ANALYSIS OF THE CRYSTALLINE PHASES OF THE MINERAL RUTAN BY MEANS OF THE X-RAY DIFFRACTION TECHNIQUE

Objective: This work aims to analyze a sample of the mineral Rutana, composed of two crystalline phases of titanium dioxide (TiO 2 ): rutile and anatase, using the X-ray diffraction technique. Theoretical reference: In 1914, the German physicist Max von Laue, using a CaSO4 crystal, successfully achieved the diffraction of X-rays. Crystalline solids, such as CaSO4, consist of regular arrangements of atoms with interatomic spacings of the order of 0.1 -1.0Å, that is, with the same order of magnitude as the wavelength of X-rays. Due to the periodic nature of the internal structure of the crystals, it was possible for them to act as a three-dimensional diffraction grating, providing science with a new method for indirect investigation of the internal structure of materials: the X-ray diffraction (XRD) technique. Methodology : In this technique, a finely ground crystalline powder of a material is placed in the path of a monochromatic x-ray beam. This material, composed of a large number of small crystallites, are randomly oriented. Diffraction occurs from planes of the crystallites that are oriented at the correct angle to fulfill the Bragg condition, in such a way that localized peaks of the same intensity as the diffracted beams are formed. Results and discussion: Based on the intensity, angles and width of the diffraction peaks, the mass percentages of each of the mineral's crystalline phases were obtained: rutile (62.08%) and anatase (37.92%). Research Implications: This work presents a contribution to future research related to the chemical characterization of initially unknown samples, by providing a comprehensive and representative theoretical framework related to the XRD technique. Originality/value: This study presents practical contributions to the literature related to the application of the XRD technique in the characterization of materials.


INTRODUCTION
In 1895, Wilhelm Röentgen studied cathodic radiation, a phenomenon that occurs when a high voltage electrical charge is applied to two plates of a metal (cathode and anode) inside a glass tube filled with rarefied gas (Crookes' tube).Although the device was isolated, he noticed the occurrence of weak light on screens that were by chance close to each other.Due to its unknown nature at the time, Röentgen temporarily named the rays produced as X-rays (Vitalij et al., 2003).
Further investigation revealed that X-rays are a type of high-energy electromagnetic radiation emitted by the metal plate located in the anode, being the result of electronic transitions of more internal levels and sublevels of atoms from the collision of the cathode rays (electrons).With shock, there is a reduction in kinetic energy and change in the direction of the electrons; this energy difference is emitted in the form of X-rays (Vitalij et al., 2003).
Unlike ordinary light, these rays were invisible, but traveled in straight lines and affected the photographic film in the same way as light.On the other hand, it was found that the X-rays are highly penetrating, easily traversing the human body, pieces of wood, as well as metallic and opaque objects.X-ray radiation has become a powerful tool for physical experiments and for the first imaging tests of the human body, and is used in the diagnosis and treatment of diseases.In 1901, Röentgen received the Nobel Prize in Physics for his discovery and also for the recognition of his services to science and humanity (Vitalij et al., 2003;Nobelprize.org, 2021).
X-rays are a form of high-energy electromagnetic radiation and small wavelengths, situated in the range of 0.5-2.5Å(ångström, equivalent to 10-10m), while the wavelength of visible light is in the order of 6000Å.X-rays therefore occupy the region between gamma and ultraviolet rays in the complete electromagnetic spectrum (Cullity, 1978).
In 1912, the nature of X-rays (wave or particle) was still unknown; a demonstration of the effects of X-ray diffraction was needed to demonstrate their wave nature.However, for diffraction to occur, the wavelength of the incident light must be of the same order of magnitude as the obstacle (Cullity, 1978).
X-ray diffraction was finally achieved by German physicist Max von Laue in 1914, using a copper sulfate crystal as a diffraction network.Crystalline solids, such as copper sulfate, consist of regular arrangements of atoms with interatomic spacings in the order of 0.1-1.0Å,i.e.
with the same order of magnitude as the wavelength of X-rays.Due to the periodic nature of the crystals' internal structure, it has been possible to act as a three-dimensional diffraction network.This discovery not only attested to the wave-like nature of X-rays, but also provided science with a new method for indirect investigation of the internal structure of materials: the technique X-ray diffraction in crystals, also known as DRX (Cheetham, 1987).
This phenomenon was immediately noticed by W.H. and W.L.Bragg (father and son), and they began experiments using X-ray diffraction as a means of determining the internal structure of different crystalline solids, such as NaCl, KCl, ZnS, CaF2, CaCO3, and ultimately diamond (Cheetham, 1987).
In this work, a sample of the mineral Rutana was analyzed, composed of two crystalline phases of titanium dioxide (TiO2): rutile and anathasium, by means of the X-ray diffraction technique.The objective was to analyze the angles, intensity and width of the diffraction peaks of the material, thus enabling its chemical characterization and the determination of the percentage by mass of each of the constituent crystalline phases.The results obtained will be analyzed and, in the end, discussed.

