Universal equation of state for compressed solids

We derive a universal equation of state for compressed solids, based on thermodynamic arguments applied to virial expansions of E(ρ,T) and p(ρ,T), of the form p(v/${\mathit{v}}_0$ ${)}^2$=${\mathit{A}}_0$+${\mathit{A}}_1$(ρ/${\mathrm{\rho }}_0$)+${\mathit{A}}_2$(ρ/${\mathrm{\rho }}_0$ ${)}^2$. The thermal pressure is included from the beginning, and the only essential approximation is the truncation of expansions, which is justified by molecular arguments. Agreement with experiment is very good for a wide range of materials, including quantum solids, noble-gas and polar-gas solids, metals, ionic compounds, and hydrocarbons. A separate assumption gives the temperature dependence of the parameters as ${\mathit{A}}_{\mathit{i}}$(T)=${\mathit{A}}_{\mathit{i}}$+${\mathit{b}}_{\mathit{i}}$T-${\mathit{c}}_{\mathit{i}}$T lnT, for T>${\mathrm{\theta }}_{\mathit{D}}$. The usual behavior of the Grüneisen number as a function of temperature and density is accounted for in a simple way by these results.