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IntermetallicsStructures, Properties, and Statistics$
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Walter Steurer and Julia Dshemuchadse

Print publication date: 2016

Print ISBN-13: 9780198714552

Published to Oxford Scholarship Online: September 2016

DOI: 10.1093/acprof:oso/9780198714552.001.0001

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Crystallographic description of crystal structures

Crystallographic description of crystal structures

(p.31) 3 Crystallographic description of crystal structures

Walter Steurer

Julia Dshemuchadse

Oxford University Press

Crystal structures, be they periodic or aperiodic, can be described in many different ways: as lattices, tilings, or coverings decorated by atoms or clusters on one hand, or as packings of structural subunits (AETs, clusters, modules, etc.) on the other hand. In this chapter the decomposition of crystal structures into AETs and clusters is discussed, as well as tilings and coverings. This ranges from the 1D quasiperiodic Fibonacci sequence to examples of 2D and 3D periodic as well as quasiperiodic tilings. The standard unit cell description of periodic crystal structures corresponds to a specific tiling approach with just a single prototile with the shape of a parallelepiped, i.e., the crystallographic unit cell. The detailed discussion of periodic and quasiperiodic tilings and packings can be quite helpful in understanding structural building principles of complex intermetallics, periodic as well as quasiperiodic ones.

Keywords:   tilings, coverings, packings, atomic environment types, coordination, polyhedra, Archimedean tilings, Archimedean polyhedra, Platonic solids, Gummelt decagon, complex intermetallics

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