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Symmetry Relationships between Crystal StructuresApplications of Crystallographic Group Theory in Crystal Chemistry$
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Ulrich Müller

Print publication date: 2013

Print ISBN-13: 9780199669950

Published to Oxford Scholarship Online: December 2013

DOI: 10.1093/acprof:oso/9780199669950.001.0001

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Derivation of crystal structures from closest packings of spheres

Derivation of crystal structures from closest packings of spheres

(p.167) 13 Derivation of crystal structures from closest packings of spheres
Symmetry Relationships between Crystal Structures

Ulrich Müller

Oxford University Press

The partial occupation of interstices in a packing of spheres can be treated in the same way as the substitution of atoms. Rhombohedral hettotypes of the hexagonal closest packing of spheres include the RhF3, α-Al2O3, BiI3, WCl6, LiSbF6, LiNbO3, and other structure types. Even as yet unknown structures can be derived, such as a hypothetical structure for WCl3 in the space group R32. Other derivative structures result as hexagonal or trigonal hettotypes such as hexagonal TiI3 or Li2ZrF6. Distortions like displacements of atoms from octahedron centres cause further symmetry reductions. Hettotypes of the cubic closest packing of spheres with occupation of octahedral or tetrahedral interstices, with or without vacant sphere sites, yield further structure types like SnF4, NbO, Cu2O, PtS, and SiS2. ThCr2Si2, regarded as NaCl derivative with vacancies, shows the limits where group-theoretical considerations become meaningless.

Keywords:   hexagonal closest packing, cubic closest packing, octahedron centres, trigonal hettotypes

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