Calculation of diffraction efficiency for curved crystals with arbitrary curvature radius

A model is proposed to calculate the diffraction efficiency of X-rays in Laue geometry for curved crystals with an arbitrary value of the curvature radius. The model generalizes the results based on the dynamical theory of diffraction, which are valid only for crystals with a radius of curvature lower than the critical curvature. The model is proposed for any kind of crystal, and its efficiency tends to one-half in the limit of a thick flat crystal. On the basis of this model, it was possible to reconsider the results of recently observed diffraction efficiency for curved crystals. Finally, the model sets an upper limit for diffraction efficiency of low-curvature curved crystals, this latter being useful in applications such as the construction of a hard X-ray Laue lens.