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In condensed matter physics and crystallography, the static structure factor (or structure factor for short) is a mathematical description of how a material scatters incident radiation. The structure factor is a critical tool in the interpretation of scattering patterns ( interference patterns ) obtained in X-ray , electron and neutron ...
In condensed matter physics, the dynamic structure factor (or dynamical structure factor) is a mathematical function that contains information about inter-particle correlations and their time evolution. It is a generalization of the structure factor that considers correlations in both space and time.
After crystallographic image processing, [21] structure factor phase angles are far more reliable than structure factor amplitudes. Further discernment of candidate structures is then mainly based on structure factor phase angles and, to a lesser extent, structure factor amplitudes (so-called 'structure factor fingerprinting'). [22] [23]
The pair correlation function is related via Fourier transform to the static structure factor, which can be determined experimentally using X-ray diffraction or neutron diffraction. The OZ equation relates the pair correlation function to the direct correlation function. The direct correlation function is only used in connection with the OZ ...
Now we see the overall structure factor may be represented as a weighted sum of structure factors () corresponding to each atom. Set the displacement between the location in space for which we would like to know the scattering density and the reference position for the nucleus equal to a new variable t → = x → − x → k 0 {\displaystyle ...
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In the Cambridge Structural Database of small-molecule structures, more than 95% of the 500,000+ crystals have an R-factor lower than 0.15, and 9.5% have an R-factor lower than 0.03. Crystallographers also use the Free R-Factor ( R F r e e {\displaystyle R_{Free}} ) [ 3 ] to assess possible overmodeling of the data.
The corresponding factor for coherent neutron or X-ray scattering is the Debye–Waller factor; often, that term is used in a more generic way to include the incoherent case as well. When first reporting on recoil-free resonance absorption, Mössbauer (1959) [ 1 ] cited relevant theoretical work by Lamb (1939). [ 2 ]