  Graphene films grown by vapor deposition tend to be polycrystalline due to
the nucleation and growth of islands with different in-plane orientations.
Here, using low-energy electron microscopy, we find that micron-sized graphene
islands on Ir(111) rotate to a preferred orientation during thermal annealing.
We observe three alignment mechanisms: the simultaneous growth of aligned
domains and dissolution of rotated domains, i.e., "ripening"; domain-boundary
motion within islands; and continuous lattice-rotation of entire domains. By
measuring the relative growth velocity of domains during ripening, we estimate
that the driving force for alignment is on the order of 0.1 meV per C atom and
increases with rotation angle. A simple model of the orientation-dependent
energy associated with the moir\'e corrugation of the graphene sheet due to
local variations in the graphene-substrate interaction reproduces the results.
This work suggests new strategies for improving the van der Waals epitaxy of 2D
materials.
