Phase Field Modelling - Department of Materials Science and ...

First, there is the free energy of a small region of the solution in isolation,given by the usual plot of the free energy of a homogeneous solutionas a function of chemical composition.The second term comes about because the small region is surroundedby others which have different chemical compositions. Fig. 2shows that the average environment that a region a feels is different (i.e.point b) from its own chemical composition because of the curvature inthe concentration gradient. This gradient term is an additional free energyin a heterogeneous system, and is regarded as an interfacial energydescribing a “soft interface” of the type illustrated in Fig. 1b. In thisexample, the soft–interface is due to chemical composition variations,but it could equally well represent a structural change.Fig. 2: Gradient of chemical composition. Point arepresents a small region of the solution, point b theaverage composition of the environment around pointa, i.e. the average of points c and d.The third term arises because a variation in chemical compositionalso causes lattice strains in the solid–state. We shall assume here thatthe material considered is a fluid so that we can neglect these coherency