Theoretical study of X-ray diffraction in homogeneously bent crystals - the Bragg case

X-ray dynamical diffraction in homogeneously bent crystals is studied theoretically in the Bragg case. The study starts from the Green function given previously by Chukhovskii, Gabrielyan and Petrashen' as an inverse Laplace transform and which can be viewed as an integral over all incident plane waves. The integrand is developed by means of an asymptotic representation of parabolic cylinder functions. Integration by the stationary-phase method leads to the evidence of curved X-ray paths and, in the case of large values of strain gradient, to the creation of a new wave field. The intensity of the new wave field is shown to be a fraction exp(-2πvertical strokeνvertical stroke) of the incident beam where vertical strokeνvertical stroke is the inverse of the strain gradient expressed in reduced units. (orig.)