues and students via transmission electron microscopy (TEM) methods. Relating to the broad range of materials covered today by The Minerals, Metals and Materials Society (TMS), various characterization-type results are shown to be obtainable for millimeter-to-centimeter size crystals exhibiting either metallic, ionic, covalent, or molecular (energetic) type bonding between their respective constituent atoms or molecules. Introduction

In retrospect, an especially important technical conference was held on the topic: “Direct Observation of Imperfections in Crystals” [ 13, that was sponsored by the Chemistry and Physics of Metals Committee of, then, The Metallurgical Society (TMS), now, The Minerals, Metals and Materials Society, American Institute of Mining, Metallurgical and Petroleum Engineers, in St. Louis, MO, during March 1-2, 1961. At the time, rather early dislocation observations were being reported, in connection with property measurements, via the several techniques of transmission electron microscopy (TEM), field ion microscopy (FIM), and x-ray diffraction topography (XRDT), as were recently pioneered along with dislocation etch pitting investigations. Professor Gareth Thomas and colleagues reported results on dislocation structures observed in deformed and recovered molybdenum polycrystals, presaging many other observations to come on a wide variety of engineering materials involved in multiple technical uses, as evidenced by the papers delivered in the present meeting by colleagues and students. Also, Professor George Smith, Oxford University, U.K., is reporting in the present TMS symposium on advances made via FIM. The present paper provides, on the one hand, updated information on characterization-type results obtained via several XRDT techniques, following a number of post-founding reports made in reference [l], for example, for transmission XRDT of sliced silicon wafers by A.E. Jenkinson and A.R. Lang. The technical conference proceedings was co-edited by J.H. Wernick and J.B. Newkirk, who, in the latter case, provided encouragement, because of his research effort with Berg-Barrett (B-B) reflection topography, to the present author and colleague, J.M. Schultz, for inclusion of first results reported for dislocation observations in cleaved zinc crystals. At the conference, G. Borrmann and K. Lehmann presented XRDT results obtained on a very nearly perfect germanium crystal via so-called anomalous transmission of x-rays; and, U. Bonse reported on crystal-monochromated XRDT results obtained on a similar low dislocation content silicon crystal.

233

R. W.Armstrong

234

Here, reflection, transmission, and monochromatic (beam conditioned) topographic observations are presented for characterization of dislocation influences in zinc, sapphire, cyclotrimethylenetrinitramine (RDX), and ammonium perchlorate (AP) crystals, plus layer deposition and diffusion implantation generated strains in otherwise perfect silicon crystals; in the latter case, achieved via line modified asymmetric crystal topography (LM-ACT). In addition, mention is made that the very appreciable advances now achievable via XRDT and related x-ray techniques were reviewed in 1995 in a Special Issue of Physics Today [2], including reference to synchrotron radiation source capabilities such as have been available, for example: CCLRC at Daresbury, U.K.; SSRL at Stanford University; CHESS at Cornell University; NSLS at Brookhaven National Laboratory; LURE at Orsay, FR, HASYLAB at DESY, Hamburg, DE; ESRF at Grenoble, FR; and, the Photon Factory, Japan. Results

Berg-Barrett (B-B) Observations in Zinc A stereographic projection description of the B-B reflection XRDT technique, as applied to dislocation observations made through the (0001) cleavage surfaces of zinc crystals, is shown in Figure 1. In the Figure, the inset drawing depicts the physical set-up corresponding to the left-side, zero laye: case, of cobalt Ka radiation being incident to the crystal (0001) at 6.1" and reflected from the inclined (1013) at a Bragg angle of 41.6" so as to give a diffracted beam at 77.1' from the (0001) specimen surface, thus traveling a distance as small as possible to the recording nuclear emulsion film. Point-by-point connection between the local diffracted intensity and the real crystal surface region is achieved by enlargement of the developed image in an optical transmission microscope [ 3 ] .

Figure 1: Stereographic standard (0001) projection, with inset physical set-up, for Berg-Barrett reflection x-ray topography of zinc employing characteristic cobalt Ka radiation.

Crystal imperfections seen by x-ray diffraction topography

235

Individual dislocations and small angle dislocation subgrain boundaries formed during solidification along the difficult [OOOl] crystal growth direction for an eight millimeter diameter zinc crystal are shown in Figure 221, to be compared with the characterized dislocation boundary structure in Figure 2b. The individual dislocation lines within the subgrain volumes are revealed by the (blackened) localized enhancement of the reflected intensity caused by reduction in (the perfect crystal) primary extinction. The occurrence of dislocation loops [4] in such crystals when chemically polished, and occurring also in separate (0001) surface oxidation experiments [ 5 ] , are observed at, say, smallest ten micrometer diameters, to be comparable to dislocation loop observations made via TEM. The dislocation subgrain boundaries are generally observed to have reduced zones of extinction contrast but are either white (via reduced intensity) or black according to whether the adjacent subgrain reflections are separated or overlapped in the film record. Stereographic [6] and diffracted vector [7] analyses have been given for specification of subgrain misorientations in zinc and nickel crystals, respectively. Different levels of subgrain structures were observed in the nickel crystals, as first reported via Debye-Scherrer x-ray results for nickel polycrystals by Weissmann [S].

Figure 2 : Individual dislocation and subgrain boundary structure within a (lOi3) B-B image through the (0001) cleavage surface of a zinc crystal solidified along the [OOOl] crystal growth direction.

Lang Transmission XRDT of (Magnesia and) Sapphire Employment of the Lang transmission XRDT method [9], as utilized with a micro-focus x-ray generator, is shown via the stereographic projection method for (200) diffraction of molybdenum Ka radiation directly incident at a small angle to the (001) crystal surface normal in Figure 3, also whereby synchronized traversing of the crystal specimen and recording film occurs on either side of collimating lead screen slits. With this technique, depth perception of the dislocation line structures is achieved via

236

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stereo-pair topographic images indicated to be obtainable in Figure 3 by the inset physical set-up actually applying, relative to the identified diffracting plane normal in the projection, for an opposite (negative) x-ray source direction being positioned on the right equatorial side of the [OOl] center of the standard projection.

Figure 3: Stereographic standard (00 1) projection, with conjugate inset physical set-up for Lang transmission x-ray topography of magnesia employing characteristic molybdenum Ka radiation. Figure 4 shows individual dislocation bundles spreading outward from a central seed as accomplished for a sapphire crystal grown by a chemical vapor deposition technique [lo]. The crystal growth process was interrupted at certain stages to show the nucleation of additional dislocation bundles then spreading outward also from new points established during the stopped operation, as modeled by Klapper [l 11, mainly, for organic crystal growth. Comparative B-B and Lang topographs were obtained also on the same crystal slice [12]. By reduction of the Lang-type lead exit slits to smaller width than a reasonably thick sapphire crystal slice, anomalous transmission imaging of a lesser dislocation-induced diffracted intensity was demonstrated in the same image for dislocation lines close to the beam entrance side of the crystal superposed on the enhanced intensity of dislocation lines close to the crystal exit side [ 131.

Hardness Strains in RDXand AP crystals A stereographic projection for (10 00) B-B reflection with copper Ka radiation of crystal regions s-Founding diamond pyramid hardness indentations put at various applied load values into an RDX (210) crystal solution-growth surface is shown in Figure 5a, along with the recorded B-B image in Figure 5b showing very limited spatial extent of the cumulative dislocation strain fields at the indentation sites. Such indentations produced cracking on { 001}, and { 241) cleavage surfaces, as indicated by the filled points, for plane normals, and particular subscripted identifications in Figure 5a.

Crystal imperfections seen by x-ray diffraction topography

23I

Assessment of the white-to-black-to-background-graylocal diffracted intensities at the indentation sites, along with complementary etch pitting results [ 141, provided first experimental evidence of very restricted dislocation slip occurring in RDX and related energetic crystals.

R"i.&

1

1 rnm

Figure 4: An (0370) Lang transmission topograph of dislocation bundles spreading from nucleation sites induced by growth interruptions for a sapphire crystal produced by chemical vapor decomposition.

H Cady

x-ray,

source

-

cu

Figure 5a: Stereographic projection for

K W

I LANL RDX Crystal

--

Nuclear Emulsion Plate

(m00) B-B image of hardness indentations in an RDX crystal.

23 8

R.W. Armstrong

-ABSENT INTENSITY

GROWTH CENTER?

LOCALIZED INTEl INTENSITY VSITY TO EXTINCTION TINCT'101v

g 7 -\ MICROINDENTA

h

Figure 5b: White-to-black-to-gray diffraction contrast for plasticityicracking at hardness indentations. A significantly greater extent of, albeit anisotropic, dislocation slip and cracking behavior is observed for two similar type diamond pyramid indentations put into a clean cleavage facet of an (ionic) AP oxidizer crystal, as shown in the matched optical and (523) B-B images of Figures 6a,b --- with interesting interpreted consequence for the role of dislocation slip being responsible for the observed cleavage cracking [ 15]! The chosen orientation of the indenter diagonals for the pair of indentations put into the (210) surface has produced (001) cleavage cracks emanating only from one side of the diagonal edges because of favorable dislocation slip on inclined intersecting systems occurring only on that one side, as clearly evidenced also by the larger size of the same half of the residual indentations. Thus, otherwise brittle-type cleavage cracking has occurred in the indentation strain field where greater dislocation strain is evidenced in the x-ray topograph and is associated with the stress concentration of dislocation pile-ups against reacted dislocation obstacles at the slip system intersections.

LM-ACTfor perfecl silicon cryslul devices A different research effort from that of employing reflection XRDT for monitoring dislocation structures came from the consideration that such topographic imaging could be applied, if the resolution were improved, to monitoring elastic strains accompanying layer depositions and/or implantation strains in electronic devices fabricated on essentially perfect silicon crystal surfaces [ 161. For the purpose, advantageous use was made both of: (1) the dynamical theory prediction for reducing the angular spread for the total reflection of x-rays, as originally proposed to play an important role in observing dislocation strain fields [17]; and, ( 2 ) further reduction of adverse geometrical vertical divergence determined at the x-ray source by employing a horizontal line geometry in a so-called line modified - asymmetric crystal

Crystal imperfections seen by x-ray diffraction topography

239

:

Figure 6a: Optical micrograph of two microindentations on a clean @lo) AP crystal surface; and, 6b: (523) B-B topograph of dislocation strains producing cleavage cracking at slip system intersections.

topography (LM-ACT) design [ 181. Predictions from such dynamical theory parameters account for reduction of oblique “rocking curve widths” in synchrotron radiation applications [I91 and are being carried forward currently for evaluation of energetic crystal powder diffraction experiments [2O]. Figure 7 shows, on top and bottom, the physical experiment and combined dispersion surface construction, respectively, employed for application to investigating diffraction contrast within, and above, the substrate of an otherwise perfect silicon crystal parametric test chip [18]. The asymmetrically-cut silicon crystal beam conditioner, in reconstruction of the beam probe, serves the purpose of reducing the spatial width of the incident horizontal beam while maintaining a small vertical divergence sighted at the x-ray source. The theoretical angular reflecting width exiting the beam conditioner is just greater than the angular range of acceptance for total reflection from the perfect silicon crystal substrate device, now with a further dynamical theory based reduction of the perfect crystal reflected beam width directed onto the emulsion film record. The described LM-ACT set-up has produced an image resolution at -1 -2 micrometers involving -500X magnification of exposed emulsion images in an optical transmission microscope [21]. An example is shown in Figure 8a,b of a fine line structure resolved near to the edge of a deposited silica graticule marking enlarged in part in 8b with two 10 micrometer scale marker separations. The graticule markers are revealed because of elastic strains produced within the silicon crystal substrate. The incident x-ray

R. W.Armstrong

240

beam direction in the Figure is from left-to-right along the horizontal lengths of the fine line structure. The imaged line structure extends past the true vertical edge of the line pattern because of the beam probe having traveled at a small angle through a depth of -2 micrometers in the silicon crystal substrate, The graininess in the Figure corresponds to the developed grain size of the nuclear emulsion. Other demonstrated application of the high resolution LM-ACT method has been to monitor sequential implantation deposition steps for fabrication of such parametric [22] and related devices [23].

TOPOGRAPHIC IMAGE

ASYMMETRICALLY CUT SILICON BEAM CONDITIONER

RAY

E Y

SPECIMEN CRYSTAL

I1

ROTATION AXIS FOR BOTH CRYSTALS

Figure 7: The LM-ACT system applied, via favorable dispersion surface geometries, to reducing the angular width for total reflection of x-rays so as to obtain improved imaging of a parametric test chip.

Crystal imperfections seen by x-ray diffraction topography

24 1

7 -

., . 1

:

- - c

hi >

.

*

I

Figure 8a,b: High resohtion LM-ACT images obtained of detailed structure in a parametric test chip. Summary

With relation to pioneering XRDT, FIM, and, especially, TEM defect observations, such as reported in the latter case by Professor Gareth Thomas and colleagues and students, a number of experimentalhodel XRDT results are reported here for a variety of relatively perfect crystals of quite different materials. The presented results cover observations made on: (1) individual dislocation strain fields; (2) dislocation subgrain boundary geometries/misorientations; (3) cumulative dislocation interactionskracking at residual hardness indentations; and, (4) elastic strains in an electronic device fabricated on an essentially dislocation-free silicon crystal. Acknowledgements

Appreciation for helpful discussion is expressed to Ms. Kinnan L. Kline during her M.Sc. thesis research at the University of Florida, Graduate Engineering and Research Center (UFGERC), and to Mr. D. Wayne Richards, among other colleagues, at the High Explosives Research and Development (HERD) Facility, Eglin Air Force Base, FL. References 1. 2.

Newkirk, J.B. and Wernick, J.H. (Eds.) (1961). Direct Observution of Imperfections in Crystals. Interscience Publishers, N.Y. Benka, S.G. and Lubkin, G.B. (1995) Physics Today 48,23.

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3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17.

Armstrong, R.W. (1980). In: The Characterization of Crystal Growth Defects by X-ray Methods. p. 535. Plenum Press, N.Y.; (1984). In: Applications ofX-ray Topographic Methods to Materials Science. p. 33. Plenum Press, N.Y. Armstrong, R.W. and Schultz, J.M. (1968) Surjiace Science 12, 19. Roessler, B. and Burns, S.J. (1974) Physica Status Solidi (a)24,285. Wu, C.Cm. and Armstrong, R.W. (1975) Physica Status Solidi (a)29,259. Armstrong, R.W., Boettinger, W.J. and Kuriyama, M. (1980) J. Applied Cryst. 13,417. Weissmann, S. (1956) J: AppliedPhys. 27,389; Ibid., 1335. Lang, A.R. (1978). In: Diffractionand Imaging Techniques in Materials Science, 11, p. 678. NorthHolland Publishers, Amsterdam. Farabaugh, E.N. and Wu, C.Cm. (1975). In: Proc. Third Intern. Con$ Crystal Growth, ACCG 111, p. 116. Stanford, CA. Klapper, H. (1980). In: The Characterization of Crystal Growth Defects by X-ray Methods, p. 133. Plenum Press, N.Y. Farabaugh, E.N., Wu, C.Cm. and Armstrong, R.W. (1977). In: Advances in X-ray Analysis, 20, p. 201, Plenum Publishing Corp., N.Y. Armstrong, R.W. (1988). In: Advanced Techniquesfor Microstructural Characterization, p. 1. Trans Tech Publications, Switzerland. Armstrong, R.W. and Elban, W.L. (1989) Mater. Science Eng. A l l l , 35. Elban, W.L. and Armstrong, R.W. (1998) Acta Mater. 46,6041. Beard, W.T. and Armstrong, R.W. (1989). In: Advances inX-ray Analysis, 32, p. 659, Plenum Publishing Corp., N.Y. Roessler, B. and Armstrong, R.W. (1969). In: Advances in X-ray Analysis, 12, p. 139, Denver,

co.

