X-ray emission spectroscopy (XES) is a form of X-ray spectroscopy in which a core electron is excited by an incident x-ray photon and then this excited state decays by emitting an x-ray photon to fill the core hole. The energy of the emitted photon is the energy difference between the involved electronic levels. The analysis of the energy dependence of the emitted photons is the aim of the X-ray emission spectroscopy.^[1][2][3]

There are several types of XES and can be categorized as non-resonant XES (XES), which includes ${\displaystyle K_{\beta }}$-measurements, valence-to-core (VtC/V2C)-measurements, and (${\displaystyle K_{\alpha }}$)-measurements, or as resonant XES (RXES or RIXS), which includes XXAS+XES 2D-measurement, high-resolution XAS, 2p3d RIXS, and Mössbauer-XES-combined measurements.^[4] In addition, Soft X-ray emission spectroscopy (SXES) is used in determining the electronic structure of materials.

The first XES experiments were published by Lindh and Lundquist in 1924^[5]

In these early studies, the authors utilized the electron beam of an X-ray tube to excite core electrons and obtain the ${\displaystyle K_{\beta }}$-line spectra of sulfur and other elements. Three years later, Coster and Druyvesteyn performed the first experiments using photon excitation.^[6] Their work demonstrated that the electron beams produce artifacts, thus motivating the use of X-ray photons for creating the core hole. Subsequent experiments were carried out with commercial X-ray spectrometers, as well as with high-resolution spectrometers.

While these early studies provided fundamental insights into the electronic configuration of small molecules, XES only came into broader use with the availability of high intensity X-ray beams at synchrotron radiation facilities, which enabled the measurement of (chemically) dilute samples.^[7] In addition to the experimental advances, it is also the progress in quantum chemical computations, which makes XES an intriguing tool for the study of the electronic structure of chemical compounds.

Henry Moseley, a British physicist was the first to discover a relation between the ${\displaystyle K_{\alpha }}$-lines and the atomic numbers of the probed elements. This was the birth hour of modern x-ray spectroscopy. Later these lines could be used in elemental analysis to determine the contents of a sample.

William Lawrence Bragg later found a relation between the energy of a photon and its diffraction within a crystal. The formula he established, ${\displaystyle n\lambda =2d\,\sin(\theta )}$ says that an X-ray photon with a certain energy bends at a precisely defined angle within a crystal.

A special kind of monochromator is needed to diffract the radiation produced in X-Ray-Sources. This is because X-rays have a refractive index n ≈ 1. Bragg came up with the equation that describes x-ray/neutron diffraction when those particles pass a crystal lattice.(X-ray diffraction)

For this purpose "perfect crystals" have been produced in many shapes, depending on the geometry and energy range of the instrument. Although they are called perfect, there are miscuts within the crystal structure which leads to offsets of the Rowland plane. These offsets can be corrected by turning the crystal while looking at a specific energy(for example: ${\displaystyle K_{\alpha 2}}$-line of copper at 8027.83eV). When the intensity of the signal is maximized, the photons diffracted by the crystal hit the detector in the Rowland plane. There will now be a slight offset in the horizontal plane of the instrument which can be corrected by increasing or decreasing the detector angle.

In the Von Hamos geometry, a cylindrically bent crystal disperses the radiation along its flat surface's plane and focuses it along its axis of curvature onto a line like feature.

The spatially distributed signal is recorded with a position sensitive detector at the crystal's focusing axis providing the overall spectrum. Alternative wavelength dispersive concepts have been proposed and implemented based on Johansson geometry having the source positioned inside the Rowland circle, whereas an instrument based on Johann geometry has its source placed on the Rowland circle.^[8][9]

X-ray sources are produced for many different purposes, yet not every X-ray source can be used for spectroscopy. Commonly used sources for medical applications generally generate very "noisy" source spectra, because the used cathode material must not be very pure for these measurements. These lines must be eliminated as much as possible to get a good resolution in all used energy ranges.

For this purpose normal X-ray tubes with highly pure tungsten, molybdenum, palladium, etc. are made. Except for the copper they are embedded in, they produce a relatively "white" spectrum.^[10] Another way of producing X-rays are particle accelerators. The way they produce X-rays is from vectoral changes of their direction through magnetic fields. Every time a moving charge changes direction it has to give off radiation of corresponding energy. In X-ray tubes this directional change is the electron hitting the metal target (Anode) in synchrotrons it is the outer magnetic field accelerating the electron into a circular path.

There are many different kind of X-ray tubes and operators have to choose accurately depending on what it is, that should be measured.

Today, XES is less used for elemental analysis, but more and more do measurements of ${\displaystyle K_{\beta }}$-line spectra find importance, as the relation between these lines and the electronic structure of the ionized atom becomes more detailed.

