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2TiO3-BaTiO3 grains in single and two-step sintering
Journal of the European Ceramic Society 36 (2016) 1159–1165
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Growth behavior of faceted Na1/2 Bi1/2 TiO3 -BaTiO3 grains in single and two-step sintering Seok-Young Ko a , Suk-Joong L. Kang a,b,∗ a Materials Interface Laboratory, Department of Materials Science and Engineering, Korea Advanced Institute of Science and Technology, Daejeon 305-701, Republic of Korea b Korea Institute of Ceramic Engineering and Technology, Jinju 660-031, Republic of Korea
a r t i c l e
i n f o
Article history: Received 24 September 2015 Received in revised form 24 November 2015 Accepted 26 November 2015 Available online 14 December 2015 Keywords: Grain growth behavior Grain shape Mixed control model Two-step sintering Microstructure evolution
a b s t r a c t The grain growth behavior in the 89Na1/2 Bi1/2 TiO3 -11BaTiO3 system has been studied at 1100 and 1200 ◦ C, and under two-step sintering at these two temperatures. When the powder compacts were sintered at 1100 and 1200 ◦ C, the growth behavior was distinctively abnormal and moderately abnormal, respectively. The difference can be explained in terms of the coupling effect between the maximum driving force for the growth of the largest grain and the critical driving force for appreciable migration of the grain boundary. In two-step sintering, abnormal grain growth was suppressed in the second step at 1100 ◦ C. This beneficial effect of two-step sintering for grain growth suppression is found to be the result of a grain size distribution right after the first sintering step narrower than that of the sample conventionally sintered at 1100 ◦ C. These results of single and two-step sintering support the general applicability of the principle of microstructural evolution. © 2015 Elsevier Ltd. All rights reserved.
1. Introduction Thermal treatment, including sintering, of ceramics is often accompanied by rapid growth of grains or a change in the relative grain size distribution. In particular, abnormal grain growth (AGG), which is typified by a bimodal distribution of grain sizes, is a result of fast growth of only a small number of grains. Several mechanisms related to a disturbance of boundary migration, including second phase particle drag [1,2], solute drag [3,4], liquid film enhancement [5–7] and interface energy and mobility anisotropy [8,9] have been proposed to explain AGG. A common feature of these mechanisms is that the migration of the interface is governed by the diffusion of atoms across the boundary or a matrix. None of the mechanisms, however, can commonly explain AGG observed in many different systems. Several thermal treatment techniques, including fast firing [10,11], rate-controlled sintering [12,13] and two-step sintering [14,15] have also been developed for suppressing grain growth, including AGG. Among these techniques, the two-step sintering
∗ Corresponding author at: Department of Materials Science and Engineering, Korea Advanced Institute of Science and Technology, Daejeon 305-701, Republic of Korea/Korea Institute of Ceramic Engineering and Technology, Jinju 660-031, Republic of Korea. Fax: +82 42 350 8920. E-mail address: [email protected] (S.-J.L. Kang). http://dx.doi.org/10.1016/j.jeurceramsoc.2015.11.035 0955-2219/© 2015 Elsevier Ltd. All rights reserved.
technique developed by Chen and Wang [14] where a powder compact is sintered stepwise, held for a short period of time at a temperature higher than the conventional sintering temperature, and cooled rapidly to and sintered at a lower temperature, has been reported to be effective in suppressing grain growth in solid-state [14–17] as well as in liquid-phase sintering [18–20]. The cause of grain growth suppression by two-step sintering, however, remains unclear. Chen and Wang [14] reported that the suppression of grain growth in two-step sintering was due to an extension of the intermediate stage of sintering without a final stage. They suggested that this lack of final stage grain growth was achievable by exploiting the difference in kinetics between grain boundary diffusion and grain boundary migration. Lee et al. [18] and Duran et al. [19] suggested that the difference in the mobility of the grain boundary in the presence and in the absence of a liquid film at high and low temperature was the cause of the suppression of grain growth in two-step liquidphase sintering. Recently, Yang et al. [20] also observed suppression of grain coarsening in sub-micron WC-Co by two-step liquid-phase sintering. Based on the measured grain size distribution and grain coarsening calculation, they suggested the cause of AGG suppression in two-step sintering is a reduction of the maximum driving force, gmax , for the largest grain in the sample immediately after the first sintering step compared with that in the sample of the same average grain size in the conventional sintering.
