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The DAFS crystallographic weights

To see how DAFS weights different crystallographically inequivalent sites, it is helpful to separate the smooth atomic amplitudes for all the atoms in the unit cell, labelled by n, from the fine structure terms for just the resonantly scattering atoms, labelled by l, yielding
The kinematic diffraction intensity is proportional to the square of the structure factor,
The first term, tex2html_wrap_inline1512, represents the smooth atomic contributions to the energy dependence of the Bragg intensities. The second and third terms are the cross terms between tex2html_wrap_inline1514 and tex2html_wrap_inline1516. The fourth term is the second order fine structure contribution and is a smooth function versus photon energy.

Because the leading order DAFS contributions to the intensity come from the cross terms between tex2html_wrap_inline1514 and tex2html_wrap_inline1520, the leading order site-specific tex2html_wrap_inline1522 and tex2html_wrap_inline1524 information appears linearly in the Bragg intensities, and can be extracted using standard crystallographic techniques. We can rewrite Eqn. 10 in terms of the crystallographic weights tex2html_wrap_inline1526,
The site specific crystallographic weights depend on the diffraction wavevector transfer tex2html_wrap_inline1434 and are given by the sum over all the occurrences in the unit cell of each equivalent site, labelled by k, producing one weight for each inequivalent site, labelled by m,