Gagné Olivier Charles, Hawthorne Frank Christopher
Geological Sciences, University of Manitoba, 125 Dysart Road, Winnipeg, Manitoba R3T 2N2, Canada.
Acta Crystallogr B Struct Sci Cryst Eng Mater. 2016 Aug 1;72(Pt 4):602-25. doi: 10.1107/S2052520616008507.
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])Be(2+), ([4])Mg(2+), ([6])Ca(2+), ([6])Sr(2+) and ([6])Ba(2+), 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 ratio Ueq(Na)/Ueq(bonded anions) is partially correlated with 〈([6])Na(+)-O(2-)〉 (R(2) = 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])Ba(2+) to 2.10 v.u. for ([12])Sr(2+). Bond-valence arguments suggest coordination numbers higher than [12] for K(+), Rb(+), Cs(+) and Ba(2+).
已对55种与氧键合的碱金属离子构型和29种与氧键合的碱土金属离子构型、4859个配位多面体和38594个键长（碱金属）以及3038个配位多面体和24487个键长（碱土金属）的键长分布进行了研究。键长通常呈现正偏态高斯分布，这源于玻恩排斥和库仑吸引随原子间距离的变化。这些分布的偏度和峰度通常随着中心阳离子配位数的增加而减小，这是由于随着配位数增加玻恩排斥减小的结果。我们确定了以下最小配位数：（[3]）Li⁺、（[3]）Na⁺、（[4]）K⁺、（[4]）Rb⁺、（[6]）Cs⁺、（[3]）Be²⁺、（[4]）Mg²⁺、（[6]）Ca²⁺、（[6]）Sr²⁺和（[6]）Ba²⁺，但需注意，一些报道的例子是广泛的动态和/或位置短程无序的结果，并非有序排列。一些键长分布明显是多峰的。这通常是由于对特定结构类型进行大量结构精修导致的，其中特定阳离子总是存在，从而导致特定键长范围的过度代表。平均键长分布中的异常值通常与组成阳离子和/或阴离子的原子位移异常值相关。对于（[6]）Na⁺样品，Ueq(Na)/Ueq(键合阴离子)的比值与〈（[6]）Na⁺-O²⁻〉部分相关（R² = 0.57），这表明对于固定配位数，平均键长与组成离子的振动/位移特性相关。平均键长通常也与相对于平均值的键长畸变呈现弱相关性，尽管一些配位数在零畸变时平均键长变化最大，例如[4] - 和[6] - 配位的Li⁺，[4] - 和[6] - 配位的Na⁺。对于碱金属和碱土金属离子，阳离子配位数与中心阳离子处的总平均入射键价和之间存在正相关，其值从（[5]）K⁺的0.84 v.u.到（[8]）Li⁺的1.06 v.u.，以及从（[7]）Ba²⁺的1.76 v.u.到（[12]）Sr²⁺的2.10 v.u.。键价论据表明K⁺、Rb⁺、Cs⁺和Ba²⁺的配位数高于[12]。
