Abstract Crystal zoning is considered in the context of the evolution of a population of crystals. Crystal size distribution (CSD) theory provides an important framework and constraints that are applied in a numerical model of crystal nucleation and growth in an infinite half-sheet which proxies for a sill. The CSD/crystal population approach is combined with a relatively simple principle of trace element (TE) partitioning for batch crystallization. A model of crystal nucleation and growth that is applied to a constrained volume of magma is modified by the addition of a co-precipitating phase and TE modeling. The coprecipitating phase does not consume the TE and so the TE's concentration in the residual liquid increases. Thus the primary phase for which the TE is compatible incorporates more as it grows. A single partition coefficient value is used and is held constant. One crystal in the much larger, evolving population of crystals is tracked and TE concentration in the crystal vs. time is recorded as the crystal grows. In general, TE concentration within the crystal initially decreases while only the primary phase is present and then begins to increase in that crystal when the second/coprecipitating phase appears. For the relatively short solidification interval utilized in the modeling, one half-cycle of oscillation: high concentration to low to high, or normal to reverse zoning, is demonstrated. Beyond the TE's partition coefficient, the presence and magnitude of zoning is dependent upon the time the second phase begins within the solidification interval and the mass proportion of crystallization of primary phase to second phase—which is held constant throughout the remainder of solidification once the second phase appears. The model, as currently implemented, is based solely on thermal and mass balances. A multi-faceted crystallization history, one involving, e.g., more complicated phase equilibria, crystal fractionation, convection, and magma mixing would expose the tracked crystal to changing surroundings such that the mass balance mechanism that yielded the half-cycle of zoning obtained here would perhaps continue to yield oscillatory zoning.

中文翻译：

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关于晶体群动力学和微量元素分配模型的综合：矿物分带的机制

摘要 晶体分带是在晶体群演化的背景下考虑的。晶体尺寸分布 (CSD) 理论提供了一个重要的框架和约束，可应用于代表基台的无限半片中晶体成核和生长的数值模型。CSD/晶体群方法与相对简单的微量元素 (TE) 分配原理相结合，用于批量结晶。通过添加共沉淀相和 TE 建模来修改应用于受限岩浆体积的晶体成核和生长模型。共沉淀相不消耗 TE，因此残留液体中 TE 的浓度增加。因此，与 TE 兼容的主要相随着它的增长而包含更多。使用单个分配系数值并保持恒定。跟踪更大、不断演化的晶体群中的一个晶体，并随着晶体的生长记录晶体中 TE 浓度与时间的关系。通常，晶体内的 TE 浓度最初会降低，而只有主相存在，然后当第二/共沉淀相出现时，该晶体中的 TE 浓度开始增加。对于建模中使用的相对较短的凝固间隔，展示了一个半周期的振荡：高浓度到低到高，或正常到反向分区。超出 TE 的分配系数，分带的存在和大小取决于第二相在凝固间隔内开始的时间以及第一相与第二相结晶的质量比例——一旦第二相出现，第二相在凝固的其余部分中保持恒定。目前实施的模型完全基于热平衡和质量平衡。多方面的结晶历史，包括更复杂的相平衡、晶体分馏、对流和岩浆混合等，将使跟踪的晶体暴露于不断变化的环境中，从而产生此处获得的半周期分区的质量平衡机制将也许会继续产生振荡分区。完全基于热平衡和质量平衡。多方面的结晶历史，包括更复杂的相平衡、晶体分馏、对流和岩浆混合等，将使跟踪的晶体暴露于不断变化的环境中，从而产生此处获得的半周期分区的质量平衡机制将也许会继续产生振荡分区。完全基于热平衡和质量平衡。多方面的结晶历史，包括更复杂的相平衡、晶体分馏、对流和岩浆混合等，将使跟踪的晶体暴露于不断变化的环境中，从而产生此处获得的半周期分区的质量平衡机制将也许会继续产生振荡分区。