Classical nucleation theory approach to two-step nucleation of crystals

•Extension of classical nucleation theory (CNT) to two-step nucleation (2SN).•CNT description of 2SN thermodynamics by means of the composite-cluster model.•CNT-based thermodynamic criterion for occurrence of 2SN of crystals.•Master equation of 2SN kinetics and general expression for 2SN rate of crystals. Crystals may not always nucleate directly in the supersaturated old phase, but rather in a precursory metastable phase. This so-called two-step (2S) nucleation of crystals has recently emerged as a subject of considerable research interest. In the present paper, the composite-cluster model of the classical nucleation theory (CNT) is used to gain insight into the thermodynamics and kinetics of 2S nucleation. The standard CNT approach is applied to examine the process and it is shown that CNT is able to provide a general conceptual and mathematical framework for describing 2S nucleation. Within the caveats of CNT, a simple thermodynamic criterion is proposed for the conditions under which 2S nucleation is strongly favored and the master equation of 2S nucleation kinetics is formulated. Finally, general expressions for the 2S nucleation rates of crystals in the old phase and in the precursory metastable phase are derived.