Surface and bulk properties of ballistic deposition models with bond breaking

TL;DR

This paper introduces a new class of ballistic deposition models with bond breaking, analyzing their crossover from random to correlated growth, and derives scaling laws for surface roughness, porosity, and crossover times through simulations and scaling arguments.

Contribution

It presents a novel growth model with surface restructuring, providing new scaling relations and demonstrating non-universality of exponents in such systems.

Findings

Crossover time scales as p^{-y} with y=(n+1)

Saturation width scales as p^{-rac{n+1}{2}}

Bulk porosity scales as p^{y-rac{n+1}{2}}

Abstract

We introduce a new class of growth models, with a surface restructuring mechanism in which impinging particles may dislodge suspended particles, previously aggregated on the same column in the deposit. The flux of these particles is controlled through a probability $p$. These systems present a crossover, for small values of $p$, from random to correlated (KPZ) growth of surface roughness, which is studied through scaling arguments and Monte Carlo simulations on one- and two-dimensional substrates. We show that the crossover characteristic time $t_{\times}$ scales with $p$ according to $t_{\times}\sim p^{-y}$ with $y=(n+1)$ and that the interface width at saturation $W_{sat}$ scales as $W_{sat}\sim p^{-\delta}$ with $\delta = (n+1)/2$, where $n$ is either the maximal number of broken bonds or of dislodged suspended particles. This result shows that the sets of exponents $y=1$ and $\delta=1/2$ or $y=2$ and $\delta=1$ found in all previous works focusing on systems with this same type of crossover are not universal. Using scaling arguments, we show that the bulk porosity $P$ of the deposits scales as $P\sim p^{y-\delta}$ for small values of $p$. This general scaling relation is confirmed by our numerical simulations and explains previous results present in literature.