Quasiperiodic models with microcrystalline structures

We show how the standard cut and project method can be adapted to build quasiperiodic geometrical models displaying a microcrystalline structure. The procedure is illustrated with the example of the octagonal tilings. First, a partial symmetry breaking allows to build new tilings with two independent scales: one is associated to the size of the unit cells while the other occurs in walls between domains. The corresponding array of unit cells has a simple modulated structure. Then the unit cells are decorated according to a periodic approximant structure, thus providing a coherent microcrystalline model. The Fourier spectrum can be computed exactly and shows characteristic satellite spots, added to the quasiperiodic reference spectrum, which depend on the approximant parameters.