18. Beard, W.T., Lipetzky, K.G. and Armstrong, R.W. (1999). In: Advances inX-ray Analysis, 41, p. 203, JCPDS, CD-ROM. 19. Hart, M., Koga, T. and Takano, Y. (1995) J: Applied Cryst. 28,568. 20. Kline, K.L. (2002). MSc Thesis, University of Florida, Graduate Engineering and Research Center. 21. Beard, W.T., Lipetzky, K.G., Zhang, X.J. and Armstrong, R.W. (1996) AppliedPhys. Lett. 69,488. 22. Lipetzky, K.G., Beard, W.T., Zhang, X.J., and Armstrong, R.W. (1995). In: Advances in X-ray Analysis, 38,227. 23. Beard, W.T., Hutchison, W.G., Armstrong, R.W., Zhang, X.J., Fitz, J.L. and Whisnant, J.K. (1993). In: Physics of Semiconductor Devices, p. 246, Lal, K. (Ed.). Narosa Publishing House, New Delhi, India.

Nan0 and Microstructural Design of Advanced Materials M.A. Meyers, R.O. Ritchie and M. Sarikaya (Editors) 02003 Elsevier Ltd. All rights reserved.

SYNTHETIC MULTI-FUNCTIONAL MATERIALS BY DESIGN USING METALLIC-INTERMETALLICLAMINATE (MIL) COMPOSITES Kenneth S. Vecchio Dept. of Mechanical and Aerospace Engineering University of CA, San Diego, La Jolla, CA 92093-041I

ABSTRACT The field of material microstructure design targeted for a specific set of structural + functional properties is now a recognized field of focus in Materials Science and Engineering. This paper described a new class of structural materials called Metallic-IntermetallicLaminate (MIL) composites, which can be have their micro, meso- and macro-structure designed to achieve a wide array of material properties, and tailored to achieve specific functionalities. The superior specific properties of this class of composites makes them extremely attractive for high performance aerospace applications, and the fabrication method for creating these MIL composites allows new embedded technologies to be incorporated into the materials further enhancing their functionality and utility.

INTRODUCTION The field of microstructural design to achieve a set of targeted mechanical + functional properties was originally pioneered by Gareth Thomas, and now this approach to Materials Science and Engineering has become a mainstay of new material development strategies. Recently, a new class of structural materials has been developed at the University of CA, San Diego, termed ‘Metallic-Intermetallic Laminate (MIL) Composites [l], and the goal of this materials development effort was to extrapolate upon the positive engineering properties exhibited by hierarchical multiphase complex natural composites such as shells [2,3] to design and synthesize multi-functional composites tailored to optimize specific structural properties, while facilitating low cost, designable and functional microstructures. Mollusk shells are known to possess hierarchical structures highly optimized for toughness. The two mollusks that have been studied most extensively are Haliotis rufescens (abalone) and Pinctata (conch) shells. Considering the weak constituents the shells are made from - namely calcium carbonate (CaC03) and a series of organic binders, the mechanical properties of these shells are outstanding. Their tensile strength varies between 100 and 300 MPa, and fracture toughness between 3 and 7 MPa-ml”. CaC03 has corresponding strength and toughness values of 30 MPa and < 1 MPa-ml”, respectively [4-81. These mollusks owe their extraordinary mechanical properties to a hierarchically organized structure starting with single crystals of CaC03, with dimensions of 4 5 nm (nanostructure), and proceeding with “bricks“ with dimensions of 0.5-1 Opm (microstructure), and finishing with layers of -0.2 mm (mesostructure).

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K.S. Vecchio

Metallic-intermetallic (Ti-Al3Ti) laminate (MIL) composites have been produced from elemental titanium and aluminum foils by a novel one-step process utilizing a controlled reaction at elevated temperature and pressure [l]. The novelty of this fabrication process lies in the fact that it is performed in open air and produces a fully dense laminate composite. Figure 1 shows an illustration of the processing setup for fabrication of the MIL composites using a simple open-air heated platen press. The thickness of the original titanium and aluminum foils is chosen to ensure that the entire aluminum layer is consumed upon reaction with the adjacent titanium layers. Such a layering scheme results in a composite with alternate layers of AI3Ti and residual Ti, and the thickness of the final layers are dependent upon the thickness of the original Ti and A1 foils. The above process is highly flexible since metal/alloy foils other than Ti can be used individually, or in combination, within the same composite, to produce their respective metal/metalaluminide composites. For example, MIL composites using Fe-based, Ni-based, and Co-based alloys as the starting metal layer (instead of Ti) have been successfully fabricated using the above technique.

Hydraulic press Heating mts

? .

-

Stackof tltanlurn and aluminum sheets

Figure 1. Schematic diagram of metallic-intermetalliclaminate composite heated platen press apparatus for fabrication of planar laminates. The composition, physical, and mechanical properties of the MIL composites can be varied and tailored within the thickness of the composite by simply varying the individual foil compositions, thickness, and layering sequence. The fabrication of metallic-intermetallic laminate (MIL) composites using this approach has several key advantages that make it ideally suited for the production of commercially-scalable structural materials, as well as microstructures designed for specific functionalities.

1. Since the initial materials utilized are in the form of commercially available metallic foils, the initial material cost is reasonably low, compared to many of the exotic material processing routes that are commonly pursued in small-scale research environments. This also means that a wide array of compositions can be ready produced, although for this paper we will focus on the Ti-A1 system because of their high specific properties.

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2. The use of initially ductile metallic foils enables the layers to be formed into complex shapes. This opens the door for non-planar structures, such as rods, tubes, shafts, and cones, as well as simple machining of individual foils for complex, 3-dimensional structures, and near-net shape forming of parts. The use of initial metallic foils also allows the individual foils to be machined to contain cavities and pathways facilitating the incorporation of embedded functionalities, such as passive damping [4] or sensors, prior to processing. 3. The processing conditions, in terms of temperature, pressure and atmosphere are very modest. Processing temperatures, in the case of Al-foil containing samples are below 700"C, and the processing pressures are below 4 MPa [ 11. Perhaps,the most remarkable feature of the processing of these metallicintermetallic laminate composites is that the processing is carried out in open air, no special inert gas or vacuum chamber facilities are necessary. The combination of these various processing features makes the processing method itself very low cost, allows for complex shape fabrication and is easily amenable to computer control.

4. The microstructure of the metallic-intermetallic laminate composites is determined by the foil thickness and composition and the processing condition. Since the material make-up is based on the selection of the metal foils, it is possible to completely tailor the microstructure from one surface to the other. In addition, the physical and mechanical properties of the MIL composites can be tailored by selection of the foil composition and thickness making the MIL composite material system ideally suited for engineering the microstructure to achieve the specific performance goals. Of the various possible aluminides in the Ti-A1 system, the formation of the intermetallic A13Ti is thermodynamically and kinetically favored over the formation of other aluminides when reacting A1 directly with Ti. This preferential formation of A13Ti is fortuitous as its Young's modulus (216 GPa) and oxidation resistance are higher, and the density (3.3 g/cm3) lower than that of the other titanium aluminides such as Ti3AI and TiAl [9]. The high compressive strength and high compressive stiffness of AllTi (and intermetallics, in general) results from their high bond strength. However, intermetallics are brittle at low temperatures due to the limited mobility of dislocations (and paired superdislocations with anti-phase boundaries), insufficient number of slip or twinning systems, andor very low surface energy resulting in little to no plastic deformation at the crack tip. For example, Al3Ti is extremely brittle at room temperature and has a very low fracture toughness of -2 MPadm [lo]. The unique properties of MIL composites arise from the combination of the high hardness and stiffness of the intermetallic-aluminide phase alternatively layered with the high strength, toughness, and ductility of metal alloys. Figure 2 shows an example of the microstructure of a Ti-AI3Ti MIL composite.

Figure 2. Micrograph of a typical Ti-AlsTi MIL composite

K.S. Vecchio

246

STRUCTURAL PERFORMANCEATTRIBUTES In the case of Ti-Al3Ti MIL composites, the specific stiffness (modulus/density) is nearly twice that of steel, the specific toughness and specific strength are similar or better than nearly all metallic alloys, and specific hardness is on par with many ceramic materials. An interesting comparison of material properties for the MIL Composites can be obtained using a material property map. Figure 3 shows a plot having as the x-axis the specific modulus of a material on a log scale and the y-axis the specific compressive strength on a log scale. In this plot numerous material locations are shown, and in terms of optimizing these properties (combined compressive strength and stiffness), the upper right-hand comer represents the goal. The location of the MIL composites (red ellipse) is shown to the right (higher specific modulus) of the typical structural metals such as steels, Ti alloys, Ni-superalloys, Al-alloys, and T-based intermetallics. The only metallic materials of higher specific stiffness are the beryllium alloys. Several ceramic materials are shown, which have higher specific stiffness than the MIL composites, including Sic, B&, A1203, and diamonds. Clearly, the MIL composites possess tremendous potential for structural applications, particularly for demanding high specific stiffness applications.

Specms Modulus

Figure 3.

OC

Materials property map comparing specific compressive strength versus specific material stiffness.

The good fracture toughness of the MIL composites is derived from the combination of the highly anisotropic layered structure of the material and the need for crack re-initiation at each successive metal layer. Figure 4 shows an example the fracture behavior of three different volume fraction Ti-AbTi MIL composites. In samples with as little as 20% remnant Ti, the crack cannot propagate through the samples without being diverted and bifurcated at each Ti metal layer. Figure 5 plots the specific fracture toughness vs. the specific modulus of various engineering materials, including the MIL composites (shown by the dark grey ellipse). Several other laminates are identified as light gray region in Figure 5. It can be seen that the Ti/A13Ti laminate composites have higher specific toughness than other laminate systems and the Ti/Al3Ti specific modulus is surpassed only by the

Synthetic multifunctional materials by design using MIL composites

241

metaVAlzO3 system. Relative to y-TiAl/TiNb, MIL composites have higher specific fracture toughness and a higher specific modulus for the same volume fraction of the ductile phase Further, relative to the various metaVAhO3 systems, the MIL composites have higher specific fracture toughness for the same volume fraction of the ductile phase. Thus, owing to the ease of fabrication of Ti/AljTi laminates, low fabrication costs, and their attractive mechanical properties, MIL (TiIA13Ti) composites are an excellent candidate for engineering applications requiring a combination of low density, high strength, high toughness and high stiffness

Figure 4.

Figure 5.

Quasi-Static Three-point bend Samples for Fracture Toughness Measurements

Specific Fracture Toughness versus Specific Modulus Property map for an array of structural materials. Plot includes MIL (Ti-A1,Ti) composites (dark gray colored) and other laminate systems (identified by (L) and colored in light gray), metals, alloys and composites.

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K.S. Vecchio

STRUCTURAL PLUS BALLISTIC ATTRIBUTES The above discussion on the specific physical and mechanical properties of the MIL composites makes them an attractive matenal for structural applicahons. However, the ballistic performance of these materials is also quite impressive, when compared on the basis of areal density for a given threat, against other structural and armor materials Figure 6 shows a photograph of a cross-section through the impact location from a ballistic test on a MIL composite The sample is a 20% TI-6-4 and 80% A13Ti laminate with an initial thickness of approximately 2 cm. This composition produces a sample with a density of 3 5 g/cm3 and therefore the specific target shown in this figure would have an areal density of 7 g/cm2 The penetrator used was a tungsten heavy alloy rod (93W-7FeCo) with a mass of approx 10 grams and initial diameter of 6 15 mm, and the penetrator was fired at a velocity of 900 m/s (2950 ft/s) at the target in a normal incidence depth-of-penetration (DOP) onentation. The depth of penetration within the MIL target is less than 1 cm.

Figure 6. Cross-section through the impact location from a ballistic test on a MIL composite.

The demonstrated mechanical properties of the MIL composites make them suitable for structural application, while the ballistic performance makes them attractive for armor applications, creating a multifunctional (structural + ballistic) material. STRUCTURAL PLUS THERMAL MANAGEMENT ATTRIBUTES

For applications such as structural heat sinks, a high performing material must possess the structural attributes descnbed above, in addition to a high specific heat capacity to store the thermal energy and a high thermal conductivity to transport the heat throughout the structural heat sink. Figure 7 shows a plot of the product of thermal conductivity and specific heat capacity (on the y-axis) versus the product of specific modulus and fracture toughness (on the x-axis) The product of specific modulus and fracture toughness was chosen because it represents an optimum for many structural applications wherein high stiffness and high fracture toughness are desired This combination of properties is usually difficult to achieve considering the highest stiffness materials, such as ceramics, usually possess the lowest fracture toughness In terms of thermal management properties, the highest stiffness materials, such as ceramics, are usually poor thermal conductors, and the high thermal conductivity materials such as Al-alloys and Cu-alloys, have relatively low specific stiffness. The exception to these trends is beryllium alloys, which possess high specific stiffness, high thermal conductivity and high heat capacity. On the other hand, Be alloys have significant drawbacks to their widespread use, such as the limited availability of Be, the high cost of Be alloys, and the serious health concerns with Be manufacturing As such, alternatives to Be alloys for combined structural plus

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249

thermal management applications are in great demand. Examination of Figure 7 shows that MIL composites are second only to Be alloys, in terms of thermal management capacity, for an equivalent structural property level. In terms of thermal management capacity, the MIL composites are only surpassed by Be-alloys, some Al-alloys, and diamond. Given the high cost of diamonds and the inability to produce structural components from them, we can eliminate diamonds as a choice. Furthermore, the specific structural performance of MIL composites is nearly 3 times greater than Al-alloys, which can be critical for high performance aerospace applications. As such, MIL composites offer an attractive alternative to Be alloys for structural heat sink (multi-functional structural + thermal) applications.

01

Figure 7.

1

(Modulus'Fracture Toughness)/Denslty

Specific Heat Capacity and Thermal Conductivity versus Specific Modulus and Fracture Toughness Property map for an array of structural materials. Plot includes MIL (Ti-Al,Ti) composites (red ellipse), which overlaps diamond and aluminum at the lower end of the structural performance range for the MIL composites and lies below Be alloys in terms of the thermal properties for a similar specific stiffness/fracture toughness value.

MULTI-FUNCTIONAL METALLIC-INTERMETALLIC LAMINATE (MIL) COMPOSITES In addition to the multi-functional nature of MIL composites described above, it is possible to incorporate additional functionalities into the materials. These functionalities are readily incorporated into the MIL composites due to the layer-by-layer assembly nature to the materials. Since each layer of the MIL composite starts out as a metal foil, it is possible to create holes and slits in these layers forming 'open space' in individual layers or multiple layers. Within these cavities and slits, additional functionalities can be embedded to further enhance the properties of the MIL composites. The approach follows, to some extent, a multi-layer electronic circuit board methodology with interconnections occurring either within a given layer or between layers, creating a 3-D architecture to the structure of embedded functionalities. Below are described some of the initial concepts for these types of functionalities envisioned for these materials.

250

K.S. Vecchio

Synthesis of MIL composites having meso-scale cavities to incorporate vibration damping By designing cavities within the A1 layers and filling these cavities with granular material, it is possible to produce MIL composites with tailored vibration damping within the intermetallic layers [l 11. Figure 8 shows an example of the presence of these cavities within a Ti-Al3Ti MIL composite. The size, distribution, and location of the cavities within the MIL composite hierarchy can be selected in the material design process by the placement of the cavities within the individual aluminum layers, and the placement of these layers within the foil stack. These cavities can be filled with granular materials to serve as particle dampers. Figure 9 shows an example of a MIL composite fabricated with a large cavity filled with steel beads to demonstrate the concept of a particle filled cavity. Initial damping results have been presented elsewhere [Ill.

Figure 8. X-ray flouroscope images through-thickness of cavities created within the intermetallic layer of a Ti-Al3Ti MIL composite. The grey circular regions are approx. 13 cm in diameter.

