Using periodic density functional theory, we calculate the structure and migration energies of fluorine vacancies and interstitials in the bulk and at the stoichiometric bulk-truncated surface of three alkali-earth fluorides: ${\text{CaF}}_{2}$, ${\text{SrF}}_{2}$, and ${\text{BaF}}_{2}$. We then study the adsorption of water and hydrogen, in both molecular and dissociated form, at the ideal surface, and at neutral and charged vacancies in the surface and subsurface layers. The results demonstrate that in nearly all cases molecular adsorption is strongly favored. For the most probable configurations on the surfaces, we also studied the migration paths and barriers, and found that water is highly mobile on the surface, even when adsorbed at defects. In general, ${\text{CaF}}_{2}$ and ${\text{SrF}}_{2}$ show similar behavior with respect to water, while adsorption energies and migration barriers for ${\text{BaF}}_{2}$ are smaller. Finally, we discuss our results in the context of recent experimental Atomic Force Microscopy studies on ${\text{CaF}}_{2}$ and compare to calculations on other insulating surfaces.
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