An expression for the intensity 9f a diffracted beam of X-rays is derived for a distorted crystal. This formula includes the results of D e h 1 i n g e r and B o a s, and the intensity caused by the distortion, which is known as the frozen heat motion. A theorem, valid for all inhomogeneous distortions, is proved with the help of this expression. This theorem can be used for the discussion of the broadening or decrease of intensity of the reflections for distorted crystals. ยง I. Introduction. The broadening of D e b y e-S c h e r r e r lines, caused by cold-working on metals, has been explained in several ways. One of them represents the theory of the inhomogeneous distortion, which has been considered by D e h I i n g e r *), B o a s 5), B r i n d 1 e y and R i d 1 e y 6) a.o. In these theories it is assumed that the atoms are displaced from their ideal positions over small distances. This distortion must be distinguished from the homogeneous distortion, e.g. a single stretch. Here the displacements cannot be small for all the atoms, as they are linear functions of the ideal coordinates of the atoms, the crystal retaining after distortion an ideal crystal structure with new parameters. Now the papers referred to deal with special inhomogeneous distortions. These distortions may cause a broadening of the reflection, or a decrease of intensity, or both. It is however not quite clear how this broadening, or the decrease of intensity can be derived from the chosen type of distortion. A general theory does not exist at present.
In this paper an attempt will be made 1 ยฐ to formulate a general theory, from which special theories may be deduced, and 2 ยฐ to put the several methods of evaluating the broadening of reflections on a common basis. Though it seems likely that not much can be said --29