linking grain boundaries and grain growth in ceramics
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DOI: 10.1002/adem.201000214Linking Grain Boundaries and Grain Growth in Ceramics
By Michael Baurer*, Heike Stormer, Dagmar Gerthsen and Michael J. Hoffmann
The macroscopic properties of most materials are strongly influenced by grain size. In ceramicmaterials the microstructure usually results from the sintering process. Understanding the basicmechanisms of grain growth on an atomic length scale in ceramics would be beneficial to tailor themicrostructure for improved macroscopic performance of devices. A method is presented using graingrowth experiments to select samples for closer examination of grain boundaries with transmissionelectron microscopy. The growth experiments are used to identify temperatures were changes at grainboundaries occur at high temperature. Subsequently samples of interest are investigated usingtransmission electron microscopy (TEM) methods. The correlation between TEM results and changesin grain growth behavior can be used to gain closer insight into the processes occurring during graingrowth at an atomic length scale. Strontium titanate is used as model system to demonstrate thecombination of growth experiments with TEM results. Normal grain growth shows two distinct dropsin growth rate in the temperature range between 1 300 and 1 425 8C, independent of the A-site to B-sitestoichiometry of the perovskite. In previous studies a high preference for grain boundary planes orientedparallel to the 100 direction of one of the adjacent grains was found in the high temperature regime.This study shows that the preference does not exist in the low temperature regime possibly explainingthe change in grain growth rate.
[*] Dr. M. Baurer, Prof. M. J. HoffmannInstitut fur Keramik im Maschinenbau, Karlsruher Institut furTechnologieKaiserstraße 12, 76131 Karlsruhe, GermanyE-mail: [email protected]
Dr. H. Stormer, Prof. D. GerthsenLaboratorium fur Elektronenmikroskopie, Karlsruher Institutfur TechnologieKaiserstraße 12, 76131 Karlsruhe, Germany
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Perovskite ceramics are widely used in electronic devices
as capacitors,[1] positive-temperature-coefficient-resistors
(PTCR)[2] or ferroelectric actuators.[3] The performance of such
devices are governed by grain size or grain boundary proper-
ties. Prominent examples are PTCR ceramics which indicate
highly resistive grain boundaries above the Curie temperature
and a drop in resistivity of several orders of magnitude below
Curie temperature or the grain size dependence of high strain
multilayer actuators based on lead zirconate titanate (PZT).[4]
All devices are usually produced by sintering of ceramic
powders. Therefore, a better understanding of the link between
the local structure of the grain boundaries and the grain growth
behavior in the ceramic would help to tailor the microstructure
for better device performance.
Grain boundaries (GB) can generally change their proper-
ties with temperature[5,6] as the GBs add additional degrees of
freedom to Gibbs phase rule allowing for grain boundary
phases which are thermodynamically not stable as isolated
phases. The reduction in GB energy can lead to structural
changes such as the formation of intergranular films (wetting
liquids at GBs)[7] multilayer adsorption of dopants[8] or
roughening transitions.[9] Monitoring such changes in poly-
crystalline materials is challenging as the selection of the right
processing conditions for further examination is difficult.
However, grain growth experiments are a convenient way of
identifying changes at GBs occurring at different tempera-
tures[10] as the process of grain growth itself is insignificant
during the heating and cooling phase of a furnace cycle.
Samples can then be selected from grain growth experiments
for further examination by transmission electron microscopy
(TEM).
In the present paper we used SrTiO3 as a model system for
grain growth in perovskite ceramics. Grain growth can
usually be described by
d2�d20 ¼ kDt¼ 2agMDt (1)
with k as growth factor, d as the average grain size at time
tþDt, d0 as the initial grain size at time t, and g as the average
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Fig. 1. Arrhenius plot of growth factor as function of the inverse temperature showingtwo distinct drops in grain growth with rising temperature. Adapted from ref.[12].
Fig. 2. Grain with grain boundaries parallel to the 100 plane in SrTiO3. Reproducedwith permission from ref.[14]. 2010, Materials Research Society.
grain boundary energy. M is the effective grain boundarymobility, the proportionality factor between average GB
velocity during growth and the driving force for growth; a is a
geometrical factor in the order of unity.[11] Intensive grain
growth studies[12] show that the growth factor 2agM is
reduced in SrTiO3 at two distinct temperatures by orders of
magnitude with increasing temperature. This behavior clearly
deviates from the expected Arrhenius type behavior (Figure 1)
and is independent of the Sr/Ti-ratio of the ceramic.
