Graph-Theory Approach to Element Miscibility and Alloy Design.

Area of Science:

• Materials Science
• Computational Chemistry
• Network Science

Background:

• Millions of elemental combinations pose challenges for discovering new materials.
• Stable mixtures are crucial for alloy design and enhanced material properties.
• Thermodynamic interactions significantly influence material characteristics.

Purpose of the Study:

• To apply graph theory for mapping thermodynamic relationships between elements.
• To identify potentially miscible element pairs and their related elements.
• To define and quantify element miscibility across the periodic table.

Main Methods:

• Utilized graph theory to represent thermodynamic parameters between elements.
• Applied closeness centrality and Lipschitz-Hölder exponent to define miscibility.
• Compared graph-based predictions with CALPHAD and Miedema's models.

Main Results:

• Identified clusters of hyper- and hypo-centrality indicating high and low solubility.
• Successfully mapped element relationships and predicted favorable mixtures.
• Validated the graph-based approach against established models.

Conclusions:

• Graph theory provides a robust framework for understanding element miscibility.
• The approach is adaptable for machine learning, enabling predictions under extreme conditions.
• This method offers a novel pathway for accelerated materials discovery.