Kinetics of polymorphic solid-state transformations

Abstract

Solid-state polymorphic transformations can have a profound influence on the processing and storage of some crystalline powders. Using classical models of nucleation and growth a framework is developed which highlights the importance of crystal size on the transformation rate. A key parameter in this theory is the ratio of the growth and nucleation times, which has a fourth-order dependence on size. For large values of this ratio many active nuclei are involved in the transition of a crystal and the existing theory of Avrami describes the kinetic process. For small values of the ratio, however, a single active nucleus may be involved and the Avrami approach is no longer valid. A theory is developed for this lower limit from which, unlike the Avrami limit, it is possible to obtain kinetics for both nucleation and growth parameters. The method of obtaining kinetics is illustrated with available data for the IV → III transition in ammonium nitrate.