Overstepping of porphyroblast-forming reactions has been shown to occur in regional, contact, and subduction zone metamorphism, calling into question the paradigm that metamorphic mineral reactions occur at or very close to thermodynamic equilibrium. These overstepped reactions result from the fact that nucleation and growth of new phases requires a thermodynamic driving force or a “departure” from equilibrium. We use phase equilibria modeling to elucidate the energetic consequences of over-stepped garnet nucleation and growth by comparing the chemical potentials of garnet-forming oxide components (MnO, CaO, FeO, MgO, Al2O3) in two sets of calculations: one in which Gibbs free energy is minimized and one in which the minimization proceeds under identical conditions but in the forced absence of garnet. We focus on 12 examples from the literature that have previously described garnet nucleation as minimally overstepped (garnet nucleation at the P-T of initial garnet stability) or garnet nucleation as more substantially overstepped (garnet nucleation at P-T conditions greater than initial garnet stability). For a small P-T interval above nominal garnet-in reactions, differences in the chemical potentials between the two calculations are commonly minimal. In all tested examples calculated using two versions of the THERMOCALC thermodynamic data set, the chemical potential of Al2O3 (μAl2O3) diverges between garnet-bearing and garnet-absent calculations at greater P-T conditions than that of MnO, CaO, FeO, and MgO. The P-T interval between thermodynamic garnet-in and the point at which μAl2O3 differs substantially between the two sets of calculations appears to be a function of bulk-rock MnO content, reemphasizing the role that small quantities of MnO play in the apparent stability of garnet in calculated phase equilibria. These results highlight the importance of considering multiple thermodynamic data sets, the location of the garnet-in curve, and the abundance of mineral phases in the discussion of overstepped metamorphic reactions. The results have implications for determining kinetic barriers to crystal nucleation and growth and considering the most appropriate way of defining “garnet-in” for samples that have experienced overstepping.

中文翻译：

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理解过度的石榴石成核和生长的（化学）潜力

斑状成矿反应的过度发生已显示在区域，接触和俯冲带的变质作用中，人们质疑变质矿物反应发生在热力学平衡或非常接近热力学平衡的范式。这些过分的反应是由于新相的成核和生长需要热力学驱动力或从平衡中“脱离”这一事实造成的。我们使用相位平衡模型，通过两组计算比较形成石榴石的氧化物成分（MnO，CaO，FeO，MgO，Al2O3）的化学势，阐明了逐步过度的石榴石成核和生长的能量后果。自由能被最小化，并且其中最小化在相同条件下但在没有石榴石的情况下进行最小化。我们集中于文献中的12个示例，这些示例先前将石榴石成核描述为最小超步（初始石榴石稳定性的PT处的石榴石成核）或石榴石成核更为实质性超步（在大于初始石榴石稳定性的PT条件下的石榴石成核）。对于在标称石榴石化反应之上的一小段PT间隔，两次计算之间的化学势差通常很小。在使用两个版本的THERMOCALC热力学数据集计算的所有测试示例中，与MnO，CaO，FeO和MgO相比，在更大的PT条件下，Al2O3（μAl2O3）的化学势在含石榴石和无石榴石的计算之间有所不同。两组计算之间热力学石榴石插入点与μAl2O3显着不同的点之间的PT间隔似乎是块岩中MnO含量的函数，再次强调了少量MnO在石榴石表观稳定性中的作用。计算的相平衡。这些结果突出了在讨论超步变质反应时考虑多个热力学数据集，石榴石插入曲线的位置以及丰富的矿物相的重要性。这些结果对于确定晶体成核和生长的动力学障碍以及考虑为超标样品定义“石榴石插入”的最合适方法具有重要意义。再次强调了在计算出的相平衡中，少量MnO在石榴石的表观稳定性中所起的作用。这些结果突出了在讨论超步变质反应时考虑多个热力学数据集，石榴石插入曲线的位置以及丰富的矿物相的重要性。这些结果对于确定晶体成核和生长的动力学障碍以及考虑为超标样品定义“石榴石插入”的最合适方法具有重要意义。再次强调了在计算出的相平衡中，少量MnO在石榴石的表观稳定性中所起的作用。这些结果突出了在讨论超步变质反应时考虑多个热力学数据集，石榴石插入曲线的位置以及丰富的矿物相的重要性。这些结果对于确定晶体成核和生长的动力学障碍以及考虑为超标样品定义“石榴石插入”的最合适方法具有重要意义。