One-Parameter Equation of State for Metals and Certain other Solids

A general isothermal equation of state for metals and certain other solids P = 3B$_{T_{0}}\left[\left(\frac{V_{0}}{V}\right)^{5/3}-\left(\frac{V_{0}}{V}\right)^{4/3}\right]$where BT0 is the bulk modulus at zero pressure, P is the pressure, and V0and V are the volumes at zero pressure and pressure P, respectively, has been discovered empirically. The fit to a straight line for twenty metals and twelve metallic halides is within a few percent mean deviation. The rationale leading to this particular relation is that of the Virial Theorem, as applied to those solids for which the potential energy scales as the mean inverse of the interatomic distance, and for which on compression the entropy change is small.