X-RAY DIFFRACTION STUDIES ON STRONTIUM BARIUM 4. 1 Introduction NIOBATE CERAMICS In this chapter we present the importance of x-ray powder diffraction method for structural analysis. Here we deal with the basic principles and physics behind the technique along with the experimental procedure followed. The results of x-ray diffiaction studies on strontium barium niobate solid solution systems with different compositions are presented in this chapter. 4.2 X- ray powder diffractometry X-ray diffraction is an effective tool for the investigation of the crystal structure of solid solutions. This technique has its beginnings in Von Loue's discovery in 1912 that crystals difiact X-rays, the manner of' the diffraction revealing the structure of the crystal. At first, x-ray diffraction was used only for the determination of crystal structure. Later on, however, other uses were developed, and today the method is applied not only to structure determination, but to such diverse problems as chemical analysis and stress measurement. The major uses of X-rays in ceramics research are listed below. 1. Identification of crystalline phases 2. Quantitative analysis of mixtures of phases. 3. Precision measurement of lattice parameters 4. Determination of degree of preferred orientation in polycrystalline ceramic materials. 5. Estimation of mean size: of very small crystalline particles, lattice strain, residual atomic vibration amplitudes, etc.
6. Distinguish between crystalline and amorphous phases. 7. With accessory instrumentation, determination of lattice parameters and structural changes of distribution of atoms in solid solutions. 8. Crystal structure determination in some cases; provision of supplementary intensity data to be used in conjunction with single crystal studies. The powder diffraction method depends on the presence of many individual crystals, randomly oriented, at an angle with the incident beam in such a way as to satisfy the Bragg equation for the appropriate of spacing and the wavelength of the X-rays. During the entire exposure of the sample to the X-ray beam, all the planes are diffracting radiation at the appropriate angles and the detector scans through the entire angle range to produce a picture of the intensity of radiation versus the angle of diffraction. A schematic diagram showing the important compounds of a X-ray diffractometer is shown in figure 4. 1 Figure 4.1 Schematic diagram showing key components of an x-ray difiactometer.
As indicated previously, the diffraction pattern, consisting of a number of diffraction peaks of different intensities, is diagnostic of a crystalline phase. In samples with a miniature of phases, the complete pattern of all the crystalline phase are present in the data set. Diffraction data for a crystalline phase are normally compiled as a list of d- spacings (in Angstrom units ) in order of decreasing value. The intensities of the strongest peak and the indices for the crystallographic orientations of the diffracting planes. Powder diffraction palterns for tens of thousands of crystalline phases have been compiled so far and are available in cord or book form along with lists of the d-spacing of the strongest lines arranged in such a way as to enable reasonably rapid identification of phases. Several propams for computer searching the powder diffraction files for matching pattern are also available. 4.3 Determination of Crystal Structure The basic principles involved in structure determination have already been introduced. We know that the crystal structure of a substance determines the diffraction pattern of that substance or, more specifically, that the shape and size of the unit cell determines the angular positions of the diffraction lines, and the arrangement of the atoms within the unit cell determines the relative intensities of the lines. It may be worthwhile to state this again in tabular form as follows.. Crystall structure Diffraction mttern Unit cell 2 Line position Atomic positions 3 Line intensities Since structure determines the diffraction pattern, it is possible to go in the various directions and deduce the structure from the pattern. It is possible to do this, but not in any direct manner. Given a structure, we can calculate its dimaction panern in a straight forward fashion. The reverse problem, that of directly calculating the structure from the observed pattern, is one of trial and error. On the basis of an educated guess, a structure is assumed, its diffraction panern is calculated, and the calculated pattern compared with the observed one. If the two agree in all detail, the assumed structure is
