Edited by

  • Takeo Fujiwara, University of Tokyo, Japan
  • Yasushi Ishii, Chuo University, Toyo, Japan

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.
View full description


Researchers, Graduate students


Book information

  • Published: November 2007
  • Imprint: ELSEVIER
  • ISBN: 978-0-444-51418-9

Table of Contents

Chapter 1. Introduction to Quasicrystals (Takeo Fujiwara)1. Discovery of non-crystalline rotational symmetry2. Quasiperiodic lattice 3. Icosahedral quasilattice and its symmetry4. Phonons and Phasons5. Electronic structure and related physical propertiesChapter 2. Recent Developments of Quasicrystallography (Akiji Yamamoto)1. Introduction2. nD Description of Quasicrystals3. Decagonal, Dodecagonal and Icosahedral Coordinate Systems4. Low-Density Elimination Method5. Modification of Models in the Structure Refinement5.1. Maximum Entropy Method5.2. Similarity Transformations5.3. Application of LDEM to quasicrystals5.4. Application of nD Maximum Entropy Method6. Higher-Dimensional Cluster Models of Decagonal Quasicrystals6.1. Arrangement of Cluster Centers6.2. Two-Dimensional Structure of d-Al-Cu-Co6.3. Three-Dimensional Structure of d-Al-Cu-Co6.4. Application of Higher-Dimensional Cluster Models in Decagonal Quasicrystals.7. Higher-Dimensional Cluster Models of Icosahedral Quasicrystals7.1. Atom Positions in Six-Dimensional Space7.2. Application of Higher-Dimensional Cluster Models in Icosahedral Quasicrystals8. Quasicrystal Models with Fractal Occupation Domains9. Symmetry Breaking in Clusters9.1. Model Building of Lower Symmetric Cluster Models9.2. Projected Structure9.3. Application of Low-Symmetric Cluster Models10. Modulation Functions for Quasicrystals11. Summary Chapter 3. New Group of Icosohedral Quasicrystals (Tsutomu Ishimasa)1. Introduction2. Classification of Icosahedral Quasicrystals3. Approximants including Tsai-type Cluster4. Preparation Method of Zn- and Cu-based Quasicrystals5. Zn-Mg-Sc Quasicrystal as a prototype6. Other Zn- and Cu-based Quasicrystals6.1. Zn-M-Sc Quasicrystals with M=Cu, Ag, Au, Pd or Pt 6.2. Zn-T-Sc Quasicrystals with T=Mn, Fe, Co or Ni6.3. Cu-based Quasicrystals7. Single-quasicryastals and microvoids8. Central Structure of the Tsai-type Cluster9. Alloy Chemistry of the Tsai-type Quasicrystals9.1. Linear relationship between a6D and average atomic radius 9.2. Substitution Rules9.3. Hume-Rothary Rules 1: Near equality in e/a9.4. Hume-Rothary Rules 2: Near equality in ratio of atomic radii10. Conclusion Chapter 4. New Family of Cd-based Quasicrystals and Cluster Structures (An-Pang Tsai, and Cesar Pay Gomez)1. Introduction2. Approximants in the Cd-M (M: RE,Ca,Y) systems2.1. History 2.2. The disordered 1/1 approximants2.3. The ordered 1/1 approximants2.4. The 2/1 approximants2.5. From approximants to quasicrystals3. Stable quasicrystals3.1. Formation of the binary stable i-QC’s3.2. Quasicrystals in Cd-Mg-M3.3. i-QC’s and approximants in the In-Ag-M systems4. Hume-Rothery conditions for the stable i-QCs4.1. Valence concentration4.2. Atomic size factor4.3. Comparison for the three classes4.4. Phase selection between the i-QC and approximants4.5. Summary5. Concluding remarks Chapter 5. Phason Modes in Aperiodic Crystals (M. de Boissieu, R. Currat, and S. Francoulual)1. Introduction: Hydrodynamic modes and Quasiperiodic Structures1.1. Outline1.2. Quasiperiodic Structures1.3. Hydrodynamic Modes1.4. Internal Space Translations2. Modulated Crystals2.1. General2.2. Displacive Modulations in the quasi-harmonic approximation2.3. Displacive Modulations: Anharmonic effects2.4. Displacive Modulations: Pinning by Defects 2.5. Order/Disorder Modulations3. Binary Composites4. Hydrodynamics of Icosahedral Phases4.1. Fundamental hypothesis4.2. Phonon and Phason Modes4.3. Equilibrium Thermal Fluctuations and Scattering Intensity4.4. Hydrodynamic and Thermodynamic instabilities4.5. Random Tiling