Graphene at Liquid Copper Catalysts: Atomic-Scale Agreement of Experimental and First-Principles Adsorption Height

Liquid metal catalysts have recently attracted attention for synthesizing high-quality two-dimensional (2D) materials facilitated via the catalysts’ perfectly smooth surface. However, the microscopic catalytic processes occurring at the surface are still largely unclear because liquid metals escape the accessibility of traditional experimental and computational surface science approaches. For this reason, numerous controversies are found regarding different applications, with graphene (Gr) growth on liquid copper (Cu) as a prominent prototype. In this work, we employ novel in situ and in silico techniques to achieve an atomic-level characterization of the graphene adsorption height above liquid Cu, reaching a quantitative agreement within 0.1 Å between experiment and theory. Our results are obtained via in situ synchrotron X-ray reflectivity (XRR) measurements over wide-range q-vectors and large-scale molecular dynamics simulations based on efficient machine-learning (ML) potentials trained to first-principles density-functional theory (DFT) data. We demonstrate our computational insight to be robust against inherent DFT errors and reveal the nature of graphene binding to be highly comparable at liquid Cu and solid Cu(111). Transporting the predictive first-principles quality via ML potentials to the scales and sampling required for liquid metal catalysis thus provides a powerful approach to reach microscopic understanding, analogous to the established computational approaches for catalysis at solid surfaces.