Observation of the effect of refraction on x rays diffracted in a grazing-incidence asymmetric Bragg geometry

The positions of x-ray diffraction peaks from a polycrystalline iron oxide thin film have been measured in a grazing-incidence, asymmetric Bragg geometry for incidence angles between 0.09° and 1.04°. The peak positions are shifted from the Bragg angles 2${\theta }_B$ due to refraction of the incident x rays as they penetrate the air-solid interface. The shifts are quantitatively consistent with those obtained by applying Fresnel boundary conditions for reflection and refraction of a plane electromagnetic wave at an interface between air and a uniform, absorbing dielectric and they provide confidence in the validity of the Fresnel boundary conditions in the x-ray regime.