A guide to lifting aperiodic structures
-
Michael Baake
,
David Écija
Abstract
The embedding of a given point set with non-crystallographic symmetry into higher-dimensional space is reviewed, with special emphasis on the Minkowski embedding known from number theory. This is a natural choice that does not require an a priori construction of a lattice in relation to a given symmetry group. Instead, some elementary properties of the point set in physical space are used, and explicit methods are described. This approach works particularly well for the standard symmetries encountered in the practical study of quasicrystalline phases. We also demonstrate this with a recent experimental example, taken from a sample with square-triangle tiling structure and (approximate) 12-fold symmetry.
Acknowledgments
It is our pleasure to thank Johannes Roth for useful hints. We are grateful to Johannes V. Barth, Nian Lin and José I. Urgel for providing the experimental image from [14]. D.É. would like to thank the TU Munich physics department for hospitality, where part of the research was done. This work was supported by the German Research Foundation (DFG), within the CRC 701, as well as by the Spanish Ministerio de Economa y Competitividad (project FIS 2015-67287-P).
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©2016 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Graphical Synopsis
- Inorganic Crystal Structures
- A guide to lifting aperiodic structures
- Crystal structure of monoclinic samarium and cubic europium sesquioxides and bound coherent neutron scattering lengths of the isotopes 154Sm and 153Eu
- Substitution disorder and photoluminescent property of a new rare-earth borate: K3TbB6O12
- Organic and Metalorganic Crystal Structures
- Synthesis and characterization of two new chiral Kemp’s acid derivatives: structures fixed by a peculiar system of N–H···O, C–H···O and C–H···N hydrogen bonds
- Methyl-2-methyl-2-(4-methyl-phenyl)sulfonamido propanoate: structural study, supramolecular architecture and analysis of molecular surface electrostatic potential
Artikel in diesem Heft
- Frontmatter
- Graphical Synopsis
- Inorganic Crystal Structures
- A guide to lifting aperiodic structures
- Crystal structure of monoclinic samarium and cubic europium sesquioxides and bound coherent neutron scattering lengths of the isotopes 154Sm and 153Eu
- Substitution disorder and photoluminescent property of a new rare-earth borate: K3TbB6O12
- Organic and Metalorganic Crystal Structures
- Synthesis and characterization of two new chiral Kemp’s acid derivatives: structures fixed by a peculiar system of N–H···O, C–H···O and C–H···N hydrogen bonds
- Methyl-2-methyl-2-(4-methyl-phenyl)sulfonamido propanoate: structural study, supramolecular architecture and analysis of molecular surface electrostatic potential
