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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

(p.52) (p.53) 4 Coordinate systems in crystallography
Symmetry in Crystallography

Paolo G. Radaelli

Oxford University Press

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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