CHAPTER - 3

MICROSTRUCTURAI, ANALYSIS OF SBN AND BNN CERAMICS

3.1 Introduction

In this chapter we concentrate: on the microstructural analysis of ferroelectric ceramics

that have been prepared. The sludy of microstructure using scanning electron microscope,

details of the techrucal aspects and preparation of sample specimens are described in the

experimental part. The microstructural analysis based on the SEM photographs are

described in the discussion part.

Microstructure is one of the important characterization methods of ceramic

materials and is also an important consideration in designing transducers, capacitors, PTC

thermistors, or devices used at high voltages. So control of microstructure is necessary

and this can be achieved by methods like (i) controlling the atomic ratios, (ii) addition of

selective cations (because grain growth is sensitive to certain additives) (iii) varying the

additive concentrations, and (iv) modifying the sintering profile. The

microstructure/phast: distribution of the final material also depend on (i) the initial

processing technique, (ii) raw ;materials used (iii) phase changes due to reaction kinetics

and (iv) grain growth.

The main characteristics of microstructure that can be determined from SEM are

(i) the number of identification phases present; (ii) the relative amount of each phase

present, and (iii) measurement of grain size, shape and orientation. The grain growth in

dense materials is associated with the grain boundary motion. Grain growth also occurs

during densification of powder compacts.

Ceramic materials are used today in all areas of engineering. The properties of the

materials are influenced significantly by their microstructures, therefore the quality of

these materials must always be carefully inspected. For this purpose the microstructure is

examined with different microscopy techniques such as scaminig electron microscopy or

transmission electron microscopy (TEM) with additional analysis techniques such as

energy dispersive analysis of x-rays (EDAX) or wavelength dispersive analysis of x-rays

(WDS). The study of microstructural features at magnifications b~eater than X 50, is a

primary analytical tool that is used to understand the nature of ceramic raw materials,

green (unfired) pieces, and fired samples. Important features are the particle size and

shape distribution in raw materials, as well as similar features in green and fired

ceramics. Other important aspects are the distribution of various phases in ceramics, the

size and spatial distribution of porosity, the nature of surface and volume flaws, and the

degree of microstructural uniformity.

Very fine scale features such as pores and large grains can act as critical flaws in a

ceramic, because of their biinle nature. A typical desirable ceramic microstructure

consists of a minimum volume of small pores and a porosity with fine grain size. Phase

heterogeneity and orientation may have a significant effect on all properties. For

example, the honeycomb monolithic catalytic converter substrate used in automotive

applications must have a carefully controlled porosity to achieve optimum catalytic

performance, coupled with controlled pain size and orientation to achieve the desired

directional thermal expansion and strength properties. Proper grain orientation is the key

to the prevention of thermal shock failure during use [I].

3 .2 Scanning electron microscopy (SEM)

Scanning electron microscopy is a useful tool for looking at fine structures and powders.

Secondary electron contrast is provided mainly by topography, atomic number, and

conductivity resulting from bombardment with a high-energy electron beam. The most

common images, employing secondary electrons, show light and shadow illumination as

if the sample were illuminated by an oblique light source. The image shows three

dimensional topographic features. Compositional contrast and information is obtained

with a back scatter electron detector and by x-ray fluorescent spectroscopy, which

permits analysis of both structure and microchemistry.

The scale of the SEbl is particularly suitable for many ceramic parts and raw

materials. The depth of focus provided by this instrument makes it very well suited for

rough failure surfaces. Indeed, many samples are prepared for SEM by fracturing in

order to reveal microstructure. This has become rather convenient to do with the advent

of computer processing of images and the application of quantitative stereology to the

computer. Major limitations are the contrast that must be obtained for the features of

interest and the operator skill that is required to analyze real features. The size and shape

distribution of powder particles, grain sizes in a green or fired ceramic, and porosity can

all be obtained. Volume fractions of various phases and pores can also be obtained.

Since two-dimensional features are analyzed, either a separate normal section must be

made or the three dimensional structure must be inferred.

The SEM has unique capabilities for analyzing surfaces. It uses electrons for

image formation, which have a much shorter wavelength than light photons, since shorter

wavelenb$hs are capable of generating higher-resolution information. Enhanced

resolutions in turn permits higher magnification without loss of details. Because of

instrumental parameters, practical magnification and resolution limits are - 75,000 X and

40 A' in a conventional SEM.

The big advantage of the scanning electron microscope is that sample surfaces can

be examined drectly with a depth of field very much greater than that of the optical

microscope at high magnifications, and in some cases with better resolution. Since

surface topography can be examined, the technique is competitive with replication

electron microscopy, although the latter is currently capable of superior resolution. The

combination of high resolution, an extensive magnification range, and high depth of field

makes the SEM uniquely suited for the study of surfaces. As such, it is an indispensable

tool in materials science research and development [2] .

3 .3 Experimental technique

Ferroelectric ceramic samples of strontium barium niobate (SBN), SBN modified with

rare earth or alkali 1 alkaline metals, and barium sodium niobate (BNN) were used for

scanning electron microscopy studies (SEW. The ferroelectric ceramics were

synthesized by the method described in the chapter 2. The specimens for SEM were

prepared by the following procedure.

