A NEW EMPIRICAL-FORMULA FOR THE CALCULATION OF AN ELEMENTARY CELL PARAMETER OF SYNTHETIC OXIDES-GARNETS

An empirical formula is proposed which allows one to calculate the lat tice constant of cubic synthetic oxides-garnets taking into account th e chemical composition, the distribution of cation in the crystallogra phically nonequivalent positions, and well-known Shannon-Prewitt catio n radii. The formula is developed assuming cation size effects on the elementary cell parameter for the cation radii r(VIII) from 0.097 to 0 .114 for the cations on dodecahedral, 0.054<r(VI)<0.079 for the cation s on octahedral, and 0.028 <r(IV)<0.049 for the cations on tetrahedral lattice sites. Selected crystal lattice parameters for 350 compositio ns, excluding garnets-silicates, have been used for derivation of the formula by means of the least-squares method for multimeasured functio ns (n-measured space with coordinates r(VIII), r(VI), r(IV), a). The a verage deviation of the calculated values a(cal) from the experimental values is less than 0.001 nm. (C) 1997 Academic Press.