I am taking the example of precipitation from a supersaturated matrix. The white box is an alloy A-B supersaturated in B. With time, B rich phases will form in this matrix. If we look along the axis drawn here, we expect the composition profile illustrated on the right. So far we cannot determine the interface composition.
The rate of transformation depends on two phenomena: the transport of solute in the matrix to the B rich particle, and the transfer at the interface.