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The DAFS technique is one of the rapidly developing structural, spectroscopic, and crystallographic methods that have been stimulated by the availability of spectacular new synchrotron radiation sources. The benefits of infusing crystallographic methods into x-ray absorption spectroscopy have been clearly demonstrated. The theory of DAFS away from the edge is well developed and in good agreement with experiment, but a practical near-edge theory is still needed. The reverse benefits that the x-ray spectroscopic sensitivities can bring to crystallography are also of great interest and are currently being developed, as illustrated throughout this book. This widespread work on the smooth and oscillatory scalar and tensor scattering amplitudes of atoms in condensed matter has turned these ``previous problems'' into ``new solutions''.

Truly comprehensive techniques should use all of the degrees of freedom of the photons: their momenta, energies and spins. Polarization analyzed DAFS uses all of these degrees of freedom in the special case of elastic scattering--there is momentum transfer, but no energy transfer. The three other closely related possibilities: 1) elastic forward scattering--no energy or momentum transfer, 2) absorption and inelastic forward scattering--energy, but no momentum transfer, and 3) inelastic resonant scattering (x-ray Raman)--both energy and momentum transfer, are all discussed in this book.

However, this book also teaches us that to encompass all resonant x-ray scattering processes, the above classification must be further enlarged to include the photon spin-angular momentum transfer and the coupling of the photon simultaneously to the charge and to the magnetism of condensed matter systems. The prospects for exciting future developments in resonant x-ray scattering seem very bright!