First-principles equation-of-state table of silicon and its effects on high-energy-density plasma simulations

Abstract

Using density-functional theory-based molecular-dynamics simulations, we have investigated the equation of state for silicon in a wide range of plasma density and temperature conditions of ρ=0.001-500g/cm^{3} and T=2000-10^{8}K. With these calculations, we have established a first-principles equation-of-state (FPEOS) table of silicon for high-energy-density (HED) plasma simulations. When compared with the widely used SESAME-EOS model (Table 3810), we find that the FPEOS-predicted Hugoniot is ∼20% softer; for off-Hugoniot plasma conditions, the pressure and internal energy in FPEOS are lower than those of SESAME EOS for temperatures above T ≈ 1-10 eV (depending on density), while the former becomes higher in the low-T regime. The pressure difference between FPEOS and SESAME 3810 can reach to ∼50%, especially in the warm-dense-matter regime. Implementing the FPEOS table of silicon into our hydrocodes, we have studied its effects on Si-target implosions. When compared with the one-dimensional radiation-hydrodynamics simulation using the SESAME 3810 EOS model, the FPEOS simulation showed that (1) the shock speed in silicon is ∼10% slower; (2) the peak density of an in-flight Si shell during implosion is ∼20% higher than the SESAME 3810 simulation; (3) the maximum density reached in the FPEOS simulation is ∼40% higher at the peak compression; and (4) the final areal density and neutron yield are, respectively, ∼30% and ∼70% higher predicted by FPEOS versus the traditional simulation using SESAME 3810. All of these features can be attributed to the larger compressibility of silicon predicted by FPEOS. These results indicate that an accurate EOS table, like the FPEOS presented here, could be essential for the precise design of targets for HED experiments.

First-principles equation-of-state table of beryllium based on density-functional theory calculations

“…Quantum molecular dynamics (QMD), [30][31][32] based on the density-functional theory (DFT), has proven to be a reliable method for studying the many-body quantum systems of dense plasmas. QMD simulations have been shown to work well for EOS calculations such as deuterium, 15,33 CH, 34,35 silicon, 36,37 carbon, 38 and quartz. 39 The most-recent firstprinciples calculations, 34,37 which combined the orbitalbased-DFT Kohn-Sham molecular dynamics (KSMD) and orbital-free molecular dynamics (OFMD), have established wide-ranged and consistent first-principles EOS (FPEOS) tables for CH and silicon.…”

“…QMD simulations have been shown to work well for EOS calculations such as deuterium, 15,33 CH, 34,35 silicon, 36,37 carbon, 38 and quartz. 39 The most-recent firstprinciples calculations, 34,37 which combined the orbitalbased-DFT Kohn-Sham molecular dynamics (KSMD) and orbital-free molecular dynamics (OFMD), have established wide-ranged and consistent first-principles EOS (FPEOS) tables for CH and silicon. These studies have also indicated that the observed EOS differences can have significant effects on hydro-simulations.…”

Fast and Universal Kohn Sham Density Functional Theory Algorithm for Warm Dense Matter to Hot Dense Plasma

“…However, due to the poor computational scaling (both in time and memory) of KS-DFT with temperature, its use is limited to systems typically < 10 eV. For high temperatures, more approximate orbital-free (OF-) DFT [19][20][21][22] or Path-Intergal Monte Carlo (PIMC) [23][24][25], typically within the fixed node approximation , become the standard . The cost of PIMC calculations significantly increases for lower temperatures.…”

Liquid-liquid Phase transitions in silicon

“…They manifest transient covalent binding (tr-cb) even after melting [1][2][3][4][5]. Warm-dense matter (WDM) techniques [6,7] can be used to study these materials over a broad density (ρ) and temperature (T ) range [8]. A recent study of WDM carbon provided pair-distribution functions (PDFs) g(r) and other data suggestive of a phase transition from a highly correlated WDM state to a weakly correlated plasma, driven by a change in ionization [5].…”