The static lattice (energy minimization) methods used in this study were conducted using the LAMMPS code suggests a high level of accuracy with reduced computational costs compared to using solely DFT-based methods. This approach allows to include in the calculations a larger number of atoms than that routinely accessible through DFT modeling. A significant advantage of these computational approach is thus the ability to handle the random distribution of strontium and lanthanum ions within this complex structure, in alignment with experimental evidence, instead of including an artificially produced long range order of the ions within the model, as normally required by DFT-based calculations . This flexibility also extends to the distribution of fluoride ions. To this end, fluoride ion vacancies were randomly distributed stepwise within the layers of the supercells, with one layer fully occupied by fluoride ions and the adjacent layer having randomly distributed vacancies. Similarly, for the low fluoride content phases, one layer was empty while the other had randomly distributed interstitial fluoride ions. This stepwise pattern is consistent with experimental evidence .