Intensity of X-ray Diffraction by a One-dimensionally Disordered Crystal (II) General Derivation in the Case of the Correlation Range <i>s</i>≥2.

Abstract

The general intensity equation for X-rays diffracted by a one-dimensionally disordered crystal i.e. \(I{=}N\text{Spur}\ \textbf{\itshape V}\textbf{\itshape F}+\sum\limits_{n{=}1}^{N-1}(N-n)\text{Spur}\ \textbf{\itshape V}\textbf{\itshape F}\textbf{\itshape Q}^{n}+\text{conj.}\) which was derived for the correlation range s =1 was found to be valid for any s -value by modifying slightly the elements of the matrices. \(\overline{S_{j}S_{j+n^{*}}}\) as used by Wilson and Jagodzinski was shown to be equal to Spur V F P n for any s -value. In our present method, layer form factors are refered to single layers and the preceding ( s -1) layers are used only to classify them into r l subgroups where r is the number of the kinds of layers and l that of combinations of ( s -1) preceeding layers. This method which we call the “antecedent” one is found to be equivalent to another one as used by Hendricks and Teller in which each layer form factor is taken over the whole s layers hence there are R = r l different layer form factors and which we call the “whole s layers” method. We discussed the relation between the cases of ranges s and ( s -1). A simple example is shown in the case of r =2 and s =2.