124 research outputs found
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 in 3+1~D and
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
Dynamic properties in a family of competitive growing models
The properties of a wide variety of growing models, generically called
, are studied by means of numerical simulations and analytic
developments. The study comprises the following 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 () that, by fixing the sample size,
scales with according to , where
is an exponent. Also, the interface width at saturation () scales
as , where is another
exponent.
It is proved that, in any dimension, the exponents and obey the
following relationship: , where is
the growing exponent for . Furthermore, both exponents exhibit universality
in the limit.
By mapping the behaviour of the average height difference of two neighbouring
sites in discrete models of type and two kinds of random walks, we have
determined the exact value of the exponent .
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.
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
New mechanism for impurity-induced step bunching
Codeposition of impurities during the growth of a vicinal surface leads to an
impurity concentration gradient on the terraces, which induces corresponding
gradients in the mobility and the chemical potential of the adatoms. Here it is
shown that the two types of gradients have opposing effects on the stability of
the surface: Step bunching can be caused by impurities which either lower the
adatom mobility, or increase the adatom chemical potential. In particular,
impurities acting as random barriers (without affecting the adatom binding)
cause step bunching, while for impurities acting as random traps the
combination of the two effects reduces to a modification of the attachment
boundary conditions at the steps. In this case attachment to descending steps,
and thus step bunching, is favored if the impurities bind adatoms more weakly
than the substrate.Comment: 7 pages, 3 figures. Substantial revisions and correction
Crossover effects in the Wolf-Villain model of epitaxial growth in 1+1 and 2+1 dimensions
A simple model of epitaxial growth proposed by Wolf and Villain is
investigated using extensive computer simulations. We find an unexpectedly
complex crossover behavior of the original model in both 1+1 and 2+1
dimensions. A crossover from the effective growth exponent to is observed in 1+1
dimensions, whereas additional crossovers, which we believe are to the scaling
behavior of an Edwards--Wilkinson type, are observed in both 1+1 and 2+1
dimensions. Anomalous scaling due to power--law growth of the average step
height is found in 1+1 D, and also at short time and length scales in 2+1~D.
The roughness exponents obtained from the
height--height correlation functions in 1+1~D () and 2+1~D
() cannot be simultaneously explained by any of the continuum
equations proposed so far to describe epitaxial growth.Comment: 11 pages, REVTeX 3.0, IC-DDV-93-00
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