An extended analytical model for solid-state phase transformation upon continuous heating and cooling processes: Application in γ/α transformation

An extended analytical model is derived for non-isothermal solid-state phase transformation assuming interface-controlled growth mode, e.g. polymorphic or allotropic transformation. In the modeling, incorporation of thermodynamic factor into kinetics of nucleation and growth is performed, so that the model can be used to describe the transformation occurring either near or far from the equilibrium state. Furthermore, the effect of the initial transformation temperature is included through a special treatment for the "temperature integral", so that the model can be used to depict the transformation during either continuous heating or continuous cooling. Numerical calculations demonstrate that the extended analytical model is accurate enough for practical use. On this basis, a general rate equation for non-isothermal (isochronal heating and cooling) transformation is derived. Applying the present model, the overall kinetic behavior of γ/α transformation in binary substitutional Fe-based alloys (e.g. Fe–Mn and Fe–Cu) upon cooling, measured by dilatometry, is described successfully. Compared with previous work, where a site saturation assumption is generally made, the prevalence of continuous nucleation deduced using the present model prediction seems more reasonable.