Equations of State

Abstract

Diffraction experiments at high pressures provide measurement of the variation of the unit-cell parameters of the sample with pressure and thereby the variation of its volume (or equivalently its density) with pressure, and sometimes temperature. This last is known as the ‘Equation of State’ (EoS) of the material. It is the aim of this chapter to present a detailed guide to the methods by which the parameters of EoS can be obtained from experimental compression data, and the diagnostic tools by which the quality of the results can be assessed. The chapter concludes with a presentation of a method by which the uncertainties in EoS parameters can be predicted from the uncertainties in the measurements of pressure and temperature, thus allowing high-pressure diffraction experiments to be designed in advance to yield the required precision in results. The variation of the volume of a solid with pressure is characterised by the bulk modulus, defined as K = − V ∂ P /∂ V . Measured equations of state are usually parameterized in terms of the values of the bulk modulus and its pressure derivatives, K′ = −∂ K /∂ P and K″ = −∂2 K /∂ P 2, evaluated at zero pressure. These zero-pressure (or, almost equivalent, the room-pressure values) are normally denoted by a subscript “0,” thus: K = − V (∂ P /∂ V ) P =0, K ′ = −(∂ K /∂ P ) P =0, and K ″ = −(∂2 K /∂ P 2) P =0. However, throughout this chapter a number of notational conventions are followed for ease of presentation. Unless specifically stated, the symbols K′ and K ″ (without subscript) refer to the zero-pressure values at ambient temperature, all references to bulk modulus, K …