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Aperiodic Crystals

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Aperiodic Crystals collects 37 selected papers from the scientific contributions presented at Aperiodic 2012 - the Seventh International Conference on Aperiodic Crystalsheld held in Cairns, Australia, 2-7 of September 2012.

The volume discusses state-of-the-art discoveries, new trends and applications of aperiodic crystals - including incommensurately modulated crystals, composite crystals, and quasicrystals - from a wide range of different perspectives. Starting with a general historical introduction to aperiodic crystals, the book proceeds to examine the complex mathematics of aperiodic long-range order, as well as the theoretical approaches aimed at understanding some of the unique properties and mechanisms underlying the existence of aperiodic crystals. The book then explores in detail such topics as complex metallic alloys, modulated structures, quasicrystals and their approximants, dynamics, disorder and defects in quasicrystals. It concludes with an analysis of quasicrystal surfaces and their properties.

By describing the latest research and the progress made on the structure determination of aperiodic crystals and the influence of this unique structure on their physical properties, this book represents a valuable resource to mathematicians, crystallographers, physicists, chemists, materials and surface scientists, and even architects and artists, interested in the fascinating nature of aperiodic crystals.

Author(s): T. Janssen (auth.), Siegbert Schmid, Ray L. Withers, Ron Lifshitz (eds.)
Edition: 1
Publisher: Springer Netherlands
Year: 2013

Language: English
Pages: 286
Tags: Structural Materials; Crystallography; Spectroscopy/Spectrometry

Front Matter....Pages I-XV
A Brief History of Aperiodic Crystals: 1962–2012....Pages 1-9
Squiral Diffraction....Pages 11-17
Random Noble Means Substitutions....Pages 19-27
Magic Numbers in the Discrete Tomography of Cyclotomic Model Sets....Pages 29-34
Some Comments on the Inverse Problem of Pure Point Diffraction....Pages 35-41
Well-Rounded Sublattices and Coincidence Site Lattices....Pages 43-48
Octagon-Based Quasicrystalline Formations in Islamic Architecture....Pages 49-57
The Ammann–Beenker Tilings Revisited....Pages 59-65
Substitution Rules and Topological Properties of the Robinson Tilings....Pages 67-73
Short-Range Spin Fluctuation in the Zn–Mg–Tb Quasicrystal and Its Relation to the Boson Peak....Pages 75-79
Anomalous Properties and the Electronic Glass-Like State in Al-Based Stable Quasicrystals....Pages 81-87
Quantum Diffusion in Separable d -Dimensional Quasiperiodic Tilings....Pages 89-94
Hume–Rothery Stabilization Mechanism of Be-Based Complex Alloys....Pages 95-100
Hume–Rothery Stabilization Mechanism in Tsai-Type Cd 6 Ca Approximant and e / a Determination of Ca and Cd Elements in the Periodic Table....Pages 101-107
Hume–Rothery Stabilization Mechanism in Low-Temperature Phase Zn 6 Sc Approximant and e / a Determination of Sc and Y in M–Sc and M–Y (M=Zn, Cd and Al) Alloy Systems....Pages 109-115
Analysis of Dislocations in Quasicrystals Composed of Self-assembled Nanoparticles....Pages 117-124
Average Unit Cell in Fourier Space and Its Application to Decagonal Quasicrystals....Pages 125-132
A Study of Phase Equilibria in the Al–Pd–Co System at 700 ∘ C....Pages 133-139
Evolution of Phases in Selected Al–Co–Cu Complex Metallic Alloys Under Near-Equilibrium Conditions at 800–1150 ∘ C....Pages 141-147
Superspace Description of the System Bi 2(n+2) Mo n O 6(n+1) ( n =3, 4, 5 and 6)....Pages 149-155
Pseudo-Commensurate GdBaCo 2 O 5+δ and Its Phase Transition at Elevated Temperatures....Pages 157-162
Al 4 (Cr,Fe): A Structure Survey....Pages 163-170
Phase Transitions in Aperiodic Composite Crystals....Pages 171-177
Pseudo-Symmetry in Tungsten Bronze Type Sr 3 TiNb 4 O 15 ....Pages 179-185
Structural Investigation of the Incommensurate Modulated Ta 2 O 5 ⋅Al 2 O 3 System....Pages 187-193
First-Principles Study for Phase Diagrams of Cd–Ca and Cd–Y Tsai-Type Approximants Under Pressure....Pages 195-201
The Choice of Vector Basis for Ammann Tiling in a Context of the Average Unit Cell....Pages 203-210
Real Space Structure Factor and Scaling for Quasicrystals....Pages 211-218
Direct Observations of Aperiodic Arrangements of Transition-Metal Atoms in Al–Co–Ni Decagonal Quasicrystals by Cs -Corrected HAADF-STEM....Pages 219-224
Arrangement of Transition-Metal Atoms in an Approximant Crystal Related to Al–Cu–Co Decagonal Quasicrystals Studied by C s-Corrected HAADF-STEM....Pages 225-230
Structure of ϵ 16 Phase in Al–Pd–Co System Studied by HREM and X-Ray Diffraction....Pages 231-236
Structure of τ 2 -Al 3 Co, a Monoclinic Approximant of the Al–Co Decagonal Quasicrystal....Pages 237-242
Reverse Monte Carlo Study of Diffuse Scattering from a Frustrated Protein System....Pages 243-251
Dynamical Flexibility in the Periodic Zn 6 Sc 1/1-Approximant....Pages 253-259
Trajectories of Colloidal Particles in Laser Fields with Eight-, Ten-, or Twelve-Fold Symmetry and Phasonic Drift....Pages 261-267
Catalytic Properties of Five-Fold Surfaces of Quasicrystal Approximants....Pages 269-274
Effect of Leaching on Surface Microstructure and Chemical Composition of Al-Based Quasicrystals....Pages 275-282
Back Matter....Pages 283-286