formed at the crystal surface. This is a kind of roughening, though at a much
larger scale than the roughening phenomena discussed in Section 15.2.1; the
diameter of a dendrite may be severalmm, the length, e.g., 0.1 mm.
Dendritic growth will mostly stop after a short while, since the
additional crystallization causes the release of more heat of melting, leading
to evening out of the temperature gradient. In aqueous solutions the
situation is more complex, but if the freezing point depression is smaller
than the local temperature difference, dendritic growth can occur. Another
condition is that the linear growth rate has to be very high, a situation that is
not very common during the freezing of foods.
Crystal Size and Shape. As mentioned, ice I crystallizes in the
hexagonal system, and ice crystals can occur in a wide variety of shapes,
with a typical threefold symmetry. Such shapes are primarily found in
snowflakes; the explanation is somewhat similar to that for the formation of
dendrites. During the freezing of liquid foods, simpler forms generally
result. Hexagonal plates or prisms can be observed, but small crystals tend
to have rounded shapes. The crystals often are fairly small; for example, a
typical ice crystal in ice cream may be 40mm. This may be due to substances
inhibiting growth rate: since these generally do not inhibit nucleation, as
mentioned, many nuclei can form before much ice has formed, and small
crystals result.
Sintering. The Hamaker constant for ice in water (A11(3)) is small,
about 0.04 timeskBT. Nevertheless, for crystals of severalmm in radius, the
van der Waals attraction would be large enough to cause their aggregation.
Moreover, ice crystals will cream, forming a layer. Touching ice crystals will
readily sinter when crystallization is not yet complete. They can then form a
polycrystalline mass, such as depicted in Figure 15.1c.
In many dispersions of ice crystals, however, the latter are clearly
separate from each other; see for example Figure 9.1, depicting ice cream.
This may be due to colloidal repulsion between crystals. Several substances
can presumably adsorb onto ice, like proteins and ions, providing steric and
electrostatic repulsion. However, this has not been systematically studied to
the author’s knowledge.
15.3.2 Phase Diagrams
Eutectics. Figure 15.14 gives a partial phase diagram of the binary
mixtureD-fructose and water. The solid curves given are calledcoexistence
lines. Such a line gives the boundary between two phases; on any point on