Theoretical estimates of equilibrium chromium-isotope fractionations

Equilibrium Cr-isotope (⁵³Cr/⁵²Cr) 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(b_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 [Cr⁶⁺O₄]^2– anion will tend to concentrate ⁵³Cr when in equilibrium with compounds containing Cr³⁺ or Cr⁰. Substances containing chromium bonded to strongly-bonding ligands like CO will concentrate ⁵³Cr relative to compounds with weaker bonds, like [CrCl₆]^3–. Substances with short Cr-ligand bonds (Cr-C in Cr(CO)₆, Cr-O in [Cr(H₂O)₆]³⁺ or [CrO₄]^2–) will also tend to concentrate ⁵³Cr relative to substances with longer Cr-ligand bonds ([Cr(NH₃)₆]³⁺, [CrCl₆]^3–, and Cr-metal). These systematics are similar to those found in an earlier study on Fe-isotope fractionation (Schauble et al., 2001). The calculated equilibrium fractionation between Cr⁶⁺ in [CrO₄]^2– and Cr³⁺ in either [Cr(H₂O)₆]³⁺ or Cr₂O₃ agrees qualitatively with the fractionation observed during experimental (probably kinetic) reduction of [CrO₄]^2– in solution (Ellis et al., 2002), 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.