Pressure and concentration effects on intermineral calcium isotope fractionation involving garnet

Abstract

To better understand the behaviors of calcium (Ca) isotopes during igneous and metamorphic processes that differentiate the Earth and other rocky planets, we investigated the effects of pressure and Ca/Fe concentration on the average CaO bond length and the reduced partition function ratio of 44Ca/40Ca (103ln44/40Caβ) in garnet using first-principles calculations. Our calculations show that (1) the average CaO bond length increases and 103ln44/40Caβ decreasing (approximately 0.41‰ at 1000 K from a Ca/(Fe + Ca + Mg) of 1/24 to 12/12) with increasing Ca concentrations. In contrast to orthopyroxene and forsterite, whose CaO bond lengths and 103ln44/40Caβ are sensitive to Ca concentrations only in narrow range, the garnet CaO bond length and 103ln44/40Caβ vary with Ca concentrations in wide ranges. (2) The average CaO bond length increases and 103ln44/40Caβ decreases with increasing Fe concentrations (by 0.12‰ at 1000 K, FeO content of 12.4 wt%). (3) The average CaO bond length decreases by ~0.014 Å, and 103ln44/40Caβ increases by 0.1‰–0.2‰ at 1000 K when the pressure increases from 0 to 3 GPa. (4) However, the pressure effect on 103ln44/40Caαgarnet–clinopyroxene is insignificant.Using our new results of the effects of pressure and Ca/Fe concentration on 103ln44/40Caαgarnet–clinopyroxene, we evaluated the observed difference in Ca isotope compositions between garnet and clinopyroxene in natural samples. Most have reached equilibrium, whereas some samples exceed our prediction, which might reflect the majorite effect or kinetic fractionation.