Interplay between kinetic roughening and phase ordering

We studied interplay between kinetic roughening and phase ordering in 1+1 dimensional single-step solid-on-solid growth model with two kinds of particles and Ising-like interaction. Evolution of both geometrical and compositional properties was investigated by Monte Carlo simulations for various strengths of coupling. We found that the initial growth is strongly affected by interaction between species, scaling exponents are enhanced and the ordering on the surface is observed. However, after certain time, ordering along the surface stops and the scaling exponents cross over to exponents of the Kardar-Parisi-Zhang universality class. For sufficiently strong strength of coupling, ordering in vertical direction is present and leads to columnar structure persisting for a long time.Comment: 8 pages, EUROLaTeX, 3 ps figures, submitted to Europhys. Let

Dynamic properties in a family of competitive growing models

The properties of a wide variety of growing models, generically called $X/RD$, are studied by means of numerical simulations and analytic developments. The study comprises the following $X$ models: Ballistic Deposition, Random Deposition with Surface Relaxation, Das Sarma-Tamboronea, Kim-Kosterlitz, Lai-Das Sarma, Wolf-Villain, Large Curvature, and three additional models that are variants of the Ballistic Deposition model. It is shown that after a growing regime, the interface width becomes saturated at a crossover time ($t_{x2}$) that, by fixing the sample size, scales with $p$ according to $t_{x2}(p)\propto p^{-y}, \qquad (p > 0)$, where $y$ is an exponent. Also, the interface width at saturation ($W_{sat}$) scales as $W_{sat}(p)\propto p^{-\delta}, \qquad (p > 0)$, where $\delta$ is another exponent. It is proved that, in any dimension, the exponents $\delta$ and $y$ obey the following relationship: $\delta = y \beta_{RD}$, where $\beta_{RD} = 1/2$ is the growing exponent for $RD$. Furthermore, both exponents exhibit universality in the $p \to 0$ limit. By mapping the behaviour of the average height difference of two neighbouring sites in discrete models of type $X/RD$ and two kinds of random walks, we have determined the exact value of the exponent $\delta$. Finally, by linking four well-established universality classes (namely Edwards-Wilkinson, Kardar-Parisi-Zhang, Linear-MBE and Non-linear-MBE) with the properties of both random walks, eight different stochastic equations for all the competitive models studied are derived.Comment: 23 pages, 6 figures, Submitted to Phys. Rev.

Kinetic Roughening in Growth Models with Diffusion in Higher Dimensions

We present results of numerical simulations of kinetic roughening for a growth model with surface diffusion (the Wolf-Villain model) in 3+1 and 4+1~dimensions using lattices of a linear size up to $L=64$ in 3+1~D and $L=32$ in 4+1~D. The effective exponents calculated both from the surface width and from the height--height correlation function are much larger than those expected based on results in lower dimensions, due to a growth instability which leads to the evolution of large mounded structures on the surface. An increase of the range for incorporation of a freshly deposited particle leads to a decrease of the roughness but does not suppress the instability.Comment: 8 pages, LaTeX 2.09, IC-DDV-93-00

Kinetic roughening and phase ordering in the two-component growth model

Interplay between kinetic roughening and phase ordering is studied in a growth SOS model with two kinds of particles and Ising-like interaction by Monte Carlo simulations. We found that, for a sufficiently large coupling, growth is strongly affected by interaction between species. Surface roughness increases rapidly with coupling. Scaling exponents for kinetic roughening are enhanced with respect to homogeneous situation. Phase ordering which leads to the lamellar structure persisting for a long time is observed. Surface profiles in strong coupling regime have a saw-tooth form, with the correlation between the positions of local minima and the domain boundaries.Comment: 6 pages, 3 postscript figures, accepted in Surface Scienc

Phase ordering and roughening on growing films

We study the interplay between surface roughening and phase separation during the growth of binary films. Already in 1+1 dimension, we find a variety of different scaling behaviors depending on how the two phenomena are coupled. In the most interesting case, related to the advection of a passive scalar in a velocity field, nontrivial scaling exponents are obtained in simulations.Comment: 4 pages latex, 6 figure