A critique on the mathematical theory of spinodal decomposition

✍ Scribed by W.A Tiller; G.M Pound; J.P Hirth

• Publisher: Elsevier Science
• Year: 1970
• Weight: 928 KB
• Volume: 18
• Category: Article
• ISSN: 0001-6160
• DOI: 10.1016/0001-6160(70)90027-1

✦ Synopsis

The mathematical theory of spinodol decomposition is reviewed. While the theory is self-consistent within its assumptions, some of the assumptions are indicated to be questionable. An alternative formulation is proposed in terms of a set of phenomenological coefficients to be determined by carrelation with experiment. The new formulation brings in first order non-homogeneous terms in the free energy as a function of derivatives of concentration, and lower order terms in the generalized form of Fick's second law than does the original theory. Gibbs' original description is recommended for the case of liquid solutions, and that of Cahn for solids, where Gibbs' term plus the elastic energy must be considered. The determination of this elastic energy is pinpointed as sn area where further theoretical aork is required.