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X-Ray Diffraction Technique

X-ray diffraction techniques based on monochromatic radiation are widely used for determining the atomic spacings from the observed diffraction angles. For determination of structures of specimens, the powder technique in conjunction with diffractometer is commonly used, In a PHILIPS X-ray diffractomerter model the specimen is mounted in the centre of the diffractometer and rotated by an angle ɵ around an axis in the specimen plane.

The X-ray source is cuka (1.54 Å) radiation. The counter is attached to an arm rotating around the same axis by angle 2ɵ, twice as large as those of specimen rotation The diameter of focussing circle continuously shrinks with increasing diffraction angle. Only (hkl) planes which are parallel to the specimen plane contribute to the diffracted intensity. After obtaining the diffraction patterns, the corresponding d-values (interatomic distance) are noted and compared with the available single crystal data Lattice parameter measurements are done using the standard extrapolation method X-ray diffraction technique is very useful for the determination of various structural properties of single crystal as well as polycrystalline aggregate. These aggregates are composed of many individual crystals usually of microscopic size The two important techniques used for structural studies of ceramics are microscopic examination and X-ray diffraction. These two methods are complementary to each other. The combination of these two techniques can provide a great deal of information about the structure of an aggregate. Even the physical and chemical properties of a single phase material can be predicted through structural investigation. If the material is polycrystalline and ferroelectric, the maximum spontaneous polarisation depends on the symmetry of the single crystallites therein. From the structural point of view, the ferroelectric materials must have non-centrosymmetric space group in its terroelectric phase. Therefore, it is interesting to find out the space group symmetry of ferroelectric materials using the X-ray diffraction method. The required extinction rule can sometimes be very useful to predict the space group symmetry. But in some cases no systematic absences are observed rather all possible combination of hkl are present. In such case detailed X-ray analysis using diffractogram as well as X-ray photograph are needed to determine space group Detailed results of our studies of crystal structural and surface morphology of the compound prepared were performed by X-ray diffraction technique and Scanning Electron Microscope (SE My respectively Their crystal data (interplanar spacing d-values. crystal system, lattice constant) and surface morphology are discussed in this paper.

After the introduction in 1967 by Rietveld of a method for the refinement [1-3] of crystal structures from powder data, interest in powder methods increased dramatically. The advent of fast computers also played a big role in making powder diffraction one of the most popular methods for studying the structure and microstructure of crystalline solids An understanding of powder diffraction studies requires a working knowledge of basic crystallography. Most crystals have distinctive flat and smooth surfaces. the faces, which exhibit con-tancy in external form. This is because crystals are built up of identical blocks regularly repeated in space. The blocks are called unit cells and the lengths of the cell edges and the angles between them the six cell parameters, identify them. The three-dimensional urray of unit cells form a lattice with a symmetry that depends on the shape of the unit cell. Fourteen different types of space lattices are possible. ranging from primitive triclinic to face centered cubic. The atoms in the unit cell may contain symmetry relationships between them. enseniently classified into the 230 possible space groups. The most common type of radiation used in powder work in X-radiation. It is a high energy form of electromagnetic radiation with wavelength in the order of 1Å. The characteristic X-rays result from displacement of electrons from the inner shells of the target atoms, which are then replaced by electrons from the outer shells, which emit their excess energy as X-rays. The most probable replacement is in the innermost shell from the next shell, resulting in the strongest line, the close k doublet. X-rays for laboratory use are usually produced in sealed N- ray tubes. X-rays can be diffracted from crystals since their electric interact with the electron clouds of the atoms in the crystals. fields X-rays scattered from adjacent atoms interfere and a diffraction pattern is produced. Bragg's law gives the condition for diffraction to occur from electrons in stacks of layers with an interplanar spacing d

nʎ = 2d sinɵ......4.1

Where ɵ is the diffraction angle. n is an integer and is the wavelenght of the X-rays. The geometry of the diffraction pattern is determined by the size and shape of the unit cell while the intensities of the individual reflections from the accessible planes are controlled by the distribution of electron density within the cell. Other sources of radiation can also be used for diffraction studies: neutrons are scattered by the nuclei of atoms and not the electrons (usually), but electrons are scattered to some extent by both.

Ferroelectric samples produce powder patterns in which the X- rays are diffracted not by one single crystal but by a sample consisting of a very large number of randomly oriented crystalline particles (a powder). When Bragg's law is satisfied for any given plane hkl all the reflections for all the tiny crystals lie on a cone with angle 2ɵ_hkl The spots of the diffraction pattern of the single crystal now extend into the smooth lines on the powder pattern, all the information from the three dimensional reciprocal lattice has thus been compressed into one dimension. Due to the complexity of such powder patterns it is usually very difficult to interpret them without further information.

The widths of the peaks in a particular phase pattern provide an indication of the average crystalline size. Large crystallites give rise to sharp peaks while the peak width increases as the crystallite size reduces. Peak broadening also occurs as a result of variations in d-spacing caused by micro- strain. However, ther relationship between broadening & the diffraction angle 2ɵ is different from that of crystallite size effects making it possible to differentiate between the two phenomenMost of the physical and chemical properties of a single phase material can be predicted through structrual investigation. X-ray diffraction technique is very useful for the determination of various structural properties of single crystal as well as polycrystalline aggregate. These aggragates are composed of many individual crystals usually of microscopic size. If the material is polycrystalline and ferroelectric, the maximum spontaneous polarisation depends on the symmetry of the single crystallities therein. From the structural point of view, the ferroelectric materials must have non-centrosymmetric space group in its ferroelectric phase. Therefore, it is interesting to find out the space group symmetry of ferroelectric materials using the X-ray diffraction method. The required extinction rule can somtimes be very useful to predict the space group symmetry. But in some cases no systematic absences are observed rather all possible combination of hkl are present. In such case detailed X-ray analysis using diffractogram as well as X-ray photograph are needed to determine space group. Detailed results of our studies of crystal structural and surface morphology of the compounds prepared were performed by X-ray diffraction technique and Scanning Electron Microscope (SEM) respectively. The crystal data (interplanar spacing d-values, crystal system, lattice constant) and surface morphology (grain size and particle distribution of the sample) are discussed in this chapter.

