How to fix some ECI in fitting

Alloy Theoretic Automated Toolkit (ATAT)
1

Dear Dr. van de Walle,
I have a question about how to fix some ECI in fitting.
The situation is that I got a set of ECI for a binary already (Fe-Ni for example) and I think it is a good set of ECI.
Now I want to investigate the Fe-Ni-Al ternary so I need to fit a ECI set for this ternary.
My question is that is there any way I can keep the ECI for interactions between Fe-Ni fixed (to the set I got before) and just fit for the rest ECI? Assuming that I use the same cluster size in binary and ternary, i.e., ECI including upto 3 NN pair and 3NN triplet clusters.
Thanks in advance,

2

Unfortunately, there is no easy way to do this exactly. (The ternary ECIs are linearly related to the binary ones but that linear relationship couples all ternary ECIs to the binary ones, with, in general, no "0" coefficients, so one can’t just "fix" some ECIs. You would have to impose a general linear constraint. I have not implemented this.)
However, you can obtain a similar effect by just copying your binary structures into the directory where you run a ternary, this will give a higher weight to fitting this binary subsystem correctly. A few cautions:

  1. this is easy if you have not started the ternary run yet, then a simple copy of the binaries, before you start running mmaps, works automatically.
  2. make sure the lattice parameters in lat.in are exactly the same.
  3. If you already have started the ternary run, then, when you copy the binaries you have to make sure not to overwrite your existing files. Typically you would prefix the binary directory with, say, "b". mmaps may warn you that some structures are duplicates, in which case you can delete one of them.
    As usual, make sure backup before doing major copying/deleting operations!
3

Thanks for your reply.
I am a little confused when you say "no "0" coefficients".
Did you mean that binary has spins of 1 and -1 but ternary also has spin 0?
If this is the case, I wouldn’t have made good example.
In fact, I am going to fit cluster expansion coefficients for quaternary Fe-Ni-Al-Co and I got a good set (I think) of ECIs for Fe-Ni-Al already. So I want to fix the interactions between Fe-Ni-Al in the fitting for quaternary.
I built a structure database and use ATAT code to fit so that all structures used in fitting ternary will be used in fitting for quaternary.
Thanks,

4

Just to clarify: the "0 coefficients" I am talking about are those of the constraint you would have to impose to freeze the binary ecis. The spin values are not -1,0,1 for the ternary. (It’s more complex than that, to make an orthogonal basis -see https://dx.doi.org/10.1016/j.calphad.2008.12.005 )

5

Thank you very much for reply.

6

Dear Dr. van de Walle,
Can I have some more questions about fixing some ECIs in fitting.
I did a simple test like following for a dataset of structures (inclusing binary, quaternary and quinternary) of 4 chemical elements:
1. Fitting for a ECI set of 4 chemical elements (allowing lattice site to host 4 elements, namely A, B, C, D in lat.in)
2. Fitting for a ECI set of 5 chemical elements (allowing lattice site to host 5 elements, namely A, B, C, D, E in lat.in)
I fitted 2 ECIs sets to the same pair and triplet range: 3NN for pair and 3NN for triplet.
Certainly two ECIs sets look very different because the correlation functions in 2 cases are different and numbers of points, pairs and triplets are also different.
But the energy of all structures in the database calculated by 2 ECIs set are exactly same (with very small difference ~ 0.0001 eV, which could be just numerial error).
I also calculated energies of some more structures (not included in the fitting) by 2 ECIs sets and the energies given by both set for each structure are also the same!
The second ECIs set have many "0.000000" ECIs because I did not feed the fiiting any structures with the "E" element.
So I think that the ECI set #2 is the transform of set #1 from 4-elements system to 5-element system. Is this correct?
And if I can fixed those "non zero" coefficients in 5-element fitting for fitting to a new dataset including structures with all A, B, C, D and E elements, I should get the ECIs for 5-element system with interactions for 4-element system (A, B, C, D) fixed to 4-element fitting.
Can you confirm me what I think is correct or not?
I think it may not be correct!
Thanks,

7

I think you rediscovered the following known fact. If a cluster expansion contains up to n-body terms in a system of m components (m>n), you only need structures containing at most n different components to fit it. So your quaternary data is enough to fit a 5-component cluster expansion if it contains quadruplets at most. Maps, by default, first generates structures with fewer than m components and gradually adds more.