Figures 1.5c,d and 1.6a,b illustrate the difference between chemical unmixing that occurs by nucleation and growth (the topic of the previous Chapter 11) and spinodal decomposition (the topic of Chapter 12). Nucleation creates a distinct surface between the new phase and the parent phase, and the two phases differ significantly in their chemical composition or structure. In addition to the surface energy, an elastic energy is often important, too.

Spinodal decomposition does not involve a surface in the usual sense because it begins with infinitesimally small changes in composition. Nevertheless, there is an energy cost for gradients in composition, specifically the square of the gradient, since a region with a large composition gradient begins to look like an interface. The “square gradient energy” is an important new concept presented in this chapter, but it is also essential to phase field theory and to the Ginzburg–Landau theory of superconductivity.

At the end of Sect. 2.7 on unmixing phase diagrams, it was pointed out that there are conceptual problems with a free energy that is concave downwards because the alloy is unstable, but the free energy pertains to equilibrium states. An unstable free energy function may prove useful for short times, however. Taking a kinetic approach, we use the thermodynamic tendencies near equilibrium to obtain a chemical potential to drive a diffusion flux that causes unmixing.