Equation of state and strength of diamond in high pressure ramp loading

Diamond is used extensively as a component in high energy density experiments, but existing equation of state (EOS) models do not capture its observed response to dynamic loading. In particular, in contrast with first principles theoretical EOS models, no solid-solid phase changes have been detected, and no general-purpose EOS models match the measured ambient isotherm. We have performed density functional theory (DFT) calculations of the diamond phase to ~10TPa, well beyond its predicted range of thermodynamic stability, and used these results as the basis of a Mie-Greuneisen EOS. We also performed DFT calculations of the elastic moduli, and calibrated an algebraic elasticity model for use in simulations. We then estimated the flow stress of diamond by comparison with the stress-density relation measured experimentally in ramp-loading experiments. The resulting constitutive model allows us to place a constraint on the Taylor-Quinney factor (the fraction of plastic work converted to heat) from the observation that diamond does not melt on ramp compression

Theoretical and experimental investigation of the equation of state of boron plasmas

We report a theoretical equation of state (EOS) table for boron across a wide range of temperatures (5.1$\times$10$^4$-5.2$\times$10$^8$ K) and densities (0.25-49 g/cm$^3$), and experimental shock Hugoniot data at unprecedented high pressures (5608$\pm$118 GPa). The calculations are performed with full, first-principles methods combining path integral Monte Carlo (PIMC) at high temperatures and density functional theory molecular dynamics (DFT-MD) methods at lower temperatures. PIMC and DFT-MD cross-validate each other by providing coherent EOS (difference $<$1.5 Hartree/boron in energy and $<$5% in pressure) at 5.1$\times$10$^5$ K. The Hugoniot measurement is conducted at the National Ignition Facility using a planar shock platform. The pressure-density relation found in our shock experiment is on top of the shock Hugoniot profile predicted with our first-principles EOS and a semi-empirical EOS table (LEOS 50). We investigate the self diffusivity and the effect of thermal and pressure-driven ionization on the EOS and shock compression behavior in high pressure and temperature conditions We study the performance sensitivity of a polar direct-drive exploding pusher platform to pressure variations based on comparison of the first-principles calculations with LEOS 50 via 1D hydrodynamic simulations. The results are valuable for future theoretical and experimental studies and engineering design in high energy density research. (LLNL-JRNL-748227)Comment: 12 pages, 9 figures, 2 table

Equation of state of warm-dense boron nitride combining computation, modeling, and experiment

The equation of state (EOS) of materials at warm dense conditions poses significant challenges to both theory and experiment. We report a combined computational, modeling, and experimental investigation leveraging new theoretical and experimental capabilities to investigate warm-dense boron nitride (BN). The simulation methodologies include path integral Monte Carlo (PIMC), several density functional theory (DFT) molecular dynamics methods [plane-wave pseudopotential, Fermi operator expansion (FOE), and spectral quadrature (SQ)], activity expansion (ACTEX), and all-electron Green's function Korringa-Kohn-Rostoker (MECCA), and compute the pressure and internal energy of BN over a broad range of densities ($\rho$) and temperatures ($T$). Our experiments were conducted at the Omega laser facility and measured the Hugoniot of BN to unprecedented pressures (12--30 Mbar). The EOSs computed using different methods cross validate one another, and the experimental Hugoniot are in good agreement with our theoretical predictions. We assess that the largest discrepancies between theoretical predictions are $<$4% in pressure and $<$3% in energy and occur at $10^6$ K. We find remarkable consistency between the EOS from DFT calculations performed on different platforms and using different exchange-correlation functionals and those from PIMC using free-particle nodes. This provides strong evidence for the accuracy of both PIMC and DFT in the warm-dense regime. Moreover, SQ and FOE data have significantly smaller error bars than PIMC, and so represent significant advances for efficient computation at high $T$. We also construct tabular EOS models and clarify the ionic and electronic structure of BN over a broad $T-\rho$ range and quantify their roles in the EOS. The tabular models may be utilized for future simulations of laser-driven experiments that include BN as a candidate ablator material.Comment: 19 pages, 14 figures, 4 table

Equation of state of boron nitride combining computation, modeling, and experiment

The equation of state (EOS) of materials at warm dense conditions poses significant challenges to both theory and experiment. We report a combined computational, modeling, and experimental investigation leveraging new theoretical and experimental capabilities to investigate warm-dense boron nitride (BN). The simulation methodologies include path integral Monte Carlo (PIMC), several density functional theory (DFT) molecular dynamics methods [plane-wave pseudopotential, Fermi operator expansion (FOE), and spectral quadrature (SQ)], activity expansion (actex), and all-electron Green\u27s function Korringa-Kohn-Rostoker (mecca), and compute the pressure and internal energy of BN over a broad range of densities and temperatures. Our experiments were conducted at the Omega laser facility and the Hugoniot response of BN to unprecedented pressures (1200–2650 GPa). The EOSs computed using different methods cross validate one another in the warm-dense matter regime, and the experimental Hugoniot data are in good agreement with our theoretical predictions. By comparing the EOS results from different methods, we assess that the largest discrepancies between theoretical predictions are ≲4% in pressure and ≲3% in energy and occur at 106K, slightly below the peak compression that corresponds to the K-shell ionization regime. At these conditions, we find remarkable consistency between the EOS from DFT calculations performed on different platforms and using different exchange-correlation functionals and those from PIMC using free-particle nodes. This provides strong evidence for the accuracy of both PIMC and DFT in the high-pressure, high-temperature regime. Moreover, the recently developed SQ and FOE methods produce EOS data that have significantly smaller statistical error bars than PIMC, and so represent significant advances for efficient computation at high temperatures. The shock Hugoniot predicted by PIMC, actex, and mecca shows a maximum compression ratio of 4.55±0.05 for an initial density of 2.26g/cm3, higher than the Thomas-Fermi predictions by about 5%. In addition, we construct tabular EOS models that are consistent with the first-principles simulations and the experimental data. Our findings clarify the ionic and electronic structure of BN over a broad range of temperatures and densities and quantify their roles in the EOS and properties of this material. The tabular models may be utilized for future simulations of laser-driven experiments that include BN as a candidate ablator material

Author Correction: Interferometric measurements of refractive index and dispersion at high pressure

An amendment to this paper has been published and can be accessed via a link at the top of the paper

X-ray diffraction of molybdenum under ramp compression to 1 TPa

Molybdenum (Mo) is a transition metal with a wide range of technical applications. There has long been strong interest in its high-pressure behavior, and it is often used as standard for high-pressure experiments. Combining powder x-ray diffraction and dynamic ramp compression, structural and equation of state data were collected for solid Mo to 1 TPa (10 Mbar). Diffraction results are consistent with Mo remaining in the body-centered-cubic structure into the TPa regime. Stress-density data show that Mo under ramp loading is less compressible than the room-temperature isotherm but more compressible than the single-shock Hugoniot