Figure Y. X-ray flouroscope image through-thickness of a large (10 cm diameter) cavity filled with steel beads created within the intermetallic layer of a Ti-Al3Ti MIL composite. Enhanced Energy Absorbing or Fluid Conduit Modified MIL Composites By embedding tubes between various layers of MIL composites it is possible to incorporate energy absorbing capacity into these materials, specifically for blast mitigation. These tubes would deform during impact and absorb the incident shock energy. Figure 10 illustrates the concept for this energy absorbing MIL composite

Synthetic multifunctional materials by design using MIL composites

25 1

system. In addition, the embedding of tubes within the MIL composites would facilitate the passage of fluids or gases within the structure, which might be used for heat exchange, fluid transport, or embedded reactions.

Blast

.

Figure 10

.

.+

.

. ..,

'

J

Schematic diagrams of MIL composites containing embedded tubes within the intermetallic layers, (a) initial microstructure, and (b) microstructure with collapsed tubes following blast.

MIL Composites with Embedded Sensing Capability Synthesis of in-plane embedded wires and tubes as electrical and/or optical pathways for damage detection and life monitoring can make these MIL composites truly multi-functional. By creating slots in the aluminum foils prior to MIL synthesis, it is possible to introduce metal wires, metal or ceramic tubes, ceramic tubes containing metal wires, optical fibers, etc. By suitable monitoring of the wires or fibers, it is possible to monitor and detect damage within the intermetallic layers. In the case of the embedded wires, these wires also serve as 'micro-rebars' within the intermetallic layers to further toughen these layers. Figure 11 shows an example of embedded ceramic tubes in the intermetallic layers. The embedded ceramic tube has 2 wires within it that are electrically isolated from the sample itself. Synthesis of MIL composites having through-thickness wires or tubes Since metal foils are used as the starting material, it is possible to machine the foils individually or in-group to facilitate fabrication steps. By drilling a hole through the entire foil stack and placing in the hole either a wire or tube, it is possible to create a through-thickness-strengthening feature. Figure 12 shows an example of a through-thickness Ti wire embedded in a Ti-A1 MIL composite plate. The location and distribution of these wires can be designed to regulate the balance between through-thickness and transverse strength. These wires can also serve as embedded electrical resistors for strain sensors or damage detection. Replacing the wires with tubes provides a method to introduce rivet-type attachment holes, and throughthickness fiber optics for imaging or environmental sensing.

K.S. Vecchio

252

Figure 11.

Figure 12

Micrograph of a Ti-ALTi MIL composite containing a ceramic tube filled with 2 metal wires.

Micrograph showing an example of a through-thickness Ti wire embedded in a Ti-A1 MIL composite plate

Fully-Functional MIL Composites The next step to 'Multi-functional' MIL composites having meso-scale cavities and electrical conduits to incorporate sensing devices, such as piezoelectric devices, accelerometers, gyroscopes, and MEMS devices I S to combine the technology of embedded cavities with the concept of embedded electrical pathways Figure 13 shows an x-ray fluoroscope image of a MIL composites containing a series of cavities with interconnected electrical insulators and a pair of wires running through the cavities These cavities can also be filled with suitable high temperature capable devices such as lithium niobate piezoelectric crystals that can be used for detection of mechanical impulses, or conversely excited electrically to produce mechanical vibration of the material Figure 14 shows an illustration of a MIL composite having an embedded piezoelectric sensor within its structure

Synthetic multifunctional materials by design using MI1 omposites

253

Figure 13. X-ray flouroscope image through-thickness of cavities, interconnected by ceramic insulators containing wires created within the intermetallic layer of a Ti-Al3Ti MIL composite.

Alunitm Tube Electrical Lead Wires Pd-& Electrode High Temperahre. Ceiiient

Figure 14.

An illustration of a MIL composite having an embedded piezoelectric sensor within its structure.

CONCLUSIONS Building on the field of micro- and meso-structural design to achieve a set of targeted mechanical + functional properties that was originally pioneered by Gareth Thomas, a new class of structural materials has been developed to embody and exploit this concept, termed ‘Metallic-Intermetallic Laminate (MIL) Composites. The development of this novel, light-weight, multi-functional, structural composites that have the potential to perform various other functions, such as. thermal management, ballistic protection, blast mitigation, heat exchange, vibration damping, sensing of various types through embedded devices, has been presented From the perspective of manufacturability, this new materials system is relatively low cost, environmentally benign, capable of near net-shape processing, and allows for the material properties to be designed and tailored to the specific performance requirements of the application Many of the additional functionahties that these materials offer are inherent in the architecture and physical properties of the

254

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material's individual phases. The fabrication approach allows these properties to be tailored, both in-plane and through-thickness in the materials. For the active sensing functions, the design approach follows the methodologies used in the electronic materials field for fabrication of circuit boards and devices. The materials are assembled layer by layer, with the functional features incorporated primarily within the intermetallic layers, and interconnections are completed within a given layer and between layers using electrically insulated wires. Constitutive and damage evolution models are actively being developed that could be integrated into largescale computer codes to predict the accuracy and effectiveness of the various performance indices. The current modeling efforts also focus on determining the "Rules and Tools" for designers to utilize these inherent and embedded functionalities, their distribution and density within the material, with experimental verification of the models in progress. REFERENCES

1. Harach, David J. and Kenneth S. Vecchio, "Microstructure Evolution in Metal-Intermetallic Laminate (MIL) Composites Synthesized by Reactive Foil Sintering in Air", Metallurgical and Materials Transactions, 32A, 2001, pp. 1493-1505. 2. R. Menig, M.H. Meyers, M.A. Meyers, and K.S. Vecchio, "Quasi-static and Dynamic Mechanical Response of Haliotis Rufescens (Abalone) Shells", Acta Materialia, 48 (2000) 2383-2398. 3. R. Menig, M.H. Meyers, M.A. Meyers, and K.S. Vecchio, "Quasi-Static and dynamic mechanical response of Strombus gigas (conch) shells", Mater. Sci. & Eng., A297 (2001) pp. 203-21 1. 4. M. Sarikaya, An Introduction to Biomimetics: A Structural Viewpoint, Microscopy Research and Technique, 1994,27,360 - 375. 5 . M. Sarikaya and I. A. Aksay, in Results and Problems in Cell Differentiation in Biopolymers, S. Case ed., Springer Verlag, Amsterdam, 1992, 1-25. 6. M. Sarikaya, K. E. Gunnison, M. Yasrebi, and J. A. Aksay, Materials Research Socieiy, Pittsburgh Pa, 174 (1990) 109-116. 7. M. Yasrebi, G. H. Kim, K. E. Gunnison, D. L. Milius, M. Sarikaya, and I. A. Aksay, Mat. Res. SOC. Symp..Proc. Vol. 180, p.625. 8. M. Sarikaya, Microsc. Res. Techn. 27(1994) 369. 9. Sauthoff G. Intermetallics, Weinheim, Federal Republic of Germany: VCH Publishers, 1995. p.14. 10. Varin RA, Zbroniec L, Czujko T, Song Y-K. Materials Science and Engineering A 2001; A300:l. 11. A. Rohatgi, J.B. Kosmatka, K.S. Vecchio, K.P. Harvey, P. Nguyen, and D.J. Harach "Development of Multifunctional Metallic-Intermetallic Laminate (MIL) Composites with Particulate-based Damping" Proceedings of the 16th Annual Technical Conference of the American Society for ComDosites, September 9-12,2001, Virginia Tech. ACKNOWLEDGEMENTS

The initial development of the MIL composites was conducted as part of a MUM program from the Army Research Office to the Univ. of CA, San Diego (Contract No. DAAH04-96-10376). The follow-on work to develop the 'Multifunctional' aspects of MIL composites has been funded by the Defense Advanced Research Projects Agency (DARPA) under Contract No. DAAD19-00-1-0511, Dr. Leo Christodoulou as program manager.

Nan0 and Microstructural Design of Advanced Materials M.A. Meyers, R.O. Ritchie and M. Sarikaya (Editors) 02003 Elsevier Ltd. All rights reserved.

TAYLOR HARDENING IN FIVE POWER LAW CREEP OF METALS AND CLASS M ALLOYS M.E. Kassner and K. Kyle Oregon State University, Materials Science Program, Rogers Hall, Corvallis, OR 97331 USA

ABSTRACT

Previous work on aluminum and stainless steel show that the density of dislocations within the subgrain interior (or the network dislocations) are associated with the rate-controlling process for five-power-law creep-plasticity. Furthermore, the hardening in stainless stress is shown to be consistent with the Taylor relation if a linear superposition of ‘‘lattice’’ hardening (T~,or the stress necessary to cause dislocation motion in the absence of a dislocation substructure) and the dislocation hardening (aMGbp”*) is assumed. It is now shown that the same relationship appears valid for aluminum with the same values of a observed in other metals where dislocation hardening is established. It appears that the constant, a, is temperature independent and, thus, the dislocation hardening is athermal. It is also shown that constant stress creep behavior where the total interior dislocation decreases during primary (hardening stage) creep, is consistent with Taylor hardening. INTRODUCTION

Steady-state creep (Stage I1 or secondary creep) is usually described by [ l ]

where the exponent, n, is typically 4-7, Dsd is the lattice self-diffusion coefficient, A is a constant, and x is the stacking fault energy. This equation is applicable above 0.6 T,. The stress and strain-rates refer strictly to steady state (or secondary, or Stage 11) creep plasticity. The steady state microstructure evolves during primary creep. The dislocations form a three-dimensional subgrain aggregate often characterized by an average subgrain size, h. Within these subgrains is an (elevated) dislocation density, p, usually presumed to form a Frank network. The subgrain boundaries typically have an associated misorientation, 8, of the order of a degree or so, much less than those boundaries of the initial polycrystalline aggregate. It is often assumed that, during steady-state, hardening processes are balanced by dynamic recovery processes [ 11. It is generally understood that for steady state structures, A,, is related to pssand that feature associated with creep resistance or the rate-controlling mechanism for five power-law creep is not obvious by simple inspection of the microstructures, since both steady-state creep-rate and creep-stress vary predictably with their A,, and pss.

255

M.E. Kussner and K. Kyle

256

Most theories for five power law creep (T, > 0.6T,) of pure metals and Class M (or Class I) alloys, that behave similarly to pure metals, rely on some aspect of the subgrain microstructure to describe the rate controlling mechanism. Many of the more recent theories rely on the details of the subgrain boundaries such as the spacing, d, of the dislocations that comprise the boundaries (related to the misorientation angle, 8, across boundaries) or the subgrain size, h [2-151. Subgrain boundaries have also been suggested to be the site of elevated long-range internal backstress [16-201 and the rate controlling process at the subgrain boundary has been associated with these stresses. Other work, however, placed this conclusion of long range internal-stresses in question [2 1-24]. The dislocations not associated with the subgrain boundaries, which are presumed to form a Frank network, are less commonly, especially recently, claimed to be associated with the rate controlling process of five power law creep. Dislocation network theories [ 1,25301 generally suppose that the creep behavior is explained in terms of network coarsening by the climb of the nodes and the activation of (critical-sized) links of the network. The acceptance of these models has been limited. This may be somewhat unjustified in view of some careful, and now well-established, experiments. For example, experiments under five-power-law conditions show that there is really no doubt that the elevated temperature flow stress of AISI 304 stainless steel (Class M alloy) is controlled by the density of dislocations, p, not associated with the subgrain boundaries [31]. Also, recent experiments have also shown that the flow properties of high purity aluminum and some (Class A) aluminum alloys under five-power-law creep conditions, appear independent of the subgrain size, A, or the nature (misorientation) of the subgrain boundaries [32-351. Traditionally, five-power-law creep theories have necessarily focused on the steady-state or secondary creep behavior. Of course, if a particular feature is associated with the rate controlling process for steady-state five-power-law creep, then the yield stress at a fixed temperature and strain-rate (within the five-power-law regime) under non-steady-state conditions would still be expected to be a function of the dimensions of this feature. This is basically equivalent to suggesting that non-steady-state behavior would be determined by the same microstructural features important for steady-state. Accordingly, it has been suggested that primary creep and creep transient conditions may obey a relationship ,

1 = A‘

[&I3

(s)” [D,,Gb/kT] ( o / G ) ~

where s is a substructural term, originally formulated by Sherby et al. [36] to be (l&J with p’ z 3. Sherby also suggested that N = 8 for aluminum in particular, and, perhaps, other metals as well. It was assumed that the activation energy for (non-steady-state) flow is equal to the activation energy for lattice self-diffusion over the five-power-law regime. Certainly, this equation has been illustrated to have some phenomenological merit, and fairly sophisticated phenomenological equations have been based on this relationship [36]. Sherby and coworkers suggested that the form of Eqn. 2 was reasonable since the established relationships [20] between the strengthening variables and the steady-state stress, e.g.,

!L= C, (l/hJ G

(3)

or

5= C, (p,,)p G

or

where p is E 0.5

(4)

Taylor hardening in five power law creep of metals and Class M alloys

251

when substituted into Eqn. 2, would yield the classic five-power-law equation (1). An important question is the nature of the “s” term in Eqn. 2 [i.e., p, d (or O), h]. There may be some problems with this logic, and N not being constant over the five-power-law regime may just be one [l]. Although outside the intended scope of this paper, another complication is that the activation energies in Eqns. 1 and 2 are not necessarily identical. Consistency with the (modified) Taylor equation [46] is expected if the influence of dislocation density on the flow stress is dominant, = oo+ aMGbp’”

where

(6)

is the applied stress at a given temperature and strain rate, G is the shear modulus, b is the

( T ~ , ~

Burgers’ vector, CL is a constant (typically 0.2-0.4 [31,38-421,although the Taylor factor, M, may not always be accurately known in the reported data leaving some uncertainty in this value), and oois the stress required to move a dislocation in the absence of other dislocations that can arise as a result of solutes, Peierls-type stresses, grain-size strengthening, etc. M can vary from 1 (pure shear) to about 3.67 for single crystals and is typically, in tension, 3.06 for polycrystals. This equation was shown to reasonably describe the 304 data within the five power law regime by assuming that oo was approximately equal to the yield stress of the annealed alloy. Furthermore, the value of CL for 304 was within the range observed in other metals at lower temperatures where dislocation hardening is confirmed. In principle, if Eqn. 6 is applicable, then the phenomenological relationship of (2) should reduce to the Taylor relationship of Eqn. 2. The first part of this work will demonstrate this same Taylor equation will.apply to pure aluminum (with a steady-state structure), having both a much higher stacking fault energy than stainless steel and an absence of substantial solute additions. Second, it will be shown that the microstructure and plastic flow characteristics of aluminum undergoing primary (Stage I) creep under either constant-stress or constant strain-rate power-law creep conditions are consistent with Taylor hardening. This latter point is important since it has long been suggested that because the total dislocation density decreases during primary creep under constunt-stress conditions, the “free” dislocations cannot rationalize hardening during this stage. ANALYSIS Steady-State Behavior Figure 1 shows earlier data [31] by the author where the elevated temperature flow stress of stainless steel is plotted as a function of the square-root of the (total) dislocation density in the subgrain interior. The data reflects steady-state structures as well as specially prepared specimens of stainless steels having various combinations of h and p microstructures produced by utilizing a variety of thermal and mechanical treatments. The specimens were mechanically tested at a given temperature and strain rate that nearly corresponded to the five-power-law creep range. It was found that the (Frank network) dislocation density not associated with subgrain boundaries dominated the strength, described by Eqn. 6. Furthermore, as just mentioned, CL = 0.28, which is consistent with observed values for Taylor hardening of about 0.2-0.4 at ambient temperature for pure metals. Some typical values of CL from the literature as well as this study are listed in Table 1. One complicating issue with Table 1 is that the value of CL is affected by the way p is calculated or reported. If p is measured as line length per unit volume, then the value of p is roughly twice that of p reported as intersections per unit area, thus affecting the constant a by a factor of about 1.4. The values by the author for Al and 304 are intersections per unit area, but the units of others of Table 1 are not known. Figure 7 utilizes line length per unit volume.

