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Chapter II Solution Growth….
shape of crystal was related to the relative surface free energies of the faces
in a very simple manner.
It was thought that on perfect crystal faces steps could be created by
the thermodynamic fluctuations in much similar way as the kinks are formed
on a step. However, in the earlier theoretical considerations the problem was
to start the nucleation on the perfect crystal face. Gibbs [22] considered that
before a new layer can grow, a two dimensional nucleus or island monolayer,
probably of 100 molecular diameters, has to be formed and on the edges of
which the growth can proceed. Once such type of layer is formed, it spreads
quickly across the whole face and the process of growth is held until a new
nucleus is formed. This has been described in Figure (2.4).
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Figure: 2.4 Surface with island monolayer.
The problem of nucleating an island monolayer on a closed-packed
crystal surface is analogous to the nucleation of a water droplet as mentioned
earlier. For a given degree of super-saturation, there a critical radius ρc of the
nucleus of circular nature such that a nucleus of radius greater than ρc will
grow and if less it will evaporate. This is due to the line energy of the step of
island monolayer causes a local equilibrium vapor pressure, which is inversely
proportional to its radius of curvature. In the case of circular nucleus of radius
ρ, the free energy is,
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