The factors controlling equilibrium inter-mineral Ca isotope fractionation: Insights from first-principles calculations

Abstract

Equilibrium isotope fractionation factors are crucial to quantitatively interpreting Ca isotope data of natural samples. Recent studies have revealed significant equilibrium Ca isotope fractionation between minerals, but the controlling factors remain poorly understood. Using density functional theory, this study calculates the reduced partition function ratios (RPFRs) among amphiboles (richterite and tremolite), sorosilicates (akermanite and gehlenite), K-bearing carbonates (butschliite), Na-bearing diopside (jadeite), and other Ca-bearing minerals (fluorapatite, anhydrite, CaTiO3 perovskite, and fluorite) at 0 GPa. The RPFRs of diopside and anorthite over a pressure range from 0 to 5 GPa are calculated to investigate the pressure effect. The effect of force constant, bond length, coordination number, anion type, solid solution composition, and pressure on RPFRs are discussed by compiling the literature data. The RPFRs show good correlations with the force constant and bond length but have no clear correlation with the coordination number. This suggests that the bond length is more reliable than the coordination number for roughly predicting the signs and magnitudes of inter-mineral isotope fractionation. Na-bearing clinopyroxene (e.g., jadeite) has similar RPFR with Na-free clinopyroxene, suggesting that the jadeite effect should be insignificant in natural samples. The RPFR of anorthite is lower than that of diopside at low pressure, and the two minerals both show a positive correlation between RPFR and pressure. Notably, the heavy Ca isotope enrichment between these two minerals can be reversed at high pressure (>3 GPa at 1000 K) because anorthite’s RPFR changes more sharply with increasing pressure than that of diopside. However, such a reverse may not occur in Earth's modern crust due to the stability of anorthite at lower pressures. Combining the theoretical predictions of amphibole and plagioclase and natural sample observation on granitoids, we infer that the RPFR of granitic magma may be lower than that of basaltic magma.