usnistgov / phasefield-precipitate-aging Goto Github PK

The intermetallics are defined in the CALPHAD database with finite domains, outside of which the free energy landscape does not exist. To provide the KKS rootsolver something to do outside these domains, the free energies are constructed as piecewise functions with CALPHAD free energy inside and the Taylor series approximation outside these regions. However, no attempt has been made to produce a smooth transition, which means the code iterates indefinitely when -DCALPHAD is provided to the compiler. W.J. Boettinger recommends using a tanh function to interpolate. Quick prototyping shows that this approach yields smooth, continuously differentiable transitions. Further, where the CALPHAD energy slopes downward toward the boundary, tanh interpolation produces a sharp edge where the rootsolver could find a solution. It might not be the "right" solution, but it's better than searching for infinity.

Choice of only one control point for Taylor series approximation to each phase introduces unacceptable errors. Adopt technique of Poulsen and Voorhees, Early stage phase separation in ternary alloys: A test of continuum simulations: lookup table of paraboloid coefficients for each phase on 1000x1000 mesh of ternary simplex.

Documentation in the readme says to build your description via "pdflatex description.tex", but that's the not the name of the file.

More importantly, *description.tex seems to have an error in the equations in section 1 describing the free energy density (after eq. 3).
phasefield-precipitate-aging_description.pdf

Could be better. Profiling output:

Each thread creates a new rootsolver object for each node in the grid. This could be expensive -- profile to see whether allocating a grid of rootsolvers, to preserve state, would accelerate the fictitious composition updates.

Fitting a tangent plane to four phases (γ, δ, μ, and Laves) is mathematically impossible. Attempting to do so may be slowing down the rootsolver and, esp. using the CALPHAD free energies, precluding solution of the equations. Recommend dropping μ phase from the model, as it is metastable at best.