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首页> 外文期刊>Contributions to Mineralogy and Petrology >Activity-composition relations for phases in petrological calculations: an asymmetric multicomponent formulation
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Activity-composition relations for phases in petrological calculations: an asymmetric multicomponent formulation

机译：岩石学计算中各相的活度-成分关系：不对称多组分公式

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摘要

For petrological calculations, including geo-thermobarometry and the calculation of phase diagrams (for example, P-T petrogenetic grids and pseudosections), it is necessary to be able to express the activity composition (a-x) relations of minerals, melt and fluid in multicomponent systems. Although the symmetric formalism-a macroscopic regular model approach to a-x relations-is an easy-to-formulate, general way of doing this, the energetic relationships are a symmetric function of composition. We allow asymmetric energetics to be accommodated via a simple extension to the symmetric formalism which turns it into a macroscopic van Laar formulation. We term this the asymmetric formalism (ASF). In the symmetric formalism, the a-x relations are specified by an interaction energy for each of the constituent binaries amongst the independent set of end members used to represent the phase. In the asymmetric formalism, there is additionally a "size parameter" for each of the end members in the inde-pendent set, with size parameter differences between end members accounting for asymmetry. In the case of fluid mixtures, for example, H_2O~CO_2, the volumes of the end members as a function of pressure and temperature serve as the size parameters, providing an excellent fit to the a-x relations. In the case of minerals and silicate liquid, the size parameters are empirical parameters to be determined along with the interaction energies as part of the calibration of the a-x relations. In this way, we determine the a-x relations for feldspars in the systems KalSi_3O_8-NaAlSi_3O_8 and KalSi_3O_8-NaAlSi_3O_8-CaAl_2Si_2O_8, for carbonates in the system CaCO_3-MgCO_3, for melt in the melting relationships involving forsterite, protoenstatite and cristobalite in the system Mg_2SiO_4-SiO_2, as well as for fluids in the system H_2OCO_2. In each case the a-x relations allow the corresponding, experimentally determined phase diagrams to be reproduced faithfully. The asymmetric formalism provides a powerful and flexible way of handling a-x relations of complex phases in multicomponent systems for petrological calculations.
机译：对于岩石学计算，包括地热气压计和相图的计算（例如，P-T岩石成因网格和伪剖面），必须能够表达多组分系统中矿物，熔体和流体的活度组成（a-x）关系。尽管对称形式主义（一种处理a-x关系的宏观规则模型方法）是一种易于制定的通用方法，但高能关系是构图的对称函数。我们允许通过对对称形式主义的简单扩展来容纳非对称能量学，从而将其转变为宏观范拉尔公式。我们称其为不对称形式主义（ASF）。在对称形式主义中，a-x关系由用于代表相位的独立端成员集合中每个组成二进制文件的相互作用能指定。在非对称形式主义中，独立集合中的每个末端成员还额外存在一个“大小参数”，末端成员之间的大小参数差异会导致不对称。在流体混合物（例如H_2O〜CO_2）的情况下，端部件的体积作为压力和温度的函数，用作尺寸参数，非常适合a-x关系。在矿物和硅酸盐液体的情况下，尺寸参数是经验参数，将与相互作用能一起确定，作为a-x关系校准的一部分。通过这种方式，我们确定了系统KalSi_3O_8-NaAlSi_3O_8和KalSi_3O_8-NaAlSi_3O_8-CaAl_2Si_2O_8中的长石的轴关系，对于系统CaCO_3-MgCO_3中的碳酸盐而言，对于涉及镁橄榄石，镁橄榄石_4和方石英的熔融关系中的熔融关系而言SiO_2以及H_2OCO_2系统中的流体。在每种情况下，a-x关系都可以忠实地复制相应的，通过实验确定的相图。非对称形式主义提供了一种强大而灵活的方法来处理多组分系统中复杂相的a-x关系，以进行岩石学计算。

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