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Springer Series in
S O L I D - S T A T E S C I E N C E S 126
Springer-Verlag Berlin Heidelberg GmbH
Springer Series in
S O L I D - S T A T E S C I E N C E S
Series Editors: M . Cardona P. Fulde K. von Klitzing R. Merlin H.-J. Queisser H. Stornier
126 Physical Properties of Quasicrystals Editor: Z.M. Stadnik
Volumes 1-125 are listed at the end of the book.
Zbigniew M. Stadnik (Ed.)
Physical Properties of Quasicrystals
With 221 Figures
Springer
Professor Dr. Zbigniew M . Stadnik
University of Ottawa, Department of Physics 150 Louis Pasteur, Ottawa Ontario K i N 6N5, Canada e-mail: [email protected]
Series Editors:
Professor Dr., Dres. h . c. Manuel Cardona Professor Dr., Dres. h . c. Peter Fulde* Professor Dr., Dres. h . c. Klaus von Kl i tz ing Professor Dr., Dres. h . c. Hans-Joachim Queisser
Max-Planck-Institut für Festkörperforschung, Heisenbergstrasse 1, D-70569 Stuttgart, Germany * Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Strasse 38
D-01187 Dresden, Germany
Professor Dr. Roberto M e r l i n Department of Physics, 5000 East University, University of Michigan A n n Arbor, M I 48109-1120, U S A
Professor Dr. Horst Stornier Dept. Phys. and Dept. Appl . Physics, Columbia University, New York, N Y 10023 and Bell Labs., Lucent Technologies, Murray H i l l , NJ 07974, U S A
ISSN 0171-1873
ISBN 978-3-642-63593-9 ISBN 978-3-642-58434-3 (eBook) DOI 10.1007/978-3-642-58434-3
Library of Congress Cataloging-in-Publication Data applied for
Die Deutsche Bibliothek - CIP-Einheitsaufnahme Physical properties of quasicrystals I Zbigniew M . Stadnik (ed.). Berlin ; Heidelberg ; New York ; Barcelona ; Hong Kong; London ; Milan; Paris; Singapore ; Tokyo : Springer 1999 (Springer series in solid-state sciences; 126) ISBN 978-3-642-63593-9
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Preface
The discovery in 1984 of crystals with "forbidden" symmetry, materials that were dubbed quasicrystals, opened a new branch of crystallography and solidstate physics. These structures possess long-range aperiodic order and crystallographically forbidden rotational symmetries, and are thus fundamentally different from the two other known types of solid structure, crystalline and amorphous. The literature devoted to the physical properties of quasicrystals has been growing so rapidly that it is very difficult for a scientist to remain well informed on more than a narrow speciality within this area. Some definite and intriguing new physical phenomena have already been discovered, and other surprising results will probably follow. Our knowledge of the physical properties of quasicrystals has now reached such a maturity that it seems necessary to provide a comprehensive review. I think this is an opportune time to produce a research-level monograph on the subject. As yet, no comprehensive treatise exists at this level. It is very unlikely that a single author could produce a monograph at the level and depth that is needed to do justice to the physical properties of quasicrystals. I hope that this book comes close to being such a monograph.
This book is intended for researchers in the field of the physics of quasicrystals, solid-state physicists, materials scientists, crystallographers, as well as for graduate students working in the area of new materials. Written by active researchers in their respective fields, it summarizes in a critical fashion much of our present knowledge and understanding of the complex, yet exciting physical properties of quasicrystals. I hope that it conveys some of the fascination I have found during my work in this field. We are still far from a complete understanding of these materials; this book will have served its purpose if it stimulates new research and helps to guide that research in fruitful directions.
I wish to thank the authon, for their thorough and competent work. I thank my departmental colleague, Dr. Brian A. Logan, for his assistance with the English of the book. I am grateful to Dr. Claus Ascheron from Springer-Verlag for his advice and friendly patience concerning some unexpected delays. Finally, I express my thanks to Dr. Gerhard Stroink from Dalhousie University who introduced me in 1986 to the fascinating research area of quai'iicrystals.
Ottawa, September 1998 Zbigniew M. Stadnik
Contents
1. Introduction Zbigniew M. Stadnik . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
References ..................................................... 3
2. Metallurgy of Quasicrystals An Pang Tsai .................................................. 5
2.1 Introduction............................................... 5 2.2 Preparation of Quasicrystals ................................ .
