  We investigate the emergence of rigid polycrystalline structures from
atomistic particle systems. The atomic interaction is governed by a suitably
normalized pair interaction energy, where the `sticky disk' interaction
potential models the atoms as hard spheres that interact when they are
tangential. The discrete energy is frame invariant and no underlying reference
lattice on the atomistic configurations is assumed. By means of
$\Gamma$-convergence, we characterize the asymptotic behavior of configurations
with finite surface energy scaling in the infinite particle limit. The
effective continuum theory is described in terms of a piecewise constant field
delineating the local orientation and micro-translation of the configuration.
The limiting energy is local and concentrated on the grain boundaries, i.e., on
the boundaries of the zones where the underlying microscopic configuration has
constant parameters. The corresponding surface energy density depends on the
relative orientation of the two grains, their microscopic translation misfit,
and the normal to the interface. We further provide a fine analysis of the
surface energies at grain boundaries both for vacuum-solid and solid-solid
phase transitions. The latter relies fundamentally on a structure result for
grain boundaries showing that due to the extremely brittle setup interpolating
boundary layers near cracks are energetically not favorable.
