Factors of 18O/16O fractionation in garnets: Evidence from calculations of isotope frequency shifts

Abstract

Based on the density functional theory (DFT), frequency shifts of garnet end-members upon isotope substitutions (¹⁸O/¹⁶O, as well as “non-traditional” stable isotopes) were calculated. According to the calculations, the temperature dependencies of fractionation factors (β-factors) suggested for garnets: 1000lnβ_prp = 9.68511x–0.19204x² + 0.00567x³; 1000lnβ_grs = 9.14697x–0.15682x² + 0.00412x³; 1000lnβ_adr = 8.72470x–0.15092x² + 0.00402x³; 1000lnβ_uvr = 8.71526x–0.14749x² + 0.00385x³; 1000lnβ_sps = 9.33600x–0.17598x² + 0.00499x³; 1000lnβ_alm = 9.45295x–0.18465x² + 0.00539x³, x = 10⁶/T (K)². The values obtained combined with with the known values of β-factors may be applied in geothermometry of garnet-bearing rocks.