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While normal grain growth (NGG) occurs in systems with rough interfaces, non-normal grain growth is observed to occur in systems with faceted interfaces [21–50]. For rounded grains with an atomically disordered surface and a huge number of surface defects, the growth of grains is controlled by diffusion because atoms can easily attach to any sites on the surface. For faceted grains with an atomically ordered surface, however, grain growth is governed either by the interface reaction or diffusion [21,22,32,51–54]. A similar conclusion was also found to be valid for the grain boundary [55–58]. From these previous studies, a mixed control model of grain growth was developed and the principle of microstructural evolution was deduced [53,58–60]. According to the microstructural evolution principle, various types of grain growth behavior can appear as a result of the coupling effect between the maximum driving force for the growth of the largest grain in the sample (gmax ) and the critical driving force for appreciable migration of the boundary (gc ). Repetitive grain growth behavior observed in a nano-sized pure nickel system was also consistently explained in the framework of the principle [61]. The purpose of this study is to understand grain growth behavior during conventional as well as two-step sintering of powder compacts with faceted grains. We considered a 89Na1/2 Bi1/2 TiO3 11BaTiO3 system with faceted grains of which the shape changes appreciably with temperature. This system also has technological importance as it is a candidate for lead-free piezoelectric materials. The observed variation of the grain growth behavior with temperature and two-step sintering is explained well by the principle of microstructural evolution. It appears that the grain growth suppression in two-step sintering is due to a change in the grain size distribution after the first sintering step. The results of the present study thus support the generality of our principle of curvaturedriven microstructural evolution in polycrystalline materials.
Fig. 1. SEM micrograph and measured particle size distribution of the synthesized 89Na1/2 Bi1/2 TiO3 -11BaTiO3 powder.
Fig. 2. Schematic of the thermal cycle of two-step sintering.
2. Experimental procedure Ceramic samples of a 89Na1/2 Bi1/2 TiO3 -11BaTiO3 composition (mol%, NBT-11BT) were prepared by the conventional ceramic fabrication process from commercial powders of Na2 CO3 (Acros Organics, NJ, USA), Bi2 O3 (Kojundo Chemical Lab Co., Saitama, Japan), BaCO3 and TiO2 (Sigma–Aldrich, St. Louis, USA). Prior to mixing the powders, each raw powder was dried in an oven at 80 ◦ C for 24 h to eliminate any adsorbed moisture. The proportioned powder was ball-milled in a polyethylene bottle for 24 h using zirconia balls and high purity ethanol. The slurry was dried on a hotplate using a magnetic stirrer and then in an oven at 80 ◦ C for 48 h. The dried slurry was crushed and sieved using a 100-mesh sieve. The powder was calcined in an alumina crucible at 800 ◦ C for 4 h in air. The calcined powder was ball-milled, dried, and sieved. The X-ray diffraction of the calcined powder showed that the powder consisted of a single perovskite phase in the detection limit of XRD. The particle size distribution of the produced powder was measured from SEM micrographs of the powder using an image analysis program (Matrox Inspector 2.1, Matrox Electronic Systems, Ltd., Canada). The particle size distribution of the powder was unimodal and the average size was 0.21 m, as shown in Fig. 1. The powder was compacted into pellets of 12 mm diameter and ∼4 mm thickness, and then cold isostatically compressed at 200 MPa for 5 min. The compacts were placed on a Pt plate in an alumina crucible with a lid and sintered at 1100 or 1200 ◦ C in air for various times. The heating rate and cooling rate for sintering were respectively 4 K/min. In the case of the two-step sintering experiment, the compacts were heated to 1200 ◦ C, immediately cooled to 1100 ◦ C at a rate of 10 K/min upon reaching 1200 ◦ C, and then held at 1100 ◦ C for various times, as schematically shown in Fig. 2.
The crystal structure was identified using X-ray powder diffraction with CuK␣ radiation (D/MAX-RB (12KW), RIGAKU, Japan). For microstructure observation, the sintered samples were cut, polished to a 0.25 m finish, and thermally etched at 950 ◦ C for 15–20 min. Grain size distributions were measured from SEM images using an image analysis program (Matrox Inspector 2.1). At least 300 grains were examined to determine the grain size distribution. The relative density of the samples was measured by the Archimedes method taking the theoretical value of 5.91 g/cm3 , which was obtained from the X-ray diffraction data. For each condition, at least three samples were prepared and measured, and their average value was presented as the measured data. 3. Results and discussion 3.1. Grain shape and grain growth behavior at different temperatures During sintering of powder compacts, considerable grain growth took place, as shown in Figs. 3 and 4. At the beginning of the sintering at 1100 ◦ C, however, the sample is quite porous with a relative density of 86% and the grains did not grow substantially, as shown in Fig. 3(a). The average grain size after 10 min sintering was 0.24 m, quite similar to the average initial powder size. During sintering for 1 h (Fig. 3(b)), however, rapid grain growth occurred with densification, showing an average grain size of 0.57 m. This result indicates that with reduction of the drag force of the pores, many grains grew rapidly within 50 min. During extended sintering, only a small number of abnormal grains started to form and their size increased with an increase of the sintering time. The size of the
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Fig. 3. SEM micrographs of 89Na1/2 Bi1/2 TiO3 -11BaTiO3 samples sintered at 1100 ◦ C for (a) 10 min, (b) 1 h, (c) 2 h, (d) 4 h, and (e) 10 h. (f) The measured grain size distributions of different samples. (The sizes of the largest abnormal grain in the samples sintered for 4 and 10 h were over 30 m and 40 m, respectively.)
