THEORETICAL ESTIMATES OF EQUILIBRIUM CHROMIUM-ISOTOPE FRACTIONATIONS

Abstract

Equilibrium Cr-isotope (^(53)Cr/^(52)Cr) fractionations are calculated using published vibrational spectra and both empirical and ab initio force-field models. Reduced partition function ratios for chromium isotope exchange, in terms of 1000×ln(β_(53–52)), are calculated for a number of simple complexes, crystals, and the Cr(CO)_6 molecule. Large (>1‰) fractionations are predicted between coexisting species with different oxidation states or bond partners. The highly oxidized [Cr^(6+)O_4]^(2−) anion will tend to have higher ^(53)Cr/^(52)Cr than coexisting compounds containing Cr^(3+) or Cr^0 at equilibrium. Substances containing chromium bonded to strongly bonding ligands like CO will have higher ^(53)Cr/^(52)Cr than compounds with weaker bonds, like [CrCl_6]^(3−). Substances with short Cr-ligand bonds (Cr–C in Cr(CO)_6, Cr–O in [Cr(H_2O)_6]^(3+) or [CrO_4]^(2−)) will also tend have higher ^(53)Cr/^(52)Cr than substances with longer Cr-ligand bonds ([Cr(NH_3)_6]^(3+), [CrCl_6]^(3−), and Cr-metal). These systematics are similar to those found in an earlier study on Fe-isotope fractionation (Geochim. Cosmochim. Acta 65 (2001) 2487). The calculated equilibrium fractionation between Cr^(6+) in [CrO_4]^(2−) and Cr^(3+) in either [Cr(H_2O)_6]^(3+) or Cr_2O_3 agrees qualitatively with the fractionation observed during experimental (probably kinetic) reduction of [CrO_4]^(2−) in solution (Science 295 (2002) 2060), although the calculated fractionation (∼6–7‰ at 298 K) does appear to be significantly larger than the experimental fractionation (3.3–3.5‰). Our model results suggest that natural inorganic Cr-isotope fractionation at the earth's surface may be driven largely by reduction and oxidation processes.