Vinet

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The finite-strain EoS do not accurately represent the volume variation of most solids under very high compression , so Vinet et al. (1986; 1987) derived an EoS from a generalised inter-atomic potential. Following Schlosser & Ferrante (1988), the expression for pressure in the Vinet EoS is:



with and . This definition of fV means that fV = 0  at P = 0, and that fV  increases as a positive quantity with increasing pressure and compression. It therefore follows the conventions in the definition of magnitude and sign of Eulerian finite strain. This is a change from the implementation in previous versions of EosFit (Angel, 2000a). The presence of K'0T as a refineable parameter also leads, by comparison with other finite strain EoS, to naming this a ‘3rd-order’ EoS. 


In order to obtain a form of the EoS with which to construct plots of ‘normalised pressure’ against the strain fV, a normalised pressure has previously been defined as  (Vinet et al., 1986; Vinet et al., 1987; Schlosser & Ferrante, 1988). Then  , which should be linear in fV with slope of . But the intercept at  fV = 0 is .  Therefore in the EoS module of CrysFML we implement , for which . The y-axis intercept of a plot of FV  against fV is thus K0T, and it will give a horizontal line for a 2nd-order EoS with K'0T = 1. A 3rd-order EoS with K'0T > 1 will have a curved line, with increasing gradient with increasing fV. For reasonable values of K'0T the curvature is very slight. The slope at any point is , so the initial slope is , a form entirely analogous to f-F plots of the Birch-Murnaghan EoS.



There is no theoretical basis for truncation of the Vinet EoS to lower order, although it yields an implied value for K'0T of 1. The implied value of K''0T for the Vinet EoS is given by Jeanloz (1988) as:



Expansions of the Vinet EoS to include a refineable K''0T have been proposed but are not required to fit most experimental data of simple solids in the absence of phase transitions.