X-ray photon correlation spectroscopy in systems without long-range order: existence of an intermediate-field regime

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 limit d(2)/λ << R, where d is the incident beam size, λ is the photon wavelength and R is the sample-to-detector distance. Here it is shown that, in an intermediate regime d(2)/λ > R >> dξ/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 regime d(2)/λ > R >> dξ(τ)/λ, where ξ(τ) is a time-dependent dynamics length scale of interest, the ensemble-averaged correlation functions g(1)(τ) and g(2)(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.