Notes on the creation and manipulation of solid solution models
Notes on the creation and manipulation of solid solution models
复制标题
关于固溶体模型的创建和操作的注释
DOI：
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发表时间：
2019
影响因子：
3.5
通讯作者：
J. Connolly
中科院分区：
文献类型：
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作者：
R. Myhill;J. Connolly
一大类固溶体模型的前提是化学物质交换发生在有限数量的独特晶体位点上，并且溶液的热力学性质是占据每个位点的物质比例的函数。这些模型大致被归类为布拉格-威廉姆斯类型。它们形成了非理想混合和长程有序的出色一阶近似。在本文中，我们提出了所有布拉格-威廉姆斯模型通用的数学框架，引入了几何、集合论和线性代数的必要概念。我们将其与一组数学工具结合起来，我们发现这些工具在构建和使用此类模型时很有用。我们提供了几个示例来说明关键概念并提供可用于所有模型的通用表达式。本文分为两部分。在第一部分中，我们展示了占据每个位点的物种的化合价和参与位点交换的物种的总电荷如何足以定义固溶体的有效位点占据的空间，并计算限制该空间的端元。我们证明这个空间可以被可视化为多面体，即 n 维多面体，并且我们描述了场地占用空间和组合空间之间的关系。在本文的第二部分中，我们提出了将修正范拉尔和次正则解模型的描述从一个独立端元基础转换为另一种独立端元基础所需的线性代数。相同的代数也可用于从微观位点相互作用推导出宏观端元相互作用。该代数在解决方案模型的初始设计以及在受限化学子系统中执行热力学计算时都很有用。热力学软件包 Perple_X 和 burnman 中使用固溶体的多面体描述。本文描述的算法以 Python 代码形式提供。
A large class of solid solution models are formulated on the premise that exchange of chemical species takes place on a finite number of unique crystallographic sites, and that the thermodynamic properties of the solution are a function of the proportions of species occupying each of the sites. These models are broadly classified as being of Bragg–Williams-type. They form an excellent first order approximation of non-ideal mixing and long-range order. In this article we present the mathematical framework common to all Bragg–Williams models, introducing necessary concepts from geometry, set theory and linear algebra. We combine this with a set of mathematical tools which we have found useful in building and using such models. We include several worked examples to illustrate key concepts and provide general expressions which can be used for all models. This paper is split into two parts. In the first part, we show how the valences of the species occupying each site and the total charge of the species involved in site exchange are sufficient to define the space of valid site occupancies of a solid solution, and to compute the endmembers bounding that space. We show that this space can be visualised as a polytope, i.e, an n -dimensional polyhedron, and we describe the relationship between site-occupancy space and compositional space. In the second part of the paper, we present the linear algebra required to transform descriptions of modified van Laar and subregular solution models from one independent endmember basis to another. The same algebra can also be used to derive macroscopic endmember interactions from microscopic site interactions. This algebra is useful both in the initial design of solution models, and when performing thermodynamic calculations in restricted chemical subsystems. A polytope description of solid solutions is used in the thermodynamic software packages Perple_X and burnman . The algorithms described in this paper are made available as python code.
影响因子：
3.9
作者：
Holland, Tim J. B.;Green, Eleanor C. R.;Powell, Roger
通讯作者：
Powell, Roger