Aperiodic crystals : from modulated phases to quasicrystals / Ted Janssen (Institute of Theoretical Physics, University of Nijmegen), Gervais Chapuis (École Polytechnique Fédérale de Lausanne) and Marc de Boissieu (CNRS and Université Grenoble Alpes).
- Author:
- Janssen, T.
- Published:
- Oxford : Oxford University Press, [2018]
- Edition:
- Second edition.
- Physical Description:
- xviii, 532 pages : illustrations ; 24 cm.
- Additional Creators:
- Chapuis, Gervais and Boissieu, Marc de
- Series:
- Contents:
- Machine generated contents note: 1.Introduction -- 1.1.Periodic crystals -- 1.1.1.History -- 1.1.2.Description -- 1.1.3.The role of space group symmetry in the structure determination -- 1.1.4.Symmetry and physical properties -- 1.1.5.Examples -- 1.1.6.Conclusion -- 1.2.Aperiodic crystals -- 1.2.1.History -- 1.2.2.Classes and examples -- 1.2.3.Modulated phases -- 1.2.4.Incommensurate composites -- 1.2.5.Quasicrystals -- 1.2.6.Morphology -- 1.3.Summary -- 2.Description and symmetry of aperiodic crystals -- 2.1.Aperiodic and quasiperiodic functions -- 2.2.Quasiperiodic structures -- 2.2.1.Modulated phases -- 2.2.2.Composites -- 2.2.3.Quasicrystals -- 2.2.4.Natural aperiodic crystals -- 2.2.5.Electromagnetic crystals in space-time -- 2.3.Description in superspace -- 2.3.1.Embedding -- 2.3.2.Modulated phases -- 2.3.3.Incommensurate composites -- 2.3.4.Quasicrystals -- 2.3.5.The classification into three (or four) types is not unique! -- 2.4.Symmetry -- 2.4.1.Point group symmetry of diffraction patterns -- 2.4.2.Superspace groups -- 2.4.3.Examples -- 2.4.4.Approximants -- 2.4.5.Superspace groups for commensurate phases -- 2.4.6.Consequences of superspace group symmetry -- 2.5.Scaling symmetries -- 2.6.Alternative descriptions -- 2.7.Magnetic symmetry of quasiperiodic systems -- 2.7.1.Magnetic systems and time-reversal symmetry -- 2.7.2.Magnetic point groups -- 2.7.3.Magnetic space groups -- 2.7.4.The magnetic groups for quasiperiodic crystals -- 2.8.Summary -- 3.Tilings: mathematical models for quasicrystals -- 3.1.Model sets -- 3.2.Introduction to tilings -- 3.3.Substitutional chains -- 3.3.1.Substitutions with an alphabet -- 3.3.2.Embedding of substitutional chains -- 3.3.3.Tilings by substitution -- 3.4.Aperiodic tilings -- 3.4.1.Construction of aperiodic tilings -- 3.4.2.Embedding of tilings -- 3.4.3.Symmetry of tilings -- 3.5.Approximants -- 3.6.Coverings -- 3.7.Random tilings -- 3.8.Summary -- 4.Structure -- 4.1.Diffraction -- 4.1.1.Diffraction from periodic and aperiodic crystals -- 4.1.2.Indexing the diffraction pattern -- 4.1.3.# Mathematical questions -- 4.2.Diffraction techniques -- 4.2.1.X-ray area detectors -- 4.2.2.Neutron area detectors -- 4.2.3.Measurement techniques -- 4.3.Determination of modulated phases and composites -- 4.3.1.Introduction -- 4.3.2.The structure factor of incommensurate structures -- 4.3.3.Possible expressions of the modulation functions -- 4.3.4.Additional expressions of modulation functions -- 4.3.5.Practical aspects of structure determination and refinement -- 4.3.6.Ab initio methods -- 4.3.7.Relation between harmonics and satellite orders -- 4.3.8.Composite structures -- 4.3.9.Commensurately modulated structures -- 4.4.Typical examples of modulated phases and composites -- 4.4.1.Introduction -- 4.4.2.The modulated phases of Na2CO3 -- 4.4.3.The composite structure of La2Co1.7 -- 4.4.4.Alkane-urea compounds -- 4.4.5.Aperiodicity in the structures of elements -- 4.4.6.p-Chlorobenzamide -- 4.4.7.Modular structures -- 4.4.8.Superspace and crystal chemistry -- 4.4.9.Conclusion -- 4.4.10.Structure determination of quasicrystals -- 4.4.11.A simple one-dimensional quasiperiodic model -- 4.4.12.Structure determination of a one-dimensional quasicrystal -- 4.4.13.Structure determination of icosahedral and decagonal phases -- 4.5.Examples of