Aperiodic crystals: from modulated phases to quasicrystals: structure and properties
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford
Oxford University Press
2018
|
| Edition: | 2nd edition |
| Series: | IUCr monographs on crystallography
28 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | xviii, 532 Seiten Illustrationen, Diagramme (teilweise farbig) |
| ISBN: | 9780198824442 |
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MARC
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| 245 | 1 | 0 | |a Aperiodic crystals |b from modulated phases to quasicrystals: structure and properties |c Ted Janssen (Institute of Theoretical Physics, University of Nijmegen), Gervais Chapuis (École Polytechnique Fédérale de Lausanne), Marc de Boissieu (CNRS and Université Grenoble Alpes) |
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Record in the Search Index
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| adam_text | Contents
4
Glossary xvii
1 Introduction 1
1.1 Periodic crystals 1
1.1.1 History 1
1.1.2 Description 2
1.1.3 The role of space group symmetry in the structure
determination 6
1.1.4 Symmetry and physical properties 7
1.1.5 Examples 9
1.1.6 Conclusion 10
1.2 Aperiodic crystals 10
1.2.1 History 10
1.2.2 Classes and examples 16
1.2.3 Modulated phases 17
1.2.4 Incommensurate composites 22
1.2.5 Quasicrystals 2 5
1.2.6 Morphology 30
1.3 Summary 31
2 Description and symmetry of aperiodic crystals 32
2.1 Aperiodic and quasiperiodic functions 32
2.2 Quasiperiodic structures 35
2.2.1 Modulated phases 35
2.2.2 Composites 40
2.2.3 Quasicrystals 4 3
2.2.4 Natural aperiodic crystals 46
2.2.5 8 Electromagnetic crystals in space-time 47
2.3 Description in superspace 49
2.3.1 Embedding 49
2.3.2 Modulated phases 60
2.3.3 Incommensurate composites 64
2.3.4 Quasicrystals 71
2.3.5 The classification into three (or four) types is not unique! 82
2.4 Symmetry 83
2.4.1 Point group symmetry of diffraction patterns 83
2.4.2 Superspace groups 86
2.4.3 Examples 88
xii Contents
2.4.4 Approximants 90
2.4.5 Superspace groups for commensurate phases 91
2.4.6 Consequences of superspace group symmetry 93
2.5 Scaling symmetries 96
2.6 Alternative descriptions 100
2.7 Magnetic symmetry of quasiperiodic systems 104
2.7.1 Magnetic systems and time-reversal symmetry 104
2.7.2 Magnetic point groups 105
2.7.3 Magnetic space groups 105
2.7.4 The magnetic groups for quasiperiodic crystals 106
2.8 Summary 109
3 Tilings: mathematical models for quasicrystals 111
3.1 Model sets 111
3.2 Introduction to tilings 113
3.3 Substitutional chains 117
3.3.1 Substitutions with an alphabet 117
3.3.2 Embedding of substitutional chains 118
3.3.3 Tilings by substitution 119
3.4 Aperiodic tilings 122
3.4.1 Construction of aperiodic tilings 122
3.4.2 Embedding of tilings 127
3.4.3 Symmetry of tilings 135
3.5 Approximants 140
3.6 Coverings 143
3.7 Random tilings 144
3.8 Summary 146
4 Structure 148
4.1 Diffraction 148
4.1.1 Diffraction from periodic and aperiodic crystals 148
4.1.2 Indexing the diffraction pattern 162
4.1.3 JJ Mathematical questions 165
4.2 Diffraction techniques 167
4.2.1 X-ray area detectors 168
4.2.2 Neutron area detectors 169
4.2.3 Measurement techniques 170
4.3 Determination of modulated phases and composites 171
4.3.1 Introduction 171
4.3.2 The structure factor of incommensurate structures 173
4.3.3 Possible expressions of the modulation functions 174
4.3.4 Additional expressions of modulation functions 176
4.3.5 Practical aspects of structure determination and refinement 177
4.3.6 Ab initio methods 184
Contents xiii
4.3.7 Relation between harmonies and satellite orders 187
4.3.8 Composite structures 189
4.3.9 Commensurately modulated structures 191
4.4 Typical examples of modulated phases and composites 193
4.4.1 Introduction 193
4.4.2 The modulated phases of Na2CC 3 193
4.4.3 The composite structure of La2Coi.7 198
4.4.4 Alkane-urea compounds 202
4.4.5 Aperiodicity in the structures of elements 203
4.4.6 p-Chlorobenzamide 208
4.4.7 Modular structures 211
4.4.8 Superspace and crystal chemistry 215
4.4.9 Conclusion 217
4.4.10 Structure determination of quasicrystals 218
4.4.11 A simple one-dimensional quasiperiodic model 218
4.4.12 Structure determination of a one-dimensional quasicrystal 222
