The CMSX4_dri now has the new name A006_CMSX4_dri and is located in the folder of the "Application" examples. There have been 3 mayor changes for MICRESS Version 6.4:
1.) The database has been changed to TCNI8/MOBNI4. This has been requested by several users, and further has the advantage that now with MOBNI4 there are also diffusion data available for gamma'. The initial temperature was changed slightly to compensate for the differences between the databases.
2.) According to our general suggestion with Version 6.4 (see here
) we have changed the example so as to use automatic mobility ("mob_corr"). This makes setup much more simple as it removes the necessity to use a calibrated temperature dependent mobility input.
3.) The new option "multi_plus
" for definition of diffusion coefficients has been used for gamma and gamma'. Before, "multi" with global updating ("multi ggggggggg") had been used. The reason for that is the following:
Normally, at the high temperatures of solidification, calculating diffusion in CMSX-4 is uncritical, and a normal spatially constant coefficient which locally only depends on temperature is fine. However, the CMSX4_dri has been used also as starting point for solid state simulations of the same or similar Ni-base alloys. Under these conditions, this approach may not be sufficient. Some elements, e.g. W and Ta, have the tendency to show negative diagonal terms of the diffusion matrix. Without taking the off-diagonal terms of diffusion into account, instabilities coming along with chess-pattern and followed by NAN values would be the results.
Although the simple "multi ggggggggg" approach includes these off-diagonal terms, diffusion still can get unstable in regions with different composition. The reason is that the effect of the off-diagonal terms scales with the composition gradients of the other elements, and thus with their concentration itself. Thus, typically under specific and nearly unreproducible conditions like a strong concentration change close to a precipitate particle, problems can arise unexpected and suddenly.
The solution (and also more exact) is the extrapolation of the concentration dependency using the identifiier "l". This requires that the slope of each diffusion term with all compositions is calculated and used for extrapolation in each diffusion time step. This can solve the mentioned problem, but strongly increases the effort for calculating diffusion coefficients as well as for diffusion itself. It must be noted that the "l" option has also been strongly improved in Version 6.4 by changing the extrapolation algorithm and implementing basic conditions for stability (e.g. negative diagonal must at least get 0 if the diffusing species vanishes).
However, if the goal is mainly to achieve numerical stability, extrapolation with respect to all compositions is overkill. Therefore, the "multi_plus" option has been invented which adds the analytical dependency of the off-diagonal terms on the composition of the diffusing species. These are the strongest dependencies of the off-diagonal terms, and no derivative has to be calculated. Instead of extrapolating, the diffusion terms are normalized, and later multiplied by the local composition of the diffusing species.
However, using "multi_plus ggggggggg" alone would not completely solve the stability issue, because "multi_plus" does not extrapolate the diagonal although this is important in case of negative diagonals. Therefore, the identifier "l" for local extrapolation should be used for the diagonal term:
1 1 multi_plus lgggggggg
2 1 multi_plus glggggggg
3 1 multi_plus gglgggggg
4 1 multi_plus ggglggggg
5 1 multi_plus gggglgggg
6 1 multi_plus ggggglggg
7 1 multi_plus gggggglgg
8 1 multi_plus ggggggglg
9 1 multi_plus ggggggggl
This setup currently provides the highest level of stability in high-alloyed systems (note that in case of a negative determinate of the diffusion matrix diffusion still is unstable!) and a good relation of accuracy and performance. Of course, accuracy can be further increased by using "l" for all terms.