A CRYSTAL-CHEMICAL MODEL FOR PBCA ORTHO-PYROXENE

The study of a crystal-chemical model for Pbca orthopyroxene was under taken 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 compositio nal and structural variables were searched for using the statistic pac kage SPSS. The coefficients and constant terms of linear equations tha t allow the prediction of cell parameters and interatomic distances fo r any orthopyroxene, starting from its crystal-chemical formula, were calculated. From the predicted distances, the geometric refinement pro gram DLS-76 yields the relevant atomic positions, which agree satisfac torily with those measured experimentally. The same results were obtai ned more quickly using coefficients that directly express the correlat ion between the atomic fractions at the structural sites and the atomi c positions. The calculation of atomic positions makes it possible to study the effects induced on the structure by any variation of chemica l composition and cation distribution; in particular it has allowed th e prediction of structural properties for fictive end-members. The coe fficients for the calculation of cation-O mean bond distances of the r egular polyhedra M1 and SiB appear to be nearly correlated to the ioni c radii of the cations at these sites, thus justifying the introductio n of (M1-O) and (SiB-O) bond distances in the linear equations used fo r determining or checking M1 and SiB site populations. The prediction of atomic positions can be used for lattice-energy calculations, in or der to develop a structure-energy model for orthopyroxene. The coeffic ients and constant terms of linear equations for the atomic fractions as a function of cell parameters, atomic positions, and mean atomic nu mbers at M1 and M2 sites were also calculated in order to test the pos sibility of predicting, for any orthopyroxene, its cation distribution in the absence of chemical analysis.