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The high brightness and tunability of synchrotron radiation makes it an ideal probe of the atomic architecture of materials. The elastic scattering of such radiation may be exploited in a variety of X-ray diffraction experiments, or else the diffraction of the electrons emitted from atomic cores due to the absorption of X-ray photons may be monitored as in the technique of photoelectron diffraction.
Given a model structure of the material, the calculation of the diffraction pattern it produces is now quite routine. However, the inverse problem of deducing the structure from the diffraction pattern is still a formidable task. In X-ray diffraction all the difficulty may be laid at the door of the phase problem, ie. the fact that only the intensities are measured, and not the amplitudes. In the diffraction of low energy electrons, even if the phase problem were solved, the multiple-scattering problem is a further obstacle to the direct recovery of the atomic structure.
In traditional X-ray crystallography, great strides have been made over the past couple of decades towards the solution of the phase problem, to the extent that so-called direct methods are now quite routine for the structure solution of smaller molecules.