X-ray scattering from stepped and kinked surfaces: An approach with the paracrystal model

TL;DR

This paper develops a comprehensive formalism using the paracrystal model to analyze X-ray scattering from various complex surface morphologies, including stepped, kinked, and faceted surfaces, over reciprocal space.

Contribution

It introduces a generalized approach for calculating X-ray scattering from non-periodic surfaces using the paracrystal model, extending to two-dimensional morphologies and new concepts like terrace and step truncation rods.

Findings

Unified formalism for 1D and 2D surface morphologies

Generalization of crystal truncation rods to include terrace and step truncation

Application to vicinal, faceted, and rough surfaces

Abstract

A general formalism of X-ray scattering from different kinds of surface morphologies is described. Based on a description of the surface morphology at the atomic scale through the use of the paracrystal model and discrete distributions of distances, the scattered intensity by non-periodic surfaces is calculated over the whole reciprocal space. In one dimension, the scattered intensity by a vicinal surface, the two-level model, the N-level model, the faceted surface and the rough surface are addressed. In two dimensions, the previous results are generalized to the kinked vicinal surface, the two-level vicinal surface and the step meandering on a vicinal surface. The concept of crystal truncation rod is generalized considering also the truncation of a terrace by a step (yielding a terrace truncation rod) and a step by a kink (yielding a step truncation rod).