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Boron carbide (B$_4$C) is of both fundamental scientific and practicalinterest in inertial confinement fusion (ICF) and high energy density physicsexperiments. We report the results of a comprehensive computational study ofthe equation of state (EOS) of B$_4$C in the liquid, warm dense matter, andplasma phases. Our calculations are cross-validated by comparisons withHugoniot measurements up to 61 megabar from planar shock experiments performedat the National Ignition Facility (NIF). Our computational methods include pathintegral Monte Carlo, activity expansion, as well as all-electron Green'sfunction Korringa-Kohn-Rostoker and molecular dynamics that are both based ondensity functional theory. We calculate the pressure-internal energy EOS ofB$_4$C over a broad range of temperatures($\sim$6$\times$10$^3$--5$\times$10$^8$ K) and densities (0.025--50g/cm$^{3}$). We assess that the largest discrepancies between theoreticalpredictions are $\lesssim$5% near the compression maximum at 1--2$\times10^6$K. This is the warm-dense state in which the K shell significantly ionizes andhas posed grand challenges to theory and experiment. By comparing withdifferent EOS models, we find a Purgatorio model (LEOS 2122) that agrees withour calculations. The maximum discrepancies in pressure between ourfirst-principles predictions and LEOS 2122 are $\sim$18% and occur attemperatures between 6$\times$10$^3$--2$\times$10$^5$ K, which we believeoriginate from differences in the ion thermal term and the cold curve that aremodeled in LEOS 2122 in comparison with our first-principles calculations. Inaddition, we have developed three new equation of state models and applied themto 1D hydrodynamic simulations of a polar direct-drive NIF implosion,demonstrating that these new models are now available for future ICF designstudies.

Benchmarking boron carbide equation of state using computation and experiment