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Acta Materialia 54 (2006) 2849–2855

Effect of oxygen partial pressure on grain boundary structure andgrain growth behavior in BaTiO3

Yang-Il Jung a, Si-Young Choi b, Suk-Joong L. Kang a,*

a Department of Materials Science and Engineering, Korea Advanced Institute of Science and Technology, 373-1 Guseong-dong, Yuseong-gu,

Daejeon 305-701, Republic of Koreab Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH, UK

Received 15 December 2005; received in revised form 14 February 2006; accepted 16 February 2006Available online 18 April 2006

Abstract

The structural transition of grain boundaries in BaTiO3 and related grain growth behaviors have been investigated for a wide range ofoxygen partial pressures ðP O2

Þ. A correlation among P O2, grain boundary structure and grain growth behavior has been found. At

P O2¼ 0:2 atm, all of the grain boundaries were faceted and abnormal grain growth occurred with the assistance of {111} twins as in

previous investigations. As P O2decreased below 10�11 atm the formation of {111} twins was inhibited. At a moderately low P O2

between10�11 and 10�17 atm, grain growth was suppressed, although a small fraction, less than 10%, of the boundary was rough. With anincreased fraction of rough boundaries on reduction of P O2

to 4 · 10�18 atm, abnormal grain growth was observed for the first timein the absence of {111} twins in BaTiO3. Further increases in the rough fraction to �80% changed the growth behavior to normal. Theseobservations show that in BaTiO3, a variety of growth behaviors can result with reduction of P O2

: from abnormal with the assistance of{111} twins, stagnant without {111} twins, abnormal again without {111} twins to normal without {111} twins. The observed differ-ence in growth behavior with P O2

and grain boundary structure has been explained in terms of the change in step free energy and thecritical driving force for appreciable migration of the boundary.� 2006 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Keywords: Barium titanate; Grain growth; Grain boundary

1. Introduction

Since the pioneering work of Burton et al. [1], which pre-dicts surface roughening by temperature increase, roughen-ing transitions of interfaces from faceted to rough havelong been studied theoretically [2–6] as well as experimen-tally [7–12]. It is well documented in the literature thatthe transition is a Kosterlitz–Thouless type [2,3], which ischaracterized by an infinite order phase transition, andweak singularity in surface energy at the roughening tran-sition temperature TR [4,5]. The structural change at thematerial interface can also occur by dopant addition andatmosphere change other than temperature change. A typ-

1359-6454/$30.00 � 2006 Acta Materialia Inc. Published by Elsevier Ltd. All

doi:10.1016/j.actamat.2006.02.025

* Corresponding author. Tel.: +82 42 869 4113; fax: +82 42 869 8920.E-mail addresses: sjkang@kaist.ac.kr, sjkang@mail.kaist.ac.kr (S.-J.L.

Kang).

ical example of the structural transition by changing oxy-gen partial pressure ðP O2

Þ has recently been found in theBaTiO3 system [13,14]. The grain boundaries of BaTiO3

were all faceted in air, while they were all defaceted (rough)in a highly reducing atmosphere [13–16].

When BaTiO3 is sintered below the eutectic tempera-ture, abnormal grain growth (AGG) usually occurs andall of the abnormally grown grains contain {111} twinlamellae [17–19]. A number of investigations suggested that{111} twins were responsible for AGG below the eutectictemperature [17–19]. The {111} twin lamellae having reen-trant edges have been considered to provide preferentialnucleation sites for rapid grain growth along the Æ211ædirections of the {111} twin plane. However, the behaviorof grain growth in BaTiO3 was recently found to alter fromabnormal – highly dependent on {111} twins – to normalas the sintering atmosphere changed from air to hydrogen

rights reserved.

