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In this paper we introduce Peierls-Nabarro type models for edge dislocationsat semi-coherent interfaces between two heterogeneous crystals, and prove theoptimality of uniformly distributed edge dislocations. Specifically, we showthat the elastic energy $\Gamma$-converges to a limit functional comprised oftwo contributions: one is given by a constant $c_\infty>0$ gauging the minimalenergy induced by dislocations at the interface, and corresponding to a uniformdistribution of edge dislocations; the other one accounts for the far fieldelastic energy induced by the presence of further, possibly not uniformlydistributed, dislocations. After assuming periodic boundary conditions andformally considering the limit from semi-coherent to coherent interfaces, weshow that $c_\infty$ is reached when dislocations are evenly-spaced on the onedimensional circle.

Uniform distribution of dislocations in Peierls-Nabarro models for semi-coherent interfaces