Rose-Vinet (Universal) equation of state

Vinet

In order to rectify the excessive stiffness of the Murnaghan equation of state as well as represent the exponential dependence of the repulsion as solid undergoes infinite compression, Vinet proposed an equation of state that has widely as either the Vinet equation of state or Universal equation of state. The latter due to the fact that the equation of state was formulated so that one form could represent all solids, depending only on the calibration point. Using the shorthand for the cube root specific volume:

$\eta =\left({\frac {V}{V_{0}}}\right)^{\frac {1}{3}}$

the equation of state is:

$p=3B_{0}\left({\frac {1-\eta }{\eta ^{2}}}\right)e^{{\frac {3}{2}}(B_{0}'-1)(1-\eta )}$