The crystallization of small particles and droplets

A general expression is derived for the volume fraction of material crystallized as a function of time for the situation where boundary effects may be important, and it is applied to a sample consisting of a monodisperse array of small particles. It is assumed that crystallization occurs via homogeneous nucleation followed by crystal growth. The crystallization rate is shown to be controlled by a single dimensionless parameter, beta. Beta exp 1/4 is a dimensionless particle radius which tends to be small when the growth rate is large or when the nucleation rate is small. When beta is large, the general expression for the volume fraction transformed reduces to the standard expression valid for bulk samples. When beta is small, it reduces to the formula used to compute the volume fraction crystallized in droplet undercooling experiments. Hence, the present results are pertinent for the interpretation of some droplet undercooling experiments as well as isothermal DSC and DTA experiments.