Monotropic polymorphism involves one or more unstable forms and a
stable one; this occurs in fats. Compound crystals contain two or more
different substances. They may be solute and solvent, usually water as in
NaCl?2H 2 O, or a range of very similar molecules.
Crystal Growth. The linear growth rate of a crystal face depends
on several factors. The first one is the growth regime. Incorporation of
molecules on a smooth face is difficult and needs two-dimensional
nucleation. However, the presence of certain types of imperfections or
dislocations in a crystal gives rise to the formation of growth spirals,
whereby the growth rate is greatly enhanced; this is a rather common
situation. In other regimes roughening of the crystal surface occurs, which
also greatly enhances growth. Growth rate naturally increases with
increasing supersaturation lnb, wherebis the supersaturation ratio, but
the relation varies with growth regime. Moreover, nonideality of the
solution may strongly affect the effective supersaturation ratio, which is an
activity ratio. Some variables that retard growth rate are (a) the difficulty of
fitting in the crystal lattice, especially occurring for large anisometric and
flexible molecules; (b) competition with very similar molecules that almost
fit the crystall lattice; and (c) the presence of molecules that strongly inhibit
growth by adsorbing onto the crystal face. All of these factors cause the
growth rate to vary by some orders of magnitude for the same value of the
supersaturation. Moreover, they greatly affect crystal shape, since the effect
on growth rate may greatly vary among crystal faces.
Theoverall crystallizationrate also depends on (a) the total crystal
surface area, which will be larger if more crystals are formed and hence if
nucleation is faster; (b) stirring, which increases the rate if diffusion of
molecules to the crystal surface is growth limiting; and (c) removal of the
released heat of fusion, since an increase in temperature causes a decrease in
supersaturation. Naturally, the growth rate will decrease when most of the
crystallizable material has crystallized.
Crystallization from Aqueous Solutions. Pure water can freeze
very fast after nucleation has occurred, because there is virtually no
retardation mechanism acting. The freezing of water is exceptional in that it
goes along with an increase in volume rather than a decrease. The physical
properties of water show a number of anomalies at low temperature.
Generally, water freezes from an aqueous solution. Aphase diagram
(temperature versus composition) then gives the phase transitions that will
occur, assuming equilibrium. Most solutes give a eutectic diagram
characterized by a eutectic temperature (Te) and solute concentration (ce).
Belowce, water will freeze upon cooling, and the solution becomes more