and Matching rule Models4.5.1. Random Tiling Model4.6. Temperature dependence of elastic constants4.7. Phason jump, phason strain, phason modes5. Phason modes in the icosahedral AlPdMn quasicrystal5.1. Local atomic hopping5.2. Phason modes at room temperature diffuse scattering measurements5.3. Temperature dependence of the diffuse scattering5.4. Dynamics of phason modes6. Phason modes in other quasicrystals6.1. AlPdRe, AlCuFe and CdYb icosahedral phases6.2. Decagonal Phases7. ConclusionChapter 6. Electronic Structures and Stability Mechanisms of Quasicrystals (Yasushi Ishii, and Takeo Fujiwara)1. Introduction2. Stability Mechanism- Hume-Rothery versus Hybridization3. Ab Initio Methods for Calculating Electronic Structures of QCs4. Electronic Structure of QC-related Compounds4.1. Al-TM Compounds4.2 Bergman phases4.3. Zn-Mg-RE Compounds4.4. Cd- and Zn-based compounds5. Concluding RemarksChapter 7. Quantum Transport in Quasicrystals and Complex Metallic Alloys (Didier Mayou, and Guy Trambly de Laissardiere)1. Introduction2. Quantum formalism for electron transport.2.1. Impulse response and analytical properties of the conductivity2.2. Relation between low frequency conductivity and quantum diffusion2.3. Relaxation time approximation (RTA)2.4. Application to periodic Hamiltonians2.5. Application to quasiperiodic Hamiltonians3. Anomalous quantum diffusion and conductivity in periodic and quasiperiodic systems3.1. Validity of the RTA and the Anderson transition3.2. Phenomena of backscattering3.3. Anomalous quantum diffusion and conductivity of periodic systems3.4. Anomalous quantum diffusion and conductivity of quasiperiodic systems4. Evidence of anomalous quantum diffusion in quasicrystals and approximants4.1. Experimental transport properties of icosahedral and related approximant phases.4.2. Ab-initio electronic structure and quantum diffusion in perfect approximants4.3. Ab-initio RTA model for the conductivity of approximants4.4. Phenomenological model for the low frequency conductivity of AlCuFe quasicrystals5. Conclusion Chapter 8. Elastic and Plasic Properties of Quasicrystals (S. Takeuchi, and K. Edagawa)1. Introduction2. Elastic Properties2.1. Phonon and phason degrees of freedom2.2. Elastic free energy2.3. Phonon elasticity2.4. Phason elasticity2.5. Phonon-phason coupling3. Dislocations and their motion3.1. Characteristics of dislocations in quasicrystals3.2. Dislocation glide3.3. Computer simulation3.4. Dislocation mobility equations4. Mechanical Properties4.1. Hardness4.2. High temperature plasticity4.2.1. Compression test of icosahedral quasicrystals4.2.2. Compression test of decagonal crystals5. Deformation Mechanisms5.1. Electron Microscopy5.1.1. High temperature deformation of i-Al-Pd-Mn5.1.2. Low temperature deformation of i-Al-Pd-Mn5.2. Microscopic deformation mechanism5.2.1. High temperature deformation in icosahedral quasicrystals5.2.2. Mechanism of work softening5.2.3. Low temperature deformation in icosahedral quasicrystals5.2.4. Deformation mechanism of decagonal quasicrystalsChapter 9. Ab-initio Studies of Quasicrystalline Surfaces (M. Krajci, and J. Hafner)1. Introduction 2. Computational Method3. Fivefold surface of i-Al-Pd-Mn3.1. Structural model of bulk i-Al-Pd-Mn3.2. Choice of the cleavage plane3.3. Atomic structure and charge density distribution at the surface3.4. Relaxation of atomic positions and surface reconstruction3.5. Surface electronic structure4. Study of the tenfold surface of d-Al-Co-Ni4.1. Structural model of bulk d-Al-Co-Ni4.2. Cleavage planes forming tenfold surfaces4.2.1. Relaxation of atomic positions and surface reconstruction4.3. Electronic structure of d-Al-Co-Ni4.3.1. Electronic structure of the bulk4.3.2. Electronic structure at the surface4.3.3. Comparison with the photoemission spectra4.4. Atomic structure and the charge density distribution4.5. Simulated STM images at the surface5. Summary