1. Ferroelectric ceramic samples are coated with a thin film of conductive metal or

carbon and examined at low voltages.

2. The sample is connected to ground using a conductive adhesive (e.g. Silver paint,

colloidal carbon paint, or metal tape.). An artefact frequently observed when the spot size

is excessively large is charging, which is manifested as bright streaks or flashes across

the width of the CRT or photograph. It results when the sample is not connected to

ground. i.e. the specimen accumulates a net negative charge.

3 All samples are cleaned with organic solvents to remove oils grease or any other

soluble films to dislodge adhering particles. The specimen should be clean and

conductive.

The sample is mounted on a conductive substrate, usually an aluminum stub and

then secured with in the sample stage of the microscope. The stage serves as an electrical

pathway to ground and is also equipped with several controls for specimen movement.

The sample can be moved in x, y or z direction or titled and rotated. Obviously, the x and

y area are manipulated to orient the specimen.

SEM magnification is the ratio of the size of the display area on the CRT to the

distance the probe is scanned. Because a change in magnification simply involves

scanning a different-size area, focus will be maintained when magnification is changed.

Direct readouts of magnification are usually accompanied by micron markers from which

dimension can be measured. The micron markers are most u s e l l when a micrograph is

enlarged; the numerical magnification readout will obviously be incorrect if enlargements

are prepared. Images should always be focused at least two steps beyond the desired

magnification levcl to ensure that the image recorded is truly in focus. It is much simpler

to raise magnification, adjust the fine focus, and return to the desired level than to strain

ones eye trying to focus at only one level.

The SEM is taken under adequate vacuum to prevent oxidation of the tungsten

filament and the samples. 'The minimum vaccum required is lo4 Torr, the SEM

micrographs are taken only &er the establishment of high vacuum. The SEM is

designed with a vacuum lock at the specimen chamber. Only when samples are changed,

the specimen chamber is brought to atmospheric pressure.

The scan speed, or the rate at which the beam passes over the specimen is variable

from 100 to 10000 lines / scan. Very rapid scan rates produce a static or nearly static

image and are analogous to conventional television images. During slower scan rates the

progression of the beam across the specimen is observed. Extremely slow scan rates

improve image clarity because the electrons have sufficient time to interact with the

specimen, which in turn releases more data signals. Rapid scan rates are used for visual

examination of the specimen to select regions of interest, focusing, column alignment,

etc. which involve any imaging related purpose except image-recording. Moderate scans

are used to evaluate focus and prepare for image recording. This visual rate produces an

image which closely approximate the subsequent photograph. Slow scan rates are used to

record the images in th~s work [I)].

Data signals result from interaction between the bombarding electrons and the

atoms of the specimen. Regardless of their format, data signals arise from either elastic

(electron-nucleus) or inelastic (electron-electron) collisions of the beam (primary

electrons with atoms of a specimen). Elastic collisions will produce back scattered

electrons (BSE), which provide both topographic and compositional information about

the specimen. Inelastic collision deposit energy within the sample, which then returns to

the ground state by releasing distinct quanta of energy in the form of secondary electrons

(2'e: or SE).

The parameters lnfluencir~g electron emission is the conductivity of the specimen.

Metals are conduct~ve and readily emit electron signals, but non conductive specimens

such as plastics, glasses, or ceramics do not behave in the same manner. The primary

beam is largely absorbed by the sample, which accumulates a net negative charge of

sufficient magnitude to deflect the primary beam, and consequently the image is poor.

Beam absorption is suppressed by coating the sample surface with a conductive paint or

thin films. Conductive thin film coating increases the density and conductivity of

ceramic that exhibit charging artefacts under normal working conditions. The

applications of thin films to the surface significantly increases the quality of the

micrographs. Conductive goltl coatings are done by sputter coating technique, which

increase the secondary electron yield of non- conductive ceramic specimen. One reason

for coating with gold is the fact that most ceramics possess a high transparency to light.

As a result, upon examination, not only can the surface be viewed, but reflected light

from the interior portions of the sample, where the light is scattered and /or reflected from

pore walls, grain boundaries or inhomogeneities of any kind, can be seen. Thls scattered

and reflected light yields a milky appearing surface with very low contrast.

SEM images are displayed on the screen of a cathode-ray tube or interfacing

computer and permanent records or scanning electron micrographs are recorded by

photographng. The SEM optical column and specimen chamber are operated under high

vacuum (2 lo4 Torr for several reasons), first, residual gas molecules would scatter the

electron beam, and the electrons would travel at different velocities, resulting in severe

chromatic aberration. This in turn drastically limits image resolution operating under low

vacuum and would also result in accelerated oxidation of the tungsten filament, random

electrical discharge along the optical axis, and contamination of the specimen. The

specimen may sublime during examination and outgas during evacuation. Clearly the

specimen and adhesion paste (silver paint) must be dry before placement in the SEM.

