Composition, order-disorder and lattice parameters of olivines; relationships in silicate, germanate, beryllate, phosphate and borate olivines

A general formula for olivine-type compounds is (M1)(M2)TO₄, where Ml and M2 represent octahedrally coordinated cations and T is the cation tetrahedrally coordinated by oxygen. Using 52 natural and synthetic olivines with known crystal structures, with Ml and M2 variously Li, Na, Mg, Al, Ca, Sc, Cr, Mn, Fe, Co, Ni, Zn, Ga, Y, Cd, Sm, Gd, and Lu, and with T = Be, B, Si, P, Ge, or (Si_xGe_1-x), we have quantified and analyzed the relationships among lattice parameters, effective ionic radii (r_M1,r_M2,r_T) and charge on the cations (q_M1,q_M2; q_T = 8.0 - q_M1- q_M2) using multiple linear regression techniques. Of the regression equations listed below, only that for the a cell dimension was significantly improved (to R² = 0.99) by the inclusion of q terms (see text). Similar and more precise sets of equations were calculated separately for silicate, phosphate and beryllate olivines. The utility of these equations for predicting whether a particular structure has an ordered, disordered or antiordered (large cation in Ml) distribution of octahedral cations has been successfully tested, especially in cases where │r_M1 - r_M2│ > 0.1 Å, and a technique is suggested for predicting both the bulk composition and the cation distribution using only the a and b cell dimensions.