Abstract
By using the Lagrange’s intermediate value theorem, it is derived mathematically that the structural distortion of a coordination polyhedron may lead to an increase in bond-valence sum of the central atom or ion. The applicabilities of the bond- valence model are discussed in the following two cases: the modeling of crystal structure, and the indication of distortion degree of a coordination polyhedron. Also it is shown that a distorted polyhedron should be in favor of a longer average bond length or a smaller coordination number.
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