**3. X-ray Raman spectroscopy**

X-ray Raman Spectroscopy (XRS) or nonresonant inelastic X-ray scattering (NIXS) is a spectroscopy that makes use of the Raman concept as sketched in **Figure 2**; there is a monochromatic incoming X-ray beam with energy E0, and the scattered X-rays are measured as function of the emitted energy Ef . The incoming and scattered X-rays do not have to directly correspond to an X-ray edge; however, the Raman energy loss ΔE due to a scattering event may be related to some core-level excitation (or to phonon excitation like in typical Raman spectroscopies).

**Figure 2.** Schematic representation of the X-ray Raman process.

level. For example, for the previously mentioned iron, there is the 1s core level (K-edge), and 2s (L1-edge), and 2p levels (L2,3-edge), and the 3s (M1-edge) and 3p levels (M2,3-edge) may also be considered as core levels. The word "edge" comes historically from the fact that at certain X-ray energies, there is a steep change in absorption: these sharp rises in X-ray absorption (or deep decreases in X-ray transmission as seen in **Figure 1**) are due to reaching the binding energy of a certain core level. The edges are named after the excited core-level electron as

From the chemistry perspective, one would like to use the X-ray edge, which is sharpest with the best energy resolution or in other words with the best chemical resolution. These "best chemical resolution edges" appear for all elements between 40 and 1000 eV [5], in the so-called

In general, X-ray energies above 2000 eV are considered to be part of the hard X-ray regime. The energy region between 1000 and 2000 eV is some intermediate tender X-ray regime, which is sometimes considered to be a separate part and sometimes part of either the soft X-ray regime or the hard X-ray regime. The terms hard X-ray and soft X-ray refer to their penetration depth in air. Soft X-ray photons below 1000 eV do not penetrate far through air (due to absorption by CO2, O2, and N2), and that is why in the soft X-ray regime, measurements are normally performed under vacuum. Hard X-rays do penetrate through air, and in this regime, Röntgen originally discovered X-ray radiation. As hard X-rays do penetrate through air, experiments with hard X-rays normally are performed with safety lead shields around the experiment in order to absorb the hard X-rays and protect the surrounding, for example, the spectroscopists/

Note that in hospitals, they actually make use of the penetration depth of hard X-rays for X-ray CT scans: since bones absorb stronger than other parts of the human body, but still a substantial part of the incident X-ray beam is completely transmitted through the body, this CT scan tells

As mentioned previously, the best chemical resolution edges are in the soft X-ray regime and this X-ray regime has limits on the measurement conditions: in general high vacuum operation conditions (below 10−7 mbar), although there are developments into operation under milder vacuum conditions, for example, soft X-ray emission on liquids in the 10−3 mbar regime [6] and X-ray photoelectron and electron yield X-ray absorption spectroscopy on solids in the 1 mbar

In the next section, it will become clear how X-ray Raman spectroscopy circumvents the constraints of the soft X-ray regime, while still leading to spectra that resemble the soft X-ray

X-ray Raman Spectroscopy (XRS) or nonresonant inelastic X-ray scattering (NIXS) is a spectroscopy that makes use of the Raman concept as sketched in **Figure 2**; there is a mono-

indicated in between brackets above (K-edge, L-edge, etc.).

(VUV to) soft X-ray regime.

228 Raman Spectroscopy and Applications

scientists from exposure to X-rays.

you something about bone breaking.

edge with the best chemical resolution.

**3. X-ray Raman spectroscopy**

[7–9] to 1 bar regime [10].

Note that in this scattering process, there are other events which are much more likely, elastic (Rayleigh) scattering and Compton scattering (see for example the relative intensities in **Figure 1** of Ref. [11]). Initially, the low cross section of XRS made this technique impractical, but intense new X-ray facilities, third-generation synchrotrons and X-ray free-electron lasers (FELs), and improvements in X-ray optics helped XRS to become an interesting spectroscopic tool.

