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Symmetry in CrystallographyUnderstanding the International Tables$
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Paolo Radaelli

Print publication date: 2011

Print ISBN-13: 9780199550654

Published to Oxford Scholarship Online: December 2013

DOI: 10.1093/acprof:oso/9780199550654.001.0001

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Coordinate systems in crystallography

Coordinate systems in crystallography

Chapter:
(p.52) (p.53) 4 Coordinate systems in crystallography
Source:
Symmetry in Crystallography
Author(s):

Paolo G. Radaelli

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199550654.003.0004

This chapter describes the coordinate system for defining the position of atoms and molecules (or more generically, ‘features’ in the symmetric patterns). The description is underpinned by the fundamental concept of basis vectors, which generate the translation operators of the symmetry group. Since these coordinate systems are typically non-Cartesian, a notation borrowed from the field of General Relativity, which distinguishes between ‘covariant’ and ‘contravariant’ quantities, is employed. Coordinate transformations, often considered to be the bane of crystallographers, are also introduced in a straightforward way.

Keywords:   crystallographic coordinates, coordinate transformations, covariant quantities, contravariant quantities, basis vectors

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