8 research outputs found
Lattice Effects in Crystal Evaporation
We study the dynamics of a stepped crystal surface during evaporation, using
the classical model of Burton, Cabrera and Frank, in which the dynamics of the
surface is represented as a motion of parallel, monoatomic steps. The validity
of the continuum approximation treated by Frank is checked against numerical
calculations and simple, qualitative arguments. The continuum approximation is
found to suffer from limitations related, in particular, to the existence of
angular points. These limitations are often related to an adatom detachment
rate of adatoms which is higher on the lower side of each step than on the
upper side ("Schwoebel effect").Comment: DRFMC/SPSMS/MDN, Centre d'Etudes Nucleaires de Grenoble, 25 pages,
LaTex, revtex style. 8 Figures, available upon request, report# UBFF30119
Spatio-temporal distribution of nucleation events during crystal growth
We consider irreversible second-layer nucleation that occurs when two adatoms
on a terrace meet. We solve the problem analytically in one dimension for zero
and infinite step-edge barriers, and numerically for any value of the barriers
in one and two dimensions. For large barriers, the spatial distribution of
nucleation events strongly differs from , where is the
stationary adatom density in the presence of a constant flux. The probability
that nucleation occurs at time after the deposition of the second
adatom, decays for short time as a power law [] in and
logarithmically [] in ; for long time it decays
exponentially. Theories of the nucleation rate based on the assumption
that it is proportional to are shown to overestimate by a
factor proportional to the number of times an adatom diffusing on the terrace
visits an already visited lattice site.Comment: 4 pages, 3 figures; accepted for publication on PR
Island nucleation in the presence of step edge barriers: Theory and applications
We develop a theory of nucleation on top of two-dimensional islands bordered
by steps with an additional energy barrier for descending atoms.
The theory is based on the concept of the residence time of an adatom on the
island,and yields an expression for the nucleation rate which becomes exact in
the limit of strong step edge barriers. This expression differs qualitatively
and quantitatively from that obtained using the conventional rate equation
approach to nucleation [J. Tersoff et al., Phys. Rev. Lett.72, 266 (1994)]. We
argue that rate equation theory fails because nucleation is dominated by the
rare instances when two atoms are present on the island simultaneously. The
theory is applied to two distinct problems: The onset of second layer
nucleation in submonolayer growth, and the distribution of the sizes of top
terraces of multilayer mounds under conditions of strong step edge barriers.
Application to homoepitaxial growth on Pt(111) yields the estimate eV for the additional energy barrier at CO-decorated steps.Comment: 13 pages, 3 figure
A Simple Model for Anisotropic Step Growth
We consider a simple model for the growth of isolated steps on a vicinal
crystal surface. It incorporates diffusion and drift of adatoms on the terrace,
and strong step and kink edge barriers. Using a combination of analytic methods
and Monte Carlo simulations, we study the morphology of growing steps in
detail. In particular, under typical Molecular Beam Epitaxy conditions the step
morphology is linearly unstable in the model and develops fingers separated by
deep cracks. The vertical roughness of the step grows linearly in time, while
horizontally the fingers coarsen proportional to . We develop scaling
arguments to study the saturation of the ledge morphology for a finite width
and length of the terrace.Comment: 20 pages, 12 figures; [email protected]
Estimation of chlorophyll and turbidity, of Kneiss archipelago gulf of Gabes, using Sentinel 2A and EO1 data
International Journal of Geosciences, 202