largest abnormal grain after 10 h of sintering exceeded 40 m. Note that the average grain size of the matrix grains with a lognormal distribution of 0.69 m in the sample sintered for 10 h is not very different from that in the sample sintered for 1 h. In contrast, at 1200 ◦ C, densification and grain growth occurred rapidly from the beginning. After sintering for 10 min (Fig. 4(a)), the relative density was 98% and the average grain size was 0.62 m. After initial rapid grain growth, grain growth appeared to occur slowly and the grain size distribution broadened. Apparently abnormal grain growth took place after sintering of several hours and the size of
abnormal grains, less than 10 m after sintering of 10 h, is much smaller than that observed at 1100 ◦ C. Fig. 5 shows the XRD patterns of the NBT-11BT samples sintered at 1100 and 1200 ◦ C for 4 h. All the peaks of these samples correspond to the standard diffraction peaks of a tetragonal phase, showing no difference in the crystalline phase between the samples sintered at different temperatures. This implies that the difference in microstructural evolution at the two different temperatures, 1100 and 1200 ◦ C, is not related to a potential difference in the crystalline phase. Instead, the shape of grains is different for samples
Fig. 4. SEM micrographs of 89Na1/2 Bi1/2 TiO3 -11BaTiO3 samples sintered at 1200 ◦ C for (a) 10 min, (b) 1 h, (c) 2 h, (d) 4 h, and (e) 10 h. (f) The measured grain size distributions of different samples. (The size of the largest abnormal grain in the sample sintered for 10 h was less than 10 m.)
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Fig. 5. X-ray diffraction patterns of 89Na1/2 Bi1/2 TiO3 -11BaTiO3 samples sintered at 1100 and 1200 ◦ C for 4 h.
Fig. 6. SEM micrographs showing 3-dimensional shapes of grains after annealing at (a) 1100 and (b) 1200 ◦ C for 4 h.
sintered at different temperatures, as shown in Fig. 6, which was obtained after annealing the calcined powder at 1100 and 1200 ◦ C for 4 h in air. At 1100 ◦ C, the grain shape is a well faceted cube with insignificant edge and corner facets, indicating a high anisotropy in surface energy. Moon et al. [37] reported that the facet planes are {1 0 0} planes. At 1200 ◦ C, however, the area fraction of {1 0 0} facets is reduced and facets of several different crystallographic planes appear. Considering the cube of {1 0 0} facets, the planes at the cube edges are {1 1 0} and those at the cube corners are {1 1 1}. The observed change in grain shape indicates that the surface energy anisotropy is reduced and the step free energy of {1 0 0} facets is also reduced with an increase in temperature from 1100 to 1200 ◦ C. According to previous investigations, the migration of faceted grain boundaries [53,54,57,58] or solid/liquid interfaces [51,52,54,59] is governed either by the interface reaction (attachment) or diffusion of atoms for a driving force smaller or larger, respectively, than a critical value, showing nonlinear migration behavior, as schematically illustrates in Fig. 7. The critical driving force, gc, for appreciable migration is governed by the step free energy of the boundary or the surface [51,53,54,59,62]. Based on the nonlinear migration behavior of the faceted interface, the principle of microstructural evolution was deduced as the coupling effect of gmax and gc [53,58–60]. According to the principle, different types of grain growth behavior manifest at the time of observation, depending on the value of gmax relative to gc : stagnant grain growth for gc > gmax , abnormal grain growth for gc ≤ gmax , pseudo-normal grain growth for 0 < gc gmax , and normal grain growth for gc = 0. This prediction has been supported by many investigations on metals as well as ceramics with or without a liquid matrix [20–50,55,56,61].
