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.