correct if not, the process is repeated as often as is necessary to find the correct solution. The determination of an unknown structure proceeds in three major steps as follows: 1. The shape and size of the unit cell are deduced from the angular positions of the diffraction lines. An assumption is first made as to which of the seven crystal systems the unknown structure belongs to, and then, on the basis of this assumption, the correct miller indices are assigned to each reflection. This step is called "indexing the pattern" and is possible only when the correct choice of the crystal system has been made. Once this is done, the shape of the unit cell is known (from the crystal system), and its size is calculable from the positions and miller indices of the diffraction lines. 2. The number of atoms per unit cell is then computed from the shape and size of the unit cell, the chemical c:omposition of the specimen and its meassured density. 3. Finally, the positions of the atoms with in the unit cell are deduced from the relative intensities of the diffraction lines. Only when these three steps arc: accomplished the structure determination is complete. 4. 4 Phase analysis The properties of ceramic materials are function of the intrinsic properties of the constituent phases and the boundaries between the phases. It is necessary therefore to know the complete chemistry, the identities and compositions of the phases, and the detailed microstructure-property relationships and, in turn the effects of processing on properties. Consequently, phase analysis is not an isolated activity but an essential part. If equilibrium phase assemblage in a ceramic system is determined experimentally, the information may be used to predict the physical structures, compositions and percentages of the phases that are present upon attainment of chemical equilibrium for any given mixtures of the raw materials. Phase diagram also define the stability limits of the phases in terms of the physical variables and can be usekl for prediction of the effects of contamination, contact with other materials, extended use at high temperature and soon. They do not, however, provide information about kinetics of the approach to equilibrium or other chemical changes. Therefore, phase analysis remains essential for the determination of the identities and compositions of phases in the
processed ceramic materials, to enswe that equilibrium has been attained or, in some cases, that a derived non-equilibrium has been produced. Phase analysis in the processed ceramic is most effectively accomplished in conjunction with microstructural analysis. The first two requirements for phase analysis are the chemical compositions and the structures of the phase in the ceramic. Each of these can be considered at a number of different levels of deta~ls. The identity of crystalline phases, for example, can be easily determined in most cases by X-ray powder hfiaction. Details of crystal perfection, lattice ordering, residual lattice strains, and so on require more detailed study by a wide variety of methods such as Mossbauer spectroscopy, nuclear magnetic resonance, or electron spin resonance. Similarly, eventhough identification of a crystalline phase by X- ray diffraction, coupled with detailed phase equilibrium information, provides a reasonably accurate picture of the phase composition, chemical inhomogeneities may be present for a variety of reasow;, and phases present in very small quantities may not be redly identifiable except by micro mechanical methods such as electron microprobe analysis, electron spectroscopy for chemical analysis (ESCA) or any other several other sophisticated techniques. It is well known that the Bragg condtion for dihction of X-rays by the planes (hkl), 2dhkl sine = 14, has a sirnple geometrical interpretation in terms of the reciprocal lattice and the Ewalds sphere, The strontium barium niobate (SBN) are reported to exist as a successive solid solution over a wide range, which are found to be ferroelectric phases with tungsten brom type structure and belong to the space group c2k -PJ~ at room temperature [I, 2, 31. The SrXBal.,NbzO6 (SBN) crystal growth, structure and its properties are studied [I, 2, 41. According to these results, BSN is closely related to the tetragonal tungsten bronze structure over a range of comlmsitions 0.20 < x < 0.70 [I] or 0.25 < x < 0.65 [2]. Framcombe found that the structure is distorted to orthorhombic for x > 0.55, while the range of the orthorhombic phase given by lsmailzade [2] is x < 0.60, and by Caruthers [5] as x < 0.45. Since there is a jump of the lattice parameter at the composition relative to the phase transition, the properties over different single phase ranges are not the same [I]. Controversy exists as to he precise nature and phase of these solid solutions. It is
