Editing Crystallization (section)

====Primary nucleation====
Primary nucleation is the initial formation of a crystal where there are no other crystals present or where, if there are crystals present in the system, they do not have any influence on the process. This can occur in two conditions. The first is homogeneous nucleation, which is nucleation that is not influenced in any way by solids. These solids include the walls of the crystallizer vessel and particles of any foreign substance. The second category, then, is heterogeneous nucleation. This occurs when solid particles of foreign substances cause an increase in the rate of nucleation that would otherwise not be seen without the existence of these foreign particles. Homogeneous nucleation rarely occurs in practice due to the high energy necessary to begin nucleation without a solid surface to catalyze the nucleation.

Primary nucleation (both homogeneous and heterogeneous) has been modeled as follows:<ref name="Tavare">Tavare, N. S. (1995). ''Industrial Crystallization''. Plenum Press, New York.{{page?|date=October 2021}}</ref>

:<math>B = \dfrac{dN}{dt} = k_n(c - c^*)^n,</math>

where
: ''B'' is the number of nuclei formed per unit volume per unit time,
: ''N'' is the number of nuclei per unit volume,
: ''k<sub>n</sub>'' is a rate constant,
: ''c'' is the instantaneous solute concentration,
: ''c''<sup>*</sup> is the solute concentration at saturation,
: (''c'' − ''c''<sup>*</sup>) is also known as supersaturation,
: ''n'' is an empirical exponent that can be as large as 10, but generally ranges between 3 and 4.