Hello, I would like to use icet to find the lowest energy structure of a quasi-quaternary compound (such as BaxSr1-xCoyFe1-yO3) at a fixed concentration. I have two questions.

The first question is, can icet obtain the cluster expansion model of two sublattice compounds?

The second question, when I use the enumeration method to generate the structure set and get a cluster model, can I use this cluster model to find the lowest energy structure of a fixed concentration at a fixed supercell size?

Thank you very much for your reply!

The first question is, can icet obtain the cluster expansion model of two sublattice compounds?

Yes this is possible, see e.g. this page, also the icet website contains a bunch of examples and tutorials that might be useful to check out.

The second question, when I use the enumeration method to generate the structure set and get a cluster model, can I use this cluster model to find the lowest energy structure of a fixed concentration at a fixed supercell size?

Cluster expansions can be trained from structures generated with enumerated method.

Yes, when you have a cluster-expansion you can find the ground-state structures for a fixed supercell and fixed concentration.

Note that if you’re only interested in a single concentration you might want to limit the training structures such that they are close to this concentration.

Also note that if you find the ground-state for a fixed supercell at a given concentration it **might not** be the true ground-state structure at that concentration.

Thank you @erikfransson !It helps a lot. But I’m still confused. After the cluster model is established, which icet module should I use to find the lowest energy structure at a fixed concentration of supercells? This seems to require a very large number of configurations and the cluster model predicts their energies to find the lowest energy structures.

Also, you mentioned “Also note that if you find the ground-state for a fixed supercell at a given concentration it **might not** be the true ground-state structure at that concentration.” How can I be sure if the ground state structure found is the true ground state structure at this concentration?

Thanks for your pointers.

which icet module should I use to find the lowest energy structure at a fixed concentration of supercells?

There are many ways one can attempt to find the ground-state structure.

If the supercell is very small you can try to enumerate all possible occupations in the supercell, and predict their energies with the cluster-expansion.

You can also try to use GroundStateFinder in icet which works well up to about ~50atoms in the supercell in my experience.

For larger supercells I think the best options is to run long and slow MC simulated annealing simulations in canonical ensemble, see here.

How can I be sure if the ground state structure found is the true ground state structure at this concentration?

I dont think you can be sure, but its probably a good idea to to use many different supercells with different number of atoms and cell-shapes etc when looking for the ground-state.

Thank you very much. Your reply has helped me a lot.

Hello, sorry to bother you, I have a new problem! When I use the enumeration method to generate the structure, there are 2000 structures for 35 atoms (of which there are only 14 of the positions that make up the cluster, and this contains two sublattices). I am concerned that these structures contain less cluster information and I would like to add more atoms, which will add more structures to the database.

What I want to ask is should I randomly sample structures as training set? After all, there are too many structures for enumeration.

Also, is the structure in the training set the relaxed structure or the initial structure? Both are ok?

Looking forward to your reply!

What I want to ask is should I randomly sample structures as training set?

Without knowing anything about your system I’d suggest to combine two sets of structures.

- Small supercells from enumeration
- Randomly occupied larger supercells (with varying supercell size)

The structures in 1) are small and thus are fast to calculate with DFT, and they are good since they will correspond to “high-symmetry” structures.

The structures in 2) will, like you say, maybe contain more information about more types of clusters etc.

So combing structures from both these approaches will likely generate a good training set.

Then after the training is done you can always add more structures. For example you can take your initial cluster-expansion and find/generate a bunch of low energy structures (or ground-state structures) and add these to the training set and then retrain the model.

Also, is the structure in the training set the relaxed structure or the initial structure? Both are ok?

I think its most common to use relaxed structures for training.