Theoretical Modelling of Equations of States for Aluminum to Pressure up to 10 TPa and Temperature to 10 eV

Nisarg K. Bhatt; R.H. Joshi; Brijmohan Y. Thakore; Ashvin R. Jani; P.R. Vyas

doi:10.4028/www.scientific.net/AMR.1141.121

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Theoretical Modelling of Equations of States for Aluminum to Pressure up to 10 TPa and Temperature to 10 eV

Abstract:

Response of materials to extreme temperature (T) and/or Pressure (P) conditions can be studied through, e.g., equations of states (EOS), which link between macroscopic observations to the microscopic consequences. Accurate knowledge of EOS is therefore always desirable, and plethora of different forms of EOS is proposed in literature. Of which, the most frequently used Mie-Grüneisen EOS coupled either with Debye-Model or Einstein-model within the quasiharmonic approximation requires prior knowledge of Grüneisen parameter (γ), characteristic temperature (θ) and their volume variation. At the pair-potential level, the Einstein characteristic temperature (θ_E) is derived through second-order potential derivatives. Although, many potential-energy-functional (PEF) are proposed for metallic systems, all including many-body effects, however, in order to compute θ_E effective pair-potential has to be deduced from PEF. But this procedure relies on some unavoidable approximations and fitting procedure. In this context, we have used energy-functional based definition of effective θ_Eand for its volume dependence. We have employed tight-binding second-moment approximation (TB-SMA) to deduce cold energy curve to deduce θ_E and γ. Further, anharmonicity associated in bonding is parameterized; and it is shown that the parameter describing it is related to the thermodynamic Grüneisen parameter. Thus, the present scheme also circumvents additional empirical relation for γ (V). The present proposal is then employed to deduce equations of states and related thermo-physical properties; taking aluminum as a prototype. Results so generated to pressures more than 10 TPa and temperatures as high as 110 kK are compared and discussed in light of other simulated and experimental findings.