Modulated corrugations in the crystal structure of the superconductor CaAlSi

We report the crystal structure analyses of CaAlSi from single-crystal and powder X-ray diffraction and the existence of two commensurately modulated phases, a sixfold and a fivefold modulated structure. This polymorphism seems to be correlated to the thermal history of the sample. We describe both modulated structures using a three-dimensional and a (3 + 1)-dimensional formalism.