XRS is a technique that retains the experimental advantages of hard X-ray measurements, for example, deeper probing depth implying more realistic samples, less beam damage due to lower scattering cross section, experiments in a gas or liquid environment or under higher pressures, while revealing the information equivalent to the soft X-ray XAS. In particular, for K-edges of the light-weight elements, which have really low VUV to soft X-ray energies as their edge, leading to a substantial low penetration depth, XRS can circumvent the problems related to soft X-rays. The difference between XRS and XAS is the transition operator. In XAS, the electronic transition can be approximated as a dipole transition, while for XRS also higherorder transitions (quadrupole) are allowed, depending on the q-vector, related to the angle between incident and scattered X-rays. At low values for q, only dipole transitions are allowed, so far low-q XRS compares well with XAS. For high-q, higher-order transitions are present in XRS, which will be shortly discussed in the next section.

XRS, RIXS, and nonresonant X-ray emission spectroscopy (XES), where RIXS and XES will be discussed in more detail later on, are second-order optical processes where the excitation and de-excitation processes are coherently correlated by the Kramers-Heisenberg formula depicted here:

$$F(\Omega, \omega) = \sum\_{f} \left| \Sigma\_i \frac{\langle f | \mathsf{T}\_2 | \mathsf{V} \rangle \langle \mathrm{l} | \mathsf{T}\_1 | g \rangle}{E\_g + \hbar \Omega - E\_l + i \Gamma\_l} \right|^2 \delta \left( E\_g + \hbar \Omega - E\_f - \hbar \omega \right) \tag{3}$$

Where ℏω and ℏΩ are the energies of the incident X-ray and emitted/scattered X-ray energy, respectively. j, i, and g present the final, intermediate, and ground states, respectively. T1 and T2 represent the radiative transitions by incident and emitted photons, and Γi represents the

spectral broadening due to the core-hole lifetime in the intermediate state. δ is the energy conservation of the process with difference in the ground state energy plus the X-ray emitted energy with the final state energy plus the incident X-ray energy. As this formula shows there is a dependence on the core-hole lifetime, which can be made use of to study core-hole state dynamics in RIXS spectroscopy (discussed later in Section 6).

In electron spectroscopies, a spectroscopy equivalent to XRS exists, which is called electron energy-loss spectroscopy (EELS). Both XRS and EELS give information similar to XAS, but because the transitions in XRS and EELS occur in a different way, the transition operator is different. However, at low momentum transfer (low q-vector), the transition operator in EELS and XRS can be approximated as a dipole operator, and in that case, the spectral shape agrees with XAS.

XRS can be measured in two modes: (A) the direct analogue of common Raman spectroscopy: a monochromatic X-ray beam is used and the emitted X-ray beam is measured as function of energy loss (or emission energy). (B) The emitted X-ray energy is fixed and the incoming Xray beam is varied, the so-called inverse energy scan technique. Currently, mode B is applied more often since it is easier to change the incoming monochromatic energy than the settings of the emission spectrometer for different emission energies; however, with dispersive X-ray emission spectrometers [12], mode A may become the standard mode, which would be beneficial for (femtosecond) time-resolved studies with X-ray FELs.

Besides the use of XRS as some correspondence spectroscopy to XAS, one can also measure low-loss features such as phonons (vibrations for molecules) and plasmons as with traditional Raman spectroscopy. In this meV energy-loss scale, the technique is actually often called as NIXS or IXS. The advantage of NIXS compared to traditional (UV-VIS regime) Raman spectroscopy is that the X-rays penetrate deeper in materials than UV-VIS photons, so the energy loss obtained related to phonons and plasmons with NIXS might give a more bulk-like picture of the phonon and plasmon behavior of the system of interest. As well a wider energy and momentum space can be probed with synchrotron radiation. This NIXS will not be discussed further, one is referred to Refs. [13–16].
