On the X-ray reflectivity of elastically bent perfect crystals

The integrated X-ray reflectivity of elastically bent, but otherwise perfect, crystals are calculated for Laue-type reflections covering the entire curvature range. Anomalous transmission and elastic anisotropy are taken into account, and it is shown that both these effects affect appreciably the reflected intensities for both weakly and strongly bent crystals. The validity of the reflectivity-versus-curvature relation thus obtained is experimentally confirmed for a number of reflections from silicon crystals. The implications of the experimental results to brittle fracture are discussed.