Deviation from local equilibrium

As discussed in Section 7.8 it is common to assume that the rate of a phase transformation in an alloy is controlled by the rate of diffusion. The local compositions at the phase interfaces are then used as boundary conditions for the diffusion problem and they are evaluated by assuming local equilibrium at the interfaces. That is a very useful approximation but there are important exceptions. It is necessary to realize that the exceptions are of two different types and they have opposite effects. The first type of exception is caused by a limited mobility of the interface. In order to keep pace with the diffusion, the interface requires a driving force which is subtracted from the total driving force and decreases the driving force for the diffusion process. Due to this effect, a partitionless transformation, which would otherwise be completely diffusion-controlled but rapid due to a very short diffusion distance, requires an increased supersaturation of the parent phase, as shown in Section 7.8. Formally, this case was treated by assuming a pressure difference between the two phases as if the interface were curved more than it actually is, and the local equilibrium assumption was modified to this case.

The other type of exception will instead decrease the driving force needed by decreasing the need for diffusion and will thus result in a higher rate of transformation and make it possible for an alloy with a lower supersaturation to transform.