2850 Y.-I. Jung et al. / Acta Materialia 54 (2006) 2849–2855

[13–16]. In a reducing atmosphere (H2), the grain bound-aries of BaTiO3 were rough and normal (continuous) graingrowth occurred irrespective of the presence of {111}twins. This result suggests that the grain growth behavioris closely related to the boundary structure. In fact, a cor-relation between grain boundary structure and growthbehavior has been studied in some metallic as well as cera-mic systems [13,14,20–23]. AGG occurred when the bound-ary was faceted but normal grain growth (NGG) occurredwhen the boundary was rough. In the case of BaTiO3, how-ever, the correlation between grain boundary structure andgrain growth behavior is not clear because of the presenceof {111} twins [17–19]. Recent investigations reported that{11 1} twins did not form in reducing atmospheres withoxygen partial pressure lower than �10�11 atm [24,25].

Our investigation studied the intrinsic effect of facetedboundaries on grain growth in BaTiO3. To observe theeffect, the oxygen partial pressure of the sintering atmo-sphere was systematically changed using CO/CO2 andN2/H2 gases. The systematic change in oxygen partial pres-sure resulted in a gradual transition of grain boundarystructure between faceted and rough, thus showing varietyin growth behavior. It may be possible to provide the prin-ciples and general directions for the fine control ofmicrostructure.

2. Experimental

Samples were prepared from BaTiO3 (HPBT-1,99.8 wt.% purity and 0.64 lm size, Fuji Titanium, Kanag-awa, Japan) with 0.1 mol% excess TiO2 (99.9 wt.% purityand 0.3 lm size, Aldrich, Milwaukee, WI) powder. Theproportioned powder was ball-milled for 24 h in ethanolusing zirconia balls and a polyethylene bottle. The driedslurry was crushed and sieved to 80 lm. The powder waspressed at 2 MPa into disks of 9 mm in diameter and�5 mm thick, and then isostatically compressed at200 MPa. The disks were sintered at 1250 �C for 50 h inatmospheres with various oxygen partial pressures from�0.2 atm (air) to �10�19 atm (H2). For the oxygen partialpressure above �10�14 atm, a mixture of CO and CO2

gases was used. The oxygen partial pressure below�10�15 atm was generated by mixing N2 and H2 gasesusing mass flowmeters.

The sintered disks were vertically cut and polished. Thepolished sections were etched in a 95H2O–4HCl–1HF(vol.%) solution. The microstructures were observed usingscanning electron microscopy (SEM) and transmissionelectron microscopy (TEM; JEM3010, JEOL, Tokyo,Japan) instruments operated at 300 kV. For TEM observa-tion the samples were ultrasonically cut into 3 mm disks,mechanically ground to a thickness of 100 lm, dimpledto a thickness of less than 10 lm and finally ion-milled untilthere was perforation for electron transparency.

The cation segregation at grain boundaries was mea-sured using electron energy loss spectroscopy (EELS) inthe TEM instrument (JEOL JEM-3000F) equipped with

Gatan imaging filter (GIF) using a 1 nm electron probe.At least three different grain boundaries and three differentplaces within bulk grains were measured. The standard forTi/Ba ratio was taken to be 1 in bulk grains. The average,maximum and minimum values were presented as data.

The fraction of faceted grain boundaries was determinedby measuring the length of the facet segments and rounded(rough) segments of grain boundaries. For the measure-ment, more than 200 grain boundaries were examinedusing SEM with a magnification of at least 10,000. Bound-ary lines with a hill-and-valley structure and apparentlystraight boundaries were considered as facet segments,and smoothly curved boundary lines as rough segments.The measurement was qualitatively confirmed by TEMobservation of more than 10 triple junctions for each sam-ple, as in a previous investigation [16].

The average grain size and grain size distribution on atwo-dimensional cross-section were measured by meanferet diameter using an image analysis program (MatroxInspector 2.1). More than 300 grains were examined forthe analysis. The log-normal distribution function wastaken as a measure for differentiation between normaland abnormal growth behavior, since the size distributionof the samples undergoing NGG is best fitted by a log-normal distribution [26,27]. When a log-normal distributionfitted the distribution of all of the grains well, the distribu-tion was considered to be normal. Otherwise, the grainsenclosed within a data-fitted log-normal distribution wereconsidered as matrix grains, and those outstripped fromthe distribution as abnormal grains.

