Origin and application of the Lorentz factor in X-ray diffraction.

Abstract

The Lorentz factor is a fundamental correction factor in quantitative analysis of X-ray diffraction experiments, enabling measured integrated peak intensities to be related to calculated structure factors. In this review, the physical origin of the Lorentz factor, its derivation and practical implementations are presented based on a unified approach, treating the Lorentz factor as the Jacobian relating the experimental measurement coordinates to the reciprocal-space volume element. This approach clarifies the trigonometric and wavelength-dependent contributions to the Lorentz factor and explains the origin of the commonly used `angular-velocity' formulation for rotational measurements. Equations for the Lorentz factor are derived systematically for a broad range of modern X-ray diffraction geometries, including single-crystal and powder diffraction, grazing-incidence diffraction methods, as well as small-angle X-ray scattering. Hereby it is demonstrated that the Lorentz factor sensitively depends not only on the experimental geometry, but also on the type of sample under investigation. In addition, we discuss how the Lorentz correction may be avoided by direct reciprocal-space integration, and the practical limitations of such approaches are pointed out. By providing a unified and comprehensive overview of the Lorentz factor, this review aims to support reliable and consistent intensity evaluation across various modern X-ray diffraction methods.