Ab initio calculation of lattice dynamics and thermodynamic properties of beryllium

Abstract

Thermal equation of state and thermodynamic Grüneisen parameter of beryllium metalWe investigate the phase transition, elastic constants, phonon dispersion curves, and thermal properties of beryllium (Be) at high pressures and high temperatures using density functional theory. By comparing the Gibbs free energy, in the quasiharmonic approximation (QHA), of hexagonal-closed-packed (hcp) with those of the face-centered cubic (fcc) and body-centered-cubic (bcc) we find that the hcp Be is stable up to 390 GPa, and then transforms to the bcc Be. The calculated phonon dispersion curves are in excellent agreement with experiments. Under compression, the phonon dispersion curves of hcp Be do not show any anomaly or instability. At low pressure the phonon dispersion of bcc Be display imaginary along C-N in the T 1 branches. Within the quasiharmonic approximation, we predict the thermal equation of state and other properties including the thermal expansion coefficient, Hugoniot curves, heat capacity, Grüneisen parameter, and Debye temperature.

Premelting hcp to bcc Transition in Beryllium

“…At P > 11 GPa, bcc Be is dynamically stabilized by pressure and the QHA might, in principle, be applied. However, the hcp/bcc boundary [23][24][25] predicted by the QHA does not agree with experiments [13], suggesting that anharmonic effects still play an important role at higher pressures.In this Letter, we report a new investigation of the phase stability of bcc Be and the associated hcp → bcc phase transition boundary up to 30 GPa and temperatures up to 2,000 K. We have used a recently developed hybrid approach [30,31] that combines first-principles molecular dynamics (MD) and lattice dynamics calculations to address anharmonic effects in the free energy. In this method, the concept of phonon quasiparticles offers a quantitative characterization of the effects of lattice anharmonicity [32,33].…”

“…It is seen that at T ≥ 1, 200 K, V bcc > V hcp , and consistently, the common tangent to these curves starts to have negative slope, indicating a transition from hcp to bcc at positive pressure. We note that the volumetric variations of both phases also provide clues to understand the predicted hcp/bcc transition at very high P (e.g., 400 GPa) [23][24][25]. More details of the variation of V bcc and V hcp is shown in Fig.…”

“…Since hcp Be is stable at low T for the entire pressure range of interest, the lattice thermal properties have been studied within the QHA [23][24][25] without further examination of the validity of the approximation. This naturally brings up a question: how important are anharmonic effects in the free energy in this seemingly stable structure?…”

“…On the theory side, the study of Be's phase diagram using conventional methods encounters significant difficulties. The lattice dynamics of bcc Be is highly anharmonic, and the widely used quasi-harmonic approximation (QHA) and Debye model are not able to capture such effect [23][24][25][26][27][28][29]. For this reason, bcc Be and the associated hcp/bcc phase transition remain poorly understood for P < 11 GPa (density < 2.1g/cc) where bcc Be is dynamically unstable at 0 K [24].…”

High-pressure–temperature phase diagram and the equation of state of beryllium

“…Also, under pressure Be is predicted to exhibit multiple solid phases which are very close in energy, with their relative stability affected by anharmonic effects at high T [4][5][6][7] . There have been some experimental reports of a new high-temperature phase: β-Be, with its structure interpreted as body-centered cubic (bcc) 8,9 or hexagonal 11 , which was later re-interpreted 12 , suggesting a smaller 4-atom orthorhombic (distorted hcp) unit cell instead.…”