3. Results and discussion

3.1. General growth behavior

The microstructures obtained after sintering at 1250 �C,below the eutectic temperature, were very different depend-ing on the oxygen partial pressure, P O2

, as shown in Fig. 1.In air with P O2

¼ 0:2 atm, large abnormal grains contain-ing {111} double twins formed (Fig. 1(a); the twins areindicated by white arrows). However, at a low P O2

of8 · 10�12 atm, no {111} double twins and no abnormalgrains formed and grain growth hardly occurred(Fig. 1(b)). The parallel strips observed in Fig. 1(b) andalso in Fig. 1(c) are not {111} twins but domain bound-aries formed on cooling during the transformation fromcubic to tetragonal. At a very low P O2

of 9 · 10�20 atm, amoderate grain growth occurred without forming anyapparent abnormal grains (Fig. 1(c)).

It has long been accepted that the abnormal growth ofBaTiO3 grains observed below the eutectic temperature ispossible only with the assistance of {111} double twinsthat provide reentrant edges for easy attachment of atoms,the so-called reentrant edge mechanism [17–19]. Somerecent investigations showed that this role of {111} twinsfor AGG was valid only when the grain boundary wasfaceted [13,14,25]. In our samples free of abnormal grains,

Fig. 1. Microstructures of 0.1 mol%-TiO2-excess BaTiO3 sintered at1250 �C (a) for 10 h under P O2

¼ 0:2 atm (air), (b) for 24 h underP O2¼ 8� 10�12 atm (70CO–30CO2) and (c) for 24 h under

P O2¼ 9� 10�20 atm (H2). The white arrows in (a) indicate {111} twins

present in abnormally large grains.

Y.-I. Jung et al. / Acta Materialia 54 (2006) 2849–2855 2851

no {111} twins are observed. Nevertheless, the growthbehavior strongly depends on the oxygen partial pressure,stagnant grain growth (Fig. 1(b)) and NGG (Fig. 1(c)).This result suggests another possibility of microstructuredevelopment in the absence of {111} twins.

Indeed, Fig. 2 shows various types of microstructures ofBaTiO3 samples in the absence of {111} twins under vari-

ous oxygen partial pressures. Despite the absence of {111}twins in these samples, abnormal grains appear in Figs.2(b) and (c). The shape of the abnormal grains, however,is isotropic, unlike the elongated abnormal grains with{111} twins in Fig. 1(a), because of the absence of {11 1}twins and directional growth. As P O2

decreases, the growthbehavior changes from suppressed (Fig. 2(a)) to abnormal(Figs. 2(b) and (c)) and finally to normal (Fig. 2(d)). Belowthe eutectic temperature, such a variation of grain growthbehavior as well as AGG in the absence of {111} twinshave never been observed before. The observed change ingrain growth behavior with P O2

can be attributed to thechange in boundary structure, as explained in Section 3.3.

3.2. Roughening transition at grain boundaries

Fig. 3 shows typical morphologies of grain boundariesunder different P O2

. The boundaries are all faceted atP O2¼ 0:2 atm (Fig. 3(a)), partially faceted at P O2

¼4� 10�18 atm and mostly rounded at P O2

¼ 9� 10�20

atm. Fig. 4 depicts the variation of the fraction of facetedboundaries as a function of P O2

. The fraction graduallydecreases from 100% to �10% as P O2

decreases from 0.2to �10�19 atm. The gradual decrease of the faceted fractionsuggests that the condition for the structural transitionfrom faceted to rough, i.e. the roughening transition, is dif-ferent from boundary to boundary, similar to the case ofthe surface roughening of a crystal with an orientationeffect. The result in Fig. 4 demonstrates that we can controlthe fraction of faceted boundaries in BaTiO3 polycrystalsvia control of P O2

