Premelting hcp to bcc Transition in Beryllium

Phase transition of Fe under extreme conditions studied by using an anharmonic phonon approach based on machine learning force fields

The phase transition structure and dynamical mechanisms of solid-state bcc phase iron (Fe) under extreme conditions remain an open question. This study systematically investigates the phase transition process and dynamical mechanisms of solid Fe at 0-1000 K and 0-30 GPa by combining machine learning force field molecular dynamics simulations and an anharmonic phonon approach. Considering the high-temperature anharmonic effects, we calculated and compared the Helmholtz and Gibbs free energies of bcc, hcp, and fcc phase Fe. At zero temperature, Fe transitions from the bcc phase to the hcp phase at 13.83 GPa. Due to the influence of temperature anharmonic effects, this transition pressure increases with rising temperature, reaching 17.20 GPa at 1000 K. During the bcc → hcp phase transition, the Gibbs free energy of the fcc phase is always higher than that of the bcc or hcp phases, indicating that the fcc phase is a metastable phase. The transverse acoustic branch (TA1) is the most sensitive to temperature and pressure, exhibiting frequency softening phenomena during the phase transition, which is the origin of the dynamic instability and strong phonon anharmonicity of the bcc phase. According to the phonon vibration polarization vector, the vibrational modes of the TA1 mode near the Γ point provide a continuous phase transition geometric pathway for the bcc phase to transition to the hcp phase through the intermediate fcc phase. These theoretical results support the experimental two-step phase transition viewpoint of Fe from bcc to hcp under high temperature and high pressure.

Unveiling the effect of Ni on the formation and structure of Earth's inner core

Ni is the second most abundant element in the Earth's core. Yet, its effects on the inner core's structure and formation process are usually disregarded because of its electronic and size similarity with Fe. Using ab initio molecular dynamics simulations, we find that the bcc phase can spontaneously crystallize in liquid Ni at temperatures above Fe's melting point at inner core pressures. The melting temperature of Ni is shown to be 700 to 800 K higher than that of Fe at 323 to 360 GPa. hcp, bcc, and liquid phase relations differ for Fe and Ni. Ni can be a bcc stabilizer for Fe at high temperatures and inner core pressures. A small amount of Ni can accelerate Fe's crystallization at core pressures. These results suggest that Ni may substantially impact the structure and formation process of the solid inner core.

Toward better understanding of the high-pressure structural transformation in beryllium by the statistical moment method

Beryllium is a vital alkaline-earth metal for plasma physics, space science, and nuclear technology. Unfortunately, its accurate phase diagram is clouded by many controversial results, even though solid beryllium can only exist with hcp or bcc crystalline structures. Herein, we offer a simple quantum-statistical solution to the above problem. Our core idea is to develop the moment expansion technique to determine the Helmholtz free energy under extreme conditions. This strategy helps elucidate the underlying correlation among symmetric characteristics, vibrational excitations, and physical stabilities. In particular, our analyses reveal that the appearance of anharmonic effects forcefully straightens up the hcp-bcc boundary. This phenomenon explains why it has been difficult to detect bcc signatures via diamond-anvil-cell measurements. Besides, we modify the work-heat equivalence principle to quickly obtain the high-pressure melting profile from the room-temperature equation of state. The hcp-bcc-liquid triple point of beryllium is found at 165 GPa and 4559 K. Our theoretical findings agree excellently with cutting-edge ab initio simulations adopting the phonon quasiparticle method and the thermodynamic integration. Finally, we consider the principal Hugoniot curve and its secondary branches to explore the behaviors of beryllium under shock compression. Our predictions would be advantageous for designing inertial-confinement-fusion experiments.