Low magnification overview of the specimen is used to locate any subsequent

photograph. While it may be difficult to interpret a single high magnification photograph,

a series of photographs frorn low to high magnification maintains perspective and

orientation, thereby simplifying interpretation. This is particularly helpful when

examining fracture surfaces.

3 .4 Results and discussions

Ceramic samples have a microstructure that is determined by their fabrication process.

For example, the outer zone of a die pressed pellet is quite different from the inner zone

of the same piece. In addition, the microstructure of the outer zone of a ceramic is

different from its interior because the surface is exposed directly to the atmosphere

during sintering. The sintering reaction is more severe on the exterior than in the interior

of the part, as a result of exposure time. The grain growth mechanisms change with

addition of cations, as b~owth behaviour is very sensitive when the cations are

introduced Addition of Some cations reduces the grain growth whereas some other

cations improve the grain size by both diffusion and densification [4].

Figure 3. 1 shows the pressed compact of Sro,7sB~.zsNb206 sintered at 1 2 0 0 ~ ~ .

The microstructure contains grain size distribution within the range of 1-10 pm, with

loosely packed grain structure. Sro.~sBao.2+JbzO~ sintered at 1400 '~ shows grain

coarsening and pore size reduction causing a high density packed structure as shown in

figure 3. 2.

Sintering of Sro slB* 39Nb2o6 powder compacts at 1200°C for 4 hours resulted in

a structure, as shown in figure: 3. 5. The magnified image ( X 5000 times) is shown in

figure 3. 6. The geometry of the grains are distinct with long rectangular or flat surface.

The microstructure was not uniform and fully dense, the grain size had a wide

distribution between 2 pm anti 10 pm. This large grain size distribution and relatively

low density resulted in poor microstructure.

Heating the compacts at 1000°C and sintering at a temperature 1 4 0 0 ~ ~ resulted in

a structure with relatively high density as shown in figure 3. 3 and 3. 4. The fractured

face on the surface of the specimen is shown in figure 3. 3. Melting, fusing and

coarsening of grains is observed near to the outer surface of the pellet, as a result the

continuity of the pores structure are lost. Abnormal grain growth is observed in

Sro.61Baa.39Nb206, in localized areas giving rise to the evolution duplex structure. The

initial compact clearly identifiable large pores in a fine gmned matrix. As sintering

proceeds, grain growth and pore coalescence cause the microstructure to become more

compact. At a relatively high density, grain growth proceeds to such as extend that it

becomes thermodynamically feasible for the large pores in the original compacts to

7 I

I I Figure 3.1 S ~ ~ . 7 & ~ 0 . & h 2 0 ~ sintered at 1200~' Figure 3. 2 S r O O I & a sinhrad at1 4 0 0 ~ '

T

Figure 3..3 S r o , 6 1 5 B ~ 34hlb206 sintered at 1400~ ' Figure 3 .4 S10,61&.39Nb206 s i n d d I&

shnnk. The onset of shrinkage of the large pores is observed as an increase in the

densification rate of the compact.

In figure 3. 7 and 3. 8 shows the normal grain size distribution in

Sro,ssB~.4sNb206 and SrosB~sNbzO6 ceramics sintered at 1 2 0 0 ~ ~ for 4 hours. The

heterogeneously packed powder contain pores are large compared with the grain size.

Under normal sintering condition such pores will limit the final density of the sample.

Figure 3. 9 and figure 3. 10 show the Sr~.~Ba~.sNblOs samples sintered at 1 4 0 0 ~ ~ . The

use of conventional conditions (1 5 0 - 1 0 0 ~ ~ below the melting temperature) gave rise to a

duplex structure comprising a mixture of small, round grains ( < 10 pn), pillar-type grain

( 50 pn), and extremely large, plate like grains (100-200 pm). Pores get trapped in

large grain during particle coarsening, and micro cracks resulting from internal stress due

to huge difference in grain size, were also observed. These are characteristic features of

abnormal grains which are observed in Sro,oBao.&b2O6. [5] Sr&&a(),4aNb206 and

Sr2KNbs06 ceramics [6] . The term abnormal grain growth is defined as abnormally rapid,

inhomogeneous grain growth in localized regions giving rise to the evolution of a duplex

structure. These are cases where, small gain covered by large grains, although they case

not always distinct. The sintering of Sru.&ao.4uNb206 at 1300'~ gave rise to a duplex

structure comprising a mixture of small grains and abnormally large grains (in excess of

100 pm). Transmission electron microscopy studies revealed a Nb-rich, Ba-poor phase at

the grain boundaries; the low melting temperature of this phase caused localized liquid

phase sintering, resulting in abnormal grain growth [7].

