Steurer / Deloudi Crystallography of Quasicrystals

Concepts, Methods and Structures
1. Auflage 2009
ISBN: 978-3-642-01899-2
Verlag: Springer
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 384 Seiten

From tilings to quasicrystal structures and from surfaces to the n-dimensional approach, this book gives a full, self-contained in-depth description of the crystallography of quasicrystals. It aims not only at conveying the concepts and a precise picture of the structures of quasicrystals, but it also enables the interested reader to enter the field of quasicrystal structure analysis. Going beyond metallic quasicrystals, it also describes the new, dynamically growing field of photonic quasicrystals. The readership will be graduate students and researchers in crystallography, solid-state physics, materials science, solid- state chemistry and applied mathematics.

Born in Vienna, Austria on December 24, 1950, Walter Steurer studied chemistry at the University of Vienna. After finishing his doctoral dissertation under the supervision of Prof. Hans Nowotny at the Institute of Physical Chemistry, he moved, in 1980, to the University of Munich, Germany, where he worked as a research assistant and lecturer. In 1987 he concluded his habilitation thesis in the field of crystallography and mineralogy. In 1990 he receive the Victor-Moritz-Goldschmid Award of the Deutsche Mineralogische Gesellschaft (DMG) for his contributions to the higher-dimensional structure analysis. His research topics were uncommon crystals and their phase transitions, and included incommensurably modulated structures, quasicrystals and polytypes. For a short period, from 1992 until 1993, he was professor of crystallography at the University of Hanover, Germany. After rejecting calls to the Universities of Hamburg and Munich, Germany, he has been full professor of crystallography at the Laboratory of Crystallography of the ETH and University of Zurich since the fall of 1993. In 2008, Walter Steurer received the Jean Marie Dubois Award for Excellence in Quasicrystal Research. At present, his research topics comprise structural studies of aperiodic crystals and their phase transformations, the modeling of order/disorder phenomena, and higher-dimensional crystallography. Sofia Deloudi, was born in Athens, Greece on March 27, 1980. She studied interdisciplinary natural sciences at the ETH Zurich and concluded her doctoral dissertation under the supervision of Prof. Walter Steurer at the Laboratory of Crystallography of the ETH. At present, she is a junior scientist with her focus on modeling of quasiperiodic structures and higher-dimensional crystallography.

Autoren/Hrsg.

