Termination interference along crystal truncation rods of layered crystals

Abstract

A destructive interference observed in high-resolution surface X-ray reflectivity data for diverse systems has been used as a `fingerprint' for determining the terminating plane of layered crystals. It is shown that this phenomenon is (a) general to layered crystal structures, (b) directly sensitive to the crystal termination as a result of phase contrast between layers within the substrate unit cell, and (c) closely related to systematic absences of bulk Bragg diffraction. A simple formalism is derived that relates the location of these destructive interferences to the terminating plane of a crystal using only knowledge of the substrate crystal structure. The factors that control the visibility of this phenomenon for different crystal symmetries and uniformity of the crystal termination are also explored. A special case, where X-ray reflectivity is nominally insensitive to crystal termination, is discussed to show that sensitivity can be obtained through the use of anomalous dispersion or ferroelectric displacements in the substrate lattice. Insight into this phenomenon is obtained by considering the influence of the spatial resolution on an effective electron density and the associated suitability of describing each of the layers in the structure as individual `pseudo-atoms'.