Figure (3.11), (3. 13) and (3. 14) show the abnormal grain growth in the

micrographs of Sro43Bao.~7Nb20~ and Sr0.35Bao.65Nb206 compositions. The geometry of

the gains are irregular with a wide range of micro structural feature. The grains are

densely packed, showing striations or channel with in the grains. The pore grain

boundary separation and the channel (or bands) are distinct features of these samples. The

laminar tracks (or domain boundary) consisting of anti parallel interlocking stripes, have

widths less than lum. These curved stripe domains form are suitable "neutral"

background for revealing ferroelectric domain related to dislocations. Figure 3.14 shows

the magnified image of (X10,OOO) Sro.43Ba0.57Nb20h polycrystalline sample sintered at

Figure 3.7 Sro s 5 & , ~ 0 6 sintered at 1200~'

--- -- - Figure 3. -9 Sro5fiao.&06 sintemd at 1400~'

Figure 3. 8 sintered at 1200~'

Figure 3.1 0 Sro 5&.50Nb206 sintered at 1400~'

Figure 3. 1 1 Sr0.43B&.57Nb206 sintered at 1270~' Figure 3. 12 S T ~ , ~ ~ B & , ~ ~ ~ ~ ~ silYbXd at 12&

1270°C. The laminar ferroelectric domains developed during grain growth and the grain

boundaries intersect the ferroelectric domain.

Ferroelectric domains:- The regions of the crystal with uniformly oriented spontaneous

polarization are called ferroelectric domains. The region separating two is called the

domain wall. The walls which separate domains with oppositely oriented polarizations

are called 180' walls and those which separate regions with mutually perpendicular

polarization are called 90' walls. Ferroelectric domains form to minimize the electrostatic

energy of depolarizing fields and the elastic enerby associated with mechanical

constraints to which the ferroelectric material is subjected to, as it is cooled through

paraelectric-ferroelectric phase transition [8,9, 101. Due to the complex set of elastic and

electric boundary conditions at each grain, grains in polycrystalline ferroelectric

Strontium barium niobate art: always split into many domains. Static and dynamic

properties of domains and domain walls in ferroelectric and ferroelastic materials

determines, to a large extend, their microscopic behavior. When domains occur

accidentally during crystal growth, defects distribute accordingly and fix the structure

[I l l .

3.4.1 Effect of alkali and rare earth ion in strontium barium niobate

The effect of alkali and earth addition on the microstructure were analyzed by

studying the fractured surface of (Sr~lBao3u)LiEuo.~Nb206 and

(Sr0.61Bao.3r)LiNdo. 1Nb206 and (Sr~~tBaotu)Nao.12KO.14Lao.08NbzO6. F i w e 3. 15 and 3. 16

show the microstructure development of (Sr~lB~.~u)Li2+,Eu,Nb206 (with x=0.3)sintered

at 1200' C. In Figure 3.16, the heterogeneously packed powder contains pores that are

very large compared to the grain size. Under normal sintenng conditions such pores will

limit the final density of the sample. Figure 3. 15 shows the magnified image (X 5000)

exhibiting the coarsening of the grains.

The effect of neodymium (Nd) addition has significant effect on the microstructure. Here

the grain size (1 pm - 5 pm) *distribution is within a small range. The abnormal grain

growth or grain coarsening is not observed. Figure 3. 17 shows the microstructure

distribution of (Sr~~B%.~~)~-~,Li~+,Nd~Nb~06 (with x = 0.1) at a magnification of X 5000.

Figure 3. 13 Sro.3SB~.6Sb&06 3htered at 1270~ ' Figure 3. 14 Sr0.43B80. J7?d%@6 sintered at 1270~'

F i w 3- 1 5 [Sr0.61B~0.39 I62r Liz+* E ~ x m 0 6 (with x = 0.3) sintered at 1200~'

Figure 3. 16 ESro.alB+.w l+zx Li* EuJ'JhOa (with x = 0.3) sintered at 12&

F w 3. 17 [Sr0.61Bao.ss jaxLi2hN&Nb206 (with x = 0.1) sinkred at 12&

Figure 3. 18 [ S ~ O . ~ I B % . ~ Q 16hr Li2+xNdxNbtO6 (with x = 0.3) sintered at 1200c0

Here the grains are distinct with grain boundary and inter granular pores. Figure 3.18

shows the magnified image ( X 10000 ) showing grain-grain boundary features and pore

structures, sintered at 1200 c'.

Figure 3. 19 and 3. 20 show the microstructural development of ( S ~ W I B ~ O B ) ~ .

2x(NaK)2t,Lao.osNb206 sintered at 1400' C. The microstructure is rather complex, with a

variety of features. Crystallization prior to full densification has been observed to cause

the retention of a considerable amount of porosity in the sintered compact. It consists of

small grains with irregular shapes, pillar type structures and large plate like grains.

Structural inhomogeneities leads to densification of some regions of the powder compact

at different rates, referred to as differential densification.

