Modeling diffusion in ionic, crystalline solids with internal stress gradients
Modeling diffusion in ionic, crystalline solids with internal stress gradients
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DOI：
10.1016/j.gca.2023.06.004
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发表时间：
2023-04
影响因子：
5
通讯作者：
Benjamin L. Hess;J. Ague
中科院分区：
文献类型：
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作者：
Benjamin L. Hess;J. Ague
晶内扩散是估算地质事件时间尺度的宝贵工具。扩散通常使用由成分变化引起的化学势梯度来建模。然而，化学势是在均匀的压力和温度条件下导出的，因此当应力存在梯度时，不能用于模拟扩散。矿物内部的应力变化将产生应变能梯度，除了成分梯度外，应变能梯度还将驱动扩散。因此，有必要有一个方法，将应力变化到diffusion models.To解决这个问题，我们已经推导出一个通量表达式，允许扩散在任意应力状态下的离子，结晶固体建模。我们的方法与标准的岩石学方法一致，但相反，利用梯度的热力学势称为“相对化学势”。相对化学势通过量化由于在任意应力条件下晶格位点上的组分交换而引起的自由能变化来解释结晶固体中的晶格约束。因此，相对化学势的梯度可用于模拟压力不均匀时的扩散（即，在非静水应力条件下）。我们将我们的推导应用于常见的四元石榴石固溶体铁铝榴石-镁铝榴石-钙铝榴石-spessartine。二价阳离子扩散的速率和方向，在应力的反应是由端元的摩尔体积或晶格参数，弹性模量，和非理想的活性相互作用参数。我们的研究结果预测，内部应力的变化一百兆帕或更高，需要转移石榴石组合物的摩尔分数的至少百分之几。石榴石中的矿物包裹体提供了一个潜在的环境来测试和应用我们的应力驱动扩散方法，因为在这些包裹体周围观察或预测的应力变化范围从数百MPa到GPa级。模拟应力诱导扩散的能力可以提供有关晶内应力的大小和它们发生的时间尺度的新信息，从而更好地理解大规模的构造变质过程。
Intracrystalline diffusion is an invaluable tool for estimating timescales of geological events. Diffusion is typically modeled using gradients in chemical potential caused by variations in composition. However, chemical potential is derived for uniform pressure and temperature conditions and therefore cannot be used to model diffusion when there are gradients in stress. Internal stress variations in minerals will create gradients in strain energy which, in addition to gradients in composition, will drive diffusion. Consequently, it is necessary to have a method that incorporates stress variations into diffusion models.To address this issue, we have derived a flux expression that allows diffusion to be modeled in ionic, crystalline solids under arbitrary stress states. Our approach is consistent with standard petrological methods but instead utilizes gradients in a thermodynamic potential called “relative chemical potential.” Relative chemical potential accounts for the lattice constraint in crystalline solids by quantifying changes in free energy due to the exchanges of constituents on lattice sites under arbitrary stress conditions. Consequently, gradients in relative chemical potential can be used to model diffusion when pressure is not uniform (i.e., under conditions of non-hydrostatic stress).We apply our derivation to the common quaternary garnet solid solution almandine–pyrope–grossular–spessartine. The rates and directions of divalent cation diffusion in response to stress are determined by endmember molar volumes or lattice parameters, elastic moduli, and non-ideal activity interaction parameters. Our results predict that internal stress variations of one hundred MPa or more are required to shift garnet compositions by at least a few hundredths of a mole fraction. Mineral inclusions in garnet present a potential environment to test and apply our stress-driven diffusion approach, as stress variations ranging from hundreds of MPa to GPa-level are observed or predicted around such inclusions. The ability to model stress-induced diffusion may provide new information about the magnitudes of both intracrystalline stresses and the timescales during which they occurred, imparting a better understanding of large-scale tectono-metamorphic processes.