2. Synchrotron radiation-based X-ray scattering techniques

#### 2.1. Wide-angle X-ray scattering (WAXS)

X-ray photons interact with matter in different ways including coherent scattering, Compton scattering, photoelectric interaction, and pair production. If the interaction of the X-ray photons is coherent and elastic, the interaction is called X-ray diffraction (XRD) or Bragg scattering. A distribution of electrons in matter will interact with a photon wave to produce an interference-modulated scattering pattern, called a diffraction pattern. If multiple identical electron distributions are periodically placed in space, the scattering from each of them will interact with that from the others and will result in destructive interference in most of the direction other than a few allowed directions. These allowed directions can be calculated by considering the lattice, and hence a crystalline structure can be fully resolved by using diffraction pattern. Bragg's law is a useful model to describe the relation between the allowed scattering angles (2θ), the photon wavelength (λ), and an inter-planar distance (d) between parallel planes; see Eq. (1):

$$2d\sin\theta = n\lambda\tag{1}$$

The recorded diffraction peak from a sample will have an angular width due to the broadening from the instrument. Additionally, the peaks can be broadened by the finite size of the crystallites. The peak broadening does not correlate with the particle size, but with the coherent domain length where long-range order is preserved [2]. Synchrotron radiation covers a large range of energies and that allows for superior data acquisition. In the case of XRD, it enables the ability to probe many different crystallographic planes at the same time, resulting in fast and rich data acquisition. The use of high energy, sometimes referred to as hard X-rays, is advantageous because these X-rays are not absorbed well in a solid material and therefore allow for deep penetration. These properties of synchrotron radiation, coupled with overall high intensities, allow for rich data collection and experimentation that were previously not possible. Experimental setup for synchrotron radiation-based high-energy XRD is shown in Figure 1. As the high-energy photons are able to fully penetrate the cell, these measurements are conducted in the transmission mode in order to obtain 2D diffraction patterns. This also means that the cathode and anode can be investigated simultaneously.

Figure 1. Schematic diagram of synchrotron radiation-based X-ray scattering technique.
