Presently there are two nucleation-based models, Avrami’s equation and Cahn’s equation .  These models have been extensively used to model cement hydration, Cahn’s model more recently, and have been introduced into other models and simulation environments in various forms, see Bishnoi and Scrivener’s model below.

Avrami applet:  Avrami published a series of three papers between 1939 and 1940 explaining the theory and illustrating the applicability of his model by comparing to experimental data.  While his model was developed for solid phase transformations, it has been extensively applied to model portland cement hydration.  Unfortunately, the  basic assumption used by Avrami, that nuclei form randomly anywhere in the untransformed phase, implies that for cement nuclei form homogeneously anywhere in the pore solution, this assumption appears to be false based on decades of microstructural research on cement hydration.

Cahn applet: Cahn recognized that for many systems nuclei frequently form at grain boundaries and in 1956 published his work on kinetics of grain boundary nucleation.  This model went unnoticed by the cements community until 2007 when Thomas illustrated that Cahn’s model provided a better and more versatile fit to cement hydration data and was more consistent with microstructural evidence for heterogeneous suface nucleated growth.

Bishnoi applet: Though Cahn’s model has been shown to be an improvement over Avrami’s approach, it is unable to explain later age hydration behavior, Stage 5 hydration, see Hydration Basics.  Bishnoi and Scrivener suggest that hydration occurs in two stages, (1) rapid low density growth via an Avramian process, followed by (2) slow densification.  This model greatly extends the applicability of nucleation and growth kinetics and has been shown to provided good fits to the entire hydration curve at least for early age hydration, e.g. through the first 24 hours and well into Stage 5.