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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 ...
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]
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.
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The Scherrer equation, in X-ray diffraction and crystallography, is a formula that relates the size of sub-micrometre crystallites in a solid to the broadening of a peak in a diffraction pattern.
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 ]
Atomic form factor patterns are often represented as a function of the magnitude of the scattering vector = (). Herein k = 2 π / λ {\displaystyle k=2\pi /\lambda } is the wavenumber and 2 θ {\displaystyle 2\theta } is the scattering angle between the incident x-ray beam and the detector measuring the scattered intensity, while λ ...