Geometrical effects in diffraction analysis

The use of X-ray and neutron scattering as a tool to study phase transitions is well established. As techniques improve and experiments are made under successively higher resolution, the need to consider the role of both the distribution of diffracting length scales and the incident-beam coherence volume is emphasized. The interplay of diffracting length scales and the beam coherence volume no longer permits calculation of diffraction profiles in terms of the sample intensity response convolved with an instrumental resolution function. Rather, the probe and sample now enter the calculation on an equal footing at the level of the scattering amplitudes. Under these conditions, it is found that the summation of coherent scattering amplitudes leads to characteristic profiles in wave-vector and, in the case of resonant X-ray scattering, energy space. In this latter case, in the vicinity of strong absorption edges, as used for example in resonant magnetic X-ray diffraction, the energy dependence of diffraction profiles may uniquely allow spatial localization of the scattering volume below the sample surface. This observation may considerably augment the range and power of resonant X-ray scattering.