In this paper we report simulation studies of equilibrium features, namely circular islands on model surfaces, using Monte-Carlo methods. In particular, we are interested in studying the relationship between the density of vapour around a curved island and its curvature. The "classical" form of this relationship is the Gibbs-Thomson formula, which assumes the vapour surrounding the island to be an ideal gas. Numerical simulations of a lattice gas model, performed for various sizes of islands, don't fit very well to the Gibbs-Thomson formula. We show how corrections to this form arise at high vapour densities, wherein a knowledge of the exact equation of state (as opposed to the ideal gas approximation) is necessary to predict this relationship.By exploiting a mapping of the lattice gas to the Ising model one can compute the corrections to the Gibbs-Thomson formula using high field series expansions. The corrected Gibbs-Thomson formula matches very well with the Monte Carlo data. We also investigate finite size effects on the stability of the islands both theoretically and through simulations. Finally the simulations are used to study the microscopic origins of the Gibbs-Thomson formula. It is found that smaller islands have a greater adatom detachment rate per unit length of island perimeter. This is principally due to a lower coordination of edge atoms and a greater availability of detachment moves relative to edge 1 moves. A heuristic argument is suggested in which these effects are partially attributed to geometric constraints on the island edge. 05.50.+q, 64.60.Qb, 82.60.Nh, 82.65.Dp

A theory based on the thermodynamic Gibbs-Thomson relation is presented which provides the framework for understanding the time evolution of isolated nanoscale features (i.e., islands and pits) on surfaces. Two limiting cases are predicted, in which either diffusion or interface transfer is the limiting process. These cases correspond to similar regimes considered in previous works addressing the Ostwald ripening of ensembles of features. A third possible limiting case is noted for the special geometry of "stacked" islands. In these limiting cases, isolated features are predicted to decay in size with a power law scaling in time: A ∝ (t 0 − t) n , where A is the area of the feature, t 0 is the time at which the feature disappears, and n = 2/3 or 1. The constant of proportionality is related to parameters describing both the kinetic and equilibrium properties of the surface. A continuous time Monte Carlo simulation is used to test the application of this theory to generic surfaces with atomic scale features. A new method is described to obtain macroscopic kinetic parameters describing interfaces in such simulations. Simulation and analytic theory are compared directly, using measurements of the simulation to determine the constants of the analytic theory. Agreement between the * Communicating author. Present Address:

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We use the Newns-Anderson Hamiltonian to describe many-body electronic processes that occur when hyperthermal alkali atoms scatter off metallic surfaces.Following Brako and Newns, we expand the electronic many-body wavefunction in the number of particle-hole pairs (we keep terms up to and including a single particle-hole pair). We extend their earlier work by including level crossings, excited neutrals and negative ions. The full set of equations of motion are integrated numerically, without further approximations, to obtain the many-body amplitudes as a function of time. The velocity and work-function dependence of final state quantities such as the distribution of ion charges and excited atomic occupancies are compared with experiment. In particular, experiments that scatter alkali ions off clean Cu(001) surfaces in the energy range 5 to 1600 eV constrain the theory quantitatively. The neutralization probability of Na + ions shows a minimum at intermediate velocity in agreement with the theory. This behavior contrasts with that of K + , which shows virtually no neutralization, and with Li + , which exhibits a monotonically increasing neutral fraction with decreasing velocity. Particle-hole excitations are left behind in the metal during a fraction of the collision events; this dissipated energy is predicted to be quite small (on the order of tenths of an electron volt). Indeed, classical trajectory simulations of the surface dynamics account well for the observed energy loss, and thus provide some justification for our truncation of the equations of motion at the single particle-hole pair level. Li + scattering experiments off low work-function surfaces provide qualitative information on the importance of many-body effects. At sufficiently low work function, the negative ions predicted to occur are in fact observed. Excited neutral Li atoms (observed via the optical 2p → 2s transition) also emerge from the collision. A peak in the calculated Li(2p) → Li(2s) photon intensity occurs at intermediate work function in accordance with measurements.

We show in this paper that measurements of charge-state distributions for S -1600 eV Li, Na, and K scattered from a clean Cu(001) surface provide an excellent probe of the dynamics of atom-surface charge transfer. The neutralization probabilities, measured as a function of the perpendicular velocities of the scattered atoms, are qualitatively different for the three species. These differences reflect the high sensitivity of the charge transfer in this energy range to the energies and lifetimes of the atomic resonances near the surface. The measured neutralization probabilities are found to depend on the parallel velocity component of the scattered atom, even though the velocities at which these experiments are conducted are relatively low. The data are compared to several models of the charge-transfer process.Agreement with the data is achieved using a model based on the one-electron Newns-Anderson Hamiltonian and using calculated values for the alkali-metal resonance parameters.