In modern X-ray emission spectroscopy, X-rays are used to excite a material of interest.

Karl Manne Georg Siegbahn from Uppsala, Sweden (Nobel Prize 1924), who painstakingly produced numerous diamond-ruled glass diffraction gratings for his spectrometers, was one of the pioneers in developing X-ray emission spectroscopy (also called X-ray fluorescence spectroscopy). He measured the X-ray wavelengths of many elements to high precision, using high-energy electrons as excitation source.

Intense and wavelength-tunable X-rays are now typically generated in so-called synchrotron radiation laboratories. In a material, the X-rays may suffer an energy loss compared to the incoming beam. This energy loss of the re-emerging beam reflects an internal excitation of the atomic system, an X-ray analogue to the well-known Raman spectroscopy that is widely used in the optical region.

In the x-ray region there is sufficient energy to probe changes in the electronic state (transitions between orbitals; this is in contrast with the optical region, where the energy loss is often due to changes in the state of the rotational or vibrational degrees of freedom). For instance, in the ultra soft X-ray region (below about 1 keV), crystal field excitations give rise to the energy loss.

We may think of the photon-in-photon-out process as a scattering event . When the x-ray energy corresponds to the binding energy of a core level electron this scattering process is resonantly enhanced by many orders of magnitude. This type of X-ray emission spectroscopy is often referred to as resonant inelastic x-ray scattering (RIXS).

Due to the wide separation of orbital energies of the core levels, it is possible to select a certain atom of interest. The small spatial extent of core level orbitals forces the RIXS process to reflect the electronic structure in close vicinity of the chosen atom. Thus RIXS experiments give valuable information about the local electronic structure of complex systems, and theoretical calculations are relatively simple to perform.

Instrumentation

There exist several efficient designs for analyzing an x-ray emission spectrum in the ultra soft X-ray region. Typically, the X-rays emerging from a sample must pass a source-defining slit, then optical elements (mirrors and/or gratings) disperse them by diffraction according to there wavelength and, finally, a detector is placed at their focal points.

Henry Augustus Rowland (1848-1901) devised an instrument that allowed the use of a single optical element that combines diffraction and focusing: a spherical grating. Reflectivity of X-rays is low regardless of the used material and therefore grazing incidence upon the grating is necessary. X-ray beams impinging on a smooth surface at a few degrees glancing angle of incidence undergo external total reflection which is taken advantage of to enhance the instrumental efficiency substantially.

Denote by R the radius of a spherical grating. Imagine a circle with half the radius R tangent to the center of the grating surface. This small circle is called the Rowland circle. If the entrance slit is anywhere on this circle, then a beam passing the slit and striking the grating will be split into a specularly reflected beam, and beams of all diffraction orders, that come into focus at certain points on the same circle.