Kinetic analysis of phase transformations during continuous heating: Crystallization of glass-forming liquids

Abstract: Phase transformations are widely studied using continuous-heating experiments. In isothermal studies, their kinetics are often described using the Johnson-Mehl-Avrami-Kolmogorov (JMAK) rate equation. For continuous-heating studies, the same analysis has only been applied numerically. Here, a JMAK rate equation for phase transformations during continuous heating is derived. The equation is applied to the crystallization of glass-forming liquids with different kinetic behaviors and validated by comparison to experimental data and numerical simulations for the crystallization of glassy $\rm Fe_{80}B_{20}$ (at.%). Kissinger's method of analyzing crystallization kinetics is subsequently justified, and it is shown that the non-Arrhenius temperature dependence of crystal growth rates in glass-forming liquids can be better determined by using the present model to fit the peak position, shape and height for a series of crystallization exotherms. The implications of these analytical expressions for the design and development of glass-forming systems for a broad range of applications are considered, and the application of this JMAK rate equation to other transformations during continuous heating is explored.