Rose–Vinet equation of state

The Rose–Vinet equation of state are 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 $B_{0}$ , the derivative of bulk modulus with respect to pressure $B_{0}'$ , the volume $V_{0}$ , and the thermal expansion; all evaluated zero pressure ( $P=0$ ) 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

\eta ={\sqrt[{3}]{\frac {V}{V_{0}}}}

then the equation of state is:

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]

References

↑ 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: 1945–1953. doi:10.1103/physrevb.35.1945.
↑ "Rose-Vinet (Universal) equation of state". SklogWiki.
↑ 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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