Successful X-ray photon correlation spectroscopy studies often require that signals be optimized while minimizing power density in the sample to decrease radiation damage and, at free-electron laser sources, thermal impact. This suggests exploration of scattering outside the Fraunhofer far-field diffraction limitd2/λ \llR, wheredis the incident beam size, λ is the photon wavelength andRis the sample-to-detector distance. Here it is shown that, in an intermediate regimed2/λ >R\ggdξ/λ, where ξ is the structural correlation length in the material, the ensemble averages of the scattered intensity and of the structure factor are equal. Similarly, in the regimed2/λ >R\ggdξ(τ)/λ, where ξ(τ) is a time-dependent dynamics length scale of interest, the ensemble-averaged correlation functionsg1(τ) andg2(τ) of the scattered electric field are also equal to their values in the far-field limit. This broadens the parameter space for X-ray photon correlation spectroscopy experiments, but detectors with smaller pixel size and variable focusing are required to more fully exploit the potential for such studies.
Ultra-small-angle X-ray scattering-X-ray photon correlation spectroscopy studies of incipient structural changes in amorphous calcium phosphate-based dental composites