Abstract
Variations in mean bond length are examined in oxide and oxysalt crystals for 55 cation configurations bonded to O2−. Stepwise multiple regression analysis shows that mean bond length is correlated to bond-length distortion in 42 ion configurations at the 95% confidence level, with a mean coefficient of determination (〈R 2〉) of 0.35. Previously published correlations between mean bond length and mean coordination number of the bonded anions are found not to be of general applicability to inorganic oxide and oxysalt structures. For two of 11 ions tested for the 95% confidence level, mean bond lengths predicted using a fixed radius for O2− are significantly more accurate as those predicted using an O2− radius dependent on coordination number, and are statistically identical otherwise. As a result, the currently accepted ionic radii for O2− in different coordinations are not justified by experimental data. Previously reported correlation between mean bond length and the mean electronegativity of the cations bonded to the oxygen atoms of the coordination polyhedron is shown to be statistically insignificant; similar results are obtained with regard to ionization energy. It is shown that a priori bond lengths calculated for many ion configurations in a single structure-type leads to a high correlation between a priori and observed mean bond lengths, but a priori bond lengths calculated for a single ion configuration in many different structure-types leads to negligible correlation between a priori and observed mean bond lengths. This indicates that structure type has a major effect on mean bond length, the magnitude of which goes beyond that of the other variables analyzed here.
Highlights
In the 1960s and 1970s, a considerable amount of work was carried out on trying to understand the reasons underlying variations in mean bond length in crystals
The following variables were systematically evaluated for all ion configurations as potential causal factors underlying mean bond-length variation: (1) bond-length distortion, (2) mean coordination number of the oxygen atoms bonded to the cation, (3) mean electronegativity of the cations bonded to the oxygen atoms of the coordination polyhedron, (4) mean ionization energy of the cations bonded to the oxygen atoms of the coordination polyhedron
A notable accidental correlation found from this study of sample size is that of mean bond length and mean ionization energy of the cations bonded to the oxygen atoms of the coordination polyhedron, which is found to be statistically significant at the 99.9% confidence level, with R2 = À0.66 for 15 polyhedra [Figs. 1(d) and 2(d)], whereas R2 = 0.08 for the parent distribution with n = 334
Summary
In the 1960s and 1970s, a considerable amount of work was carried out on trying to understand the reasons underlying variations in mean bond length in crystals This resulted from the improving precision of structure refinements which began showing variations in mean bond length that significantly exceeded experimental error. Several factors were examined as possible sources of this variation, and many studies were reported as ‘reasonably successful’ in correlating variation in mean bond length with one or more possible causal factors, e.g. variation in mean coordination number of the bonded anions, variation in mean electronegativity of the nextnearest-neighbour cations, dispersion of bond lengths about their mean value (distortion). These studies were typically limited to a single configuration of the oxidation state and coordination number of an ion, and often consisted of few data
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