The steady-state flow stress is sometimes described by Eqn. 4:

258

M.E. Kussner and K. Kyle

120

m

h

$

v

80

4LL

2

5

0) S

9?

T~ (annealed)

c. v)

a,

F

40

304 stainless steel 750°C = 9.6 X l o 4 5.’ Compression

0

L

0

I

I

5

10

Figure 1: The elevated temperature yield strength of 304 stainless steel as a hnction of the square root of the dislocation density (not associated with subgrain boundaries) for specimens of a variety of subgrain sizes. (Approximately five-power-law temperature/strain-rate combination.) Based on [3 11.

where p is an exponent 1-2. Sometimes, p is chosen as 2 and

(where C is a constant) and the “classic” Taylor equation (e.g., Eqn. 6) has been suggested. However, this relationship between the steady state stress and the steady-state dislocation density is not for a fixed temperature and strain rate. Hence, it is not of a same type of equation as the classic Taylor equation. That is, this later equation tells us the dislocation density not associated with subgrain boundaries that can be expected for a given steady-state stress which varies with the temperature and strain-rate. However, according to Eqn. 2, if the strength is exclusively provided by pm t, then the strength is temperature dependent. Equation 7 is expected to be athermal [43,44]. Equation 6, however, contains a temperature dependent ooterm. A similar experiment illustrated in Figure 1 has also been performed on steady state structures of aluminum [36,45]. In one case [36], aluminum specimens were deformed to various steady state stresses at a given temperature by varying the applied strain-rate. The strain-rate was quickly changed to a common strain-rate after steady state was achieved and the new plastic flow stress (at a fixed temperature and strain-rate) was noted. The subgrain sizes were measured at each steady-state, so that the dependence of the flow stress at a

Taylor hardening in five power law creep of metals and Class M alloys

259

TABLE 1 TAYLOR EQUATION Cf VALUES FOR VARIOUS METALS

Metal

TIT,

304

0 57

cu

0 22

Fe

1

0 28

o,$0, polycrystal

[311

0.34

o,= 0, single crystal

~421

0 22

0.31

o,= 0, polycrystal

0.15

0 37

o,z 0.25-0.75 flow stress,

I: I 1: 1 TI

Ref.

1-6 slip crystal

-_

cu

Notes

6)

0 51-0 83 -

I

polycrystal

0 19-0.34

Stage 1 and I1 single crystal M = 1.78 - 1 Go f 0

031

oo= 0, polycrystal

0 20

oo# 0, polycrystal

0.23

oo# 0, polvcrystal

I

I

I

I I

I

[38] [391

[401 [411 This study

[381

Note: Q values of A1 and 304 stainless stress are based on dislocation densities of intersections per unit area. The units of the others is not known and these values would be adjusted lower by a factor of 1.4 if line-length per unit volume is utilized. specific temperature and strain-rate on the subgrain size could be determined. Equation 2 was basically formulated based on these experiments. In another case [45] three specimens were deformed at various temperatures and strain-rates, again, to steady-state. The specimens were quickly cooled to 300°C and redeformed at a fixed strain-rate. The new flow stress (again, at a fixed temperature and strain-rate) was also related to the measured (steady-state) subgrain sizes produced at the higher temperatures. The data in both cases suggests a phenomenological relationship between the flow stress at a fixed temperature and strain rate and the (steady-state) subgrain size (the network or the dislocation density within the subgrain was not considered):

where kl is a constant. It should be noted that the oo term is a substantial fraction of the steady-state flow curve (as illustrated subsequently) despite the high purity (also, see Fig. 6(a)). Thus a “friction stress” unrelated to dislocation hardening is still appropriate, just as with the stainless steels case. Again, the two phenomenological equations, Eqn. 2 and Eqn. 6, in principle, are equivalent at a fixed temperature and strain-rate. Equation 3 is based on steady-state deformation. Since the steady-state subgrain size is generally related to the steady-state dislocation density pss,

where, as pointed out earlier, p may vary from 1-2 [20]. Blum and coworkers’ [46] careful measurements suggest a value of about 1.6. Substituting Eqn. 9 into Eqn. 8 suggests that for steady state structures of aluminum (deforming under a non-steady-state “reference” temperature and strain-rate),

M.E. Kussner and K. Kyle

260

where oois roughly the yield stress of the annealed aluminum at the reference temperature and strain rate. This suggests that the same classic Taylor equation that can be used to describe elevated temperature dislocation hardening in stainless steel is applicable here, as well. An important additional question to assess the validity of the Taylor equation is to modify the dislocation density exponent to 0.5 in Eqn. 10 and assess the value of a. If both the phenomenological description of the influence of the strength of dislocations in high purity metals such as aluminum have the form of the Taylor equation and also have the expected values for the constants, then it would appear that the elevated temperature flow stress is provided by the Frank network rather than the subgrain walls. Figure 2 plots modulus-compensated steady-state stress versus diffusion-coefficient-compensated steadystate strain-rate. Figure 3 illustrates the well-established trend between the steady-state dislocation density (line length per unit volume) and the steady-state stress. The steady-state flow stress can be predicted at a reference strain rate (e.g., 5 x lo4, s-'), at a variety of temperatures, with an associated steady-state dislocation density from these two figures. If Eqn. 6 is valid, then the values for u could be calculated for each temperature, by assuming that the annealed dislocation density and the o0 values account for the annealed yield strength measured in this study and reported in Figure 4. 1oo

1o4

1o 8

1o-'*

10-l6

1o Z 0 1o - ~

1o

-~

1o 3

10'

osJG Figure 2: The compensated steady-state strain-rate versus the modulus compensated steady-state stress for 99.999 pure Al, based on [59].

Taylor hardening in five power law creep of metals and Class M alloys __

lo4

1014

.

9‘ I

1013

26 1

I

I

c!

E 10’2

n,’ lo1’

I

,

,

,

, u , d

, , , ,,,,

n

, , ,

, , , ,,,,,,

,,llii

, , ,

Lu

”%

n o d

On

o,JG Figure 3: The average steady-state subgrain intercept, h, density of dislocations not associated with subgrain walls, p, and the average separation of dislocations that comprise the subgrain boundaries for A1 [and A1-5 at%Zn that behaves, mechanically, essentially identical to Al, but is suggested to allow for a more accurate determination of p by TEM]. Based on [60]. Figure 5 reports the resulting a values. Figure 5 indicates, first, that typical values of a are within the range of those expected for Taylor strengthening. Said another way, strengthening of (steady-state) structures can be reasonably predicted based on a Taylor equation. The strength we predict, based only on the (network) dislocation density and completely independent of the heterogeneous (subgrain) dislocation substructure.

262

250

150

300

350

Temperature (C)

400

5w

450

550

Figure 4: The yield strength of 99.999% pure A1 as a function of temperature.

1

p=10”m-’

0.30

o p=2 5x10” m.’

025{

150

200

250

300

350

400

450

500

T (“C)

Figure 5: The values of the constant alpha in the Taylor equation (6) as a function of temperature. The alpha values depend somewhat on the assumed annealed dislocation density. Hollow dots, p = 2.5 x 10” m-2; solid, p = 10” m-*.

Taylor hardening in five power law creep of metals and Class M alloys

263

This point is consistent with the observation that the elevated-temperature yield strength of annealed, polycrystalline aluminum [high-angle boundaries (HABs) only] is essentially independent of the grain size [47]. It has further been established that for a fixed grain sizeisubgrain size, the flow stress is independent of large variations in the misorientation [33]. Furthermore, the values of a are completely consistent with the values of a in other metals (at high and low temperatures) in which dislocation hardening is established (see Table 1). The fact that the higher temperature a values of Al and 304 stainless steel are consistent with the ambient-temperature values is consistent with the athermal behavior of Figure 5. The non-near-zero annealed dislocation density observed experimentally may be consistent with Ardell et al. suggestion of network frustration creating a lower limit to the dislocation density. One point to note is that in Figure 5 the variation in a with temperature depends on the value selected for the annealed dislocation density. For a value of 2.5 x 10” m-*, the values of the alpha constant are nearly temperature independent, suggesting that the dislocation hardening is, in fact, theoretically palatable in that it is athermal. The annealed dislocation density for which athermal behavior is observed is that which is very close to the value observed by the author (Figure 6), and suggested by Blum [48]. The suggestion of athermal dislocation hardening is consistent with the model by Nes [44], where, as in the present case, the temperature dependence of the constant (or fixed dislocation substructure) structure flow stress is provided by the important temperature-dependent ooterm. It perhaps should be mentioned that if it is assumed both that oo= 0 and that the dislocation hardening is athermal (i,e., Eqn. 7 is “universally” valid) then a is about equal to 0.53, or about a factor of two larger than anticipated for dislocation hardening. Hence, aside from not including a oo term which allows temperature-dependence, the alpha term appears somewhat large. Primary Creep Behavior The trends in dislocation density during primary creep have been less completely investigated for the case of constant-strain-rate tests than constant-stress creep tests. Earlier work by the author [3 11 on 304 stainless steel found that at 0.57 T,,, (and the same strain-rates as Figure l), the increase in flow stress by a factor of three is associated with increases in dislocation density with strain that are consistent with the Taylor equation. That is, the p versus strain and stress versus strain give a o versus p that “falls” on the line of Figure 1 [49]. Similarly, the aluminum primary transient in Figure 6, where the dislocation density monotonically increases to the steady state value under constant strain-rate conditions, can also be shown consistent with the Taylor equation.

Challenges to the proposition of Taylor hardening for 5-power-law creep in metals and class M alloys include the microstructural observations during primary creep under constant-stress conditions. For example, it has nearly always been observed during primary creep of pure metals and Class M alloys that the density of dislocations not associated with subgrain boundaries increases from the annealed value to a peak value, but then gradually decreases to a steady-state value that is between the annealed and the peak density [50-551 (e.g., Figure 7). Typically, the peak dislocation density value, pp, measured at a strain level that is roughly one-fourth of the strain required to attain steady-state (cSs/4),is a factor of 1.5-4 higher than the steady-state pssvalue. It was believed, by some, difficult to rationalize hardening by network dislocations if the overall density is decreasing while the strain rate is decreasing. Therefore, an important question is whether the Taylor hardening, observed under constant strain-rate conditions, is consistent with this observation. This behavior could be interpreted as evidence that most of these dislocations have a dynamical role rather than a (Taylor) hardening role, since the initial strain-rates in constant-stress tests may require by the equation,

1 = (b/M) p, v

(1 1)

a high mobile (nonhardening) dislocation density, pm, that gives rise to high initial values of total density of dislocations not associated with subgrain boundaries, p, where v is the dislocation velocity. That is, of the

M.E. Kussner and K. Kyle

264

10

50

40

30

20

10 0

I

Al (99.999%) 371°C

= 5.04x lo-* s.'

c

!

_.

1

(4

....

Figure 6 : The work-hardening at a constant strain-rate creep transient for A1 illustrating the variation of h, p, d, and ex, over primary and secondary creep. The bracket refers to the range of steady-state dislocation density values observed at larger strains [e.g., see (b)]. From [33].

Taylor hardening in five power law creep of metals and Class M alloys

40 50

t

265

Al (99.999%) 371'C

0 ' ~

~

..

..i

.....

I

-1-

.....

L

i

..

1.50 1.oo

0.50

0.00

0

L-

0

2

4

6

8

10

12

........

14

1.

16

Strain,Y cb) Figure 6 (continued): The work-hardening at a constant strain-rate creep transient for A1 illustrating the variation of h, p, d, and Oh,,, over primary and secondary creep. The bracket refers to the range of steadystate dislocation density values observed at larger strains [e.g., see (b)]. From [33].

M.E. Kussner and K. Kyle

266 1o s

IU - 5 at% Zn

0

0.1

0.3

0.2 E

0.4

Figure 7: The constant-stressprimary creep transient in Al-Sat %Zn (essentially identical behavior to pure Al) illustrating the variation of the average subgrain intercept, h, density of dislocations not associated with subgrain walls, p, and the spacing, d, of dislocations that comprise the boundaries. The fraction of material occupied by subgrains is indicated by fsub.The subgrain size during primary creep reflects those regions of the grain where subgrain formation is observed. Based on [61].

Taylor hardening in five power law creep of metals and Class M alloys

261

total density of dislocations not associated with subgrain boundaries, at any instant, some are mobile (p,) while some are obstacles, perhaps as links of the Frank network (p - pm).As steady state is achieved and the strain rate decreases, so does pm and in turn, p. More specifically, Taylor hardening during primary constant-stress creep may be valid based on the following argument:

From Eqn. 11 B = p,,,vb/M. We assume [56] v = k, o'

and, therefore, for constant strain-rate tests,

The E~ (plastic strain) is small at the onset of yielding in a constant strain-rate test (E = E,, ), and there is only

minor hardening, and the mobile dislocation density is a fraction, f: , of the total density,

therefore, for aluminum (see Figure 6) pm(6,=n) = f:0.64 p,,

(based on p at E p = 0.03)

(14)

where f: is basically the fraction of dislocations in the annealed metal that are mobile at the yield stress (half the steady-state flow stress) in a constant strain-rate test. Also from Figure 6, oy/oss= 0.53. Therefore, at small strains,

is,= f: 0.64(0.53)[k1b/M] pssass (constant strain rate at E~

= 0.03)

At steady-state, o = oSsand pm =fkp,,, where fk is the fraction of the total dislocation density that is mobile at steady-state and

(constant strain rate at E~ > 0.20) By combining Eqns. 15 and 16 we find that f, at steady state is about 113 the fraction of mobile dislocations in the annealed polycrystals (0.34f: = f:). This suggests that during steady state only 113, or less, of the total dislocations (not associated with subgrain boundaries) are mobile and the remaining 213, or more, participate in hardening. The finding that a large fraction are immobile is consistent with the observation that increased dislocation density is associated with increased strength for steady-state deformation and constant strain-rate testing. Of course, there is the assumption that the stress acting on the dislocations as a finction of strain (microstructure) is proportional to the applied flow stress. This is sensible (and the fraction is probably unity) for a network model. Furthermore, we have presumed a 55% increase in p over primary creep with some uncertainty in the density measurements.

