Department of Earth and Planetary Science, University of California, Berkeley, California 94720, USA.
J Chem Phys. 2017 Feb 21;146(7):074505. doi: 10.1063/1.4976559.
As one of the simple alkali metals, sodium has been of fundamental interest for shock physics experiments, but knowledge of its equation of state (EOS) in hot, dense regimes is not well known. By combining path integral Monte Carlo (PIMC) results for partially ionized states [B. Militzer and K. P. Driver, Phys. Rev. Lett. 115, 176403 (2015)] at high temperatures and density functional theory molecular dynamics (DFT-MD) results at lower temperatures, we have constructed a coherent equation of state for sodium over a wide density-temperature range of 1.93-11.60 g/cm and 10-1.29×10 K. We find that a localized, Hartree-Fock nodal structure in PIMC yields pressures and internal energies that are consistent with DFT-MD at intermediate temperatures of 2×10 K. Since PIMC and DFT-MD provide a first-principles treatment of electron shell and excitation effects, we are able to identify two compression maxima in the shock Hugoniot curve corresponding to K-shell and L-shell ionization. Our Hugoniot curves provide a benchmark for widely used EOS models: SESAME, LEOS, and Purgatorio. Due to the low ambient density, sodium has an unusually high first compression maximum along the shock Hugoniot curve. At beyond 10 K, we show that the radiation effect leads to very high compression along the Hugoniot curve, surpassing relativistic corrections, and observe an increasing deviation of the shock and particle velocities from a linear relation. We also compute the temperature-density dependence of thermal and pressure ionization processes.
作为简单碱金属之一，钠一直是冲击物理实验的基础研究对象，但对于其在热致密状态下的状态方程（EOS）知之甚少。通过结合高温下部分电离态的路径积分蒙特卡罗（PIMC）结果[B. Militzer 和 K. P. Driver, Phys. Rev. Lett. 115, 176403 (2015)]和低温下密度泛函理论分子动力学（DFT-MD）的结果，我们构建了一个涵盖广泛密度-温度范围（1.93-11.60 g/cm 和 10-1.29×10 K）的钠的连贯状态方程。我们发现，PIMC 中的局域 Hartree-Fock 节面结构产生的压力和内能与 DFT-MD 在 2×10 K 的中间温度下是一致的。由于 PIMC 和 DFT-MD 提供了电子壳层和激发效应的第一性原理处理，我们能够在冲击 Hugoniot 曲线上识别出两个与 K 壳层和 L 壳层电离对应的压缩最大值。我们的 Hugoniot 曲线为广泛使用的 EOS 模型（SESAME、LEOS 和 Purgatorio）提供了基准。由于环境密度较低，钠在冲击 Hugoniot 曲线上的第一次压缩最大值异常高。在 10 K 以上，我们表明辐射效应导致沿 Hugoniot 曲线的非常高的压缩，超过相对论修正，并观察到冲击和粒子速度从线性关系的偏差不断增加。我们还计算了热和压力电离过程的温度-密度依赖性。