important to know the exact phase region and phase transition behavior. In light of the above facts we have cam4 out the structural investigations of SrXBal.,Nb2Oc, solid solutions in the range 075 < x < 0.35 with x-ray powder diffraction method. Details of experimental procedure, results obtained and analysis of the results are given in the following sections. 4.5 Experimental procedure Strontium barium niobate samples are prepared by solid state reaction method as described in the chapter-2. The following solid solutions with the specified ratio are selected for x-ray powder diffraction studies. They are The polycrystalline ferroelectnic ceramics pellets are crushed in to fine powder in an agate mortar. The powder is then placed in the sample holder and smoothed to produce a flat surface (Alternately a solid polycrystalline sample may be cut with a flat surface). In any case the sample should have a very large number of crystals randomly oriented, with a flat surface. The sample is placed in a suitable clamping device in the center of the rotating, motor driven goniometer. The detector, a scintillation counter or a Geiger counter which is mounted on to the goniometer, will rotate in a circular arc around the sample.. The mechanism is calibrated so that sample rotates at half the speed (scanning rate) of the detector so that the angle at which the X-ray beam impinges on the sample is the same as the angle from which radiation is sensed by the detector. Angles are measured as 20, twice the angle of diffraction, in this arrangement. The filter or monochromator and collimatinj; slits are placed conveniently in the beam paths. A schematic diagram of the geometry of powder diffractometer is shown in figure 4. 1. As the sample and detector are rotated from nearly 0' (20) to near 180 (20) normally, at rates between 0.125' and 4.0" (28) 1 minute, radation observed by the detector is amplified and recorded as a function of 20 by mans of the interfacing computer. The
intensity data may be retrieved in a number of different graphical or numerical formats or fed directly to a computer for evaluation. The diffraction patterns for the individual compositions are recorded using Philips X-ray dimactometer with Cu K, radiation operating at 20 ma current at a scan rate of 3'1 minute. The d-spacing and the peak intensities are compared with the standard value of SBN solid solution material (JCPDS card no. 6-0452). 4.6 Results and discussions X-ray dimaction spectra of powders calcined at 1000'~ show the presence of intermediate phase (SrNbO6 and BaNbOs), in addition to the SBN phase. Powders calcined above 1200'~ reveal only single phase SBN. In the polycrystalline grains we may observe compositional &ff'erence between grains and grain boundaries. Usually the grain boundary phases are Nb205 rich. It is anticipated that X-ray diffraction analysis might show the presence of second phase in SBN containing the grain boundary phase. In fact, all the X-ray spectral peaks correspond to a?tb SBN phase. This indicate that grain boundary phase is either structurally similar to the primary phase or more likely that there is less than 5% by volume of the grain boundary phase. However, the X-ray diffraction spectra of specimen exhibit noticeable difference in the peak intensities compared to the standard spectra (i) Peak splitting above 40' and (ii) an increase of the (OOn) peak intensities. The Bragg angle diff'erence (AO) due to the difference in the x-ray wavelength ( ha) between a, and a2 is so small that A0 contributes only to the line broadening at relatively low angles. X-ray diffraction is essentially a scattering phenomena in which a large number of atoms co-operate. Since the atoms are arranged period~cally on a lattice, the rays scattered by them have definite phase relations between them. These phase relations are such that destructive interference occurs in most mrections of scattering, but in a few directions constructive interference takes place and diffracted beams are formed. The two essentials are a x-ray wave motion capable of interference and a set of periodically arranged scattering centers ( the atoms of the crystal). Two geometric factors involved in X-ray diffraction are the following. (1) The angle between the diffracted beam and
