J O U R NA L O F M AT E R I A L S S C I E N C E L E T T E R S 1 8 ( 1 9 9 9 ) 1 6 3 ± 1 6 5

Grain growth of BaTiO3

E. T. PARKEnergy Technology Division, Argonne National Laboratory, Argonne, IL 60439, USA

The perovskite oxide BaTiO3 is a ferroelectric whoseelectrical properties have been studied extensivelybecause of its many technical applications, as sen-sors, transducers, and actuators [1±13], for example.The technological importance of BaTiO3 has beendemonstrated repeatedly, and its physical propertiesin ceramic form have been thoroughly investigated.Knowledge of high-temperature processes, such ascreep, sintering, and grain growth is very importantin optimizing processing to achieve satisfactoryproperties.

The purpose of this letter is to investigate thegrain growth of BaTiO3 and to compare results withthose of high-temperature creep tests [14±16]. Theactivation energy value of 720 � 70 kJ molÿ1,measured for coarse-grained BaTiO3 [14], agreeswell with the value of �800 kJ molÿ1 determined ina higher-stress region in superplastic ¯ow of ®ne-grained BaTiO3 [15]. However, creep for BaTiO3

single crystals [16] oriented to glide on {0 0 1}planes showed an activation energy of469� 27 kJ molÿ1. The activation energy for creepshows a disparity among the tests. Therefore, grain-growth studies can help to clarify the interpretationof creep results.

Sintering has been viewed as occurring in threestages: an initial, intermediate, and ®nal stage [17±19]. According to Coble's model [19], in the initialstage, surface roughness decreases and the inter-particle contact area increases by neck growth. Theintermediate stage is characterized by continuousgrowth of grains that are coincident with three-grainedges. During the ®nal stages of sintering, inaddition to the elimination of pores, a generalcoarsening of the microstructure by grain growthoccurs. Controlling and understanding the processesthat lead to grain growth are important for tworeasons. The ®rst is related to the fact that grain sizeis a major factor that determines many of themechanical, electrical, magnetic, and optical proper-ties of ceramics. The second is related to suppressingwhat is known as abnormal grain growth, which isthe process whereby a small number of grains growvery rapidly to a size that is more than an order ofmagnitude larger than the average size. In addition

to the detrimental effect that the large grains have onmechanical properties, the walls of these large grainscan pull away from pores, leaving them trappedwithin, which in turn limits the possibility ofobtaining theoretical densities in reasonable times.

The phenomenological kinetic grain-growth equa-tion [20] is given by:

Ga ÿ Ga0 � K0 t exp ÿ Q

RT

� �(1)

where G is the average grain size at time t, G0 theinitial grain size, a the kinetic grain-growthexponent, K0 a preexponential constant, and Q theapparent activation energy for grain growth. WhenG0 is signi®cantly smaller than G, Ga

0 can beneglected relative to Ga. The grain-growth exponentis then readily determined as the inverse of the slopeof a log G versus log t plot. The activation energiesfor the grain growth can be determined from theslopes of the Arrhenius plots of log (Ga=t) versus1=T .

High-density polycrystalline BaTiO3 specimenswere prepared from reagent-grade BaTiO3 powder,having an average particle size of 1.1 ìm (JohnsonMatthey, 99.9%). The powders were isostaticallypressed into rectangular bars at a pressure of�200 MPa for 5 min. To obtain microstructures ofvarious grain size, the resulting compacts were thensintered at 1250±1400 8C for times ranging from 0.5to 52 h in ¯owing O2 or air, with a heating rate of200 8C hÿ1 and a cooling rate of 60 8C hÿ1.

