Pendellösung Fringes in Distorted Crystals III. Application to homogeneously bent crystals

Abstract

The dynamical diffraction theory developed in Part I and II of this paper (J. Phys. Soc. Japan 18 (1963) 1785; 19 (1964) 67) is applied to homogeneously bent crystals. The Laue cases of X-ray diffraction are treated specifically. For a small bending Pendellösung fringes are still observable but fringe distances decrease with increasing the curvature. The fringes take the form of hyperbola in the same way as the perfect crystal. For a large bending and in the parts of the crystal far from the entrance surface the fringes fade out. Connecting with these aspects the trajectories, the phase changes and the intensity distributions of crystal waves are discussed in details both for non-absorbing and absorbing crystals. The formula of integrated intensity of diffracted beam is given in non-absorbing cases.
The Borrmann absorption in distorted crystals is reformulated in a neat form for general cases of lattice distortions.