Wu Christine J, Myint Philip C, Pask John E, Prisbrey Carrie J, Correa Alfredo A, Suryanarayana Phanish, Varley Joel B
Lawrence Livermore National Laboratory, Livermore, California 94588, United States.
College of Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, United States.
J Phys Chem A. 2021 Feb 25;125(7):1610-1636. doi: 10.1021/acs.jpca.0c09809. Epub 2021 Feb 15.
We construct a family of beryllium (Be) multiphase equation of state (EOS) models that consists of a baseline ("optimal") EOS and variations on the baseline to account for physics-based uncertainties. The Be baseline EOS is constructed to reproduce a set of self-consistent data and theory including known phase boundaries, the principal Hugoniot, isobars, and isotherms from diamond-anvil cell experiments. Three phases are considered, including the known hexagonal closed-packed (hcp) phase, the liquid, and the theoretically predicted high-pressure body-centered cubic (bcc) phase. Since both the high-temperature liquid and high-pressure bcc phases lack any experimental data, we carry out density functional theory (DFT) calculations to obtain new information about the EOS properties for these two regions. At extremely high temperature conditions (>87 eV), DFT-based quantum molecular dynamics simulations are performed for multiple liquid densities using the state-of-the-art Spectral Quadrature methodology in order to validate our selected models for the ion- and electron-thermal free energies of the liquid. We have also performed DFT simulations of hcp and bcc with different exchange-correlation functionals to examine their impact on bcc compressibility, which bound the hcp-bcc transition pressure to within 4 ± 0.5 Mbar. Our baseline EOS predicts the first density maximum along the Hugoniot to be 4.4-fold in compression, while the hcp-bcc-liquid triple-point pressure is predicted to be at 2.25 Mbar. In addition to the baseline EOS, we have generated eight variations to accommodate multiple sources of potential uncertainties such as (1) the choice of free-energy models, (2) differences in theoretical treatments, (3) experimental uncertainties, and (4) lack of information. These variations are designed to provide a reasonable representation of nonstatistical uncertainties for the Be EOS and may be used to assess its sensitivity to different inertial-confinement fusion capsule designs.
我们构建了一族铍（Be）多相状态方程（EOS）模型，该模型族由一个基线（“最优”）EOS 以及基于基线的变体组成，以考虑基于物理的不确定性。构建 Be 基线 EOS 的目的是再现一组自洽的数据和理论，包括已知的相界、主雨贡纽曲线、等压线以及金刚石对顶砧实验中的等温线。考虑了三个相，包括已知的六方密堆积（hcp）相、液相以及理论预测的高压体心立方（bcc）相。由于高温液相和高压 bcc 相都缺乏任何实验数据，我们进行了密度泛函理论（DFT）计算，以获取有关这两个区域 EOS 属性的新信息。在极高温度条件下（>87 eV），使用最先进的谱求积方法对多种液体密度进行基于 DFT 的量子分子动力学模拟，以验证我们为液体的离子热和电子热自由能所选的模型。我们还使用不同的交换关联泛函对 hcp 和 bcc 进行了 DFT 模拟，以研究它们对 bcc 压缩性的影响，这将 hcp - bcc 转变压力限制在 4 ± 0.5 Mbar 范围内。我们的基线 EOS 预测沿雨贡纽曲线的第一个密度最大值为压缩 4.4 倍，而 hcp - bcc - 液相三相点压力预测为 2.25 Mbar。除了基线 EOS 之外，我们还生成了八个变体，以适应多种潜在不确定性来源，例如（1）自由能模型的选择，（2）理论处理的差异，（3）实验不确定性，以及（4）信息缺失。这些变体旨在合理表示 Be EOS 的非统计不确定性，并且可用于评估其对不同惯性约束聚变靶丸设计的敏感性。
