METAL-SULFUR RADII FOR USE IN GEOCHEMISTRY

The ionic radii proposed by Shannon and Prewitt [1] and Shannon [2] for oxides have contributed greatly to our understanding of silicate geochemistry. However, similar applications to sulfide geochemistry are more complex as sulfides may contain metal-sulfur, sulfur-sulfur and metal-metal bonded interactions [3]. With the crystal ionic radii, valences and coordination numbers for the M cations from Shannon [4] and an assumed radius of 1.70 Å for the sulfide anion, scatter diagrams were prepared for sulfide bond lengths, R(M-S), and normalized bond strengths, s/r, for sulfides where s is the Pauling bond strength and r is the periodic table row number of M. A regression analysis completed for first- and second-row cations resulted in R(M-S) = 1.84(s/r)^-0.20 with 99% of the variation in R(M-S) accounted for in terms of the normalized bond strength. This expression is comparable with that obtained by Bartelmehs et al. [5] for sulfide molecules, R(M-S) = 1.83(s/r)^-0.21. A plot for lanthanoid and actinoid cations for all rows of the periodic table resulted in R(M-S) = 1.84(s/r)^-0.18 . A similar expression, R(M-O) = 1.45(s/r)^-0.20, is obtained for the 470 M-O bond lengths provided by the Shannon [2] table of crystal radii, assuming a radius of 1.24 Å for the oxide anion. The 1.84 and 1.24 coefficients are the M-S and M-O bond lengths, respectively, for bonded interactions with unity s/r bond strengths. When transition metal bond lengths are added to sulfide data set, they cluster and are substantially less depended on s/r. Given that M-M bonded interactions may exist, as seen in the Ni sulfides [3], s does not always provide a faithful measure of the cohesion of the M-S bonded interactions. The occurrence of S-S dimers in sulfides is another factor that may impact bond strength considerations. A mapping of the electron density distributions for the sulfides is currently underway to establish whether a connection exists between bond length and ρ(r_c)/r as found for oxides and whether other unexpected bonded interactions may exist.

Refs: [1] R.D. Shannon and C.T. Prewitt (1969) Acta Cryst. B25, 925; [2] R.D. Shannon (1976) Acta Cryst. A32, 751; [3] G.V. Gibbs et al. (2005) J Phys Chem B 109, 21788; [4] R.D. Shannon (1981), In Structure and Bonding in Crystals, Vol. II, 53-70; [5] Bartelmehs et al. (1989) Amer. Miner., 74,620.