Interaction potentials for fast atoms in front of Al surfaces probed by rainbow scattering

Rainbow scattering for grazing-angle incidence of atoms at surfaces along low-indexed channeling directions provides a sensitive probe of quasistatic atom-surface potentials. The dependence of the rainbow angle on the kinetic energy for the projectile motion perpendicular to the surface, $E_{\perp }$, varies with the electronic structure of the projectile as well as the crystallographic face of the aluminum surface. Comparison between experiment and classical Monte Carlo trajectory simulations demonstrates that the superposition of binary atom-atom potentials fails to adequately represent the equipotential surfaces. Ab initio atom-surface potentials based on density-functional theory are required to reach satisfactory agreement with experiment.

Figure 1

(Color online) (a) Schematic picture of the scattering geometry. The 2D intensity distribution on the detector plane arises from scattering of 10 keV Ar atoms from Al(111) along a $⟨1\overline{1}0⟩$ direction at angle of incidence ${\varphi }_{in}=2.35°$. This corresponds to an energy perpendicular to the surface of $E_{\perp }=16.81\text{eV}$. Positions of rainbow angles ${\theta }_{rb}$ are indicated by straight lines. Color code: red to blue ($=\text{high}$ to low). (b) Integral over the 2D intensity within the two concentric circles along fixed values of $\theta$. The two concentric circles represent the region of (elastically) scattered projectiles. (c) Angular distributions calculated with CTMC simulations and matter-wave simulations (for details see Ref. 10), both including thermal lattice vibrations, for He scattered off an Al(111) surface along the $⟨1\overline{1}0⟩$ direction with $E_{\perp }=9\text{eV}$. The thin blue line indicates the classical result without thermal broadening.

Figure 2

(Color online) Experimentally observed rainbow angles ${\theta }_{rb}$ as function of normal component of kinetic energy of projectiles $E_{\perp }$ for scattering of (a) rare gases, [(b) and (c)] metal atoms (alkali and Fe), and the high-affinity atoms (d) S and (e) Cl from Al surfaces along low-indexed directions with different total energies from $E_0=3$ to 80 keV. Fits through data points are drawn to guide the eye.

Figure 3

(Color online) Pair potentials for Ar interacting with Al atoms: OCB (Ref. 17) (dashed curve), ZBL (Ref. 16) (full curve), HF (Ref. 21) (points), and DFT potentials (squares).

Figure 4

(Color online) (a) Surface unit cell and channeling directions of the Al(111) surface (topview). Atomic layers are represented by shaded circles. Topmost layer: dark gray with solid circumference; second layer: medium gray with dashed circumference; third layer: light gray with dotted circumference. The surface cell is indicated by the dashed parallelogram, the irreducible cell by the triangle. Two channeling directions are indicated by arrows. (b) Positions (large points) within the irreducible surface unit cell (shaded triangle) required to determine averaged center and edge potentials for the $⟨1\overline{1}0⟩$ channel of the Ar-Al(111) potential. Equivalent points within the surface unit cell (parallelograms) have same color (shading). Additional grid points at which potentials were calculated are indicated by small black dots.

Figure 5

(Color online) Rainbow angles as function of normal component of kinetic energy, $E_{\perp }$, for Ar atoms scattered off Al(111) along the $⟨1\overline{1}0⟩$ and $⟨11\overline{2}⟩$ directions. Symbols: experimental data for different total kinetic energies $E_0$. Curves: results from trajectory simulations based on (a) surface potentials constructed by summation of Ar-Al pair potentials and (b) full Ar-Al(111) potentials from ab initio DFT slab calculations.

Figure 6

Isopotential lines of the string potential along the $⟨1\overline{1}0⟩$ direction above an Al(111) surface for Ar. Contours derived from (a) OCB pair potential and (b) ab initio DFT slab calculations.

Figure 7

(Color online) Rainbow angles of Ar atoms scattered from Al(110) along low-indexed directions. Experimental results: solid symbols; simulations using ab initio DFT potentials: solid curves.

Figure 8

(Color online) Rainbow scattering angles for He atoms scattered from Al(111) along $⟨1\overline{1}0⟩$ and $⟨11\overline{2}⟩$ as indicated. Symbols: experimental results for different total energies as indicated. Curves: results from trajectory simulations based on a full He-Al(111) potential from ab initio DFT slab calculations (red, solid line) and surface potentials constructed by summation of He-Al DFT pair potentials (blue, dashed line).

Figure 9

Isopotential lines of the channel potential along the (a) $⟨1\overline{1}0⟩$ and (b) the $⟨11\overline{2}⟩$ directions above an Al(111) surface as seen by an impinging Al atom.

Figure 10

(Color online) Rainbow angles of Al atoms scattered off an Al(111) surface along the $⟨1\overline{1}0⟩$ and $⟨11\overline{2}⟩$ directions. Symbols: experimental results for different total energies $E_0$, black dashed lines: simulations using the OCB potential, and red solid curves: simulations based on complete Al-Al(111) ab initio DFT surface potentials.

Figure 11

(Color online) Electron density near an unperturbed Al(111) surface (upper panel) and perturbed by the presence of an Al (mid panel) and by an Ar atom (lower panel) located 2 a.u. above a surface atom. Only electrons from the outermost atomic shells are explicitly included.

Figure 12

(Color online) Rainbow angles of N atoms scattered off an Al(111) surface along the $⟨1\overline{1}0⟩$ direction. Symbols: experimental data for different total energies, black dashed lines: simulation using the OCB potential, red solid curves: simulation based on N-Al(111) ab initio DFT surface potentials.

Figure 13

(Color online) Cut through ELFs for (top panel) Na projectiles at $z=5\text{a}\text{.u}\text{.}$ (mid panel) Ne and (bottom panel) F projectiles at $z=3\text{a}\text{.u}\text{.}$ above a surface atom of an Al(111) surface. The nearest-neighbor distance of the Al surface atoms (on the $y$ axis) is $\approx 5.411\text{a}\text{.u}\text{.}$

Figure 14

(Color online) Number of electrons attached (positive)/detached (negative) to/from the projectiles F, Ne, and Na at different distances above an atom of the topmost Al(111) surface layer (Bader charge states $-Z_p$).

Figure 15

(Color online) Planar-averaged projectile-surface potentials for Ar atoms incident on (left panel) Al(111) and (right panel) Al(110) surfaces as a function of the distance from surface.