The rapid growth of grains in 1 h at 1100 ◦ C implies that the number of grains exceeding gc,1100 ◦ C was large and they grew rapidly (pseudo-normal growth in a fine matrix) and impinged upon each other. The formation of abnormal grains in samples sintered for 2 h suggests that the driving force for the largest grain after impingement of grains is comparable with the critical driving force for appreciable migration of the boundary (Fig. 7). Only a small number of grains can grow further and become abnormal grains, as shown in Fig. 3. If we accept the mean field concept, we can estimate the maximum driving force in a sample from the measured grain size distribution, as in a previous investigation [61], using the following equation: gmax = 4
1 ¯ G
−
1 Gmax
␥b
(1)
¯ is the average grain size, Gmax is the size of the largest grain, Here, G and b is the grain boundary energy. Taking b to be 0.5 J m−2 and considering the measured average particle and grain size distribution in Figs. 1 and 3(f), gmax estimated at the beginning (gmax I ) and after sintering of 1 h at 1100 ◦ C (gmax II ) is 5.0 × 106 J m−3 and 2.7 × 106 J m−3 , respectively, as shown in Fig. 7. With an increase in temperature from 1100 to 1200 ◦ C the growth rate of grains increases considerably while the critical driving force decreases because of a reduction of the step free energy with an increase in temperature [53,54,59,61]. As gmax is much larger than gc , grain growth occurs rapidly from the early stage of sintering, exhibiting pseudo-normal growth behavior, and the maximum driving force decreases with grain growth. During extended sintering, however, several apparently large grains appear, as a result of the reduction of gmax with grain growth, as shown in Fig. 4. The estimated maximum driving force, gmax III , in the sample sintered at 1200 ◦ C for 10 min
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fgr8
Fig. 7. Schematic representation of the growth rates with respect to the driving force together with the critical driving forces at 1100 and 1200 ◦ C, and the maximum driving forces. gmaxI is for the synthesized powder. gmax II and gmax III are for the samples sintered at 1100 ◦ C for 1 h and at 1200 ◦ C for 10 min, respectively. The maximum driving forces were estimated from the measured grain size distributions. The mean field concept was adopted and a constant grain boundary energy of 0.5 J/m2 was assumed.
Fig. 8. SEM micrographs of 89Na1/2 Bi1/2 TiO3 -11BaTiO3 samples two-step sintered at 1200 ◦ C for 0 h and at 1100 ◦ C for (a) 1 h, (b) 2 h, (c) 4 h, (d) 10 h. (e) The measured grain size distributions of different samples.
is indicated in Fig. 7. As apparently abnormal grains appear to form between 4 and 10 h of sintering (Fig. 4), the critical driving force at this temperature (gc, 1200 ◦ C ) can also be estimated from the grain size distribution after 4 h. The estimated value is 1.5 × 106 J m−3 and is depicted in Fig. 7. Such a change in the grain growth behavior from pseudo-normal to abnormal was also observed in a 95NBT-5BT system with round-edged cube grains [37].
3.2. Effect of two-step sintering Two-step sintering of NBT-11BT has been performed in an attempt to suppress grain growth, in particular abnormal grain growth, and also to reveal the cause of grain growth suppression in this system. Fig. 8(a)–(d) is micrographs obtained after two-step sintering with the first step at 1200 ◦ C for 0 h and the second step at 1100 ◦ C for various times. Fig. 8(e) plots the measured grain size distributions of the samples in Fig. 8(a)–(d). During the first sin-
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growth of many grains at a temperature higher than the conventional sintering temperature appears to reduce the broadening of the grain size distribution compared with the change in the grain size distribution in conventional sintering, as previously calculated for a two-phase system [20]. 4. Conclusions Grain growth behavior in 89Na1/2 Bi1/2 TiO3 -11BaTiO3 was studied at 1100 and 1200 ◦ C, and also under two-step sintering at these two temperatures. At the low temperature, distinctive abnormal grain growth was observed after the initial growth of many grains. At the high temperature, the grain growth behavior was quite normal, followed by indistinctive abnormal grain growth behavior. The grain growth behavior at the two different temperatures, including the differences, can be explained in terms of the coupling effect of the maximum driving force for the growth of the largest grain and the critical driving force for appreciable migration of the grain boundary. The two-step sintering at 1200 and 1100 ◦ C suppressed further growth of grains after the first sintering step at 1200 ◦ C. From the measured grain size distributions of the two-step sintered and conventionally sintered samples, it was found that the beneficial effect of two-step sintering for grain growth suppression is related to a narrower grain size distribution than that of the conventionally sintered sample, and hence a reduction of the maximum driving force for the growth of the largest grain. Our experimental results of conventional and two-step sintering support the general applicability of the recently deduced principle of microstructural evolution in polycrystals [53,59,60] to understanding grain growth in polycrystalline materials. Acknowledgements
Fig. 9. (a) Grain size distributions and the estimated maximum driving forces in the sample conventionally sintered at 1100 ◦ C for 1 h and that in the sample immediately after the first sintering step at 1200 ◦ C for 0 h. (b) Schematic showing the growth rate of grains together with the maximum driving forces in the two different samples in (a).
