Kinetic theory of cluster impingement in the framework of statistical mechanics of rigid disks

The paper centres on the evaluation of the function n(theta)=N(theta)/N0, that is the normalized number of islands as a function of coverage 0<theta<1, given N0 initial nucleation centres (dots) having any degree of spatial correlation. A mean field approach has been employed: the islands have the same size at any coverage. In particular, as far as the random distribution of dots is concerned, the problem has been solved by considering the contribution of binary collisions between islands only. With regard to correlated dots, we generalize a method previously applied to the random case only. In passing, we have made use of the exclusion probability reported in [S. Torquato, B. Lu, J. Rubinstein, Phys.Rev.A 41, 2059 (1990)], for determining the kinetics of surface coverage in the case of correlated dots, improving our previous calculation [M. Tomellini, M. Fanfoni, M. Volpe Phys. Rev.B 62, 11300, (2000)].Comment: 10 pages, 3 figure

Experimental study of self-similarity in the coalescence growth regime

Theoretical Physic

Decay of isolated surface features driven by the Gibbs-Thomson effect in analytic model and simulation

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 is proportional to (t0-t)^n, where A is the area of the feature, t0 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 two is very good over a range of surface parameters, suggesting that the analytic theory properly captures the necessary physics. It is anticipated that the simulation will be useful in modeling complex surface geometries often seen in experiments on physical surfaces, for which application of the analytic model is not straightforward.Comment: RevTeX (with .bbl file), 25 pages, 7 figures from 9 Postscript files embedded using epsf. Submitted to Phys. Rev. B A few minor changes made on 9/24/9

Breakdown of Scale Invariance in the Phase Ordering of Fractal Clusters

Our numerical simulations with the Cahn-Hilliard equation show that coarsening of fractal clusters (FCs) is not a scale-invariant process. On the other hand, a typical coarsening length scale and interfacial area of the FC exhibit power laws in time, while the mass fractal dimension remains invariant. The initial value of the lower cutoff is a relevant length scale. A sharp-interface model is formulated that can follow the whole dynamics of a diffusion controlled growth, coarsening, fragmentation and approach to equilibrium in a system with conserved order parameter.Comment: 4 pages, 4 figures, RevTex, submitted to PR

Weak selection and stability of localized distributions in Ostwald ripening

We support and generalize a weak selection rule predicted recently for the self-similar asymptotics of the distribution function (DF) in the zero-volume-fraction limit of Ostwald ripening (OR). An asymptotic perturbation theory is developed that, when combined with an exact invariance property of the system, yields the selection rule, predicts a power-law convergence towards the selected self-similar DF and agrees well with our numerical simulations for the interface- and diffusion-controlled OR.Comment: 4 pages, 2 figures, submitted to PR

Normal scaling in globally conserved interface-controlled coarsening of fractal clusters

Globally conserved interface-controlled coarsening of fractal clusters exhibits dynamic scale invariance and normal scaling. This is demonstrated by a numerical solution of the Ginzburg-Landau equation with a global conservation law. The sharp-interface limit of this equation is volume preserving motion by mean curvature. The scaled form of the correlation function has a power-law tail accommodating the fractal initial condition. The coarsening length exhibits normal scaling with time. Finally, shrinking of the fractal clusters with time is observed. The difference between global and local conservation is discussed.Comment: 4 pages, 3 eps figure

Equilibrium shapes and energies of coherent strained InP islands

The equilibrium shapes and energies of coherent strained InP islands grown on GaP have been investigated with a hybrid approach that has been previously applied to InAs islands on GaAs. This combines calculations of the surface energies by density functional theory and the bulk deformation energies by continuum elasticity theory. The calculated equilibrium shapes for different chemical environments exhibit the {101}, {111}, {\=1\=1\=1} facets and a (001) top surface. They compare quite well with recent atomic-force microscopy data. Thus in the InP/GaInP-system a considerable equilibration of the individual islands with respect to their shapes can be achieved. We discuss the implications of our results for the Ostwald ripening of the coherent InP islands. In addition we compare strain fields in uncapped and capped islands.Comment: 10 pages including 6 figures. Submitted to Phys. Rev. B. Related publications can be found at http://www.fhi-berlin.mpg.de/th/paper.htm