Machine learning predicts atomistic structures of multielement solid surfaces for heterogeneous catalysts in variable environments

Solid surfaces usually reach thermodynamic equilibrium through particle exchange with their environment under reactive conditions. A prerequisite for understanding their functionalities is detailed knowledge of the surface composition and atomistic geometry under working conditions. Owing to the large number of possible Miller indices and terminations involved in multielement solids, extensive sampling of the compositional and conformational space needed for reliable surface energy estimation is beyond the scope of ab initio calculations. Here, we demonstrate, using the case of iron carbides in environments with varied carbon chemical potentials, that the stable surface composition and geometry of multielement solids under reactive conditions, which involve large compositional and conformational spaces, can be predicted at ab initio accuracy using an approach that combines the bond valence model, Gaussian process regression, and ab initio thermodynamics. Determining the atomistic structure of surfaces under working conditions paves the way toward identifying the true active sites of multielement catalysts in heterogeneous catalysis.