Electronic for: Predicting stable lithium iron oxysulphides for battery cathodes

Cathode materials that have high specific energies and low manufacturing costs are vital for the scaling up of lithium-ion batteries (LIBs) as energy storage solutions. We perform an extensive computational search for iron-based oxysulphides using ab initio random structure searching (AIRSS). Several new oxysulphide phases have been discovered which are predicted to be less than 50 meV/atom from the convex hull. Among the predicted phases, two anti-Ruddlesden-Popper structured materials Li2Fe2S2O and Li4Fe3S3O2 have been found to be attractive as they have high theoretical capacities. With band gaps as low as about 2.0 eV, they are expected to exhibit good electronic conductivities. Climbing-image NEB calculations show that the Li-ion transport in these materials has low activation barriers between 0.3 eV and 0.5 eV. The richness of new materials in the Li-Fe-S-O phase field illustrate the great opportunity in these mixed anion systems for energy storage applications and beyond.

and Oxide only is calculated using GGA for sulphides and with corrections applied to oxides.
The MP-ORIG refers to the data extracted directly from the Materials Project with their corrections applied. The Oxide only is refitted using the methodology that MP-ORIG refers to, 4,5 as we are not able to reproduce the fitting of corrections for the latter (U = 5.3 eV, ∆E M = −2.733eV ). Interestingly, our refitted U and the ∆E M terms are very close to the ones reported in the two methodology papers. 4,5 Recently, a revised correction scheme was 1 Using the data from the NIST-JANAF 9 table give similar results with negligible differences.
2 proposed by the Materials Project group 10 and made available online. The results obtained using this scheme is labelled as MP-2020 (U = 5.3 eV, ∆E M = −2.256eV ). One should note that here the newer PBE 54 PAW data set is used with Fe pv for Fe, Li sv for Li, O for O and S for S. The two papers mentioned above did not report the exact pseudopotential version that was used. The Materials Project also uses the Fe pv potential, from an older pseudopotential set PBE.
The reaction FeS + Li 2 S −−→ FeO + Li 2 O can be used as benchmark for the treatment of sulphides, as it does not contain any elemental phases so the errors involved there would have no effect. Assuming that most of the DFT errors come from the treatment of the Fe, having an formation energy that is too negative means that the oxides are overly favoured, and vice versa. As shown in Figure S1, using U for both oxides and sulphides makes FeO slightly favoured (the All scheme), whereas if it is only applied to the oxides, the FeS is more favoured. If one assumes that the ∆E M correction for mixing GGA/GGA+U is sufficient for oxides, this implies that the standard GGA calculation favours FeS and its energy is predicted to be lower. The same behaviour is found in oxides using plain GGA, where the errors from overly localised the d electrons are found to compensate some of that from the oxygen over-binding. 4 The error from the original Material Project scheme (MP-ORIG) for this particular reaction may appear to be small, but it is for the wrong reason as two other oxide/sulphide exchange reactions gives very large errors. In fact, the data from the Materials Project appear to be incorrectly calibrated for reproducing the reaction energy of oxidizing FeO to Fe 2 O 3 and Fe 3 O 4 (shown in the Fitting U for Fe of Figure S1), nor does it reproduces the binary formation energies of iron oxides (shown in the GGA+U/GGA Mixing of Figure   S1). The new material project corrections (MP-2020 ) appears to be correctly calibrated to the binary oxide formation energies with a revised ∆E M , but it suffers from the same problem for the reaction energies of oxidising FeO, due to the inconsistent U F e calibration.
On the other hand, both two sets of reaction energies are well reproduced by the Oxide only data, which is not a surprise, since it was to calibrated to reproduce them. The All scheme does not include the ∆E M term and hence is not expect to give accurate formation energies for iron oxides, but we are only interested in the competition between the quaternary and binary phases here so including this extra term has no effect. Hence, the All scheme is most suitable for investigating the stabilities of the oxysulphides.
Gibbs's free energy at finite temperature using machined learned descriptors The energies from the DFT calculations can only be used to access the thermodynamic stability at 0 K. At finite temperature, the synthesisbility of a material depends on its Gibbs's free energy, but the incorporation of temperature effects is not trivial using first-principles calculations. The vibrational entropy may be accounted for using phonon density of states under the quasi-harmonic approximation, which can be very resource intensive. Recently, a machine learning model for estimating the Gibbs's free energy has been reported. 11 In that work, it was found that the Gibbs energy may be estimated to a good accuracy using the enthalpy given by DFT plus an additional analytical term that is data mined using the sure independence screening and sparsifying operator (SISSO) method. This additional term takes only takes the composition of the material, the volume of the DFT relaxed structures, and the temperature as the input.
Applying this approach allows us to estimate the synthesisbility at finite temperature.
The results are plotted in the Figure S2. It is found that the phases that are predicted to be close to the convex hull remain close at finite temperatures. Interestingly, the number of stable phases appear to increase with increasing temperature. This is reflected in both the computed distance to hull as well as the distance to hull formed by the known non-quaternary phases.
However, we note that these results under finite temperatures can have several caveats.
First, the contribution of configurational entropy is not explicitly included, which could make 4 disordered phases more favourable at high temperatures, and one example is the Li 2 FeSO. Second, the physical descriptor was fitted using the Materials Project's data, which are computed using a similar but not identical pseudopotential set. In addition, the U for Fe d electron is 4 eV here whereas the Materials Project uses 5.3 eV. This could result in inconsistency in the both the energy of Fe-containing phases and their equilibrium volumes. Second, the training and testing set of the descriptor only includes the known experimental phases, whereas here we are applying it to a large set of newly predicted structures. During the search, many metastable phases that have higher volume per atom are found, which would have much reduced G δ SISSO term due to its volume dependency. In some cases, predicted phases that are more than 100 meV above the hull at 0K can be stabilised. Since such hypothetical structures are clearly not included in the training set, and the model is essentially being extrapolated, making it less reliable. Hence, we have limited the phase considered in Figure S2 to those having the lowest energy at 0 K for each composition. Finally, it should be noted that the descriptor was shown to have a Mean Absolute Error (MAE) of 46 meV, which is not negligible although some of the error cancellations are expected as we are limited to four elements here.

Data availability
The structure searching results, raw calculation data for phonon, neb and hybrid functional calculations, an archive containing the provenance of all calculations for the AiiDA frame-