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

University Of Washington, Seattle WA

Investigators

Abstract

Ghiorso and Sack EAR-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.