Relativistic peculiarities at stepped surfaces: Energetics and diffusion patterns obtained from ab initio calculations

We revive intriguing, yet still unexplained, experimental results of Ehrlich and co-workers [Phys. Rev. Lett. 77, 1334 (1996); Phys. Rev. Lett. 67, 2509 (1991)] who have observed, that $5d$ adatoms distributed on (111) surface islands of $5d$ metals favor the adsorption at the cluster’s edge rather than at the cluster’s interior, which lies in contrast with the behavior of $4d$ and $3d$ elements. Our state of the art ab initio calculations demonstrate that such behavior is a direct consequence of the relativity of $5d$ metals.

Figure 1

(Color online) Schematics of the potential-energy landscape (a) which govern diffusion in $3d$ and $4d$ metallic systems (Refs. 3, 5) and a landscape (b) which corresponds to the diffusion behavior observed in experiments on Pt and Ir (Ref. 1).

Figure 2

System setup for (a) VASP and (b) KKR calculations. (a) A stripe 14 atomic rows wide aligned along the $\left[\overline{1}10\right]$ direction of a Pt(111) surface. (b) Hexagonal Pt islands of $\sim 25\text{Å}$ in diameter adsorbed homoepitaxially on a clean Pt(111) surface, a single atom adsorbed along the shorter diameter of the island ($\left[\overline{1}\overline{1}2\right]$ direction).

Figure 3

(Color online) Adsorption energies of a Pt adatom diffusing in a straight line across a Pt(111) stripe [Fig. 2a] for a fully relaxed (black squares) and ideal (red circles) geometries. Atom position is given in numbered adsorption sites and angstrom with respect to the center of the stripe. Integer numbers (filled squares and circles) denote fcc and noninteger numbers (empty squares and circles) correspond to hcp sites.

Figure 4

(Color online) LDOS at a single Pt adatom residing at the center of a hexagonal Pt(111) island calculated nonrelativistically (thin filled curves) and with scalar-relativistic corrections (thick solid curves) for $s$ (red solid curves) and $d$ (black broken curves) electrons. The $s$ electron densities are scaled up by a factor of 20 for clarity.

Figure 5

(Color online) (a) LDOS at a single Pt adatom residing at the center (thin filled curves, red solid for $s$ and black broken for $d$ electrons) and at the B-step edge (thick curves, red solid for $s$ and black broken for $d$ electrons) of a hexagonal Pt(111) island, calculated nonrelativistically. (b) The same LDOS calculated with scalar-relativistic corrections. The $s$ electron densities are scaled up by a factor of 20 for clarity.