Quasicrystals - 1st Edition - ISBN: 9780444514189, 9780080555973

Quasicrystals, Volume 3

1st Edition

Series Volume Editors: Takeo Fujiwara Yasushi Ishii
Hardcover ISBN: 9780444514189
eBook ISBN: 9780080555973
Imprint: Elsevier Science
Published Date: 15th November 2007
Page Count: 374
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Table of Contents

Chapter 1. Introduction to Quasicrystals (Takeo Fujiwara)

  1. Discovery of non-crystalline rotational symmetry
  2. Quasiperiodic lattice
  3. Icosahedral quasilattice and its symmetry
  4. Phonons and Phasons
  5. Electronic structure and related physical properties Chapter 2. Recent Developments of Quasicrystallography (Akiji Yamamoto)
  6. Introduction
  7. nD Description of Quasicrystals
  8. Decagonal, Dodecagonal and Icosahedral Coordinate Systems
  9. Low-Density Elimination Method
  10. Modification of Models in the Structure Refinement 5.1. Maximum Entropy Method 5.2. Similarity Transformations 5.3. Application of LDEM to quasicrystals 5.4. Application of nD Maximum Entropy Method
  11. Higher-Dimensional Cluster Models of Decagonal Quasicrystals 6.1. Arrangement of Cluster Centers 6.2. Two-Dimensional Structure of d-Al-Cu-Co 6.3. Three-Dimensional Structure of d-Al-Cu-Co 6.4. Application of Higher-Dimensional Cluster Models in Decagonal Quasicrystals.
  12. Higher-Dimensional Cluster Models of Icosahedral Quasicrystals 7.1. Atom Positions in Six-Dimensional Space 7.2. Application of Higher-Dimensional Cluster Models in Icosahedral Quasicrystals
  13. Quasicrystal Models with Fractal Occupation Domains
  14. Symmetry Breaking in Clusters 9.1. Model Building of Lower Symmetric Cluster Models 9.2. Projected Structure 9.3. Application of Low-Symmetric Cluster Models
  15. Modulation Functions for Quasicrystals
  16. Summary
    Chapter 3. New Group of Icosohedral Quasicrystals (Tsutomu Ishimasa)
  17. Introduction
  18. Classification of Icosahedral Quasicrystals
  19. Approximants including Tsai-type Cluster
  20. Preparation Method of Zn- and Cu-based Quasicrystals
  21. Zn-Mg-Sc Quasicrystal as a prototype
  22. Other Zn- and Cu-based Quasicrystals 6.1. Zn-M-Sc Quasicrystals with M=Cu, Ag, Au, Pd or Pt 6.2. Zn-T-Sc Quasicrystals with T=Mn, Fe, Co or Ni 6.3. Cu-based Quasicrystals
  23. Single-quasicryastals and microvoids
  24. Central Structure of the Tsai-type Cluster
  25. Alloy Chemistry of the Tsai-type Quasicrystals 9.1. Linear relationship between a6D and average atomic radius 9.2. Substitution Rules 9.3. Hume-Rothary Rules 1: Near equality in e/a 9.4. Hume-Rothary Rules 2: Near equality in ratio of atomic radii
  26. Conclusion
    Chapter 4. New Family of Cd-based Quasicrystals and Cluster Structures (An-Pang Tsai, and Cesar Pay Gomez)
  27. Introduction
  28. Approximants in the Cd-M (M: RE,Ca,Y) systems 2.1. History 2.2. The disordered 1/1 approximants 2.3. The ordered 1/1 approximants 2.4. The 2/1 approximants 2.5. From approximants to quasicrystals
  29. Stable quasicrystals 3.1. Formation of the binary stable i-QC’s 3.2. Quasicrystals in Cd-Mg-M 3.3. i-QC’s and approximants in the In-Ag-M systems
  30. Hume-Rothery conditions for the stable i-QCs 4.1. Valence concentration 4.2. Atomic size factor 4.3. Comparison for the three classes 4.4. Phase selection between the i-QC and approximants 4.5. Summary
  31. Concluding remarks Chapter 5. Phason Modes in Aperiodic Crystals (M. de Boissieu, R. Currat, and S. Francoulual)
  32. Introduction: Hydrodynamic modes and Quasiperiodic Structures 1.1. Outline 1.2. Quasiperiodic Structures 1.3. Hydrodynamic Modes 1.4. Internal Space Translations
  33. Modulated Crystals 2.1. General 2.2. Displacive Modulations in the quasi-harmonic approximation 2.3. Displacive Modulations: Anharmonic effects 2.4. Displacive Modulations: Pinning by Defects
    2.5. Order/Disorder Modulations
  34. Binary Composites
  35. Hydrodynamics of Icosahedral Phases 4.1. Fundamental hypothesis 4.2. Phonon and Phason Modes 4.3. Equilibrium Thermal Fluctuations and Scattering Intensity 4.4. Hydrodynamic and Thermodynamic instabilities 4.5. Random Tiling and Matching rule Models 4.5.1. Random Tiling Model 4.6. Temperature dependence of elastic constants 4.7. Phason jump, phason strain, phason modes
  36. Phason modes in the icosahedral AlPdMn quasicrystal 5.1. Local atomic hopping 5.2. Phason modes at room temperature diffuse scattering measurements 5.3. Temperature dependence of the diffuse scattering 5.4. Dynamics of phason modes
  37. Phason modes in other quasicrystals 6.1. AlPdRe, AlCuFe and CdYb icosahedral phases 6.2. Decagonal Phases
  38. Conclusion Chapter 6. Electronic Structures and Stability Mechanisms of Quasicrystals (Yasushi Ishii, and Takeo Fujiwara)
  39. Introduction
  40. Stability Mechanism- Hume-Rothery versus Hybridization
  41. Ab Initio Methods for Calculating Electronic Structures of QCs
  42. Electronic Structure of QC-related Compounds 4.1. Al-TM Compounds 4.2 Bergman phases 4.3. Zn-Mg-RE Compounds 4.4. Cd- and Zn-based compounds
  43. Concluding Remarks Chapter 7. Quantum Transport in Quasicrystals and Complex Metallic Alloys (Didier Mayou, and Guy Trambly de Laissardiere)
  44. Introduction
  45. Quantum formalism for electron transport. 2.1. Impulse response and analytical properties of the conductivity 2.2. Relation between low frequency conductivity and quantum diffusion 2.3. Relaxation time approximation (RTA) 2.4. Application to periodic Hamiltonians 2.5. Application to quasiperiodic Hamiltonians
  46. Anomalous quantum diffusion and conductivity in periodic and quasiperiodic systems 3.1. Validity of the RTA and the Anderson transition 3.2. Phenomena of backscattering 3.3. Anomalous quantum diffusion and conductivity of periodic systems 3.4. Anomalous quantum diffusion and conductivity of quasiperiodic systems
  47. Evidence of anomalous quantum diffusion in quasicrystals and approximants 4.1. Experimental transport properties of icosahedral and related approximant phases. 4.2. Ab-initio electronic structure and quantum diffusion in perfect approximants 4.3. Ab-initio RTA model for the conductivity of approximants 4.4. Phenomenological model for the low frequency conductivity of AlCuFe quasicrystals
  48. Conclusion
    Chapter 8. Elastic and Plasic Properties of Quasicrystals (S. Takeuchi, and K. Edagawa)
  49. Introduction
  50. Elastic Properties 2.1. Phonon and phason degrees of freedom 2.2. Elastic free energy 2.3. Phonon elasticity 2.4. Phason elasticity 2.5. Phonon-phason coupling
  51. Dislocations and their motion 3.1. Characteristics of dislocations in quasicrystals 3.2. Dislocation glide 3.3. Computer simulation 3.4. Dislocation mobility equations
  52. Mechanical Properties 4.1. Hardness 4.2. High temperature plasticity 4.2.1. Compression test of icosahedral quasicrystals 4.2.2. Compression test of decagonal crystals
  53. Deformation Mechanisms 5.1. Electron Microscopy 5.1.1. High temperature deformation of i-Al-Pd-Mn 5.1.2. Low temperature deformation of i-Al-Pd-Mn 5.2. Microscopic deformation mechanism 5.2.1. High temperature deformation in icosahedral quasicrystals 5.2.2. Mechanism of work softening 5.2.3. Low temperature deformation in icosahedral quasicrystals 5.2.4. Deformation mechanism of decagonal quasicrystals Chapter 9. Ab-initio Studies of Quasicrystalline Surfaces (M. Krajci, and J. Hafner)
  54. Introduction
  55. Computational Method
  56. Fivefold surface of i-Al-Pd-Mn 3.1. Structural model of bulk i-Al-Pd-Mn 3.2. Choice of the cleavage plane 3.3. Atomic structure and charge density distribution at the surface 3.4. Relaxation of atomic positions and surface reconstruction 3.5. Surface electronic structure
  57. Study of the tenfold surface of d-Al-Co-Ni 4.1. Structural model of bulk d-Al-Co-Ni 4.2. Cleavage planes forming tenfold surfaces 4.2.1. Relaxation of atomic positions and surface reconstruction 4.3. Electronic structure of d-Al-Co-Ni 4.3.1. Electronic structure of the bulk 4.3.2. Electronic structure at the surface 4.3.3. Comparison with the photoemission spectra 4.4. Atomic structure and the charge density distribution 4.5. Simulated STM images at the surface
  58. Summary


