Editing Crystallization (section)

===Nucleation===
{{Main|Nucleation}}
Nucleation is the initiation of a phase change in a small region, such as the formation of a solid crystal from a liquid solution. It is a consequence of rapid local fluctuations on a molecular scale in a homogeneous phase that is in a state of metastable equilibrium. Total nucleation is the sum effect of two categories of nucleation – primary and secondary.

====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.

====Secondary nucleation====
Secondary nucleation is the formation of nuclei attributable to the influence of the existing microscopic crystals in the magma.<ref name="McCabeSmith">McCabe & Smith (2000). ''Unit Operations of Chemical Engineering''. McGraw-Hill, New York.{{page?|date=October 2021}}</ref> More simply put, secondary nucleation is when crystal growth is initiated with contact of other existing crystals or "seeds".<ref>{{Cite web |url=http://www.reciprocalnet.org/edumodules/crystallization/ |title=Crystallization |website=www.reciprocalnet.org |access-date=2017-01-03 |url-status=live |archive-url=https://web.archive.org/web/20161127173509/http://www.reciprocalnet.org/edumodules/crystallization/ |archive-date=2016-11-27 }}</ref> The first type of known secondary crystallization is attributable to fluid shear, the other due to collisions between already existing crystals with either a solid surface of the crystallizer or with other crystals themselves. Fluid-shear nucleation occurs when liquid travels across a crystal at a high speed, sweeping away nuclei that would otherwise be incorporated into a crystal, causing the swept-away nuclei to become new crystals. Contact nucleation has been found to be the most effective and common method for nucleation. The benefits include the following:<ref name="McCabeSmith" />
* Low kinetic order and rate-proportional to supersaturation, allowing easy control without unstable operation.
* Occurs at low supersaturation, where growth rate is optimal for good quality.
* Low necessary energy at which crystals strike avoids the breaking of existing crystals into new crystals.
* The quantitative fundamentals have already been isolated and are being incorporated into practice.

The following model, although somewhat simplified, is often used to model secondary nucleation:<ref name="Tavare" />
:<math>B = \dfrac{dN}{dt} = k_1 M_T^j(c - c^*)^b,</math>
where
: ''k''<sub>1</sub> is a rate constant,
: ''M<sub>T</sub>'' is the suspension density,
: ''j'' is an empirical exponent that can range up to 1.5, but is generally 1,
: ''b'' is an empirical exponent that can range up to 5, but is generally 2.

[[Image:Crystal growth.PNG|thumb|upright|Crystal growth]]