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.

Experimental investigation of the shock response of bismuth under one-dimensional shock-loading

“…However, the response of the rear surface gauge is more complex, with a dual-stage rise apparent. This inflection during the rise occurs at 2.75 GPa and is consistent with the known Bi-I Bi-II and Bi-II Bi-III phase transitions which occur at ~2.6 and 2.8 GPa respectively [1]. Shock velocities presented in Fig.…”

“…Bismuth is a post-transition metal which shows a series of clear phase changes under relatively low pressure shock loading, key amongst which are [1][2][3][4]: phase I II (rhombohedral monoclinic) [~2.6 GPa]; phase II III (body-centred tetragonal; bct) [2.8 GPa]; phase III V (body-centred cubic; bcc) [c.a. 7 -7.7 GPa].…”

Femtosecond diffraction studies of solid and liquid phase changes in shock-compressed bismuth

“…We observe Bi-V at conditions where it was previously thought to be elastically unstable under dynamic compression 16 . The measured lattice parameter of the Bi-V phase at these low pressures is typically a = 3.87 Å ( V / V 0 = 0.82), entirely consistent with that estimated by extrapolating the room-temperature static compression data for Bi-V down to this pressure 26 (Fig.…”

“…Similarly, while the melting behavior of Bi upon dynamic loading and unloading has been the subject of numerous theoretical and experimental studies 14 – 16 , nothing is known about the structure of the liquid at the very high-pressure conditions (>8 GPa) where melting is predicted to occur under shock compression. Given the number of solid-state phase transformations, and known liquid structural changes at lower pressure 17 , 18 , there is a pressing need to establish liquid structural properties at higher pressures such as above the shock melting point.…”

Lattice Dynamics Study of Elemental Bismuth under High Pressure

“…Given the exotic nature of some HP crystal structures of elemental Bi such as the host–guest structure Bi-III, a study of their lattice dynamics is notably interesting to understand the guest dynamics in the Bi-III phase, as it can permit a better understanding of the coupling between phonons and electrons, which produces the low-T superconductivity in HP phases of Bi. Until now, the DFT lattice dynamics calculations using different exchange-correlation functionals have focused on the simpler phase I − and only one such calculation was performed on phase V . Only very recently, two new studies have focused on calculations of the lattice dynamics of the Bi-III phase but only using DFT. , The phonon density of states (DOS) has been calculated for the Bi-II phase very recently .…”