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首页> 外文期刊>Acta Crystallographica, Section B. Structural science, crystal engineering and materials >Bond-length distributions for ions bonded to oxygen: alkali and alkaline-earth metals
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Bond-length distributions for ions bonded to oxygen: alkali and alkaline-earth metals

机译：与氧键合的离子的键长分布：碱金属和碱土金属

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摘要

Bond-length distributions have been examined for 55 configurations of alkalimetal 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 U_(eq(Na))/U_(eq(bonded anions)) is partially correlated with<~([6])Na~+—O~(2-)i (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+).
机译：已检查了键合长度分布，分析了与氧键合的55种碱金属离子和29种碱土金属离子，4859配位多面体和38 594键距（碱金属），以及3038配位多面体和24487键距离（碱土金属）。键长通常显示出正偏高斯分布，其起源于天生斥力和库仑吸引力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降低，这是由于随着配位数的增加而降低了玻恩排斥力的结果。我们确认以下最小配位数：〜（[3]）Li〜+，〜（[3]）Na〜+，〜（[4]）K〜+，〜（[4]）Rb〜+，〜（ [6]）Cs〜+，〜（[3]）Be〜（2 +），〜（[4]）Mg〜（2 +），〜（[6]）Ca〜（2 +），〜（[ 6]）Sr〜（2+）和〜（[6]）Ba〜（2+），但请注意，一些已报道的实例是广泛的动态和/或位置短距离无序的结果，并非有序排列。键长的某些分布显然是多峰的。这通常是由于总是存在特定阳离子的特定结构类型的大量结构改进的出现，导致键长的特定范围的过度表示。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的异常值相关。对于〜（[6]）Na〜+的样品，比率U_（eq（Na））/ U_（eq（键合阴离子））与<〜（[6]）Na〜+ -O〜（ 2-）i（R〜2 = 0.57），表明在固定配位数下，平均键长与构成离子的振动/位移特征相关。一般而言，平均键长还显示与键长失真相对于平均值的弱相关性，尽管某些配位数显示零失真时平均键长变化最大，例如Li〜+在[4]-和[6]配位，Na〜+在[4]-和[6]配位。对于碱金属和碱土金属离子，阳离子配位数与中心阳离子的平均入射键价和之和呈正相关，其值范围为0.84v.u。 〜（[5]）K〜+至1.06v.u。 〜（[8]）Li〜+，且从1.76 v.u起。 〜（[7]）Ba〜（2+）至2.10 v.u.对于〜（[12]）Sr〜（2+）。键价论证表明，对于K〜+，Rb〜+，Cs〜+和Ba〜（2+），配位数高于[12]。

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