Modelling crystallization: When the normal growth velocity depends on the supersaturation

TL;DR

This paper develops a general model for crystallization where the growth velocity depends on supersaturation, deriving transformation rates for various dimensions and orders, and validates it against established models and experimental data.

Contribution

It introduces a new general equation for crystallization transformation rates considering supersaturation dependence, applicable across different dimensions and growth orders.

Findings

Derived a universal transformation rate equation for crystallization.

Validated the model by fitting it to the Johnson-Mehl-Avrami-Kolmogorov (JMAK) model.

Initial validation in 2D with published experimental results.

Abstract

The crystallization proceeds by the advance of the crystal faces into the disordered phase at the expense of the supersaturation which is not sustained in our model. Using a conservation constraint for the transformation ratio and a kinetic law, we derive a general equation for the rate of transformation. It is integrated for the six combinations of the three spatial dimensions D = 1, 2, 3 and the two canonical values of the growth order (1 and 2). The same equation with growth order 1 is obtained when taking only the linear term from the Taylor's expansion around 0 transformation of the model of Johnson-Mehl-Avrami-Kolmogorov(JMAK). We verify our model by fitting it with JMAK. We start the validation of our model in 2D with published results.