## 2 Materials and Methods  
The experiments were performed at the SuperXAS and microXAS beamlines of the Swiss Light Source (Paul Scherrer Institute, Villigen, Switzerland). We employed the von Hamos spectrometer described in detail in [5], thus only the general characteristics and operational details specific to its application to inelastic X-ray scattering studies will be presented here. The schematic drawing of the von Hamos geometry employing segmented crystals is presented in Figure 1. The von Hamos setup consists of three main components: the X-ray source located at the sample position, the analyzer crystal and a position-sensitive detector. The crystal and sample/detector axes are separated at a distance equal to the radius of curvature (\(R\)) of the analyzer crystal, and the detector axis is positioned along the interaction point of the incoming X-rays on the sample (see Figure 1). The X-rays scattered from the sample will undergo a diffraction process from the crystal if the Bragg law criteria is met. In the von Hamos geometry, the Bragg angle is defined by the X-ray direction with respect to the crystal position (along crystal axis \(CRY_{POS}\)) and is described by the following formula:  
\[\theta_{B}=tan^{-1}\bigg{(}\frac{R}{CRY_{POS}}\bigg{)}. \tag{1}\]  
The formula implies that the Bragg angle range, and hence the energy range, covered by the spectrometer is limited only by the length, along the dispersive axis, of the crystal or detector. In the  
Figure 1: (**a**) Schematic of the von Hamos spectrometer layout employing segmented crystals for X-ray diffraction in a vertical scattering geometry; (**b**) Schematic view of the spectrometer geometry along the dispersive axis as applied to inelastic X-ray scattering (IXS) studies. typical von Hamos geometry, the crystal is continuously bent in the focusing plane in order to direct the diffracted X-rays onto a single spot on the detector. In the present setup, we used a segmented crystal design that allows one to maintain the energy resolution at the level of the Darwin width of the reflection provided by a perfect, flat crystal. Indeed, crystal segmentation does not introduce strain in the crystal when the crystal segments are attached to the curved crystal support. The strain induced by the crystal curvature is the major source of the poor energy resolution obtained using bent crystals. The application of a segmented crystal leads to similar quasi-focusing properties of the von Hamos setup as when bent crystals are used. As schematically shown in Figure 1 by the blue dashed line, after diffraction on one crystal segment, the X-rays will focus onto the detector plane. This focus will have a size equal to two times the size of the crystal segment. Since all the segments are placed on a common radius, the total spot size on the detector will be the same, independently of the number of segments used (Figure 1, red dashed line). In the present experiment, we used an Si(111) crystal glued to a cylindrically shaped support. The crystal consists of 100 segments, each 1 \(\times\) 50 mm (focusing \(\times\) dispersion) size, and a radius of curvature of the support of 250 mm. The diffracted X-rays were measured by means of either a two-dimensional Pilatus 100 K detector [29; 30] consisting of 195 \(\times\) 490 pixels with 172 \(\times\) 172 \(\upmu\)m\({}^{2}\) size, or a Mythen strip detector consisting of a linear array of 1280 pixels of dimension 50 \(\upmu\)m \(\times\) 8 mm [31; 32]. Both detectors are photon-counting, so all reported signals are directly in counted photons. To measure the IXS signals, the spectrometer was operated at a Bragg angle (marked as \(\Theta_{\text{B}}\) in Figure 1b) of around 80 degrees and Si(444) diffraction, and arranged in the backscattering geometry. Using such a setup, the spectrometer could record X-rays of energy around 8030 eV and a dispersive energy bandwidth of 80 eV.