Rose-Vinet (Universal) equation of state: Difference between revisions
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==Vinet== | ==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'''<ref> | 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'''<ref>[http://dx.doi.org/10.1103/PhysRevB.35.1945 Pascal Vinet, John R. Smith, John Ferrante and James H. Rose "Temperature effects on the universal equation of state of solids", Physical Review B '''35''' pp. 1945-1953 (1987)]</ref>. 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: | ||
:<math>\eta=\left(\frac{V}{V_0}\right)^{\frac{1}{3}}</math> | :<math>\eta=\left(\frac{V}{V_0}\right)^{\frac{1}{3}}</math> | ||
the equation of state is: | the equation of state is (Eq. 4.1): | ||
:<math>p=3B_0\left(\frac{1-\eta}{\eta^2}\right)e^{\frac{3}{2}(B_0'-1)(1-\eta)}</math> | :<math>p=3B_0\left(\frac{1-\eta}{\eta^2}\right)e^{\frac{3}{2}(B_0'-1)(1-\eta)}</math> | ||
Revision as of 13:13, 7 November 2011
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[1]. 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:
the equation of state is (Eq. 4.1):
