Last time: Spinodal decomposition--I.
Background
Today: Spinodal decomposition--II.
Gradient energy
Elastic energy
Improved diffusion equation
Spinodal decomposition--II.
Gradient energy
The "uphill" diffusion that results within the spinodal leads to the evolution of a high density of material in which there are significant gradients of composition. These gradients have an associated excess energy that diminishes the available driving force for diffusion. Thus, there must be a gradient energy modification to the diffusion potential and consequent modifications to Fick's laws for diffusion.
Elastic energy
If there is a change of molar volume with composition, solid-state
diffusion will be accompanied by changes of elastic energy. The
elastic energy contribution for compositional inhomogeneities enters
the expressions for the 
, as well as the diffusion potential and
Fick's laws.
When the material is elastically anisotropic, the elastic energy will depend on the orientation of the developing composition wave. The wavevector will tend to align along elastically soft directions in the material.
When elastic energy is significant, the region of compositional instability in the phase diagram is reduced, and the smaller unstable region is known as the coherent spinodal.
Improved diffusion equation
Solution to modified diffusion equation
Spinodal microstructures
Later stages of spinodal decomposition: nonlinear effects