tering step, grains growth took place rapidly, similar to the case of the conventional sintering at 1200 ◦ C. However, as the temperature was decreased to 1100 ◦ C after the first sintering step, no significant grain growth occurred at 1100 ◦ C during the second sintering step and no apparent abnormal grains formed even after sintering of 10 h, unlike in the case of the conventional sintering at 1100 ◦ C (Fig. 3). This observation shows the beneficial effect of the twostep sintering in the NBT-BT system for suppressing grain growth, including AGG. The measured grain size distributions of the sample conventionally sintered at 1100 ◦ C for 1 h and that first-step sintered at 1200 ◦ C for 0 h are shown in Fig. 9(a). Although the average grain sizes are similar, 0.57 m for the conventional sintering case and 0.60 m for the two-step sintering case, the grain size distributions are quite different from each other. The grain size distribution in the first-step sintered sample is much narrower than that in the conventionally sintered sample at 1100 ◦ C. The estimated gmax from the measured grain size distribution of the sample immediately after the first sintering step is 2.1 × 106 J m−3 . This value is distinctly smaller than that (2.7 × 106 J m−3 ) in the sample conventionally sintered at 1100 ◦ C for 1 h and the estimated critical driving force for appreciable migration of the boundary at 1100 ◦ C, as schematically shown in Fig. 9(b). Our experimental observations and estimation indicate that the beneficial effect of two-step sintering for grain growth suppression is related to a change in the grain size distribution and a reduction of gmax below gc . Rapid
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Journal of the European Ceramic Society journal homepage: www.elsevier.com/locate/jeurceramsoc
Growth behavior of faceted Na1/2 Bi1/2 TiO3 -BaTiO3 grains in single and two-step sintering Seok-Young Ko a , Suk-Joong L. Kang a,b,∗ a Materials Interface Laboratory, Department of Materials Science and Engineering, Korea Advanced Institute of Science and Technology, Daejeon 305-701, Republic of Korea b Korea Institute of Ceramic Engineering and Technology, Jinju 660-031, Republic of Korea
a r t i c l e
i n f o
Article history: Received 24 September 2015 Received in revised form 24 November 2015 Accepted 26 November 2015 Available online 14 December 2015 Keywords: Grain growth behavior Grain shape Mixed control model Two-step sintering Microstructure evolution
a b s t r a c t The grain growth behavior in the 89Na1/2 Bi1/2 TiO3 -11BaTiO3 system has been studied at 1100 and 1200 ◦ C, and under two-step sintering at these two temperatures. When the powder compacts were sintered at 1100 and 1200 ◦ C, the growth behavior was distinctively abnormal and moderately abnormal, respectively. The difference can be explained in terms of the coupling effect between the maximum driving force for the growth of the largest grain and the critical driving force for appreciable migration of the grain boundary. In two-step sintering, abnormal grain growth was suppressed in the second step at 1100 ◦ C. This beneficial effect of two-step sintering for grain growth suppression is found to be the result of a grain size distribution right after the first sintering step narrower than that of the sample conventionally sintered at 1100 ◦ C. These results of single and two-step sintering support the general applicability of the principle of microstructural evolution. © 2015 Elsevier Ltd. All rights reserved.
1. Introduction Thermal treatment, including sintering, of ceramics is often accompanied by rapid growth of grains or a change in the relative grain size distribution. In particular, abnormal grain growth (AGG), which is typified by a bimodal distribution of grain sizes, is a result of fast growth of only a small number of grains. Several mechanisms related to a disturbance of boundary migration, including second phase particle drag [1,2], solute drag [3,4], liquid film enhancement [5–7] and interface energy and mobility anisotropy [8,9] have been proposed to explain AGG. A common feature of these mechanisms is that the migration of the interface is governed by the diffusion of atoms across the boundary or a matrix. None of the mechanisms, however, can commonly explain AGG observed in many different systems. Several thermal treatment techniques, including fast firing [10,11], rate-controlled sintering [12,13] and two-step sintering [14,15] have also been developed for suppressing grain growth, including AGG. Among these techniques, the two-step sintering
∗ Corresponding author at: Department of Materials Science and Engineering, Korea Advanced Institute of Science and Technology, Daejeon 305-701, Republic of Korea/Korea Institute of Ceramic Engineering and Technology, Jinju 660-031, Republic of Korea. Fax: +82 42 350 8920. E-mail address: [email protected] (S.-J.L. Kang). http://dx.doi.org/10.1016/j.jeurceramsoc.2015.11.035 0955-2219/© 2015 Elsevier Ltd. All rights reserved.
