Application of the Thermodynamic Extremal Principle to Massive Transformations in Fe-C Alloys

The thermodynamic extremal principle was applied to propose a model in which trans-interface diffusion from the product phase to the interface, from the interface to the parent phase and interface migration are integrated for diffusion-controlled phase transformations in Fe-C alloys. Compared with the classical models with either a local-equilibrium condition or a constrained carbon equilibrium condition, the current model is able to predict massive transformations in the two-phase region. Application to isothermal phase transformations showed that the phase transformation mode is independent of (dependent on) trans-interface diffusion when the initial composition is close to the T0 line (close to the α/α + γ boundary). Ascribed to the large solute diffusivity of C, the thickness of the spike upon massive transformations could be much larger than the atomic spacing and the diffusion-controlled phase transformations could be faster than the interface-controlled phase transformations. Three stages, i.e., the diffusive transformation, massive transformation and the soft impingement stages, were predicted for phase transformations upon continuous cooling, according to which the critical limit between diffusive and massive transformations was determined to be within the two-phase region, being consistent with the experimental results in ultra-low-carbon Fe-C alloys. The current work could be very useful to control diffusion-controlled phase transformations and modulate the mechanical properties of steels.