quasicrystal structures -- 4.5.1.Introduction -- 4.5.2.Structure of the i-AIPdMn phase -- 4.5.3.Atomic structure of the CdYb icosahedral phase -- 4.5.4.Structure of the AINiCo decagonal phase -- 4.5.5.Dodecagonal quasicrystals -- 4.5.6.Reversible phase transitions -- 4.6.Diffraction by an imperfect crystal -- 4.6.1.Diffuse scattering when an average lattice exists -- 4.6.2.Diffuse scattering when there is no average lattice -- 5.Physical properties -- 5.1.Introduction -- 5.2.Tensorial properties -- 5.3.Hydrodynamics of aperiodic crystals -- 5.3.1.Hydrodynamic theory of fluids and periodic crystals -- 5.3.2.Hydrodynamic theory of aperiodic crystals and phason modes -- 5.4.Phonons and phasons: Theory -- 5.4.1.Introduction -- 5.4.2.Simple models -- 5.4.3.Eigenvectors and spectrum -- 5.4.4.Damping -- 5.4.5.Calculation of phonons for real incommensurate phases -- 5.4.6.Dynamics of quasicrystals -- 5.4.7.Diffuse scattering and Debye-Waller factors -- 5.5.Non-linear excitations -- 5.6.Electrons -- 5.6.1.Introduction -- 5.6.2.Simple models -- 5.6.3.Electrical conductivity -- 5.6.4.Realistic potentials -- 5.6.5.Quantum criticality in a magnetic quasicrystal -- 5.7.Summary of the theoretical situation -- 5.8.Phonons: Experimental findings -- 5.8.1.Scattering -- 5.8.2.Modulated phases and composites -- 5.8.3.Quasicrystals -- 5.9.Phasons: Experiment -- 5.9.1.Introduction -- 5.9.2.Phason modes in modulated crystals -- 5.9.3.Diffuse scattering and phason modes in icosahedral quasicrystals -- 5.9.4.Phason modes in the i-AlPdMn icosahedral quasicrystal -- 5.9.5.Phason modes in other quasicrystals -- 5.10.Summary of the experimental findings -- 6.Origin and stability -- 6.1.Introduction -- 6.2.The Landau theory of phase transitions -- 6.3.Semi-microscopic models -- 6.3.1.Substrate models -- 6.3.2.Spin models -- 6.3.3.Models with continuous degrees of freedom -- 6.3.4.Specific models for incommensurate phases -- 6.4.Composites -- 6.5.Quasicrystals -- 6.6.Electronic instabilities -- 6.6.1.Charge-density and spin-density systems -- 6.6.2.Hume-Rothery compounds -- 6.7.Growth of quasicrystals -- 6.8.Summary -- 7.Other topics -- 7.1.Morphology of aperiodic crystals -- 7.1.1.The puzzling habit of the mineral calaverite -- 7.1.2.The morphology of the TMA Zn phases -- 7.1.3.The morphology of icosahedral and decagonal quasicrystals -- 7.2.Surfaces -- 7.2.1.Introduction -- 7.2.2.Structure of surfaces of aperiodic crystals -- 7.2.3.Generalization of the morphological laws -- 7.2.4.Physical properties of quasicrystalline surfaces -- 7.3.Magnetic quasiperiodic systems -- 7.4.Incommensurate multiferroics -- 7.5.Aperiodic photonic crystals -- 7.6.Mesoscopic quasicrystals -- 7.7.Defects -- Appendix A Space groups in arbitrary dimensions -- A.1.Crystallographic operations in n dimensions -- A.2.Lattices -- A.3.Crystal classes -- A.4.Space groups -- A.5.Classification -- A.6.Space groups for aperiodic crystals -- A.7.Notation -- A.7.1.Superspace groups for incommensurate phases -- A.7.2.General space groups -- A.8.Equivalence of (super)space groups -- A.9.Extinction rules -- A.10.Tables -- A.10.1.Introduction -- A.10.2.Tables for irreducible representations of point groups: Point groups of 5-, 8-, 10-, 12-fold, or icosahedral symmetry -- A.10.3.Examples of superspace groups for modulated phases -- A.10.4.Superspace groups for quasiperiodic structures with 5-, 8-, 10-, 12-fold, or icosahedral symmetry -- Appendix B Exercises: Solutions.
- Subject(s):
- ISBN:
- 9780198824442 (pbk.)
0198824440 (pbk.) - Note:
- Previous edition: 2007.
- Bibliography Note:
- Includes bibliographical references and index.
- Source of Acquisition:
- Purchased with funds from the Dorothy L. Lesh Libraries Endowment ; 2018
- Endowment Note:
- Dorothy L. Lesh Libraries Endowment
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