Supplementary information

Some sections of this module is based on a Module 3 in Part IV of the NPTEL course, Computational Methods in Materials Science and Engineering; as shown in that module, even though the accounting of the curvature of free energy versus composition curve can explain the phase separation process in terms of concentration changes, the Eq. 4 is not sufficient to describe the process of spinodal phase separation. This is because when phase separation happens, even though the system prefers AA and BB bonds, there are incipient interfaces between the A and B-rich phases which contain AB bonds. Hence there is an increase in interfacial energy which is not accounted for in the classical picture, and as noted above, it can be accounted for usign the gradient energy coefficent $\kappa$. Including this contribution of incipient interfaces and deriving the non-classical diffusion equation involves calculus of variations; the equation, when derived is known as the Cahn-Hilliard equation. In the Computational Methods in Materials Science and Engineering course module referred to above, the Cahn-Hilliard equation as well as a way of solving it numerically are shown.