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

Properties of carbon up to 10 million kelvin from Kohn-Sham density functional theory molecular dynamics

Accurately modeling dense plasmas over wide-ranging conditions of pressure and temperature is a grand challenge critically important to our understanding of stellar and planetary physics as well as inertial confinement fusion. In this work, we employ Kohn-Sham density functional theory (DFT) molecular dynamics (MD) to compute the properties of carbon at warm and hot dense matter conditions in the vicinity of the principal Hugoniot. In particular, we calculate the equation of state (EOS), Hugoniot, pair distribution functions, and diffusion coefficients for carbon at densities spanning 8 g/cm^{3} to 16 g/cm^{3} and temperatures ranging from 100 kK to 10 MK using the Spectral Quadrature method. We find that the computed EOS and Hugoniot are in good agreement with path integral Monte Carlo results and the sesame database. Additionally, we calculate the ion-ion structure factor and viscosity for selected points. All results presented are at the level of full Kohn-Sham DFT-MD, free of empirical parameters, average-atom, and orbital-free approximations employed previously at such conditions.

The phase diagrams of beryllium and magnesium oxide at megabar pressures

We performab initiosimulations of beryllium (Be) and magnesium oxide (MgO) at megabar pressures and compare their structural and thermodynamic properties. We make a detailed comparison of our two recently derived phase diagrams of Be (Wuet al2021Phys. Rev.B104014103) and MgO (Soubiran and Militzer 2020Phys. Rev. Lett.125175701) using the thermodynamic integration technique, as they exhibit striking similarities regarding their shape. We explore whether the Lindemann criterion can explain the melting temperatures of these materials through the calculation of the Debye temperature at high pressure. From our free energy calculations, we find that the melting line of both materials is well represented by the Simon-Glazel fitT_m(P) =T₀(1 +P/a)^1/c, whereT₀= 1564 K,a= 15.8037 GPa andc= 2.4154 for Be, whileT₀= 3010 K,a= 10.5797 GPa andc= 2.8683 for the MgO in the B1. For the B2 phase, we use the valuesa= 26.1163 GPa andc= 2.2426. Both materials exhibit negative Clapeyron slopes on the boundaries between the two solid phases that are strongly affected by anharmonic effects, which also influence the location of the solid-solid-liquid triple point. We find that the quasi-harmonic approximation underestimates the stability range of the low-pressure phases, namely hcp for Be and B1 for MgO. We also compute the phonon dispersion relations at low and high pressure for each of the phases of these materials, and also explore how the phonon density of states is modified by temperature. Finally, we derive secondary shock Hugoniot curves in addition to the principal Hugoniot curve for both materials, and study their offsets in pressure between solid and liquid branches.

Minimization of Gibbs Energy in High-Pressure Multiphase, Multicomponent Mixtures through Particle Swarm Optimization

We present a global optimization method to construct phase boundaries in multicomponent mixtures by minimizing the Gibbs energy. The minimization method is, in essence, an extension of the Maxwell construction procedure that is used in single-component systems. For a given temperature, pressure, and overall mixture composition, it reveals the mole fractions of the thermodynamically stable phases and the composition of these phases. Our approach is based on particle swarm optimization (PSO), which is a gradient-free, stochastic method. It is not reliant on good initial guesses for the phase fractions and compositions, which is an important requirement for the high-pressure applications considered in this study because data on phase boundaries at high pressures tend to be extremely limited. One practical use of this method is to create equation-of-state tables needed by continuum-scale, multiphysics codes that are ubiquitous in high-pressure science. Currently, there does not exist a method to generate such tables that rigorously account for changes in phase boundaries due to mixing. We have done extensive testing to demonstrate that PSO can reliably determine the Gibbs energy minimum and can capture nontrivial features like eutectic and peritectic temperatures to produce coherent phase diagrams. As part of our testing, we have developed a PSO-based Helmholtz-energy minimization procedure that we have used to cross-check the results of the Gibbs energy minimization. We conclude with a critique of our approach and provide suggestions for future work, including a PSO-based entropy-maximization method that would enable the aforementioned continuum codes to perform on-the-fly, phase-equilibria calculations of multicomponent mixtures.