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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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(p.1) 1 Introduction
Symmetry Relationships between Crystal Structures

Ulrich Müller

Oxford University Press

This introductory chapter outlines the symmetry principle in crystal chemistry states: in crystal structures the arrangement of the atoms has a tendency towards the highest possible symmetry; counteracting factors may enforce a reduced symmetry; and during phase transitions and topotactic reactions which result in products of lower symmetry, the higher symmetry of the starting material is often indirectly preserved by the formation of oriented domains. Many crystal structures can be derived from a few simple, highly symmetrical crystal structures. A family of structures is headed by a most symmetrical structure — the aristotype — and the space groups of the derivative structures or hettotypes are subgroups of the space group of the aristotype. A Bärnighausen tree depicts the group-subgroup relations. An example is the relation diamond-zinc blende. Symmetry reduction to a subgroup can take place during a phase transition, and a twinned crystal can be the result.

Keywords:   symmetry principle, diamond-zinc blende, aristotype, hettotype, group-subgroup relations, Bärnighausen tree, phase transition, diamond, twinned crystal, calcium chloride

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