Abstract Diffusional isotope fractionation occurs in geochemical processes (such as magma mixing, bubble growth, and crystal growth), even at magmatic temperatures. Isotopic mass dependence of diffusion is commonly expressed as D i D j = m j m i β , where D i and D j are diffusion coefficients of two isotopes whose masses are m i and m j . How the dimensionless empirical parameter β depends on temperature, pressure, and composition remains poorly constrained. Here, we conducted a series of first-principles molecular dynamics simulations to evaluate the β factor of Mg isotopes in MgSiO3 and Mg2SiO4 melts using pseudo-isotope method. In particular, we considered interactions between Mg isotopes by simultaneously putting pseudo-mass and normal-mass Mg atoms in a simulation supercell. The calculated β for Mg isotopes decreases linearly with decreasing temperature at zero pressure, from 0.158 ± 0.004 at 4000 K to 0.121 ± 0.017 at 2200 K for MgSiO3 melt and from 0.150 ± 0.004 at 4000 K to 0.101 ± 0.012 at 2200 K for Mg2SiO4 melt. Moreover, our simulations of compressed Mg2SiO4 melt along the 3000 K isotherm show that the β value decreases linearly from 0.130 ± 0.006 at 0 GPa to 0.060 ± 0.011 at 17 GPa. Based on our diffusivity results, the empirically established positive correlation between β and solvent-normalized diffusivity (Di/DSi) seems to be applicable only at constant temperatures or in narrow temperature ranges. Analysis of atomistic mechanisms suggests that the calculated β values are inversely correlated with force constants of Mg at a given temperature or pressure. Good agreement between our first principles results with available experimental data suggests that interactions between isotopes of major elements must be considered in calculating β for major elements in silicate melts. Also, we discuss diffusion-controlled crystal growth by considering our calculated β values.

中文翻译：

---

硅酸盐熔体中扩散镁同位素分馏的第一性原理计算

摘要 扩散同位素分馏发生在地球化学过程（如岩浆混合、气泡生长和晶体生长）中，即使在岩浆温度下也是如此。扩散的同位素质量依赖性通常表示为 D i D j = mjmi β ，其中 D i 和 D j 是质量为 mi 和 mj 的两种同位素的扩散系数。无量纲经验参数 β 如何依赖于温度、压力和成分仍然没有很好的约束。在这里，我们进行了一系列第一性原理分子动力学模拟，以使用拟同位素方法评估 MgSiO3 和 Mg2SiO4 熔体中 Mg 同位素的 β 因子。特别是，我们通过同时将伪质量和正常质量的 Mg 原子放入模拟超胞中来考虑 Mg 同位素之间的相互作用。计算出的 Mg 同位素 β 在零压力下随着温度的降低而线性降低，从 4000 K 下的 0.158 ± 0.004 到 2200 K 下 Mg SiO3 熔体的 0.121 ± 0.017 和 4000 K 下 0.150 ± 0.004 到 0.150 ± 0.004 到 0.150 ± 0.004 到 0.150 ± 0.004 到 0.1202 K SiO22 Mg 熔体. 此外，我们对压缩 Mg2SiO4 熔体沿 3000 K 等温线的模拟表明，β 值从 0 GPa 时的 0.130 ± 0.006 线性降低到 17 GPa 时的 0.060 ± 0.011。根据我们的扩散率结果，β 和溶剂归一化扩散率 (Di/DSi) 之间的经验建立的正相关似乎仅适用于恒定温度或窄温度范围。对原子机制的分析表明，计算出的 β 值与给定温度或压力下 Mg 的力常数成反比。我们的第一性原理结果与可用实验数据之间的良好一致性表明，在计算硅酸盐熔体中主要元素的 β 时必须考虑主要元素同位素之间的相互作用。此外，我们通过考虑我们计算的 β 值来讨论扩散控制的晶体生长。