Equation of state and thermodynamic properties of BCC metals

Abstract

The moment method in statistical dynamics is used to study the equation of state and thermodynamic properties of the bcc metals taking into account the anharmonicity effects of the lattice vibrations and hydrostatic pressures. The explicit expressions of the lattice constant, thermal expansion coefficient, and the specific heats of the bcc metals are derived within the fourth order moment approximation. The thermodynamic quantities of W, Nb, Fe, and Ta metals are calculated as a function of the pressure, and they are in good agreement with the corresponding results obtained from the first principles calculations and experimental results. The effective pair potentials work well for the calculations of bcc metals. INTRODUCTIONThe study of high pressure behaviour of materials has become quite interesting in recent years since the discovery of new crystal structures and due to many geophysical and technological applications. A lot of theoretical models have been proposed in order to predict the P-V-T equation of state (EQS) at the high pressure domain. Using the input data as the volume , the bulk modulus ,etc., at the available low-pressure, these EQS models predict the highpressure behaviours of materials. However, the results obtained from these semi-empirical models depend on the input data and the kinds of model. [3,4] have been restricted to the calculation of structural and thermal properties of quantum solids or to the calculation of equations of state of condensed rare gases. Within the framework of the density-functional theory (DFT) [5], the thermodynamic properties of solids under a constant pressure can be calculated from the first-principles caculations . For ordered solids, the free energy at finite temperature has contributions from both the lattice vibrations and the thermal excitation of electrons. In the quasiharmonic approximation, the free energy is calculated by adding a dynamical contribution which is approximated by the free energy of a system of harmonic oscillators corresponding to the crystal vibrational modes (phonons)-to a static contribution-which is accessible to standard DFT calculations [6]. Vibrational modes are treated quantum mechanically, but the full Hamiltonian is approximated by a harmonic expansion about the equilibrium atomic