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X-ray scattering techniques

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Family of non-destructive analytical techniques

This is an X-ray diffraction pattern formed when X-rays are focused on a crystalline material, in this case a protein. Each dot, called a reflection, forms from the coherent interference of scattered X-rays passing through the crystal.

X-ray scattering techniques are a family of analyticaltechniques which reveal information about thecrystal structure, chemical composition, and physical properties of materials and thin films. These techniques are based on observing thescattered intensity of anX-ray beam hitting a sample as a function of incident and scattered angle, polarization, and wavelength or energy.

Note thatX-ray diffraction is sometimes considered a sub-set of X-ray scattering, where the scattering is elastic and the scattering object is crystalline, so that the resulting pattern contains sharp spots analyzed byX-ray crystallography (as in the Figure). However, bothscattering anddiffraction are related general phenomena and the distinction has not always existed. ThusGuinier's classic text^[1] from 1963 is titled "X-ray diffraction in Crystals, Imperfect Crystals and Amorphous Bodies" so 'diffraction' was clearly not restricted to crystals at that time.

Scattering techniques

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Elastic scattering

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X-ray diffraction, sometimes called Wide-angle X-ray diffraction (WAXD)
Small-angle X-ray scattering (SAXS) probes structure in the nanometer to micrometer range by measuring scattering intensity at scattering angles 2θ close to 0°.
X-ray reflectivity is an analytical technique for determining thickness, roughness, and density of single layer and multilayer thin films.
Wide-angle X-ray scattering (WAXS), a technique concentrating on scattering angles 2θ larger than 5°.

Inelastic X-ray scattering (IXS)

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In IXS the energy and angle ofinelastically scattered X-rays are monitored, giving the dynamicstructure factor $S(\mathbf {q} ,\omega )$ . From this many properties of materials can be obtained, the specific property depending on the scale of the energy transfer. The table below, listing techniques, is adapted from.^[2] Inelastically scattered X-rays have intermediate phases and so in principle are not useful forX-ray crystallography. In practice X-rays with small energy transfers are included with the diffraction spots due to elastic scattering, and X-rays with large energy transfers contribute to the background noise in the diffraction pattern.

Technique	Typical Incident Energy, keV	Energy transfer range, eV	Information on:
Compton scattering	100	1,000	Fermi Surface Shape
Resonant IXS (RIXS)	4-20	0.1 - 50	Electronic Structure & Excitations
Non-Resonant IXS (NRIXS)	10	0.1 - 10	Electronic Structure & Excitations
X-ray Raman scattering	10	50 - 1000	Absorption Edge Structure, Bonding, Valence
High resolution IXS	10	0.001 - 0.1	Atomic Dynamics, Phonon Dispersion

References

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^Guinier, A. (1963).X-ray diffraction in Crystals, Imperfect Crystals and Amorphous Bodies. San Francisco: W.H. Freeman & Co.
^Baron, Alfred Q. R (2015). "Introduction to High-Resolution Inelastic X-Ray Scattering".arXiv:1504.01098 [cond-mat.mtrl-sci].