The crystal chemistry of the silicate garnets

Refined structures of eight natural garnets [Cr-pyrope, almandine, spessartine, Mngrossular, 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-O bonds in these garnets constitute two populations whichcan be related to (r!X!), the mean radius of the X dodecahedra] cation. If (r{X}) is lessthan 1.0 A, then Si-O= 1.635 :1:0.005A, but if (r!X\) exceeds 1.0 A, then Si-O = 1.650 to.005 A. However, the X-O and Y-O bond lengths and the O-X-O, O-Y-O, and O-Si-O anglesare linearly dependent on (r{X!) and on (r[Y]) (where (r[Y])= the mean radius of the Y octahedral cation). A multiple linear regression analysis indicates the positional parameters of these garnets to be related to (1'{X} ) and (1'[ V]) using Shannon and Prewitt's effectiveradii as follows: x = 0.006 + 0.022(r{X} > + 0.014(r[Y]) y = 0.051 - 0.023(r{X}) + 0.037(r[Y]) z = 0.643 - 0.009(r{X}) + 0.034(r[Y]). 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{XD+1.89(r[YJ)], the predicted positional parameters give bond lengthsand 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{XI) values between 0.80 and 1.50 A and (r[Y]) values between 0.50 and 1.15 A (at 0.05 A intervals). Using criteria based on reasonable 0-0, Si-O, X-O, and Y-O 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]).