Figure 3. 21 and 3. ;!2 show the microstructure of [Sr0.~1Bao.~s]0.&.4Nb206

sintered at 1200" C for 4 hours. The presence of potassium inhibits grain growth. The

microstructure develops relatively small grains around 1 pm in size. The distribution of

grains is relatively loose with large porous space. Figure 3. 23 and 3. 24 exhibit the effect

of sodium ions on microstructure of [Sro.61Ba~.3s]~.8N~.4Nb206 sintered at 1200" C for 4

hours. The grains are more or less uniformly distributed with porous spaces. The

magnified picture (x 5000) shows the onset of grain boundary fusing or inter granular

bonding. A part~al coarsening effect is observed with sodium addition. Figures 3. 25 and

3. 26 show the effect of sodium and potassium on [Sro.61Bao.3~]~.s [KNa]o.sNb206 sintered

at 1200~ C for 4 hours. Here the: presence of potassium decreases the grain growth.

3. 4.2 Microstructural development of BNN ceramics

Figure 3. 27 shows microstructure of Ba.Ba~Nb100xo taken from a fractured surface. The

grain size is uniform around :I pm and well dstributed with porous spacing, whereas

figure 3. 28 shows the structure of Ba3Na2Nblo0xo sintered 1200" C for 3 hours. The

increase in sodium content ha!; significant effect on the microstructures. The grain size

varies from 1 pm - 10 pm. The grain boundary separation is more difise due to partial

melting or the development of liquid phase during sintering process.

Figure 3. 29 and 3. 30 show the effect of Nd addition on the microstructure of

barium sodium niobate ceramics with the chemical formula Bai.2,N~+xNd,NbloOlo

Figure 3- 19 FSro.6lBao.39 1.1-zx INaKlwxLao.oe~Os sintered at 1 2 7 0 ~ '

Figure 3. 20 [Sro.aBao.39 ] e x [NaK12+. Lrb.08NbzO6 sintered at 1270~ '

Figure 3.25 CSr0.61B~0.39 10.8 Emalo.5Nbz06 sinkred at 1200c0

Figure 3.27 Ba *Nbto Om ~intdted at 1200 CO

Figure 3.29 Ba26N+,2Nr& zNbloOw Sintered at 1200 CO Figure 3.30 Ba22N~,4Nd o.4NbloOso Sintered

at 1200 c0

where x has the typical values 0.2, 0.4, respectively. The microstructure shows variation

with the change in chemical constituents. One significant feature of the microstructure is

the development of abnormal grain growth in Ba2.zNa44N&4Nb10O30, as shows in figure

3. 30.

3.5 Grain boundaries

The microstructure of polycrystalline ceramics is usually complex and distinguished by

the existance of gain boundaries, which are not seen in single crystals. Also the existance

of pores, imperfections, and rnultiphase compositions lead to a variety of microstructurs.

Up to now, grain boundaries and additional phases are thought to be undesirable, and the

goal was to eliminate them and obtain a structure as close to single crystals as possible.

However, new processes have been found in ceramics in which these properties are

important from application point of view and are developing rapidly.

ain boundary lmpunty

Mcrocxystal grm

boundary pore

ain boundary

(20A -1 um)

boundary

Figure 3. 31. representative ceramic microstructure (a) a typical grain boundary. (b)

grain boundary divided deposit (c) diffused deposit (e) granular deposit.

In the grain boundary region, enerby is increased, so impurities tend to gather

there. The impurities exist as a second or third phase among the constituent particles or

segregate in to the gain boundaries. With an increase in the amount of impurities and

additives, the grain boundary thickness increases. In such case, the shapes of the grain

boundaries or crystallites depend on the material, its constituents, and the sintering

process. In electronic ceramics, the existance of grain boundaries is very important for

applications in devices.

The microsbucture of ceramics contains fine crystalline gains, grain boundaries,

impurities segregated in the grain boundanes, pores in the grain boundanes, fine particles

and pores with in the grains. 'The grains or fine particles whch are the main constituents

of ceramics, range from one micrometer to tens of micrometer in size, and the direction

of their axes are arbitrary. The size of the grains depend on the size of the partjcles in the

raw material, impurities, and sintering conditions. Within ceramic grain boundaries, there

are crystal lattice defects such as dislocation and pores, as well as crystal lattice

deformations. Correspondingly impurities tend to gather in these areas and form grain

boundary divided deposits, diffused deposits, and granular deposits as depicted in figure

3. 31.

Grain boundary divided deposits: In general, the ionic stratifications of impurities which

are separated along the grain boundary are called 'grain boundary divided deposits'. They

range in thickness from 20 A' tcl 1 pm. In the grain boundary, impurities are very easily

dissolved, and therefore, their cr]/stal phase are considered to be very different from those

inside the grains.

D i f / u d deposit: When the amount of impurities is large, higher than the saturation point

of the solution, they are precip~tated into the grain boundary in a separate crystalline

phase. These precipitates are either diffused or granular. Generally, diffused deposits are

brought on by liquid phase sintering. Liquid phase sintering can be initiated when the

melting point of the precipitates in the grain boundary is lower than the sintering

temperature of the ceramics. If' there is good or complete wetting, the liquid flows

completely into the grain boundary and surrounds each of the fine particles, forming a

diffused deposit.