THEORETICAL FRAME
W.L. Bragg observed that X-ray diffraction behaved as a "reflection" of the planes of atoms within a crystal, and that only in specific crystal orientations relative to the source and detector are the X-rays reflected from the planes.In X-ray diffraction, reflection only occurs when the conditions for constructive interference are satisfied, following the Bragg equation In Bragg's equation ( 1), when n=1, the reflections are called first-order, and, when n= 2, the reflections are named second-order, and so on.The letters h, k, and l represent the coordinates of the crystalline plane in a network of Bravais, also called Miller indices.It is observed that there is a specific dependence of the angle of incidence with the intensity of the reflected wave, so that peaks located at the angles at which the Bragg condition is satisfied can be observed (Cheetham, 1987).
In the X-ray diffraction technique, a finely ground crystalline powder of a material is placed in the path of a monochrome X-ray beam.This material, composed of a large number of small crystals, known as crystallites, are oriented in a random manner.The diffraction occurs from the planes of the crystallites that are oriented at the correct angle to fulfill the Bragg condition, such that peaks of intensity of the diffracted beams are formed (Cheetham, 1987).

MATERIALS
The sample analyzed consists of a mineral called Rutana, composed of two crystalline phases of titanium dioxide (TiO2), rutile and anathasium, presented in Figure 1: As illustrated in Figure 1, both rutile and anathasium present the crystalline form of a tetragonal prism, however, their net parameters are quite distinct, as shown in Table 1: Table 1 Rutile and anathasium net parameters.

METHOD
Because of the differences in the net parameters, the rutile crystals have a more compact structure than the anathasium crystals.Thus, the rutile has a higher refractive index, greater stability and greater density.These fundamental differences make possible, by means of the X-ray diffraction technique, the differentiation of phases and the detection of the percentage by mass of each crystalline phase that makes up the mineral.
The refinement of the crystalline structure and the theoretical diffraction profiles were carried out in the FullProf software according to the Rietveld Method, using the crystalline plugs (CIF's) of rutile and anathasium, ICSC 16636 and ICSD 9852, respectively, obtained in the Base of Crystalline Structures.
The Rietveld refinement method is used worldwide in the characterization of crystalline materials in powder form and in the quantification of phases.This method makes use of the mathematical method of least squares to refine the theoretical profiles of the diffraction peaks, calculated from crystallographic information, until these profiles are very close to the profiles measured experimentally (Rietveld, 1967;Rietveld, 1969).
The diffraction geometry was defined as Bragg-Brentano and the shape of the diffraction peaks was defined as pseudo-Voigts.

RESULTS AND DISCUSSION
The diffraction profiles obtained in the FullProf software are shown in Figure 2. In red the experimental diffraction profile; in black the theoretical diffraction profile; in blue the  As can be seen, the experimentally obtained diffraction profile presents a high degree of adjustment to the theoretical profile.The refinement was reliable, with values obtained for the chi2 index very close to 1.
The non-generation of noise in the spectrum makes it possible to infer that the stages of sample preparation, equipment calibration and experimental analysis were carried out correctly, strictly following the standard operating procedure for the use of the diffractometer.
The main intensity peaks obtained and the corresponding diffraction angles are shown in Table 2.The diffraction peak 1 refers to anathasium, while the diffraction peaks 2, 3 and 4 refer to rutile.
Based on the intensity, angles and width of the main diffraction peaks, the FullProf _________________________________________________________________________ Rev. Gest.Soc.Ambient.| Miami | v.18.n.7 | p.1-09 | e08414 | 2024 between the planes of a crystal θhkl = the angle of radiation incidence λ = wavelength of this radiation n = wavelength multiplicity factor.