Development of a Multiphase Beryllium Equation of State and Physics-based Variations

We construct a family of beryllium (Be) multiphase equation of state (EOS) models that consists of a baseline ("optimal") EOS and variations on the baseline to account for physics-based uncertainties. The Be baseline EOS is constructed to reproduce a set of self-consistent data and theory including known phase boundaries, the principal Hugoniot, isobars, and isotherms from diamond-anvil cell experiments. Three phases are considered, including the known hexagonal closed-packed (hcp) phase, the liquid, and the theoretically predicted high-pressure body-centered cubic (bcc) phase. Since both the high-temperature liquid and high-pressure bcc phases lack any experimental data, we carry out ab initio density functional theory (DFT) calculations to obtain new information about the EOS properties for these two regions. At extremely high temperature conditions (>87 eV), DFT-based quantum molecular dynamics simulations are performed for multiple liquid densities using the state-of-the-art Spectral Quadrature methodology in order to validate our selected models for the ion- and electron-thermal free energies of the liquid. We have also performed DFT simulations of hcp and bcc with different exchange-correlation functionals to examine their impact on bcc compressibility, which bound the hcp-bcc transition pressure to within 4 ± 0.5 Mbar. Our baseline EOS predicts the first density maximum along the Hugoniot to be 4.4-fold in compression, while the hcp-bcc-liquid triple-point pressure is predicted to be at 2.25 Mbar. In addition to the baseline EOS, we have generated eight variations to accommodate multiple sources of potential uncertainties such as (1) the choice of free-energy models, (2) differences in theoretical treatments, (3) experimental uncertainties, and (4) lack of information. These variations are designed to provide a reasonable representation of nonstatistical uncertainties for the Be EOS and may be used to assess its sensitivity to different inertial-confinement fusion capsule designs.

Temperature effect on the phase stability of hydrogenC2/cphase from first-principles molecular dynamics calculations

The structural stability of hydrogenC2/cphase from 0 K to 300 K is investigated by combining the first-principles molecular dynamics (MD) simulations and density functional perturbation theory. Without considering the temperature effect, theC2/cphase is stable from 150 GPa to 250 GPa based on the harmonic phonon dispersion relations. The hydrogen molecules at the solid lattice sites are sensitive to temperature. The structural stability to instability transition of theC2/cphase upon temperature is successfully captured by the radial distribution function and probability distribution of atomic displacements from first-principles MD simulations, confirmed by the phonon power spectrum analysis in the phase space. The existence of phonon quasiparticle for different normal modes is observed directly. The phonon power spectrum of specific normal modes corresponding to the Raman and infrared (IR) activations are depicted at different temperatures and pressures. The changes of frequency with temperature are in agreement with experimental results, supporting theC2/cas the hydrogen phase III. For the first time, the anharmonic phonon dispersion curves and density of states are predicted based on the phonon quasi-particle approach. Therefore, the temperature dependence of lattice vibrations can be observed directly, providing a more complete physical picture of phonon frequency distribution with respect to the Raman and IR spectra. It is found that the high-frequency regions adopt significant frequency shifts compared to the harmonic case.

Lattice thermal conductivity of monolayer AsP from first-principles molecular dynamics

Our first-principles molecular dynamics simulation demonstrates that puckered AsP monolayer has reduced thermal conductivity and increased anisotropy as compared to black phosphorene.

Two-phase thermodynamic model for computing entropies of liquids reanalyzed

The two-phase thermodynamic (2PT) model [S.-T. Lin et al., J. Chem. Phys. 119, 11792-11805 (2003)] provides a promising paradigm to efficiently determine the ionic entropies of liquids from molecular dynamics. In this model, the vibrational density of states (VDoS) of a liquid is decomposed into a diffusive gas-like component and a vibrational solid-like component. By treating the diffusive component as hard sphere (HS) gas and the vibrational component as harmonic oscillators, the ionic entropy of the liquid is determined. Here we examine three issues crucial for practical implementations of the 2PT model: (i) the mismatch between the VDoS of the liquid system and that of the HS gas; (ii) the excess entropy of the HS gas; (iii) the partition of the gas-like and solid-like components. Some of these issues have not been addressed before, yet they profoundly change the entropy predicted from the model. Based on these findings, a revised 2PT formalism is proposed and successfully tested in systems with Lennard-Jones potentials as well as many-atom potentials of liquid metals. Aside from being capable of performing quick entropy estimations for a wide range of systems, the formalism also supports fine-tuning to accurately determine entropies at specific thermal states.