Transition metal surfaces catalyse a broad range of thermally-activated reactions involving carbon-containing-species -- from atomic carbon to small hydrocarbons or organic molecules, and polymers. These reactions yield well-separated phases, for instance graphene and the metal surface, or, on the contrary, alloyed phases, such as metal carbides. Here, we investigate carbon phases on a rhenium (0001) surface, where the former kind of phase can transform into the latter. We find that this transformation occurs with increasing annealing time, which is hence not suitable to increase the quality of graphene. Our scanning tunneling spectroscopy and reflection high-energy electron diffraction analysis reveal that repeated short annealing cycles are best suited to increase the lateral extension of the structurally coherent graphene domains. Using the same techniques and with the support of density functional theory calculations, we next unveil, in real space, the symmetry of the many variants (two six-fold families) of a rhenium surface carbide observed with diffraction since the 1970s, and finally propose models of the atomic details. One of these models, which nicely matches the microscopy observations, consists of parallel rows of eight aligned carbon trimers with a so-called $(7timessqrt{mathrm{19}})$ unit cell with respect to Re(0001).
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