X-Ray Interference in Partially Ordered Layer Lattices

The x-ray interference is calculated for layer lattices in which the phase shifts between consecutive layers and the scattering powers of individual layers do not follow a strictly periodic arrangement. In the second section the scattering power of all layers is assumed to be the same but the phase shifts can take on different values. In the third section neither the scattering powers nor the phase shifts have fixed values but a simplifying assumption is made about the phase shifts according to which distances between neighboring layers can be represented as sums of two distances characteristic of the individual layers. In both these sections a random sequence of the layers is assumed. In the fourth section the problem of arbitrary scattering powers and phase shifts is treated, and furthermore a statistical correlation between neighboring layers is introduced. In the following section the general theory is applied to a specific partially ordered stacking of layers encountered in micas and other similar minerals. The last section treats irregularities in close packed structures of spheres and irregular sequences of layers in graphite.