The thermodynamic quantities of metals and alloys are studied using the moment method in the quantum statistical mechanics, going beyond the quasi-harmonic approximations [1-3]. Including the power moments of the atomic displacements up to the fourth order, the free energies of alloy systems are derived explicitly in closed analytic forms. The configurational entropy term is taken into account by coupling the moment expansion scheme with the cluster variation method (CVM). The internal energies of metals and alloys are evaluated by using the first principles TB-LMTO scheme and the thermodynamic quantities like thermal lattice expansion, specific heats, mean square atomic displacements and elastic moduli have been calculated successfully. The applications of the present combined scheme are given both for the phase separating and order-disordered alloys. For phase-separating binary alloys the change of lattice constant with the composition and the reduction of the transition temperature are shown in detail. For the order-disordered alloys, the effects of thermal lattice vibration (anharmonicity of thermal lattice vibrations) on the long range order (LRO) parameter and order-disorder transition temperatures are investigated. The equilibrium phase diagrams are calculated for some binary alloys, like CuAu, NiAl and FeAl systems.
[1] K. Masuda-Jindo, V. V. Hung and P. D. Tam, Calphad, 26, No. 1, 15 (2002).
[2] R. Kikuchi and K. Masuda-Jindo, Calphad, 26, No. 1, 33 (2002).
[3] K. Masuda-Jindo, V. V. Hung and P. D. Tam, Phys. Rev. B67, 094301 (2003).