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

First-principles equation of state of CHON resin for inertial confinement fusion applications

A wide-range (0 to 1044.0 g/cm^{3} and 0 to 10^{9} K) equation-of-state (EOS) table for a CH_{1.72}O_{0.37}N_{0.086} quaternary compound has been constructed based on density-functional theory (DFT) molecular-dynamics (MD) calculations using a combination of Kohn-Sham DFT MD, orbital-free DFT MD, and numerical extrapolation. The first-principles EOS data are compared with predictions of simple models, including the fully ionized ideal gas and the Fermi-degenerate electron gas models, to chart their temperature-density conditions of applicability. The shock Hugoniot, thermodynamic properties, and bulk sound velocities are predicted based on the EOS table and compared to those of C-H compounds. The Hugoniot results show the maximum compression ratio of the C-H-O-N resin is larger than that of CH polystyrene due to the existence of oxygen and nitrogen; while the other properties are similar between CHON and CH. Radiation hydrodynamic simulations have been performed using the table for inertial confinement fusion targets with a CHON ablator and compared with a similar design with CH. The simulations show CHON outperforms CH as the ablator for laser-direct-drive target designs.

Unraveling the intrinsic atomic physics behind x-ray absorption line shifts in warm dense silicon plasmas

We present a free-energy density functional theory (DFT)-based methodology for optical property calculations of warm dense matter to cover a wide range of thermodynamic conditions and photon energies including the entire x-ray range. It uses Mermin-Kohn-Sham density functional theory with exchange-correlation (XC) thermal effects taken into account via a fully temperature dependent generalized gradient approximation XC functional. The methodology incorporates a combination of the ab initio molecular dynamics (AIMD) snapshotted Kubo-Greenwood optic data with a single atom in simulation cell calculations to close the photon energy gap between the L and K edges and extend the K-edge tail toward many-keV photon energies. This gap arises in the standard scheme due to a prohibitively large number of bands required for the Kubo-Greenwood calculations with AIMD snapshots. Kubo-Greenwood data on snapshots provide an accurate description of optic properties at low photon frequencies slightly beyond the L edge and x-ray absorption near edges structure (XANES) spectra, while data from periodic calculations with single atoms cover the tail regions beyond the edges. To demonstrate its applicability to mid-Z materials where the standard DFT-based approach is not computationally feasible, we have applied it to opacity calculations of warm dense silicon plasmas. These first-principles calculations revealed a very interesting phenomenon of redshift-to-blueshift in K-L (1s→2p) and K-edge absorptions along both isotherm and isochore, which are absent in most continuum-lowering models of traditional plasma physics. This new physics phenomenon can be attributed to the underlying competition between the screening of deeply bound core electrons and the screening of outer-shell electrons caused by warm-dense-plasma conditions. We further demonstrate that the ratio of 1s→2p to the K-edge x-ray absorptions can be used to characterize warm-dense-plasma conditions. Eventually, based on our absorption calculations, we have established a first-principles opacity table (FPOT) for silicon in a wide range of material densities and temperatures.

Liquid-Liquid Phase Transitions in Silicon

We use computationally simple neutral pseudoatom ("average atom") density functional theory (DFT) and standard DFT to elucidate liquid-liquid phase transitions (LPTs) in liquid silicon. An ionization-driven transition and three LPTs including the known LPT near 2.5  g/cm^{3} are found. They are robust even to 1 eV. The pair distributions functions, pair potentials, electrical conductivities, and compressibilites are reported. The LPTs are elucidated within a Fermi liquid picture of electron scattering at the Fermi energy that complements the transient covalent bonding picture.

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

Understanding many processes, e.g., fusion experiments, planetary interiors, and dwarf stars, depends strongly on microscopic physics modeling of warm dense matter and hot dense plasma. This complex state of matter consists of a transient mixture of degenerate and nearly free electrons, molecules, and ions. This regime challenges both experiment and analytical modeling, necessitating predictive ab initio atomistic computation, typically based on quantum mechanical Kohn-Sham density functional theory (KS-DFT). However, cubic computational scaling with temperature and system size prohibits the use of DFT through much of the warm dense matter regime. A recently developed stochastic approach to KS-DFT can be used at high temperatures, with the exact same accuracy as the deterministic approach, but the stochastic error can converge slowly and it remains expensive for intermediate temperatures (<50  eV). We have developed a universal mixed stochastic-deterministic algorithm for DFT at any temperature. This approach leverages the physics of KS-DFT to seamlessly integrate the best aspects of these different approaches. We demonstrate that this method significantly accelerated self-consistent field calculations for temperatures from 3 to 50 eV, while producing stable molecular dynamics and accurate diffusion coefficients.

Pressure in warm and hot dense matter using the average-atom model

Expressions of pressure in warm and hot dense matter using the average-atom model are presented. They are based on the stress-tensor approach. Nonrelativistic and relativistic cases are considered. The obtained formulas are simple and can be easily implemented in an average-atom model code. Comparisons with experimental data and quantum molecular dynamics and path integral Monte Carlo simulations are shown. The present formalism agrees well with experimental results for a large variety of elements in the warm dense matter regime and with ab initio simulations in the warm and hot dense matter regime for aluminum.

Anharmonic and Anomalous Trends in the High-Pressure Phase Diagram of Silicon

A multifaceted first-principles approach utilizing density functional theory, evolutionary algorithms, and lattice dynamics was used to construct the phase diagram of silicon up to 4 TPa and 26 000  K. These calculations predicted that (i) an anomalous sequence of face-centered cubic to body-centered cubic to simple cubic crystalline phase transitions occur at pressures of 2.87 and 3.89 TPa, respectively, along the cold curve, (ii) the orthorhombic phases of Imma and Cmce-16 appear on the phase diagram only when the anharmonic contribution to the Gibbs free energy is taken into account, and (iii) a substantial change in the slope of the principal Hugoniot is observed if the anharmonic free energy of the cubic diamond phase is considered.

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

Beryllium has been considered a superior ablator material for inertial confinement fusion (ICF) target designs. An accurate equation-of-state (EOS) of beryllium under extreme conditions is essential for reliable ICF designs. Based on density-functional theory (DFT) calculations, we have established a wide-range beryllium EOS table of density ρ = 0.001 to 500 g/cm3 and temperature T = 2000 to 108 K. Our first-principle equation-of-state (FPEOS) table is in better agreement with the widely used SESAME EOS table (SESAME 2023) than the average-atom INFERNO and Purgatorio models. For the principal Hugoniot, our FPEOS prediction shows ∼10% stiffer than the last two models in the maximum compression. Although the existing experimental data (only up to 17 Mbar) cannot distinguish these EOS models, we anticipate that high-pressure experiments at the maximum compression region should differentiate our FPEOS from INFERNO and Purgatorio models. Comparisons between FPEOS and SESAME EOS for off-Hugoniot conditions show that the differences in the pressure and internal energy are within ∼20%. By implementing the FPEOS table into the 1-D radiation-hydrodynamic code LILAC, we studied the EOS effects on beryllium-shell-target implosions. The FPEOS simulation predicts higher neutron yield (∼15%) compared to the simulation using the SESAME 2023 EOS table.