@article {Kronenburg:2004-05-01T00:00:00:0108-7673:250,
author = "Kronenburg, M. J.",
title = "Atomic displacement parameters and anisotropic thermal ellipsoid lengths and angles",
journal = "Acta Crystallographica Section A",
volume = "60",
number = "3",
year = "2004-05-01T00:00:00",
abstract = "Relations between direct and reciprocal basis vectors and the atomic displacement matrix and anisotropic temperature-factor matrix are provided for generic dimension n, introducing a few new symbols. The moments of the probability distribution of the anisotropic thermal ellipsoids are provided as functions of dimension n. For specific dimensions n=2 and n=3, new explicit formulas for the semi-axis lengths and rotation angles of the thermal ellipsoids are derived from the atomic displacement matrix, taking into account certain special cases. For dimension n=3, the Euler angles are defined. The resulting formulas can be used, for example, to display the thermal ellipsoids of atoms or for further analysis of molecular vibrations.",
pages = "250-256",
url = "http://www.ingentaconnect.com/content/bsc/aya/2004/00000060/00000003/art00009",
doi = "doi:10.1107/S0108767304007688",
keyword = "anisotropic temperature factor matrix, anisotropic thermal ellipsoid, metric matrix, mixed matrix, atomic displacement matrix, Euler angles"
}