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Chapter II Solution Growth….
diffusion of adsorbed molecules along the edge of the steps towards kinks.
This process is shown in figure (2.3 b).
The proportion ns of the surface sites covered by adsorbed molecules
has been given by Burton, Cabrera and Frank [21] approximately as,
ns = exp [-Ws / kT] (2.5)
Where, Ws is the energy of evaporation from the kinks on to the surface, that
is, the energy required to transfer a molecule from a site A to site B in figure
(2.3 b), which was estimated to be about ½ W.
The mean displacement xs of adsorbed molecules, which is the
average distance a molecule would wander on the crystal surface between
the time it hits the surface and the time it evaporates again, is given by Burton
et al [21] as,
xs= a exp { ( W’s – Us )/ 2k T} (2.6)
Where, Us is the activation energy for surface diffusion, that is, migration from
one surface site to another and this has been estimated to be of the order of
1/20 ; W’s is the evaporation energy from the surface to the vapor and is
given by, Ws =3 Φ, that is, half the total evaporation energy W. One can
further neglect Us and estimate that xs ≈ a exp (3 Φ / 2 kT), which is of the
order of 4 x 10 2 for the typical values of Φ / kT ≈ 4. This indicates that xs>>a,
therefore, the molecules diffuse considerable distance before evaporating.
This leads to conclude that the direct arrival of molecules from vapor at any
particular point on a crystal surface is, generally, small as compared with the
rate of indirect arrival through the surface migration.
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