Structure factor

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 si

Official source

https://en.wikipedia.org/wiki/Structure_factor

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The Neutron Scattering Structure Factor

Jérôme Egger

In the experience of neutron scattering, the structure factor is a value that can be almost directly measured (through the differential inelastic neutron scattering cross section). Thus it can be interesting to have a calculation which could give a theoretical point of view, even if the system used in the calculation cannot be as complex as in the real case. Although this calculation (of a simplified system) could be a bad representation of the real system, it is already a point of comparison which yields finally to a better understanding. The present work has the aim to provide a useful matlab code for the computation of the structure factor of small magnetic cluster in “spin-only” scattering. A concrete exemple and the result for a special configuration will be also given.

2010

Crystal structure evaluation: calculating relative stabilities and other criteria: general discussion

Rui Guo

2018

Incommensurate crystallography without additional dimensions

Philippe Kocian

It is shown that the Euclidean group of translations, when treated as a Lie group, generates translations not only in Euclidean space but on any space, curved or not. Translations are then not necessarily vectors (straight lines); they can be any curve compatible with the parameterization of the considered space. In particular, attention is drawn to the fact that one and only one finite and free module of the Lie algebra of the group of translations can generate both modulated and non-modulated lattices, the modulated character being given only by the parameterization of the space in which the lattice is generated. Moreover, it is shown that the diffraction pattern of a structure is directly linked to the action of that free and finite module. In the Fourier transform of a whole structure, the Fourier transform of the electron density of one unit cell (i.e. the structure factor) appears concretely, whether the structure is modulated or not. Thus, there exists a neat separation: the geometrical aspect on the one hand and the action of the group on the other, without requiring additional dimensions.

Wiley-Blackwell2013