First-principles investigation of the concentration effect on equilibrium fractionation of Ca isotopes in forsterite

Abstract

Previous theoretical studies have found that the concentration variations within a certain range have a prominent effect on inter-mineral equilibrium isotope fractionation (103lnα). Based on the density functional theory, we investigated how the average Ca–O bond length and the reduced partition function ratios (103lnβ) and 103lnα of 44Ca/40Ca in forsterite (Fo) are affected by its Ca concentration. Our results show that Ca–O bond length in forsterite ranges from 2.327 to 2.267 A with the Ca/(Ca + Mg) varying between a narrow range limited by an upper limit of 1/8 and a lower limit of 1/64. However, outside this narrow range, i.e., Ca/(Ca + Mg) is lower than 1/64 or higher than 1/8, Ca–O bond length becomes insensitive to Ca concentration and maintains to be a constant. Because the 103lnβ is negatively correlated with Ca–O bond length, the 103lnβ significantly increases with decreasing Ca/(Ca + Mg) when 1/64 orthopyroxene > clinopyroxene > calcite ≈ diopside > dolomite > aragonite. Olivine and pyroxenes are enriched in heavier Ca isotope compared to carbonates. The 103lnα between forsterite with a Ca/(Ca + Mg) of 1/64 and clinopyroxene (Ca/Mg = 1/1, i.e., diopside) is up to ~ 0.64‰ at 1200 K. The large 103lnαFo-diopside relative to the current analytical precision for Ca isotope measurements suggests that the dependence of 103lnαFo-diopside on temperature can be used as a thermometer, similar to the one based on the 103lnα of 44Ca/40Ca between orthopyroxene and diopside. These two Ca isotope thermometers both have a precision approximate to that of elemental thermometers and provide independent constraints on temperature.