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.

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]

This section does not cite any sources. (March 2008)

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

• X-ray absorption spectroscopy