I will describe a recent result in collaboration with M. Fortuna and E. Spadaro, based on a model introduce by Lauteri and Luckhaus for the analysis of small angle grain boundaries in crystals. The latter is a semi-discrete model where the elastic distortion of the bulk of the crystal is described by a continuum deformation field and a small parameter is reminiscent of the lattice spacing of the underlying discrete structure. It also accounts for the crystal symmetry and the presence of defects. In the asymptotic analysis as the lattice spacing tends to zero we recover a sharp interface model for polycrystalline grain boundaries which, for small angles, agrees with the classical Read-Schokley formula.