This book is aimed at researchers who are working in a field of quasicrystals to provide a reference to recent developments and ideas in the field and also at graduate students, who intend to study quasicrystals, to provide introduction of ideas. Topics in this book cover an entire field of quasicrystals, both experimental and theoretical, including new developments: the state of the art in quasicrystallography, new families of quasicrystals, phasons in aperiodic solids, ab initio studies on stability mechanism, quantum transport phenomena, elastic/plastic properties and surface of quasicrystals.

Key Features

· Comprehensive reviews by experts in the field · Complete reference of original papers and new topics · Intelligible introduction of quasicrystals by experts


Researchers, Graduate students


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About the Series Volume Editors

Takeo Fujiwara Series Volume Editor

Takeo Fujiwara has been working on quasicrystals since soon after the discovery of quasicrystals and contributing to developing new ideas on quasicrystals: TF are working on mainly electronic structures of quasiperiodic systems and real quasicrystalline materials and YI are working on “phason”-related instability of quasicrystals as well as electronic structures.

Affiliations and Expertise

University of Tokyo, Japan

Yasushi Ishii Series Volume Editor

Yasushi Ishii has been working on quasicrystals since soon after the discovery of quasicrystals and contributing to developing new ideas on quasicrystals: TF are working on mainly electronic structures of quasiperiodic systems and real quasicrystalline materials and YI are working on “phason”-related instability of quasicrystals as well as electronic structures.

Affiliations and Expertise

Chuo University, Toyo, Japan