Multiple regression analysis has been used to determine the relationships among the formal charges and Shannon-Prewitt radii of the non-tetrahedarl M1 and M2 cationsin thirteen C2/c (or C2) pyroxenes and their lattice parameters, their mean M-O and Si-O bond lengths, and their O3-O3-O3 chain angles. Crystal-structure data from three groups of silicate pyroxenes (both natural and synthetic) were used in the regression analyses: Li pyroxenes with trivalent Al, Fe, and Sc in the M1, sites, Na pyroxenes with trivalent Al, Cr, Fe, Sc, and In in the M1 sites, and Ca pyroxenes with divalent Ni, Mg, Co, Fe, and Mn in the M1 sites.

Using only first-order linear regression equations in terms of the radii of the M1 and M2 cations (rM1 and rM2) and the charge q on the M2 cation, it was found statistically that more than 98.5 percent of the variation in the a cell dimension can be attributed to the variation in rM1 alone, and 97.5 percent in b can be attributed to variations in both rM1 and rM2. The parameters c sin β and unit-cell volume require athird term, q, to produce the most highly significant regression equations: c sin β has a standard error of estimate (SEE) of 0.011 A and volume 2.2 A3. The mean M1-O distance is linearly related only to rM1 (SEE = 0.007 A) and the mean M2-O distance to both rM1, and rM2, (SEE : 0.013A) or, more significantly, to rM1, rM2, and (SEE: 0.009 A). Both the mean Si-O bridge bond lengths (range: 1.624-1.688 A) and the grand mean Si-O distances (range: 1.618 to 1.644 A) may be estimated to better than 0.004 A, and the tetrahedral chain angle O3-O3-O3 (range: from 163.8° in the O-rotated chain of johannsenite to 189.5° in the S-rotated chain of spodumene) to better than 2.6°, using a regression equation in three terms.

Because it has been shown that the effective radius of the M2 cation (or the <MZ-O> distance) is not independent of the size of the M1 cation, it is possible to rationalize the distinctly non-linear curves of volume vs. (rM1)3 for the isostructural series NaAl-NaCr-NaFe-NaTi-NaSc-NaIn, and LiAl-LiFe-LiSc, as well as the series CaNi-CaMg-CaCo-CaFe-CaMn, which has an opposite curvature from the pyroxenes with monovalent M2 cations

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First page of Stereochemical systematics of ordered C/ silicate pyroxenes
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