A simple method for analyzing peak broadening due to tilt and twist distributions in X-ray diffraction measurements of materials of arbitrary type

A method for simply identifying the X-ray diffraction peak broadening caused by tilt and twist distributions through analysis of their hkl dependence is proposed. The development of a new general formulation for the hkl-dependence analysis is presented. This makes the hkl-dependence analysis generally applicable to any material with any type of crystal structure. It also makes it possible to analyze the hkl dependence of broadening in terms of whole profile shapes, which improves the reliability of the analysis. Another advantage of the formulation is that the analysis procedures for broadening due to both tilt and twist distributions can be derived in a straightforward manner from the same general version. Owing to these advantages, the method is applicable to GaN-based epitaxial films. The method for twist distributions is experimentally demonstrated using GaN epitaxial films on sapphire substrates.