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The Physics of Solids$
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J. B. Ketterson

Print publication date: 2016

Print ISBN-13: 9780198742906

Published to Oxford Scholarship Online: December 2016

DOI: 10.1093/acprof:oso/9780198742906.001.0001

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Lattices and Crystal Structures

Lattices and Crystal Structures

(p.107) 8 Lattices and Crystal Structures
The Physics of Solids

J. B. Ketterson

Oxford University Press

This chapter begins with a definition of space lattice. For most pure materials, the lowest energy state at low temperatures is a crystalline solid, where the atoms or molecules making up the substance bind together in a manner which periodically repeats itself in space. The atoms are not points but have a finite spatial extent, and they execute thermal and quantum mechanical zero-point motions. If the crystal structure involves only one kind of atom and if there is only one atom per unit cell, then we may locate each atom at the origin of a unit cell. However, if there are multiple atoms per unit cell we must specify their location within the unit cell. The collection of atom coordinates is referred to as a basis and together with the lattice defines a crystal structure: lattice + basis = crystal structure. The remainder of the chapter covers point groups, Bravais lattices, and space groups in two dimensions; point groups, Bravais lattices, and space groups in three dimensions; common crystal structures; Miller indices; and the Wigner–Seitz polyhedra and coordination polyhedra.

Keywords:   space lattice, crystalline solid, atoms, crystal structure, point group, Bravais lattice, space group, Miller indices, Wigner–Seitz polyhedra, coordination polyhedra

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