4.4.13 Structure determination of icosahedral and decagonal phases 232
4.5 Examples of quasicrystal structures 233
4.5.1 Introduction 233
4.5.2 Structure of the i-AlPdMn phase 234
4.5.3 Atomic structure of the CdYb icosahedral phase 269
4.5.4 Structure of the AlNiCo decagonal phase 282
4.5.5 Dodecagonal quasicrystals 290
4.5.6 Reversible phase transitions 293
4.6 Diffraction by an imperfect crystal 296
4.6.1 Diffuse scattering when an average lattice exists 298
4.6.2 Diffuse scattering when there is no average lattice 301
5 Physical properties 305
5.1 Introduction 305
5.2 Tensorial properties 306
5.3 Hydrodynamics of aperiodic crystals 312
5.3.1 Hydrodynamic theory of fluids and periodic crystals 312
5.3.2 Hydrodynamic theory of aperiodic crystals and phason modes 314
5.4 Phonons and phasons: Theory 316
5.4.1 Introduction 316
5.4.2 Simple models 320
5.4.3 Eigenvectors and spectrum 348
5.4.4 Damping 349
5.4.5 Calculation of phonons for real incommensurate phases 350
5.4.6 Dynamics of quasicrystals 350
5.4.7 Diffuse scattering and Debye-Waller factors 351
5.5 Non-linear excitations 353
5.6 Electrons 357
xiv Contents
5.6.1 Introduction 357
5.6.2 Simple models 358
5.6.3 Electrical conductivity 363
5.6.4 Realistic potentials 363
5.6.5 Quantum criticality in a magnetic quasicrystal 364
5.7 Summary of the theoretical situation 364
5.8 Phonons: Experimental findings 365
5.8.1 Scattering 365
5.8.2 Modulated phases and composites 367
5.8.3 Quasicrystals 368
5.9 Phasons: Experiment 378
5.9.1 Introduction 378
5.9.2 Phason modes in modulated crystals 378
5.9.3 Diffuse scattering and phason modes in icosahedral
quasicrystals 383
5.9.4 Phason modes in the i-AlPdMn icosahedral quasicrystal 386
5.9.5 Phason modes in other quasicrystals 398
5.10 Summary of the experimental findings 404
6 Origin and stability 405
6.1 Introduction 40 5
6.2 The Landau theory of phase transitions 406
6.3 Semi-microscopic models 412
6.3.1 Substrate models 412
6.3.2 Spin models 416
6.3.3 Models with continuous degrees of freedom 418
6.3.4 Specific models for incommensurate phases 424
6.4 Composites 437
6.5 Quasicrystals 437
6.6 Electronic instabilities 438
6.6.1 Charge-density and spin-density systems 438
6.6.2 Hume-Rothery compounds 440
6.7 Growth of quasicrystals 441
6.8 Summary 442
7 Other topics 444
7.1 Morphology of aperiodic crystals 444
7.1.1 The puzzling habit of the mineral calaverite 444
7.1.2 The morphology of the TMA Zn phases 448
7.1.3 The morphology of icosahedral and decagonal quasicrystals 450
7.2 Surfaces 453
7.2.1 Introduction 453
7.2.2 Structure of surfaces of aperiodic crystals 455
7.2.3 Generalization of the morphological laws 458
7.2.4 Physical properties of quasicrystalline surfaces 460
Contents
xv
7.3 Alagnetic quasiperiodic systems 462
7.4 Incommensurate multiferroics 466
7.5 Aperiodic photonic crystals 470
7.6 Mesoscopic quasicrystals 471
7.7 Defects 472
Appendix A Space groups in arbitrary dimensions 475
A.l Crystallographic operations in n dimensions 475
A.2 Lattices 476
A. 3 Crystal classes 478
A.4 Space groups 479
A. 5 Classification 482
A.6 Space groups for aperiodic crystals 485
A. 7 Notation 486
A.7.1 Superspace groups for incommensurate phases 486
A.7.2 General space groups 488
A.8 Equivalence of (super)space groups 489
A. 9 Extinction rules 490
A. 10 Tables 491
A. 10.1 Introduction 491
A. 10.2 Tables for irreducible representations of point groups: Point
groups of 5-, 8-, 10-, 12-fold, or icosahedral symmetry 492
A. 10.3 Examples of superspace groups for modulated phases 493
A. 10.4 Superspace groups for quasiperiodic structures with 5-, 8-,
10-, 12-fold, or icosahedral symmetry 496
Appendix B Exercises: Solutions 499
References 503
Index 529
Until the 1970s all materials studied consisted of periodic arrays of unit cells, or were
amorphous. A new class of solid state matter called aperiodic crystals has since been
uncovered. It is a long-range ordered structure, but without lattice periodicity. It is found
in a wide range of materials: organic and anorganic compounds, minerals (including a
substantial portion of the earth s crust), and metallic alloys, under various pressures and
temperatures. Because of the lack of periodicity, the usual techniques for the study of
structure and physical properties no longer work, and new techniques have to be developed.
