  In the limit of vanishing lattice spacing we provide a rigorous variational
coarse-graining result for a next-to-nearest neighbor lattice model of a simple
crystal. We show that the $\Gamma$-limit of suitable scaled versions of the
model leads to an energy describing a continuum mechanical model depending on
partial dislocations and stacking faults. Our result highlights the necessary
multiscale character of the energies setting the groundwork for more
comprehensive models that can better explain and predict the mechanical
behavior of materials with complex defect structures.
