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Methods of computer molecular dynamics have been applied to model a J = 5 symmetric‐tilt coincidence grain boundary. A pairwise Lennard‐Jones 6–12 potential was used to simulate the atomic interactions in a bicrystal containing up to 396 atoms. At simulated temperatures of approximately half the potential well depth the boundary undergoes spontaneous sliding coupled with migration. The observations are consistent with a geometrical model based on the coincidence model of grain boundaries and also with the results of a separate calculation of the Peierls‐Nabarro‐like energy barrier for such coupled sliding and migration, using a static relaxation method on a model constrained to have various displacements.