配位多面体Coordination geometry

在离子晶体中，阳离子与阴离子半径比 r⁺/r⁻ 决定配位数：0.225–0.414 倾向四面体（4 配位，如 ZnS），0.414–0.732 倾向八面体（6 配位，如 NaCl），0.732–1 倾向立方体（8 配位，如 CsCl）。这一规则假定离子为硬球且阴离子相互接触，只是近似指导，例外很多。

In ionic crystals the cation-to-anion radius ratio r⁺/r⁻ guides coordination number: 0.225–0.414 favours tetrahedral (4, as in ZnS), 0.414–0.732 octahedral (6, as in NaCl) and 0.732–1 cubic (8, as in CsCl). The rule assumes hard spheres with touching anions and is only approximate, with many exceptions.

1929 年鲍林提出描述复杂离子晶体结构的五条规则：阴离子围绕阳离子形成配位多面体，其配位数由半径比决定；电价规则——一个阴离子从所有相邻阳离子获得的静电键强度之和等于其电荷；多面体共顶、共棱、共面时稳定性依次降低，高价低配位阳离子尤甚；不同阳离子的多面体倾向不共用顶点以外的元素；结构类型数目趋于最少。这些规则广泛用于硅酸盐矿物结构分析。

In 1929 Pauling set out five rules for complex ionic structures: anions surround each cation in a coordination polyhedron whose coordination number follows the radius ratio; the electrostatic valence rule says the bond strengths reaching an anion from its neighbouring cations sum to its charge; sharing edges and especially faces between polyhedra lowers stability, especially for highly charged, low-coordinate cations; different cations' polyhedra tend not to share elements; and the number of essentially different kinds of site tends to be small. The rules are widely used for silicate minerals.

硅酸盐的基本单元是 SiO₄ 四面体，按共用顶点数可形成岛状、链状、层状和架状结构；钙钛矿中 B 位离子位于 BO₆ 八面体中心，八面体共顶连接成三维骨架。过渡金属配合物中，d 电子数和配体场强度决定是八面体、四面体还是平面正方形构型，例如 d⁸ 的 Pt²⁺、Pd²⁺ 常为平面正方形。

The basic silicate unit is the SiO₄ tetrahedron, which shares corners to build isolated, chain, sheet and framework structures; in perovskites the B ion sits at the centre of BO₆ octahedra linked by corners into a three-dimensional framework. In transition-metal complexes, d-electron count and ligand-field strength decide between octahedral, tetrahedral and square-planar geometry; d⁸ Pt²⁺ and Pd²⁺, for example, are usually square planar.