Quasicrystals (eBook)

Cover 1
Contents 12
Preface 8
Chapter 1. Introduction to Quasicrystals 16
1.1. Discovery of non-crystalline rotational symmetry 16
1.2. Quasiperiodic lattice 17
1.3. Icosahedral quasilattice and its symmetry 19
1.4. Phonons and phasons 21
1.5. Electronic structure and related physical properties 23
Chapter 2. Recent Developments of Quasicrystallography 26
2.1. Introduction 26
2.2. nD description of quasicrystals 29
2.3. Decagonal, dodecagonal, and icosahedral coordinate systems 30
2.4. Low-density elimination method 32
2.5. Modification of models in the structure refinement 34
2.6. Higher-dimensional cluster models of decagonal quasicrystals 38
2.7. Higher-dimensional cluster models of icosahedral quasicrystals 44
2.8. Quasicrystal models with fractal occupation domains 51
2.9. Symmetry breaking in clusters 54
2.10. Modulation functions for quasicrystals 58
2.11. Summary 58
Chapter 3. New Group of Icosahedral Quasicrystals 64
3.1. Introduction 64
3.2. Classification of icosahedral quasicrystals 65
3.3. Approximants including Tsai-type cluster 65
3.4. Preparation methods of Zn- and Cu-based quasicrystals 69
3.5. Zn–Mg–Sc quasicrystal as a prototype 70
3.6. Other Zn- and Cu-based quasicrystals 73
3.7. Single-quasicrystals and microvoids 78
3.8. Central structure of the Tsai-type cluster 79
3.9. Alloy chemistry and the Tsai-type quasicrystals 82
3.10. Conclusion 86
Chapter 4. Quasicrystals and Approximants in Cd-M Systems and Related Alloys 90
4.1. Introduction 90
4.2. Approximants in the Cd-M systems 93
4.3. Stable quasicrystals of the Cd–Yb class 105
4.4. Hume-Rothery conditions for the stable quasicrystals 113
4.5. Concluding remarks 119
Chapter 5. Phason Modes in Aperiodic Crystals 122
5.1. Introduction: Hydrodynamic modes and quasiperiodic structures 122
5.2. Modulated crystals 131
5.3. Binary composites 141
5.4. Hydrodynamics of icosahedral phases 144
5.5. Phason modes in the icosahedral AlPdMn quasicrystal 157
5.6. Phason modes in other quasicrystals 170
5.7. Conclusion 177
Chapter 6. Electronic Structures and Stability Mechanism of Quasicrystals 186
6.1. Introduction 186
6.2. Stability mechanism – Hume-Rothery versus hybridization 188
6.3. Ab initio methods for calculating electronic structures of QCs 191
6.4. Electronic structure of QC-related compounds 194
6.5. Concluding remarks 218
Chapter 7. Quantum Transport in Quasicrystals and Complex Metallic Alloys 224
7.1. Introduction 224
7.2. Quantum formalism for electronic transport 226
7.3. Anomalous quantum diffusion and conductivity in periodic and quasiperiodic systems 243
7.4. Evidence of anomalous quantum diffusion in quasicrystals and approximants 260
7.5. Conclusion 276
Chapter 8. Elastic and Plastic Properties of Quasicrystals 282
8.1. Introduction 282
8.2. Elastic properties 283
8.3. Dislocations and their motion 297
8.4. Mechanical properties 306
8.5. Deformation mechanisms 312
Chapter 9. Ab-Initio Studies of Quasicrystalline Surfaces 328
9.1. Introduction 328
9.2. Computational method 331
9.3. Fivefold surface of i-Al–Pd–Mn 331
9.4. Study of the tenfold surface of d-Al–Co–Ni 352
9.5. Summary 364
9.6. Outlook 366
Index 372