268

M.E. Kussner and K. Kyle

For the constant-stress case we again assume

t6p=o = f: [k,b/M]ppoSs

(constant stress)

where f i is the fraction of dislocations that are mobile at the peak (total) dislocation density of pp, the peak dislocation density, which will be assumed equal to the maximum dislocation density observed experimentally in a p-Eplot of a constant stress test. Since at steady-state from Eqn. 15, is, 0.34f: [ k , b / M ] p s , ~ , s by combining with Eqn. 17, t,p,o/~ss =[F)3pp/pss f",

(constant stress)

(18)

(fi/f:) is not known but if we assume that at macroscopic yielding, in a constant strain-rate test, for annealed metal, f: 2 1, then we might also expect at small strain levels and relatively high dislocation densities in a constant stress test, f i z 1. This would suggest that fractional decreases in t in a constant stress test are not equal to those of p. This apparent contradiction to purely dynamical theories (i,e., basted strictly on Eqn. 11) is reflected in experiments [50,51,53,55] where the kind of trend predicted in Eqn. 18 is in fact observed. Equation 18 and the observations of t against E in a constant stress test at the identical temperature can be used to roughly predict the expected constant-stress p-Ecurve in aluminum at 371°C and about 7.8 MPa; the same conditions as the constant strain-rate test of Figure 6 . If we use small plastic strain , p values have been measured in constant-stress tests), we can determine the levels, (e.g., E z ~ i 4 where ratio (e.g., iE=(E,,,4)/EE=E,,) in constant stress tests. This value seems to be roughly 6 at stresses and temperatures comparable to Figure 6 [11,50,51,57,58]. This ratio was applied to Eqn. 18 [assuming (fi/f:)z 11; the estimated p-E trends, in a constant-stress test in Al at 371"C, are shown in Figure 8. This estimate, which predicts a peak dislocation density of 2.0 pss,is consistent with the general observations discussed earlier for pure metals and Class M alloys, that pp is between 1.5 an 4 pss(1 5 2 . 0 for aluminum [50]). Thus, the peak-behavior observed in the dislocation density versus strain trends, which at first glance appear to impugn dislocation network hardening, is, actually, consistent, in terms of the observed p values, to Taylor hardening. Two particular imprecisions in the argument above are that it was assumed (based on some experimental work in the literature) that the stress exponent for the elevated temperature (low stress) dislocation velocity, v, is one. This exponent may not be well known and may be greater than 1. The ratio (pp/pss)is multiplied from a value of 3 in Eqn. 18 to higher values of 3[2"-'], where n is defined by v = d"'This means that the observed strain-rate "peaks" would predict smaller dislocation peaks or even an absence of peaks for the observed initial strain-rates in constant-stress tests. In a somewhat circular argument, the consistency between the predictions of Figure 8 and the experimental observations may suggest that the exponents of 1-2 may be reasonable. Also, the values of the peak dislocation densities and strain-rates are not unambiguous, and this creates additional uncertainty in the argument.

SUMMARY Previous work on aluminum and stainless steel show that the density of dislocations within the subgrain interior influences the flow stress for steady-state substructures and primary creep under constant strain-rate conditions. The hardening is consistent with the Taylor relation if a linear superposition of soluteilattice

Taylor hardening in five power law creep of metals and Class M alloys

269

~

1 E+11

0 00

015

0 30

0 45

0 60

stran

Figure 8: The predicted dislocation density (- - -) in the subgrain interior against strain for aluminum deforming under constant stress conditions is compared with that for constant strain-rate conditions (-). The predicted dislocation density is based on Eqn. 18 which assumes Taylor hardening. hardening (u0,or the stress necessary to cause dislocation motion in the absence of a dislocation substructure) and the dislocation hardening ( z uMGbp”2) is assumed. Here is assumed that the fraction of immobile dislocations (p - pm) is a constant fraction of the total dislocation density. It appears that the constant, a, is temperature independent and, thus, the dislocation hardening is athermal. Furthermore, it is shown that constant stress creep behavior where the total dislocation density (p) decreases during primary (hardening stage) creep, is actually consistent with Taylor hardening. The increase in total dislocation density simply reflects the high initial strain-rates in a constant-stress test. The obstacles for dislocation motion in this case are still the network dislocations. ACKNOWLEDGEMENTS This work was supported by Basic Energy Sciences, U.S. Department of Energy, under grant DE-FG0399ER45768. The mechanical testing by Dr. M.-Z. Wang is greatly appreciated. The comments to this manuscript by Prof. W. Blum are appreciated. REFERENCES 1. 2. 3. 4. 5.

Kassner, M.E. and Perez-Prado, M.T. (2000) Prog. Muter. Sci. 45, 1. Morrism, M.A. and Martin, J.L. (1984) ActaMetall. 32, 1609. Morris, M.A. and Martin, J.L. (1984) Acta Metall. 32, 549. Derby, B. and Ashby, M.F. (1987) Acta Metall. 35, 1349. Nix, W.D. and Ilschner, B. (1980). In: Strength of Metals and Alloys, pp. 1503-1530, Haasen, P., Gerold, V., and Kostorz, G. (Eds). Pergamon, Oxford.

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6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40.

41. 42. 43. 44. 45.

M.E. Kassner and K. Kyle Straub, S., Blum, W., Maier, H.J., Ungar, T., Borberly, A. and Renner, H. (1996) Acta Muter. 44, 4337. Argon, A.S. and Takeuchi, S. (1981) Acta Metall. 29, 1877. Gibeling, J.C. and Nix, W.D. (1980) Acta Metall. 29, 1769. Blum, W., Cegielska, A,, Rosen, A., and Martin, J.L. (1989) Acta Metall. 37, 2439. Hasegawa, T., Ikeuchi, Y., and Karashima, S., (1972) Metal. Sci. 6,78. Ginter, T.J. and Mohamed, F.A. (1982) J. Muter. Sci. Eng. 17,2007. Barrett, C.R., Nix, W.D., and Sherby, O.D. (1966) Trans. ASM59,3. Blum, W., Hausselt, J. and Konig, G. (1976) Acta Metall. 24,293. Weertman, J. (1 984). In Creep and Fracture of Engineering Materials and Structures, p. 1, Wilshire, B. (Ed). Pineridge, Swansea. Maruyama, K., Karachima, S., and Oikawa, H. (1983) Res. Mechanica 7,21. Mughrabi, H. (1983) Acta Metall. 31, 1367. Borbely, A., Blum, W., and Ungar, T. (2000) Muter. Sci. Eng. 276, 186. Borbely, A., Hoffinann, G., Aemoudt, E., and Ungar, T. (1997) Acta Muter. 45, 89. Lepinoux, J. and Kubin, L.P. (1985) Phil. Mag. A 57, 675. Mughrabi, H. and Ungar, T. (in press). In: Dislocations in Solids, Nabarro, F.R.N. (Ed). North Holland. Sleeswyk, A.W., James, M.R., Plantinga, D.H., and Maathuis, W.S.T. (1978)Acta Metall. 126, 1265. Kassner, M.E., PCrez-Prado, M.-T., Vecchio, K.S., and Wall, M.A. (2000) Acta Muter. 48,4247. Orowan, E. (1959). In: Internal Stress and Fatigue in Metals, p. 59. General Motors Symposium, Elsevier, Amsterdam. Gaal, I. (1984). In: Proc. 5th Inter. Riso Symp., pp. 249-254, Andersen, N.H., Eldrup, M., Hansen, N., Juul Jensen, D., Leffers, T., Lilholt, H., Pedersen, O.B., and Singh, B.N. (Eds). Riso National Lab., Roskilde, DK. Ostrom, P. and Lagneborg, R. (1980) Res Mechanica 1, 59. Kassner, M.E., Perez-Prado, M.T., Long, M., and Vecchio, K.S. (2002) Metall. and Muter. Trans 33A, 311. Ardell, A.J. and Przstupa, M.A. (1984) Mech. Muter. 3 , 3 19. Evans, H.E. and Knowles, G. (1977) Acta. Metall. 25, 963. McLean, D. (1968) Trans. AIME 22,1193. Przystupa, M.A. and Ardell, A.J. (2002) Metall. andMater. Trans. 33A, 231. Kassner, M.E. (1990) J. Muter. Sci. 25, 1997. Kassner, M.E. (1 993) Muter. Sci. and Eng. 166, 8 1. Kassner, M.E. and McMahon, M.E. (1987) Metall. Trans. 18A, 835. Doherty, R.D., Hughes, D.A., Humphreys, F.J., Jonas, J.J., Juul Jensen, D., Kassner, M.E., King, W.E., McNelley, T.R., McQueen, H.J., and Rollett, A.D. (1997) Muter. Sci. and Eng. A238,2 19. McQueen, H.J., Evangelista, E., and Kassner, M.E. (1991) 2. Metall. 82, 336. Young, C.M., Robinson, S.L., and Sherby, O.D. (1975) Acta Metall. 23, 633. Miller, A.K. (1 987). Constitutive Equations for Creep and Plasticity, Elsevier Applied Science, Essex, U.K. Widersich, H. (1963) J Metals, 423. Jones, R.L. and Conrad, H. (1969) TMS-AIME245,779. Levinstein, H.J. and Robinson, W.H. (January 1963). “The Relations between Structure and the Mechanical Properties of Metal.” In: Symp. at the National Physical Lab, p. 180. Her Majesty’s Stationery Office. From Weertman, J. and Weertman, J.L. (1983). In: Physical Metallurgy, p. 1259, Cahn, R.W. and Hassen, P. (Eds). Elsevier. Bailey, J.E. and Hirsch, P.B. (1960) PhilMag. 5,485. Taylor, G.I. (1934) Proc. Royal SOC.A145,362. Weertman, J. (1999). Mechanics and Materials Interlinkage, J. Wiley, New York. Nes, E. (1997) Prog. Muter. Sci. 41, 129. Kuchi, S.K. and Yamaghuchi, A. (1985). In: Strength of Metals and Alloys, p. 899, McQueen, H.J., Baillon, J.-P., Dickson, J.I., Jonas, J.J., and Akben, M.G. (Eds). Pergamon, Oxford.

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49. SO.

51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 61.

27 1

Livingston, J.D. (1962) Actu Metall. 10, 229. Kassner, M.E. and Li, X. (1991) Scriptu Met. et Muter. 25,2833. Blum, W. (2002) private communication. Kassner, M.E., Miller, A.K., and Sherby, O.D. (1982) Metall. Trans. 13A, 1977. Blum, W., Absenger, A., and Feilhauer, R. (1980). In: Strength ofMetuls and Alloys, p. 265, Haasen, P., Gerold, V., and Kostorz, G. (Eds). Pergamon, Oxford. Daily, S. and Ahlquist, C.N. (1972) Scriptu Metall. 6, 95. Sikka, V.K., Nahm, H., and Moteff, J. (1975) Muter. Sci.and Eng. 20,95. Orlova, A,, Pahutova, M., and Cadek, J., (1972) Phil. Mag. 25, 865. Stang, R.G., Nix, W.D., and Barrett, C.R. (1971) Metall. Trans. 2, 1233. Clauer, A.H., Wilcox, B.A., and Hifih, J.P., (1970) ActaMetall. 18, 381. Gorman, J.A.,Wood, D.S., and Vreeland, T. (1969) J. App. Phys. 40,833. Parker, J.D. and Wilshire, B. (1980)Mater. Sci. and Eng. 43 271. Raymond, L. and Dorn, J.E. (1964) Trans. AIME 230, 560. Straub, S. and Blum, W. (1990) Scriptu Metall. et Mater. 24 1837. Blum, W. (1993). In: Materials Science and Technology, Vol. 6, p. 339, Cahn, R.W., Haasen, P., Kramer, E.S. and Mughrabi, H. (Eds). Wienheim, Verlag Chemie. Blum, W. (1991). In: Hot Deformation ofAluminumAlloys, p. 181, Langdon, T.G., Merchant, H.D., Morris, J.G., and Zaidi, M.A. (Eds). TMS.

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Nan0 and Microstructural Design of Advanced Materials M.A. Meyers, R.O. Ritchie and M. Sarikaya (Editors) 02003 Elsevier Ltd. All rights reserved.

MICROSTRUCTURAL DESIGN OF 7x50 ALUMINUM ALLOYS FOR FRACTURE AND FATIGUE

F. D. S. Marquis Department of Materials and Metallurgical Engineering College of Materials Science & Engineering South Dakota School of Mines and Technology, Rapid City, SD 57701

ABSTRACT This paper focuses on the microstructural design of the 7050 and 7150 aluminum alloys for the control of recrystallization, grain and subgrain morphologies, fracture toughness, fatigue crack initiation and fatigue crack growth of these alloys. An investigation of the evolution of the microstructure during primary, secondary and intermediate thermo-mechanical processing has been carried out. The study of the recrystallization behavior, the grain morphology and the sub-grain morphology has been carried out. Other microstructural features such as the morphology of the constituent particles, as the formation of primary hydrogen porosity and its evolution during intermediate thermo-mechanical processing have also been studied. The paper discusses the effect of these microstructural parameters on the fracture and fatigue behavior of these alloys. INTRODUCTION The high strength aluminum-zinc-magnesium-copper alloys gain strength by solution heat treatment, quenching and artificial aging through the formation of a complex sequence of intermediate microstructures, such as the Mg (Zn, Cu, Al)2 phase, that finally, in equilibrium, produce stable precipitates such as MgZn2 and Mg3Zn3A12. For higher strength, up to 3 wt% copper can be added. The copper content must be limited if the weldability and general corrosion resistance are necessary. Small amounts of manganese, chromium (7075, 7178), and zirconium (7049, 7050, 7150) are added to control the recrystallization and develop the highly directional wrought grain structure in wrought alloys. This structure is beneficial for stress corrosion cracking (SCC) resistance if the load is applied in the longitudinal rolling direction, because it is extremely difficult to propagate intergranular SCC cracks perpendicular to the highly elongated grain structure. For the same reasons this microstructure becomes very vulnerable if the load is applied in the short transverse (ST) direction, with consequent intergranular crack propagation in the longitudinal rolling (LR) or long transverse (LT) directions. The short transverse SCC susceptibility of these alloys is considerable in the underaged (W or T4) and peak aged (T6) tempers and is minimized in certain overaged (T7) tempers.

213

F.D.S. Marquis

214

These age-hardened high-strength alloys have been used successfully as structural materials due to their unique combination of low density, high strength, and high corrosion resistance. In addition their incorporation in airframe structures (aircraft and space vehicles) and light weight armored carriers has been critical to vehicle performance and cost due to their high strength-to-weight ratio, high specific stiffness, high durability, good machinability and formability, and low cost. In recent years, however, the more stringent demands established by the newer generation of aircraft and spacecraft have reactivated considerable scientific and technological interest in the development of improved high-strength alumipum alloys. This has been reinforced by the slow development of reproducible and reliable data (appropriate for design incorporation) on the fracture toughness and fatigue resistance of carbon fiber reinforced epoxy composites. These and other alloys are also being used in the design and manufacturing of advanced aluminum based metal matrix composites. 100

80

1

I

I

I

I

1

I

707 7178-T651

0

~

I

MD11 7150-T6151

0

4 400

LlOIl 7075T7651

DC-3 0 2024-T3

4

Junkers F-13

2o 10

I

01 1910

-I

2017-T4

Commerclat and mllitary alrcraff

I

1920

I

1930

I

1940

I

1950

1

757-767 0 0 OC-17

829 0 7470 7075-T651 7075T651

0

I

I

1960

I

1970

I

1980

I

1990

200 100

I

2000

Year first used in airplane

Figure 1 : Upper wing skin plate alloy and temper chronology In order to meet the demands of the aerospace industry, Alcoa in cooperation with Boeing developed a new aluminum alloy 7150 having improved combinations of strength and corrosion resistance. This alloy is a modified composition, modified processing, high purity version of the 7050 alloy, which was developed by J.T. Staley and co-workers at Alcoa (1, 2). In the T6 temper 7150 plates and extrusions developed high strength and adequate fracture toughness and fatigue resistance. However, in this temper the enhanced strength resulted in the degradation of the resistance to exfoliation corrosion, especially in the short transverse direction. In order to improve the resistance to exfoliation corrosion in the short transverse direction, without sacrificing strength, Alcoa developed a new temper, T77. This led to the incorporation of the 7150-T7751 in both plate and extrusions in the upper wing structures of the C-17 military transport plane and the 7150-T6151 in the upper wing structures of the European Airbus A310, McDonnell Douglas MD-11 and Boeing 757 and 767, as shown in figure 1 (3). The major portion of commercial 7x50 alloys are produced through conventional ingot casts typically 200"-190" x 60"-50" x 20"-16", which are subsequently processed into plates typically 2" to 12" thick, and then machined or formed into structural components. These components are subjected in service to multidirectional stresses and must possess the best combination of strength, ductility, fiacture toughness, and resistance to fatigue and stress corrosion cracking. For most

Microstructural design of 7x50 aluminum alloysfor fracture and fatigue

215

aerospace applications in recent years, the improvement of fracture toughness and fatigue resistance, especially in the short transverse direction, has become of crucial importance. The objective of this investigation was to evaluate the relative magnitude of various parameters such as design, microstructure, manufacturing, that significantly influence the above mechanical properties. MATERIALS AND EXPERIMENTAL METHODS Typical chemical compositions of the materials used in this investigation are presented in table 1.

