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

Abstract

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 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 10 6 K, 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 2.26 g/cm 3 , higher than the Thomas-Fermi predictions by about 5%. In addition, we construct new 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. (LLNL-JRNL-767019-DRAFT)

Path integral Monte Carlo and density functional molecular dynamics simulations of warm dense MgSiO3

“…It is also interesting to note that we do not see a separate L shell ionization peak. We conclude that this shell is ionized gradually, as it occurs in dense carbon and boron materials [8,64,65,100]. Excitations of K shell electrons set in at 1.01 ×10 6 K, 37700 GPa, ρ/ρ 0 = 4.26, u p = 94.8 km/s and u s = 124 km/s.…”

Thermal and Pressure Ionization in Warm, Dense MgSiO$_3$ Studied with First-Principles Computer Simulations

“…The general idea of our approach is to perform simulations along isochores at high temperatures (T 10 6 K) using PIMC and at low temperatures (T 10 6 K) using DFT-MD simulations. We find the two methods produce consistent results at overlapping temperatures [12,25].…”

“…We have constructed a consistent EOS of MgSiO 3 over a wide range of temperature and density conditions by combining results from DFT-MD and PIMC simulations in order to bridge the warm dense matter and plasma regimes [12,43]. One goal of performing high-precision computer simulations based on first principles is to guide the design of inertial confinement fusion (ICF) experiments under conditions where the K and L shell electrons are gradually ionized, which is challenging to predict accurately with analytical EOS models.…”

“…In planetary collision events, for example, the amount of heat generated during the shock can be sufficient to melt and even vaporize these minerals [9], and an accurate EOS is needed to describe these processes quantitatively. On the other hand, precise first-principles computer simulations of silicates can guide the design of inertial confinement fusion (ICF) experiments [10][11][12] under conditions where the K and L shell electrons are gradually ionized, which is challenging to predict accurately with analytical EOS models.…”

Spectral quadrature for the first principles study of crystal defects: Application to magnesium

“…It also showed that purification methods using Chebyshev polynomials are equivalent to the use of Clenshaw-Curtis quadratures. This understanding led to a series of efficient algorithms using spectral quadratures [45,58] and applications to first-principles molecular dynamics [58,67,50].…”