230 / 2023-04-17 14:12:43

Simple Models of Equations of State for Refractory Metals at High Energy Densities

equations of state,hafnium,tantalum,rhenium,shock compressibility,high pressures,high temperatures

Knowledge of the properties of various materials in a wide range of thermodynamic parameters is necessary for the analysis and numerical simulation of physical phenomena at high energy concentrations. Refractory metals are widely used in engineering as structural materials that take intense thermal and mechanical loads. In the processes of interaction of energy flows with matter, the thermodynamic parameters of the state of the medium change over a wide range. In particular, in this case, an increase in internal energy can be accompanied by an increase in the density of the substance, and at the stage of unloading, the density decreases along with the internal energy. The material can undergo phase transformations, including those with a change in the state of aggregation. The adequacy of the model of the equation of state of matter depends on the qualitative and quantitative correspondence of the simulation results to the course of the process under consideration.

To describe the properties of refractory metals (such as hafnium, tantalum, and rhenium) in a wide range of densities and pressures, various semiempirical models of equations of state with a small number of parameters are proposed. Two groups of models can be distinguished, one of which determines the dependence of internal energy on specific volume and pressure, and the other determines the dependence of free energy on specific volume and temperature. Within the framework of these models, calculations of the thermodynamic characteristics of metals are carried out under the conditions of experiments on isothermal compression, shock compression of samples of different initial porosity, and isentropic expansion of shock-compressed samples. Comparison of the calculation results with the available experimental data shows that the proposed models make it possible to adequately describe the behavior of metals at high energy densities.

The constructed equations of state can be used in modeling various phenomena under extreme conditions, including those at high pressures and internal energies.

This work was supported by the Russian Science Foundation, grant no. 19-19-00713, https://rscf.ru/project/19-19-00713/.

Knowledge of the properties of various materials in a wide range of thermodynamic parameters is necessary for the analysis and numerical simulation of physical phenomena at high energy concentrations. Refractory metals are widely used in engineering as structural materials that take intense thermal and mechanical loads. In the processes of interaction of energy flows with matter, the thermodynamic parameters of the state of the medium change over a wide range. In particular, in this case, an increase in internal energy can be accompanied by an increase in the density of the substance, and at the stage of unloading, the density decreases along with the internal energy. The material can undergo phase transformations, including those with a change in the state of aggregation. The adequacy of the model of the equation of state of matter depends on the qualitative and quantitative correspondence of the simulation results to the course of the process under consideration.

To describe the properties of refractory metals (such as hafnium, tantalum, and rhenium) in a wide range of densities and pressures, various semiempirical models of equations of state with a small number of parameters are proposed. Two groups of models can be distinguished, one of which determines the dependence of internal energy on specific volume and pressure, and the other determines the dependence of free energy on specific volume and temperature. Within the framework of these models, calculations of the thermodynamic characteristics of metals are carried out under the conditions of experiments on isothermal compression, shock compression of samples of different initial porosity, and isentropic expansion of shock-compressed samples. Comparison of the calculation results with the available experimental data shows that the proposed models make it possible to adequately describe the behavior of metals at high energy densities.

The constructed equations of state can be used in modeling various phenomena under extreme conditions, including those at high pressures and internal energies.

This work was supported by the Russian Science Foundation, grant no. 19-19-00713, https://rscf.ru/project/19-19-00713/.