Surface spiral step control, crystal

Surface Spiral Step Control. Many crystals grow faster at small supersaturation than allowed by Equation 7. This lead Frank (17) to suggest that steps may also originate from the presence of a screw dislocation, and that this kind of steps is not destroyed by spreading to the crystal edge, but continues infinitely. The rate law according to this theory is parabolic (7). We shall use the following version of the kinetic equation (10)... 

It is often observed in tiny crystals of micrometer order, such as clay minerals, that the entire surface of a crystal face is covered by elementary spiral layers originating from one screw dislocation (Fig. 5.3). Figure 5.10(a) shows such an exceptional case observed on a (0001) face of a SiC crystal synthesized by the Acheson method. However, such a situation is almost exceptional on crystal faces larger than millimeter size, and is encountered only on crystals synthesized under very precisely controlled conditions. In general, there are many growth centers on one crystal face, and steps from these centers bunch together to form macro-steps, which constitute the step patterns of the face. 

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... 

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