technique developed by Chen and Wang [14] where a powder compact is sintered stepwise, held for a short period of time at a temperature higher than the conventional sintering temperature, and cooled rapidly to and sintered at a lower temperature, has been reported to be effective in suppressing grain growth in solid-state [14–17] as well as in liquid-phase sintering [18–20]. The cause of grain growth suppression by two-step sintering, however, remains unclear. Chen and Wang [14] reported that the suppression of grain growth in two-step sintering was due to an extension of the intermediate stage of sintering without a final stage. They suggested that this lack of final stage grain growth was achievable by exploiting the difference in kinetics between grain boundary diffusion and grain boundary migration. Lee et al. [18] and Duran et al. [19] suggested that the difference in the mobility of the grain boundary in the presence and in the absence of a liquid film at high and low temperature was the cause of the suppression of grain growth in two-step liquidphase sintering. Recently, Yang et al. [20] also observed suppression of grain coarsening in sub-micron WC-Co by two-step liquid-phase sintering. Based on the measured grain size distribution and grain coarsening calculation, they suggested the cause of AGG suppression in two-step sintering is a reduction of the maximum driving force, gmax , for the largest grain in the sample immediately after the first sintering step compared with that in the sample of the same average grain size in the conventional sintering.
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While normal grain growth (NGG) occurs in systems with rough interfaces, non-normal grain growth is observed to occur in systems with faceted interfaces [21–50]. For rounded grains with an atomically disordered surface and a huge number of surface defects, the growth of grains is controlled by diffusion because atoms can easily attach to any sites on the surface. For faceted grains with an atomically ordered surface, however, grain growth is governed either by the interface reaction or diffusion [21,22,32,51–54]. A similar conclusion was also found to be valid for the grain boundary [55–58]. From these previous studies, a mixed control model of grain growth was developed and the principle of microstructural evolution was deduced [53,58–60]. According to the microstructural evolution principle, various types of grain growth behavior can appear as a result of the coupling effect between the maximum driving force for the growth of the largest grain in the sample (gmax ) and the critical driving force for appreciable migration of the boundary (gc ). Repetitive grain growth behavior observed in a nano-sized pure nickel system was also consistently explained in the framework of the principle [61]. The purpose of this study is to understand grain growth behavior during conventional as well as two-step sintering of powder compacts with faceted grains. We considered a 89Na1/2 Bi1/2 TiO3 11BaTiO3 system with faceted grains of which the shape changes appreciably with temperature. This system also has technological importance as it is a candidate for lead-free piezoelectric materials. The observed variation of the grain growth behavior with temperature and two-step sintering is explained well by the principle of microstructural evolution. It appears that the grain growth suppression in two-step sintering is due to a change in the grain size distribution after the first sintering step. The results of the present study thus support the generality of our principle of curvaturedriven microstructural evolution in polycrystalline materials.
Fig. 1. SEM micrograph and measured particle size distribution of the synthesized 89Na1/2 Bi1/2 TiO3 -11BaTiO3 powder.
Fig. 2. Schematic of the thermal cycle of two-step sintering.
2. Experimental procedure Ceramic samples of a 89Na1/2 Bi1/2 TiO3 -11BaTiO3 composition (mol%, NBT-11BT) were prepared by the conventional ceramic fabrication process from commercial powders of Na2 CO3 (Acros Organics, NJ, USA), Bi2 O3 (Kojundo Chemical Lab Co., Saitama, Japan), BaCO3 and TiO2 (Sigma–Aldrich, St. Louis, USA). Prior to mixing the powders, each raw powder was dried in an oven at 80 ◦ C for 24 h to eliminate any adsorbed moisture. The proportioned powder was ball-milled in a polyethylene bottle for 24 h using zirconia balls and high purity ethanol. The slurry was dried on a hotplate using a magnetic stirrer and then in an oven at 80 ◦ C for 48 h. The dried slurry was crushed and sieved using a 100-mesh sieve. The powder was calcined in an alumina crucible at 800 ◦ C for 4 h in air. The calcined powder was ball-milled, dried, and sieved. The X-ray diffraction of the calcined powder showed that the powder consisted of a single perovskite phase in the detection limit of XRD. The particle size distribution of the produced powder was measured from SEM micrographs of the powder using an image analysis program (Matrox Inspector 2.1, Matrox Electronic Systems, Ltd., Canada). The particle size distribution of the powder was unimodal and the average size was 0.21 m, as shown in Fig. 1. The powder was compacted into pellets of 12 mm diameter and ∼4 mm thickness, and then cold isostatically compressed at 200 MPa for 5 min. The compacts were placed on a Pt plate in an alumina crucible with a lid and sintered at 1100 or 1200 ◦ C in air for various times. The heating rate and cooling rate for sintering were respectively 4 K/min. In the case of the two-step sintering experiment, the compacts were heated to 1200 ◦ C, immediately cooled to 1100 ◦ C at a rate of 10 K/min upon reaching 1200 ◦ C, and then held at 1100 ◦ C for various times, as schematically shown in Fig. 2.
