Comparison between an analytical model and JMA kinetics for isothermally and isochronally conducted transformations

Applying an analytical model, both isothermally and isochronally conducted transformations are formulated, using time/temperature-dependent kinetic parameters. In specific cases, the analytical model reduces to the Johnson-Mehl-Avrami (JMA) kinetics. Fits of JMA kinetics to exact numerical calculations and analytical solutions using the same values for model parameters (as chosen in the numerical calculation) have been performed for different temperatures (isothermal) or different heating rates (isochronal), respectively. According to the error analysis, only in the extreme cases where pure site saturation or pure continuous nucleation prevails, JMA kinetics with constant kinetic parameters is applicable; but for intermediate cases where mixed nucleation or Avrami nucleation dominates, kinetic parameters change with progressing transformation. This implies that the effective activation energy and the growth exponent generally depend on time/temperature, even if the transformation mechanism is constant (isokinetic).