First-principles study of bismuth films on the Ni(111) surface

A recent experiment suggested that bismuth forms hexagonal films on the Ni(111) surface, of heights three, five, and seven layers. A quantum size effect based on free electrons was proposed in explanation. To test this idea, we calculate the total energies of Bi on the Ni(111) surface using density functional theory. We find that hexagonal film stabilities disagree with the observed odd layer preferences, and the structures are mechanically destabilized by adding capping atoms which pucker the hexagonal layers. Furthermore, we find that rhombohedral films based on the bulk Bi structure are energetically more favorable than the proposed hexagonal films. These structures also favor odd numbers of layers, but owing to covalent chemical bonding rather than confinement of free electrons. Specifically, a strongly bound adsorbed surface monolayer forms, followed by bulk-like rhombohedral bilayers.

Figure 1

Top view (top left) and side view (top middle) of relaxed four-layer hexagonal Bi film on Ni(111) ($3\times 3$) cell (dashed). Same for three-layer $hR2$ Bi film (bottom). Insert at top of the left-hand figure is a histogram of atoms at different heights. Shading in insert conveys the region illustrated containing the top layer of Ni, the Bi surface monolayer, and additional Bi layers. Atom size indicates depth (large below small). Length units are in Å. Chemical bonding is shown at right (slightly tilted).

Figure 2

Relative surface energies of hexagonal Bi films with ($3\times 3$) (top) and [3-112] (bottom) Ni(111) surface cells. Note the energy conversion factor is 1 eV/${\text{Å}}^2=16.0$ J/m${}^2$. Red and blue points are from collinear calculations, green points are noncollinear. Data points connected by line segments correspond to coverage of integer numbers of monolayers (1–9 for ($3\times 3$), 1–11 for [3-112]). Extra data points in the ($3\times 3$) cell are three-layer films with one extra capping atom at a valley site. Extra points in the [3-112] cell are four layer plus one atom, and eight layer plus one atom at valley sites.

Figure 3

Enthalpy of formation. Dot-dashed orange points are the (sub)monolayer structures with ($3\times 3$) cell. Cyan and green stars are the ($7\times 7$) and ($8\times 8$) surface monolayer, respectively. Red points are hexagonal films and black are $hR2$ Bi films on the ($3\times 3$) cell. Blue points are hexagonal Bi films on the [3-112] cell. Color and plotting symbol are shared with Fig. 2 for ($3\times 3$) and [3-112] cells.

Figure 4

Surface free energy. Dashed-dotted lines stand for monolayer or less. Solid and dotted lines stand for hexagonal and $hR2$ films on ($3\times 3$) cells, respectively. Different slopes indicate different coverage according to Eq. (3). Stable sequence is indicated by arrows for monolayer or more. Vertical line at $\Delta \mu =0$ indicates chemical potential of unstrained bulk Bi.

Figure 5

Bi bulk energy of hexagonal and $hR2$ structures. Black is the relaxed $hR2$ structure. Red is the relaxed hexagonal structure. Blue is the evenly spaced hexagonal structure. Points (a), (b), (c), and (d) correspond to the structures whose energies are plotted in Fig. 6.

Figure 6

Surface energies of freestanding Bi films with different in-plane lattice constants $a$ (units of Å). Black and red curves are using collinear calculation, green using noncollinear.