Abstract
Refined structures of eight natural garnets [Cr-pyrope, almandine, spessartine, Mn-grossular, grossular, uvarovite, goldmanite, and andradite] are compared with that of synthetic pyrope to determine the effects of the substituent cations on polyhedral interactions, bond lengths, and angles. The Si-0 bonds in these garnets constitute two populations which can be related to ‹r{X}›, the mean radius of the X dodecahedral cation. If ‹r{X}› is less than 1.0 Å, then Si-0 = 1.635 ± 0.005 Å, but if ‹r)X|‹ exceeds 1.0 Å, then Si-0 = 1.650 ± 0.005 Å. However, the X-0 and Y-0 bond lengths and the O-X-O, O-F-O, and O-Si-O angles are linearly dependent on ‹r{X}› and on ‹r[Y]› (where ‹r[Y]›= the mean radius of the F octahedral cation). A multiple linear regression analysis indicates the positional parameters of these garnets to be related to ‹r{X}› and ‹r[F]› using Shannon and Prewitt’s effective radii as follows:
x = 0.006 + 0.022‹r{x}› + 0.014‹r[F]›
y = 0.051 - 0.023‹r{X}› + 0.037‹r[F]›
z = 0.643 - 0.009‹r{x}› + 0.034‹r[F]›.
The positional parameters of Fe-pyrope calculated with these equations [x = 0.0336; y = 0.0491; z = 0.6530] are in statistical agreement with the observed [x = 0.0339(5); y = 0.0491(6); z = 0.6535(6)[ (Euler and Bruce, 1965). Furthermore, using a cell edge calculated from an equation obtained by regression analysis of 56 well characterized silicate garnets [a = 9.04+1.61‹r{X}›+1.89‹r[F]›], the predicted positional parameters give bond lengths and angles that are statistically identical with those observed.
These equations were used to predict the structural details of over 200 hypothetical cubic silicate garnet compounds by assigning ‹r{X}› values between 0.80 and 1.50 A and ‹r[F]› values between 0.50 and 1.15 A (at 0.05 A intervals). Using criteria based on reasonable O-O, Si-O, X-O, and F-0 distances, a diagram was prepared in which the structural “stability” field of silicate garnets is delineated as a function of ‹r{X}› and ‹r[Y]›.
