Effect of Ca content on equilibrium Ca isotope fractionation between orthopyroxene and clinopyroxene

Abstract

Concentration effect on equilibrium inter-mineral isotope fractionation is ubiquitous in solid solution systems, but it is not clear in which concentration range such effect is prominent. Using first-principles calculations, we examine the effect of Ca and Fe contents in orthopyroxene (opx) on its average CaO bond length and the equilibrium Ca isotope fractionation factor (103lnα) between opx and clinopyroxene (cpx). Our results reveal that the average CaO bond length in opx is much smaller than that in cpx and it does not change with variable Ca content x (x and y are mole ratios in CaxFeyMg1−x−ySiO3 thereafter here) when x≤1/48. Incorporation of Fe (y≥1/32) into opx with a fixed Ca content can only slightly increase the average CaO bond length. 103lnαopx-cpx of 44Ca/40Ca is linearly correlated with the average CaO bond length in opx, suggesting that 103lnαopx-cpx of 44Ca/40Ca is controlled by opx CaO bond strength. Our calculations indicate that the Ca concentration effect on 103lnαopx-cpx is significant when x in opx ranges from 2/16 to 1/48, while Fe in natural opx only causes a slight decrease in 103lnαopx-cpx.Our results provide insights into Ca isotope fractionation in high-temperature geochemical processes. Given that Ca content x in opx from natural peridotites is usually lower than 1/32 and Fe content y is generally ∼10mol%, Ca and Fe concentration effects on 103lnαopx-cpx in natural samples are negligible. Rather, 103lnαopx-cpx is mainly controlled by temperature. 103lnαopx-cpx of 44Ca/40Ca decreases from 0.50‰ to 0.26‰ when temperature increases from 1000K to 1400K if the Fe effect is taken into account. Therefore, if Ca isotope fractionation between opx and cpx (Δ44/40Caopx-cpx) in natural peridotites is greater than 0.50‰ or lower than 0.26‰, it may indicate disequilibrium of Ca isotopes. Finally, the large 103lnαopx-cpx relative to our current analytical precision suggests that Δ44/40Caopx-cpx can be used as an independent thermometer with a precision comparable to elemental thermometers. Because most naturally occurring minerals are solid solutions with variable chemical compositions, this study presents a guideline to explore the concentration effect on equilibrium isotope fractionation among minerals.