Effects of X-Ray Polarization on Pendellösung Fringes

A theory of Pendellösung fringes due to the incident beam of an unpolarized spherical wave is presented. The agreement with the observations pertaining to the fading of the fringes is very well. The observed fringe distance \(\varLambda\) is given by \begin{aligned} \frac{1}{\varLambda}{=}\frac{1}{2}(1+\cos 2\theta_{B})\frac{1}{\varLambda}_{\bot}, \end{aligned} where θ _B the Bragg angle and \(\varLambda_{\bot}\)is the fringe distance for a planepolarized spherical wave, the electric vector of which is perpendicular to the plane of reflection. The positions of maxima and minima of the fringes are interchanged before and after the fading position. These results give the theoretical and experimental bases to the new method of determining crystal structure factors (H. Hattori, H. Kuriyama, T. Katagawa and N. Kato: J. Phys. Soc. Japan 20 (1965) 988).