Spurred by theoretical predictions from Spohn and coworkers [Phys. Rev. E {bf 69}, 035102(R) (2004)], we rederived and extended their result heuristically as well as investigated the scaling properties of the associated Langevin equation in curved ge
ometry with an asymmetric potential. With experimental colleagues we used STM line scans to corroborate their prediction that the fluctuations of the step bounding a facet exhibit scaling properties distinct from those of isolated steps or steps on vicinal surfaces. The correlation functions was shown to go as $t^{0.15(3)}$ decidedly different from the $t^{0.26(2)}$ behavior for fluctuations of isolated steps. From the exponents, we were able to categorize the universality, confirming the prediction that the non-linear term of the KPZ equation, long known to play a central role in non-equilibrium phenomena, can also arise from the curvature or potential-asymmetry contribution to the step free energy. We also considered, with modest Monte Carlo simulations, a toy model to show that confinement of a step by another nearby step can modify as predicted the scaling exponents of the steps fluctuations. This paper is an expansion of a celebratory talk at the 95$^{rm th}$ Rutgers Statistical Mechanics Conference, May 2006.
We have argued that the capture-zone distribution (CZD) in submonolayer growth can be well described by the generalized Wigner distribution (GWD) $P(s)=a s^beta exp(-b s^2)$, where $s$ is the CZ area divided by its average value. This approach offers
arguably the best method to find the critical nucleus size $i$, since $beta approx i + 2$. Various analytical and numerical investigations, which we discuss, show that the simple GWD expression is inadequate in the tails of the distribution, it does account well for the central regime $0.5 < s < 2$, where the data is sufficiently large to be reliably accessible experimentally. We summarize and catalog the many experiments in which this method has been applied.
Using a van der Waals density functional (vdW-DF) [Phys. Rev. Lett. 92, 246401 (2004)], we perform ab initio calculations for the adsorption energy of benzene (Bz) on Cu(111) as a function of lateral position and height. We find that the vdW-DF inclu
sion of nonlocal correlations (responsible for dispersive interactions) changes the relative stability of eight binding-position options and increases the binding energy by over an order of magnitude, achieving good agreement with experiment. The admolecules can move almost freely along a honeycomb web of corridors passing between fcc and hcp hollow sites via bridge sites. Our diffusion barriers (for dilute and two condensed adsorbate phases) are consistent with experimental observations. Further vdW-DF calculations suggest that the more compact (hexagonal) Bz-overlayer phase, with lattice constant a = 6.74 AA, is due to direct Bz-Bz vdW attraction, which extends to ~8 AA. We attribute the second, sparser hexagonal Bz phase, with a = 10.24 AA, to indirect electronic interactions mediated by the metallic surface state on Cu(111). To support this claim, we use a formal Harris-functional approach to evaluate nonperturbationally the asymptotic form of this indirect interaction. Thus, we can account well for benzene self-organization on Cu(111).
