X-RAY DIFFRACTION STUDIES ON STRONTIUM BARIUM

NIOBATE CERAMICS

4. 1 Introduction

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, i t 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

r e d l y 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 d ihc t ion 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

b r o m type structure and belong to the space group c2k - P J ~ 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 c a m 4 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 m a n s 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'

h k l

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 . ~ S B ~ ~ . . , + 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'). The

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'.

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 -0.01 115 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 2 1 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 4 5 B ~ ~~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. d l c a ~ . 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.) h k l

2 8 (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.) h k l

Figure 4. 8 X-ray powder diffraction patterns of the solid solution.

Figure 4. 9 X-ray powder diffraction patterns of the S ~ O 3 i B ~ 6 5 N b ~ b 2 0 6 solid solution

The calculated lattice pamete r s 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 e h b i t s 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 f e l ~ 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 F a n 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] .

4. 7 Keferences

1. Framcombe M H., Actsr. CSyst. 13, 13 1 (1 960).

3. Jamieson P B., Abrahams S C. and Bernstein J L., J. C'hem. Phys. 48, 5048

(1968).

4. Ballman A A. and Bro'wn H., J. Ciyst. Growth. 1,3 1 1 (1 967)

5. Carmthers J R. and Grisso M., J. electrochem Soc. 117, 1427 (1970)

6. Han Yuang Lee and Freer, J. Appl. Phys. 81(1) 376-382 (1997).

7. Han Yuang Lee and Freer, In Fourth Euro-Cerumrcs, (Electroceramics), edited

by G . Gusmuno et.al. 1701. 5,219-226 (1995).

8. B.D.Cullity, Element>: of X-ruy drffracrion. 2* edition, Addition-Wesley

Publishing Company, INC (1978).

9. Mario Calliigaris, Third Inlemtional School and Worhhop oj' C'rystullogrcrphy

on x-ray Powder d~flracrion and its application^, Cairo. Egypt, January 1990.

10. Robin Shirley, C.7<YYCF~'lU3 Automutic Powder indexing Cornpuler I'rogrummefor

(PC under MSUOS) htt:l/~www. CCPlA.ac.UK/ solution1 indexing, (1999).

1 1. Wen-Jiung Lee and Tsang-Tse Fang, J. Am C:erum Soc. 81 [ I ] 193-1 99 (1 998)

12. R. C. Baetzold, Phys Hav. B, 48,9 (1993) 5789-5796.

13. J. Ian Langford and Daniel Louer, Rep. Pro. Phys. 59(1996) 13 1-234

14. Suorti P., The liietveld Mkthod ed. R. A. Young (Oxford: IUCrlOUP) pp 167-1 85

(1995).