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 1000K) 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.

平衡同位素分馏因子对于定量解释天然样品的 Ca 同位素数据至关重要。最近的研究揭示了矿物之间显着的平衡 Ca 同位素分馏，但控制因素仍然知之甚少。利用密度泛函理论，本研究计算了闪石（锂辉石和透闪石）、钠硅酸盐（akermanite 和gehlenite）、含K 碳酸盐（butschliite）、含Na透辉石（硬玉）和其他Ca - 含矿物（氟磷灰石、硬石膏、CaTiO ₃钙钛矿和萤石）在 0 GPa。计算透辉石和钙长石在 0 到 5 GPa 压力范围内的 RPFR，以研究压力效应。通过整理文献数据，讨论了力常数、键长、配位数、阴离子类型、固溶体组成和压力对RPFRs的影响。RPFRs 与力常数和键长具有良好的相关性，但与配位数没有明显的相关性。这表明在粗略预测矿物间同位素分馏的符号和大小方面，键长比配位数更可靠。含钠单斜辉石（如翡翠）与不含钠的单斜辉石具有相似的 RPFR，这表明天然样品中的翡翠效应应该是微不足道的。钙长石在低压下的RPFR低于透辉石，两种矿物的RPFR均与压力呈正相关。值得注意的是，这两种矿物之间的重钙同位素富集可以在高压下逆转（在 1000K 时>3 GPa），因为钙长石的 RPFR 随着压力的增加比透辉石的变化更剧烈。然而，由于钙长石在较低压力下的稳定性，在地球的现代地壳中可能不会发生这种逆转。结合闪石和斜长石的理论预测以及对花岗岩的自然样品观测，我们推断花岗质岩浆的RPFR可能低于玄武质岩浆。这两种矿物之间的重钙同位素富集可以在高压下逆转（在 1000K 时>3 GPa），因为钙长石的 RPFR 随着压力的增加而变化比透辉石更剧烈。然而，由于钙长石在较低压力下的稳定性，在地球的现代地壳中可能不会发生这种逆转。结合闪石和斜长石的理论预测以及对花岗岩的自然样品观测，我们推断花岗质岩浆的RPFR可能低于玄武质岩浆。这两种矿物之间的重钙同位素富集可以在高压下逆转（在 1000K 时>3 GPa），因为钙长石的 RPFR 随着压力的增加而变化比透辉石更剧烈。然而，由于钙长石在较低压力下的稳定性，在地球的现代地壳中可能不会发生这种逆转。结合闪石和斜长石的理论预测以及对花岗岩的自然样品观测，我们推断花岗质岩浆的RPFR可能低于玄武质岩浆。