First principles calculations of thermodynamic and mechanical properties of high temperature bcc Ta–W and Mo–Ta alloys

The thermodynamic quantities of high temperature metals and alloys are studied using the statistical moment method, going beyond the quasi-harmonic approximations. Including the power moments of the atomic displacements up to the fourth order, the Helmholtz free energies and the related thermodynamic quantities are derived explicitly in closed analytic forms. The configurational entropy term is taken into account by using the tetrahedron cluster approximation of the cluster variation method (CVM). The energetics of the binary (Ta–W and Mo–Ta) alloys are treated within the framework of the first-principles TB-LMTO (tight-binding linear muffin tin orbital) method coupled to CPA (coherent potential approximation) and GPM (generalized perturbation method). The equilibrium phase diagrams are calculated for the refractory Ta–W and Mo–Ta bcc alloys. In addition, the mechanical properties, i.e., temperature dependence of the elastic moduli C11, C12 and C44 and those of the ideal tensile and shear strengths of the bcc Ta–W and Ta-Mo alloys have been also studied.