Examination of an analytical phase-transformation model

Abstract

A comparison between results of a recently published quasi-exact solution of the temperature integral used for the Avrami model of isochronal phase transformations and an analytical phase-transformation model in relation to exact solutions from numerical integration has been performed. The results for the transformed fraction from the quasi-exact solution are more precise than the corresponding results of the analytical model, whereas the results for the transformation rate from both models are sufficiently precise for the nucleation mode of site saturation or continuous nucleation. It has been further shown that an analytical solution of the transformation rate cannot be obtained using a quasi-exact solution of the temperature integral in case of mixed nucleation, and that the results of the corresponding solution with the analytical model substantially alleviate the influence of the approximated temperature integral. By this method, an analytical approach of modeling, which can substantially alleviate the deviation (of model prediction) arising from approximations to the temperature integral, has been developed. The proposed approach has been successfully applied to experimental data of the crystallization of bulk amorphous Pd-Ni-P-Cu alloys.

The Kinetic Description for Solid State Phase Transformation

“…Transformation rate From Eqs. (5a,b,c), a compact equation for isothermal transformation rate can be generally given as [7,12]:…”