# Graph‐Theory Approach to Element Miscibility and Alloy Design

## TL;DR

This paper uses graph theory to predict which elements can mix well, helping in designing new alloys and materials.

## Contribution

A novel graph-theoretic approach is introduced to predict element miscibility and alloy design possibilities.

## Key findings

- Graph theory identifies miscible element pairs and clusters based on thermodynamic parameters.
- The approach is validated against CALPHAD and Miedema's models and is suitable for machine learning.
- Network clusters reveal elements with high or low interaction potential for material design.

## Abstract

With 118 currently known elements, hence millions of possible quinary combinations, understanding and discovering potentially beneficial mixtures is challenging. Possible stable mixtures, however, are vital for alloy design or realization of new materials. Thermodynamically favorable interactions can also lead to enhanced materials properties. We apply graph theory to map relation in key thermodynamic parameters between elements, therefore revealing possible favorable (miscible) pairs and their congeners. Using closeness centrality and Lipschitz‐Hölder exponent, we define miscibility across the whole period table, albeit at ambient conditions. Whereas most metals have fair solubility, hyper‐ and hypo‐ centrality (high and low solubility respectively) clusters are identified. We confirm our graph‐based approach in understanding miscibility by comparing results to CALPHAD and Miedema's model. Unlike the heuristic models, the graph‐based approach is amenable to machine learning enabling prediction at extreme environments by extrapolating known scaling laws.

Graph and network theory enables pathway toward complex multiscale interactions between different elements for alloy design or interface engineering. Utilizing element's inherent properties and preferential interactivity, favorable mixed material formation, solubility and miscibility can be predicted. Network clusters ease the identification of elements with higher/lower degree of interaction from large groups of elements.