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

The thermodynamic properties of metals and alloys are studied using the moment method in the statistical dynamics, which allows us to take into account the anharmonicity of thermal lattice vibrations and size mismatch of constituent atoms, going beyond the quasi-harmonic approximation. Within the fourth-order moment approximation, the free energy and equilibrium lattice spacing of the binary alloys are given explicitly in terms of the effective pair potentials and the second- and fourth-order vibrational constants. The long-range order (LRO) parameter η and order-disorder transition temperatures (ODTs) T_c of binary alloys are obtained by solving the explicit transcendental equations. The numerical calculations of thermodynamic quantities for Cu₃Au and β-CuZn alloys show that the inclusion of the anharmonicity of lattice vibration plays an essentially important role in determining the phase stabilities of metals and alloys.