Ideal centric distributions

Shmueli, U.; Wilson, A. J. C.

doi:10.1107/97809553602060000554

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

pdf | chapter contents | chapter index | related articles

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

Section 2.1.5.2. Ideal centric distributions

U. Shmueli^a ^* and A. J. C. Wilson^b ^‡

^a School 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

| top | pdf |

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 $[p(|E|)\;{\rm d}|E| = (2/\pi)^{1/2}\exp(-|E|^{2}/2)\;{\rm d}|E|. \eqno(2.1.5.11)]$

References

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