2.2.1 Rapid Solidification .................................. . 2.2.2 Vapor Condensation .................................. . 2.2.3 Mechanical Alloying .................................. . 2.2.4 Crystallization of Melt-Quenched Amorphous Ribbons .... . 2.2.5 Conventional Solidification ............................ .
6 6 7 8 9 9
2.3 Structural Classification from Diffraction Patterns. . . . . . . . . . . . .. 10 2.3.1 Three-Dimensional Quasicrystals . . . . . . . . . . . . . . . . . . . . . . .. 11 2.3.2 Two-Dimensional Quasicrystals ........................ 13 2.3.3 One-Dimensional Quasicrystals ......................... 17
2.4 Quasicrystalline Alloy Systems and the Formation of Quasicrystals . . . . . . . . . . . . . . . . . . . . . . . . . .. 17 2.4.1 Metastable Quasicrystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 17 2.4.2 Stable Quasicrystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 20 2.4.3 Quasicrystals as Hume-Rothery Phases .................. 23
2.5 Phase Transformation from Amorphous to Icosahedral Phase. . . . . . . . . . . . . . . . . . . . . . . .. 26
2.6 Phase Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 29 2.6.1 AI-Li-Cu............................................. 29 2.6.2 AI-Cu-Fe............................................. 31 2.6.3 Al-Pd-Mn............................................ 31 2.6.4 Zn-Mg-Y............................................. 33 2.6.5 Al-Ni-Co............................................. 33
2.7 Growth of Quasicrystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 35 2.7.1 Morphologies of Quasicrystals .......................... 35 2.7.2 Solidification of Quasicrystals. . . . . . . . . . . . . . . . . . . . . . . . . .. 39 2.7.3 Growing Large Single Grains. . . . . . . . . . . . . . . . . . . . . . . . . .. 43
VIII Contents
2.8 Summary.................................................. 44 References ..................................................... 45
3. Crystallography of Quasicrystals Walter Steurer and Torsten Haibach. . . .. . . . . . . . . . . . . . . . . . . . . . . . . .. 51
3.1 Introduction............................................... 51 3.2 N-Dimensional Description of Quasicrystals. . . . . . . . . . . . . . . . . . .. 52
3.2.1 Embedding of Direct and Reciprocal Space. . . . . . . .. . . . . .. 52 3.2.2 Structure Factor ........ . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 57
3.3 One-Dimensional Quasicrystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 58 3.3.1 Indexing............................................. 59 3.3.2 Symmetry............................................ 60 3.3.3 Example of a One-Dimensional Quasicrystal:
Fibonacci Phase ...................................... 60 3.4 Decagonal Quasicrystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 65
3.4.1 Indexing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 65 3.4.2 Symmetry............................................ 66 3.4.3 Example of a Decagonal Phase: Layers of Penrose Tilings .. 68
3.5 Icosahedral Quasicrystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 76 3.5.1 Indexing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 76 3.5.2 Symmetry............................................ 79 3.5.3 Example of a Three-Dimensional Quasilattice:
Ammann Tiling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 82 References ..................................................... 89
4. Experimental Determination of the Structure of Quasicrystals
Michel Boudard and Marc de Boissieu . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 91
4.1 Introduction............................................... 91 4.2 X-ray and Neutron Diffraction ............................... 94
4.2.1 Patterson Analysis .................................... 95 4.2.2 Contrast Variation .................................... 96
4.3 Structure of the AI-Pd-Mn Icosahedral Phase. . . . . .. .. . . . . . . . .. 97 4.3.1 Space Group Determination. . . . . . . . . . . . .. . . . . . . . . . . . . .. 98 4.3.2 Patterson Analysis .................................... 101 4.3.3 First-Order Model ..................................... 105 4.3.4 About the Resulting Atomic Structure ................... 106 4.3.5 Limitations of the Direct Approach ...................... 110 4.3.6 Modeling ............................................. 110
4.4 Structure of the AI-Ni-Co Decagonal Quasicrystal .............. 119 4.5 Conclusions ................................................ 124 References ..................................................... 124
Contents IX
5. Electronic Transport Properties of Quasicrystals - Experimental Results
Osten Rapp .................................................... 127
