The Diffuse Interface Approach in Materials Science : Thermodynamic Concepts and Applications of Phase-Field Models

Many inhomogeneous systems involve domains of well-de?ned phases se- rated by a distinct interface.

If they are driven out of equilibrium one phase will grow at the cost of the other.

Examples are phase separation by sp- odal decomposition or nucleation and subsequent growth of the nucleus in the nourishing phase [139].

Another example which has often been discussed as a paradigmatic problem is that of dendritic solidi?cation [29, 64, 79, 199].

The phenomenological description of these phenomena involves the de?- tion of a precisely located interfacial surface on which boundary conditions are imposed.

One of those boundary conditions typically yields a normal - locity at which the interface is moving.

This is the so-calledsharp interface approach, adopted both in analytical and numerical studies for a variety of contexts involving a moving boundary.

The origin of such a description is - ten transparent, being obtained by symmetry arguments and common sense.