Thermodynamic Roughening. A crystal in a solution that is
precisely saturated may have faces that are not flat and smooth on a
microscopic scale. This means that there is a transition zone of some
molecules thick between the solid and the liquid phase. This roughness
persists at increasing supersaturation. Whether roughening occurs depends
on the surface entropy parameter
a¼4 e
kBTð 15 : 2 Þwhereeis the net binding energy of a growth unit (often a molecule) to a flat
crystal surface. Ifais smaller than about 3—which will generally be the case
for small molecules that are bound by van der Waals forces only—the
surface tends to be rough. At such a surface, the growth rate is distinctly
FIGURE15.6 Normalized linear growth rate of crystal faces as a function of
supersaturation lnb. Calculated curves for thermodynamic roughening (TR), surface
nucleation and growth (N), and spiral growth (S); for the last two cases additional
calculations including the effect of surface diffusion (D) are also shown. The curve
denoted ‘‘max’’ gives the hypothetical maximum for growth rate. Only meant to
illustrate trends. (From results of Bennema; see in Bibliography.)