We report on temperature-programmed growth of graphene islands on Ru(0001) at annealing temperatures of 700°C,800°C,and 900°C.The sizes of the islands each show a nonlinear increase with the annealing temperature.In 700°C and 800°C annealings,the islands have nearly the same sizes and their ascending edges are embedded in the upper steps of the ruthenium substrate,which is in accordance with the etching growth mode.In 900°C annealing,the islands are much larger and of lower quality,which represents the early stage of Smoluchowski ripening.A longer time annealing at 900°C brings the islands to final equilibrium with an ordered moir’e pattern.Our work provides new details about graphene early growth stages that could facilitate the better control of such a growth to obtain graphene with ideal size and high quality. We report on temperature-programmed growth of graphene islands on Ru (0001) at annealing temperatures of 700 ° C, 800 ° C, and 900 ° C. The sizes of the islands each show a nonlinear increase with annealing temperature. C and 800 ° C annealings, the islands have nearly the same sizes and their ascending edges are embedded in the upper steps of the ruthenium substrate, which is in accordance with the etching growth mode. 900 ° C annealing, the islands are much larger and of lower quality, which represents the early stage of Smoluchowski ripening. A longer time annealing at 900 ° C brings the islands to final equilibrium with an ordered moir’e pattern. Our work provides new details about graphene early growth stages that could facilitate the better control of such a growth to obtain graphene with ideal size and high quality.