A priori bond‐valence and bond‐length calculations in rock‐forming minerals

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. A priori bond valences and bond lengths are calculated for a series of rock‐forming minerals. Comparison of a priori and observed bond lengths allows structural strain to be assessed for those minerals.