A Crystal-chemical Model For Pbca Ortho-pyroxene

The study of a crystal-chemical model for Pbca orthopyroxene was undertaken using the results of X-ray single-crystal structure refinements and chemical analyses of about 200 samples with different compositions and degrees of order. Multiple linear correlations between compositional and structural variables were searched for using the statistic package SPSS. The coefficients and constant terms of linear equations that allow the prediction of cell parameters and interatomic distances for any orthopyroxene, starting from its crystal-chemical formula, were calculated. From the predicted distances, the geometric refinement program DLS-76 yields the relevant atomic positions, which agree satisfactorily with those measured experimentally. The same results were obtained more quickly using coefficients that directly express the correlation between the atomic fractions at the structural sites and the atomic positions. The calculation of atomic positions makes it possible to study the effects induced on the structure by any variation of chemical composition and cation distribution; in particular it has allowed the prediction of structural properties for fictive end-members. The coefficients for the calculation of cation-O mean bond distances of the regular polyhedra M1 and SiB appear to be nearly correlated to the ionic radii of the cations at these sites, thus justifying the introduction of (M1-O) and (SiB-O) bond distances in the linear equations used for determining or checking M1 and SiB site populations. The prediction of atomic positions can be used for lattice-energy calculations, in order to develop a structure-energy model for orthopyroxene. The coefficients and constant terms of linear equations for the atomic fractions as a function of cell parameters, atomic positions, and mean atomic numbers at M1 and M2 sites were also calculated in order to test the possibility of predicting, for any orthopyroxene, its cation distribution in the absence of chemical analysis.