Crystal truncation rods and surface roughness

TLDR

We present x‑ray‑diffraction profiles from various crystals that are diffuse perpendicular to the surface but sharp parallel to it. Understanding the origin of these streaks of intensity will have significant impact on the practice of x‑ray crystallographic determinations of surface structure. To explain the precise momentum‑transfer dependence of the intensity across the reciprocal‑space zone, surface roughness on an atomic scale must be included. These effects arise from truncation of the crystal lattice at the surface, and such measurements allow highly sensitive roughness determinations.

Abstract

We present x-ray-diffraction profiles from a variety of different crystals which are characteristically diffuse in the direction perpendicular to the surface through which the incident and diffracted beams pass, but sharp in both parallel directions. We show that these effects arise from truncation of the crystal lattice at the surface. To explain the precise form of the momentum-transfer dependence of the intensity across the reciprocal-space zone, it is necessary to include the effects of surface roughness on an atomic scale. Such measurements therefore allow highly sensitive roughness determinations to be made. Understanding the origin of these streaks of intensity will have significant impact on the practice of x-ray crystallographic determinations of surface structure.