Sample surfaces were polished to achieve amirrorlike surface ®nish that contained only a fewwell-dispersed, very ®ne pores. Samples were etchedin dilute HNO3 and HF solution for �15 s. Themean grain size of etched samples was measured bythe linear-intercept method (Table I). The grain sizeincreased with increasing sintering temperature andtime. The grains were uniform in size and shape.Sample densities were approximately equal for dif-ferent sintering temperatures and times. Fig. 1 showsthe microstructures having the smallest- and largest-

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The submitted manuscript has been created by the Univeristy of

Chicago as Operator of Argonne National Laboratory (`̀ Argonne'')

under Contract No. W-31-109-ENG-38 with the US Department of

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its behalf, a paid-up, nonexclusive, irrevocable worldwide license

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TABLE I Average linear-intercept grain size (ìm) of sintered

BaTiO3 specimens as a function of sintering temperature and time

1320 8C 1340 8C 1360 8C 1400 8C

0.5 h 19:3� 1:62 h 30:9� 2:2 35:6� 2:4 52:4� 4:4 53:0� 2:9

12 h 43:3� 3:552 h 46:5� 1:6

163

grain-sized specimen sintered at 1320 8C and1400 8C for 2 h, respectively.

The grain-growth exponent, a, was determined asthe inverse of the slope of log G versus log t plot atconstant sintering temperature:

a � @ ln G

@ ln t

� �ÿ1

� ln G2=G1

ln t2=t1

� �ÿ1

T

(2)

Fig. 2 shows the average grain size as a function ofsintering time for sintering at 1320 8C. The slope ofthe plot of log G versus log t is 0.20 � 0.02. Thus,the grain-growth exponent, a from Equation 2, is�5. The parameter, a, even if a constant value isobserved over a wide temperature and grain sizerange, does not indicate a speci®c mechanism [20].

Assuming that the grain-growth exponent of 5 isindependent of temperature, it can be used todetermine the activation energy for BaTiO3 graingrowth, which can be determined from the slope ofan Arrhenius plot of log (Ga=t) versus 1=T atconstant sintering times:

Q � ÿR@ ln Ga

@1=T� ÿR

ln Ga2=Ga

1

1=T2 ÿ 1=T1

� �t

(3)

An Arrhenius plot is shown in Fig. 3 for samplessintered between 1320±1400 8C. The activationenergy for BaTiO3 grain growth is 750 �

80 kJ molÿ1. This value agrees with the value of720� 70 kJ molÿ1, measured in recent high-tem-perature creep tests of our grain-growth samples [14]and with the value of �800 kJ molÿ1 determined insuperplastic ¯ow of ®ne-grained BaTiO3 [15]. Theagreement between activation energy measured ingrain growth, creep [14], and superplastic ¯ow [15]of BaTiO3 suggests that the same diffusing speciescontrols these processes. The value of the activationenergy reported for the deformation of single-crystalBaTiO3, 469� 27 kJ molÿ1 [16], is much lower thanthat found for the polycrystalline grain growthresults reported here and the creep results [14].Although Beauchesne and Poirier [16] observed thatclimb was active, it may not have been the rate-controlling step. If creep was glide-controlled, theactivation energy could be lower than the activationenergy observed for diffusional creep of polycrystal-line BaTiO3, which is equal to self-diffusionactivation energy [21].

Grain-growth results of BaTiO3 strongly supportthe polycrystalline creep data and indicate theactivation energy in single crystals was not diffu-sion-controlled. Of course, cation tracer diffusionstudies would be de®nitive, but such studies have notbeen performed.

Figure 1 Microstructure of polycrystalline BaTiO3 sintered at: (a)

1320 8C for 0.5 h; (b) 1400 8C for 2 h.

100

100.1 1 10 100

Sintering Time (h)

Gra

in S

ize

(µm

)

Figure 2 Log G (grain size) vs. log t (sintering time) for samples

sintered at 1320 8C.

109

108

107

5.9 6.0 6.1 6.2 6.3

10000/T (1/K)

GS

5 /t (

µm5 /

h)

Figure 3 Log (G5=t) vs. 1=T Arrhenius for samples sintered at 1320,

1340, 1360, and 1400 8C for 2 h.

164

AcknowledgmentsKen Goretta and Jules Routbort are thanked forhelpful discussions. This work was supported by theUS Department of Energy, under Contract W-31-109-Eng-38.

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Received 5 Apriland accepted 15 May 1998

165