Analytic many-body potential for GaAs(001) homoepitaxy: Bulk and surface properties

We employ atomic-scale simulation methods to investigate bulk and surface properties of an analytic Tersoff- Abell type potential for describing interatomic interactions in GaAs. The potential is a modified form of that proposed by Albe and colleagues [Phys. Rev. B 66, 035205 (2002)] in which the cut-off parameters for the As-As interaction have been shortened.With this modification, many bulk properties predicted by the potential for solid GaAs are the same as those in the original potential, but properties of the GaAs(001) surface better match results from first-principles calculations with density-functional theory (DFT). We tested the ability of the potential to reproduce the phonon dispersion and heat capacity of bulk solid GaAs by comparing it to experiment and the overall agreement is good. In the modified potential, the GaAs(001) β2(2 × 4) reconstruction is favored under As-rich growth conditions in agreement with DFT calculations. Additionally, the binding energies and diffusion barriers for a Ga adatom on the β2(2 × 4) reconstruction generally match results from DFT calculations. These studies indicate that the potential is suitable for investigating aspects of GaAs(001) homoepitaxy

Communication: Diverse nanoscale cluster dynamics: Diffusion of 2D epitaxial clusters

The dynamics of nanoscale clusters can be distinct from macroscale behavior described by continuum formalisms. For diffusion of 2D clusters of N atoms in homoepitaxial systems mediated by edge atom hopping, macroscale theory predicts simple monotonic size scaling of the diffusion coefficient, DN ∼ N−β, with β = 3/2. However, modeling for nanoclusters on metal(100) surfaces reveals that slow nucleation-mediated diffusion displaying weak size scaling β \u3c 1 occurs for “perfect” sizes Np = L2 and L(L+1) for integer L = 3,4,… (with unique square or near-square ground state shapes), and also for Np+3, Np+4,…. In contrast, fast facile nucleation-free diffusion displaying strong size scaling β ≈ 2.5 occurs for sizes Np+1 and Np+2. DN versus N oscillates strongly between the slowest branch (for Np+3) and the fastest branch (for Np+1). All branches merge for N = O(102), but macroscale behavior is only achieved for much larger N = O(103). This analysis reveals the unprecedented diversity of behavior on the nanoscale

Kinetics of catalysis with surface disorder

We study the effects of generalised surface disorder on the monomer-monomer model of heterogeneous catalysis, where disorder is implemented by allowing different adsorption rates for each lattice site. By mapping the system in the reaction-controlled limit onto a kinetic Ising model, we derive the rate equations for the one and two-spin correlation functions. There is good agreement between these equations and numerical simulations. We then study the inclusion of desorption of monomers from the substrate, first by both species and then by just one, and find exact time-dependent solutions for the one-spin correlation functions.Comment: LaTex, 19 pages, 1 figure included, requires epsf.st

Voting and Catalytic Processes with Inhomogeneities

We consider the dynamics of the voter model and of the monomer-monomer catalytic process in the presence of many ``competing'' inhomogeneities and show, through exact calculations and numerical simulations, that their presence results in a nontrivial fluctuating steady state whose properties are studied and turn out to specifically depend on the dimensionality of the system, the strength of the inhomogeneities and their separating distances. In fact, in arbitrary dimensions, we obtain an exact (yet formal) expression of the order parameters (magnetization and concentration of adsorbed particles) in the presence of an arbitrary number $n$ of inhomogeneities (``zealots'' in the voter language) and formal similarities with {\it suitable electrostatic systems} are pointed out. In the nontrivial cases $n=1, 2$, we explicitly compute the static and long-time properties of the order parameters and therefore capture the generic features of the systems. When $n>2$, the problems are studied through numerical simulations. In one spatial dimension, we also compute the expressions of the stationary order parameters in the completely disordered case, where $n$ is arbitrary large. Particular attention is paid to the spatial dependence of the stationary order parameters and formal connections with electrostatics.Comment: 17 pages, 6 figures, revtex4 2-column format. Original title ("Are Voting and Catalytic Processes Electrostatic Problems ?") changed upon editorial request. Minor typos corrected. Published in Physical Review

Catalytic CO Oxidation on Nanoscale Pt Facets: Effect of Inter-Facet CO Diffusion on Bifurcation and Fluctuation Behavior

We present lattice-gas modeling of the steady-state behavior in CO oxidation on the facets of nanoscale metal clusters, with coupling via inter-facet CO diffusion. The model incorporates the key aspects of reaction process, such as rapid CO mobility within each facet, and strong nearest-neighbor repulsion between adsorbed O. The former justifies our use a "hybrid" simulation approach treating the CO coverage as a mean-field parameter. For an isolated facet, there is one bistable region where the system can exist in either a reactive state (with high oxygen coverage) or a (nearly CO-poisoned) inactive state. Diffusion between two facets is shown to induce complex multistability in the steady states of the system. The bifurcation diagram exhibits two regions with bistabilities due to the difference between adsorption properties of the facets. We explore the role of enhanced fluctuations in the proximity of a cusp bifurcation point associated with one facet in producing transitions between stable states on that facet, as well as their influence on fluctuations on the other facet. The results are expected to shed more light on the reaction kinetics for supported catalysts.Comment: 22 pages, RevTeX, to appear in Phys. Rev. E, 6 figures (eps format) are available at http://www.physik.tu-muenchen.de/~natali

Heterogeneous Catalysis on a Disordered Surface

We introduce a simple model of heterogeneous catalysis on a disordered surface which consists of two types of randomly distributed sites with different adsorption rates. Disorder can create a reactive steady state in situations where the same model on a homogeneous surface exhibits trivial kinetics with no steady state. A rich variety of kinetic behaviors occur for the adsorbate concentrations and catalytic reaction rate as a function of model parameters.Comment: 4 pages, gzipped PostScript fil

Influence of adatom interactions on second layer nucleation

We develop a theory for the inclusion of adatom interactions in second layer nucleation occurring in epitaxial growth. The interactions considered are due to ring barriers between pairs of adatoms and binding energies of unstable clusters. The theory is based on a master equation, which describes the time development of microscopic states that are specified by cluster configurations on top of an island. The transition rates are derived by scaling arguments and tested against kinetic Monte-Carlo simulations. As an application we reanalyze experiments to determine the step edge barrier for Ag/Pt(111).Comment: 4 pages, 4 figure

Island diffusion on metal fcc(100) surfaces

We present Monte Carlo simulations for the size and temperature dependence of the diffusion coefficient of adatom islands on the Cu(100) surface. We show that the scaling exponent for the size dependence is not a constant but a decreasing function of the island size and approaches unity for very large islands. This is due to a crossover from periphery dominated mass transport to a regime where vacancies diffuse inside the island. The effective scaling exponents are in good agreement with theory and experiments.Comment: 13 pages, 2 figures, to be published in Phys. Rev. Let