Tables for
Volume C
Mathematical, physical and chemical tables
Edited by E. Prince

International Tables for Crystallography (2006). Vol. C, ch. 9.4, p. 778

Section 9.4.3. Interpretation of frequency distributions

G. Bergerhoffa and K. Brandenburga

aInstitut für Anorganische Chemie der Universität Bonn, Gerhard-Domagkstrasse 1, D-53121 Bonn, Germany

9.4.3. Interpretation of frequency distributions

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It is obvious that the results have to be interpreted carefully when they are applied to crystal-structure discussions. In performing the analysis, the frequency distribution was inspected for each pair of ions. If all values were distributed around a single maximum, then [d_1] and [d_2] were set equal to zero and 500 pm, respectively. If there were two or more maxima, one was carefully selected and [d_1] and [d_2] were set to the left and right in such a way that the frequency was zero at both limits. In combinations with oxygen, so many distances were available for the most probable maximum that the program could select [d_1] and [d_2] automatically.

Maxima outside the selected range may come from errors in data or distances to ions in the second coordination sphere [e.g. Mg2+–Cl in Mg(H2O)6Cl2]. Generally, different oxidation states give rise to different maxima, which therefore have been tabulated separately (e.g. Cr2+, Cr3+, Cr4+, Cr5+, Cr6+ in combination with O2−). In some typical cases, oxidation states cannot be clearly defined. Then the oxidation states have been omitted (e.g. Os—F, Rh—Br, N—S). Nevertheless, sometimes one oxidation state can be separated (e.g. W—Cl and W6+—Cl1−). Atomic distances between equally charged ions will be contact distances and vary over a wide range (e.g. O2−—O2− distances within [{\rm SO}_4^{2-}] ions and between such ions).

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