Within the framework of the bond‐valence model, one may write equations describing the valence‐sum rule and the loop rule in terms of the constituent bond valences. These are collectively called the network equations, and can be solved for a specific bond topology to calculate its a priori bond valences. A priori bond valences are the ideal values of bond strengths intrinsic to a given bond topology that depend strictly on the formal valences of the ion at each site in the structure, and the bond‐topological characteristics of the structure (i.e. the ion connectivity). The a priori bond valences are calculated for selected rock‐forming minerals, beginning with a simple example (magnesiochromite, = 1.379 bits per atom) and progressing through a series of gradually more complex minerals (grossular, diopside, forsterite, fluoro‐phlogopite, phlogopite, fluoro‐tremolite, tremolite, albite) to finish with epidote (= 4.187 bits per atom). The effects of weak bonds (hydrogen bonds, long Na⁺—O²⁻ bonds) on the calculation of a priori bond valences and bond lengths are examined. For the selected set of minerals, a priori and observed bond valences and bond lengths scatter closely about the 1:1 line with an average deviation of 0.04 v.u. and 0.048 Å and maximum deviations of 0.16 v.u. and 0.620 Å. The scatter of the corresponding a priori and observed bond lengths is strongly a function of the Lewis acidity of the constituent cation. For cations of high Lewis acidity, the range of differences between the a priori and observed bond lengths is small, whereas for cations of low Lewis acidity, the range of differences between the a priori and observed bond lengths is large. These calculations allow assessment of the strain in a crystal structure and provide a way to examine the effect of bond topology on variation in observed bond lengths for the same ion‐pair in different bond topologies.

中文翻译：

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岩石成矿矿物的先验键价和键长计算

在键价模型的框架内，可以编写方程式，以组成键价描述价和规则和循环规则。这些统称为网络方程，可以针对特定的键拓扑进行求解，以计算其先验键价。先验键价是给定键拓扑固有的键强度的理想值，严格取决于结构中每个位置处离子的形式价和结构的键拓扑特征（即离子连接性）。该先验从一个简单的例子（镁铬铁矿= 1.379位/原子）开始，到一系列逐渐更复杂的矿物（钙镁矿，透辉石，镁橄榄石，氟金云母，金云母，氟土透闪石，透闪石，钠长石）并附有附子（每原子4.187位）。研究了弱键（氢键，长的Na ⁺ -O ^2-键）对先验键价和键长计算的影响。对于选定的一组矿物，先验和观察到的键价和键长在1：1线附近散布，平均偏差为0.04 vu和0.048Å，最大偏差为0.16 vu和0.620Å。相应的先验和观察到的键长的散布强烈地取决于组成阳离子的路易斯酸度。对于高路易斯酸度的阳离子，先验和观察到的键长之间的差异范围很小，而对于低路易斯酸度的阳离子，先验之间的差异范围并且观察到的键长很大。这些计算可以评估晶体结构中的应变，并提供一种方法来检查键拓扑对不同离子拓扑中相同离子对观察到的键长变化的影响。