# Crystal Symmetries at Different Steps of Battery Voltage Profiles

Hello community, with different crystal symmetries observed for the different stoichiometries/steps in the voltage profiles of batteries, can anyone please help me understand how to know or what calculations are carried out to determine the crystal symmetries for the different steps of the voltage profile? For instance with Li0–1TiO2, you start with tetragonal (I41/amd) and go to orthorhombic (Pnnm). What method of calculation is carried out to obtain the orthorhombic symmetry? I will appreciate your help on the symmetry determination please.

The determination of symmetry is performed using pymatgen and spglib. The symmetry is determined with respect to all the atoms shown in the crystal. This includes any intercalant ions, which is why the symmetry changes as lithiation increases.

Best,

Matt

Great!

Thanks a lot for the response.

Can you please be more detailed on " symmetry is performed using pymatgen and spglib".

I mean, how do I reproduce the calculation?

I will really appreciate your help.

If you are just interested in using pymatgen to obtain symmetry, a short script like the following will work for a file named ‘test.vasp’. Of course it will be more complicated if you want to analyze the symmetry yourself and check that pymatgen is getting the right answer.

from pymatgen.core.structure import Structure
from pymatgen.symmetry.analyzer import SpacegroupAnalyzer

struct = Structure.from_file(‘test.vasp’)
sga = SpacegroupAnalyzer(struct, symprec=0.1)
print(sga.get_space_group_symbol())

I really appreciate your response Steven.

I’m sorry that I’ve not been clear enough. Let me try rephrasing the question. Now, as an example, I do have TiO2 in tetragonal (I41/amd) symmetry and want to intercalate it with Li to obtain LiTiO2. One way I can do this is to just grasp a crystal structure with LiTiO2 stoichiometry and tetragonal (I41/amd) symmetry and optimize it. But, from the profiles in the Material Project, it does seem that the intercalation is carried out such that you can get a different symmetry from what you started with. My question is, what calculation did you do to intercalate the TiO2 that will result in the ‘right’ symmetry when you increase the lithiation? Is it some kind of molecular dynamics simulation? Is the method documented in any publication that you can kindly refer me to? Your help is highly appreciated.

(disclaimer: I’m not affiliated with the Materials Project, I just use it a lot)
First, the easy method. If you search LiTiO2 on the Materials Project website, you’ll see that two of the phases (I41/amd and Fd-3m) are highlighted in green, meaning that they are experimentally known on the ICSD diffraction database. That’s always the best place to start.

The other seven phases were probably generated by comparison with other experimentally known ABO2 structures where A is chemically similar to Li and B is similar to Ti. As you might expect, none of these are as stable as the experimentally known I41/amd - but some of them are close, and might be synthesizeable with effort. Structure Predictor - Materials Project Documentation

If you’re working in a novel or obscure system which doesn’t have many possible structures predicted by these two methods, Pymatgen also has some tools you can use to guess the most favorable sites for adding an interstitial atom. pymatgen.analysis.defects.utils module — pymatgen 2022.0.9 documentation But typically the Materials Project doesn’t do an explicit intercalation calculation like that - the voltage profiles are just calculated from the energies of the TiO2 and LiTiO2 phases which are already known or predicted.