microstructurai, analysis of sbn and bnn 3.1...
TRANSCRIPT
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.
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