Thermal equation of states for body-centered cubic tungsten using extended analytic embedded-atom model

Abstract

Here the thermal equation of states (EOS) for body-centered cubic (bcc) tungsten (W) is evaluated using embedded-atom method (EAM). To reproduce the materials properties under high pressure and high temperature reasonably well, we extend EAM by improving the analytic expressions of the functions of electron density and embedding energy based on the quantum-mechanical results of the electron density distribution in crystal lattice and the variation of energy with respect to the electron density. Then we determine the parameters of the extended analytic model for bcc W. We evaluate the volume dependence of structure energy and phonon frequencies to simulate the variation of the Gibbs free energy with respect to temperature, pressure and volume within the framework of the quasiharmonic approximation (QHA). By minimizing the Gibbs free energy, we determine the variation of volume or lattice parameter with respect to pressure at the various temperatures. All calculation results fit well to the experimental and other reliable theoretical calculation results, showing the reliability of the extended analytic EAM in the extended domains of electron density, atomic volume, temperature and pressure.