It is commonly assumed that finite temperature electronic contributions to the free energy of insulators and semiconductors may be neglected due to the lack or absence of electron density near the Fermi level. This may be the case when treating ideal, pristine systems since there are no electronic levels available for population due to thermal excitation of electrons near the valence band maximum. This sizable bandgap in medium to wide gap materials limit the number of electronic configurations accessible to the highest occupied levels. The validity of this assumption is highly questionable however, especially when charged defect levels are present within the energy gap increasing the density of states near the Fermi level. Shallow defect levels with unpaired electrons near the VBM would allow for an increase in the number of microstates for thermal population of electrons contributing to the electronic configurational free energy. The electronic density-of-states data from a structural relaxation at the HSE06 level of theory with a 12-atom Ce4O8 bulk supercell was implemented to calculate the Fermi level (electron chemical potential) as a function of temperature. The Fermi-Dirac distribution along with the normalized DOS were utilized to estimate the majority carrier concentration (assuming only electronic charge carriers) via the difference between the conduction band and valence band integrals.

Estimation of electronic entropy contributions to redox thermodynamics in ceria

ACS Fall 2020 Virtual Meeting

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