Multifractal based topological characterization of perovskite crystal and predictive analysis on its physical...

Perovskite material has gained popularity and attracted much attention in recent years. Calcium Titanium Oxide $\left(CaTi{O}_3\right)$ is a perovskite crystal structure, which has the molecular formula $AB{X}_3$ , widely employed in geosciences, electronic ceramic materials, and radioactive waste immobilization. The powerful mathematical tool called topological descriptors or index is used to analyze $CaTi{O}_3$ perovskite. It provides a numerical representation of certain physical and chemical features on the crystal structure. Additionally, topological indices are frequently used by chemical scientists to determine the strain energy, melting and boiling points, distortion, and stability of chemical substances. In this paper, the topological indices are derived from the M-polynomial for $CaTi{O}_3$ perovskite crystal structure depends on reverse degree using the edge partitioning technique and the behavior of this crystal structure is presented as numerically derived equations and topological descriptors. The Generalized Fractal Dimensions (GFD) are calculated using Renyi entropy based on the equations of the reverse degree dependent indices derived from the M-polynomial, which are compared graphically and tabularly with respect to given indices. Furthermore, the molecular mass and collision diameter physical properties of the $CaTi{O}_3$ crystal structure are analyzed and correlated with the generalized fractal dimensions derived from topological indices, leading to the development of a predictive correlation model explaining the highest and lowest correlation coefficient values of each index defined in this phenomenon. Therefore, GFD aids to understand how the fractal nature, connectivity, and branching of the crystal affect its properties in the growth pattern of the $CaTi{O}_3$ crystal structure.