In order to understand this interesting phenomenon, we
analyzed the grain boundaries formed during grain growth in
the low temperature regime (1 300 8C) and compared them
with previously published data of the GB morphology taken
from samples processed at 1 425 8C.[13] In the high temperature
regime a high fraction of the GBs is parallel to a 100-type plane
of one of the adjacent grains. The microstructure is dominated
by these facets, as shown in Fig. 2.[14] For an evaluation of the
influence of the GBmorphology on grain growth the GBs have
been classified as ordered flat (A), disordered flat (B), stepped
(C), or curved (D). The first two classes (AþB)were parallel to
a 100-type plane. Despite of the high fraction of GBs with 100
facets, the growth rate is not dominated by the morphology
distribution. In both, Ti-rich and Sr-rich material approxi-
mately 50% of the GBs are of the types A and B but with a
different growth rate.
Experimental
Ceramic powder with a nominal Sr/Ti-ratio of Sr/
Ti¼ 1.005 was prepared by a conventional mixed oxide route.
TiO2 (Sigma–Aldrich, 99.9þ ) and SrCO3 (Sigma–Aldrich
99.9þ ) were attrition milled with 2mm zirconia milling balls
in isopropanol. The powder slurry was dried in a rotary
evaporizer and subsequently in a vacuum furnace at 80 8C for
24 h. After sieving it has been calcined at 975 8C for 6 h in air to
form the perovskite. In order to break up agglomerates
formed during calcination, the powder was milled again in a
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planetary mill, dried and sieved as described above. Green
bodies were prepared by uniaxial pressing of the powder in a
steel die and subsequently cold isostatically pressed at
400MPa. Samples were sintered at 1 300 8C for 10 h in oxygen
and quenched to room temperature after soaking by removing
it from the hot zone of the furnace. Further details on powder
characteristics[15] and sample preparation[12] are published
elsewhere.
TEM plan-view samples were prepared conventionally by
grinding, polishing, and Ar-ion etching. TEM characterization
by means of conventional and high-resolution TEM (CTEM/
HRTEM) imaging as well as selected-area electron diffraction
(SAED) was performed with an aberration-corrected FEI
Titan3 80–300 microscope.
For comparison with the results from the high temperature
sintered ceramics [13], eight grains were aligned with the 100
direction of the crystal parallel to the electron-beam direction
(Figure 3) which gives approximately 50GBs to neighboring
grains with different misorientations and GB-planes. Addi-
tionally four grainswere alignedwith the 110 or 112 directions
parallel to the electron beam (Figure 4).
Results and Discussion
None of the GBs surrounding the grains oriented in 100
direction is aligned parallel to a 100-type (i.e., 010 or 001)
direction (Figure 3 and 5) after sintering at 1 300 8C. Taking the
value of 55% of the GBs being parallel to a 100-type plane in
one of the adjacent grains for ceramics with the same
composition (Sr/Ti¼ 1.005) at 1 425 8C, approximately a
quarter of the GBs should be parallel to this crystallographic
plane if the preference for 100-type planes as GB planes would
be similar at 1 300 and 1425 8C. As pointed out by Saylor
et al.[16] the grain boundary energy can be approximated by
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M. Baurer et al./Linking Grain Boundaries and Grain . . .
Fig. 3. Left-hand side: bright-field TEM micrograph of grain aligned with the 100 direction parallel to the electron beam. Right-hand side: high-resolution TEM images of selectedgrain boundaries of the aligned grain with 100-type (010 and 001) directions marked with white lines.
averaging the energy of the free surfaces of the crystals.
Therefore the GB energy is a function of the orientation of the
GB plane relative to both adjacent grains and only indirectly
linked to the misorientation of the grains. The high frequency
of 100 parallel GB planes inmaterial sintered at 1 425 8C[13] had
been explained with the highly anisotropic surface energy of
SrTiO3 crystals, leading to a minimum in GB energy if the GB
plane is parallel to 100 in one of the grains, the plane with the
lowest surface energy.
The temperature dependence of the surface energy g may
be described by
g ¼ E�TS (2)
where E is the surface enthalpy and S is the surface entropy,[17]
with different values of E and S for every orientation. From
this the very pronounced existence of 100 parallel facets at
Fig. 4. Left-hand side: bright-field TEM micrograph with electron beam aligned parallel toimage of GB in the lower part of the image on the left side.
1232 http://www.aem-journal.com � 2010 WILEY-VCH Verlag GmbH & C
1 425 8C and their absence at 1 300 8C seems counter intuitive
as the total magnitude of the surface energies will be lower at
the higher temperature. A possible explanation is, that with
rising temperature local minima in the GB-energy landscape
flatten out and that therefore the global minima comprising a
100 plane of one of the grains are more likely to reduce the GB
energy despite of enlarging the GB area by faceting (Figure 6).
