On equation of state, elastic, and lattice dynamic stability of bcc bismuth under high pressure: Ab-initio calculations

Abstract

First principles calculations have been carried out using density functional theory based Vienna Ab-initio Simulation Package to analyze the elastic and lattice dynamic stability and determine the equation of state of bismuth in bcc phase. The 0 K isotherm has been determined from total energy calculations. The 300 K isotherm obtained after adding thermal corrections to 0 K isotherm compares well with experimental data. The elastic stability of the bcc phase examined from 0 GPa to 220 GPa suggests that this phase is elastically stable throughout this pressure range. The calculated phonon spectra of bcc phase suggest that this phase will be unstable lattice dynamically at ambient pressure but it will attain lattice dynamic stability at ∼8 GPa (the pressure around which this phase gets stabilized energetically). Further, from theoretically calculated elastic moduli, we have derived the volume dependent Gruneisen parameter and used this in Lindemann melting rule to determine the pressure effect on the melting point, i.e., the melting curve. The Hugoniot of bismuth has been generated from 0 K isotherm after adding thermal corrections in conjunction with Rankine-Hugoniot relation. The theoretical Hugoniot and melting curve yielded the shock induced melting pressure to be ∼23.1 GPa with corresponding melting temperature of ∼1333 K, in reasonable agreement with the experimental value of 18–28 GPa.