Crystal size distributions (CSDs) of natural and synthetic samples are observed to have several distinct and different shapes. We have simulated these CSDs using three simple equations: the Law of Proportionate Effect (LPE), a mass balance equation, and equations for Ostwald ripening. The following crystal growth mechanisms are simulated using these equations and their modifications: (1) continuous nucleation and growth in an open system, during which crystals nucleate at either a constant, decaying, or accelerating nucleation rate, and then grow according to the LPE; (2) surface-controlled growth in an open system, during which crystals grow with an essentially unlimited supply of nutrients according to the LPE; (3) supply-controlled growth in an open system, during which crystals grow with a specified, limited supply of nutrients according to the LPE; (4) supply- or surface-controlled Ostwald ripening in a closed system, during which the relative rate of crystal dissolution and growth is controlled by differences in specific surface area and by diffusion rate; and (5) supply-controlled random ripening in a closed system, during which the rate of crystal dissolution and growth is random with respect to specific surface area. Each of these mechanisms affects the shapes of CSDs. For example, mechanism (1) above with a constant nucleation rate yields asymptotically-shaped CSDs for which the variance of the natural logarithms of the crystal sizes (??2) increases exponentially with the mean of the natural logarithms of the sizes (??). Mechanism (2) yields lognormally-shaped CSDs, for which ??2 increases linearly with ??, whereas mechanisms (3) and (5) do not change the shapes of CSDs, with ??2 remaining constant with increasing ??. During supply-controlled Ostwald ripening (4), initial lognormally-shaped CSDs become more symmetric, with ??2 decreasing with increasing ??. Thus, crystal growth mechanisms often can be deduced by noting trends in ?? versus ??2 of CSDs for a series of related samples.
Additional publication details
Deducing growth mechanisms for minerals from the shapes of crystal size distributions