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In the 50's Read and Shockley proposed a formula for the energy of smallangle grain boundaries in polycrystals based on linearised elasticity and anansazt on the distribution of incompatibilities of the lattice at theinterface. In this paper we derive a sharp interface limiting functionalstarting from a nonlinear semidiscrete model for dislocations proposed byLauteri--Luckhaus. Building upon their analysis we obtain, via$\Gamma$-convergence, an interfacial energy depending on the rotations of thegrains and the relative orientation of the interface which agrees for smallangle grain boundaries with the Read and Shockley logarithmic scaling.

On the Read-Shockley energy for grain boundaries in poly-crystals