Granular deposit: When the amount of impurities is much greater than the saturation

point of the solution, and the melting point is higher than the sintering temperature,

particle-like impurities may be precipitated in the grain boundary. The physical and

chemical phenomena in peculiar to grain boundaries are: (a) gain boundary diffusion (b)

control of the formative reaction mechanism with respect to the grain boundary (c) grain

boundary potential (d) high re:sistance in the grain boundary, (e) Grain boundary bonding

[121.

3 .6 Grain growth

Grain growth occurs during the high temperature fabrication of ceramics in response to

the excess energy associated with interfaces or boundary between neighboring grains.

The control of grain growth is a major goal of the ceramics processor for two reasons.

Firstly, the size and morphology of grains generally play important roles in the resulting

material properties, as, for example, in strength or electrical behavior. Secondly the

attainment of hgh density requires that coarsening processes be suppressed during firing.

Associated with both these motivations is the prevention of abnormal gain growth in

which a few grains grow rapidly to sizes many times the matrix grain size. The basics of

the mechanism of grain growth relevant to ceramics is reviewed below. Particular

attention is devoted to the interactions between densification and coarsening, together

with the problem of abnormal grain growth.

3.6.1 Occurance of grain growth

In the widely accepted picture, the grain boundary is considered to be a region of disorder

between two crystalline regions (the grains). High resolution electron microscopy

indicates that the hckness of the grain boundary region is 2 lpm. Grain growth occurs

as atoms (or ions) diffuse less than an inter atomic distance to new positions. Thus one

grain grows at the expense of another. The atoms move from the "convex" surface on

one side of the gain boundary to the "concave" surface on the other side more readily

than in the reverse direction. The reason for the net flow from the convex to the concave

side is that the chemical potential of the atoms under the convex surface is higher than

that of the atoms under the c:oncave surface. Atomic flux occurs down the chemical

potential gradient. The result of the net flux is that the boundary moves toward its center

of curvature. The atoms in the grain boundary have a higher energy than those in the bulk

of the crystalline grain The grain boundary is characterized by a specific energy,

denoted by y,b, is typically of the order of 0.2-1.0 ~ / m ~ . The driving force for grain

growth is the decrease in grain boundary energy that results from a decrease in the grain

boundary area.

3.6.2Mechanisms and kinetics of grain growth

Drivingforce : The change in volume of an individual grain is determined by migration

of its component boundaries under the influence of chemical potential gradients arising

from grain boundary cwaturs. Curvature develops in order to balance surface tension

forces acting between intersecting boundaries under the constraint of filling space

analogous to c w e d interface:; in soap films. The resulting gradient induces a flux of

ions from the concave side to the convex side of the boundary, causing it to migrate

against the flow of matter. 'The driving force for boundary motion, Ft,' expressed as the

chemical potential gradient, duldx per ion across the interface, is related to the boundary

curvature, k, by :

where 0 is the volume of matter transported along with the rate limiting ion, &, is the

interface thickness and yb is the interfacial energy [13].

The specific grain shape determines the direction of boundary migration relative

to its center, and therefore determines whether shrinkage or growth occurs. Inspection of

hypothetical microstructure reveals that grains with less than six sides shrink. The sign

and magnitude of local boundary curvatures is related approximately to the size of the

grain containing the boundary, L', and the size of the stable site sided grain, L', by

Hillert's expression [14],

with 5 a constant (312 2 5 2 1 ). Substituting fork in equation (3. I) yields,

Fb is positive (with respect to motion of the boundary) for L' 2 L* (that is, growth) and is

negative for L' 5 L' (shrinkage). During normal grain growth the microstructure scales

in a continuous self-similar manner with the following characteristics:

L,, < 2 ~ '

Average grain size L = i y ~ ' , where w is a geometrical constant (v = 619 for three

dimensions). The average driving force for boundary notion, Fb, derived from equation 3.

The driving force scales linearly with inverse grain size.

3.6.3 General kinetic formulation

The average rate of gain growth dL/dt, is related directly to the average velocity,

vb of the migrating boundaries through the differential equation:

dL1dt = pvo (3.5)

where p is a constant (= 2). The velocity can in turn be represented as a product of the

average grain boundary mobility, &, and the average driving force, Fb, namely:

Vh = Mb .Fh % (UP) dWdt (3.6)

A specific mechanism governing boundary migration is treated via the mobility term and

kinetic laws describing the grain growth are derived by integrating the complete form of

equation (3.6) with respect to time [IS, 161.

3.6.4 Intrinsic mechanism

The intrinsic motion of grain boundaty in a pure system is determined by the diffusional

transfer of matter from the contracting grain to the expanding grain. The mobility of an

ion crossing the boundary, M,, is given the relationship.

where ~ b * is the diffusion coefficient of the rate limiting ion crossing the boundary by the

earliest route, k and T are the Boltzman's constant and the absolute temperature,

respectively[l7]. Combing of equations (3.6) and (3.7) we get

therefore L~ - L'? -. [ 2 ~ 5 D b * ~ y b / ( k ~ 8 b ~ ) ] . t (3.9) -.

where 1, is the initial grain s~u: at t = 0. Note that the main assumption made in deriving

the parabolic law 1s that all properties are considered to be isotropic and independent of

the detailed atomic structure ofthe boundary structure.

