The interplay between energetics and entropy in determining defect distributions at ceria(111) is studied using a combination of DFT+U and lattice Monte Carlo simulations. Our main example is fluorine impurities, although we also present preliminary results for surface hydroxyl groups. A simple classical force-field model was constructed from a training set of DFT+U data for all symmetrically inequivalent (F−)n(Ce3+)n nearest-neighbor clusters with n = 2 or 3. Our fitted model reproduces the DFT energies well. We find that for an impurity concentration of 15% at 600 K, straight and hooked linear fluorine clusters are surprisingly abundant, with similarities to experimental STM images from the literature. We also find that with increasing temperature the fluorine cluster sizes show a transition from being governed by an attractive potential to being governed by a repulsive potential as a consequence of the increasing importance of the entropy of the Ce3+ ions. The distributions of surface hydroxyl groups are noticeably different.
Kullgren, J., Wolf, M. J., Mitev, P. D., Hermansson, K., & Briels, W. J. (2017). DFT-based Monte Carlo Simulations of Impurity Clustering at CeO2(111). Journal of physical chemistry C, 121(28), 15127-15134. https://doi.org/10.1021/acs.jpcc.7b00299