A geometric basis for materials families in inorganic solids

Justin Tahmassebpur; Sarvesh Chaudhari; Cristóbal Méndez; Rushil Choudhary; Sudipta Kundu; Raymond E. Schaak; Héctor Abruña; Peter Frazier; Tomás Arias

arXiv · 2602.00254

A geometric basis for materials families in inorganic solids

Justin Tahmassebpur·Sarvesh Chaudhari·Cristóbal Méndez·Rushil Choudhary·Sudipta Kundu·Raymond E. Schaak·Héctor Abruña·Peter Frazier·Tomás Arias

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Abstract

The thermodynamic stability of inorganic solids spans a vast compositional space, yet materials scientists have long organized their intuition around a manageable number of materials families. Here we show that this organization has a precise geometric basis. The formation-energy convex hull of all inorganic compounds from the Materials Project, spanning 92-dimensional elemental composition space, is captured to near DFT accuracy by a polyhedron with only seven facets. Each facet corresponds to a family of materials sharing similar chemical potentials. This low-dimensional structure is not merely an economical description of energies: without retraining or structural input, the same framework reproduces trends in DFT-calculated defect energies and elemental spatial correlations in high-entropy nanoparticles. These results reveal that a small number of material families, corresponding to geometric features of composition-energy space, govern bulk stability, defect energetics, and elemental mixing, and provide a unified, interpretable framework for rapid screening across diverse materials systems.

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Justin Tahmassebpur, Sarvesh Chaudhari, Cristóbal Méndez, Rushil Choudhary, Sudipta Kundu, Raymond E. Schaak, Héctor Abruña, Peter Frazier, Tomás Arias. 2026-01-30. A geometric basis for materials families in inorganic solids. https://arxiv.org/abs/2602.00254

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