On the mathematical modelling of cellular (discontinuous) precipitation

Abstract

assisted by John W. Cahn 2 2 John W. Cahn died on 14 March 2016. There is an obituary at https://www.washingtonpost.com/local/obituaries/ john-w-cahn-who-fled-nazi-germanyand-became-a-foremost-materials-scientist-dies-at-88/2016/03/15/ 890fe246-eac6-11e5-a6f3-21ccdbc5f74e story.html 2010 Mathematics Subject Classification. Primary: 74N20 Dynamics of phase boundaries; Secondary: 34B15 Nonlinear boundary value problems, 74A50 Structured surfaces and interfaces, coexistent phases, 74G15 Numerical approximation of solutions, 74N25 Transformations involving diffusion.phase in which at the concentration of solute Zn atoms is at least 60% . Thermodynamic data tell us what new phases are possible, but we would also like to understand the shapes, sizes and positions of the new phases.Of the various possible configurations, one of the most straightforward, from the theoretical point of view, is cellular precipitation (also known as discontinuous precipitation) in which an approximately planar (but corrugated) boundary advances into the metastable phase, leaving behind it interleaved plates ("lamellas") of the two stable phases, as illustrated schematically in Fig. 1.