Differences in the equilibrium and critical degrees of coating in a phase transition in a carbon layer on a metal at the formation of graphene

Equilibrium processes in the (rhodium-graphene islands) system have been studied. It has been shown that the critical degree of carbon coating $\vartheta_{\text{cr}}$ in the chemisorbed “gas” phase on the surface is significantly different from the equilibrium degree of coating $\vartheta_{\text{eq}}$. When $\vartheta_{\text{cr}}$ is reached, a phase transition occurs and graphene islands are nucleated, whereas graphene islands with different relative areas are in equilibrium at $\vartheta_{\text{eq}}$ with chemisorbed carbon gas; these degrees of coating are related as $\vartheta_{\text{eq}}>\vartheta_{\text{cr}}$. This effect occurs for metals dissolving carbon in the bulk and is explained by the dominating role of the perimeter of islands through which exchange of atoms between islands and carbon gas occurs.