Quasicrystals
- 1st Edition, Volume 3 - December 17, 2007
- Editors: Takeo Fujiwara, Yasushi Ishii
- Language: English
- Paperback ISBN:9 7 8 - 0 - 4 4 4 - 5 6 0 0 3 - 2
- Hardback ISBN:9 7 8 - 0 - 4 4 4 - 5 1 4 1 8 - 9
- eBook ISBN:9 7 8 - 0 - 0 8 - 0 5 5 5 9 7 - 3
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,… Read more
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.
· Comprehensive reviews by experts in the field
· Complete reference of original papers and new topics
· Intelligible introduction of quasicrystals by experts
· Complete reference of original papers and new topics
· Intelligible introduction of quasicrystals by experts
Researchers, Graduate students
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)
1. Introduction
2. nD Description of Quasicrystals
3. Decagonal, Dodecagonal and Icosahedral Coordinate Systems
4. Low-Density Elimination Method
5. 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
6. 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.
7. 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
8. Quasicrystal Models with Fractal Occupation Domains
9. 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
10. Modulation Functions for Quasicrystals
11. Summary
Chapter 3. New Group of Icosohedral Quasicrystals (Tsutomu Ishimasa)
1. Introduction
2. Classification of Icosahedral Quasicrystals
3. Approximants including Tsai-type Cluster
4. Preparation Method of Zn- and Cu-based Quasicrystals
5. Zn-Mg-Sc Quasicrystal as a prototype
6. 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
7. Single-quasicryastals and microvoids
8. Central Structure of the Tsai-type Cluster
9. 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
10. Conclusion
Chapter 4. New Family of Cd-based Quasicrystals and Cluster Structures (An-Pang Tsai, and Cesar Pay Gomez)
1. Introduction
2. 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
3. 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
4. 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
5. Concluding remarks
Chapter 5. Phason Modes in Aperiodic Crystals (M. de Boissieu, R. Currat, and S. Francoulual)
1. Introduction: Hydrodynamic modes and Quasiperiodic Structures
1.1. Outline
1.2. Quasiperiodic Structures
1.3. Hydrodynamic Modes
1.4. Internal Space Translations
2. 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
3. Binary Composites
4. 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
5. 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
6. Phason modes in other quasicrystals
6.1. AlPdRe, AlCuFe and CdYb icosahedral phases
6.2. Decagonal Phases
7. Conclusion
Chapter 6. Electronic Structures and Stability Mechanisms of Quasicrystals (Yasushi Ishii, and Takeo Fujiwara)
1. Introduction
2. Stability Mechanism- Hume-Rothery versus Hybridization
3. Ab Initio Methods for Calculating Electronic Structures of QCs
4. 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
5. Concluding Remarks
Chapter 7. Quantum Transport in Quasicrystals and Complex Metallic Alloys (Didier Mayou, and Guy Trambly de Laissardiere)
1. Introduction
2. 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
3. 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
4. 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
5. Conclusion
Chapter 8. Elastic and Plasic Properties of Quasicrystals (S. Takeuchi, and K. Edagawa)
1. Introduction
2. 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
3. Dislocations and their motion
3.1. Characteristics of dislocations in quasicrystals
3.2. Dislocation glide
3.3. Computer simulation
3.4. Dislocation mobility equations
4. 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
5. 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)
1. Introduction
2. Computational Method
3. 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
4. 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
5. Summary
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)
1. Introduction
2. nD Description of Quasicrystals
3. Decagonal, Dodecagonal and Icosahedral Coordinate Systems
4. Low-Density Elimination Method
5. 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
6. 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.
7. 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
8. Quasicrystal Models with Fractal Occupation Domains
9. 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
10. Modulation Functions for Quasicrystals
11. Summary
Chapter 3. New Group of Icosohedral Quasicrystals (Tsutomu Ishimasa)
1. Introduction
2. Classification of Icosahedral Quasicrystals
3. Approximants including Tsai-type Cluster
4. Preparation Method of Zn- and Cu-based Quasicrystals
5. Zn-Mg-Sc Quasicrystal as a prototype
6. 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
7. Single-quasicryastals and microvoids
8. Central Structure of the Tsai-type Cluster
9. 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
10. Conclusion
Chapter 4. New Family of Cd-based Quasicrystals and Cluster Structures (An-Pang Tsai, and Cesar Pay Gomez)
1. Introduction
2. 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
3. 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
4. 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
5. Concluding remarks
Chapter 5. Phason Modes in Aperiodic Crystals (M. de Boissieu, R. Currat, and S. Francoulual)
1. Introduction: Hydrodynamic modes and Quasiperiodic Structures
1.1. Outline
1.2. Quasiperiodic Structures
1.3. Hydrodynamic Modes
1.4. Internal Space Translations
2. 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
3. Binary Composites
4. 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
5. 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
6. Phason modes in other quasicrystals
6.1. AlPdRe, AlCuFe and CdYb icosahedral phases
6.2. Decagonal Phases
7. Conclusion
Chapter 6. Electronic Structures and Stability Mechanisms of Quasicrystals (Yasushi Ishii, and Takeo Fujiwara)
1. Introduction
2. Stability Mechanism- Hume-Rothery versus Hybridization
3. Ab Initio Methods for Calculating Electronic Structures of QCs
4. 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
5. Concluding Remarks
Chapter 7. Quantum Transport in Quasicrystals and Complex Metallic Alloys (Didier Mayou, and Guy Trambly de Laissardiere)
1. Introduction
2. 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
3. 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
4. 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
5. Conclusion
Chapter 8. Elastic and Plasic Properties of Quasicrystals (S. Takeuchi, and K. Edagawa)
1. Introduction
2. 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
3. Dislocations and their motion
3.1. Characteristics of dislocations in quasicrystals
3.2. Dislocation glide
3.3. Computer simulation
3.4. Dislocation mobility equations
4. 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
5. 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)
1. Introduction
2. Computational Method
3. 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
4. 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
5. Summary
- Edition: 1
- Volume: 3
- Published: December 17, 2007
- Language: English
TF
Takeo Fujiwara
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, JapanYI
Yasushi Ishii
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, JapanRead Quasicrystals on ScienceDirect