A solute drag treatment of the effects of alloying elements on the rate of the proeutectoid ferrite transformation in steels

The problem of diffusional growth of a proeutectoid constituent in a ternary steel is considered, taking into account the interfacial diffusion of a slow-diffusing substitutional solute, under conditions which do not permit its long-range redistribution between parent and daughter phases. It is assumed that the faster diffusing interstitial solute (carbon) controls the rate of the transformation. The substitutional solute profile within (across) the interface is estimated as a function of interface velocity; the interstitial chemical potential difference is allowed to vary with, and balance, the solute drag due to the substitutional component. A transition to paraequilibrium is found at high interface velocities, and a variety of behaviour is predicted for intermediate states, depending on the relative rates of diffusion of the two solutes and their energetic interactions with each other and with the interphase boundary.