.The roughening transition at grain boundaries is related

to the step free energy (also called edge energy) of theboundary as it is to that at the surface [6,28–30]. As the stepfree energy decreases, a faceted (atomically ordered)boundary tends to become rough (atomically disordered).In our case of BaTiO3, it is clear that the step free energyof the boundary varies with P O2

and the roughening transi-tion occurs in a range of P O2

.The roughening transition of grain boundaries by reduc-

tion of P O2may be related to a change in chemistry at grain

boundaries. Fig. 5 shows the Ti/Ba ratio measured byEELS analysis for BaTiO3 samples sintered in air and inH2. From this measurement it is evident that Ti is segre-gated at the boundary and the degree of Ti segregation isessentially the same irrespective of the oxygen partial pres-sure. We may therefore conclude that the structural transi-tion is not related to a change in cation segregation at theboundary. The possibility of a cation segregant effect onthe boundary structure is eliminated.

It is well documented in the literature that surfaceroughening can be induced by increasing the vacancy con-centration at the surface as a result of an increased entropycontribution [1,31–34]. Although these results are for thesurface vacancies and surface roughening, a similar rela-tion should hold for grain boundaries. Since the totalvacancy concentration in BaTiO3 increases as oxygen

Fig. 2. Microstructures of 0.1 mol%-TiO2-excess BaTiO3 sintered at 1250 �C for 50 h under P O2of (a) 2 · 10�17 atm (90 N2–10H2), (b) 8 · 10�18 atm

(85N2–15H2), (c) 4 · 10�18 atm (80N2–20H2) and (d) 4 · 10�19 atm (50N2–50H2).

2852 Y.-I. Jung et al. / Acta Materialia 54 (2006) 2849–2855

partial pressure decreases [35], the vacancy concentrationat the boundary should also increase as in the case ofSrTiO3 [34]. According to our EELS analysis for the sam-ples shown in Fig. 5, the O/Ti ratio at the boundary waslower in H2 (2.5 ± 0.5) than in air (3.1 ± 0.1) with the stan-dard being 3.0 in the bulk grains. The boundary roughen-ing in samples under a very low oxygen partial pressuremust, therefore, be due to increased oxygen vacancies atthe boundary and increased entropy contribution.

3.3. Boundary structure-controlled growth behavior

The growth behavior of BaTiO3 grains varies consider-ably with boundary structure as shown in Fig. 6(a) of thetwo-dimensional size distribution. In this figure, the sizedistribution of the samples with {111} twins are notincluded so as to consider only the effect of grain boundarystructure on grain growth behavior. Fig. 6(b) plots the vari-ations of the average size of matrix grains and the size ratioof the largest grain to the average grain with the fraction offaceted boundaries. For the figure, the grains included in alog-normal size distribution were considered to be thematrix grains while others outside the distribution wereconsidered to be abnormal grains. In the samples withthe faceted fraction of 1.0–0.9, the grain size distributionis normal and the average size of grains is �1 lm, a mar-ginal increase in size from the initial powder size of0.64 lm, despite the long sintering time of 50 h. As the frac-

tion of faceted boundaries decreases (in the range 0.8–0.6),abnormally large grains appear and the distributionbecomes bimodal. With further reduction of the facetedfraction, abnormal grains gradually disappear and the sizedistribution becomes normal.

The migration of faceted boundaries has been suggested[36–38] and observed [39–41] to occur via the step growthor the atom shuffle mechanisms. In addition, the migrationvelocity of faceted boundaries was measured to be nonlin-ear to the driving force for migration, showing a drasticincrease in the velocity with an increased driving force[42]. These migration mechanisms and migration behaviorsare similar to those of a faceted single crystal in a liquid,in particular, two-dimensional nucleation and growth[38,43,44]. Fig. 7 depicts a schematic of the relationshipbetween the rate of grain boundary migration and the driv-ing force for the migration, which is similar to that betweencrystal growth rate and its driving force [38,43–45]. Forappreciable migration of a faceted boundary, there is essen-tially a critical driving force, Dgi (i is a subscript in Fig. 7).Similar to the case of the crystal growth, the critical drivingforce must decrease as the step free energy of the boundarydecreases [38].