5.1 Introduction ............................................... 127 5.1.1 Background .......................................... 127 5.1.2 Resistance Anomalies .................................. 128 5.1.3 Outline .............................................. 130
5.2 Experimental Results ....................................... 130 5.2.1 Overview ............................................ 130 5.2.2 High-Temperature Electrical Resistivity .................. 134 5.2.3 Hall Effect and Thermoelectric Power .................... 135 5.2.4 Icosahedral Approximants .............................. 137 5.2.5 Decagonal Quasicrystals ............................... 138
5.3 Towards Understanding Transport Properties .................. 140 5.3.1 Strong Sensitivity to Electron Concentration .............. 141 5.3.2 Magnitude of the Electrical Resistivity ................... 144 5.3.3 The Magnetoresistivity ................................ 147 5.3.4 p(T) at Low and Intermediate Temperatures .............. 154 5.3.5 Is There a Metal-Insulator Transition
in Icosahedral AI-Pd-Re? ............................... 156 5.4 Concluding Remarks ........................................ 159 References ..................................................... 162
6. Theory of Electronic Structure in Quasicrystals
Takeo Fujiwara ................................................. 169
6.1 Introduction ............................................... 169 6.2 Electronic Structure
in One- and Two-Dimensional Quasilattices . . . . . . . . . . . . . . . . . . .. 172 6.2.1 One-Dimensional Quasilattice: Fibonacci Lattice .......... 172 6.2.2 Two-Dimensional Quasilattice: Penrose Lattice ............ 175
6.3 Electronic Structure in Quasicrystals .......................... 179 6.3.1 Method of Calculations:
Tight-Binding LMTO and Related Methods . . . . . . . . . . . . . . 179 6.3.2 Quasi-Brillouin Zone
and Modification of DOS of Model Icosahedral Al ......... 180 6.3.3 Electronic Structure in MI-Type Icosahedral Quasicrystals . 181 6.3.4 Electronic Structure in TC-Type Icosahedral Quasicrystals . 185 6.3.5 Electronic Structure in Decagonal Quasicrystals ........... 185 6.3.6 General Characteristics of DOS and Wave Functions ....... 188 6.3.7 Experimental Study of Electronic Structures .............. 194
6.4 Transport Properties in Quasicrystals ......................... 194 6.4.1 Scenario of Transport in Random Systems ................ 194 6.4.2 Experimental Observations ............................. 196
X Contents
6.4.3 Effects of Randomness ................................. 196 6.4.4 Boltzmann Theory and Relaxation-Time Approximation ... 197 6.4.5 Anomalous Diffusion ................................... 200 6.4.6 Scaling Behavior ...................................... 200 6.4.7 Scenario of Transport in Quasicrystals ................... 202
6.5 Summary .................................................. 203 References ..................................................... 204
7. Elementary Excitations and Physical Properties
Jurgen Hafner and Marian KrajCf ................................. 209
7.1 Introduction ............................................... 209 7.1.1 Quasiperiodic Structure ................................ 209 7.1.2 Physical Properties .................................... 210 7.1.3 Spectral Properties of Quasiperiodic Hamiltonians ......... 211
7.2 Quasiperiodicity, Symmetry, and Elementary Excitations .................................. 214
7.3 Modelling Quasicrystalline Structures and Approximant Phases .................................... 216 7.3.1 Icosahedral Quasicrystals ............................... 216 7.3.2 Decagonal Quasicrystals ............................... 218 7.3.3 Approximant Structures ............................... 219
7.4 Numerical Characterization of Elementary Excitations ................................... 222 7.4.1 Direct Diagonalization ................................. 222 7.4.2 Real-Space Recursion .................................. 223 7.4.3 Comparison With Experiment .......................... 224
7.5 Phonons in Quasicrystals .................................... 224 7.5.1 Interactomic Force Law
and Quasiperiodicity - Modulated Quasicrystals .......... 224 7.5.2 Phonons in Icosahedral Quasicrystals .................... 226 7.5.3 Phonons in Decagonal Quasicrystals ..................... 231 7.5.4 Phonons - Summary ................................... 234
7.6 Electrons in Quasicrystals ................................... 234 7.6.1 s,p-Bonded Icosahedral Alloys as Hume-Rothery Phases ... 235 7.6.2 Icosahedral
and Decagonal Aluminum-Transition Metal Alloys ......... 238 7.6.3 Titanium-Based Quasicrystals .......................... 242 7.6.4 Fine Structure of the Electronic Spectrum,
