The distortion theorem of the bond-valence theory predicts that the mean bond length 〈D〉 increases with increasing deviation of the individual bond lengths from their mean value according to the equation 〈D〉 = (D' + ?D), where D0 is the length found in a polyhedron having equivalent bonds and ?D is the bond distortion. For a given atom, D0 is expected to be similar from one structure to another, whereas 〈D〉 should vary as a function of ?D. However, in several crystal structures 〈D〉 significantly varies without any relevant contribution from ?D. In accordance with bond-valence theory, 〈D〉 variation is described here by a new equation: 〈D〉 = (D_(RU) + ?D_(top) + ?D_(iso) + ?D_(aniso) + ?D_(elec)), where D_(RU) is a constant related to the type of cation and coordination environment, ?D_(top) is the topological distortion related to the way the atoms are linked, ?D_(iso) is an isotropic effect of compression (or stretching) in the bonds produced by steric strain and represents the same increase (or decrease) in all the bond lengths in the coordination sphere, ?D_(aniso) is the distortion produced by compression and stretching of bonds in the same coordination sphere, ?D_(elec) is the distortion produced by electronic effects. If present, ?Delec can be combined with ?D_(aniso) because they lead to the same kind of distortions in line with the distortion theorem. Each D-index, in the new equation, corresponds to an algebraic expression containing experimental and theoretical bond valences. On the basis of this study, the ?D index defined in bond valence theory is a result of both the bond topology and the distortion theorem (?D = ?D_(top) + ?D_(aniso) + ?D_(elec)), and D0 is a result of the compression, or stretching, of bonds (D' = D_(RU) + ?D_(iso)). The deficiencies present in the bond-valence theory in explaining mean bond-length variations can therefore be overcome, and the observed variations of 〈D〉 in crystal structures can be described by a self-consistent model.
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