Phase field models: Chapter outline

I have accepted an invitation to be a co-author of a chapter on simulation techniques in alloy physics; this chapter will cover Monte Carlo, molecular dynamics and phase field techniques. You have guessed it: my main contribution is in the last section.

I am still trying to figure out who the audience will be (senior undergraduates, graduate students, or practising researchers), and whether they may be expected to know some of this stuff. So, I am still not able to decide how to pitch the section on phase field models. For example, should it be a high level overview, a tutorial, or something in between? Should I (a) try to solve some example problems, (b) include (possibly gory) details of numerical implementation, (c) give chapter-end problems? I need answers to these questions before I can decide on things such as the number of sketches and microstructures, number and level of equations, etc.

As for content, which has to be covered in about 15 pages or so, I am looking at the following generic outline:

• Accessible length and time scales
• Cahn-Hilliard and Cahn-Allen models as prototypes
• Their extension to models with multiple order parameters
• Implementation details: periodic boundary conditions, finite difference methods, Fourier spectral methods
• Survey of applications: phase separation, ordering, precipitation of an ordered phase, elastic stress effects, grain boundary effects, grain growth, solidification

When I did a quick mind-map of phase field models, I realized that they can be introduced or approached from quite a few different angles: (a) models rooted in statistical physics (e.g., Cahn-Hilliard or Cahn-Allen models), (b) models that "just happen to" mimic real systems (grain growth models), or (c) models that simply provide mathematical convenience (solidification models with a rather fictitious order parameter that helps differentiate a solid from a liquid). There are probably other angles as well.

I guess I am in for a rather interesting experience. I am sure it will be fun, and I am excited.