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Chapter II Solution Growth….
vapor. Equilibrium is reached when the rates of these two processes are
equal. Now, the surface will look like as shown in figure (2.3 b).
One can notice the changes in the surface easily by comparing the
figures (2.3 a) and (2.3 b). The two main changes are noticeable; which are
(1) the step has acquired a number of kinks such as A and (2) a small number
of molecules have been adsorbed on the crystal surface and on the step,
indicated as B in the figure (2.3 b), and also a similar number of surface
vacancies C, a small number of pairs of adsorbed molecules D or pairs of
vacancies have been created.
The mean distance xo between the kinks is estimated in terms of the
inter-atomic distance, a, by
xo = ½ [ exp( ω / k T)+ 2] ≈ ½ a [ exp (ω / k T)] (2.2)
Now, introducing the nearest neighbor interaction as, Φ, which is
related to the evaporation energy, W, by the expression as follows
Therefore, the mean distance xo can be obtained as
Φ = 1/6 (W) (2.3)
xo = ½ exp [Φ / 2kT] (2.4)
It was first realized by Volmer [20] in 1922 that the adsorbed
molecules diffuse with considerable ease over the crystal surfaces. The
process of growth of a crystal surfaces with steps is the result of mainly three
processes; (1) a transport of molecules from the vapor to the adsorbed layer,
(2) the diffusion of the adsorbed molecules towards the steps and (3) the
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