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Symmetry of Crystals and Molecules$
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Mark Ladd

Print publication date: 2014

Print ISBN-13: 9780199670888

Published to Oxford Scholarship Online: April 2014

DOI: 10.1093/acprof:oso/9780199670888.001.0001

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Lattices

Lattices

Chapter:
(p.119) 4 Lattices
Source:
Symmetry of Crystals and Molecules
Author(s):

Mark Ladd

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199670888.003.0004

The definition of ‘lattice’ in one, two, and three dimensions is discussed, together with the choice of unit cell. The Bravais lattices are explained with stereoscopic illustrations, system by system, and the reciprocal lattice introduced. The law of rational intercepts and its ramifications are described, leading to an examination of preferential crystal growth planes. Transformation of unit cell vectors, zone symbols, coordinates of points in a unit cell, Miller indices and reciprocal unit cell vectors are described in detail, with examples. The Wigner–Seitz cell is discussed as an alternative crystal unit cell. Matrix representations of point groups are introduced,

Keywords:   lattices, transformation, unit cell, Wigner–Seitz cells, Bravais lattices, reciprocal lattice, crystal growth planes, Miller indices, matrix representations, point groups

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