On the Properties of Alpha/Alpha + Beta Diffusion Couples
William J. Boettinger, Sam R. Coriell, Carelyn E. Campbell, Geoffrey B. McFadden
The properties of diffusion couples in a ternary system are examined theoretically when one end member is composed of single-phase material (alpha) and the other end member is composed of two-phase material (α + Β). Using the model of Morral and co-workers, we examine the cases in which the two-phase region either grows or dissolves. We prove that when the two-phase material grows, there can be no jump in concentration (or phase fraction of Β) at the boundary between the two materials. When it dissolves a jump is necessary. We present numerical examples to demonstrate this result. We also show how the diffusion path varies depending on the composition of the single-phase α end member for a fixed α + Β end member composition. Under some conditions, three solutions are found for the same initial end member compositions. When these multiple solutions exist, either two or three are virtual (path involves supersaturation). Whenever all three solutions are virtual, a single solution with three interfaces can be found. In this case an intermediate layer of α phase forms within the α + Β material to relieve the supersaturation.