X-ray Pendellösung fringes in Darwin reflection

Oscillations have been observed in the tails of the Darwin curve from thin specimens of silicon. Dynamical theory predicts such oscillations (Pendellösung) for plane wave incident conditions in which two wave points on the same branch of the dispersion surface interfere and produce beating in the diffracted intensity. The usual Pendellösung is observed in transmission in which beating occurs between wavefields on different branches of the dispersion surface related by spherical rather than plane wave conditions. The present experiment uses an asymmetrically cut first crystal to increase the effective width of the incident wave and therefore approach the plane wave condition. Quantitative fringe measurements versus thickness are in fair agreement with theory. The intensity and contrast of the fringes are in poor agreement with theory. Several of the more important factors which reduce the contrast are discussed. With a relatively simple assumption, the observed and expected intensity dislocations can be brought into good agreement.