Pseudogaps, and Real Gaps ............................ 242 7.6.5 Band-Structure Effects in Electronic Transport ........... 246 7.6.6 Magnetic Properties of Quasicrystals .................... 248 7.6.7 Electrons - A Summary ................................ 249
7.7 Final Remarks ............................................. 251 References ..................................................... 251
Contents XI
8. Spectroscopic Studies of the Electronic Structure
Zbigniew M. Stadnik ............................................ 257
8.1 Introduction ............................................... 257 8.2 Theoretical Predictions ...................................... 258
8.2.1 Pseudogap in the Density of States ...................... 258 8.2.2 Fine Strucure of the Density of States ................... 259
8.3 Experimental Results ....................................... 260 8.3.1 s,p-Bonded Icosahedral Alloys .......................... 260 8.3.2 AI-Cu-Transition Metal Icosahedral Alloys ................ 263 8.3.3 AI-Pd-Mn Icosahedral Alloys ........................... 271 8.3.4 AI-Pd-Re Icosahedral Alloys ............................ 275 8.3.5 AI-Co-Cu Decagonal Alloys ............................. 277 8.3.6 AI-Ni-Co and AI-Ni-Rh Decagonal Alloys ................. 278 8.3.7 Fine Structure of the Density of States ................... 280
8.4 Uniqueness of the Electronic Structure of Quasicrystals ............................................ 284
8.5 Quasiperiodicity and Unusual Physical Properties ............... 287 8.6 Conclusions and Outlook .................................... 288 References ......................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289
9. Magnetic Properties of Quasicrystals Kazuaki Fukamichi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295
9.1 Introduction ............................................... 295 9.2 AI-Based Quasicrystals ...................................... 296
9.2.1 Paramagnetism, Effective Magnetic Moment and Saturation Magnetization .......................... 296
9.2.2 Fraction of Magnetic Mn Atoms and Giant Magnetic Moment ........................... 299
9.2.3 Difference Between Magnetic Moments in Icosahedral and Decagonal Phases .......... . . . . . . . . . . . . . . . . . . . . . . . 301
9.2.4 Spin-Glass Behavior ................................... 303 9.2.5 Low-Temperature Specific Heat ......................... 306 9.2.6 Model for Magnetism and Pauling Valence ............... 308 9.2.7 Phasons, Diamagnetism, and Pauli Paramagnetism ........ 309 9.2.8 Ferromagnetism ....................................... 312
9.3 Mg-RE-Zn Quasicrystals ..................................... 315 9.3.1 Susceptibility and Spin-Glass Behavior ................... 316 9.3.2 Low-Temperature Specific Heat ......................... 318 9.3.3 Antiferromagnetism ................................... 321
9.4 Summary .................................................. 323 References ..................................................... 324
XII Contents
10. Surface Science of Quasicrystals Patricia A. Thiel, Alan I. Goldman, and Cynthia J. Jenks ............ 327
10.1 Introduction ............................................... 327 10.1.1 Background ......................................... 327 10.1.2 Outline ............................................. 328
10.2 Oxidized Surfaces ........................................... 328 10.2.1 Overview ........................................... 328 10.2.2 Oxide Composition ................................... 329 10.2.3 Oxide Depth ........................................ 329 10.2.4 Comparison to Crystalline Materials .................... 331 10.2.5 Oxide Structure ...................................... 333 10.2.6 Oxidation-Induced Phase Transformations ............... 333
10.3 Surface Energies ............................................ 334 10.4 Clean Surfaces ............................................. 337
10.4.1 Methods of Clean Surface Preparation .................. 337 10.4.2 Surface Composition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 340 10.4.3 Surface Structure and Topography ..................... 341 10.4.4 Surface Chemistry .................................... 351
10.5 Friction ................................................... 352 10.6 Concluding Remarks ........................................ 355 References ..................................................... 355
11. Mechanical Properties of Quasicrystals Knut Urban, Michael Feuerbacher, Markus Wollgarten, Martin Bartsch, and Ulrich Messerschmidt ......................... 361
11.1 Introduction ............................................... 361 11.2 Low-Temperature Mechanical Properties ....................... 362
