Intensity of X-ray Diffraction by an One-Dimensionally Disordered Crystal (1) General derivation in cases of the “Reichweite” S=0 and 1

Abstract

The present paper shows the calculation of the intensity of X-rays diffracted by a one-dimensionally, disordered crystal by the matrix method of Hendricks and Teller and has two purposes; the one is to make clear the relation between the above mentioned matrix method and the difference equation method used by Wilson and Jagodzinski, and the other is to rearrange the results obtained by Hendricks and Teller by introducing the general intensity equation from a rather simple and intuitive standpoint, assuming a finite number N of layers. The obtaind result for the former is \(\overline{S_{j}S^{*}_{j+n}}\)=Spur VFP n . For the latter case, it is concluded that the matrix φ containing the phase shift exp (- i ϕ s ) is not a general matrix but a diagonal one, and the assumption of a finite number N of layers gives rise to a higher term in addition to the normal diffuse term and this higher term becomes the Laue function in special cases and can hardly be neglected at and near a special point and also when N is very small. In addition the physical meanings of some quantities which appeared in their paper are made clear. More general treatments for the general structure with any “Reichweite” and their relation to Wilson and Jagodzinski's results will be discussed in following papers.