Thermal electronic properties of aluminum under pressure: The role of sp to 3d electron transfer

Abstract

As a simple metal, aluminum's valence band is usually described as a free-electron gas with three electrons per atom. The discrepancies between the experimental electronic Gr\uneisen parameter and heat capacity and their free-electron-gas counterparts are usually attributed to electron-phonon coupling. We recently calculated thermal electronic contributions to aluminum's internal energies with our average-atom code paradisio and obtained results that contradict this point of view. Our code also pointed out the overlap of the $sp$ valence band by the $3d$ one, resulting in an $sp$ to $d$ electron transfer. Applying Sommerfeld's temperature expansion method to the electron-electron Coulomb part of the internal energy, we relate the electronic Gr\uneisen parameter, $T=0$ K isotherm, and thermal contributions to the internal energy to a parameter $\ensuremath{\alpha}$ describing the fraction of $d$ electrons resulting from $p$ to $d$ transfer. Finally, we find a unique value of this parameter that provides a consistent explanation for the experimental Gr\uneisen parameter, for $T=0$ K energy deduced from experimental shock Hugoniot data, as well as for our average-atom thermal contributions to internal energy.