Stacking faults in the limit of a discrete model for partial edge dislocations

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 $\mathrm{\Gamma }$-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.