Migration of point defects at charged Cu, Ag, and Au (100) surfaces

We report ab initio values for the electrical dipole moment and for the formation and activation energies of adatoms and vacancies migrating on Cu, Ag, and Au (100) surfaces, and we discuss the effect of the electrical dipole energy of these point defects on the rate of mass transport along charged metal-electrolyte interfaces. We find that adatoms and vacancies exhibit positive surface dipole moments, which for positive electrode potentials tend to reduce the formation and activation energies and increase the mobility of the point defects. We also consider atom migration by an exchange process involving the intermediate formation of dimers, and find that the surface dipole moment of the Cu and Ag dimers is negative, which means that they tend to become more mobile for negative potentials. However, because of their large activation energies, we conclude that the exchange process is not likely to provide an energetically favorable mechanism for migration in these systems. The Au dimer has a small positive dipole moment, which implies that the exchange process may contribute to surface transport but only in neutral surfaces.

Figure 1

(a) Cluster utilized to study the reaction path involved in the desorption of an atom from a kink in a step at the (100) surface. (b) Variation of the energy and (c) surface dipole moment of the adatom moving along the path $K\to S\to T$, indicated in inset (a), for the Au (full), Ag (dotted), and Cu (dashed) surfaces.

Figure 2

53-atom clusters utilized to represent an adatom adsorbed on a (100) surface, moving from (a) the ground state above a fourfold coordinated hollow site to (b) the transition state above a twofold coordinated bridge site.

Figure 3

(a) Schematic view of an adatom adsorbed on an Au(100) surface in the ground state geometry. (b) Change in the charge density induced in the [110] plane by the adsorption of the adatom. The continuous and dashed contour lines represent increase and decrease of charge, with densities given by $2n^3\times {10}^{-4}e{\mathrm{\AA }}^{-3}$, for $n=-15,\dots ,15$.

Figure 4

(a) Cluster utilized to study the annihilation of a vacancy moving from the terrace to a kink in the (100) surface. The arrows indicate the movement of the atoms, which has the opposite direction than the movement of the vacancy. (b) Variation of the energy and (c) surface dipole moment of the vacancy moving along the path $T\leftarrow S\leftarrow K$, indicated in inset (a), for the Au (full), Ag (dotted), and Cu (dashed) surfaces.

Figure 5

51-atom clusters utilized to represent a vacancy of the (100) surface, moving from (a) its ground state to (b) the transition state.

Figure 6

(a) Schematic view of a vacancy at the an Au(100) surface in the ground state geometry. (b) Change in the charge density difference induced in the [110] plane by the creation of the vacancy. The continuous and dashed contour lines represent increase and decrease of charge, with densities given by $2n^3\times {10}^{-4}e{\mathrm{\AA }}^{-3}$, for $n=-15,\dots ,15$.

Figure 7

(a) Cluster utilized to study the desorption of an atom from a kink in a step at the (100) surface by Feibelman’s exchange process. Here $D$ denotes the formation of the dimer. (b) Variation of the energy and (c) surface dipole moment along the migration path indicated in inset (a) for Au (full), Ag (dotted), and Cu (dashed).

Figure 8

49-atom clusters utilized to represent migration by atom exchange at the (100) surface. (a) In the ground state we see an adatom in a fourfold hollow site. (b) In the transition state a neighbor of the adatom moves upwards leaving a vacancy in the surface plane and forms a dimer with the adatom. In a further stage (not shown) the adatom fills the vacancy.

Figure 9

(a) Schematic view of an atom dimer in an exchange process at the Au(100) surface. (b) Change in the charge density difference induced in the [110] plane by the formation of the dimer. The continuous and dashed contour lines represent increase and decrease of charge, with densities given by $2n^3\times {10}^{-4}e{\AA }^{-3}$, for $n=-15,\dots ,15$.