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首页> 外文期刊>Contributions to Mineralogy and Petrology >The elastic solid solution model for minerals at high pressures and temperatures
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The elastic solid solution model for minerals at high pressures and temperatures

机译：高压和温度下矿物的弹性固溶体模型

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Non-ideality in mineral solid solutions affects their elastic and thermodynamic properties, their thermobaric stability, and the equilibrium phase relations in multiphase assemblages. At a given composition and state of order, non-ideality in minerals is typically modelled via excesses in Gibbs free energy which are either constant or linear with respect to pressure and temperature. This approach has been extremely successful when modelling near-ideal solutions. However, when the lattice parameters of the solution endmembers differ significantly, extrapolations of thermodynamic properties to high pressures using these models may result in significant errors. In this paper, I investigate the effect of parameterising solution models in terms of the Helmholtz free energy, treating volume (or lattice parameters) rather than pressure as an independent variable. This approach has been previously applied to models of order-disorder, but the implications for the thermodynamics and elasticity of solid solutions have not been fully explored. Solid solution models based on the Helmholtz free energy are intuitive at a microscopic level, as they automatically include the energetic contribution from elastic deformation of the endmember lattices. A chemical contribution must also be included in such models, which arises from atomic exchange within the solution. Derivations are provided for the thermodynamic properties of n-endmember solutions. Examples of the use of the elastic model are presented for the alkali halides, pyroxene, garnet, and bridgmanite solid solutions. Elastic theory provides insights into the microscopic origins of non-ideality in a range of solutions, and can make accurate predictions of excess enthalpies, entropies, and volumes as a function of volume and temperature. In solutions where experimental data are sparse or contradictory, the Helmholtz free energy approach can be used to assess the magnitude of excess properties and their variation as a function of pressure and temperature. The formulation is expected to be useful for geochemical and geophysical studies of the Earth and other planetary bodies.
机译：矿物固体溶液中的非理想性影响其弹性和热力学性质，其热性稳定性和多相组合中的均衡相位关系。在给定的组合物和顺序状态下，矿物质中的非理想性通常通过在GIBBS自由能中的过量建模，这对于压力和温度是恒定的或线性的。在建模近乎理想的解决方案时，这种方法非常成功。然而，当解决方案终点的晶格参数有显着差异，使用这些模型的高压热力学性质的外推可能导致显着的误差。在本文中，我研究了参数化解决方案模型在亥姆霍兹自由能，处理体积（或晶格参数）而不是压力作为独立变量的影响。这种方法以前已经应用于秩序障碍的模型，但对热力学和固体解决方案的弹性的影响尚未得到充分探索。基于Helmholtz自由能的固体解决方案模型在微观水平上直观，因为它们自动包括从端环格格子的弹性变形的能量贡献。化学贡献也必须包括在这些模型中，从而从解决方案中的原子交换中出现。提供了N-EndMember解决方案的热力学性能的衍生。弹性模型的使用的实例用于碱卤化物，辉石，石榴石和桥甲酸盐固溶体。弹性理论在一系列溶液中提供了对非理想性的显微性起源的见解，并且可以精确地预测过量焓，熵和体积，作为体积和温度的函数。在实验数据稀疏或矛盾的解决方案中，亥姆霍兹自由能量方法可用于评估多余性质的大小及其随压力和温度的函数的变化。预计该配方对于地球和其他行星体的地球化学和地球物学研究有用。

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