Possible evidence of the existence of facets parallel to planes
other than 100 are steps on GBs as shown in the bottom part of
Figure 5. This fits well to a study on the faceting behavior of aP
5 bicrystal that showed that the faceting behavior of the
GB changes with rising temperature, loosing facets in this
process.[18]
After these energetical arguments for the existence of
different types of grain boundaries a link to the effective
mobilities of the grain boundaries has to be established. It has
the 112 direction in the grain with dark contrast. Right-hand side: high-magnification
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M. Baurer et al./Linking Grain Boundaries and Grain . . .
Fig. 5. Top right: bright-field TEM image of a grain (with dark contrast) with the 100 direction aligned parallelto electron beam. The grain shows macroscopically curved GBs. Left: magnified images of selected GBs with 100directions marked by white lines. Bottom: GB containing a step.
been shown that the 100 parallel facets in the high temperature
range exhibit a higher mobility than the average grain
boundaries[13] possibly due to the high number of Ti and O
vacancies at such grain boundaries.[19] This is in agreement
with the findings of Sursaeva et al.[20] that a facetted boundary
can move faster than a curved boundary. Despite of this, the
effective mobility is lower at 1 425 8C than at 1 300 8C when
normalized to the thermal energy (Figure 1). From the current
experimental data it is hard to explain this unusual grain
growth behavior. An explanation solely due to the mobility of
Fig. 6. Arbitrary GB energy function for fixed misorientation between neighboring grains and tilt of GB plane aindicates the direction between two triple lines fixing the global direction of the GB. Although the depth of all minminimum at T2. The change in faceting changes the length of the GB. Note that the energy function is not relat
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single facets is not possible because the
behavior of the facets is closely linked to
the surrounding GBs and themobility itself is
hard to access experimentally. A good
possibility to understand the dominant
mechanism is to use grain growth simula-
tions that allow a systematic and indepen-
dent variation of the GB-energy and mobi-
lity-landscape.[21]
Another important point when analyzing
grain boundaries is the possibility that the
identified effects are superposed or even
caused by impurities present in the material.
In the case of perovskites a convenient way
of doing this is to vary the A to B site
stoichiometry of the ceramic, as most impu-
rities have an affinity to occupy either the A-
or B-site of the crystal structure. Experimen-
tally observed effects that occur in both, A-
and B-site rich materials are not related to
impurities. This can be illustrated by the
example of Si4þ in strontium titanate. In the
absence of TiO2 excess and in the case of
SrO-excess Si4þ is incorporated on the Ti-site
as it is close in ionic radius and has the same
charge. By addition of TiO2 it can be expelled
from the lattice to form intergranular films at
GBs[22,23]. In other materials without possi-
bility of changing the cation ratio, the
detection of impurities and their impact
might be much more difficult.
In the case of chemical changes at grain boundaries such as
formation of liquid films, careful control of cooling rate is
necessary as the films can recede during cooling. Again this
possibility is general for all types of materials, but can also be
illustrated in strontium titanate. Waser et al.[24] stated that ‘‘A
TEM investigation of the ceramics did not reveal any
enrichment of TiO2 at the boundary between perovskite
grains’’ and that ‘‘this indicates that the wetting of the grains
recedes during cooling and the TiO2 accumulates in triple
points’’. For a quenched material Stenton and Harmer stated
round an arbitrary direction u for two temperatures T. Red lineima decreases, faceting changes with a preference for the globaled to the crystallography and GB energy of SrTiO3.
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that a crystalline TiO2 phase was present between the grains
after quenching from above the eutectic temperature of
1 440 8C in TiO2 rich material.[25] In the present study,
although the sample was quenched from sintering tempera-
ture, the cooling rate is not as important as the structural
features of the GBs such as the general GB orientation changes
in the timescale of grain growth which is much longer
compared to the overall cooling time.
Conclusions
Grain growth experiments are a convenient way of
selecting samples for further examination in TEM to gain a
better understanding of the influence of structural features of
the grain boundaries on grain growth. In the case of strontium
titanate it has be shown that the faceting behavior of the grain
boundaries is highly different at 1 300 8C compared to 1 425 8C.The high frequency of GB-planes parallel to 100 in one of the
adjacent grains at high temperature does not persist at low
temperature, giving a possible explanation for the significant
reduction in grain growth with rising temperature in SrTiO3.
Received: July 16, 2010
Final Version: August 27, 2010
Published online: November 10, 2010
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