Quantifying distortion from ideal closest-packing in a crystal structure with analysis and application.

A parameter, U(cp), that quantifies the distortion of the anion skeleton in a crystal from ideal closest-packing has been developed. It is a measure of the average isotropic displacement of the observed anions from their ideal equivalents. An ideal closest-packed structure can be fit to an observed structure by varying the radius of the ideal spheres, orientation and translation, such that U(cp) is minimized. Ideal structures were fit to the M1M2TO(4) polymorphs, pyroxenes and kyanite. The distortions of these crystals were analyzed in terms of the two parameters, U(cp) and the ideal radius. Changes in structures due to temperature, pressure and compositional effects were characterized in terms of these parameters.