Integrating across all of computation space with memc2

Alloy Theoretic Automated Toolkit (ATAT)
1

Hi Axel,

I’m working on the problem of finding energies at all compositions for a ternary at arbitrary temperature. The problem is that I don’t see a simple way to set me boundaries of integration for memc2 such that all of multicomponent space is integrated over. For emc2 this isn’t a problem because the space being integrated over is one dimensional. For memc2 however, it is three dimensional, and its not possible to tile a three dimensional space with cubes centered at each groundstate. The only thing I can think of is to somehow integrate across all of composition space for each ground state, then find the true energies at each possible composition by using a common tangent line method between energy curves from adjacent groundstates, but that seems pretty incredibly complex to set up. Do you have any intuition/advice about a better way to deal with this problem?

Thanks very much,
Adam

2

I think the most pragmatic solution to this is to

  1. abandon the idea of having a uniform grid in composition, for each phase. The region of stability of each phase can have a very nonregular shape.
  2. it’s easier to just use whatever data point (regular grid or not) you can get for each phase and then fit a simple functional form (e.g. polynomial, perhaps with some x ln(x) terms ) through your data points. Then you would work with the fitted function instead of a grid.

BTW, is there are reason your are taking about energies rather than free energies? The latter is what you need to assess phase stability.