The crystal structure was identified using X-ray powder diffraction with CuK␣ radiation (D/MAX-RB (12KW), RIGAKU, Japan). For microstructure observation, the sintered samples were cut, polished to a 0.25 m finish, and thermally etched at 950 ◦ C for 15–20 min. Grain size distributions were measured from SEM images using an image analysis program (Matrox Inspector 2.1). At least 300 grains were examined to determine the grain size distribution. The relative density of the samples was measured by the Archimedes method taking the theoretical value of 5.91 g/cm3 , which was obtained from the X-ray diffraction data. For each condition, at least three samples were prepared and measured, and their average value was presented as the measured data. 3. Results and discussion 3.1. Grain shape and grain growth behavior at different temperatures During sintering of powder compacts, considerable grain growth took place, as shown in Figs. 3 and 4. At the beginning of the sintering at 1100 ◦ C, however, the sample is quite porous with a relative density of 86% and the grains did not grow substantially, as shown in Fig. 3(a). The average grain size after 10 min sintering was 0.24 m, quite similar to the average initial powder size. During sintering for 1 h (Fig. 3(b)), however, rapid grain growth occurred with densification, showing an average grain size of 0.57 m. This result indicates that with reduction of the drag force of the pores, many grains grew rapidly within 50 min. During extended sintering, only a small number of abnormal grains started to form and their size increased with an increase of the sintering time. The size of the
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Fig. 3. SEM micrographs of 89Na1/2 Bi1/2 TiO3 -11BaTiO3 samples sintered at 1100 ◦ C for (a) 10 min, (b) 1 h, (c) 2 h, (d) 4 h, and (e) 10 h. (f) The measured grain size distributions of different samples. (The sizes of the largest abnormal grain in the samples sintered for 4 and 10 h were over 30 m and 40 m, respectively.)
largest abnormal grain after 10 h of sintering exceeded 40 m. Note that the average grain size of the matrix grains with a lognormal distribution of 0.69 m in the sample sintered for 10 h is not very different from that in the sample sintered for 1 h. In contrast, at 1200 ◦ C, densification and grain growth occurred rapidly from the beginning. After sintering for 10 min (Fig. 4(a)), the relative density was 98% and the average grain size was 0.62 m. After initial rapid grain growth, grain growth appeared to occur slowly and the grain size distribution broadened. Apparently abnormal grain growth took place after sintering of several hours and the size of
abnormal grains, less than 10 m after sintering of 10 h, is much smaller than that observed at 1100 ◦ C. Fig. 5 shows the XRD patterns of the NBT-11BT samples sintered at 1100 and 1200 ◦ C for 4 h. All the peaks of these samples correspond to the standard diffraction peaks of a tetragonal phase, showing no difference in the crystalline phase between the samples sintered at different temperatures. This implies that the difference in microstructural evolution at the two different temperatures, 1100 and 1200 ◦ C, is not related to a potential difference in the crystalline phase. Instead, the shape of grains is different for samples
Fig. 4. SEM micrographs of 89Na1/2 Bi1/2 TiO3 -11BaTiO3 samples sintered at 1200 ◦ C for (a) 10 min, (b) 1 h, (c) 2 h, (d) 4 h, and (e) 10 h. (f) The measured grain size distributions of different samples. (The size of the largest abnormal grain in the sample sintered for 10 h was less than 10 m.)
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Fig. 5. X-ray diffraction patterns of 89Na1/2 Bi1/2 TiO3 -11BaTiO3 samples sintered at 1100 and 1200 ◦ C for 4 h.
