attributable to the influence of the existing microscopic crystals in the magma. Simply put, secondary nucleation is when crystal growth is initiated with contact of other existing crystals or "seeds". 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: 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: where k1 is a rate constant, MT 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. Growth Once the first small crystal, the nucleus, forms it acts as a convergence point (if unstable due to supersaturation) for molecules of solute touching – or adjacent to – the crystal so that it increases its own dimension in successive layers. The pattern of growth resembles the rings of an onion, as shown in the picture, where each colour indicates the same mass of solute; this mass creates increasingly thin layers due to the increasing surface area of the growing crystal. The supersaturated solute mass the original nucleus may capture in a time unit is called the growth rate expressed in kg/(m2*h), and is a constant specific to the process. Growth rate is influenced by several physical factors, such as surface tension of solution, pressure, temperature, relative crystal velocity in the solution, Reynolds number, and so forth. The main values to control are therefore: Supersaturation value, as an index of the quantity of solute available for the growth of the crystal; Total crystal surface in unit fluid mass, as an index of the capability of