Direct Determination of Stacking Disorder in Layer Structures

Abstract

A stack of $N$ identical, parallel, and equidistant layers is used as a simple model of a layer structure. Irregularities in the relative displacements $\mathbf{\ensuremath{\delta}}$ parallel to the plane of the layers correspond to stacking disorder. The stacking disorder is described by means of a set of functions ${W}_{M}(\mathbf{\ensuremath{\delta}})$ which measure the probability of finding a relative displacement $\mathbf{\ensuremath{\delta}}$ for layers $M$ spacings apart. It is shown that x-ray diffraction data permit a direct determination of the Fourier coefficients of the functions ${W}_{M}$. Thus these functions can be synthesized and the nature of the stacking disorder directly deduced.