Steurer, Walter

Deloudi, Sofia

Inhaltsverzeichnis

1;Preface;6
2;Contents;8
3;Part I Concepts;15
3.1;1 Tilings and Coverings;21
3.1.1;1.1 1D Substitutional Sequences;23
3.1.1.1;1.1.1 Fibonacci Sequence (FS);24
3.1.1.2;1.1.2 Octonacci Sequence;27
3.1.1.3;1.1.3 Squared Fibonacci Sequence;28
3.1.1.4;1.1.4 Thue--Morse Sequence;29
3.1.1.5;1.1.5 1D Random Sequences;30
3.1.2;1.2 2D Tilings;30
3.1.2.1;1.2.1 Archimedean Tilings;32
3.1.2.2;1.2.2 Square Fibonacci Tiling;33
3.1.2.3;1.2.3 Penrose Tiling (PT);35
3.1.2.4;1.2.4 Heptagonal (Tetrakaidecagonal) Tiling;45
3.1.2.5;1.2.5 Octagonal Tiling;50
3.1.2.6;1.2.6 Dodecagonal Tiling;52
3.1.2.7;1.2.7 2D Random Tilings;56
3.1.3;1.3 3D Tilings;57
3.1.3.1;1.3.1 3D Penrose Tiling (Ammann Tiling);57
3.1.3.2;1.3.2 3D Random Tilings;58
3.1.4;References;59
3.2;2 Polyhedra and Packings;62
3.2.1;2.1 Convex Uniform Polyhedra;63
3.2.2;2.2 Packings of Uniform Polyhedra with Cubic Symmetry;67
3.2.3;2.3 Packings and Coverings of Polyhedra with Icosahedral Symmetry;69
3.3;3 Higher-Dimensional Approach;73
3.3.1;3.1 nD Direct and Reciprocal Space Embedding;75
3.3.2;3.2 Rational Approximants;80
3.3.3;3.3 Periodic Average Structure (PAS);82
3.3.4;3.4 Structure Factor;84
3.3.4.1;3.4.1 General Formulae;84
3.3.4.2;3.4.2 Calculation of the Geometrical Form Factor;85
3.3.5;3.5 1D Quasiperiodic Structures ;90
3.3.5.1;3.5.1 Reciprocal Space;90
3.3.5.2;3.5.2 Symmetry;92
3.3.5.3;3.5.3 Example: Fibonacci Structure;93
3.3.6;3.6 2D Quasiperiodic Structures ;104
3.3.6.1;3.6.1 Pentagonal Structures;106
3.3.6.2;3.6.2 Heptagonal Structures;113
3.3.6.3;3.6.3 Octagonal Structures;120
3.3.6.4;3.6.4 Decagonal Structures;133
3.3.6.5;3.6.5 Dodecagonal Structures;159
3.3.6.6;3.6.6 Tetrakaidecagonal Structures ;167
3.3.7;3.7 3D Quasiperiodic Structures with Icosahedral Symmetry;182
3.3.7.1;3.7.1 Reciprocal Space;183
3.3.7.2;3.7.2 Symmetry;186
3.3.7.3;3.7.3 Example: Ammann Tiling (AT);189
3.3.8;References;198
4;Part II Methods;201
4.1;4 Experimental Techniques;204
4.1.1;4.1 Electron Microscopy;207
4.1.2;4.2 Diffraction Methods;208
4.1.3;4.3 Spectroscopy;212
4.1.4;References;213
4.2;5 Structure Analysis;215
4.2.1;5.1 Data Collection Strategy;217
4.2.2;5.2 Multiple Diffraction (Umweganregung);218
4.2.3;5.3 Patterson Methods;220
4.2.4;5.4 Statistical Direct Methods;224
4.2.5;5.5 Charge Flipping Method (CF);225
4.2.6;5.6 Low-Density Elimination;226
4.2.7;5.7 Maximum Entropy Method;228
4.2.8;5.8 Structure Refinement;232
4.2.9;5.9 Crystallographic Data for Publication;235
4.2.10;References;236
4.3;6 Diffuse Scattering and Disorder;240
4.3.1;6.1 Phasonic Diffuse Scattering (PDS) on the Example of the Penrose Rhomb Tiling;244
4.3.2;6.2 Diffuse Scattering as a Function of Temperatureon the Example of d-Al--Co--Ni;245
4.3.3;References;250
5;Part III Structures;252
5.1;7 Structures with 1D Quasiperiodicity;255
5.1.1;References;256
5.2;8 Structures with 2D Quasiperiodicity;257
5.2.1;8.1 Heptagonal Phases;258
5.2.1.1;8.1.1 Approximants: Borides, Borocarbides, and Carbides;260
5.2.1.2;8.1.2 Approximants: -Gallium;262
5.2.2;8.2 Octagonal Phases;262
5.2.3;8.3 Decagonal Phases;264
5.2.3.1;8.3.1 Two-Layer and Four-Layer Periodicity;264
5.2.3.2;8.3.2 Six-Layer Periodicity;281
5.2.3.3;8.3.3 Eight-Layer Periodicity;283
5.2.3.4;8.3.4 Surface Structures of Decagonal Phases;285
5.2.4;8.4 Dodecagonal Phases;287
5.2.5;References;291
5.3;9 Structures with 3D Quasiperiodicity;298
5.3.1;9.1 Mackay-Cluster Based Icosahedral Phases (Type A);301
5.3.2;9.2 Bergman-Cluster Based Icosahedral Phases (Type B);302
5.3.3;9.3 Tsai-Cluster-Based Icosahedral Phases (Type C);307
5.3.4;9.4 Example: Icosahedral Al--Cu--Fe;312
5.3.5;9.5 Surface Structures of Icosahedral Phases;317
5.3.6;References;320
5.4;10 Phase Formation and Stability;327
5.4.1;10.1 Formation of Quasicrystals;328
5.4.2;10.2 Stabilization of Quasicrystals;330
5.4.3;10.3 Clusters;334
5.4.4;10.4 Phase Transformations of Quasicrystals;339
5.4.4.1;10.4.1 Quasicrystal Quasicrystal Transition;340
5.4.4.2;10.4.2 Quasicrystal Crystal Transformation;343
5.4.4.3;10.4.3 Microscopic Models;351
5.4.5;References;355
5.5;11 Generalized Quasiperiodic Structures;364
5.5.1;11.1 Soft Quasicrystals;365
5.5.2;11.2 Photonic and Phononic Quasicrystals;367
5.5.2.1;11.2.1 Interactions with Classical Waves;368
5.5.2.2;11.2.2 Examples: 1D, 2D and 3D Phononic Quasicrystals;371
5.5.3;References;375
6;Glossary;377
7;Index;381