transmitted beam is always 28. This is known as the diffraction angle, and it is this angle, rather than 8, which is usually measured experimentally (2) The incident beam, the normal to the reflecting pane, and the diffracted beam are always coplanar. From the powder diffrdction data, the individual Bragg reflections corresponding to peak positions and intensity are obtained with sufficient accuracy by using peak search program installed in the interfac~ng computer ( PC-APD diffraction computer software). The lattice constants a and c are calculated using the following relations. for tetragonal symmetry. The value of d, the distance between adjacent planes in the set (hkl) is found from the relation for monclinic symmetry 181, where d is the spacing between lattice planes, a, b and c are the unit cell axial length, P the angle between a and c axes, h k I are the Miller indices. Computer programs are used for indexing and calculating the lattice parameter of diffraction patterns. 'The SrxBal.,Nb20a solid solutions with x > 0.47 are indexed in tetragonal symmetry using a computer program called "Powder Diffraction Package (PDP-11)" 191. The compositions with x 0.47 are indexed in monoclinic symmetly using CRYSFIRE indexing computer program (sub program DICVOL) [lo]. Table 4.1 shows the x-ray powder diffraction data of Sro 75Ba 25Nb~b~06. Here the lattice parameters calculated using the computer program are a = b = 12.376 A' and c = 3.920 A' for wavelen@h L(CuK,) = 1.54056 A'. All the major 22 peaks are listed with their hkl indices corresponding to their 20 values. One characteristic of the x-ray pattern of this composition is the relatively intense (001) and (002) reflections, which appear around 22.8 lo and 46.52' respectively. The observed d-spacing of the crystal lattice is given along with the calculated d- spacing for the above mentioned lattice parameters which, show tetragonal symmetry. From the examination of Ad values, it is evident that the observed and calculated values
are nearly equal for all major peaks, and the lattice parameter fits From the measured data for d-values, it is evident that the maximum d to the 20 value of 22.81'. The c:orresponding hkl indices are (0 0 I), th directly gives the value of c-parameter which is 3.895 A'. From data, the maximum intensity corresponds to a peak 20 = 29.75', wit A'. The corresponding h k l indices are (4 1 0). Figure 4. 2 shows the x-ray dimaction pattem of Sro.7sBao.2sNb20~. The pattem shows sharp peaks, which is distinct from the background intensity. The absence of any other peaks in the observed pattern, apart from the tetragonal symmetry, is a clear evidence of single phase composition of the sample. Table 4. 2 shows the x-ray powder diffraction data of Sr0.61Ba0.39Nb206 including observed and calculated values. All the major peaks are listed with their corresponding 20 values. The experimentally observed d-spacing of the crystal lattice is given along with the calculated d-spacing. The lattice parameter calculated using the computer program are a = b = 12. 403 A'; c = 3.914 A' for wavelength X(C&) = 1.54056 A'. The hkl indices corresponding to iill major 22 peaks are listed. The difference between observed and calculated d-spacing, Ad, is less than 0.01 A'; for all major peaks. Hence the calculated lattice parameters fit the experimental data. The maximum d-value corresponds to 20 = 22.55'. The corresponding hkl indices are (0 0 1); hence the d-value directly gives the value of c-parameter, which is 3.914 A'. From the relative intensity data, the maximum intensity corresponds to a peak at 20 = 32.26', with the lattice spacing d = 2.7861 AD, with corresponding h k I indices (31 1). Figure 4.3 shows the XRD pattem of Sro.brBao39Nb20~. The pattern shows sharp peaks which are distinct from the background intensity. There are no other peaks apart from those corresponding to TTB structure. This confirms the single phase composition of the crystal. The change in intensity of the peaks is due to the variation in the relative atomic positions. Here also the pattem shows relatively intense (0 0 1) and (0 0 2) reflections, which appear around 22.7' and 46.27', respectively, indicating the preferred orientation along c-axis.
Table 4. 2 X-ray powder diffraction data of Sr0hlBa0.39Nb206. a = b = 12.403 A"; c = 3.914 A' ; h (Cu K, ) = 1.54056 A' hkl
2000 5 10 20 30 40 50 60 28 (Degrees) Figure 4. 2 X-ray powder diffraction patterns of the Sr0.75Ba0.25Nbt06 solid solution. 10 20 30 40 50 60 28 (Degrees) Figure 4. 3 X-ray powder diffraction patterns of the SroslBao.~rNbzO,j solid solution.
