Small-parameter equation of state of copper

A small-parameter equation of state in the Lie–Grüneisen form is proposed to describe shock compression of condensed matter. The equation is based on a postulated dependence of the Grüneisen coefficient on the specific volume and temperature $\Gamma(V,T)$, which provides a qualitative description of compression of metal samples in strong shock waves. The curve of cold compression is found on the basis of the dependence $\Gamma(V,T)$ with the use of a generalized formula for the Grüneisen function. Heat-induced oscillations of the crystal lattice are described in the Debye approximation. The resultant Grüneisen function has two free parameters. The values of other coefficients of the equation of state are determined from the reference data for the substances under standard conditions and also from the limiting values under extreme conditions. The model is tested by an example of copper. The derived equation of state describes the cold compression curve, normal isotherm, shock compressibility, as well as the copper unloading curves in density, pressure, and internal energy ranges for which experimental data are available. The thermodynamic characteristics of copper (isentropic modulus of volume compression, velocity of sound, Debye temperature, specific heat, linear expansion coefficient, and melting temperature) are calculated. Comparisons with available experimental data shows that the proposed model, despite its simplicity, ensures a consistent description of a large array of experimental data in the region of high energy densities.