I have a question on CE implemented in ATAT regarding structure generation. Two relevant sub-questions are: which structure and how many? While the latter may be answered in terms of CV score, the former is kind of grey area.
Frankly speaking, I have not understood how, for a given underlying lattice, ordered structures are generated sequentially. I can think of at least two scenarios: (i) hard coded, say look-up table, and (ii) employ group theory where you make sure that every lattice point of the ordered structure is mapped into the underlying lattice. I really do not know what is actually implemented in ATAT. Also, I am curious to know, how ATAT is different from that in a GA approach.
I vaguely remember, you mentioned a paper by Zunger et al regarding the structure generation, but somehow I can not remember or locate it. Can you give me the reference?
Structure selection is not based on CV score, but on (i) variance reduction and (ii) ground state prediction. Structures are not hard coded (because ATAT can do any lattice).
The "Zunger" reference that explain how structures can be enumerate from small to big cells is:
ATAT uses more or less the same method with efficient improvements based on
Essentially, one enumerate possible lattice vectors in a way that cell volume gradually increases. For a given cell, one can determine the sites of that supercell and just enumerate all occupations of these sites in lexicographic order while eliminating symmetrically equivalent structures.
Hi Axel,
Sorry, I had to come back to the issue of "Structure Generation" in the context of "which structure" and "how many"?
While the latter (how many) is easy to understand, I still have not understood the former (which structure) yet. Earlier, you had said it involves enumeration from small to big cells! This really answers only a part of my question. Don’t you have to ensure that every lattice point in the ordered structure is mapped into the underlying lattice? In ATAT, have you or do you ensure it? I am not an expert, but it seems to you need employ group theory to enforce this criterion! Otherwise, how would you?
It’s hard to describe this code in a few words…
For a given supercell, the way I find all sites is by looping over all lattice points in some sphere of a "safe" radius that is guaranteed to enclose the supercell (there is a simple geometric argument for finding this safe radius). Then I just keep the lattice sites (lattice vector+offsets for each atom in the unit cell) that are within the parallelipiped of the supercell (with some care so that the sites at the boundary are not included twice…).
Hi Axel,
I am sorry to come back to an issue I had raised earlier, though I can not tell you the date. The issue I am talking about is "predicted structure" (shown by + symbol) in MAPS plot.
Puzzling issues to me are:
(i) What is(are) the structure(s) of these phases you show by + symbol? Is it really possible to define their crystal structure(s)?;
(ii) What is(are) volume(s) of these structure(s);
(iii) How do you define energie(s) of these structure(s);
(iv) How is it possible to create so many structure(s) based on few DFT calculations?
(v) I consulted your earlier papers (CALPHAD, 2002), JPE (2002), but could not find one where you have defined/addressed these questions! May be, I am too stupid! Is there a paper (by you or anyone else) where these questions have been addressed? If so, please let me know.
(vi) The harder I try to understand these issues, more I get frustrated!
maps create an internal database of structures as it runs: all structure up to some volume (that volume is reported in maps.log). (You can force to enumerate up to a given volume with the -g=[volume] option.)
Those predicted structures are among them.
If you do
touch ready
, they will be written out to numbered directories, starting from the lowest energy ones.
The energy of those predicted structures is based on the cluster expansion built from the structure from which maps has the ab initio energies.