Observations of the parabolic rate law are rare in single phase ceramic systems.

Deviations from the parabolic rate law in which the sensitivity to grain size is decreased

are usually associated with the presence of soluble pinning precipitates on the initiation

of abnormal grain growth. An increased sensitivity to grain size (for example, cubic or

higher order kinetics) generally results from the impeding influence of attached species

such as solutes and second phases.

3.6 .5 Solute segregation

Impurities present in solid solutions tend to segregate to or away from the grain

boundaries in response to an elastic driving force resulting from the lattice parameter

mismatch and/or electrostatic driving force(s) resulting from valency differences and

space charge effects [18]. During migration, the impurities must diffuse along to

maintain the energetically favorable spatial configuration.

For the case of normal grain growth under low driving force and strong

segregation the velocity of the boundary may be expressed as,

where $ is the volume concentration of impurity ions, 6 is the width of a zone over which

the impurities interact with the boundary, Q is the partition coefficient for the impurity

between the boundary and bulk crystal, and C, is the bulk impurity concentration [19].

The velocity is linearly related to the inverse of the impurity concentration and therefore

significant retardation arises from strong segregation.

A kinetic law for the use of impurity drag can be obtained by recognizing that the

bulk impurity concentration (2, is related to the total impurity concentration C and the

grain size through the relation

where f ( (61/L) (Q-1)) is a linear function of grain size, L substituting for Fb, I&,, and

Co in equation 3. 9 and expressing the equation in terms of the grain size dependencies

alone.

Therefore L~ - L , , ~ = Y.t (3.12. b)

where Y is a constant. Cubic kinetics are therefore expected if a strong solute drag

mechanism controls the boundary motion. Note that several assumptions have again

been made in the derivation of equation 3.12 .b. If these assumptions do not hold, then

segregation may produce more complex kinetic behavior.

Observation for cubic kinetics have been made for several single phase systems

containing either un~ntentional impurities or deliberate solute additions. It may be argued

that the majority of ceramics are sufficiently impure such that background impurities

always control boundary migration in single-phase systems.

3 .7 Grain growth and coarsening

Grain growth is the term used to describe the increase in the grain size of a single-phase

solid or in the matnx grain size of a solid containing second-phase particles. Grain

growth occurs in both dense: and porous polycrystalline solids at sufficiently high

temperatures. For the conservation of matter, the sum of the individual grain sizes must

remain constant; the increase in the average size of sum of the p i n s is therefore

accompanied by the disapperance of some other grains, usually the smaller ones. The

densification of a polycrystalline powder compact is normally accompanied by a

coarsening of the microstructure; the average size of the grains and the average size of

the pores become larger.

In porous solids, both the gains and the pores normally increase in size, while

decreasing in number. There is considerable interaction between the grains and the

pores, and the microstructural evolution is considerably more complex than for dense

solids. Frequently the term coarsening is used to describe the process by which grains

and pores grow. Coarsening also occurs in the earlier stages of sintering but is less

pronounced than in the final stage. Since the microstructural evolution in the earlier

stages of sintering influences that in the later stages, an understandmg of the coarsening

of very porous compacts is also important. However, the complexity of the

microst~cture makes a quantitative analysis of the process very difficult.

3.8 Normal and abnormal grain growth

Grain growth in a ceramic is generally divided into two types (i) normal grain growth and

(ii) abnonnal grain growth, which is sometimes referred to a exaggerated grain growth,

discontinuous growth, or in the case of metals, secondary recrystallization. In addition,

for some relatively soft ceramics that have been highly deformed, another class of grain

growth, called primary recrystallization, may occur. In primary recrystallization, a new

generation of strain-free grams nucleate and grow at the expense of the highly deformed

grains. The driving force for the primary recrystallization is the decrease in strain energy

of the solid. Here we are concerned only with normal and abnormal grain growth, the

driving force for which is the decrease in grain boundary energy.

Normal grain growth is generally defined by two main characteristics: (i) the

grain sizes and shape occur wlthin a fairly narrow range and ii) the distribution in grain

sizes at a later time is fairly similar to that at an early time except for a magnification

factor.

In abnormal grain growth, a few large grains develop and grow fairly rapidly at

the expense of the smaller ones. The grain size distribution may change significantly,

giving rise to a bimodal distribution. In such a case, the property of time invariance of

the distribution is lost. Eventually, the large grains impinge on each other and may revert

to a normal distribution of sizes. Grain growth in porous ceramics is also described as

normal or abnormal. However, the interactions of the pores with the grains must also be

taken into account. The normal grain growth in porous ceramics is characterized by the

pores remaining in the grain boundaries. When the boundaries break away from the

pores, leaving them inside the: grain, the situation is usually indicative of abnormal gram

growth.

