  Grain boundaries in epitaxial graphene on the SiC(000$\bar{1}$) substrate are
studied using scanning tunneling microscopy and spectroscopy. All investigated
small-angle grain boundaries show pronounced out-of-plane buckling induced by
the strain fields of constituent dislocations. The ensemble of observations
allows to determine the critical misorientation angle of buckling transition
$\theta_c = 19 \pm~2^\circ$. Periodic structures are found among the flat
large-angle grain boundaries. In particular, the observed $\theta =
33\pm2^\circ$ highly ordered grain boundary is assigned to the previously
proposed lowest formation energy structural motif composed of a continuous
chain of edge-sharing alternating pentagons and heptagons. This periodic grain
boundary defect is predicted to exhibit strong valley filtering of charge
carriers thus promising the practical realization of all-electric valleytronic
devices.