Table 4. 3 contain powder diffraction data of SrO.S~i3~45Nb~06. There are 30 peaks in the 5' to 70" range. The 28 values along with the relative intensity values and d- spacing are tabulated. The solid solution is found to exist in tetragonal tungsten bronze type structure, with lattice parameters a = b = 12.328 A", c = 3.9102 A'. The hkl indices corresponding to all the major peaks are calculated and listed. From the examination of Ad values it is evident that the observed and calculated values are in good agreement; hence the lattice parameter fits the experimental data. The major peak with Iflo = 100 is found at 32.44', with lattice spacing d = 2.7576 A'. The corresponding h k I indices are (420). Figure 4. 4 shows the correspondng XRD pattern for S~O.~SB~~..,+J~~O~. The 20 versus intensity is plotted in the range 5' to 70'. Here one significant deviation from the previous pattern is the appearance of two weak peaks at 27.075' and 28.955'. The preferred orientation along c-axis is not well defined because of the absence of (0 0 1) reflection. The (0 0 2) reflection intensity is relatively low compared to previous two samples. Table 4. 4 shows the x-ray powder diffraction data of SrosBao.sNbz06. There are 22 peaks in the observed pattern. The 28 values along with the relative intensity values and d-spacings are tabulated. 'The solid solution is found to exist in TTB structure; with lattice parameters a - b = 12.4032 A', c = 3.936 A'. The h k I indices corresponding to all the major peaks are calculated and listed. From the Ad values listed, it is clear that the observed and calculated values are in good agreement. The major peak with relative intensity 100 is found at 32.18' (with the lattice spacing d = 2.779 A'). corresponding h k 1 indices are (4 2 0). Figure 4. 5 shows the corresponding XRD pattern of Sro sbao.5nb2o6 plotted from the experimental intensity value versus 28 for the range 5' to 70'. The pattern shows sharp peaks, which are characteristic of tetragonal tungsten bronze structure. Here the pattern shows preferred orientation along c-axis because of the intense (0 0 2) reflection around 46.09'. The
Table 4. 3 X-ray powder diffraction data of Sro.ssBao4~Nb206, a = b = 12.328 A'; c = 3.9102 A'; h (Cu K, ) = 1.54056 A'. - Peak No. 20 ' d-o,,. d cd. Ad I(rel.) h k l -.- 1 22.93 3.8753 3.89846-0.02316 18.51 3 1 0 2 26.095 3.412 3.41917-0.00717 31.04 3 2 0 3 27.075 3.2906 3.30176-0.01 116 5.07 2 0 1 4 28.05 3.1784 3.18935-0.01095 64.48 2 1 1 5 28.955 3.0811 3.082-0.0009 5.97 4 0 0 6 29.865 2.9893 2.98998-0.00068 64.48 4 1 0 7 30.735 2.9066 2.90574 0.00086 32.24 3 3 0 8 32.44 2.7576 2.75662 0.00098 100 4 2 0 9 34.83 2.5737 2.57387-0.00017 20.6 3 2 1 10 37.045 2.4247 2.42047 0.00423 3.28 4 0 1 11 38.45 2.3393 2.33223 0.00707 19.1 3 3 1 12 39.19 2.2968 2.28925 0.00755 5.37 5 2 0 13 42.565 2.1222 2.11423 0.00797 12.54 5 3 0 14 44.67 2.0269 2.02671 0.00019 34.93 6 1 0 15 46.405 1.9551 1.955 1E-04 26.27 0 0 2 16 49.3 1.8469 1.84258 0.00432 9.55 2 1 2 17 49.885 1.8266 1.83775-0.01115 12.54 6 3 0 18 52.155 1.7523 1.74757 0.00473 32.84 3 1 2 19 52.68 1.7361 1.74344-0.00734 16.42 7 1 0 1.74344-1.74344 11.34 5 5 0 20 53.86 1.7008 1.69716 0.00364 0 3 2 2 21 54.89 1.6713 1.6632 0.0081 13.43 6 3 1 22 56.005 1.6406 1.63627 0.00433 30.45 4 1 2 23 57.5 1.6015 1.60577-0.00427 52.24 7 0 1 24 60.1 1 1.5382 1.541-0.0028 8.96 8 0 0 25 61.7 1.5021 1.49564 0.00646 10.45 7 3 1 26 64.1 1.4516 1.45287-0.00127 9.55 6 6 0 27 64.6 1.4415 1.44288-0.00138 9.85 8 3 0 28 65.15 1.4307 1.4331-0.0024 14.93 7 5 0 29 67.5 1.3865 1.38035 0.00615 14.93 6 2 2 30 68.9 1.3617 1.3614 0.0003 10.45 9 I 0
