Si Isotope Fractionation in Metamorphic Rocks From Cryogenic Temperature Crystallographic Data and Quantum Phonon Model

Abstract In this study, we demonstrate that it is possible to fit the resilience at the high temperature limit using only the atomic mean square displacement determined from cryogenic temperature single crystal diffraction data. Our method introduces the Debye phonon model, under which the atomic mean square displacement displays quantum behavior at cryogenic temperatures and deviates from a linear temperature dependence. From the resilience of Si extrapolated from cryogenic temperature X‐ray diffraction data, one can calculate the Si isotope fractionation using our recently developed force constants approach. We applied our method to epidote and coesite, which are common minerals in ultra‐high pressure metamorphic rocks, and our predicted Si isotope fractionation lnα Si30/28 are consistent with mass spectroscopy observations of Δ 30 Si in Dabie eclogite and Alps whiteschist. Our results indicate that the geofluid involved in the fluid‐rock interaction in Dabie and Alps orogens doesn't significantly alter the Si‐isotope composition of ultrahigh pressure metamorphism. Our manuscript presents a novel experimental methodology to determine the high‐temperature resilience and equilibrium isotope fractionation factors of silicon in minerals, which can be applied to the metastable upper mantle silicates that are non‐quenchable at high temperatures and room pressure.