TABLE 1 TYPICALCHEMICAL COMPOSITIONS (WT%) OF 7x50 ALLOYS Zn

Mg

cu

Zr

Cr

MU

Ti

Si Fe

6.316

2.135

2.25

0.102

0.002

0.01

0.029

0.027

V

BI

Be

Ni

Na

Ca

Pb

Cr-Eqv

Li

0.003

0.002

0.0004

0.004

0.0003

0.0004

0.003

0.037

---

Zr-2Ti

FeISi

Fe+Si

CuIMg Fe+Mu

0.078

Al

0.160 2.826 0.106 1.05 0.089 89.022 Typical values of Fe+ Si are approximately 0.1 in 7150 and 0.3 in 7050 The design of sampling of specimens for fracture toughness (Klc), fatigue crack initiation (FCI), and fatigue crack propagation (FCP) is discussed elsewhere (4, 5, 6). The rational for this design is based on macro and micro segregation and porosity distribution studies carried out by the author (7) and on the need to understand the correspondent scale up effects. Thus sections A and B are transverse (width x thickness) plates, taken at approximately 8" and 27" from the top (north) of the ingot. These sections have the benefit of representing microstructural gradients as function of the thickness, width and size of the ingots. Sections C and D are longitudinal (rolling direction x width) plates taken at T/4 and T2/2 respectively. T is the thickness of the ingot, which is 16" in this investigation. Since these plates have a typical thickness between 1 and 1 1/2", each of them has the benefit of representing relatively homogeneous microstructures, but quite different microstructures with different solute contents, from plate to plate. This design would thus allow an evaluation of the scale up effects from laboratory to commercial size ingots. This is so since the development of microstructural features such as micro and macro segregation, volume fraction and morphology of second phase particles and of the hydrogen induced porosity are microstructural variables that are ingot scale dependent. In addition, the microstructural evolution during advanced thermomechanical processing is very much dependent on the prior cast microstructure. Thus, in order to investigate the evolution of microstructures during industrial processing, four thermomechanical processes (A to D) were carried. Figure 2 shows processes A and B.

In addition and in order to investigate the effect of strain on the degree of static and dynamic recrystallization and grain morphology, three deformation processes (1 to 3), each with five or six

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216

pass hot rolling breaking sequences, were carried out, as shown in table 2. Both the thermomechanical processes (A to D) and the deformation Processes (1 to 3) were carried out on sections A to D. In order to determine the degree of recrystallization an HN03 etching technique was found to be preferable to the conventionally used Keller's etch. Specimens were etched 5 minutes in a 30% HN03-70% water at 85 "C. After this treatment, subgrain and grain boundaries were visible. Hardness measurements (five on each sample) were measured by using a Vickers Diamond Pyramid Hardness Tester at room temperature with a load of 20 kilograms. Specimens for

PROCESS E

Figure 2: Typical simulation of industrial type thermo-mechanical processing TABLE 2

AMOUNT OF DEFORMATION (%) FOR INDUSTRIAL AND LABORATORY INGOT PROCESSING

Pass Number

Industrial Simulation

Laboratory Processing Process 1 Process 2 Process 3

13 15 18 22

20 25 22 14

13 15 14 16

28 ---

16

18 23

___

13 15 14 16 18

_-_

Transmission Electron Microscopy (TEM) were prepared by a jet polishing technique from the materials in the thermomechanically processed and aged conditions. Scanning Electron Microscopy (SEM) was used to examine laboratory induced monotonic fracture surfaces and fatigue fracture surfaces. Plane strain fracture toughness tests (KIc) were carried out in compact

Microstructural design of 7x50 alurninum alloysfor fracture and fatigue

211

tension specimens, under ASTM E399-83 standards. Fatigue crack growth tests were carried out in compact tension specimens, under ASTM E647-86 standards. Both tests were conducted on a Materials Test System (MTS) Closed-loop Electrohydraulic Testing System. The pre-cracking and the crack growth testing were performed at a frequency of 16 and 7.5 hertz respectively. Crack lengths were measured visually using a traveling microscope and on microstructural sections.

In order to investigate and fully characterize typical microstructures Analytical Electron Microscopy (AEM), quantitative x-ray microanalysis using Energy Dispersive Spectroscopy (EDS) techniques, electron and x-ray diffraction techniques were used. Techniques of conventional electron diffraction with Selected Area Diffraction Patterns (SADPs) and Convergent Beam Electron Diffraction Patterns (CBEDPs) were used. In analytical electron microscopy the probe size was controlled by the standard objective apertures and by the use of convergent beams of appropriate size for the characterization of very fine coherent precipitate particles. Quantitative optical, transmission, and scanning electron metallography with elemental x-ray mapping were carried out directly or through camera scanning of direct micrographs on a Quantitative Image Analysis System. RESULTS AND DISCUSSION In this investigation, various parameters were observed to influence significantly the fracture toughness, fatigue crack initiation and fatigue crack propagation of these materials, as shown in figure 3. As stated earlier, the scope of this investigation does not include the detailed study of

Ingot

Type and Volume Fraction of Porosity

Chemical Design

Processing Parameters

Fracture Toughness

Fntigue Crack Propagation

Figure 3: Flow diagram of parameters that influence significantly the fracture toughness and fatigue resistance of 7x50 alloys

27 8

F.D.S. Marquis

the individual contributions of each and every of these parameters, but only evaluates the relative magnitude of their effects and establishes combinations that could optimize the mechanical behavior of these materials. In order to achieve this, various thermomechanical processes were designed, as shown in figure 2 and table 3. Process A achieved a completely recrystallized TABLE 3 EFFECT OF THERMOMECHANICAL PROCESSING ON MICROSTRUCTURE

Industrial Processing Recrystallized VolumeFraction % Grain

Morphology

Laboratory Processing Process 1 Process 2 Process 3

.55

.45

Elongated 70

.50

Elongated 50

Equiaxed

50

.20 Equiaxed

I0

microstructure as a result of the low temperature of deformation. In this process the large amount of strain energy introduced into the ingot at the relatively low deformation temperature (final pass at 270 'C) provides a large driving force for the recrystallization to occur during later heat treatments. Process A applied to section A generates a similar microstructure but with considerable amount of intergranular precipitation of both second phase particles and hydrogen induced porosity. This is explained by the proximity of the top (north) of the large ingot. Process B generated a most unrecrystallized microstructure, and process C generated a partially recrystallized microstructure. Process D achieved a partially recrystallized microstructure with significant coarse intergranular precipitation of second phase particles. The effect of strain, at a constant entry temperature of 425 "C, on the degree of recrystallization and grain morphology is shown in table 3. This temperature was selected since a significant increase in the hardness was observed during rolling within a temperature range, which includes 425 "C (4). This is attributed to the precipitation of very fine Cu and Zn bearing particles, which formed during rolling, and, together with metastable ZrA13 dispersoids, inhibited significantly the recrystallization process. TABLE 4 EFFECT OF THERMO-MECHANICAL PROCESSING ON KIC IN T-L ORIENTATION

Process

A

B

C

D

KIC, Ksi(in)lR

22

29

25

24

K,c for specimensfrom section A and process A was 18 Ksi(in)1I2 Typical plane strain fracture toughness results, in the T-L orientation, are shown in table 4. The high fracture toughness of process B (unrecrystallized microstructure) is attributed to both the strength of the grains and grain boundaries. Typical subgrain morphologies and substructures are represented in figures 4, 5 and 6. These subgrains are elongated in the rolling direction and contain multidispersions of coherent and semicoherent precipitates. Homogeneous distributions

Microstructural design of 7 x 0 aluminum alloysfor fracture and fatigue

279

Figure 4: Partially recrystallized morphologies: (a) columnar and (b) equiaxed

F

S

f

?

. -

' - .

t

f

t

I urn

Figure 5: Subgrains elongated in the rolling direction, with semicoherent precipitates at low angle boundaries and multidispersions of coherent precipitates inside the subgrains.

280

F.D.S. Marquis

I

I

I

Figure 6 : Semicoherent precipitates at low angle boundaries and multi-dispersions of coherent precipitates inside the subgrains. of very fine coherent precipitates are observed inside the subgrains, and the semicoherent precipitates are observed both at the sub-boundaries and inside the subgrains. A detailed investigation of the nature of these particles was carried out in different areas of many specimens. Analytical electron microscopy, with quantitative x-ray microanalysis using energy dispersive spectroscopy techniques showed that the semicoherent precipitate particles nucleated at the subboundaries are rich in Cu and to a less extent in Zn. These Cu and Zn rich precipitates explain the capability of these 7x50 materials to develop high strength during aging at high temperatures, with simultaneous improvement of the fracture toughness and fatigue resistance. Representative selected area diffraction pattern, micro diffraction and convergent beam electron diffraction pattern analysis were carried out and discussed elsewhere (6). The analysis show that most of the semicoherent precipitates can be indexed as intermediate modifications of the q' phase and that their composition is consistent with the Mg (Zn, Cu, A1)2 formula. This phase could be indexed as a face centered orthorhombic crystal structure. The results of this microstructural analysis agree with very recent work (8, 9, 10) and are discussed in detail elsewhere (1 1). The large number of fine subgrains and the high density of dislocations acted as sites for the precipitation of fine q' phase (6), as shown in figure 7a. These partially coherent precipitates were observed to promote homogeneous slip by forcing dislocations to bow around the precipitate particles through Orowan type by-pass mechanisms, leaving fine dislocation loops around these precipitates (Fig. 7b). In addition, the growth of incipient slip bands was impeded by sub-boundaries and the dislocation substructures within the grains, which prevent the formation of dislocation pile-ups at the grain boundaries rendering crack initiation, by the Zener precipitates and the formation of wide precipitate fiee zones, which retarded crack initiation and decreased the rate of fatigue crack propagation (da/dN) by prevention of interface decohesion. This explains the fact that these specimens were observed to fracture mostly by the transgranular dimple rupture mode, were both deep and shallow dimples have been observed associated with subgrain

Microstructural design of 7 x 0 aluminum alloysfor fracture and fatigue

28 1

Figure 7: (a) Pined screw dislocations and (b) dislocation loops around q' precipitate particles. structures. This suggests that this type of advanced processing influences beneficially crack initiation and decreases the crack growth rate at both low and high AK. The low fracture toughness of process A (completely recrystallized microstructure) is attributed mostly to the large proportion of intergranular fracture due to strain concentrations in the grain boundanes caused by alterations in the dislocations, precipitates and grain boundary structures The high angle grain boundaries were observed to be preferred sites for thc formation of coarse intergranular precipitates and hydrogen gas porosity (fig 8) Both features promoted fracture at or near grain boundanes with low dissipation of elastic strain energy Although other morphologies for the porosity and second phase particles were observed, thc intergranular oncs werc observed to be the least desirable The partially recrystallized microstructures generated by processes C and D exhibit intermediate values of plane strain fracture toughness and mixed Eracture consisting of both transgranular and intergranular modes. This is in general agreement with the work of Alarcon, Nazar and Montciro (12) although significant diffcrcnccs in thc proccssing and microstructures were observed, such as the subgrain morphology and substructure, which lead to higher fracture toughness values in the present investigation. Typical data for the resistance to fatigue crack growth, plotted as the crack growth rate (da/dN) versus the stress intensity factor (AK) is presented in figures 9 left and 9 right In all cases these curves followed a sigmoidal shape, the second stage of which could be well descnbed by a Paris type of equation da/dN = A ((UOP, where p is the slope of the curve and A is the value of the crack growth for AK=l . Within the low stress intensity range and for recrystallized microstructures, the lowest crack growth rates were observed in microstructures developed by process A In this range the microstructure played a very important role as shown by the data obtained by process A, section A and B (fig. 9 left) and processes A and B (fig. 9 right) The lowest value of all microstructures was observed in process B (fig 9). Within the intermediate stress intensity range, process B exhibited the lowest values and the lowest slope of fatigue crack growth, although processes A and B exhibited significant overlapping

F.D.S. Marquis

282

Figure 8: Typical morphologies of Hydrogen Gas Porosity: (a) and (c) thermomechanical processed, (b) and (d) recrystallized.

D-3

z" 9 4 10-5 5

I0

l5

S T R E S S INTENSITY FALTOR. AqM?UET)

27

5 10 l5 irl STRESS INTENSITY FACTOR, A!+fPa?fEiii)

Figure 9: Fatigue crack growth rate dependence on AK and microstructure These results are significantly different from those reported by Zaiken and Ritchie (13, 14) This is explained by the difference in processing and microstructures developed prior to aging The very fine textured subgrains developed in the present work rendered the aged microstructures with higher resistance to fatigue crack propagation Within the high stress intensity range the microstructures developed by process B continued to exhibit crack propagation at much higher stress intensity values Within this range of stress intensity the crack growth rate was considerably influenced by the microstructure. The main inicrostructural features that were observed to contnbute significantly to the differences in the fatigue crack growth of these specimens were. (a) the type and volume fraction of porosity, (b) the type and volume fraction of constituent particles, and (c) the grain structure, as shown in figure 3 Type I1 and 111 crack paths

Microstructural design of 7 x 0 aluminum alloysfor fracture and fatigue

283

were the most predominant in microstructures developed by process B. Type I was most frequently observed in recrystallized microstructures. A typical example is shown in figure 10. Typical data for the resistance to fatigue crack initiation is shown in table 5. This is in general agreement with the work of Sanders and Starke (15 ) .

Figure 10: Fatigue crack growth (2,700 cycles) in microstructures developed by process C. A tortuous crack path with crack with significant arrest are observed in unrecrystallized areas TABLE 5 RESISTANCE TO FATIGUE CRACK INITIATION MEASURED AS THE NUMBER OF KILOCYCLES TO PRODUCE A PRE-CRACK OF 0.4 MM UNDER THE SAME LOADING CONDITION

Recystallized high fpo 46

Recystallized high @a 59

Recystallized

Recysta1lized-k Unrecystallized

Unrecystallized

low fpo & fpa

low fpo & fpa

low fpo & fpa

71.8

Note: fpo = volumefraction ofporosi@, a n d f i a

61 = volumefraction

58

of secondphaseparticles.

The very fine recrystallized microstructures with low volume fracture of porosity and low volume fraction of large particles exhibited the highest resistance. This is attnbuted to the randomly oriented fine grains and the effectiveness of their high angle grain boundaries in preventing the transfer of plasticity to the adjacent grains. This inhibits the formation of long-range persistent slip bands. This resistance dropped considerably when either the porosity and or the particle volume fractions were increased. All other factors being equal, the increment in either the volume fraction or size of the Hydrogen porosity was observed to have the most deleterious effect. Primary hydrogen induced porosity was observed to play the most deleterious role in providing nucleation sites (Fig. 1l a and b) and propagation paths (Fig. 1l c and d) for cracks. The mechanisms of formation of this porosity are discussed elsewhere (18). The very fine intermediate semicoherent dispersoids of the type ZrAllj played a beneficial role in refining the grain and subgrain structure under all the processing conditions. They were indexed as a A3B-type superlattice structure. Both the crystallographic and the grain refining results are in agreement with recent work of Yan, Chunzhi and Minggao (10).

284

F.D.S. Marquis

I

. a

.

