Subhankar Ray

Revisiting surface diffusion in random deposition

AbstractAn investigation of the effect of surface diffusion in random deposition model is made by analytical methods and reasoning. For any given site, the extent to which a particle can diffuse is decided by the morphology in the immediate neighbourhood of the site. An analytical expression is derived to calculate the probability of a particle at any chosen site to diffuse to a given length, from first principles. This method may become particularly important in cases where obtaining the continuum limit and solving the corresponding differential equation may not be feasible. Numerical simulation of surface diffusion in random deposition model with varying extents of diffusion are performed and their results are interpreted in the light of the analytical calculations. Systems with surface diffusion show an initial random deposition-like growth upto monolayer deposition, then a deviation due to correlation effects and eventual saturation. An explanation for this behaviour is discussed and the point of departure from the linear form is estimated analytically.

Multistep surface diffusion sensitive to diffusion length

Random deposition model with surface diffusion over several next nearest neighbours is studied. Several extensions of diffusion models to include multistep diffusion gives Family’s surface diffusion model in the nearest neighbour diffusion limit. The results for the various extensions agree with the results obtained by Family for the case of nearest neighbour diffusion. However, for larger allowed diffusion length, the growth exponent and roughness exponent show interesting dependence on diffusion length. The variation of values of exponents are fitted to empirical equations. The probable mechanism for dependence of exponents on the diffusion length is discussed.

Surface properties and scaling behavior of a generalized ballistic deposition model.

The surface exponents, scaling behavior, and bulk porosity of a generalized ballistic deposition (GBD) model are studied. In nature, there exist particles with varying degrees of stickiness ranging from completely nonsticky to fully sticky. Such particles may adhere to any one of the successively encountered surfaces, depending on a sticking probability that is governed by the underlying stochastic mechanism. The microscopic configurations possible in this model are much larger than those allowed in existing models of ballistic deposition and competitive growth models that seek to mix ballistic and random deposition processes. In this article, we find the scaling exponents for surface width and porosity for the proposed GBD model. In terms of scaled width W[over ̃] and scaled time t[over ̃], the numerical data collapse onto a single curve, demonstrating successful scaling with sticking probability p and system size L. Similar scaling behavior is also found for the porosity.