Nonempirical phase equilibria in the W-Mo-Cr system

The solid-state portion of the W-Mo-Cr phase diagram is computed without the use of empirically adjustable parameters. The phase diagram is calculated using the bcc tetrahedron approximation of the cluster variation method (CVM) formulated with an independent set of multisite correlation functions. A set of volume-independent effective cluster interactions (ECI's) are used to parametrize the configurational energetics of the system; they are obtained using the method of direct configurational averaging based on a tight-binding, linearized muffin-tin-orbital Hamiltonian. The nearest- and next-nearest-neighbor pair ECI's are found to be dominant and indicate clustering tendencies for all binary systems (W-Mo, W-Cr, and Mo-Cr), consistent with experiment; triplet and higher-order pair interactions are significantly smaller. The ternary phase diagram for W-Mo-Cr is analyzed using twelve ECI's within the bcc tetrahedron, and while there is no experimental data for this ternary system, the results are quite encouraging even though transition temperatures on the binary edges are overestimated. The latter discrepancy is most likely due to the neglect of elastic relaxations driven by the large size mismatch of the constituent elements or to the neglect of vibrational contributions to the free energy.