  The grain boundary (GB) energy is a quantity of fundamental importance for
understanding several key properties of graphene. Here we present a
comprehensive theoretical and numerical study of the entire space of symmetric
and asymmetric graphene GBs. We have simulated over 79,000 graphene GBs to
explore the configuration space of GBs in graphene. We use a generalized
Read-Shockley theory and the Frank-Bilby relation to develop analytical
expressions for the GB energy as a function of the misorientation angle and the
line angle, and elucidate the salient structural features of the low energy GB
configurations.