Figure 11: Effect of hydrogen porosity on faligue crack initiation (a) and (b) and on crack propagation: (c) and (d)

These metastable ZrA13 dispersoids were not observed to provide direct crack initiation sites or crack propagation paths under fatigue conditions. This role was observed only when they were associated with hydrogen and hydrogen induced porosity. Sub-boundaries were not observed to provide sites for crack initiation or paths for crack propagation in either theunaged or aged conditions. These results differ significantly with those of Karashima, Oikawa and Ogura (16) which reported that subgrain boundaries were preferred paths for fatigue crack propagation. A possible explanation may reside in the different processing parameters and consequent different substructures. Upon aging it was observed that the subgrain structures containing very fine dispersions of coherent and semicoherent precipitates were often associated with ductile fracture with characteristic deep an shallow dimples. In low purity materials large Fe, Cu and Si rich second phase particles were observed to influence significantly, especially in low purity materials (7050), the fracture toughness and the resistance to fatigue crack initiation and fatigue crack propagation and to enhance intergranular fracture. These results are in general agreement with models for the mechanics and kinetics of fracture processes discussed recently by Srivatsan (17). However in high purity materials (7150) this role of second phase particles was considerably reduced, the major role being played by the hydrogen induced porosity, which is discussed in more detail in a separate publication (18). It is important to notice that the effects of second phase particles and porosity change quantitatively and qualitatively during scaling up from laboratory castings to commercial size ingots. From the point of view of fracture toughness, resistance to fatigue crack initiation, and resistance to fatigue crack propagation, a good optimization of the microstructure consisted of finc unrecrystallized grains, (10 to 20 pm) with very fine subgrains (0.1 to 0.5 pm) containing a multidispersion of semicoherent and coherent precipitates and a considerable dislocation substructure. These microstructures could be achieved, representatively, through the type of advanced processing suggested in this work.

Microstructural design of 7x50 aluminum alloysfor fracture and fatigue

285

CONCLUSIONS In low purity materials recrystallized microstructures exhibited the lowest fracture toughness and intergranular fracture mode. In high purity materials, without intergranular porosity or intergranular coarse second phase particles, recrystallized microstructures, exhibited improved resistance to fatigue crack initiation. Unrecrystallized microstructures exhibited the highest fracture toughness and transgranular fracture mode. Subgrain structures developed during advanced processing containing fine dispersions of coherent and semicoherent precipitates, developed during double aging, showed with fracture. These microstructures exhibited improved fracture toughness and resistance to fatigue crack propagation. Hydrogen induced porosity was observed to play a considerable role in providing nucleation sites and propagation paths for cracks. In the manufacturing of thick structural plates through the casting of large ingots, special procedures must be implemented in order to decrease the size and volume fraction of hydrogen related porosity (both primary and secondary) and/or to change its morphology into a less deleterious one. In order to minimize the extent of recrystallization and to increase the resistance to fatigue crack initiation and fatigue crack propagation the following recommendations are made: (a) the amount of reduction per pass should not be higher than 24%, (b) the amount of reduction of the final pass should not be higher than 16%, (c) the hot rolling temperature should be adjusted in order to develop a very tine unrecrystallized microstructure.

ACKNOWLEDGEMENTS The author wants to acknowledge finding from the Institute for Mechanics and Materials at University of California-San Diego, the South Dakota School of Mines and Technology, and the Alcoa Foundation. In addition the author wants to thank Drs. J. Staley, D. Chakrabarti, and D. Granger for rewarding discussions.

REFERENCES 1.

Staley, J.T., Hunsicker, H.Y. and Schmidt, R. “New Aluminum Alloy 7050,”The Minerals, Metals, & Materials Society (1971).

2.

Staley, J.T. “Aging Kinetics of Aluminum Alloy 7050,” Met. Trans,, 5 (1974), 929.

3.

Staley, J.T. ”Advanced Aluminum Alloys,“ in Encyclopedia of Advanced Materials (Pergamon Press, 1994).

4.

Marquis, F.D.S. “Recrystallization Dynamics in 7050/7150 Aluminum Alloys”, Report to GOED, (1988).

5.

Marquis F.D.S, “Fatique Crack Propagation in 7050-7150 Aluminium Alloys,” Report to GOED, (1988).

6.

Marquis, F.D.S. “Design and Advanced Manufacturing for the Optimization of the Fracture Toughness and Fatigue Resistance of 7x50 Aluminum Alloys”, Institute for Mechanics and Materials, University of California, San Diego, Report 94-16, (1994).

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F.D.S. Marquis

7.

Marquis, F.D.S., "Macro and Micro Segregation and Porosity Distribution in 7050/7150 Ingot Materials," Unpublished Work.

8.

Yan, J., Chunzhi, L. and Minggao, Y. "On the q' Precipitate Phase in 7050 Aluminum Alloy", Muter. Sci. & Eng., A, 141 (1991), 123.

9.

Brenner, S.S., Kowalik, J., and Ming-Jian, H. "FIM/Atom Probe Analysis of a Heat Treated 7150 Aluminum Alloy," Surface Sci. 246 (1991), 210.

10.

Yan, J., Chunzhi, L. and Minggao, Y. " Transmission Electron Microscopy on the Microstructure of 7050 Aluminum Alloy in the T74 Condition", J. Muter. Sci., 27 (1992), 197.

11.

Marquis, F.D.S. "Analytical Electron Microscopy of Advanced Processed 7x50 Aluminum Alloys," Unpublished Work.

12.

Alarcon, O.E., Nazar, A. M. M. and Monteiro, W. M. "The Effect of Microstructure on the Mechanical Behavior and Fracture Mechanism in a 7050-T76 Aluminum Alloy", Muter. Sci. & Eng., A138 (1991), 275.

13.

Zaiken, E. and Ritchie, R.O. "Effects of Microstructure on Fatigue Crack Propagation and Crack Closure Behavior in Aluminum Alloy 7150," Muter. Sci. & Eng., 70 (1985), 151.

14.

Zaiken, E. and Ritchie, R.O. "On The Development of Crack Closure and the Threshold Condition for Short and Long Fatigue Cracks in 7150 Aluminum Alloy," Met. Trans:, 16A (1985), 1467.

15.

Sanders, R.E. Jr. and Starke, E. A. Jr., "The Effect of Intermediate Thermomechanical Treatments on the Fatigue Properties of a 7050 Aluminum Alloy," Met. Trans:, 9A (1987), 1087.

16.

Karashima, S., Oikawa, H. and Ogura, T. "Studies on Substructures Around a Fatigue Crack in FCC Metals and Alloys," Trans. Japan Inst. Metals, 9, 3 (1968), 205.

17.

Srivatsan, T.S. "Microstructure, Tensile Properties and Fracture Behavior of Aluminum Alloy 7150," J. Muter. Sci:, 27 (1992), 4772.

18.

Marquis, F.D.S. "Mechanisms of Formation of Hydrogen Porosity in 7x50 and 2x24 Aluminum Alloys. Effects on Mechanical Behavior," in Gus Interactions in Nonferrous Metals Processing, ed. D. Saha (The Minerals, Metals & Materials Society, 1996), 43.

Nan0 and Microstructural Design of Advanced Materials M.A. Meyers, R.O. Ritchie and M. Sarikaya (Editors) Published by Elsevier Ltd.

ELASTIC CONSTANTS OF DISORDERED TERNARY CUBIC ALLOYS Craig S. Hartley Air Force Research Laboratory, A FO SW A Arlington, VA 22203-1954

ABSTRACT Single crystal elastic constants of disordered alloys having body-centered cubic and face-centered cubic Bravais lattices can be calculated as functions of composition by modelling the lattice as a virtual crystal. The technique is based on the method of long waves applied to the virtual crystal. The three independent elastic constants are related to four, axisymmetric force constants (ASFC) for first and second neighbors. The ASFC are defined in terms of the first and second derivatives of a three-parameter, virtual pair potential, which is determined from the corresponding pair potentials of like and unlike atom pairs in the crystal weighted by the probabilities of their existence in the first and second neighbor shells. This technique permits calculation of single crystal elastic constants of multicomponent disordered alloys using data obtained from elastic constants of terminal solid solutions of binary alloys and pure elements when the elements have the same crystal structure as the alloys. An illustration of the technique is given for ternary alloys of copper, aluminium and nickel.

INTRODUCTION Single crystal elastic constants of pure elements and stoichiometric compounds can be calculated ab initio with very good accuracy by calculating the quadratic variation in energy with strain of a computational cell as a function of the state of strain. Elastic constants of disordered alloys are not easily computed by these methods because of the difficulty of modelling structures for which the exact position and species of each atom is not known. Approximations to the disordered state include the Coherent Potential Approximation (CPA) for alloy potentials [ 11 and employing a large computational cell to perform calculations for several atomic configurations to simulate disorder. Alternatively, the semi-empirical Modified Embedded Atom Method (MEAM) [2] can be employed. For these techniques, the identity of atoms present on each lattice site of the computational cell must be specified and the energy of the computational cell minimized not only with respect to external boundary conditions but also with respect to the positions of all of the atoms in the computational cell. A recent development proposed by Hartley [3] models elastic constants of disordered alloy single crystals by assuming a homogeneous virtual crystal with interactions between first and second neighbors. Axisymmetric force constants for the first and second neighbor shells are derived from a virtual pair potential that is a sum of the pair potentials of the various types of atomic pairs weighted by the probability of existence of each type of pair. A similar approximation is employed for the nearest neighbor distance in the virtual crystal. Pair potentials for like and unlike pairs are assumed to depend only on the nature of the

287

C.S. Hurtley

288

atomic species and the position vector connecting the atom centers and not otherwise on the surroundings. Thus, to a first approximation, potentials for unlike pairs derived from elastic constant measurements on binary disordered alloys can be employed to construct virtual potentials in multicomponent alloys that contain the two atomic species. In the following sections, the construction of the virtual potential is summarized, followed by a review of the connection between ASFC and single crystal elastic constants for bcc and fcc lattices. These concepts are then applied to demonstrate the calculation of the composition dependence of the single crystal elastic constants of a representative disordered ternary alloy using data on the binary alloys and pure substances.

ELASTIC CONSTANTS AND THE VIRTUAL POTENTIAL General Considerations The internal energy per atom, U, is approximated as the sum of two terms: 1) the sum of painvise interaction energies between a limited number of neighbors, Up, and 2) a many body term, UV, that depends on the total volume of the crystal and accounts for the interaction of electrons with one another and with individual ions. If the painvise interaction term arises entirely from the Coulomb energy of positive point charges arranged on a lattice immersed in a uniform environment of negative charge, forces between neighboring ions are directed towards the centers of the atoms. However, if the deviation of electron energies from those of a free electron is included in the pair potential, these forces depend not only on the distance between ion centers but also on the crystallographicdirection connecting them. To determine Up, select any atom as the origin of a coordinate system with directions as the associated coordinate axes. Since interatomic forces are generally of short range, sum the painvise interaction term over only first and second neighbor atoms. Expanding Up in terms of atomic displacement about the origin gives* [4,5],

where s is the number of atoms interacting with the atom at the origin and the primes indicate the order of partial differentiation of the interatomic pair potential, , with respect to components of the position vectors connecting the origin to each neighboring atom, evaluated at the equilibrium spacing between the atoms. The term involving first derivatives corresponds to the total force exerted by neighboring atoms on the atom at the origin. To avoid imposition of the Cauchy condition on the elastic constants of the crystal it is customary to choose UV such that the first order term in its Taylor series expansion exactly cancels this force. The zerofhand higher order terms are subsumed into the corresponding terms in the expansion of 4 . The complete Taylor series expansion of U, therefore, contains contributions from both the pair potential and the many-body contributions represented by Uv. With the above restrictions, the internal energy can be represented as an appropriate sum over a net pair potential, cp, that contains many-body terms.

+

, The second derivatives form a force constant matrix such that the second derivatives, cp0”(’) = f,,@)represent the force exerted on the atom at the origin in the x, direction when an atom at the rh lattice point experiences a unit displacement in the x, direction. Independence of the order of differentiation requires that the force constant matrix be symmetric. Neglecting terms O(luf) results in the harmonic approximation for the total potential energy of the crystal at absolute zero. The quasi-harmonic approximation, in which elements of f,,@) are regarded as temperature-dependent material parameters, is a similar form that describes the potential energy at temperatures above zero K.

* Summation from 1 to 3 over repeated Latin suffixes

is implied unless otherwise indicated.

Elastic constants of disordered ternary cubic alloys

289

Applying conditions that insure that the force constant matrix possesses the symmetry of the cubic crystal system reduces the number of independent force constants to two each for the first and second neighbors [6]. The axisymmetric force constants (ASFCs) for each of the first and second neighbor shells are 1) a,,, corresponding to stretching bonds between nthneighbors (n = 1,2), and 2) Pa, corresponding to bending such bonds away from the direction joining the atom centers. In terms of appropriate derivatives of the pair potential:

where r(") is the position vector connecting an atom at the origin to an atom in the nth neighbor shell. Derivatives appearing in equation (1) can be expressed in terms of the ASFC:

where

= xi"' /Ir('')l. The relationship between the ASFC and the single crystal elastic moduli can then

be obtained by comparing appropriate terms in the equations of motion of the atom at the origin [7,8]. The magnitudes and signs of the ASFC give useful information on the dependence of the pair potential on interatomic distance. If the minimum in cp occurs between the first and second neighbors, a1 would be expected to be positive and PI, negative. The second neighbor stretching constant, a2, will be positive also unless the potential exhibits oscillations in the vicinity of this distance [9], and p 2 will be positive. The relative magnitudes of the ASFC will depend on the shape of the potential curve near the first and second neighbor distances. Since there are four independent ASFC but only three independent elastic constants for cubic crystals, either additional experimental information is required or some assumptions must be made about the potential to determine the force constants in terms of the elastic constants. If neutron scattering data are available, a fourth independent, equation can be derived to provide a unique solution for the four ASFC [lo]. Since such information is rare for alloys, it is convenient to make an assumption that links the ASFC through a potential that can be determined by fitting data to elastic constants alone. For cubic metals, the three independent elastic constants depend on the first and second derivatives of the pair potential. Consequently, a general cubic expression in Irl, cp(r) = Q~ + Q,r + Q z r z+ ~

~

r

~

,

(4)

suffices to provide the required number of independent parameters to construct the potential. The parameters to be determined are the coefficients of the first, second and third powers of the interatomic distance, since the constant term does not enter into the expressions for the ASFC. The potential so obtained cannot give accurate values for absolute energies since the constant term is not determined from the elastic constants. Coefficients of the cubic polynomial potential can be related to other mathematical forms, such as the Morse Potential Function (MF'F) [ 111, by expanding the latter in a Taylor series about the minimum in the potential to third order in the interatomic distance, then comparing coefficients of like powers of Irl [3]. Since the

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 symmetric in p and v. the pair potential for the pv pair. Both pPvand qPV) 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 ( 5 ) 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 1

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 4 1 0 > directions, while the eight nearest neighbors in BCC are a0d3/2 from the origin along -411> directions. The 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 3 X 4 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, 1

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, define the M (M+1)/2 dimensional pair probability vector, P(M)as

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 3 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 1.

Table 1. Pair Spacings and Polynomial Potential Coefficients

The data in Table 1 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

1

to obtain the room-temperature elastic constants of single crystals of ternary alloys in the range 0


<

C.S. Hurtley

294

0.15, 0 SCN~ I 1.O. This range of compositions contains single-phase alloys based on the Cu-Ni system with A1 additions of up to 15 atomic percent. Not all alloys in this range are single phase at all temperatures [16], however the range contains most of the stable compositions.

Results of calculations for the three independent elastic coefficients, C11, C44 and C12 referred to the cube axes in reduced Voigt notation, are given in Figures 1-3 in the form of contour plots with level curves showing constant values of the elastic constants in units of GPa. The horizontal axes are the atomic percent of Al and the vertical axes are the atomic percent of Ni.

80

170

-170-

0-

c

5

10

c11

Figure 1. C1 I vs. composition for Al-Ni-Cu Alloys

Cl2

Figure 2. C12 vs. composition for Al-Ni-Cu Alloys

Elastic constants of disordered ternary cubic alloys

295

c44

Figure 3. C44 vs. composition for Al-Ni-Cu Alloys Results are also displayed as contour plots of the Fuchs constants, K = (CII+ 2ciz)/3 and C' in Figures 4 and 5.

