We discussed in lecture how in the early phase of a phase transformation, for example as a

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Question:

We discussed in lecture how in the early phase of a phase transformation, for example as a β phase forms in a matrix of an α phase as shown in Fig 1.38(a), the interface between the two phases contributes to the Gibbs free energy of the β phase.

(a) In Figure 1.38(b), the Gibbs free energy curves of the β phase are shown for a case (1) where theβ phase is of radius r and (2) for the case where the β phase has a radius of size ∞. Write an expression for the difference in the Gibbs free energy of the two cases.

(b) Notice the Gibbs free energy curve for the α phase on the left side of Figure 1.38(b). What can you say is different about the α phase in equilibrium with the β phase when the β phase is (1) of size r versus when the β phase is (2) of size ∞.