11.2.1 Mechanical Property Data ............................. 362 11.2.2 Fracture ............................................ 363
11.3 Dislocations in Quasicrystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365 11.3.1 Background ......................................... 365 11.3.2 Dislocations in a Quasilattice ......................... 366 11.3.3 Dislocation Analysis .................................. 368
11.4 High-Temperature Plastic Deformation ........................ 371 11.4.1 Background ......................................... 371 11.4.2 Theoretical .......................................... 371 11.4.3 Results of Mechanical Testing .......................... 375 11.4.4 Microscopic Observations ............................. 380
11.5 Discussion ................................................. 388 11.5.1 Model of Dislocation Friction in Quasicrystals ........... 392
11.6 Concluding Remarks ........................................ 396 References ..................................................... 397
Contents XIII
12. Toward Industrial Applications Patrick C. Gibbons and Kenneth F. Kelton ........................ 403
12.1 Introduction ............................................... 403 12.2 The Relevant Properties of Quasicrystals ...................... 403
12.2.1 Electronic Structure and Transport ..................... 403 12.2.2 Visible and Infrared Optical Properties ................. 405 12.2.3 Thermopower ........................................ 406 12.2.4 Lattice Dynamics .................................... 407 12.2.5 Ductility ............................................ 409 12.2.6 Surface Properties .................................... 411 12.2.7 Corrosion Resistance ................................. 413 12.2.8 Hydrogen Storage .................................... 414
12.3 Possible Applications ........................................ 421 12.3.1 Coatings ............................................ 421 12.3.2 Dispersion Hardening of Crystalline, Quasicrystalline,
and Amorphous Alloys ................................ 423 12.3.3 Selective Absorbers for Solar-Thermal Converters ........ 424 12.3.4 Thermoelectric Devices ............................... 425 12.3.5 Hydrogen Storage and Battery Applications ............. 425
12.4 Conclusion ................................................. 426 References ..................................................... 427
Subject Index ................................................ 433
List of Contributors
Martin Bartsch Max-Planck-Institut fur Mikrostrukturphysik, Weinberg 2 D-06120 Halle/S. Germany
Michel Boudard Laboratoire de Thermodynamique et de Physico-Chimie Metallurgiques UMR 5614 CNRS, INPG, UJF, BP 75,38402 Saint Martin d'Heres Cedex France
Marc de Boissieu Laboratoire de Thermodynamique et de Physico-Chimie Metallurgiques UMR 5614 CNRS, INPG, UJF, BP 75,38402 Saint Martin d'Heres Cedex France
Michael Feuerbacher Institute fUr Festkorperforschung Forschungszentrum Jiilich GmbH D-52425 Julich Germany
Takeo Fujiwara Department of Applied Physics University of Tokyo Hongo 7-3-1, Bunkyo-ku Tokyo 113 Japan
Kazuaki Fukamichi Department of Materials Science Faculty of Engineering Tohoku University Sendai 980-77 Japan
Patrick C. Gibbons Department of Physics Washington University St. Louis, Missouri 63130 USA
Alan I. Goldman Department of Physics and Astronomy, and Ames Laboratory Iowa State University Ames, IA 50011 USA
J iirgen Hafner Institute fUr Theoretische Physik and Center for Computational Materials Science Technische Universitiit Wien A-1040 Wien Austria
Torsten Haibach Laboratory of Crystallography ETH-Zurich, 8092-Zurich Switzerland
XVI List of Contributors
Cynthia Jenks Department of Chemistry and Ames Laboratory Iowa State University Ames, IA 50011 USA
Kenneth F. Kelton Department of Physics Washington University St. Louis, Missouri 63130 USA
Marian Krajci Institute of Physics Slovak Academy of Sciences SK-84228 Bratislava Slovak Republic
Ulrich Messerschmidt Max-Planck-Institut fUr Mikrostrukturphysik, Weinberg 2 D-06120 Halle/S. Germany
Osten Rapp Physics Department Kungliga Tekniska Hogskolan SE 100 44 Stockholm Sweden
Zbigniew M. Stadnik Department of Physics University of Ottawa Ottawa, Ontario KIN 6N5 Canada
Walter Steurer Laboratory of Crystallography ETH-Ziirich, 8092-Ziirich Switzerland
Patricia A. Thiel Department of Chemistry and Ames Laboratory Iowa State University Ames, IA 50011 USA
An Pang Tsai National Research Institute for Metals Tsukuba 305 Japan
KnutUrban Institute fiir Festkorperforschung Forschungszentrum Jiilich GmbH D-52425 Jiilich Germany
Markus Wollgarten Centre d'Etudes de Chimie Metallurgique 15, rue Georges Urbain F-94407 Vitry-sur-Seine Cedex France
