Figure 1

The two mirror symmetrical ground state configurations of the 169-atom island. We classify island states by the position of vacancies on the horizontal edges. The notation, $n:8-n|m:8-m$, means that the top edge has $n$ atoms, a vacancy, and then $8-n$ atoms, with a similar notation for the bottom edge. For configurations with no vacancy, the notation “8” is used.Reuse & Permissions

Figure 2

Temperature dependence of island hopping rates (limits from Poisson statistics at 95% confidence). At 300 K, the 169- and 217-atom islands diffuse much faster than the monomer or 127-atom island. At 300 K, the 37-, 61-, 91-, and 271-atom islands did not hop: only an upper rate bound is plotted in the inset. The Arrhenius fit for the 169-atom island (blue line) suggests an activation energy of 0.178 eV, in serious disagreement with our NEB calculation (Fig. 4) of 0.243 eV. The curved green line resolves the problem by having a slope equal to the temperature-dependent effective energy of activation (see text).Reuse & Permissions

Figure 3

Center of mass coordinate for a 169-atom island MD run at 275 K. On the left-hand side is a scatter plot of quenched c.m. position versus potential energy. The system occupies a very large set of metastable states even at low temperatures. On the right-hand side is a plot of quenched c.m. coordinate versus time. The red points show the states in the immediate vicinity of the ground states ($E_{\mathrm{quenched}}<0.04\mathrm{eV}$). Transitions between red points are of two types: a rapid, glide-centric process which repeats frequently between $5:3|5:3$ and $3:5|3:5$ without completing a hop. The rate-limiting vacancy-assisted transitions ($3:5|3:5$ to $5:3|5:3\mathrm{T}$) cross the double black horizontal lines, allowing a complete hop and determining the diffusion rate.Reuse & Permissions

Figure 4

Minimum energy path for surface diffusion of a 169-atom Ag hexagonal island based on 175 K PRD run and subsequent NEB analysis. States are labeled as in Fig. 1. The highest energy barrier is 0.243 eV. The intermediate state ($3:5|3:5$) is reached by extensive core glide with a few vacancy hops. The rate-limiting process ($3:5|3:5$ to $5:3|5:3\mathrm{T}$) involves vacancy annihilation at one end and vacancy creation at the opposite end of the island edge.Reuse & Permissions

Figure 5

The histogram inset shows the energy distribution of 169-atom island states quenched from a 275 K MD run. The mean energy $\overline{E}(T)$ of the quenched states is 0.081 eV. The plot shows $\overline{E}(T)$ vs $1/\mathrm{kT}$. The curved green line in the Arrhenius plot of Fig. 2 was fit using a temperature-dependent slope (effective activation energy), $\Delta E(T)=E_A-\overline{E}(T)$, with $E_A=0.243\mathrm{eV}$ from the NEB pathway in Fig. 4.Reuse & Permissions