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The existing Grneisen coefficient γ expressions and the experimental data fitting relations consider only the γ data fitting, rather than the change rule of γ. In this paper, the universal function of Grneisen γ is established according to the property of Grneisen γ function and the high pressure characteristics of thermodynamic γ, such as γ changing quickly at low pressure but slowly at high pressure. This universal function is substituted into the thermodynamic function γ(v, T) to obtain the isentropic temperature Ts(v), and then the Hgoniot temperature is deduced by using the relationship between isentropic temperature and Hgoniot temperature, thus Hgoniot equation becomes the complete equation of state. All the thermodynamic state variables can be calculated by the thermodynamic relations. The universal function of Grneisen γ is applied to several metals, such as Al, Ta and Cu, and the Hgoniot equation is deduced according to the isothermal equation, or the isothermal equation is calculated by the Hgoniot equation. The results are in good agreement with experimental data. There are good compatibility between the universal Grneisen γ and the heat capacity Cv. It is shown that the proposed universal function of Grneisen γ can reasonably describe the thermodynamic properties of many metals at high pressure and high temperature.
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Keywords:
- Grü /
- neisen γ /
- thermodynamic γ /
- universal function /
- complete equation of state
[1] Anderson O L 2000 Geophys. J. Int. 143 279
[2] Wu Q 2004 Ph. D. Dissertation (Mianyang: China Acedemy of Engineering Physics) (in Chinese) [吴强 2004 博士学位论文(绵阳: 中国工程物理研究院)]
[3] Song P, Cai L C 2009 Acta Phys. Sin. 58 1879 (in Chinese) [宋萍, 蔡灵仓 2009 58 1879]
[4] Zhang D, Sun J X 2012 Chin. Phys. B 21 080508
[5] Zhai D, Wei Z, Feng Z F, Shao X H, Zhang P 2014 Acta Phys. Sin. 63 206501 (in Chinese) [翟东, 韦昭, 冯志芳, 邵晓红, 张平 2014 63 206501]
[6] Anderson O L 2001 Geophys. Res. Lett. 28 15
[7] Marsh S P 1980 LASL Shock Hgoniot Data (Berkeley American: University of California Press) p57
[8] Mitchell A C, Nellis W J 1981 J. Appl. Phys. 52 3363
[9] Dewaele A, Loubeyre P, Mezouar M 2004 Phys. Rev. B 70 094112
[10] Marcus D K 2010 From Static to Dynamic, 1st Annual Meeting of the Institute for Shock Physics London, Britain, February 22, 23, 2010 p23
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[1] Anderson O L 2000 Geophys. J. Int. 143 279
[2] Wu Q 2004 Ph. D. Dissertation (Mianyang: China Acedemy of Engineering Physics) (in Chinese) [吴强 2004 博士学位论文(绵阳: 中国工程物理研究院)]
[3] Song P, Cai L C 2009 Acta Phys. Sin. 58 1879 (in Chinese) [宋萍, 蔡灵仓 2009 58 1879]
[4] Zhang D, Sun J X 2012 Chin. Phys. B 21 080508
[5] Zhai D, Wei Z, Feng Z F, Shao X H, Zhang P 2014 Acta Phys. Sin. 63 206501 (in Chinese) [翟东, 韦昭, 冯志芳, 邵晓红, 张平 2014 63 206501]
[6] Anderson O L 2001 Geophys. Res. Lett. 28 15
[7] Marsh S P 1980 LASL Shock Hgoniot Data (Berkeley American: University of California Press) p57
[8] Mitchell A C, Nellis W J 1981 J. Appl. Phys. 52 3363
[9] Dewaele A, Loubeyre P, Mezouar M 2004 Phys. Rev. B 70 094112
[10] Marcus D K 2010 From Static to Dynamic, 1st Annual Meeting of the Institute for Shock Physics London, Britain, February 22, 23, 2010 p23
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