As the oxygen partial pressure decreases, the fraction offaceted boundaries decreases. This result indicates that thestep free energy of each faceted boundary decreases withoxygen partial pressure reduction. The growth behaviorof BaTiO3 under different oxygen partial pressures can be

Fig. 3. TEM microstructures showing grain boundary morphology of0.1 mol%-TiO2-excess BaTiO3 sintered at 1250 �C for 50 h under P O2

of(a) 0.2 atm, (b) 4 · 10�18 atm and (c) 9 · 10�20 atm. Faceted boundaries,in particular those with a hill-and-valley shape, are indicated by arrows.

10-19

10-18

10-17

10-16

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Fra

ctio

n of

Fac

eted

GB

s

Oxygen Partial Pressure, [atm]

Fig. 4. Fractional variation of faceted grain boundaries of 0.1 mol%-TiO2-excess BaTiO3 sintered at 1250 �C for 50 h with respect to the oxygenpartial pressure.

0.96

1.00

1.04

1.08

1.12

1.16

-100 -50 0 50 100

Distance from Grain Boundary, [nm]

Ti/B

a R

atio

AirH2

Fig. 5. Ti/Ba atomic ratio measured by EELS at grain boundaries and inthe bulk of air-sintered and H2-sintered 0.1 mol%-TiO2-excess BaTiO3

samples.

Y.-I. Jung et al. / Acta Materialia 54 (2006) 2849–2855 2853

explained in terms of the variation of the overall step freeenergy of grain boundaries. Since the initial particle sizeis the same, the driving force for grain growth must be sim-ilar among different samples. The suppression of graingrowth in samples with a high fraction of faceted bound-aries suggests that the maximum driving force for bound-ary migration is below the critical value as is shownschematically in curve H in Fig. 7. In these samples, a high

driving force is needed for the movement of a facetedboundary that has a high step free energy. It appears thatthe movement of faceted boundaries governs the overallgrain growth although a small fraction of boundaries arerough.

As the step free energy decreases and the fraction offaceted boundaries decreases with the reduction of P O2

,the critical driving force decreases as shown in curve Min Fig. 7, and the step growth is promoted. Large grainshaving driving forces larger than the critical value grow fastwhile the growth of other grains having driving forcessmaller than the critical value must be insignificant. As aresult, AGG occurs. In reality, however, migration behav-ior of a boundary with both faceted and rough segmentsshould be complex. The end of a rough segment may pro-vide nucleation steps and can enhance the mobility of alinked faceted segment. It seems that both the promotionof step growth by the reduction of step free energy andthe enhancement of boundary mobility by rougheningtransition are operative in the growth of grains with par-tially rough boundaries. This type of boundary movementvaries from boundary to boundary, and may cause fast

0.10.20.30.40.50.60.70.80.91.00

1

2

3

4

5

6

7

8

9

Fraction of Faceted Grain Boundaries

Nor

mal

ized

Siz

e of

the

Larg

est G

rain

Ave

rage

Siz

e of

Mat

rix G

rain

s, [μ

m]

0

1

2

3

4

5

6

7

8

9

(a)

(b)

0 2 4 6 8 100

5

10

15

20

25

Grain Size, [μm] Fraction of Faceted Boundaries

0.95 0.91 0

.78 0.69 0

.61 0.15

Fraction of Grains, [%

]

Fig. 6. (a) Grain size distributions in samples with different factions offaceted grain boundaries, and (b) variations in average grain size (d) andthe size of the largest grain relative to the matrix grain size (j).

