Empirical constraints on the mass dependence of isotope diffusion in minerals by modeling sub-solidus exchange: Calcium isotopes in the two-pyroxene system
Empirical constraints on the mass dependence of isotope diffusion in minerals by modeling sub-solidus exchange: Calcium isotopes in the two-pyroxene system
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DOI：
10.1016/j.gca.2022.11.022
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发表时间：
2022-11
影响因子：
5
通讯作者：
Z. Xiong;Shichun Huang;James A. Van Orman
中科院分区：
文献类型：
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作者：
Z. Xiong;Shichun Huang;James A. Van Orman
扩散是高温下同位素分馏的重要驱动因素，但由于扩散系数的同位素质量依赖性数据稀疏，在许多情况下很难评估其精确作用。特别是在矿物扩散方面缺乏此类数据。同一材料中同一元素的两种同位素的扩散系数之比可以表征为经验指数β的反质量比，但确定β的实验具有挑战性，并且很少有测量报告。在此，开发了一种方法，基于缓慢亚固相线冷却过程中矿物之间扩散控制的元素和同位素重新分布的数值模拟，并将结果与天然矿物对的数据进行比较，凭经验确定β。该方法适用于斜方辉石 (opx) 和单斜辉石 (cpx) 之间的 Ca 再分配，其中元素分配平衡作为温度的函数已通过实验得到了很好的表征，并且在经历缓慢冷却的天然样品中可以获得 Ca 同位素分馏数据。我们表明，冷却过程中的 Ca 同位素分馏对大范围条件下的初始温度、冷却速率或晶粒尺寸不敏感，前提是扩散足以在早期冷却过程中在接近峰值温度下重新均匀化 opx 晶粒。此外，我们发现，只要 cpx 主导系统中的 Ca 预算，冷却过程中建立的 Ca 同位素分馏对 opx 中 β 值的依赖性强于 cpx 中 β 值。瞬态加热事件产生与冷却过程中产生的分馏相反的分馏，这可以减少或逆转冷却后经历此类事件的样品的同位素分馏。根据自然样品中 opx 和 cpx 之间已记录的最大 Ca 同位素分馏，推断对于 Ca，βopx= 0.04(1)。尽管βopx 的推断值相对较小，但在很宽的冷却速率范围内，opx 和cpx 之间Ca 同位素的扩散分馏是显着的。对于具有与温度相关的矿物间分配系数的其他元素，预计在亚固相线冷却过程中也会出现类似的行为，并且这里开发的方法有可能用于对许多元素的β施加限制，即使在实验测量不可行的矿物中也是如此。
Diffusion is a significant driver of isotope fractionation at high temperatures, but its precise role is difficult to evaluate in many situations due to the sparsity of data on the isotopic mass dependence of the diffusion coefficient. Such data are lacking particularly for diffusion in minerals. The ratio of diffusion coefficients of two isotopes of the same element in the same material can be characterized as the inverse mass ratio raised to an empirical exponentβ, but experiments to determineβare challenging and few measurements have been reported. Here, a method is developed to empirically determineβbased on numerical modelling of the diffusion-controlled elemental and isotopic redistribution between minerals during slow subsolidus cooling, and comparison of the results to data from natural mineral pairs. The method is applied to the Ca redistribution between orthopyroxene (opx) and clinopyroxene (cpx), where the elemental partitioning equilibrium as a function of temperature has been well characterized experimentally and Ca isotope fractionation data are available in natural samples that experienced slow cooling. We show that the Ca isotope fractionation during cooling is insensitive to the initial temperature, cooling rate or grain size over a broad range of conditions, provided that diffusion is sufficient to re-homogenize opx grains at near-peak temperatures during early cooling. Furthermore, we find that the Ca isotope fractionation established during cooling is much more strongly dependent on the value ofβin opx than the value ofβin cpx, as long as cpx dominates the Ca budget in the system. Transient heating events produce fractionation in the opposite sense to that developed during cooling, which can diminish or reverse the isotope fractionation for samples that experienced such events after cooling. Based on the largest Ca isotope fractionation that has been documented between opx and cpx in natural samples, it is inferred that for Ca,βopx= 0.04(1). Despite the relatively small inferred value ofβopx, diffusive fractionation of Ca isotopes between opx and cpx is significant over a broad range of cooling rates. Similar behavior during sub-solidus cooling is anticipated for other elements with temperature-dependent inter-mineral partition coefficients, and the method developed here has the potential to be used to place constraints onβfor many elements, even in minerals where experimental measurements are not feasible.