Silicon isotope fractionation constrained by single crystal X-ray diffraction

Isotopic fractionation of Si is believed to reflect the evolution of the Earth. An essential parameter of interest to isotopic fractionation, the reduced partition function ratio (-factor) of Si, is yet to be constrained experimentally. We present a new force-constant approach that combines experimental and theoretical data to constrain the reduced partition function ratio (-factor) of tetrahedrally coordinated silicon (IVSi) in the crust and upper mantle minerals. We determined the resilience of IVSi from the Debye-Waller factor, which is derived from the temperature dependence of single crystal X-ray diffraction data, and calculate the stiffness of IVSi from the density-functional theory results. The relationship between the resilience the stiffness is calibrated, and we have used an experimentally measurable parameter, the effective coordination number of the SiO4 tetrahedron, to correct the stiffness. The corrected stiffness is used to calculate the equilibrium isotope fractionation -factor of each mineral, and the -factors are calculated by analyzing the ratio of -factors of different minerals. We calculate the isotope fractionation between minerals that contain SiO4 tetrahedra, and our results are consistent with DFT calculations and mass spectrometry results. Our results suggest that the Si isotopic equilibrium temperature between cristobalite and pyroxene in lunar basalt was underestimated by ~250 C, and the pyroxene sample in IL-14 marble is in equilibrium with -quartz. Our results have demonstrated that the single crystal X-ray diffraction technique is a great tool to explore the atomic dynamics within minerals.