Diffusion of a graphene flake on a graphene layer is analyzed and a new diffusion mechanism is proposed for the system under consideration. According to this mechanism, rotational transition of the flake from commensurate to incommensurate states takes place with subsequent simultaneous rotation and translational motion until the commensurate state is reached again, and so on. The molecular dynamics simulations and analytic estimates based on ab initio and semi-empirical calculations demonstrate that the proposed diffusion mechanism is dominant at temperatures T ~ Tcom, where Tcom corresponds to the barrier for transitions of the flake between adjacent energy minima in the commensurate states. For example, for the flake consisting of ~ 40, 200 and 700 atoms the contribution of the proposed diffusion mechanism through rotation of the flake to the incommensurate states exceeds that for diffusion of the flake in the commensurate states by one-two orders of magnitude at temperatures 50 - 150 K, 200 - 600 K and 800 - 2400 K, respectively. The possibility to experimentally measure the barriers to relative motion of graphene layers based on the study of diffusion of a graphene flake is considered. The results obtained are also relevant for understanding of dynamic behavior of polycyclic aromatic molecules on graphene and should be qualitatively valid for a set of commensurate adsorbate-adsorbent systems.Comment: 33 pages, 6 figure
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