Tables for
Volume B
Reciprocal space
Edited by U. Shmueli

International Tables for Crystallography (2006). Vol. B. ch. 2.1, p. 203


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:

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Closed expressions for [\gamma_{2k}] [equation ([link]] for space groups of low symmetry

The normalized moments [\gamma_{2k}] are expressed in terms of [M_{k}], where [M_{k} = {(2k)! \over 2^{k}(k!)^{2}} = {(2k - 1)!! \over k!},] and [l'], which takes on the values 1, 2 or 4 according as the Bravais lattice is of type P, one of the types A, B, C or I, or type F, respectively. The expressions for [\gamma_{2k}] are identical for all the space groups based on a given point group, except Fdd2 and Fddd. The expressions are valid for general reflections and under the restrictions given in the text.

Point group(s)Expression for [\gamma_{2k}]
1 1
[\bar{1}, 2, m] [l'^{k - 1} M_{k}]
[2/m, mm2] [l'^{k - 1} M_{k}^{2}]
mmm [l'^{k - 1} M_{k}^{3}]
222 [{l'^{k - 1} \over 2^{k} (k!)^{2}} \sum\limits_{p=0}^{k} (M_{p}M_{k - p})^{3}[p! (k - p)!]^{2}]