Order-disorder transition lines about pycalphad HOT 5 CLOSED

I received another question about this at the CALPHAD meeting. I'd mostly been thinking this would be pretty difficult to implement for general second-order transitions, but I now think I have a solution for atomic ordering. In the plotting code we normally define the tie-line for a miscibility gap based on the RMS distance between the two points in composition space. Once that distance is "significantly" greater than the density of our grid, we assume it's a tie-line instead of a single-phase region.

For atomic ordering defining the transitions is a little more complicated. What we can do is define a "degree of ordering" for each point on the candidate tie-line as the magnitude of the difference between the overall composition and the constitution of each sublattice. Each sublattice has a "degree of ordering" calculated such that a transition boundary can be defined as anywhere the magnitude of the difference of degrees-of-ordering vectors is "large".

Magnetic transitions are easy: Compute TC where the phase is stable, and where TC approaches T draw a boundary.

from pycalphad.

Or am I thinking about this incorrectly, and I should be looking at the mixed second-derivatives of the site fractions with temperature?

from pycalphad.

So equilibrium can reasonably minimize internal degrees of freedom in step/map calculations now, so in principle this is pretty easy to implement:

• At some T_i and x, compute the degree of ordering and compare to the same at T_{i+1}
• When the degree of ordering change is "large", set T_ord = (T_i + T_{i+1}) / 2
• Draw T_ord for all x where the given phase of interest is stable

I'll put this on the roadmap for 0.4.

from pycalphad.

With the new degree_of_ordering and curie_temperature properties implemented, writing code to overplot these transition lines should be pretty straightforward.

from pycalphad.

I made a first attempt at this, which you can find in the sandbox (requires 0.3.1 to run): https://github.com/pycalphad/pycalphad/blob/356b12422bbfe191deb3a902e10088aa47c4afd9/research/ContourMap.ipynb

The result, which shows lines of constant degree_of_ordering in solid black and the magnetic transition temperature on the grey dashed line, looks pretty good.

from pycalphad.