A seven-facet polyhedron captures the composition-only formation-energy landscape of inorganic solids

TL;DR

This paper introduces a simple, interpretable polyhedral model with seven facets that accurately captures the formation-energy landscape of inorganic solids based solely on composition, enabling broad predictions and materials screening.

Contribution

The authors develop a seven-facet polyhedral model trained on DFT data that unifies various materials properties into a compact, interpretable, composition-only framework.

Findings

Model accurately reconstructs DFT formation energies with seven facets.

Generalizes to defect energies, elemental mixing, and electrochemical stability.

Enables rapid, interpretable screening across vast chemical spaces.

Abstract

This work demonstrates that the convex hull of formation energies for solid compounds involving elements from hydrogen to uranium admits a remarkably simple description over the 92-dimensional space of chemical compositions, despite the enormous combinatorial complexity of possible atomic structures. By training an interpretable max-affine model directly on near-hull formation energies from the Materials Project density-functional theory (DFT) database, we find that the hull can be reconstructed to DFT accuracy using a polyhedron with only seven facets. These facets define seven chemically coherent materials classes, with just seven coefficients per element sufficing to capture the dominant energetic trends across composition space. Remarkably, this compact, composition-only representation generalizes far beyond bulk formation energies. Without retraining or structural input, the same model reproduces trends in DFT-calculated defect formation energies, captures experimentally observed elemental mixing correlations in high-entropy materials, and enables the construction and optimization of Pourbaix diagrams for electrochemical stability. Together, these results show that many materials properties governed by energy differences can be expressed as simple linear combinations of a small set of interpretable, element-specific parameters. The result is a bonding-geometry-free thermodynamic framework that unifies stability, defects, mixing, and electrochemistry, and enables rapid, interpretable screening across vast chemical spaces.