X-ray diffraction in the case of three strong rays. I. Crystal composed of non-absorbing point atoms

The conditions of propagation of a three-ray X-optical field in a crystal built of non-absorbing point atoms are discussed. The discussion follows the outline published in 1937 by one of the authors and is held as general as possible, so as to be applicable to cases not yet studied experimentally. A point of special interest is the closest approach of the Surface of Dispersion to the Laue point, i.e. the point in reciprocal space which represents the three-ray field according to the primitive kinematical theory. This approach determines the extent to which absorption is reduced in the corresponding wavefield and has therefore a direct bearing on the Borrmann effect. It is shown that for some cases of two simultaneous reflections the surface of dispersion gets much closer to the Laue point than for the reflections occurring singly or in pairs; this explains the `double Borrmann effect' and is discussed numerically for the simultaneous reflections (111/11) in germanium.