Cluster Variation Method (CVM) Modeling of Order-Disorder in Mineral Solutions

我们建议开发现实的固溶体热力学模型，利用新版本的聚类变化方法（CVM）充分描述短程有序。该版本的CVM能准确描述混合晶体的构型熵、内能和体积；它不会有与传统CVM方法相关的计算困难和限制。这些解决方案模型将扩展Balabin和Sack（2000）开发的方法，其中通常用作CVM配置变量的相关多项式被集群配置概率之间线性关系的显式公式所取代。该方法将应用于（Zn,Fe）S闪锌矿和（Ca,Na,Mg,Fe2+）（Mg,Al,Fe3+,Fe2+）Si2O6辉石（辉石）。在前者中，由于第一个最近邻居(nn)-三角形内的强相互作用，短程排序似乎导致了远距离排序，并形成了具有有限组成范围的有序化合物（Balabin和Sack， 2000）。在复辉石中，耦合取代（如NaAl - MgCa）引起的强短程有序导致空间群对称性从C2/c降低到P2/n。铁闪闪矿的CVM处理将利用立方体（13个原子）和fcc立方（14个原子）基簇，它将允许任意程度的短期和长期有序，但限制是上层结构的基本单元的任何边缘不超过初始晶格参数ao的四倍。含8个和20个原子的基团簇将用于复辉石模型。明确规定了晶格和神经网络中的局部电荷平衡，最近邻（nnn）和madn体相互作用。在拟议的研究中发展的方法将广泛适用于其他矿物系统。

Ghiorso and SackEAR-0003679 We propose to develop realistic thermodynamic models for solid solutions that will adequately describe short-range ordering utilizing a new version of the Cluster Variation Method (CVM). This version of CVM will afford accurate descriptions for configurational entropy, internal energy and volume of mixed crystals; it will not have the computational difficulties and limitations associated with conventional CVM approaches. These solution models will expand upon the approach developed by Balabin and Sack (2000) wherein the correlation polynomials that are typically employed as configuration variables in CVM are replaced by explicit formulations of linear relations between the probabilities of cluster configurations. This approach will be applied to (Zn,Fe)S sphalerites and (Ca,Na,Mg,Fe2+)(Mg,Al,Fe3+,Fe2+)Si2O6 pyroxenes (omphacites). In the former short-range ordering due to strong interactions within the first nearest neighbor(nn)-triangle appear to result in long-range ordering and formation of ordered compounds with limited compositional ranges (Balabin and Sack, 2000). In omphacitic pyroxenes strong short-range ordering induced by coupled substitutions (e.g., NaAl - MgCa) results in a reduction of the space group symmetry from C2/c to P2/n. The CVM treatment for Fe-sphalerite will utilize cuboctahedron (13 atoms) and fcc-cube (14 atoms) basis clusters, and it will allow for an arbitrary degree of both short- and long-range ordering subject to the restriction that any edge of the elementary cell of a superstructure does not exceed four times the parameter ao of the initial lattice. Basis clusters containing 8 and 20 atoms will be utilized in the model for omphacitic pyroxenes. Explicit provision will be made for local charge balance in the lattice and nn, next to nearest neighbor (nnn) and madn body interactions. The methods developed in the proposed research will be widely applicable to other mineral systems.