If an 1s-Core-Electron gets excited into the continuum(out of the atoms energy levels in MO), electrons of higher energy orbitals need to lose energy and "fall" to the 1s-Hole that was created to fulfill Hund's Rule.(Fig.2) Those electron transfers happen with distinct probabilities. (See Siegbahn notation)

Scientists noted that after an ionization of a somehow bonded 3d-transition metal-atom the ${\displaystyle K_{\beta }}$-lines intensities and energies shift with oxidation state of the metal and with the species of ligand(s). This gave way to a new method in structural analysis:

By high-resolution scans of these lines the exact energy level and structural configuration of a chemical compound can be determined. This is because there are only two major electron transfer mechanisms, if we ignore every transfer not affecting valence electrons. If we include the fact that chemical compounds of 3d-transition metals can either be high-spin or low-spin we get 2 mechanisms for each spin configuration.^[4]

These two spin configurations determine the general shape of the ${\displaystyle K_{\beta 1,3}}$ and ${\displaystyle K_{\beta '}}$-mainlines as seen in figure one and two, while the structural configuration of electrons within the compound causes different intensities, broadening, tailing and piloting of the ${\displaystyle K_{\beta 2,5}}$ and ${\displaystyle K_{\beta ''}}$-lines.^[4] Although this is quite a lot of information, this data has to be combined with absorption measurements of the so-called "pre-edge" region. Those measurements are called XANES (X-ray absorption near edge structure).

In synchrotron facilities those measurement can be done at the same time, yet the experiment setup is quite complex and needs exact and fine tuned crystal monochromators to diffract the tangential beam coming from the electron storage ring. Method is called HERFD, which stands for High Energy Resolution Fluorescence Detection. The collection method is unique in that, after a collection of all wavelengths coming from "the source" called ${\displaystyle I_{0}}$, the beam is then shone onto the sample holder with a detector behind it for the XANES part of the measurement. The sample itself starts to emit X-rays and after those photons have been monochromatized they are collected, too. Most setups use at least three crystal monochromators or more. The ${\displaystyle I_{0}}$ is used in absorption measurements as a part of the Beer-Lambert Law in the equation

${\displaystyle E_{\lambda }=\log _{10}\left({\frac {I_{0}}{I_{1}}}\right)=\varepsilon _{\lambda }\cdot c\cdot d}$

where ${\displaystyle I_{1}}$ is the intensity of transmitted photons. The received values for the extinction ${\displaystyle E_{\lambda }}$ are wavelength specific which therefore creates a spectrum of the absorption. The spectrum produced from the combined data shows clear advantage in that background radiation is almost completely eliminated while still having an extremely resolute view on features on a given absorption edge.(Fig.4)

In the field of development of new catalysts for more efficient energy storage, production and usage in form of hydrogen fuel cells and new battery materials, the research of the ${\displaystyle K_{\beta }}$-lines is essential nowadays.

The exact shape of specific oxidation states of metals is mostly known, yet newly produced chemical compounds with the potential of becoming a reasonable catalyst for electrolysis, for example, are measured every day.

Several countries encourage many different facilities all over the globe in this special field of science in the hope for clean, responsible and cheap energy.^[11]

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Soft X-ray emission spectroscopy or (SXES) is an experimental technique for determining the electronic structure of materials.

X-ray emission spectroscopy (XES) provides a means of probing the partial occupied density of electronic states of a material. XES is element-specific and site-specific, making it a powerful tool for determining detailed electronic properties of materials.

Emission spectroscopy can take the form of either resonant inelastic X-ray emission spectroscopy (RIXS) or non-resonant X-ray emission spectroscopy (NXES). Both spectroscopies involve the photonic promotion of a core level electron, and the measurement of the fluorescence that occurs as the electron relaxes into a lower-energy state. The differences between resonant and non-resonant excitation arise from the state of the atom before fluorescence occurs.

In resonant excitation, the core electron is promoted to a bound state in the conduction band. Non-resonant excitation occurs when the incoming radiation promotes a core electron to the continuum. When a core hole is created in this way, it is possible for it to be refilled through one of several different decay paths. Because the core hole is refilled from the sample's high-energy free states, the decay and emission processes must be treated as separate dipole transitions. This is in contrast with RIXS, where the events are coupled, and must be treated as a single scattering process.

Soft X-rays have different optical properties than visible light and therefore experiments must take place in ultra high vacuum, where the photon beam is manipulated using special mirrors and diffraction gratings.

Gratings diffract each energy or wavelength present in the incoming radiation in a different direction. Grating monochromators allow the user to select the specific photon energy they wish to use to excite the sample. Diffraction gratings are also used in the spectrometer to analyze the photon energy of the radiation emitted by the sample.

• X-ray absorption spectroscopy

• Soft X-ray Emission Spectroscopy - Description at beamteam.usask.ca