Kinetic Monte Carlo simulations of fluorine and vacancies concentration at the CeO₂(111) surface

Recently, a new identification of the experimental depressions of scanning tunnelling microscopy images on the ${CeO}_2\left(111\right)$ surface as fluorine impurities has been proposed in Kullgren et al (2014 Phys. Rev. Lett. 112 156102). In particular, the high immobility of the depressions seems to be in contradiction with the low diffusion barrier for the oxygen vacancies. Consequently, the oxygen vacancies concentration has to disappear. The first aim of this paper is to confirm dynamically the recent interpretation of the experimental finding. For this purpose, we investigate the competition between fluorine and oxygen vacancies using two dimensional kinetic Monte Carlo simulations (kMC) as compared to an appropriate Langmuir model. We calculate the concentration of the vacancies and of the fluorine for the surface (111) of ${CeO}_2$ for a UHV condition as a function of the fluorine–oxygen mixture in the gas phase as well as of the binding energies of fluorine and oxygen. We found that at a temperature of $T=573K$, at which the experimental measurements were conducted, vacancies cannot exist. This confirms the possibility of fluorine impurities in Kullgren et al (2014 Phys. Rev. Lett. 112 156102). The second aim of the present paper is to perform a first dynamical estimation of the fluorine binding energy value $E_{Fl}$ that allows one to describe the experimental data in Pieper et al (2012 Phys. Chem. Chem. Phys. 14 15361). Using 2D-kMC simulations, we found $E_{Fl}\in [-5.53,-5.27]eV$ which can be used for comparison to density functional theory calculations in further works. (paper)