Computation and visualization of accessible reciprocal space and resolution element in high-resolution X-ray diffraction mapping

TL;DR

This paper presents a method to visualize and calculate accessible reciprocal space regions and resolution elements in high-resolution X-ray diffraction mapping, accounting for goniometer limitations and detector geometry.

Contribution

It introduces an algorithm to determine accessible reciprocal space regions and resolution elements, extending previous methods with experimental validation.

Findings

Successfully visualized accessible reciprocal space regions.

Calculated resolution elements at various reciprocal space points.

Validated the method with experimental reciprocal space maps.

Abstract

An approach to visualize the accessible reciprocal space accounting the goniometer angles limitation and the resolution element in the reciprocal space is presented. The shapes of the accessible reciprocal space region for coplanar and non-coplanar geometries are given employing the additional degree of freedom provided by detector arm. The examples of the resolution elements in different points of the reciprocal space are shown. The equations obtained permit to find these regions and to calculate the experimental geometry to obtain the diffraction from any accessible reflections, which makes a further extension of previously reported methods. The introduced algorithm has been testified by experimental measurements of reciprocal space maps in coplanar and non-coplanar geometries. The examples of the resolution elements in different points of the reciprocal space are calculated to illustrate the method proposed.