Boron carbide (${\mathrm{B}}_4\mathrm{C}$) is of both fundamental scientific and practical interest due to its structural complexity and how it changes upon compression, as well as its many industrial uses and potential for use in inertial confinement fusion (ICF) and high-energy density physics experiments. We report the results of a comprehensive computational study of the equation of state (EOS) of ${\mathrm{B}}_4\mathrm{C}$ in the liquid, warm dense matter, and plasma phases. Our calculations are cross-validated by comparisons with Hugoniot measurements up to 61 megabar from planar shock experiments performed at the National Ignition Facility (NIF). Our computational methods include path integral Monte Carlo, activity expansion, as well as all-electron Green's function Korringa-Kohn-Rostoker and molecular dynamics that are both based on density functional theory. We calculate the pressure-internal energy EOS of ${\mathrm{B}}_4\mathrm{C}$ over a broad range of temperatures ($\sim 6\times {10}^3$–$5\times {10}^8$ K) and densities (0.025–50 $\mathrm{g}/{\mathrm{cm}}^3$). We assess that the largest discrepancies between theoretical predictions are $\lesssim 5\%$ near the compression maximum at 1–$2\times {10}^6$ K. This is the warm-dense state in which the K shell significantly ionizes and has posed grand challenges to theory and experiment. By comparing with different EOS models, we find a Purgatorio model (LEOS 2122) that agrees with our calculations. The maximum discrepancies in pressure between our first-principles predictions and LEOS 2122 are $\sim 18\%$ and occur at temperatures between $6\times {10}^3$–$2\times {10}^5$ K, which we believe originate from differences in the ion thermal term and the cold curve that are modeled in LEOS 2122 in comparison with our first-principles calculations. To account for potential differences in the ion thermal term, we have developed three new equation-of-state models that are consistent with theoretical calculations and experiment. We apply these new models to 1D hydrodynamic simulations of a polar direct-drive NIF implosion, demonstrating that these new models are now available for future ICF design studies.

中文翻译：

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使用计算和实验对标碳化硼状态方程

碳化硼${\mathrm{乙}}_4\mathrm{C}$）由于其结构复杂性及其在压缩时的变化方式，以及其许多工业用途以及在惯性约束聚变（ICF）和高能密度物理实验中的应用潜力，因此具有重要的科学和实践意义。我们报告了对状态方程（EOS）的全面计算研究的结果${\mathrm{乙}}_4\mathrm{C}$在液态，热致密物质和等离子体相中。通过与国家点火装置（NIF）进行的平面冲击实验中高达61兆巴的Hugoniot测量结果进行比较，我们的计算得到了交叉验证。我们的计算方法包括基于积分泛函理论的路径积分蒙特卡罗，活度展开以及全电子格林函数Korringa-Kohn-Rostoker和分子动力学。我们计算压力的内部能量EOS${\mathrm{乙}}_4\mathrm{C}$ 在很宽的温度范围内（$〜6\times {10}^3$–$5\times {10}^8$ K）和密度（0.025–50 $\mathrm{G}/{\mathrm{厘米}}^3$）。我们估计理论预测之间最大的差异是$\lesssim 5％$ 接近最大压缩率1–$2\times {10}^6$ K。这是K壳显着电离的热密状态，对理论和实验提出了巨大挑战。通过与不同的EOS模型进行比较，我们发现了与我们的计算结果吻合的Purgatorio模型（LEOS 2122）。我们的第一原则预测和LEOS 2122之间的最大压力差异为$〜\mathrm{18岁}％$ 并发生在 $6\times {10}^3$–$2\times {10}^5$ 我们认为K是由LEOS 2122中建模的离子热项和冷曲线的差异与我们的第一性原理计算得出的。为了解决离子热项中的电势差，我们开发了三个新的状态方程模型，这些模型与理论计算和实验一致。我们将这些新模型应用于极性直接驱动NIF内爆的一维流体动力学模拟，表明这些新模型现在可用于将来的ICF设计研究。