Structure and diffusion of intrinsic defects, adsorbed hydrogen, and water molecules at the surface of alkali-earth fluorides calculated using density functional theory

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.

Figure 1

(Color online) Calculated formation energies as a function of electron chemical potential for (a) bulk interstitials and (b) bulk vacancies. The formation energies for neutral and charged defects are calculated with respect to the reference chemical potential of fluorine, and are plotted as a “pair” in the same color. The reference chemical potentials are as follows: the isolated F atom (blue solid line); fluorine rich, the energy of F in the ${\text{F}}_2$ molecule (red dashed line); fluorine-poor, the energy of F in bulk ${\text{CaF}}_2$ (green dot-dashed line).

Figure 2

(Color online) Calculated structures of the ideal (111) surface (a) top view, (b) side view, (c) neutral adatom $\left({\text{F}}_s^0\right)$, (d) charged adatom $\left({\text{F}}_s^{-}\right)$, (e) a neutral vacancy $\left(V_s^0\right)$ including (f) a plot of the spin density isosurface at 0.03 Hartree/Bohr, (g) a charged vacancy $\left(V_s^{+}\right)$, and (h) a subsurface charged vacancy $\left(V_{sub}^{+}\right)$. The structures shown are for ${\text{CaF}}_2$, but the geometries for the other surfaces are almost identical when scaling for the different lattice constant is taken into account. For clarity, in top views only the upper three atomic layers are shown.

Figure 3

(Color online) Calculated structures for water adsorbed on the ideal surfaces of (a) ${\text{CaF}}_2$ top view, (b) ${\text{CaF}}_2$ side view, (c) ${\text{SrF}}_2$, and (d) ${\text{BaF}}_2$.

Figure 4

(Color online) (a) Barrier for a water molecule diffusing on the ideal ${\text{CaF}}_2$ (111) surface, and (b)–(f) snapshots of the diffusion path at points labeled in the barrier plot.

Figure 5

(Color online) Calculated structures for water adsorbed on the ${\text{CaF}}_2$ surface (a) molecularly adsorbed at a $V_s^0$, (b) dissociated at a $V_s^0$, (c) molecularly adsorbed at a $V_s^{+}$, (d) molecularly adsorbed at a $V_{sub}^{+}$, and on the ${\text{BaF}}_2$ surface, (e) dissociated at the ideal surface $V_s^0$, and (f) molecularly adsorbed at a $V_s^{+}$.

Figure 6

(Color online) (a) Barrier for a water molecule adsorbed at a $V_s^{+}$ site diffusing on the ${\text{CaF}}_2$ (111) surface, and (b)–(f) snapshots of the diffusion path at points labeled in the barrier plot. The diffusing fluorine ion is labeled by “X.”

Figure 7

(Color online) Schematic diagrams showing the different possible reactions and energies for (a) a hydrogen atom adsorbing near a neutral vacancy in the surface, and (b) a water molecule adsorbing onto the ideal surface.