Question
Does the absence of certain crystal faces necessarily imply that such faces do not
grow at all?
Answer
No. It can also be due to some faces growing faster than others. Referring to Figure
15.5b, the cubic shape at left results when the faces involved grow faster than the
slanting faces depicted, whereby the latter disappear. If the relative growth rates are
reversed, the octahedron shape at right results. For about equal growth rates of all of
these faces, the shape depicted in the middle is formed.
Note A face can also exist if it has not grown at all. An example is
discussed at the end of Section 15.2.2.15.2 CRYSTAL GROWTH
The rate of crystal growth can vary by several orders of magnitude. It is
therefore important to understand the factors involved that control
crystallization rate, which is often desirable during the processing or storage
of foods. Moreover, theshapethat a crystal will attain depends on the
relative growth rates of the various crystal faces, which may vary markedly.
Growth rate can be expressed in various ways. The growth of a given crystal
face can be given in kg?m^2 ?s^1 (mass basis), or as the linear growth rate in
m?s^1 (volume basis). The overall growth rate of a dispersion of crystals
can be expressed in kg?m^3 ?s^1 ,orasdj/dt, where jis the volume
fraction of crystals in the system.
Growth occurs by attachment (binding) of molecules (or ions, etc.) to
a crystal surface. On the other hand, molecules will also become detached.
There is thus a continuous transport of molecules across the crystal surface
in both directions. The resultant of these two processes (reactions)
determines growth rate.
Supersaturation. The rate of growth of a crystal face will always
increase with the difference in chemical potentialDmbetween crystal and
solution or melt. For crystallization from solution we have
Dm¼RTlnaRTlnaeq¼RTlnb ð 15 : 1 Þ*where ais the activity of the solute andaeq the activity at saturation,
assumed to equal that at the crystal surface; lnb is called the