0 1

K

Figure 4. K vs. composition for Al-Ni-Cu Alloys

80 60

40

ao 0 0 L'

5

10

Figure 5. C' vs. composition for Al-Ni-Cu Alloys

= (CII

- C12)/2,

C.S. Hurtley

296

Finally, contours of the Zener Anisotropy Factor, A = 2C44/(Cl1-C12),are shown in Figure 6. 1

0 -0.5

0 1

A

Figure 6 . A vs. composition for Al-Ni-Cu Alloys The most remarkable result of these calculations is the prediction of a maximum in A in the Cu-Ni binary system, which develops into a “ridge” of locally high values of A as A1 is added to alloys having a Cu:Ni ratio of approximately 4: 1. Such alloys have a maximum solubility for A1 near 10 atomic percent at 1000°C [16]. In general, the calculations indicate that additions of A1 to both alloys of Ni and Cu and the pure elements increase the value of A This result is contrary to the intuitive assumption based on the Law of Mixtures, which suggests that the addition of Al, relatively isotropic in the unalloyed state, would be expected to decrease A in the alloys. Another noteworthy result of this treatment is the observation, in agreement with experimental results, that the composition dependence of the single crystal elastic constants of Ni-rich Ni-A1 alloys is opposite to that expected from the Law of Mixtures [3]. Experiments to verify the predictions of these calculations for ternary alloys are in progress.

ACKNOWELDGEMENTS Facilities for this research were provided by the Air Force Research Laboratory at both the Air Force Office of Scientific Research and the Munitions Directorate. Helpful discussions with colleagues in AFRL are gratefully acknowledged.

REFERENCES 1. Vitos, L., Abrikosov, I. A. and Johansson, B. (2001) Phys. Rev. Let; 8 Oct. 2001; 87, 15640111-4. 2. Baskes, M.I. (1987) Phys. Rev. Let., 59,2666. 3. Hartley, C.S., Acta Materialia, (2003) (in press). 4. Johnson, R. A,, Phys. Rev. B, 1972,6,2094.

5 . Johnson, R. A,, Phys. Rev. B, 1974,9,1304. 6. Zaretsky, J. L. (1 979) Laftice Dynamics of hcp and bcc Zirconium, Ph.D. Dissertation, Iowa State University. 7. De Launay, J. in Solid State Physics, ed. F. Seitz and D. Tumbull ,Academic Press, 1956,2, New York, 285. 8. Squires, G. L., Arkivfor Fysik, 1963, 25, 21

9. Englert, A., Tompa, H. and Bullough, R. (1971) Fundamental Aseects of Dislocation Theory, edited by J. Simmons, R. deWit and R. Bullough, NBS Special Publication 317,1,273.

Elastic constants of disordered ternary cubic ulloys

291

10. Bullough, R. and Hardy (1968) J. R., Phil. Mag., 17, 833. 1I. Morse, P. M. (1929) f'hys. Rev.,3437. 12. Guggenheim, E. A,, Proc.Ro.v. Soc. (London), 1935, A148,304.

13. Hartley, C. S., Metallic Alloys: Experimental and Theoretical Perspectives, edited by I. S. Faulkner and R.G. Jordan, Kluwer Academic Press, Amsterdam, Netherlands, 1994, 171.

14. Moreen, H. A,, Taggart, R. and Polonis, D. H., Met. Trans., 1971,2,265.

15. Hartley, CS, Mat. ResSoc. Symp.Proc,, 2000,278, 279. 16. Prince, A,, Ternarv Allow, Vol. 4, edited by G. Petzow and G. Effenberg, VCH Publishers, New York, NY,1991,597. 17 . Pearson, W. B., Handbook of Lattice Spacings of Metals and Alloys, First Edition, Pergamon Press, New York, 1958.

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Index

ABC-Sic ceramics see silicon carbon (Sic) Advanced materials: demand for miniaturization 93-94 development: atomic level characterization 3 guided by assessment 3 microstructural characterization 4 microchemical design 11-19 structure-property relationship 93, 117 Aerospace industry: use of 7x50 aluminum alloys 274 use of metal injection molding (MIM) technique 69-78 Agar-based aqueous binder: benefits 71 description 70-72 mechanical properties: 17-4PH stainless steel 72-74 aerospace components example 76-77 dimensional control 78 nickel-based super alloy inconel 718 74-76 Al-Fe-Ti-Cr alloys: mechanical alloying (MA) process 191 experimental procedures 192-193 potential advantage over rapid quenching 192 Al-Mg-Si alloys: and atom probe field-ion microscopy (APFIM) 24 P“ phase 24-27, 32 Guinier Preston (GP-1) zones 23, 32 and high-resolution transmission electron microscopy (HREM) 24 materials/experiment details 24 poorly-developed pre-p’ or highly coherent GP-1 zones 30-31 poorly-developed Q particles 3 1-32 pre-P” or GP-1 zones 27-30 precipitation 23 strength enhancement 23-24 and through-focus exit-wave function reconstruction (TF-EWR) 24,32 Alloys: age-hardening 4 alloy-forming systems 204-205

aluminum (AL) 191-192 7x50 aluminum alloys 274-284 Al-Fe-Ti-Cr alloys 191-197 Al-Mg-Si alloys 24-32 bioactive glass coatings on Ti- and Cr-based alloys 61-66 bismuth alloying process 52-55 elastic constants of disordered alloys 288-296 Fe-Pd alloys 129-141 laser alloying 35-48 low-alloy steels 14-15 nanometer-sized particles 5 1-58 nickel-based superalloy inconel 71 8 74-76 stainless steel alloy 17-4PH 72-74 Aluminum (Al) alloys: applications 191 tensile strength 191-192 see also 7x50 aluminum alloys; Al-Fe-Ti-Cr alloys; Al-Mg-Si alloys 7x50 aluminum alloys: aerospace applications 274-275 fracture/fatigue behavior: agreement with recent work 280-281 crystallographic/grain-refining structure 283-284 low fracture toughness 281-283 thermomechanical processes 278-280 materials/experimental methods: deformation processes 275-277 typical compositions 275 use of AEMEDS techniques 277 use of electrodx-ray diffraction techniques 277 use of SADPdCBEDPs 277 use of TEM/SEM 276-277 microstructural design 273-275 strength gain 273 use of TEM/SEM techniques 276-277 Analytical electron microscopy (AEM) 11 and 7x50 aluminum alloys 277 Atomic level identities 3 Atomic level positions 3 Atomic Resolution Microscope (ARM) 7-8 299

300

Berkeley International Materials Conference (1964) 211 Beryllium silicon nitride 6 Bioactive glass coatings, on Ti- and Cr-based alloys 61-66 Bismuth alloying process 52-55 Bottom-up approach 211-212 Brittle failure: experimental techniques: automated crystallography for TEM (ACT) 13 electron energy loss spectroscopy (EELS) 13-14 X-ray energy dispersive spectroscopy (XEDS) 13 forms of 12 records of 11-1 2 using AEM technique 12 Bulk metallic glasses (BMGs): background 199-200 importance 209 mechanical behavior: free volume theory 209 hardness tests 208-209 strength/elasticity 206 temperature effects 206-209 viscosity 208 MG-Y-transition metal system 200-201 microstructural development 202 alloy-forming systems 204-205 crystallization behavior 203-205 diffusion 202 ex-situ composites 202 in-situ composites 202 nanocrystals 204, 209 nonequilibrium processing techniques 202-203 phase separation 203-204 reinforcement phases 202 use of Johnson-Mehl-Avrami (JMA) model 204 microstructure/properties dependence 199-209 Pd-based alloys 202 synthesis 200-202 thermal behavior 202

Index

Carbon nanotubes: characteristics 117-1 18 fabrication of vacuum microtriodes 118-1 26 as field emitters 118 stability of 118 Carbon steel, laser alloying 35-48 Cast iron, laser alloying 35-48 Chromium, alloying with 41-47 Co/Pt multilayered films 81 analysis as function of growth temperature 88-89 basis 85 magnetic properties 90 microstructural characterization 85-87 structure as function of Co thickness 89 Communications industry 93-94 Convergent beam electron diffraction patterns (CBEDPS), and 7x50 aluminum alloys 277 Creep see five-power-law-creep Cubic alloys see elastic constants of disordered alloys Diffraction analysis 5 Disordered alloys see elastic constants of disordered alloys Elastic constants of disordered alloys: application to ternary alloy system 293-296 background 287-288 virtual potential 290-291 axisymmetric force constants 291 composition dependence 291-293 general considerations 288-290 Electron microscopy 7-8 Electrons, sources in vacuum microelectronic devices 117 Energy dispersive spectroscopy (EDS), and 7x50 aluminum alloys 277 Fe-Pd alloys: microstructural evolution of cold-deformed Fe-Pd during isothermal annealing 129 background 130-131 backscatter electron (BSE) mode 131-132 experimental procedure 131 SEM and TEM studies 134-138,140-141 VSM experiments 132-133 XRD experiments 133

Index

Five-power-law-creep: background 255-257 Taylor hardening of metaldclass M alloys: challenges to 263 primary creep behavior 263-268 steady-state behavior 255, 257-263 theories 256-257 Ideal strength 173-175 see also iron (Fe) Inconel 7 18 74-76 Iron (Fe): ideal strength 173 ab initio calculations 174-175, 189 equilibrium structures 176-178 identification of saddle point structures 174 in multiaxial loading 187-1 89 useful tensile strength/fcc phase combination 175 ideal strength computation 173-174, 176 Cauchy stress 176 full potential linearized augmented plane wave (FLAPW) method 176 general gradient approximation (GGA) method 176 projector augmented wave (PAW) method 176 ideal strength in shear 189 magnetic instabilities 186-1 87 shear strength of FM bcc Fe 183-1 86 ideal strength in tension 179, 189 comparison with previous calculations/ experiment 182 magnetic instabilities 181-182 tetragonal vs orthorhombic instability 179-181 use of 173 Kikuchi electron diffraction

5-6

Laser alloying 35 with chromium 41-47 experimental procedure 36-37 LAZ/HAZ characteristics 4 7 4 8 with silicon 3 9 4 1 surface layer methods 35-36 with tantalum 37-39 Lattice imaging 6 , 7

301

Length scale effects: bottom-up approach 21 1-212 experimental procedures 213 importance 219 load-displacement response 213-214 nanosphere deformation 214-21 7 theoretical basis 212-213 thin films 217-219 Lorentz transmission electron microscopy (LTEM) 93,94-99 magnetic film: effect of micromagneticripple/2D-topgraphy of the film 100-103 experimental observations 95-99 Fresnel contrast of image 99-100 ID-wave film topography 103-105 Magnesia, Lang transmission x-ray topography 235-236 Magnetic film: knowledge of local properties 94 LTEM technique 94-95 experimental observations 95-99 theoretical analysis 99-105 quantitative analysis 94 uses 94 Medical implants, use of bioactive glass coatings on Ti- and Cr-based alloys 61-66 MEMS (Micro-Electro-Mechanical Systems) 117-1 18 Metal injection molding (MIM): aerospace application 69 Agar-based aqueous binder: comparison with traditional MIM system 71 description 70-72 mechanical properties 72-78 cost effectiveness 69 use of binder systemshstrumentation 69-70 Metauglass interface during enameling: and bioactive glass coatings on Ti- and Cr-based alloys 61-66 effectiveness of 61 evolution 63 experimental procedures 62 main reactions 63-64 medical applications 61 optimum adhesion 64-66

302

Metallic glasses see bulk metallic glasses Metallic-intermetalic laminate (MIL) composites 243 advantages 244-245 composition, physical, mechanical properties 244 mollusk shells 243 multi-functional 249 embedded sensing capability 25 1 enhanced energy absorbing/fluid conduit modified 250-25 1 fully-functional 252 synthesis having meso-scale cavities to incorporate vibration damping 250 through-thickness wiredtubes 251-252 production from elemental titanium/ aluminum foils 244 structural performance attributes 246-247 structural plus ballistic attributes 248 structural plus thermal management attributes 248-249 uniqueness 245 Microstructures 4 phase contrast ‘lattice’ imaging 6 spinodal decomposition in 5-6 Nano-layer microstructures 81 C o p t multilayered films 85-90 steels-microcomposite martensite 82-85 Nanometer-sized particles: alloy phase formation experimental procedures 50-5 1 alloying processes 52-59 In-Sn system 55-58, 59 Sn-Bi system 52-55,58-59 studies on 49-50 National Center for Electron Microscopy 7, 11 Nolder 221, 228 Pearlite 3 Phase contrast methods 6 Plastic deformation: martensitic transformation 221-223 calculational procedure 223-228 constitutive description of slip 223-225 constitutive equation for twinning 226

Index

martensitic strains and strain rates 226-228 predicted values in shock compression 228-229 nanospheres 213-21 7 thin films 217-219 Primary creep behavior see five-power-law-creep Sapphire, Lang transmission x-ray topography 235-236 Scanning electron microscopy (SEM), and 7x50 aluminum alloys 276-277 Screw dislocation between two cavities 109-1 11 solutions for different discontinuity cuts 11-14 Selected area diffraction patterns (SADPS), and 7x50 aluminum alloys 277 Shock compression 221,228-229 Silicon, alloying with 39-41 Silicon carbon (Sic): microstructure/properties of in situ toughened S i c 145 applications 145 effects of additive content 152-154 effects of post-annealing 148-151 experimental procedures 145 general aspects 145-148 procesdstrategy 145 Silicon crystal devices, line-modified-asymmetric crystal topography (LM-ACT) 238-240 Size effects 21 1 Slip induced stress amplification in thin ligaments 114-116 Slip-twinning transition 221-222, 226, 230 calculations 223-8 shock compression experiments 228-229 Spinodal decomposition 5-6 Stainless steel alloy 17-4PH 72-74 Steady-state creep behavior see five-power-law-creep Steel: brittle failure 14-1 5 laser alloying 35-58 multilayered retained austenite/martensite 8 1,82-85 stainless steel alloy 17-4PH 72-74 Stress amplification 114-1 16 Surface layer alloying see laser alloying

303

Index

Tantalum, alloying with 37-39 Taylor hardening see five-power-law-creep Ternary cubic alloys see elastic constants of disordered alloys Thomas, Gareth 148, 199, 211, 221, 228 awardskontributions 9 background 4 broad-based research 93 early developments 5-6 innovations 7-8 legacy 9 in praise of 10 Tin alloying process 55-58 Top-down approach 21 1 Transformation toughened materials 199-200 Transmission electron microscopy (TEM) 4,6, 11,93 and 7x50 aluminum alloys 276-277 and early-stage precipitation in Al-Mg-Si alloys 23-32 and testing of 7x50 aluminum alloys 276 Two-beam ‘sideband’ imaging method 6 Vacuum microelectronic devices 117 Vacuum microtriodes: MEMS based: applications 119 electric breakdown problem 126 evaluation of dc characteristics 123-125 experimental procedures 118 flexibility in designing microwave deviceslcircuitries 122

operation of 125 performance 125 transconductance of use of cold cathodes

125 119-120

WC-Co cermets: creep deformation behavior 171, 163-1 65 designing cermets superior to WC-Co 166-168, 171 development 157 fracture toughness 165-1 66, 171 hierarchically structured ‘functional’ WC-Co cermets 168-171 microelement models 158-1 60, 171 micromechanics 157-158 microstructure 157 strength 160-163, 171 X-ray diffraction topography (SRDT): Berg-Barrett (B-B) observations in zinc 234-235 hardness strains in RDX and AP crystals 236-238 Lang transmission XRDT of (Magnesia and) sapphire 235-236 LM-ACT for perfect silicon crystal devices 238-240 St Louis conference (1961) 233 Zinc, X-ray topography

234-235

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