**3.1.1. X-ray diffraction analysis**

The diffraction of a beam of X-rays by a crystalline material is the process of beam scattering1 by electrons associated with atoms in the crystal and of the interference of these scattered Xrays because of the periodic arrangement of atoms in the crystal and its symmetry.2 X-ray diffraction analysis (XRD) is used for the determination of mineralogical composition and quantitative X-ray diffraction analysis (Rietveld method) for the refinements of structure of apatite from measured data using specialized software [3],[4],[5],[6].

Following the discovery of *X*-rays by RÖENTGEN3 [8],[10],[11] in 1895 and the proof that *X*-rays have the wave properties and diffract from a periodic atomic array by VON LAUE [12] and his students in 1912–1913, the analytical application of *X*-ray diffraction has developed slowly over the next 20 years. Most of the earliness efforts were aimed at the solution of crystal structures of common phases. DEBYE and SHEERER (1916) and HULL (1917) suggested that powder diffraction patterns could be used for the identification of quantification of crystalline compounds. However, because most of the early developments were directed toward solving single-crystal structures, it was really the middle 1930s when the powder diffraction method began to attract the follower with the publication of the procedure of HANAWALT and RINN and the database of patterns by HANAWALT, RINN and FREVEL (1938). With the conversion of data sets into the first set of the Powder Diffraction File in 1941, the phase identification applica‐ tions expanded, and the modern counter diffractometer was developed by PARRISH, HAMACH‐ ER and LOWITZSCH [5].

The phase identification was one of the first applications to grow to useful level. Other major applications of diffraction analysis include following phase changes under nonambient conditions and atmospheres. The first diffraction experiments were actually done on single crystals. The method is primarily directed toward determining the crystal periodicity and symmetry and solving the arrangement of atoms in the material because this information is

<sup>1</sup> Scattering is the process where the beam of radiation or particles is deviated from its initial trajectory by the inhomo‐ geneity in the medium which it transverses [7].

<sup>2</sup> Other kinds of radiation commonly used for diffraction analysis are neutrons (**Section 3.1.2**) and electrons (**Chapter 3.1.10**).

<sup>3</sup> Wilhelm Conrad Röentgen (1845–1923) was the rector of the University of Würzburg [8]. The first X-ray photography was published in 1896 [9].

difficult to obtain from powder experiment. Powder diffraction is one of the most important material characterization techniques in the material research and industry [5].

Single-crystal diffraction studies are not limited to crystal structure analysis. The diffraction topography is a large field that has provided much information on the perfection of crystals used in industry as integral parts of devices. The examples include crystals used in sensing and control devices, substrates for electronic components, tools and dies, turbine blades and many other applications [5].
