Surface integration models continuous growth

Some authors have observed that the growth rate at very small supersatirration is greater than predicted by the nucleation models. This can be explained by the so-called BCF model (Bruton et al. 1951). The authors assume that the presence of spiral dislocations which end somewhere on the crystal surface creates steps, which are thus a continuous soirrce of favorable integration sites. The soirrce of such screw dislocations is a lattice imperfection which prevents an ideally smooth crystal surface. The steps of these spiral dislocations are remote from the centers and considered to be parallel and the same distance apart from each other. The linear displacement rate of a face is controlled by surface diffusion. With the siuface diffusion coefficient the growth rate Vg p according to Burton, Cabrera, and Frank is... 

According to the Watzky-Finke model [6], the reactions (6) and (7) correspond to slow continuous nucleation, and fast autocatalytic growth of Au NP s surface, respectively. Using this model, integral kinetic equation of Au NP s formation for isolation conditions (excess of reductant) can be derived ... 

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