Application of statistical moment method to thermodynamic quantities of metals and alloys

The thermodynamic quantities of metals and alloys are studied using the moment method in the quantum statistical mechanics, going beyond the harmonic approximation, and fully taking into account the anharmonicity of lattice vibrations. Including the power moments of the atomic displacements up to the fourth order, the free energy, specific heats Cv and Cp, mean square relative displacements and thermal lattice expansion coefficients are given explicitly in terms of the second and fourth order vibrational coupling constants. The effects of anharmonicity of lattice vibration on the long range order (LRO) parameter and order-disorder transitions of the binary alloys are investigated in detail. The changes in the root mean square atomic displacements upon the order-disorder phase transition are evaluated and compared with the available experimental results. We also discuss the melting transitions of metals and alloys within the framework of the present statistical moment method, and estimate the melting temperatures through the limiting temperature of the crystalline stability.