Ab initio study of the density dependence of the Grϋneisen parameter at pressures up to 360 GPa

An equation of state based on the scaling properties of vibrational spectra at high pressure

“…Equation (3) implies that the product of the speed of sound and one-third power of density is proportional to the Debye frequency. We next combine this with the observation [36] (based on first-principles calculations that make use of Density Functional Theory) that, at high pressure, the Debye frequency is related linearly to density for many elemental solids. This suggests that the velocity of sound varies in a non-linear way with density at higher pressure.…”

“…Thus, if an accurate expression for ω D is known in terms of density ρ it is possible to obtain an equation of state at high pressure. This is where we use the previously mentioned observation that ω D has a linear dependence on density at a high level of accuracy for many elemental solids [36] i.e. We will choose this reference density to be the density (ρ 0 ) at zero pressure.…”

“…However, first-principle methods make it possible to calculate this quite accurately. Recently [36] a simple functional form for the dependence of the Debye Grüneisen parameter on density was proposed on the basis of such calculations of lattice vibrational spectra [16]-the latter being calculated using ab initio methods based on the application of the Density Functional Theory (DFT) of electronic structure calculations. It was found that Debye frequency satisfies a linear relationship against density to high accuracy [36].…”

“…Recently [36] a simple functional form for the dependence of the Debye Grüneisen parameter on density was proposed on the basis of such calculations of lattice vibrational spectra [16]-the latter being calculated using ab initio methods based on the application of the Density Functional Theory (DFT) of electronic structure calculations. It was found that Debye frequency satisfies a linear relationship against density to high accuracy [36]. The existence of such a relation also suggests a non-linear dependence of sound velocity on the density of a material [37,38] (in contrast to the Birch's law [39,40] which proposes a linear dependence).…”

“…According to this scaling law the dependence of the phonon frequency on the wave vector becomes independent of pressure if the phonon frequency and wave vector are expressed in suitable pressure-dependent units. Motivated by the observation of linear dependence [36,38] of the Debye frequency on density and the scaling relation [14] just mentioned a new functional form for an equation of state (EOS) is presented in this article. The EOS has been tested for several type of materials (such as elemental metals, ionic solids, insulators, and rare-gas solids) against experimental data available in the literature for room temperature (300 K or 298 K).…”