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 an 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 [math]\displaystyle{ B_0 }[/math], the derivative of bulk modulus with respect to pressure [math]\displaystyle{ B_0' }[/math], the volume [math]\displaystyle{ V_0 }[/math], and the thermal expansion; all evaluated zero pressure ([math]\displaystyle{ P=0 }[/math]) and at a single (reference) temperature. And the same equation holds for all classes of solids and a wide range of temperatures.

Let the cube root of the specific volume be

[math]\displaystyle{ \eta=\left({\frac{V}{V_0}}\right)^{\frac{1}{3}} }[/math]

then the equation of state is:

[math]\displaystyle{ P=3B_0\left(\frac{1-\eta}{\eta^2}\right)e^{\frac{3}{2}(B_0'-1)(1-\eta)} }[/math]

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

## References

1. ↑ Pascal Vinet, John R. Smith, John Ferrante and James H. Rose (1987). "Temperature effects on the universal equation of state of solids". Physical Review B 35 (4): 1945–1953. doi:10.1103/physrevb.35.1945.
2. ↑ "Rose-Vinet (Universal) equation of state". http://www.sklogwiki.org/SklogWiki/index.php?title=Rose-Vinet_(Universal)_equation_of_state&action=edit&section=1.
3. ↑ F. D. Stacey; B. J. Brennan; R. D. Irvine (1981). "Finite strain theories and comparisons with seismological data". Surveys in Geophysics 4 (4): 189–232. doi:10.1007/BF01449185.

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