Experimental

The X-ray powder diffractograms of all the prepared polycrystalline ferroelectric samples were recorded with PHILLIPS (PW 1710) X-ray diffractometer fitted with recorder using Cuk_∞ radiation (λ=0.15418mm) with Ni filter in a wide range of 2ɵ (10⁰ to 70⁰) at a scanning rate of 2⁰/min. It is a known fact that the size of crystallites or powders is of great importance in this analysis. Klug and Alexander [4] illustrated that powders with crystallite sizes less then 5µm to 50 µm exhibited an average deviation value of 18% If the crystallite sizes were not allowed to exceeds 5 µm,. then the effects of micro- absorption and particle orientation statistics can be neglected. The powder was packed into a slotted glass slide using free-falling technique described by NBS Monograph [5] in order to avoid preferred orientation and induced packing. The operating voltage and current of the X-ray tube were 30 KV and 15mA respectively. The divergence of the X-ray beam was limited to 3⁰ to 5⁰ in the vertical direction. For recording the intensity distribution of the profiles, the calibration and accuracy of adjustment of the diffractometer were checked with the Si standard sample provided with the instrument. To check the formation of the single phase compound, an X-ray diffractogram of the pellet simple was taken by Rigaku MINIFLEX Japan) X-ray powder diffractometer using Cuk_∞ radiation (ʎ = 0.15418) for a wide range of Bragg angle 2ɵ (15⁰ ≤ 2ɵ ≤80⁰). The scanning electron microscope (SEM) (CAMS CAN-180) was used to take the micrographs on the pellet sample (C B TN) at different magnifications to study the surface morphology (grain size and the particle distribution) of the sample.

The XRD pattern of CBTN is shown in the fig. 4.1 and followed an appropriate discussion and explanation. The X-ray diffractogram C BTN reveals the formation of monophase material because the diffraction lines are found to be very sharp and single (unsplit) ones. by of The diffraction peaks in each case have been indexed and their lattice parameters have been obtained from least-squares refinement method using a standard computer software [6] The complete absences of the peaks of constituent materials of the prepared CBTN further confirm the formation of the desired samples in desired phases. The nonavailability of any files in respect of structures in the existing up- dated (Joint Commission on Powder Diffraction Source) files points towards the importances and utilities of reporting their structural studies 171 This has been the reason indeed that we have not been able to compare our results (lattice parameters of our material) with those of any others. The detailed structural analysis of our material are however given below. All the peak profiles of the CBTN samples were indexed with different cell configurations and it suitable cell with its lattice parameters was then refined using least squares technique. Using refined cell parameters, indexed reflections, and wavelength of Cuk radiation, interplanar spacing (d) of all the 21 reflections was calculated and compared with the respective observed values (table 4.1) The fair match also reflects the good quality of sample formation in terms of its chemical homogeneity. In conclusion, we must say that the preliminary X-ray analysis of the samples of the compound CBTN provided the lattice parameters a = 6.771 Å, b = 11.124 Å and c= 19.623 Å and also formation of single-phase orthorhombic structure at room temperature (299K)-A good agreement between the observed d-values and the calculated d-values suggests that the choice of unit cells and the preliminary crystal system are correct. With limited powder data, we have not been able to determine the space group of the compound CBTN .

The structural characteristics of other two members of this group of materials viz M₄ Bi₂ Ti₄ Nb₆ O₃₀ (where M=Ba & Sr) have already been reported [9-10]. Their cell parameters and crystal classes have been obtained. For the case of Ba₄ Bi₂ Ti₆ Nb₆ O₃₀ the cell parameters have been determined as a = 6.6359Å, b = 10.26 Å and c = 14.125 Å while those for Sr₄ Bi₂ Ti₄ Nb₆ O₃₀ are a = 7.7334 Å b= 11.0126 Å c = 17.608 Å .Both of these materials are reported to possess a single phase orthorhombic crystal class at room temperature. The effect of the substitution of Sr by Ca is discernible in the room temperature X- ray diffractograms (XR Ds) of Sr₄ Bi₂ Ti₄ Nb₆ O₃₀ (its XRD is not between Ca & Sr is accompanied by some significant structural ramifications. These aspects therefore need to be further investigated by trying many other compositions involving (M_4-x Bi_24x) Ti₄ Nb₆ O₃₀ Where 0<x<4 and M stands for Ca & Ba.] Summarily speaking the compound C B T N has been synthesized in single phase form by high- temperature solid state reaction route. The analysis of the XRD data reveals that the material CBTN also possesses a single phase orthorhombic symmetry in the paraelectric phase at room temperature (299 K) with the lattice parameters a = 6.771 (1) Å, b = 11.124 (1) Å, and c = 19.623 (1) Å (1) A.

The average linear particle size calculated from different reflections profile of a wide 20 range using the following Scherrer is equation [8] is

was found to be .250 Å which is comparable and consistent with the particle size obtained from particle size analyzer, and also with the grain size obtained from S EM (Fig. 4.2). The uniform distribution of grains and not much voids and islands in S E M photograph suggest the formation of high density homogeneous pellet samples.

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