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 s tructure by varying the radius of the ideal spheres, orientation and transl ation, such that U-cp is minimized. Ideal structures were fit to the M1M2TO (4) polymorphs, pyroxenes and kyanite. The distortions of these crystals we re analyzed in terms of the two parameters, U-cp and the ideal radius. Chan ges in structures due to temperature, pressure and compositional effects we re characterized in terms of these parameters.