Abstract
The theory of lattice dynamics shows that the atomic thermal Debye–Waller factor is related to the atomic displacements. In the harmonic approximation, these are fully described by a fully symmetric second-order tensor. Anharmonicity and disorder, however, cause deviations from a Gaussian distribution of the atomic displacements around the atomic position. A generalized description of atomic displacements therefore also involves first-, third-, fourth- and even higher-order displacement terms.The description of the properties of these tensors is the purpose of this chapter. The number of independent tensor coefficients depends on the site symmetry of the atom and are given in tables. The symmetry restrictions according to the site symmetry are tabulated for second- to sixth-rank thermal motion tensors. A selection of representation surfaces of higher-rank tensors showing the distribution of anharmonic deformation densities is given at the end of the chapter. This chapter is also available as HTML from the International Tables Online site hosted by the IUCr.
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© 2006 International Union of Crystallography
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Kuhs, W.F. (2006). Atomic displacement parameters. In: Authier, A. (eds) International Tables for Crystallography Volume D: Physical properties of crystals. International Tables for Crystallography, vol D. Springer, Dordrecht. https://doi.org/10.1107/97809553602060000636
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DOI: https://doi.org/10.1107/97809553602060000636
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-0714-9
Online ISBN: 978-1-4020-5409-9
eBook Packages: Springer Book Archive