Lesson plan
Structure factor
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 diffraction experiments. Confusingly, there are two different mathematical expressions in use, both called 'structure factor'. One is usually written S(\mathbf{q}) ; it is more generally valid, and relates the observed diffracted intensity per atom to that produced by a single scattering unit. The other is usually written F or F_{hk\ell} and is only valid for systems with long-range positional order — crystals. This expression relates the amplitude and phase of the beam diffracted by the (hk\ell) planes of the crystal ( (hk\ell) are the Miller indices of the planes) to that produced by a single scattering unit at the vertices of the primitive unit cell. F_{hk\ell} is not a special case of S(\mathbf{q}) ; S(\mathbf{q}) gives the scattering intensity, but F_{hk\ell} gives the amplitude. It is the modulus squared |F_{hk\ell}|^2 that gives the scattering intensity. F_{hk\ell} is defined for a perfect crystal, and is used in crystallography, while S(\mathbf{q}) is most useful for disordered systems.…
Article summary
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 diffraction experiments. Confusingly, there are two different mathematical expressions in use, both called 'structure factor'. One is usually written S(\mathbf{q}) ; it is more generally valid, and relates the observed diffracted intensity per atom to that produced by a single scattering unit. The other is usually written F or F_{hk\ell} and is only valid for systems with long-range positional order — crystals. This expression relates the amplitude and phase of the beam diffracted by the (hk\ell) planes of the crystal ( (hk\ell) are the Miller indices of the planes) to that produced by a single scattering unit at the vertices of the primitive unit cell. F_{hk\ell} is not a special case of S(\mathbf{q}) ; S(\mathbf{q}) gives the scattering intensity, but F_{hk\ell} gives the amplitude. It is the modulus squared |F_{hk\ell}|^2 that gives the scattering intensity. F_{hk\ell} is defined for a perfect crystal, and is used in crystallography, while S(\mathbf{q}) is most useful for disordered systems.…
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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
Bibliography
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Key claims and bibliography are generated from the same tracked claims and sources as the article page.