Direct parameterization of the pressure-dependent volume by using an inverted approximate Vinet equation of state

Abstract

Parametric refinement is used for the simultaneous modeling of a series of diffraction data, replacing single independent parameters with physical or empirical equations that are valid for the full sequence of data. For the parametric treatment of diffraction data at high pressure, pressure-dependent constraints can be introduced in the form of an equation of state (EoS). However, the parameterization needs inverse functions of the EoS and most of them are not analytically invertible. In order to overcome this drawback, Taylor series expansions of different orders of the Vinet EoS were calculated and analytically inverted. It is shown that the inverted third-order Vinet EoS approximation, in its volume and linearized version, is applicable to a wide range of materials under high pressure.