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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：不对称的多组分公式

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For petrological calculations, including geothermobarometry 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 independent set, with size parameter differences between end members accounting for asymmetry. In the case of fluid mixtures, for example, H2O–CO2, 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 KAlSi3O8–NaAlSi3O8 and KAlSi3O8–NaAlSi3O8–CaAl2Si2O8, for carbonates in the system CaCO3–MgCO3, for melt in the melting relationships involving forsterite, protoenstatite and cristobalite in the system Mg2SiO4–SiO2, as well as for fluids in the system H2O–CO2. 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，PT岩石成因网格和伪剖面），必须能够表达矿物，熔体和流体中的活度-成分（a-x）关系。多组件系统。尽管对称形式主义（一种处理ax关系的宏观正则模型方法）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。在不对称形式主义中，对于独立集中的每个末端成员，另外还有一个“大小参数”，末端成员之间的大小参数差异会导致不对称。对于混合流体，例如H2 O–CO2 ，端部件的体积作为压力和温度的函数，作为尺寸参数，非常适合a– x关系。对于矿物和硅酸盐液体，尺寸参数是经验参数，将与相互作用能一起确定，作为ax关系的一部分。通过这种方式，我们确定了KAlSi3 O8 -NaAlSi3 O8 和KAlSi3 O8 -NaAlSi3系统中长石的a–x关系 O8 –CaAl2 Si2 O8 ，用于系统CaCO3 –MgCO3 中碳酸盐的熔融，涉及的熔融关系涉及Mg2 SiO4 –SiO2 系统中的镁橄榄石，原钙钛矿和方石英，以及H2 O-CO2 系统中的流体。在每种情况下，ax关系都允许忠实地复制相应的，由实验确定的相图。非对称形式主义提供了一种强大而灵活的方式来处理用于岩石学计算的多组分系统中复杂相的a–x关系。

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