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 B 0 {\displaystyle B_{0}} , the derivative of bulk modulus with respect to pressure B 0 {\displaystyle B_{0}'} , the volume V 0 {\displaystyle V_{0}} , and the thermal expansion; all evaluated at zero pressure ( P = 0 {\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

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

then the equation of state is:

P = 3 B 0 ( 1 η η 2 ) e 3 2 ( B 0 1 ) ( 1 η ) {\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]

References

  1. ^ Pascal Vinet; John R. Smith; John Ferrante; James H. Rose (1987). "Temperature effects on the universal equation of state of solids". Physical Review B. 35 (4): 1945–1953. Bibcode:1987PhRvB..35.1945V. doi:10.1103/physrevb.35.1945. hdl:2060/19860019304. PMID 9941621. S2CID 24238001.
  2. ^ "Rose-Vinet (Universal) equation of state". SklogWiki.
  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. Bibcode:1981GeoSu...4..189S. doi:10.1007/BF01449185. S2CID 129899060.


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