Thermodynamics of the Cr-Ta-W system by combining the Ab Initio and CALPHAD methods

The thermodynamic properties of alloys can be described from the knowledge of the underlying lattice and the atomic numbers of the alloy species by using a first-principles electronic structure approach based on the tight-binding linear muffin-tin orbital method within the coherent potential approximation (TB-LMTO-CPA) and the local density approximation of density functional theory. The generalized perturbation method (GPM) permits direct mapping of the configurational part of the effective one-electron Hamiltonian onto an Ising-like model thus insuring the necessary link between quantum mechanics and statistical thermodynamics. To test the practical application of this approach to multi-component alloys, data assessment has been successfully performed for the Cr-Ta-W alloy system by using the thermodynamic results derived from the TB-LMTO-CPA-GPM and the cluster variation method (CVM) in the tetrahedron approximation for Ta-W alloys as functions of temperature and concentration. These later results predict B2 ordering for the bcc-based Ta-W system with a maximum ordering temperature near 1000 K at 43 at.% Ta. The output thermodynamics were converted to a Redlich-Kister/Bragg-Williams format with an acceptable level of accuracy. The results were then combined with those of the CALPHAD description of the Cr-W and Cr-Ta systems to calculate isothermal sections of the ternary phase diagram of the Cr-Ta-W system.