Rose–Vinet equation of state

The Rose–Vinet equation of state is a set of equations used to describe the equation of state of solid objects. It is a modification of the Birch–Murnaghan equation of state.^[1][2] The initial paper discusses how the equation only depends on four inputs: the isothermal bulk modulus ${\displaystyle B_{0}}$, the derivative of bulk modulus with respect to pressure ${\displaystyle B_{0}'}$, the volume ${\displaystyle V_{0}}$, and the thermal expansion; all evaluated at zero pressure (${\displaystyle P=0}$) and at a single (reference) temperature. The same equation holds for all classes of solids and a wide range of temperatures.

Let the cube root of the specific volume be

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

then the equation of state is:

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

A similar equation was published by Stacey et al. in 1981.^[3]