A Universal Machine Learning Model for Elemental Grain Boundary Energies

The grain boundary (GB) energy has a profound influence on the grain growth and properties of polycrystalline metals. Here, we show that the energy of a GB, normalized by the bulk cohesive energy, can be described purely by four geometric features. By machine learning on a large computed database of 361 small $\mathrm{\Sigma }$ ($\mathrm{\Sigma }<10$) GBs of more than 50 metals, we develop a model that can predict the grain boundary energies to within a mean absolute error of 0.13 J m${}^{-2}$. More importantly, this universal GB energy model can be extrapolated to the energies of high $\mathrm{\Sigma }$ GBs without loss in accuracy. These results highlight the importance of capturing fundamental scaling physics and domain knowledge in the design of interpretable, extrapolatable machine learning models for materials science.