LAUSR

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 Ca O bond length and the equilibrium Ca isotope fractionation factor (103lnα) between opx and clinopyroxene (cpx). Our results reveal that the average Ca O 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 Ca O bond length. 103lnαopx-cpx of 44Ca/40Ca is linearly correlated with the average Ca O bond length in opx, suggesting that 103lnαopx-cpx of 44Ca/40Ca is controlled by opx Ca O 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 ∼10 mol%, 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 1000 K to 1400 K 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.