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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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Basics of crystallography, part 2

Basics of crystallography, part 2

Chapter:
(p.41) 4 Basics of crystallography, part 2
Source:
Symmetry Relationships between Crystal Structures
Author(s):

Ulrich Müller

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199669950.003.0004

A space group consists of an infinity of crystallographic symmetry operations which are represented by matrix-column pairs W,w. However, the number of different matrices W always is finite. Rotations are restricted to rotation angles of 360°/N with the orders of N = 1, 2, 3, 4, and 6. Symmetry operations are designated by Hermann-Mauguin symbols. These include: 1 for the identity; the number N for rotations; Np for screw rotations; for rotoinversions; m for reflections; a, b, c, d, e, and n for glide reflections. A plane perpendicular to an axis is specified by a fraction sign like 4/m. The geometric meaning of a matrix-column pair W,w can be inferred from the determinant and the trace of W.

Keywords:   matrix-column pair, crystallographic symmetry operation, Hermann-Mauguin symbol

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