Empirical method for modeling crystal lattice parameters of A2XY6 cubic crystals using grid search-based extreme learning machine

The lattice parameters of A(2)XY(6) (A=K, Cs, Rb, and Tl; X=tetravalent cation; Y=F, Cl, Br, and I) cubic crystals play significant roles in designing materials for specific technological applications and uniquely describe the material crystal structure. Despite the importance of its lattice parameters, the experimental determination of these parameters requires special sophisticated equipment, while the first principle calculation consumes appreciable time and might need complex software packages. The existing empirical relation in the literature is characterized by large percentage deviation, and the recently proposed machine learning support vector regression method cannot be empirically implemented on new compounds. This present work fills the research gap through the development of empirical relation between the lattice parameters, electronegativity and ionic radii of the constituting ions using extreme learning machine (ELM) with the grid search (GS) hyper-parameters optimization method. The proposed model is developed through the analysis of atomic structural properties of 85 crystals that serve as representatives of the A(2)XY(6) group. On the basis of a mean absolute percentage error, the developed GS-ELM model outperforms the existing Brik and Kityk [J. Phys. Chem. Solids 72(11), 1256-1260 (2011)] model with a percentage improvement of 58.37%, while it performs better than Alade et al. [J. Appl. Phys. 127(1), 15303 (2020)] model with the percentage enhancement of 37.90%. The outstanding performance of the proposed GS-ELM model coupled with its ease of implementation would be of great significance by enhancing the search for new materials tailored to targeted application and preventing lattice constant mismatch in thin film fabrication.