International
Tables for
Crystallography
Volume F
Crystallography of biological macromolecules
Edited by E. Arnold, D. M. Himmel and M. G. Rossmann

International Tables for Crystallography (2012). Vol. F, ch. 18.4, p. 485   | 1 | 2 |

Figure 18.4.1.1 

Z. Dauter,a G. N. Murshudovb and K. S. Wilsonb*

aNCI Frederick & Argonne National Laboratory, Building 202, Argonne, IL 60439, USA, and bYork Structural Biology Laboratory, Department of Chemistry, University of York, York YO10 5YW, UK
Correspondence e-mail:  keith@ysbl.york.ac.uk

[Figure 18.4.1.1]
Figure 18.4.1.1

The thermal-ellipsoid model used to represent anisotropic atomic displacement, with major axes indicated. The ellipsoid is drawn with a specified probability of finding an atom inside its contour. Six parameters are necessary to describe the ellipsoid: three represent the dimensions of the major axes and three the orientation of these axes. These six parameters are expressed in terms of a symmetric U tensor and contribute to atomic scattering through the term [\exp[-2\pi ^{2}(U_{11}h^{2}a^{*2}] + [U_{22}k^{2}b^{*2}] + [U_{33}l^{2}c^{*2}] + [2U_{12}hka^{*}b^{*} \cos \gamma^{*}] + [2U_{13}hla^{*}c^{*} \cos \beta^{*}] + [2U_{23}klb^{*}c^{*} \cos \alpha^{*})].]