**4. Some applications of X-ray Raman spectroscopy**

#### **4.1.** *In situ* **X-ray spectra of light elements**

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, 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

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

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

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

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

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

T2 represent the radiative transitions by incident and emitted photons, and Γi

dynamics in RIXS spectroscopy (discussed later in Section 6).

beneficial for (femtosecond) time-resolved studies with X-ray FELs.

(3)

represents the

XRS, which will be shortly discussed in the next section.

here:

230 Raman Spectroscopy and Applications

with XAS.

XAS of light elements, such as lithium (Li), boron (B) and carbon (C), occurs in the soft X-ray energy range at about 60, 180, and 280 eV, respectively. In general, XAS can be measured in transmission, electron, or ion yield or fluorescence yield mode. Due to the path lengths of soft X-rays, transmission X-ray absorption measurements in this soft X-ray energy range of 50–300 eV are very difficult. The electron yield mode of XAS is an alternative surface-sensitive measure for the standard transmission XAS mode. Concerning *in situ* XAS studies, it can as yet only be performed at the mbar to bar pressure range, for example, as shown in Refs. [7, 9]. Fluorescence yield XAS probes deeper into the sample, but this probe has very low yield for soft X-ray energies and may suffer from saturation effects in concentrated systems. At the same time, the incoming X-ray probe of 60–280 eV does not penetrate deep enough and still mostly surface is probed with fluorescence yield XAS. With XRS, one is able to measure more bulk-like properties of light elements [11]. There are a few dedicated XRS setups in the world, where I would like to mention a setup at the European Synchrotron Radiation Facility (ESRF) [17, 18] and another setup at the Stanford Synchrotron Radiation Lightsource (SSRL) [19, 20].

As an example, we discuss XRS measurements performed on (nanosized) LiBH4 hydrogen storage materials [21, 22] at the setup of SSRL [19]. For those experiments, the XRS scans were performed using the inverse energy scan technique with a fixed analyzer energy of 6462.20 eV (mode B mentioned in Section 3). The XRS spectra of this example were measured using 25 detector crystals with an average q-vector of 1.3 atomic units, implying essentially pure dipole transitions, while this dedicated XRS setup had many more detector crystals (at that time 40) which may allow as well higher-order transitions [19], see next sections, but for these studies the other detector crystals were covered. The main additional reason besides the issues mentioned at the beginning of this subchapter for performing XRS experiments on these hydrogen storage materials was that the samples need to be under humid-free environment, and with hydrogen release as well as the pressure is rising, measurements with soft X-rays would be difficult. This example showed that it is possible to study the electronic properties of Li, B, and C of bulk and LiBH4-carbon nanocomposites (LiBH4-C) during de-hydrogenation and the first step of re-hydrogenation.

In particular, for nanocomposites, this is important since there are no many techniques, like XRD used on the bulk samples, able to grasp the electronic structure information on such small and often amorphous materials. In addition, XRS was used to study the decomposition of NaBH4–C nanocomposites (shown in the ESI,† Section S10 of Ref [22]). Note that XRS studies on the lithium edge have as well become relevant for other lithium systems [23] and battery applications, *in situ* de- and re-charging [20]. On the other hand, there are other borohydrides where the B K-edge XRS (and in addition the Mg L-edge XRS) has recently been measured for another possible hydrogen storage material, Mg(BH4)2 [24].

#### **4.2. Materials under pressure and in the liquid phase**

Although the previously mentioned hydrogen storage materials were only under 1 bar of nitrogen/hydrogen, XRS is also applied in studies with even higher pressures to study the effect of it on materials [25], for example, on iron to gain information on the behavior of it in the inner core of earth [26]. In these higher-pressure studies, phonon scattering is often studied with XRS [27, 28] (NIXS or IXS mentioned in the previous section) to study pressure-induced phase transitions and how the phonon spectrum changes. Since XRS is applied in the hard Xray regime, it is also easier to get electronic structure measures, similar to direct XAS, on liquid phase systems [29, 30].

## **4.3. Higher-order electronic transitions**

In Section 3, it was mentioned that XRS and XAS may give similar results, but with XRS one is as well able to obtain higher-order transitions above the dipole transition. It has been shown in Ref [31] that octupole transitions can be observed in XRS on rare earth phosphates RePO4 with Re = La, Ce, Pr, and Nd. In this respect, XRS might potentially be used in measuring otherwise spectroscopically unavailable excited states or "optically dark states."

#### **4.4. Summary**

In summary, XRS has been mostly used for (*in situ*) electronic structure studies on light elements as the alternative to XAS, and there is a strong focus on materials under high-pressure conditions. In general, XRS studies may become important as well for studies on (heterogenous) catalysts under (close to) industrial operation conditions, because of the advantage of the edge with best chemical resolution without the constraints of the soft X-ray regime (vacuum). As well, XRS is used to gain understanding of the momentum space of phonons of materials of interest (which was not covered in this section).
