Automated Calibrated Modeling Method of Multiphase Equations of States: Applied to Tin
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摘要: 状态方程与描述能量、动量、质量守恒的偏微分方程一起，构成了可求解材料动态压缩行为的完备流体力学方程组。动态压缩下，相变会导致材料内能、密度、强度等物理性质的不连续变化，需要构建多相状态方程模型才能精确描述这些变化。通过多相状态方程模型的自动组装，采用计算机智能优化算法自动校准状态方程模型参数，发展了自动化的多相状态方程建模程序AEOS（automated equation of state）。利用AEOS，构建了锡的3套状态方程模型，3套模型的计算结果与相关实验结果基本一致，验证了AEOS程序的适用性。将构建的状态方程模型应用于一维流体力学模拟，发现锡冲击到17 GPa再等熵卸载到常压的压力-温度路径会经过β相-体心四方相-液相三相点，并且可以很好地解释在15.4 GPa的冲击压力下锡的微喷颗粒呈现固-液混合态的实验现象。AEOS的良好表现证明其在大型数字化科研平台以及高通量材料物性计算中将具有广泛的应用前景。Abstract: Equations of state (EOS), combined with the partial differential equations of describing conservations of energy, momentum and mass, form a complete set of fluid dynamics equations on solving dynamic compression behaviors of material. Under dynamic compression, phase transition of material may lead to discontinuous changes of its internal energy, density, strength and other properties, and a multiphase EOS is needed to accurately describe these changes. An automated modeling code of multiphase equations of state (AEOS) is developed, which can construct multiphase EOS model in an automatic way and calibrate parameters of EOS models with a computer intelligent optimization algorithm. By applying AEOS to tin, we obtain three sets of multiphase EOSs. The theoretical results of all the three sets of EOSs are consistent well with the experimental results, which validates the good performance of the AEOS code. And we find that the isentropic release path of tin passes through the three-phase point of the β, the body centered tetragonal (bct), and the liquid phases, when tin is impacted to 17 GPa and then isentropically released to atmospheric pressure. In addition, this result can well explain the experimental phenomenon that tin ejection particles are in a solid-liquid mixture state under the very low impact pressure of 15.4 GPa. The good performance of AEOS insures that it can be widely applied to integrated digital scientific research platforms and scenarios of high-flux material property calculations in the near future.
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Key words:
- multiphase equation of state /
- automated calibrating /
- high pressure /
- tin
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图 1 AEOS建模程序的基本功能组成和建模流程示意图
Figure 1. Basic functional components of the AEOS program and a schematic diagram of the modeling process
图 2 压力-温度相图中的压力-温度网格以及纯相区、相边界、三相点的指标化方法示意图
Figure 2. Pressure-temperature meshes in the p-T phase diagram and the schematic diagram of the digital representation method of the pure phase regions, the phase boundaries and the three-phase points
图 3 由AEOS模型1计算的锡的高压物性理论结果与实验结果对比
Figure 3. Comparison of the high-pressure compression properties of tin between the experimental results and the theoretical results calculated by AEOS model 1
表 1 锡的固-液两相状态方程模型１的校准参数
Table 1. Calibrated parameters of the solid-liquid two-phase EOS model 1 for tin
V0/(cm3·g−1) C/(km·s−1) S γ a Ne 0.1341 2.612 1.482 1.47 0 4.0 ΔS Tm0/K γ0m am 1.16R 836.9 2.20 0.035 
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表 2 锡的多相状态方程模型2的校准参数
Table 2. Calibrated parameters of the multiphase EOS model 2 for tin
Phase E0/(J·g−1) V0/(cm3·g−1) B0/GPa a1 γ a ΔS β 0 0.1369 56.75 1.39 1.85 0.78 0 bct 36.3 0.1329 59.78 0.70 2.66 3.57 1.23R Liquid −16.6 0.1425 45.06 1.89 1.56 1.75 3.22R
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表 3 锡的多相状态方程模型3的校准参数
Table 3. Calibrated parameters of the multiphase EOS model 3 for tin
Phase E0/(J·g−1) V0/(cm3·g−1) B0/GPa a1 γ a cV0/(J·g−1·K−1) ΔS β 0 0.1369 56.7 0.75 1.54 1.64 0.233 0 bct 32.5 0.1338 54.8 1.14 2.42 3.48 0.254 1.18R Liquid −14.7 0.1413 48.0 1.75 1.53 1.74 0.302 3.43R
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