A critical evaluation of equations of state by piezo-optic measurements

Abstract

Precision optical interferometric measurements on a number of liquids at high pressure reveal pronounced nonlinear piezo-optical (Δn versus P) behavior, but linear elasto-optic (Δn versus ε where ε is the Eulerian strain) relationship. This paper reexamines this linear Δn-ε relationship rather critically by a least-squares analysis and it is shown that it can be used to discriminate between the various equations of state prevalent in the literature. It is found that the second-order Murnaghan (ME2), second-order Birch (BE2), and the Keane equations of state yield the best fits to the experimentally observed piezo-optic data. Further, purely from thermodynamic and physical reasoning we can rule out ME2 and BE2, thus leaving the Keane equation as the only equation of state among those considered that can satisfactorily describe the elastic and elasto-optic behavior of liquids in its entire stability field. Since the various equations of state considered in this paper are also used for the study of isotropic solids as well, it is believed that the above conclusions should be valid in general for all isotropic solids and liquids.