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Investigating topological indices and entropy measures for titanium diboride network.
Rimsha Saher1, Hani Shaker1, Imran Zulfiqar Cheema1
1Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore, Pakistan.
Discover Nano
|March 18, 2026
Summary
We computationally analyzed titanium diboride's crystal structure using graph theory. This reveals how network connectivity influences material properties, differentiating stable from variable regions.
Area of Science:
- Materials Science
- Computational Materials Science
- Nanotechnology
Background:
- Titanium diboride (TiB2) is a high-performance ceramic with exceptional hardness, wear resistance, and electrical conductivity.
- It finds critical applications in aerospace, defense, and high-temperature material sectors.
- Understanding its structural properties is key to optimizing its performance.
Purpose of the Study:
- To computationally analyze the structural properties of titanium diboride using graph-theoretical indices.
- To investigate the impact of network size on the complexity and diversity of TiB2's crystal lattice.
- To establish a quantitative framework for interpreting TiB2's structural features.
Main Methods:
- Modeling the crystal lattice of titanium diboride as a molecular graph.
- Utilizing graph-theoretical indices for connectivity and information content analysis.
- Employing entropy-based descriptors to quantify disorder, uniformity, and coordination within the lattice.
- Developing Python algorithms for automated, real-time, and reproducible computation of structural properties.
Main Results:
- Clear trends were identified, distinguishing highly variable structural regions from more repetitive and stable ones.
- The study demonstrated the significant contribution of network connectivity to the macroscopic behavior of titanium diboride.
- Computational analysis revealed how network size influences structural complexity and diversity.
Conclusions:
- The developed computational methodology provides a quantitative basis for understanding titanium diboride's structural characteristics.
- This approach offers a reproducible and scalable method for analyzing materials at the atomic level.
- The findings can be extended to study other materials in materials science and nanotechnology.
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