“Formation and spreading”
The number of nuclei appearing per unit of surface is:
The progression rate of the steps is:
Hence, the growth rate:
Example 2.5.
Note that if AG2 is nullified, that is, if the linear energy у_{t} is nullified, growth becomes:
Growth becomes of the same order as that of a K face and is consequently limited for the transfer through the diffusion layer.
Diffusionintegration combination
According to results obtained previously, the growth rate’s integration mechanisms are announced by the following equations:
Formation and spreading R, = D c^{5/6} exp (B / 3LnS)
Spiral dislocations R, = Ec^{2}th (Cj / a)
All of these functions increase monotonically according to the relative supersaturation a. They are zero for c = 0 .
The molar flow density crossing the diffusion layer is:
This corresponds to a growth rate of:
c*: solution concentration at equilibrium (kmol.m^{3})
П : molecular volume (m^{3}.kmol^{j}).
In addition, we can write out:
c_{0} is the concentration at the interface separating the diffusion layer and the integration layer.
The calculation of a, is performed by equating rate R, (a,) for integration and rate R_{D} (a_{D}) for diffusion.
An analytical solution is possible in both extremes of the dislocation mechanism (oi << о and Oi >> a).
The “formation and spreading” mechanism is not susceptible to a numerical resolution.
