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

Ghiorso和Sackdaughter-0003679 我们建议开发切实可行的固溶体热力学模型，充分描述短程有序利用新版本的集群变分法（CVM）。这个版本的CVM将提供准确的描述的组态熵，内能和体积的混合晶体，它不会有计算困难和限制与传统的CVM方法。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中配置变量的相关多项式被集群配置概率之间的线性关系的显式公式所取代。这种方法将适用于（Zn，Fe）S闪锌矿和（Ca，Na，Mg，Fe ~（2+））（Mg，Al，Fe ~（3+），Fe ~（2+））Si_2O_6辉石（绿辉石）。在前者中，由于第一最近邻（nn）三角形内的强相互作用而产生的短程有序似乎导致长程有序和形成具有有限组成范围的有序化合物（Balabin和Sack，2000）。在绿辉石中，耦合取代诱导了强短程有序（例如，NaAl-MgCa）导致空间群对称性从C2/c降低到P2/n。铁闪锌矿的CVM处理将利用立方八面体（13个原子）和fcc立方体（14个原子）的基础集群，它将允许任意程度的短程和长程有序的限制，任何边缘的基本单元的超结构不超过四倍的参数ao的初始晶格。含8和20个原子的基础集群将用于绿辉石的模型。明确规定将在晶格和NN，旁边的最近邻（nnn）和madn体相互作用的局部电荷平衡。在拟议的研究中开发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.