Spectroscopic determination of equilibrium Fe isotopes fractionation factor for spinels with varying Fe oxidation states

Spinels form a solid solution series with the formula (Mg,Fe)(Al,Cr,Fe)₂O₄. The Fe³⁺/Fe²⁺ ratios in the spinels are often used to constrain mantle oxygen fugacity. It was found that the ⁵⁷Fe/⁵⁴Fe ratios correlate negatively with Fe³⁺/Fe²⁺ ratios in the spinels [1]. The results were unexpected because theoretical and experimental studies all show that Fe³⁺ in equilibrium with Fe²⁺ should have heavier Fe isotopic compositions. Without equilibrium Fe isotopes fractionation factors for spinels, the results of [1] are difficult to interpret. Nuclear Resonant Inelastic X-ray Scattering (NRIXS) provides the means to probe the vibrational properties of ⁵⁷Fe-bearing phases. At high temperature, the equilibrium Fe isotopes fractionation factors are directly proportional to force constants measured for the Fe sub-lattices [2]. The advantage of this technique is that any ⁵⁷Fe-bearing material can be analyzed, without meeting the requirement of isotopic equilibrium with a coexisting phase. Equilibrium Fe isotopes partitioning data between phases can be obtained as long as those phases can be synthesized. Spinels were synthesized using the flux growth method [3] in either air or gas mixing furnace. NRIXS data obtained at APS show that Fe³⁺ spinels consistently display higher force constants than their Fe²⁺ counterparts. This trend is similar to that observed for silicate glasses [4], which confirms that redox is an important controlling factor in changing force constants whether the material is amorphous or crystalline, and that force constants always increase with increasing Fe³⁺/Fe²⁺ ratios. The negative trend of ⁵⁷Fe/⁵⁴Fe vs. Fe³⁺/Fe²⁺ found in spinels reported by [1] proves to be a strong departure from equilibrium Fe partitioning in a closed system. Our data allow for the first time to put those results in a quantitative petrogenetic context.