growing sucrose crystals. The spirals greatly enhance crystal growth rate. A
calculated curve (S) is in Figure 15.6 (the calculation is for the combined
effect of spontaneous nucleation and spiral growth). The number of screw
dislocations greatly depends on the purity of the system, and it is well
known that very pure solutions tend to give very slow crystal growth. The
number also depends on the crystal face.
Also for spiral growth, the rate can be enhanced by surface diffusion.
Figure 15.6 gives a calculated example (curve SþD), but it should be noted
that there is no agreement among researchers on the importance of this effect.
Spiral growth is quite common in practice, and the growth rate then would be
probably somewhere between the curves NþD and SþD. It should be added
that Figure 15.6 gives examples and that the actual growth curves within each
regime vary widely among systems, as discussed in the next section.
Kinetic Roughening. If the value ofDG becomes of orderkBT,
which means lnb&gxg*y=ðkBTÞ^2 , the nucleus size becomes about one growth
unit. This implies that many nuclei form on the crystal face, which thereby
becomes rough. The growth rate of such a face is thereby enhanced. Another
FIGURE15.8 Illustration of the development of a growth spiral on a crystal face;
stages 1–4.