Table 4. 4 X-ray powder diffraction data of SroroBao.soNbz06, a - b = 12.4032 A"; c = 3.936 A' ; 1,(Cu K, ) = 1.54056 A'. Peak No. 26 O
Figure 4. 4 X-ray powder diffraction patterns of the Sr0ssBao~~Nb~06 solid solution
Table 4. 5 shows the powder diffraction data of Sr0,47Ba,.siNbzO~. All the 28 major peaks observed in the range 5' to 70' are listed. The 20 values along with the relative intensity values and d-spacing are tabulated. The data shows peaks in addition to tetragonal symmetry which indicate multiphase nature of the system. Figure 4. 6 shows the corresponding XRD pattern of Sr0.47Ba0.53Nb206 plotted from the experimental intensity value versus 20 for the range 5' to 70'. The lattice parameters calculated for tetragonal symmetry are a = b = 12.403 A' and c = 3.914 A'. The presence of additional phase causes the variations in dimaction pattem. The XRD pattem depends on the structure of each phase present and the percentage of these phases in the aggregate. The size, quality and orientation of the grains of the one phase differ from those of the other phase or phases. Another characteristic of the X-ray diffraction spectra of this sample is the highly intense (0 0 1) and (0 0 2) reflections, which appear around 20 angles 22.7' and 46.15', respectively. Since the X-ray diffraction samples are in the form of plycrystalline gains, it is unlikely that such strong reflections are due to texture effects. The relative intensities of (0 0 1) and (0 0 2) peaks compared to the maximum intensity peaks (1 3 I), (2 4 0) are approximately two to three times stronger than those of the same peaks listed in JCPDS file. This inlcates that the grains have preferential orientation along c-axis. Th~s is similar to the reported studies on SrumBa04uNb~06 and Sr~.~sBao 75Nb201 (81 ceramics with large grains. Table 4.6 shows the x-ray powder diffraction data of Sro 45B~~Nb206. All the 26 peaks observed in the range 5' to 70' are listed. The 20 values along with the relative intensity values and d-spacings are tabulated. The solid solution is found to exist in monoclinic symmetry. The Lattice parameters are a = 12.5765 A'; b = 3.993 A', c = 12.5042 A', P = 90.30' with a volume 627.92 (A0) '. The hkl indices corresponding to all major peaks are calculated and listed. From the examination of Ad values it is evident that the observed and calculated values are in good agreement, hence the lattice parameter fits the experimental data. The highest intensity peak is found at 31.82' with the lattice spacing d = 2.81 A'. The corresponding hkl indices are (3 1 1). This is a deviation from the previous compositions. From the above observations we can infer that the tetragonal cell distorts to monoclinic symmetry. The angle between c and a axis is 90.30~. When we compare this symmetry with tetragonal symmetry, we can verify that this is only a
Table 4. 5 X-ray powder diffraction data of Sr0~7Ba053NbzO6, a = b = 12.403 A', c = 3.914 A'; A (Cu K, ) = 1.54056 A' - NO. 28 ' d-ch. dlca~. Ad I(rel.) h k I
Table 4. 6 X-ray powder diffraction data of Sr0.4jBa0.5jNb206, a = 12.5765 A'; b = 3.993 A'; c = 12.5042 A' ; P = 90.30' h (Cu K, ) = 1.54056 A'. Volume = 627.92 (A0)'. - PeakNo. 28 O d-i&. d C~I. Ad I(rel.) hkl
28 (Degrcas) Figure 4. 6 X-ray powder diffraction patterns of the Sro47Baa.~3Nb206 solid solution. 10 20 30 40 50 60 70 20 (degrees) Figure 4. 7 X-ray powder diffraction patterns of the Sro.4sBao.ssNb206 solid solution.
