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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 1

Basics of crystallography, part 1

(p.10) (p.11) 2 Basics of crystallography, part 1
Symmetry Relationships between Crystal Structures

Ulrich Müller

Oxford University Press

A crystal can be considered to be a finite section from an infinite ideal crystal (a crystal pattern). This is an infinite periodic, three-dimensional array of atoms. A shift by a translation vector which brings a crystal to superposition with itself is a symmetry translation. The infinite set of all translation vectors is the lattice. Crystal coordinates are referred to a coordinate system which is set up by three basis vectors (the lattice basis). The basis vectors span a parallelepiped called the unit cell. The lattice is primitive if, referred to this lattice basis, all lattice vectors have integral coefficients; otherwise the lattice is centred. The lengths of the basis vectors and the angles between them are the lattice parameters. They serve to define the metric tensor which is useful to calculating distances and angles.

Keywords:   symmetry translation, translation vector, lattice, lattice vector, basis vector, unit cell, primitive lattice, lattice parameters, coordinates, metric tensor

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