Mig

ratio

n R

ate

Driving Force, Δg

air

ΔgH

L M

air {111}

Δgmax

H VH

ΔgVHΔgL ΔgM

Fig. 7. Schematic showing the relationship between boundary migrationrate and driving force for migration, Dg, for different step free energiesVH, H, M and L. The critical driving force for appreciable migration isdenoted by Dgi. Dgmax denotes the maximum driving force for boundarymigration in the sample. The dotted curve (air {111}) represents themigration rate of a boundary with a {111} twin in air.

2854 Y.-I. Jung et al. / Acta Materialia 54 (2006) 2849–2855

growth of some large grains with high driving forces andsuppressed growth of small grains. However, with a furtherreduction of step free energy as in the case of curve L inFig. 7, the fraction of faceted segments becomes very smalland their contribution to overall boundary movement maynot be significant. Therefore, NGG should result, asobserved in Fig. 2(d).

The critical driving force for boundary migration in thesample sintered in air must be the highest, as curve VHdepicts in Fig. 7, because the step free energy of the bound-ary increases as P O2

increases. No grain growth is expectedin this case because the maximum driving force for bound-ary migration is far below the critical driving force. Never-theless, AGG occurred in the presence of {111} twins.Moreover, the abnormal grains are well faceted and muchlarger than those observed in Figs. 2(b) and (c). This resultindicates that the critical driving force for the growth of thegrains containing {111} twins is below the maximum driv-ing force, as schematically depicted as a dotted curve(air{111}) in Fig. 7, although the critical driving forcefor grains without {111} twins is much larger (curve VHin Fig. 7) than the maximum driving force. This result thusconfirms experimentally that the twin-assisted grain growthmechanism, the so-called twin reentrant edge mechanism[17–19], is operative for AGG in BaTiO3 with well-facetedboundaries.

4. Conclusions

The structural transition of grain boundaries betweenfaceted and rough has been quantified and the resultantgrain growth behavior has been characterized in BaTiO3

by systematically changing oxygen partial pressure. Thegradual decrease in facet fraction with P O2

reduction sug-gests that the roughening transition occurs at different con-ditions from boundary to boundary, similar to the case ofsurface roughening. Grain growth behavior and thus grainboundary structure were very different depending on P O2

.At a high P O2

of 0.2 atm, {111} twins formed and {11 1}twin-assisted AGG occurred. As P O2

decreased, the forma-tion of {111} twins was suppressed and a fraction of fac-eted boundaries became rough. When P O2

was between10�11 and 10�17 atm, no {111} twins formed and a smallfraction of boundaries were defaceted. In these samplesgrain growth was suppressed showing stagnant graingrowth behavior. Further reduction of P O2

changed thegrowth behavior from stagnant to abnormal in the absenceof {111} twins. These changes in growth behavior fromabnormal in the presence of {111} twins to stagnant toabnormal in the absence of {111} twins confirm experi-mentally the twin reentrant edge mechanism for AGG.When P O2

was very low and a considerable fraction ofboundaries was defaceted, the growth behavior wasnormal.

Since the fraction of rough boundaries increased withP O2

reduction, the step free energy of the boundarydecreased with P O2

reduction. The observed change in

Y.-I. Jung et al. / Acta Materialia 54 (2006) 2849–2855 2855

growth behavior can be explained in terms of the step freeenergy change and nonlinear mobility of grain boundarieswith driving force. It appears that the growth behavior in asingle-phase system can also be explained by consideringthe step growth mechanism of grain boundary migration,similar to the two-dimensional nucleation and growth ofa single crystal from a solution.

Acknowledgments

This research was supported by a grant (Code No.05K1501-01210) from the Center for NanostructuredMaterials Technology under ‘21st Century Frontier R&DPrograms’ of the Ministry of Science and Technology,Korea, and also by the Air Force Office of ScientificResearch, USA (Grant Contract No. AOARD-05-4065).

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