distortion or deviation from the tetragonal symmetry. The line splitting observed is due to the presence of monoclinic phase. Figure 4. 7 shows the corresponding XRD pattern of Sro4sBao.ssNb206 plotted from the experimental intensity values versus 20 for the range 5' to 70'. Table 4.7 shows the X-ray powder diffraction data of Sr0.43Ba0.57Nb206 All the 28 peaks observed within the range 5' to 70' are listed in the table. The 20 values along with the relative intensity values and d-spacings are tabulated. The solid solution is found to exist in monoclinic symmeuy,with lattice parameter a = 12.4623 A', b = 3.9335 A', c = 12.3256 A', P = 90.287', having volume V = 604.19 (A0)'. The h k l indices corresponding to all major peaks are calculated and listed. From the examination of Ad values it is evident that the observed and calculated values are in good agreement, hence the lattice parameters fit the experimental data. The highest intensity peak is found at 32.1S0with the lattice spacing d = 2.7815~'. The corresponding hkl indices are (3 I -I). Figure 4. 8 shows the corresponding XRD pattern of Sr0.4'Bao.57Nb206. All the major peaks observed within the range 5' to 70'are listed. Table 4. 8 shows the x-ray powder dimaction data of S ~O.~~B~O.&~~O~. All the 23 peaks observed within the range 5' to 70' are listed. The 28 values along with the relative intensity values and d-spacings are tabulated. The solid solution is found to exist in monoclinic symmetry. The lattice parameters are a = 12.6743 A'; b = 3.9819 A", c = 12.5964 A', = 90.871 with a volume V = 635.64 (A') 3. The hkl indices corresponding to all major peaks are calculated and listed. From the examination of Ad values it is evident that the observed and caculated values are in good agreement, hence the lattice parameters fit the experimental data. The highest intensity peak is found at 31.770 with the lattice spacing d = 2.81432 A". The corresponding h k I indices are (3 1 1). From the above observation it can be inferred that the tetragonal cell distorts to monoclinic symmetry. The angle between c and a axis is 90.871'. When we compare this symmetry with tetragonal symmetry, we can verify that this is only a distortion or deviation from the tetragonal symmetry. The line splitting observed is due to the presence of monoclinic phase. Figure 4. 9 shows the corresponding XRD pattern plotted from the experimental intensity value versus 28 for the range 5' to 70'. The pattern shows sharp peaks.
Table 4. 7 X-ray powder diffraction data of Sr0~~B%.57Nb20~, a = 12.4623 A'; b = 3.9335 A'; c = 12.3256 A'" 113 = 90.287'; Volume = 604.19 (A')~.
Table 4. 8 X-ray powder diffraction data of Sro.&3o,6sNb206, a = 12.6743 A'; b = 3.9819 A'; c = 12.5964 A'; = 90.871'; 1 (Cu Ka ) = 1.54056 A', V= 635.64 (Ao)'. - PeakNo. 28 ' d-c>b. d ca1. Ad I(re1.) hkl
Figure 4. 8 X-ray powder diffraction patterns of the solid solution. Figure 4. 9 X-ray powder diffraction patterns of the S ~O 3iB~65Nb~b206 solid solution
The calculated lattice pameters for tetragonal and monoclinic symmetries for different compositions are given in Table 4.8. In the case of tetrayonal symmetry, the axial ratio is given by is (d10)cla is close to unity, which is a characteristic of tetragonal tungsten bronze structure. For every composition in the 0.47 < x < 0.75 range, the SBN is found to exist in tetragonal syrruneby. For x < 0.45, the solid solutions are found to distort to monoclinic symmetry, with small variations in the lattice parameters. The tetragonal tungsten bronze type structure with a unit cell formula of [(AI)Z(AZ)4Cd (BJ)(BZ)X]030 has a tetragonal lattice with a = 12. 4 ~Oand c = 3. 9 A' with the P4bm space group having: five formula units per cell. This structure consists of framework of Nb06 octahedra that share corners in such a way that there are three intersitial sites, two of which (Aland Az, may be occupied by the BdSr ion [I 11. [ Composition a(ab) a(t) &Ao) a p y (d10)da Volume ( Table 4. 9 shows the lattice parameter, axial ratio, volume of various compositions of strontium barium mobate solid solution. The niobium ions are coordinated to six oxygen ions. The Ba and Sr layer are disordered. The niobium atoms have six nearest 0 ion neighbors and are located at sites possessing distorted octahedral symmetry. The Sr ions have 12-15 nearest 0 ion neighbors and are located at sites that are denot'ed as 4C and 2A sites. Barium ions only occupy the 4C, but not the 2A sites. A unit cell o~f SBN has one unoccupied site from among the six possible 4C and 2A sites. This vacant site is potentially available for interstitial substitution of impurity ions. There is another potential interstitial site which is completely unoccupied
