Bond-length distributions for ions bonded to oxygen: alkali and alkaline-earth metals

Abstract

Bond-length distributions have been examined for 55 configurations of alkali-metal ions and 29 configurations of alkaline-earth-metal ions bonded to oxygen, for 4859 coordination polyhedra and 38 594 bond distances (alkali metals), and for 3038 coordination polyhedra and 24 487 bond distances (alkaline-earth metals). Bond lengths generally show a positively skewed Gaussian distribution that originates from the variation in Born repulsion and Coulomb attraction as a function of interatomic distance. The skewness and kurtosis of these distributions generally decrease with increasing coordination number of the central cation, a result of decreasing Born repulsion with increasing coordination number. We confirm the following minimum coordination numbers:[3]Li+,[3]Na+,[4]K+,[4]Rb+,[6]Cs+,[3]Be2+,[4]Mg2+,[6]Ca2+,[6]Sr2+and[6]Ba2+, but note that some reported examples are the result of extensive dynamic and/or positional short-range disorder and are not ordered arrangements. Some distributions of bond lengths are distinctly multi-modal. This is commonly due to the occurrence of large numbers of structure refinements of a particular structure type in which a particular cation is always present, leading to an over-representation of a specific range of bond lengths. Outliers in the distributions of mean bond lengths are often associated with anomalous values of atomic displacement of the constituent cations and/or anions. For a sample of[6]Na+, the ratioUeq(Na)/Ueq(bonded anions)is partially correlated with 〈[6]Na+—O2−〉 (R2= 0.57), suggesting that the mean bond length is correlated with vibrational/displacement characteristics of the constituent ions for a fixed coordination number. Mean bond lengths also show a weak correlation with bond-length distortion from the mean value in general, although some coordination numbers show the widest variation in mean bond length for zero distortion,e.g.Li+in [4]- and [6]-coordination, Na+in [4]- and [6]-coordination. For alkali-metal and alkaline-earth-metal ions, there is a positive correlation between cation coordination number and the grand mean incident bond-valence sum at the central cation, the values varying from 0.84 v.u. for[5]K+to 1.06 v.u. for[8]Li+, and from 1.76 v.u. for[7]Ba2+to 2.10 v.u. for[12]Sr2+. Bond-valence arguments suggest coordination numbers higher than [12] for K+, Rb+, Cs+and Ba2+.