Accurate geochemical models of magmatic processes require an understanding of crystal-melt partitioning of trace elements. Many major igneous processes at different tectonic environments in Earth occur in the presence of garnet as a residual phase. Since the pioneering crystal lattice-strain model, several attempts have been made to quantify garnet-melt partitioning coefficients over a wide range of conditions. However, high pressure high-temperature experimental data demonstrate distinct differences in partitioning determined at anhydrous conditions and partitioning determined in the presence of H2O. In this study, we present for the first time a constraint on the partitioning of REE, Y, and Sc between garnet and hydrous fluids as a function of the water content in the fluid phase. We analysed published hydrous experimental partitioning data using different statistical methods and modelled key parameters in the crystal lattice strain model (r0,D0, and E). We show a robust correlation between r0, temperature and garnet-fluid partitioning of Mg. We further show that D0 can be predicted using the garnet-fluid partitioning of Fe and that E can be predicted using various parameters describing the fluid phase. We validate and illustrate the ability to predict partitioning of REE in H2O-bearing systems using major element analysis of garnet and fluid only. Consequently, our statistical model paves the way to integrate thermodynamic models based on major element chemical equilibria with trace element studies on hydrous magmatic systems, allowing a description of the transfer of key trace elements in more realistic conditions.

中文翻译：

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模拟含 H2O 系统中的石榴石流体分配：将晶格应变理论扩展到含水系统的初步统计尝试

岩浆过程的准确地球化学模型需要了解微量元素的晶体-熔体分配。地球不同构造环境中的许多主要火成岩过程都发生在石榴石作为残余相的情况下。自从开创性的晶格应变模型以来，已经进行了多次尝试来量化各种条件下的石榴石熔体分配系数。然而，高压高温实验数据表明在无水条件下确定的分配和在 H2O 存在下确定的分配存在明显差异。在这项研究中，我们首次提出了对 REE、Y 和 Sc 在石榴石和含水流体之间分配的限制，作为流体相中水含量的函数。我们使用不同的统计方法分析了已发表的含水实验分区数据，并对晶格应变模型（r0、D0 和 E）中的关键参数进行建模。我们显示了 r0、温度和 Mg 的石榴石-流体分配之间的强相关性。我们进一步表明，可以使用 Fe 的石榴石流体分配来预测 D0，并且可以使用描述流体相的各种参数来预测 E。我们仅使用石榴石和流体的主要元素分析验证并说明了预测含 H2O 系统中 REE 分配的能力。因此，我们的统计模型为将基于主要元素化学平衡的热力学模型与含水岩浆系统的微量元素研究相结合铺平了道路，允许在更现实的条件下描述关键微量元素的转移。