Gruneisen parameters and isothermal equations of state

The Gruneisen parameter (fl is of considerable importance to Earth scientis ts because it sets limitations on the thermoelastic properties of the lower mantle and core. However, there are several formulations of the Gruneisen parameter in frequent use which nor only give different values for gamma at ambient pressure but also predict a varying dependence of gamma as a funct ion of compression. The Gruneisen parameter is directly related to the equa tion of state (EOS), yet it is often the case that both the form of gamma a nd the EOS are chosen independently of each other and somewhat arbitrarily. In this paper we have assessed some of the more common definitions of the Gruneisen parameter and the EOS, and have applied them to a test material. OF the EOS considered, when compared against ab initio compressional data f or hcp-Fe as our exemplar, we find that the fourth order logarithmic and Vi net relations describe the material with the highest accuracy. Of the expre ssions for gamma considered it has been suggested, on theoretical grounds, that the modified free-volume formulation should be expected to give the mo st realistic description of the thermoelastic behavior of a material. Howev er, when we use the fourth order logarithmic EOS to obtain the compressiona l behavior of the various Gruneisen parameters, we find that there is, in f act, poor agreement between the modified free-volume formulation and the Mi e-Gruneisen parameter obtained directly from ab initio free energy calculat ions on hcp-Fe. We conclude that none of the analytical forms of gamma are sufficiently sophisticated to describe the thermoelastic behavior of real m aterials with great accuracy, and care must therefore be taken when attempt ing to model the thermoelastic behavior of solids to ensure that the approp riate gamma (ideally obtained from experiments or ab initio calculations) a nd equations of state are used.