# X-ray Diffraction Data Analysis by Machine Learning Methods--A Review
## 1 Introduction
### Overview of X-ray Diffraction (XRD) Technique  
More than 100 years after its discovery, X-ray diffraction is still one of the most powerful and versatile techniques widely employed for understanding crystalline materials' phase composition, structure, and microstructural features. The technique was developed in the early twentieth century when [PERSON] discovered that crystals diffract X-rays, and the obtained pattern reveals the crystal's structure [43]. The findings suggested both the wave-particle duality of the X-ray and the validity of the space lattice hypothesis [44]. When monochromatic X-rays interact with a crystalline material, they undergo constructive and destructive interference caused by the periodic arrangement of atoms within the crystal lattice. The interference generates a diffraction pattern, which is recorded on a detector and, subsequently, used to deduce structural information about the sample. Since its discovery, XRD has been used by engineers, particularly in materials science, chemists, physicists, and biologists, aiding them in the discovery, development, and optimization of novel compounds with tailored properties for numerous practical and research applications [45]. The foundation of XRD lies in Bragg's law, formulated by Sir [PERSON] and his father Sir [PERSON] [46]. [PERSON]'s law states that the conditions for the constructive interference of X-rays in a crystal lattice are determined using the equation:  
\[\text{n}\cdot\lambda=2\cdot\text{d}\cdot\text{sin}\theta \tag{1}\]  
where:  
* n is the order of the diffraction peak (usually 1 for primary peaks);
* \(\lambda\) is the wavelength of the incident X-rays;
* d is the lattice spacing of the crystal planes;
* \(\theta\) is the angle between the incident X-rays and the crystal plane. From an experimental setup perspective, XRD typically involves an X-ray source, such as a sealed tube or a synchrotron radiation source, which emits X-rays of a specific wavelength [47]. Next, the X-rays pass either through a system of slits to produce a divergent beam or through a collimator to produce a parallel beam that interacts with the crystalline sample [48; 49]. The diffracted X-rays are then collected with a detector, such as a scintillation counter or a semiconductor detector, which records the intensity of diffracted X-rays as a function of the diffraction angle (20) [50]. The analysis of an obtained XRD pattern allows researchers to identify the phases in the studied material, determine their relative abundances, and estimate the crystallite size and microstrain of the sample [51; 52; 53; 54]. Additionally, the crystallographic orientation can be deduced by analyzing the preferred orientation of the crystallites [55]. X-ray diffraction finds extensive applications in multiple scientific fields. Professionals in chemistry, physics, geology, and materials science use this technique for both qualitative and quantitative analysis [56]. The first application of XRD was in the field of geology for the identification of minerals and rocks, and the technique has decisive contribution in crystal system determination [57]. In the microelectronics industry, qualitative phase analyses, stress measurements, and microstructural features determinations are routinely performed using XRD [58]. In the pharmaceutical industry, XRD is applied to examine formulations by providing polymorph identification, relative abundance, and degree of crystallinity. Moreover, nonambient XRD analysis is useful for the study of moisture influence on drug properties [59]. Although not as popular, XRD is also used in the forensic sciences for the analysis of soils, explosives, pigments and paints, alloys, metals, or drugs. Compared with other techniques, XRD has several advantages such as the ability to work with small-volume samples; it is a nondestructive method, and it allows for the identification of phases in mixtures [60].