Abstract
Substrate-catalyzed growth offers a highly promising approach for the controlled synthesis of carbon nanostructures. However, the growth mechanisms on dynamic catalytic surfaces and the development of more general design strategies remain ongoing challenges. Here we show how an active machine-learning model effectively reveals the microscopic processes involved in substrate-catalyzed growth. Utilizing a synergistic approach of molecular dynamics and time-stamped force-biased Monte Carlo methods, augmented by the Gaussian Approximation Potential, we perform fully dynamic simulations of graphene growth on Cu(111). Our findings accurately replicate essential subprocesses-from the preferred diffusion of carbon monomer/dimer, chain or ring formations to edge-passivated Cu-aided graphene growth and bond breaks by ion impacts. Extending our simulations to carbon deposition on metal surfaces like Cu(111), Cr(110), Ti(001), and oxygen-contaminated Cu(111), our results align closely with experimental observations, providing a practical and efficient approach for designing metallic or alloy substrates to achieve desired carbon nanostructures and explore further reaction possibilities.