A General and Interpretable Adatom Model for Classifying Surface Morphologies of Nonmetallic Elements on Metal Substrates

We present a general and interpretable adatom model that enables the prediction and understanding of stable surface morphologies of nonmetallic elements deposited on metal substrates. By calculating the formation energies of isolated adatoms on various metal surfaces, we reveal the competition between interfacial interactions and the self-aggregation tendencies of the deposited elements. Based on this model, we classify four distinct surface morphologies that arise from nonmetal-metal substrate combinations. First-principles calculations across 15 nonmetallic elements and nine close-packed metal substrates show strong agreement between model predictions and experimentally reported morphologies. The model also identifies inconsistencies in certain experimentally observed structures and predicts previously unexplored stable morphologies, offering valuable guidance for future studies. Furthermore, we propose substrate engineering strategies, such as surface alloying, to modulate interfacial interactions, thereby enabling the controlled epitaxial growth of targeted two-dimensional materials, as supported by experimental validation.