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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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How to handle space groups

How to handle space groups

(p.121) 9 How to handle space groups
Symmetry Relationships between Crystal Structures

Ulrich Müller

Oxford University Press

Among the Wyckoff positions of a space group there often are different positions that are mutually equivalent in the Euclidean normalizer of the space group. Origin shifts or basis transformations can cause an interchange among these Wyckoff positions. The relations between the Wyckoff positions are uniquely determined for every group-subgroup pair. Nonconventional settings of space groups differ from those listed in International Tables for Crystallography. They result from interchange or transformation of the basis vectors and have different Hermann-Mauguin symbols and atomic coordinates.

Keywords:   Wyckoff positions, Hermann-Mauguin symbols, space group

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