Kenneth G Libbrecht, The physics of snow crystals, Rep. Prog. Phys. 68 (2005) 855–895 doi:10.1088/0034-4885/68/4/R03
2.6.1. Surface roughening. For a crystal at finite temperature, there are two contributions
to the surface free energy, F = E − T S. The first is the binding energy, which favours a
smooth surface with the least number of dangling bonds, and the second is the surface entropy,
which favours a rougher surface with the greatest number of possible configurations. At low
temperatures the binding energy wins and the equilibrium structure is close to a flat, faceted
surface. Near the melting point, however, it becomes favourable for the surface to contain a
greater number of molecular edges and kinks . Depending on the details of the molecular
structure of the crystal, there may exist a roughening temperature TR, above which the surface
becomes completely rough.
Much has been written about the roughening transition, in part because of its mathematical
simplicity [34, 48, 49], and also because surface roughening is observed in many real crystals.
Without measuring the surface structure directly (which is difficult for a high vapour pressure
material like ice), there are two indirect observations that are likely indicators of surface
roughening: (1) above TR the attachment kinetics are described by α ≈ 1, and (2) the growth
form is nonfaceted even at low supersaturations. The evidence for surface roughening in ice
will be discussed in the experimental section below.
Sometimes a faceted surface will exhibit a relatively sharp transition fromα < 1 to α ≈ 1
as σ is increased, even if it is not above its equilibrium roughening temperature. This may be an
indication of kinetic roughening, in which surface roughening is induced by rapid growth .
Kinetic roughening is not a well-defined thermodynamic phase transition, and it occurs when
island formation on the surface is relatively easy. As with static surface roughening, kinetic
roughening precludes the formation of crystal facets. This phenomenon has not been studied
much in ice crystal growth, but it may be important for the formation of ice dendrites, which
occurs at high supersaturations.