Systems of Cahn–Hilliard Equations

Source abstract

The phase separation of alloys with two or more components is studied, with emphasis on more than two components. Particular attention is given to differences between multicomponent and binary alloys.Specific topics of the paper include equilibrium theory, aspects of the dynamics, and numerical simulations. In the equilibrium theory, it is found that there is an enriched equilibrium structure that allows for multiple coexisting phases and the presence of triple points in the solution. Dynamic results include the characterization of the spinodal region and of the concentration variations that lead to spinodal decomposition. Unlike the binary theory, not all composition variations lead to separation, and the compositions are not restricted to the convex hull of the equilibrium concentrations. Linear analysis is used to predict that a pseudo-binary will initially result from spinodal decomposition. Numerical simulations of the dynamics for a ternary alloy verify this initially, but more than two phases often separate. A sequential application of the dominant growth mode in linearly independent directions of composition variations appears to explain these additional phases. Finally,intermediate products are found that have both separated and metastable phases. This is not seen in binary materials.