Techniques

Diffraction

Diffraction, discovered in 1912, is at the origin of x-ray crystallographyLink opens in a new windowLink opens in a new window. It is an interference effect. The incident x-ray beam can be considered as an electromagnetic wave. The wavelength λ is the distance between two consecutive wave crests. Diffraction occurs when atoms in adjacent crystal planes, separated by a distance d, scatter the incident x-ray beam such that the emerging waves add together constructively. In other words, the emerging waves scattered from the adjacent crystal planes are in phase. This requires that the difference in optical path length for x-rays scattered from the adjacent planes be an integral number of wavelengths. The difference in path length is 2 d sin θ, where θ is the angle of incidence. This leads to Bragg's law, which describes the condition on θ for the constructive interference to be at its strongest.

2 d sin θ = n λ

A diffraction pattern is obtained by measuring the intensity of scattered waves as a function of scattering angle. Very strong intensities known as Bragg peaks are obtained in the diffraction pattern at the points where the scattering angles satisfy the Bragg condition.

Diffraction can be used to measure strains in materials under external stimuli (e.g. temperature, magnetic field, electric field) by monitoring changes in the spacing of atomic planes.

Resonant Elastic X-ray Scattering

Resonant elastic x-ray scattering (REXS) occurs when the energy of the incident x-ray photon is tuned close to some absorption edge of an element in the target sample under study. Thus, by definition, in order to perform resonant scattering, a tuneable energy x-ray source is required. Conventional x-ray sources rely on the deceleration of electrons on collision with an anode and produce x-rays predominantly at energies characteristic of the anode material (usually tungsten, molybdenum or copper). In addition, lower intensity x-rays are produced over a wide spectrum where the high energy cut off is determined by the accelerating voltage. Although early determinations of REXS scattering factors were derived from such sources, the advent of synchrotron radiation providing sources of tuneable x-rays energy marked an explosion in the field of REXS research.

In both x-ray absorption spectroscopy (XAS) and REXS, a core electron is excited from an initial state to some energy above the Fermi level. Specifically, where in XAS the final state involves a core hole, in REXS the initial and final states are the same and intermediate states are probed with virtual core electron transitions.

Today, REXS provides a unique tool in the study of solid state systems providing spatial information from diffraction combined with electronic information through the absorption process. This combination of diffraction and absorption allows the probing of magnetic, charge, spin and orbital degrees of spatial order together with electronic structure.

Grazing Incidence Scattering

Under the generic name of grazing incidence scattering, several techniques are comprised: Grazing Incident Small and Wide Angle ScatteringLink opens in a new windowLink opens in a new window (GISAXS & GIWAXS), Grazing Incidence DiffractionLink opens in a new windowLink opens in a new window (GID) and Surface X-Ray DiffractionLink opens in a new windowLink opens in a new window (SXRD), although this nomenclature is not universal. In grazing incidence (GI) techniques, the x-ray beam impinges on the sample at a very shallow angle with respect to the surface plane. By modifying the incidence angle, the penetration depth of the x-ray beam into the sample can be controlled, and thus, at very shallow angles (typically below 1°), the signal coming from the surface area is enhanced.

GISAXS is a variant of SAXS in which the small angle scattering from a surface is measured. In GIWAXS, one measures the wide angle scattering. These two techniques are generally used to study surfaces and interfaces of non-crystalline materials (see for example hereLink opens in a new windowLink opens in a new window, and references therein). They can also be used to study buried and internal structures.

GID and SXRD are used to study the structure of crystalline surfaces and interfaces. GID is usually, but not exclusively, done in grazing incidence and exit geometry. GID is employed to determine the lattice parameters and strain in films and at interfaces. Typically the signal close to Bragg peaks from the film or from the substrate is measured. In SXRD, surface reconstruction and the so-called crystal truncation rods (CTRs) are measured. From the intensity measured between Bragg peaks along the direction perpendicular to the surface, the atomic structure of surfaces, films or interfaces can be determined. For that, initial models are refined using adequate software, such as GenXLink opens in a new windowLink opens in a new window, RODLink opens in a new windowLink opens in a new window or WinRODLink opens in a new windowLink opens in a new window.

Spectroscopy

X-ray absorption spectroscopy (XAS) is nowadays a widely used technique at synchrotron radiation sources to study the local geometric and electronic structure or the chemical state of matter under various conditions of application.

XAS refers to the details of how x-rays are absorbed by an atom at energies near or above the cole-level binding energies of that atom. X-ray absorption spectra are especially sensitive to the formal oxidation state, coordination chemistry and the distances, coordination number and species of the atoms immediately surrounding the selected element. Since XAS is an atomic probe, it places few constraints on the samples that can be studied.

For example crystallinity is not required for XAS measurements, making it one of the few structural probes available for noncrystalline and highly disordered materials, including solutions and gas phases.

The x-ray absorption spectrum is typically divided into two regimes:

1. The x-ray absorption near-edge structure (XANES), also called near-edge x-ray absorption fine structure
(NEXAFS) extending about 50 - 100 eV around the absorption edge.

2. The extended x-ray absorption fine structure (EXAFS) extending a few hundred eV above the absorption edge.

Both have the same physical origin, but their distinction is convenient for the interpretation. XANES (or NEXAFS) is strongly sensitive to formal oxidation state and coordination chemistry of the absorbing atom, while EXAFS is used to determine the distances, coordination number and species of the neighbours of the absorbing atom.

REFERENCES

Fundamentals of XAFS by Matthew NewvilleLink opens in a new window

Small Angle Scattering

Tab content The small angle scattering regime (i.e. momentum transfers Q→0) yields information about long length scales or distances in real space. SAXSLink opens in a new window

Link opens in a new windowLink opens in a new window is the technique of choice to obtain structural information (size, morphology and correlations) of systems with typical length scales between few nanometers and the micron scale. These length scales are especially relevant in soft matter systems such as polymers, lamellae, micelles, ...

The accessible Q-range depends on the x-ray energy, the sample-to-detector distance and the detector and beam stop sizes. At XMaS, the maximum sample-to-detector distance is ~1.5 m and a Q-range between 0.02 to 0.34 Å-1 is typically accessible at 12.4 keV, which corresponds to real space length scales between ~1.8 nm to 30 nm (the calculations have been done with the beam hitting the centre of the MAR detector).

SAXS experiments at XMaS can be done under applied magnetic fields up to 4 T. The available 2D detectors are described here.