Figure 3. 21 and 3. 22 show the normal grain in [Sr0.6,Bao.39]0.8Ko.4Nb~O~ and

[Sro61B~.3r]o.&ao.&Jbfi respectively. Figure 3. 8 shows the normal grain growth in

Sro.sBa~.sb&06 sintered at 12110 'c. When the specimen is heated at elevated temperature

(1400 OC) abnormal grains growth develops as shown in figure 3.9 and figure 3. 10. The

pores well inside the large, abnormal grains can be observed. Since these pores are

difficult to remove during siwtering, it limits the final density that can be achieved during

firing. Figure 3. 11 shows the abnormal grain growth in sintered at

1270' C. Large grains with i~~egular structures are developed. If the structure is heated

further, more abnormal grains may start to develop; they grow rapidly consuming the

smaller grains.

3. 8. 1 Abnormal grain growth

During abnormal grain growth, a fraction of the gram population grows at a rapid rate,

generally leading to a broad or even bimodal grain size distribution. Abnormal grain

growth during fabrication should be avoided for two reasons. Firstly, a degradation in

material property may result from the ensuing microstructural heterogeneities; for

example, large grains are effec:tive nucleation sites for large creep cavities that limit high-

temperature component life [:lo]. Secondly abnormal gain growth is often associated

with the separation of second phases from grain boundaries; if the second phase is

porosity densification, processes are effectively terminated.

Initiation of abnormal grain growth is often linked to the occurance of local

fluctuations in boundary or particle velocities. Common mechanisms are characterized

in terms of either an intrinsic or extrinsic origin and whether the velocity fluctuation

arises from variations in mobility or the driving force.

Inirinsicconditions: Experimental and theoretical evidences are available to show

anisotropy in both intrinsic grain-boundary energies and mobilities. Boundary

anisotropies may be enhanced or diminished by the presence of impurities either relieving

or exacerbating abnormal grain growth. When impurities exist in sufficient quantities to

form a liquid phase during firing, a characteristic plate like grain morphology may

develop. High resolution transmission electron microscopy reveals that the liquid wets

the long facets but not the facets making up the grain ends. This anisotropic wetting is

believed to lead to strong variability in grain interface mobilities. The shapes that evolve

in materials therefore result from a combined anisotropy in surface energies and grain

boundary mobilities [2 I].

Extrinsic conditions : Extrinsic influences embody a variety of microstructural

phenomena and are the most common cause of abnormal grain growth. A wide

distribution in particle size of the starting powder tends to promote abnormal gain

growth Grains larger than twice the critical size may develop abnormally due to the large

driving force from highly curved boundaries between the large grain and the matrix. A

disparity in dnving force leads to linear growth kinetics of the abnormal grain. In many

cases, after a pronounced growth stage, abnormal grains that initiate via this mechanism

impinge on each other and their migration rate diminishes as they now effectively

become matrix gains. The smaller grains continue growing and reach the size of the

larger matrix grains leading to a normal but coarse microshucture. Bimodal

microstructures may, in some instances, be transient in nature if initiated by a wide

distribution in size of the starting powder.

Distributions in other microstructural characteristics may also trigger abnormal

grain growth. Porosity gmhents lead to variable growth rates when pore drag controls

boundary motion. Such gradients may be introduced during green fabrication, for

example, from non-uniform powder compaction during pressure fonning. In addition,

agglomeration of the starting powder often results in non-uniform packing and shrinkage

during firing [22]. Poor distribution of a dopant or contaminant may also affect local

densification and gain growth indirectly or the dopant may influence grain growth

directly through solute or second-phase drag mechanisms 1231. The common link

between these mechanisms 1s that spatial variation in the boundary velocities occur

leading to the relatively rapid growth of a few grains.

Variations in dnving force and solute content from boundary to boundary may

result in velocity transitions t h t can initiate abnormal grain growth. Fluctuations along a

boundary may also occur leadrng to unstable velocity perturbations and abnormal gains

with a distinct finger like morphology [24]. In general, solute breakaway is believed to be

uncommon because as grain growth proceeds the driving force decreases and solute

accumulates, which tend to push migration behavior toward the low velocity control

regime.

3 .9 Importance of controlling grain growth

The control of grain g r o d during firing process is one of the most important

considerations in the fabrication of ceramics. Its importance has the following two main

causes. First, the grain size (of the fabricated article is one of the major factors that

control its engineering properties. Control of grain growth is therefore directly related to

the achievement of the desired properties. Second, many engineering properties can be

improved with higher density, typically close to the theoretical density. Control of grain

growth forms an important fabrication approach for the attainment of high density.

3. 10 Effect of grain size on properties

Few of the properties are completely independent of grain size. We can provide only a

few well-known relat~onships for the effect of grain size on properties. The subject is

covered in many excellent texts and review articles. The fracture strength of many

ceramics is found to very as l i ~ ' " , where G is the grain size. In the diffusional creep of

polycrystalline materials, a very strong dependence of the creep rate on the grain size has

been found. A wide range of electrical and magnetic phenomena are affected by the grain

size, and it is in this area that the manipulation of the grain size has been and most

significant to produce materials with properties suitable for a variety of applications.

3.11 References

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