A thermodynamically complete multi-phase equation of state for dense and porous metals at wide ranges of temperature and pressure

doi:10.1088/1674-1056/ada54b

中国物理B ›› 2025, Vol. 34 ›› Issue (3): 36401-036401.doi: 10.1088/1674-1056/ada54b

A thermodynamically complete multi-phase equation of state for dense and porous metals at wide ranges of temperature and pressure

Yanhong Zhao(赵艳红)†, Li-Fang Wang(王丽芳)†, Qili Zhang(张其黎), Le Zhang(张乐), Hongzhou Song(宋红州), Xingyu Gao(高兴誉), Bo Sun(孙博), Haifeng Liu(刘海风), and Haifeng Song(宋海峰)‡

National Key Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100094, China

收稿日期:2024-10-21 修回日期:2025-01-02 接受日期:2025-01-03 发布日期:2025-03-15
通讯作者: Haifeng Song E-mail:songhaifeng@iapcm.ac.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 12205023, U2230401, 12374056, U23A20537, and 11904027).

A thermodynamically complete multi-phase equation of state for dense and porous metals at wide ranges of temperature and pressure

National Key Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100094, China

Received:2024-10-21 Revised:2025-01-02 Accepted:2025-01-03 Published:2025-03-15
Contact: Haifeng Song E-mail:songhaifeng@iapcm.ac.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 12205023, U2230401, 12374056, U23A20537, and 11904027).

摘要/Abstract

摘要： A thermodynamically complete multi-phase equation of state (EOS) applicable to both dense and porous metals at wide ranges of temperature and pressure is constructed. A standard three-term decomposition of the Helmholtz free energy as a function of specific volume and temperature is presented, where the cold component models both compression and expansion states, the thermal ion component introduces the Debye approximation and melting entropy, and the thermal electron component employs the Thomas-Fermi-Kirzhnits (TFK) model. The porosity of materials is considered by introducing the dynamic porosity coefficient $\alpha $ and the constitutive $P$-$\alpha $ relation, connecting the thermodynamic properties between dense and porous systems, allowing for an accurate description of the volume decrease caused by void collapse while maintaining the quasi-static thermodynamic properties of porous systems identical to the dense ones. These models enable the EOS applicable and robust at wide ranges of temperature, pressure and porosity. A systematic evaluation of the new EOS is conducted with aluminum (Al) as an example. 300 K isotherm, shock Hugoniot, as well as melting curves of both dense and porous Al are calculated, which shows great agreements with experimental data and validates the effectiveness of the models and the accuracy of parameterizations. Notably, it is for the first time Hugoniot $P$-$\sigma $ curves up to 10$^{6}$ GPa and shock melting behaviors of porous Al are derived from analytical EOS models, which predict much lower compression limit and shock melting temperatures than those of dense Al.

关键词: equation of state, multi-phase model, porous metal

Abstract: A thermodynamically complete multi-phase equation of state (EOS) applicable to both dense and porous metals at wide ranges of temperature and pressure is constructed. A standard three-term decomposition of the Helmholtz free energy as a function of specific volume and temperature is presented, where the cold component models both compression and expansion states, the thermal ion component introduces the Debye approximation and melting entropy, and the thermal electron component employs the Thomas-Fermi-Kirzhnits (TFK) model. The porosity of materials is considered by introducing the dynamic porosity coefficient $\alpha $ and the constitutive $P$-$\alpha $ relation, connecting the thermodynamic properties between dense and porous systems, allowing for an accurate description of the volume decrease caused by void collapse while maintaining the quasi-static thermodynamic properties of porous systems identical to the dense ones. These models enable the EOS applicable and robust at wide ranges of temperature, pressure and porosity. A systematic evaluation of the new EOS is conducted with aluminum (Al) as an example. 300 K isotherm, shock Hugoniot, as well as melting curves of both dense and porous Al are calculated, which shows great agreements with experimental data and validates the effectiveness of the models and the accuracy of parameterizations. Notably, it is for the first time Hugoniot $P$-$\sigma $ curves up to 10$^{6}$ GPa and shock melting behaviors of porous Al are derived from analytical EOS models, which predict much lower compression limit and shock melting temperatures than those of dense Al.

Key words: equation of state, multi-phase model, porous metal

中图分类号: (General theory of equations of state and phase equilibria)

64.10.+h

64.30.Ef (Equations of state of pure metals and alloys) 64.90.+b (Other topics in equations of state, phase equilibria, and phase transitions)

Yanhong Zhao(赵艳红), Li-Fang Wang(王丽芳), Qili Zhang(张其黎), Le Zhang(张乐), Hongzhou Song(宋红州), Xingyu Gao(高兴誉), Bo Sun(孙博), Haifeng Liu(刘海风), and Haifeng Song(宋海峰). A thermodynamically complete multi-phase equation of state for dense and porous metals at wide ranges of temperature and pressure[J]. 中国物理B, 2025, 34(3): 36401-036401.

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A thermodynamically complete multi-phase equation of state for dense and porous metals at wide ranges of temperature and pressure

A thermodynamically complete multi-phase equation of state for dense and porous metals at wide ranges of temperature and pressure

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