The Grüneisen parameter at high pressure: a molecular dynamical study

The method of molecular dynamics is used to calculate values for the thermal Grüneisen parameter, γ, for a face-centred cubic crystal with several simple central force atomic potential functions at three compressions for comparison with free volume and acoustic γ formulations. Neither is found to agree with the computer experiments. A defect in the free-volume formula for γ is shown to arise from the assumption that motions of neighbouring atoms in a crystal at high temperature are uncorrelated whereas the computer models demonstrate a 25–35% correlation of in-line motions and 5% correlation of transverse motions. The formula can be modified to allow for the empirically observed correlations, but it is concluded that there are still difficulties in analytical approaches to equation-of-state studies of the Earth's deep interior and that the computer modelling method of molecular dynamics has important advantages.