Kinetics of diffusion-controlled transformations: Application of probability calculation

An analytical model has been developed to describe the overall kinetics of diffusion-controlled transformations assuming site saturation or continuous nucleation, in combination with one-dimensional growth. On the basis of linear approximation of the concentration gradient, the method of probability calculation is adopted to model the transformed fraction. First, the so-called geometrical model was re-derived, assuming that the diffusion-controlled growth, according to the parabolic growth law, stops due to geometrical impingement of grains plus their diffusion fields. Then, the transformation kinetics subjected to soft impingement was described, following an analogous approach. The effect of soft impingement, depending on the degree of supersaturation, has been interpreted by evolution of the transformed fraction and the growth exponent. The model was applied to describe the isothermal austenite-ferrite transformation of 0.37C-1.45Mn-0.11 V microalloyed steel, and a good agreement between model predictions and experimental results has been obtained.