by Ba or Sr ions. This site, denoted C, has nine nearest 0 ion neighbors and is located at the centre of an oxygen ion triangle. In SBN the minimum experimental metal - oxygen ion distance is 2.547~' at the 2A site and 2.707 A' in the 4C site. This contrasts with the more restricted enviomment at the C site where a significantly shorter metal oxygen distance would be required for occupancy. Thus possible occupation of the C sites is restricted to the smaller size impurities. There is also considerable disorder on the oxygen ion sublattice in SBN 1121. The diffraction pattern of a polycrystalline powder consists of cones, which are assumed to be always continuous and of constant intensity around their circumference. But actually such rings are not formed unless the individual crystals in the specimen have completely random orientations. If the specimen ehbits preferred orientation, the Debye rings are of non-uniform intensity around their circumference (if the preferred orientation is slight), or actually discontinuous (if there is a high degree of preferred orientation). In the latter case, certam portions of the Debye rings are missing because the orientation which would reflect to those parts of the ring are simply not present in the specimen. Non-uniform Debye rings can therefore be taken as a conclusive evidence of preferred orientation, and by analyzing the non uniformity we can determine the kind and degree of preferred orientations present. Each grain in a polycrystalline aggregate normally has a crystallographic orientation different from that of its neighbor. The orientation of all the gains may be randomly distributed in relation.to some selected frame of reference, or they may tend to cluster to a greater or lesser degree, about some particular orientation or orientations. Any aggregate characterized by the latter condition is said to have a preferred orientation, or texture, which may be defined simply as a condition in which the distribution of crystal orientations is non random. Preferred orientation exists in rocks, ceramics, and in both natural and artificial polyme:ric fibers and sheets. In fact preferred orientation is generally the rule, not the exception, and the preparation of an awegate with completely random crystal orientation is rarely achieved.
Effect of gain boundaries have a pronounced effect on the sintered polycrystalline cenunic samples. The different crystallites (also called grains) usually have different orientations which may be quite randomin some cases. Their interfaces are known as grain boundaries, and can be considered to have extended surface defects of the solid specimen. However, even a single crystal is normally divided into a mosaic of crystallites, which are only slightly misoriented with respect to one another. So in this case we speak of small-angle grain boundaries for the surfaces separating the crystallites. Two parts of a crystal with slightly different orientations, separated by a small-angle grain boundary, are considered. The wedge-shaped gap in between tends to be filled by portions of lattice planes, giving lise to an array of edge dislocations on the surface of the grain boundary. The size of the grain i n a polycrystalline ceramic samples has pronounced effects on the XRD pattern. The governing effect here is the number of grains which take part in diffraction. This number is in tun1 related to the cross sectional area of the incident beam, and its depth of penetration or the specimen thickness (in transmission). When the grain size is quite coarse, only a fel~ crystals diffract and the photograph consists of a set of superimposed Laue patterns, one from each crystal, due to the white radiation present. A somewhat finer grain size increases the number of Laue spots, and those which lie on potential Debye rings generally are more intense than the remainder, because they are formed by the strong characteristic component of the incident radiation. When the Fan size reaches a value some where in the range 10 to lpm, the exact value depending on experimental condtions, the Debye rings have their spotty character and become continuous. Between this value and 0.1 pm, no change occurs in the diffraction pattern. At about 0.1 pm the first signs of line broadening, due to small crystal size, begin to be detectable [I 11. The other causes of difhction line broadening are structural imperfections which give rise to spread of intensity around each reciprocal lattice point. The second category is due to distortion of the crystal lattice, which amounts to a variation of d-spacing with in domains. This can arise from microstrain due to applied or residual stress or from a compositional gradlent in the mple[l2].
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