Introduction to Crystallization of Fine Chemicals and Pharmaceuticals - Molecules: Nucleation, Aggregation and Crystallization - page 152

The growth rate of a crystal as a whole is normally discussed in terms
of the linear growth rate G , i.e. the rate of change in a characteristic

linear dimension of the crystal, L

[ m/s ]

[ m ] , with time t [ s ] :

dL
dt

G = . (4)

This characteristic linear dimension can be an actual dimension of the
crystal, or for example the diameter of a sphere with the same volume as
the crystal. The growth rate will depend on the choice of the characteris-
tic linear dimension. Growth rates are often of the magnitude 10 −7 -
10 −9 m/s, and the values for some substances are available in the literature
(Mullin, 1979, 1993).
Crystal growth is governed by two sources of resistance in series.
Molecules have to be transported from the bulk solution to the crystal
surface — boundary layer transport . At the surface, the molecules are
inserted into the crystal lattice — surface integration . Normally a certain
amount of energy — the heat of crystallization — is released, which has to be
transferred out into the bulk solution. In general, though, the amount of energy
is moderate, and the heat transfer is much faster than the mass transfer. Crystal
growth in solution is sometimes governed by the resistance to mass transfer
through the boundary layer. This step can be considered as a normal diffusive/
convective mass transfer from the solution to the surface of the solid particle.
In the literature, a large number of studies of mass transfer from solution to
solid particles are available. Different relationships are given for different par-
ticle sizes, hydrodynamic conditions and material properties. In the case of a
stirred tank, the equation of Levins and Glastonbury (1972) is recommended.
Note that the mass transfer coefficient increases with decreasing particle size
and increasing mixing intensity. The resistance to surface integration
depends on the properties of the crystal surface and is normally assumed to
be independent of the hydrodynamics. At increasing molecular size and flex-
ibility, the surface integration resistance is expected to increase. Impurities
can easily block growth sites, however, and sometimes concentrations in the
parts-per-million range can dramatically reduce the growth rate. The rate of
surface integration differs for the different faces of the crystal.