This book deals with the characterization of the structure, the structure determination, and
the study of the physical properties, especially dynamical and electronic properties of
aperiodic crystals. The treatment is based on a description in a space with more dimensions
than three, the so-called superspace. This allows us to generalize the standard crystallography
and to look differently at the dynamics. The three main classes of aperiodic crystals,
modulated phases, incommensurate composites, and quasicrystals, are treated from a unified
point of view, which stresses similarities of the various systems. The book assumes as a
prerequisite a knowledge of the fundamental techniques of crystallography and the theory
of condensed matter, and covers the literature at the forefront of the field.
Since the first edition of this book in 2007, the field ofaperiodic crystals has developed
considerably, with the discovery of new materials and new structures. Progress has been made
in structure determination, in the interpretation and understanding of the structural
characteristics and in the calculation of electrons and phonons. This new edition reflects these
new developments, and it includes discussions of natural quasicrvstals, incommensurate
magnetic and nuiltifcrroic structures, and photonic and mesoscopic quasicrvstals. The
second edition also includes a number of new exercises that give the reader an opportunity to
check their understanding of the material.
|
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| language | English |
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| spelling | Janssen, Ted 1936-2017 Verfasser (DE-588)13943562X aut Aperiodic crystals from modulated phases to quasicrystals: structure and properties Ted Janssen (Institute of Theoretical Physics, University of Nijmegen), Gervais Chapuis (École Polytechnique Fédérale de Lausanne), Marc de Boissieu (CNRS and Université Grenoble Alpes) 2nd edition Oxford Oxford University Press 2018 xviii, 532 Seiten Illustrationen, Diagramme (teilweise farbig) txt rdacontent n rdamedia nc rdacarrier IUCr monographs on crystallography 28 Molecular crystals / Structure Aperiodicity Aperiodischer Kristall (DE-588)4492275-9 gnd rswk-swf Aperiodischer Kristall (DE-588)4492275-9 s DE-604 Chapuis, Gervais 1944- Verfasser (DE-588)1089423675 aut Boissieu, Marc de Verfasser (DE-588)1164176722 aut IUCr monographs on crystallography 28 (DE-604)BV005455767 28 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030378300&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030378300&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Janssen, Ted 1936-2017 Chapuis, Gervais 1944- Boissieu, Marc de Aperiodic crystals from modulated phases to quasicrystals: structure and properties IUCr monographs on crystallography Molecular crystals / Structure Aperiodicity Aperiodischer Kristall (DE-588)4492275-9 gnd |
| subject_GND | (DE-588)4492275-9 |
| title | Aperiodic crystals from modulated phases to quasicrystals: structure and properties |
| title_auth | Aperiodic crystals from modulated phases to quasicrystals: structure and properties |
| title_exact_search | Aperiodic crystals from modulated phases to quasicrystals: structure and properties |
| title_full | Aperiodic crystals from modulated phases to quasicrystals: structure and properties Ted Janssen (Institute of Theoretical Physics, University of Nijmegen), Gervais Chapuis (École Polytechnique Fédérale de Lausanne), Marc de Boissieu (CNRS and Université Grenoble Alpes) |
| title_fullStr | Aperiodic crystals from modulated phases to quasicrystals: structure and properties Ted Janssen (Institute of Theoretical Physics, University of Nijmegen), Gervais Chapuis (École Polytechnique Fédérale de Lausanne), Marc de Boissieu (CNRS and Université Grenoble Alpes) |
| title_full_unstemmed | Aperiodic crystals from modulated phases to quasicrystals: structure and properties Ted Janssen (Institute of Theoretical Physics, University of Nijmegen), Gervais Chapuis (École Polytechnique Fédérale de Lausanne), Marc de Boissieu (CNRS and Université Grenoble Alpes) |
| title_short | Aperiodic crystals |
| title_sort | aperiodic crystals from modulated phases to quasicrystals structure and properties |
| title_sub | from modulated phases to quasicrystals: structure and properties |
| topic | Molecular crystals / Structure Aperiodicity Aperiodischer Kristall (DE-588)4492275-9 gnd |
| topic_facet | Molecular crystals / Structure Aperiodicity Aperiodischer Kristall |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030378300&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030378300&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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