“Formation and spreading”
The number of nuclei appearing per unit of surface is:
The progression rate of the steps is:
Hence, the growth rate:
Note that if AG2 is nullified, that is, if the linear energy уt 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.
According to results obtained previously, the growth rate’s integration mechanisms are announced by the following equations:
Formation and spreading R, = D c5/6 exp (B / 3LnS)
Spiral dislocations R, = Ec2th (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 (m3.kmol-j).
In addition, we can write out:
c0 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 RD (aD) 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.