Editing Crystallization (section)

====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]]