Comprehensive Determination of Kinetic Parameters in Solid-State Phase Transitions: An Extended Jonhson–Mehl–Avrami–Kolomogorov Model with Analytical Solutions

Abstract

An extended Jonhson–Mehl–Avrami–Kolomogorov model with analytical solutions is developed to achieve the comprehensive determination of kinetic parameters in solid-state phase transitions. A new subexpression is given for the case of adequately small activation energy of nucleation, which is ignored in previous works. Exact or approximate analytical solutions to the expressions in this model for isothermal and non-isothermal conditions are improved by introducing the Euler integral of the first kind, which are proved to be valid, accurate, and simple for possible parameters. On the basis of this model, five kinetic parameters (pre-exponential factor, activation energy of nucleation, activation energy of growth, nucleation index, and growth index) can be comprehensively determined by simultaneous analysis of isothermal and non-isothermal experimental data. Three practical examples, including two simulated examples and one experimental example, are then presented to illustrate and validate the comprehensive determination in detail, in which the kinetic parameters determined by this approach are confirmed to be highly plausible. This is of great importance for in-depth understanding the kinetic mechanisms and taking full advantage of the solid-state phase transitions.