Calculation of thermodynamic quantities of metals and alloys by statistical moment method

The thermodynamic quantities of metals and alloys are studied using the moment method in the quantum statistical mechanics, going beyond the quasi-harmonic approximations. Including the power moments of the atomic displacements up to the fourth order, the free energy, specific heats Cv and Cp, mean square atomic displacements and thermal lattice expansion coefficients are derived explicitly in terms of the second and fourth order vibrational coupling constants. The thermodynamic quantities are calculated both for cubic (fcc and bcc) and closed packed hexagonal (hcp) metals. The Lennard–Jones type of potentials as well as the effective interatomic potentials derived from the tight-binding (TB) total energy calculation scheme are used. The calculated thermodynamic quantities are favorably compared with the experimental results. For the calculations of alloys, we investigate the effects of thermal lattice vibration on the long range order (LRO) parameter and order–disorder transitions of the ordered binary alloys.