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

Ghiorso和SackEAR-0003679我们建议发展现实的固体溶液热力学模型，该模型将充分利用新版本的团簇变分方法来描述短程有序化。这一版本的CVM将为混合晶体的构型熵、内能和体积提供准确的描述；它将不会有与传统CVM方法相关的计算困难和限制。这些解决方案模型将在Balabin和Sack(2000)开发的方法的基础上进行扩展，其中在CVM中通常用作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。这一方法将应用于(锌，铁)S闪锌矿和(钙，钠，镁，铁)(镁，铝，铁，铁)二氧化硅辉石(绿辉石)。在前一种短程有序中，由于第一近邻(Nn)-三角形之间的强烈相互作用，似乎导致了长程有序化，形成了组成范围有限的有序化合物(Balabin和Sack，2000)。在绿辉石辉石中，由耦合取代(如NaAl-MgCa)引起的强烈短程有序导致空间群对称性从C2/c降低到P2/n。对Fe闪锌矿的CVM处理将利用立方八面体(13个原子)和fcc-Cube(14个原子)基团簇，并允许任意程度的短程和长程有序化，但超结构的基本晶胞的任何边不得超过初始晶格参数Ao的四倍。包含8个和20个原子的碱性团簇将在模型中用于绿辉石辉石。将明确规定晶格和nn、近邻(Nnn)和Madn体相互作用中的局部电荷平衡。本研究开发的方法将广泛应用于其他矿物体系。

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.