Investigating topological indices and entropy measures for titanium diboride network

Titanium diboride is a high performance ceramic material with excellent hardness, wear resistance and electrical conductivity, which has important applications in aerospace, defense, and high temperature materials. In this work, we conducted a computational analysis of the structural properties of its network based on graph-theoretical indices for connectivity and information content. We study model the crystal lattice of the material as a molecular graph to investigate how network size affects structure complexity and diversity. The lattice is characterized with descriptors based on entropy that quantify trends of disorder, uniformity, and coordination. Python algorithms make these structural properties automatically computable, both in real time and over huge amounts of data, and reproducible (synthetically or in simulations). The results exhibit clear trends that differentiate highly variable structure regions from more repetitive and stable ones, revealing the contribution of the connectivity on the macroscopic behavior. The computational methodology developed provides a quantitative background for interpreting the structural features of titanium diboride and can be applied to study other problems in materials science and nanotechnology.