International
Tables for
Crystallography
Volume B
Reciprocal space
Edited by U. Shmueli

International Tables for Crystallography (2006). Vol. B. ch. 2.1, p. 196   | 1 | 2 |

Section 2.1.5.2. Ideal centric distributions

U. Shmuelia* and A. J. C. Wilsonb

aSchool of Chemistry, Tel Aviv University, Tel Aviv 69 978, Israel, and bSt John's College, Cambridge, England
Correspondence e-mail:  ushmueli@post.tau.ac.il

2.1.5.2. Ideal centric distributions

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When a non-dispersive crystal is centrosymmetric, and the space-group origin is chosen at a crystallographic centre of symmetry, the imaginary part B of its structure amplitude is zero. In the simplest case, space group [P\bar{1}], the contribution of the jth atom plus its centrosymmetric counterpart is [2f_{j}\cos\vartheta_{j}]. The calculation of [p(A)] goes through as before, with allowance for the fact that there are [N/2] pairs instead of N independent atoms, giving [p(A)\;{\rm d}A = (2\pi\Sigma)^{-1/2}\exp[-A^{2}/(2\Sigma)]\;{\rm d}A \eqno(2.1.5.9)] or equivalently [p(|F|)\;{\rm d}|F| = [2/(\pi\Sigma)]^{1/2}\exp[-|F|^{2}/(2\Sigma)]\;{\rm d}|F| \eqno(2.1.5.10)] or [p(|E|)\;{\rm d}|E| = (2/\pi)^{1/2}\exp(-|E|^{2}/2)\;{\rm d}|E|. \eqno(2.1.5.11)]








































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