surface science
EI.SEVIER Applied Surface Science92 (1996) 257-260
Computer simulation of nucleation on (001) Kossel crystal surface
with and without diffusion
Tong B. Tang *
Physics Department, H.K. Baptist University, Kowloon Tong, Kowloon, Hong Kong
Received 14 December 1994; acceptedfor publication2 March 1995
Abstract
The Monte Carlo technique was applied to nucleation-controlled growth of a (001) Kossel crystal surface, either with or
without surface diffusion. The sizes of critical nucleus, no, and of supercritical cluster, n+, have been obtained at different
temperatures and supersaturations. With the inclusion of diffusion, both sizes are reduced, and this explains why the
nucleation dip of nucleation growth is shortened. However, n+/n o -- 2, as predicted by the theory of Burton, Carbrera and
Frank, only in the absence of diffusion. Also, when diffusion operates the kink site density along steps is no longer
independent of supersaturation. It is concluded that surface diffusion brings the system further away from thermodynamic
equilibrium.
1. Introduction
Crystal growth involves the transportation of
masses and energy from one phase to another and
cannot be adequately treated by equilibrium thermo-
dynamics. However, kinetic theories suffer from a
problem with spatial inhomogeneity, namely the in-
stantaneous distribution of clusters with different
sizes. It is natural to resort therefore to computer
simulation, for which the Monte Carlo method proved
most effective, since we may with sufficient general-
ity model the elementary steps of absorption, evapo-
ration and surface migration of the growth units by a
sequence of stochastic events. Indeed, since the pio-
neering works by Chernov and Lewis [1] and others,
' Tel.: + 852 2 339 7036; fax: + 852 2 304 6558; e-mail:
tbtang@hkbu.edu.hk.
Monte Carlo simulations of crystal growth have
reached increasing levels of sophistication in dealing
with greater degrees of freedom and more compli-
cated boundary conditions [2,3].
Nevertheless, early theoretical considerations
based on reversible thermodynamics have succeeded
in determining a number of equilibrium properties of
the crystal surface, that serve as parameters in its
growth process, but a few basic questions remain
concerning their validity under various conditions.
The growth of a low-index, defect-free surface at
low temperature proceeds from layer to layer and is
preceded by the continuous formation and disappear-
ance of two-dimensional nuclei (the Zeldovich fluc-
tuation regime). The critical nucleus size n o is de-
fined as the size at which the probabilities to grow
and to dissolve are equal. Supercritical clusters, how-
ever, are those that sustain steady average growth.
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