faster than at a smooth surface for a given supersaturation. The sticking
probability of a molecule at a smooth surface is small because it involves
only one intermolecular contact. At a rough surface, however, attachment
of a molecule can involve contacts, i.e., bonds, with more than one molecule,
considerably enhancing the chance that the molecule remains attached.
Growth rate in the regime of thermodynamic roughening is propor-
tional to the value of lnb(see Figure 15.6, curve TR) and higher for a lower
avalue, because that means stronger roughening. Eq. (15.2) shows that the
extent of roughening will also increase with increasing temperature, as
would intuitively be expected. In practice, thermodynamic roughening is
observed for a limited number of systems.
Smooth Surfaces. If the value ofais larger than 3.5, the crystal
faces tend to be smooth and hard. This is the most common situation.
Growth now has to occur via surface nucleation, followed by two-
dimensional growth. This is illustrated in Figure 15.7. The activation free
energy for attachment (adsorption) of a growth unit (often a single
molecule) is given by
DG*¼
g*xg*yNAV
Dm¼
g*xg*yNAV
kBTlnb
ð 15 : 3 Þwhereg* is the increase in edge free energy in the x- or y-direction upon
adsorption of a growth unit. These quantities can be calculated (by use of
FIGURE15.7 Illustration of attachment of growth units onto nonroughened
crystal faces.