A study of pendellösung fringes in X-ray diffraction

Abstract

X-ray topographs of a new type have revealed fine fringes in the diffraction images of wedge-shaped parts of perfect and nearly perfect crystals. The fringes are analogous to those seen in electron microscope images of wedge-shaped parts of magnesium oxide crystals and can be interpreted according to the theory applicable to the electron case. Fringe spacing depends upon X-ray wavelength, wedge-angle, inclination of reflecting plane to the wedge surfaces, and the structure amplitude of the reflection. Discovery of these fringes shows that (a) parts of real crystals behave as ideally perfect from the X-ray diffraction standpoint (b) the dynamical theory of diffraction may be applied quantitatively under practical experimental conditions, and (c) structure amplitudes of low-order reflections may be determined by fringe-spacing measurements, without any need for measuring reflection intensities. Tests of the theory on prepared wedges of silicon and quartz indicate a slight systematic discrepancy of 4 to 5 % between calculated and observed values of structure amplitude, and suggest also that Wei's (1935) F-values for quartz 10T1 and 1T22 are too low by 9% and 4% respectivcly. Experiments suggest that to explain fully the observations some modification of the dynamical theory is required in the direction of allowing for a spherical wavefront of the incident beam.

Modeling perfect crystals in transmission geometry for synchrotron radiation monochromator design

“…The Pendellösung effect manifests itself in intensity variations of the diffracted intensity as a function of the rocking angle in the case of thin absorbing crystals, as in our case. It also manifests itself in the generation of interference fringes in the diffraction topographs of wedge-shaped parts of a perfect crystal [4].The oscillatory behavior is highly dependent on the crystal thickness, and its frequency increases with increasing thickness. In the limit of the thick crystal approximation, sin 2 (av) takes the mean value of 1/2.…”

Notizen: Dynamical X-ray Diffraction Theory of Spherical Waves

“…That the wave fields are confined within a wedgeshaped region between and + corresponds to the behavior of crystal waves propagating in a direction normal to the dispersion surface 1_3, 5_7 . The present theory can explain hook-shaped Pendellösung fringes 4 , which are not explainable in terms of the plane-wave theory. Since /0 and Jt are oscillating functions we can expect fringe patterns.…”

Accurate Determination of Structure Factors by Pendellosung Methods Using White Radiation

“…1 band measuring the fringe spacing. This is the method called 'section topograph ' and Kato and Lang (1959) first observed the fringes. When the wedge-shaped specimen is horizontally transversed simultaneously with the photographic plate, the thickness extinction fringe pattern will be photographed as shown in Fig.…”

“…The fringes have usually been observed on topographs using characteristic X rays and wedge-shaped perfect single crystals. Kato and Lang (1959) first observed the fringes on the topograph to measure the structure factors of Si and other materials and many workers have applied this technique for evaluating the structure factors of various materials. The method requires accurate collimation of characteristic X rays and precise shaping of a large single crystal.…”