Preface ....................................................... vii
Chapter 1. INTRODUCTION TO QUASICRYSTALS
Takeo Fujiwara and Yasushi Ishii
1.1 Discovery of non-crystalline rotational symmetry ........... 1
1.2 Quasiperiodic lattice ...................................... 2
1.3 Icosahedral quasilattice and its symmetry .................. 4
1.4 Phonons and phasons ........................................ 6
1.5 Electronic structure and related physical properties ....... 8
Chapter 2. RECENT DEVELOPMENTS OF QUASICRYSTALLOGRAPHY
Akiji Yamamoto and Hiroyuki Takakura
2.1 Introduction .............................................. 11
2.2 nD description of quasicrystals ........................... 14
2.3 Decagonal, dodecagonal and icosahedral coordinate
systems ................................................... 15
2.4 Low-density elimination method ............................ 17
2.5 Modification of models in the structure refinement ........ 19
2.6 Higher-dimensional cluster models of decagonal
quasicrystals ............................................. 23
2.7 Higher-dimensional cluster models of icosahedral
quasicrystals ............................................. 29
2.8 Quasicrystal models with fractal occupation domains ....... 36
2.9 Symmetry breaking in clusters ............................. 39
2.10 Modulation functions for quasicrystals .................... 43
2.11 Summary ................................................... 43
Chapter 3. NEW GROUP OF ICOSAHEDRAL QUASICRYSTALS
Tsutomu Ishimasa
3.1 Introduction .............................................. 49
3.2 Classification of icosahedral quasicrystals ............... 50
3.3 Approximants including Tsai-type cluster .................. 50
3.4 Preparation methods of Zn- and Cu-based quasicrystals ..... 54
3.5 Zn-Mg-Sc quasicrystal as a prototype ...................... 55
3.6 Other Zn- and Cu-based quasicrystals ...................... 58
3.7 Single-quasicrystals and microvoids ....................... 63
3.8 Central structure of the Tsai-type cluster ................ 64
3.9 Alloy chemistry and the Tsai-type quasicrystals ........... 67
3.10 Conclusion ................................................ 71
Chapter 4. QUASICRYSTALS AND APPROXIMANTS IN CD-M SYSTEMS
AND RELATED ALLOYS
An-Pang Tsai and Cesar Pay Gomez
4.1 Introduction .............................................. 75
4.2 Approximants in the Cd-M systems .......................... 78
4.3 Stable quasicrystals of the Cd-Yb class ................... 90
4.4 Hume-Rothery conditions for the stable quasicrystals ...... 98
4.5 Concluding remarks ....................................... 104
Chapter 5. PHASON MODES IN APERIODIC CRYSTALS
M. de Boissieu, R. Currat, and S. Francoual
5.1 Introduction: Hydrodynamic modes and quasiperiodic
structures ............................................... 107
5.2 Modulated crystals ....................................... 116
5.3 Binary composites ........................................ 126
5.4 Hydrodynamics of icosahedral phases ...................... 129
5.5 Phason modes in the icosahedral AlPdMn quasicrystal ...... 142
5.6 Phason modes in other quasicrystals ...................... 155
5.7 Conclusion ............................................... 162
Chapter 6. ELECTRONIC STRUCTURES AND STABILITY MECHANISM OF
QUASICRYSTALS
Yasushi Ishii and Takeo Fujiwara
6.1 Introduction ............................................. 171
6.2 Stability mechanism - Hume-Rothery versus hybridization .. 173
6.3 Ab initio methods for calculating electronic structures
of QCs ................................................... 176
6.4 Electronic structure of QC-related compounds ............. 179
6.5 Concluding remarks ....................................... 203
Chapter 7. QUANTUM TRANSPORT IN QUASICRYSTALS AND COMPLEX
METALLIC ALLOYS
Didier Mayou and Guy Trambly de Laissardière
7.1 Introduction ............................................. 209
7.2 Quantum formalism for electronic transport ............... 211
7.3 Anomalous quantum diffusion and conductivity in
periodic and quasiperiodic systems ....................... 228
7.4 Evidence of anomalous quantum diffusion in quasicrystals
and approximants ......................................... 245
7.5 Conclusion ............................................... 261
Chapter 8. ELASTIC AND PLASTIC PROPERTIES OF QUASICRYSTALS
S. Takeuchi and K. Edagawa
8.1 Introduction ............................................. 267
8.2 Elastic properties ....................................... 268
8.3 Dislocations and their motion ............................ 282
8.4 Mechanical properties .................................... 291
8.5 Deformation mechanisms ................................... 297
Chapter 9. AB-INITIO STUDIES OF QUASICRYSTALLINE SURFACES
M. Krajči and J. Hafner
9.1 Introduction ............................................. 313
9.2 Computational method ..................................... 316
9.3 Fivefold surface of i-Al-Pd-Mn ........................... 316
9.4 Study of the tenfold surface of d-Al-Co-Ni ............... 337
9.5 Summary .................................................. 349
9.6 Outlook .................................................. 351
Index ......................................................... 357
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