Surface reconstruction of fluorites in vacuum and aqueous environment

Surfaces and interfaces of bulk materials with liquids are of importance for a wide range of chemical processes. In this work, we systematically explore reconstructions on the (100) surface of calcium fluoride $\left({\mathrm{CaF}}_2\right)$ and other fluorites $\left(M{\mathrm{F}}_2\right)$, $M=\{\text{Sr},\text{Cd},\text{Ba}\}$ by sampling the configurational space with the minima hopping structure prediction method in conjunction with density functional theory calculations. We find a large variety of structures that are energetically very close to each other and are connected by very low barriers, resulting in a high mobility of the topmost surface anions. This high density of configurational states makes the ${\mathrm{CaF}}_2$ (100) surface a very dynamic system. The majority of the surface reconstructions found in ${\mathrm{CaF}}_2$ are also present in ${\mathrm{SrF}}_2,{\mathrm{CdF}}_2$, and ${\mathrm{BaF}}_2$. Furthermore, we investigate in detail the influence of these reconstructions on the crystal growth of ${\mathrm{CaF}}_2$ in solvents by modeling the fluorite-water interface and its wetting properties. We perform a global structural search both by explicitly including water molecules and by employing a recently developed soft-sphere solvation model to simulate an implicit aqueous environment. The implicit approach correctly reproduces both our findings with the explicit-water model and the experimentally reported contact angles for the partial-hydrophobic (111) and hydrophilic (100) surfaces. Our simulations show that the high anion mobility and the low coordination of the (100) surface atoms strongly favors the adsorption of water molecules over the (111) surface. The aqueous environment makes terminations with low-coordination surface atoms more stable, promoting (100) growth instead of the (111).

Figure 1

(a) Top view onto the $\left(111\right){\mathrm{CaF}}_2$ surface (topmost two layers). The outermost fluorine anion layer is denoted with small dark (red) spheres, and the calcium cation layer just below is denoted with large light (gray) spheres. The cross sectional area of the orthogonal supercell is shaded (red). (b) The top seven (triple-) layers of the relaxed $\left(111\right)$ supercell consisting of 13 (triple-) layers and 156 atoms. Numbered and highlighted atoms are related to the analysis of the atomic displacement $\mathrm{\Delta }z$ shown in Fig. 2. Arrows indicate the direction of the atomic displacements after relaxation, and their length qualitatively represents the displacement amplitude with respect to their bulk positions.

Figure 2

Inward/outward relaxation (PBE) amplitudes with respect to the bulk positions in units of $\%a_{0,\mathrm{PBE}}$ for the topmost layers of the (111) ${\mathrm{CaF}}_2$ supercell. Negative values indicate an inward displacement (towards the bulk); positive values indicate a displacement towards the surface. Atom indexes are related to Fig. 1.

Figure 3

(a) Top view onto the (100) ${\mathrm{CaF}}_2$ surface with F termination (topmost two layers). The cross section area of the unit cell is shaded in dark gray; the cross section area of the simulation box is shaded in light gray (red). (b) Surface top view after removing every second F ion from the bulk terminated surface. (c) 10 outermost layers of the F-terminated (100) supercell (relaxed) consisting of 19 layers.

Figure 4

(a) Ca-terminated (100) surface (topmost two layers) for ${\mathrm{CaF}}_2$. The cross section area of the unit cell is shaded in dark gray and the supercell area in light gray (red). (b) Surface top view after removing every second Ca atom of the outermost layers. (c) Seven outermost layers of the relaxed (100) supercell with Ca termination consisting of 13 layers.

Figure 5

Inward/outward relaxation (PBE) amplitudes of the (100) ${\mathrm{CaF}}_2$ slab in units of $\%a_{0,\mathrm{PBE}}$. (a) F-terminated slab consisting of 19 layers; (b) Ca-terminated slab consisting of 13 layers. Atom indexes correspond to Figs. 3 and 4, respectively.

Figure 6

Normal view onto the $\left(100\right)$ reconstructed surfaces of ${\mathrm{CaF}}_2$ (topmost two layers), ordered into groups of energetically degenerate structures. With the exception of structure J1, all surfaces are F terminated. F and Ca atoms are denoted by small dark (red) and large light (gray) spheres. The topmost Ca atoms in J1 are denoted by shaded dark-gray spheres.

Figure 7

Lowest energy C1 reconstruction of the (100) ${\mathrm{CaF}}_2$ surface.

Figure 8

Disconnectivity graph of the ${\mathrm{CaF}}_2$ (100) reconstructions (LDA calculations). For clarity a threshold value of $40\mathrm{mJ}/{\mathrm{m}}^2$ was chosen to bin the saddle point energies.

Figure 9

Structures of the most stable configurations of the hydrated (111) ${\mathrm{CaF}}_2$ surface for 100% (left) and 200% coverage (right) in side view (top) and top view (bottom). Top views show only the two topmost anion and cation layers. H atoms denoted by small dark (blue), O atoms by medium light gray (yellow), F atoms by medium dark (red), and Ca atoms by large light-gray (white) spheres. Additionally shown are the H-F bonds (thin, red) and the Ca-O bonds (bold, dark gray) and hydrogen bonds (bold, green) together with their typical bond lengths in Å.

Figure 10

Structures of the most stable configurations of the hydrated (100) ${\mathrm{CaF}}_2$ surface for 100% (left) and 200% coverage (right) in side view (top) and top view (bottom). Color description as Fig. 9. Top views show the underlying reconstructions (bold, dark gray) which are of type D for 100% and 200% coverage.