I seem to have a problem with a Cluster expansion on LixMgSi. The ECIs do not decrease significantly with distance between the atoms of a cluster. It appears to me that this is responsible for the fact that my Cluster expansion does not converge even after having calculated 130 structures.
Could this be an inherent problem of the material system?
Yes: it could be due to large relaxations (try checkrelax) or electrostatic effects .
For 1st issue either drop str that relax too much or see https://dx.doi.org/10.1038/ncomms8559
I do not think that it is due to relaxation. I have excluded all structures, which appear to relax too much already (there are clearly two groups/populations of structures) that can be seen when the Lithium content increases above 50 %.
So the conclusion would be electrostatic effects? How can I check on this problem? Actually I would not have thought of electrostatics since the compound should be metallic, or am I wrong?
Another possibility is that there many competing ground states and ATAT has to work really hard to get them in the right order, so the criteria of the quality of the fit get worse.
If there is any composition range you can exclude (with the -c0 and -c1 options), try that.
It is also possible that although the cells do not relax much the atom positions do (and checkrelax only checks for the cell). Use nnshell to see if the coordination of each atom changes a lot.