Equation of state and shock compression of warm dense sodium—A first-principles study

Abstract

As one of the simple alkali metals, sodium has been of fundamental interest for shock physics experiments, but knowledge of its equation of state (EOS) in hot, dense regimes is not well known. By combining path integral Monte Carlo (PIMC) results for partially-ionized states [B. Militzer and K. P. Driver, Phys. Rev. Lett. 115, 176403 (2015)] at high temperatures and density functional theory molecular dynamics (DFT-MD) results at lower temperatures, we have constructed a coherent equation of state for sodium over a wide densitytemperature range of 1.93 − 11.60 g/cm 3 and 10 3 − 1.29 × 10 8 K. We find that a localized, Hartree-Fock nodal structure in PIMC yields pressures and internal energies that are consistent with DFT-MD at intermediate temperatures of 2×10 6 K. Since PIMC and DFT-MD provide a first-principles treatment of electron shell and excitation effects, we are able to identify two compression maxima in the shock Hugoniot curve corresponding to K-shell and L-shell ionization. Our Hugoniot curves provide a benchmark for widely-used EOS models, SESAME, LEOS, and Purgatorio. Due to the low ambient density, sodium has an unusually high first compression maximum along the shock Hugoniot curve. At beyond 10 7 K, we show that the radiation effect leads to very high compression along the Hugoniot curve, surpassing relativistic corrections, and observe an increasing deviation of the shock and particle velocities from a linear relation. We also compute the temperature-density dependence of thermal and pressure ionization processes.

Path integral Monte Carlo simulations of warm dense aluminum

“…Rigorous discussions of the PIMC [76][77][78] and DFT molecular dynamics (DFT-MD) [79][80][81] methods have been provided in previous works, and the details of our simulations have been presented in some of our previous publications [74,75,[82][83][84][85][86][87][88][89][90][91][92][93]. Here, we summarize the methods and provide the simulation parameters specific to simulations of aluminum plasma.…”

“…PIMC uses a small number of controlled approximations, whose errors can be minimized by converging parameters, such as the time step and system size. To address the fermion sign problem, we used the restricted path approach with Hartree-Fock nodes [75,90]. The nodes were enforced in imaginary time steps of 1/8192 Ha, while the pair density matrices were evaluated in steps of 1/1024 Ha.…”

Magnesium oxide at extreme temperatures and pressures studied with first-principles simulations

“…In subsequent articles, this method was applied to study hydrogen [53][54][55][56][57][58], helium [29,39,59], hydrogen-helium mixtures [60] and one-component plasmas [61][62][63]. In recent years, the PIMC method was extended to simulate plasmas of various first-row elements [30,40,47,[64][65][66] and with the development of Hartree-Fock nodes, the simulations of second-row elements became possible [32,[36][37][38].…”

Influence of shell effects on thermodynamic properties of matter at high pressures

“…However, interaction effects are still quite strong in the region of shockinduced ionization in metals therefore first-principle simulations of shock Hugoniots may shed light on the magnitude of shell effects at very high pressures. Pronounced shell effects on the shock Hugoniot of sodium have been predicted recently using the restricted PIMC method [66]; however, this approach is based upon the single-particle fixed-node approximation which introduces an uncontrollable error to the results. Among other methods, QMD shows excellent results for shock Hugoniots (see [50] and references therein) and melting curves [67,68] of different materials at low and moderate pressures.…”