Posts Tagged ‘phase field crystal’

Impressions from TMS Annual Meeting 2008

March 12, 2008

TMS Annual Meeting is a rather large and varied affair; the program and abstract booklet, for example, runs into nearly 350 pages. So, not surprisingly, not only the quality and quantity of talks across different symposia are varied, but even within any given symposia, the talks are more varied in style, depth, philosophy and methodologies.

In any case, I have confined myself exclusively (barring a few exceptions) to the symposia on Computational Thermodynamics and Kinetics. Based on my attendance and understanding, here are my impressions (especially with regard to those areas of computational thermodynamics that interests me)

The attitude towards phase field modelling seems to be ambivalent; people like it because one does not have to track interfaces explicitly, and, in most of the problems of interest to the community — it is the interfaces and surfaces that are of interest and need to be tracked. However, phase field models are not satisfactory in cases where the defects that are of interest are at the atomic level, and/or, when such defects interact with extended defects such as grain boundaries and antiphase boundaries — microstructural evolution in irradiated systems, where a large number of point defects interact with extended defects and creep in Ni-base superalloys where dislocations interact with extended defects are a couple of examples that comes to my mind immediately.

I saw that the attempts to remedy the above-mentioned shortcoming of phase field models are generally of two types; one is the mixed method, in which, one decides to use both discrete and continuum descriptions either in parallel or in series. The other approach is to try and reformulate the phase field model based on the inputs from a lower level model — the most successful approach along these lines comes from the phase field crystal community; the general understanding in this community seems to be to consider phase field model as some approximation obtained from phase field crystal (which, in itself is considered as an approximation to the classical density function theory of freezing).

The two areas where a huge number of efforts have gone in and are still going on are in (a) extending phase field models (like, for example, the attempts to get phase field models for electrochemical problems, piezeoelectric problems, and hydrodynamic problems) and (b) extending phase field crystal models to study plasticity, coupled electric and magnetic material problems and so on. The works in these areas are also at some level look very glamorous to me since getting a formulation and getting it working to solve some important, model problem is the surest way to attain some immortality, and even a citation classic.

I have also found that most of the phase field models that are presented are not on model systems, and in those rare cases where such a result was presented the author(s) were apologetic; on the other hand, there have been several attempts to either use values from some database, or to derive the input parameters using a lower level model such as molecular dynamics or phase field crystal.

The numerical methods used for solving the phase field methods are also becoming more complex and involved — parallel computations, moving meshes and adaptive meshes seem to be the norm — in fact, I was told by Jim Warren that one has to bite that bullet at some point — the earlier the better.

The symposium was not without its own fireworks, either. When Martin Glicksman tried to argue that stochastic noise is not needed for dendritic side branching but just the anisotropy in interfacial energy is sufficient, Alain Karma told him “In your next presentation, I dare you to present a system with 2% anisotropy evolved for a long time, and show us a plot of velocity versus time”.

Finally, for those of you who are so inclined, some of the open problems that got mentioned explicitly are (and, frankly, I think some of them are very involved, if not impossible, and might also need access and facility with fairly advanced mathematical tools — mostly, linear and non-linear analyses):

  • An approximate model for quantum density function theory along the lines of PFC which is an approximate model for classical density function theory — such a model can incorporate information about chemical bonds I understand — I can also see why such a model would incorporate information about magnetic, optic and other such properties;
  • Derivation of phase field models using entropy based formulations that include hydrodynamics; and,
  • Imposing some kind of constraints on the density fields in the usual PFC.