Fig. 6. SEM micrographs showing 3-dimensional shapes of grains after annealing at (a) 1100 and (b) 1200 ◦ C for 4 h.
sintered at different temperatures, as shown in Fig. 6, which was obtained after annealing the calcined powder at 1100 and 1200 ◦ C for 4 h in air. At 1100 ◦ C, the grain shape is a well faceted cube with insignificant edge and corner facets, indicating a high anisotropy in surface energy. Moon et al. [37] reported that the facet planes are {1 0 0} planes. At 1200 ◦ C, however, the area fraction of {1 0 0} facets is reduced and facets of several different crystallographic planes appear. Considering the cube of {1 0 0} facets, the planes at the cube edges are {1 1 0} and those at the cube corners are {1 1 1}. The observed change in grain shape indicates that the surface energy anisotropy is reduced and the step free energy of {1 0 0} facets is also reduced with an increase in temperature from 1100 to 1200 ◦ C. According to previous investigations, the migration of faceted grain boundaries [53,54,57,58] or solid/liquid interfaces [51,52,54,59] is governed either by the interface reaction (attachment) or diffusion of atoms for a driving force smaller or larger, respectively, than a critical value, showing nonlinear migration behavior, as schematically illustrates in Fig. 7. The critical driving force, gc, for appreciable migration is governed by the step free energy of the boundary or the surface [51,53,54,59,62]. Based on the nonlinear migration behavior of the faceted interface, the principle of microstructural evolution was deduced as the coupling effect of gmax and gc [53,58–60]. According to the principle, different types of grain growth behavior manifest at the time of observation, depending on the value of gmax relative to gc : stagnant grain growth for gc > gmax , abnormal grain growth for gc ≤ gmax , pseudo-normal grain growth for 0 < gc gmax , and normal grain growth for gc = 0. This prediction has been supported by many investigations on metals as well as ceramics with or without a liquid matrix [20–50,55,56,61].
The rapid growth of grains in 1 h at 1100 ◦ C implies that the number of grains exceeding gc,1100 ◦ C was large and they grew rapidly (pseudo-normal growth in a fine matrix) and impinged upon each other. The formation of abnormal grains in samples sintered for 2 h suggests that the driving force for the largest grain after impingement of grains is comparable with the critical driving force for appreciable migration of the boundary (Fig. 7). Only a small number of grains can grow further and become abnormal grains, as shown in Fig. 3. If we accept the mean field concept, we can estimate the maximum driving force in a sample from the measured grain size distribution, as in a previous investigation [61], using the following equation: gmax = 4
1 ¯ G
−
1 Gmax
␥b
(1)
¯ is the average grain size, Gmax is the size of the largest grain, Here, G and b is the grain boundary energy. Taking b to be 0.5 J m−2 and considering the measured average particle and grain size distribution in Figs. 1 and 3(f), gmax estimated at the beginning (gmax I ) and after sintering of 1 h at 1100 ◦ C (gmax II ) is 5.0 × 106 J m−3 and 2.7 × 106 J m−3 , respectively, as shown in Fig. 7. With an increase in temperature from 1100 to 1200 ◦ C the growth rate of grains increases considerably while the critical driving force decreases because of a reduction of the step free energy with an increase in temperature [53,54,59,61]. As gmax is much larger than gc , grain growth occurs rapidly from the early stage of sintering, exhibiting pseudo-normal growth behavior, and the maximum driving force decreases with grain growth. During extended sintering, however, several apparently large grains appear, as a result of the reduction of gmax with grain growth, as shown in Fig. 4. The estimated maximum driving force, gmax III , in the sample sintered at 1200 ◦ C for 10 min
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fgr8
Fig. 7. Schematic representation of the growth rates with respect to the driving force together with the critical driving forces at 1100 and 1200 ◦ C, and the maximum driving forces. gmaxI is for the synthesized powder. gmax II and gmax III are for the samples sintered at 1100 ◦ C for 1 h and at 1200 ◦ C for 10 min, respectively. The maximum driving forces were estimated from the measured grain size distributions. The mean field concept was adopted and a constant grain boundary energy of 0.5 J/m2 was assumed.
Fig. 8. SEM micrographs of 89Na1/2 Bi1/2 TiO3 -11BaTiO3 samples two-step sintered at 1200 ◦ C for 0 h and at 1100 ◦ C for (a) 1 h, (b) 2 h, (c) 4 h, (d) 10 h. (e) The measured grain size distributions of different samples.
is indicated in Fig. 7. As apparently abnormal grains appear to form between 4 and 10 h of sintering (Fig. 4), the critical driving force at this temperature (gc, 1200 ◦ C ) can also be estimated from the grain size distribution after 4 h. The estimated value is 1.5 × 106 J m−3 and is depicted in Fig. 7. Such a change in the grain growth behavior from pseudo-normal to abnormal was also observed in a 95NBT-5BT system with round-edged cube grains [37].
3.2. Effect of two-step sintering Two-step sintering of NBT-11BT has been performed in an attempt to suppress grain growth, in particular abnormal grain growth, and also to reveal the cause of grain growth suppression in this system. Fig. 8(a)–(d) is micrographs obtained after two-step sintering with the first step at 1200 ◦ C for 0 h and the second step at 1100 ◦ C for various times. Fig. 8(e) plots the measured grain size distributions of the samples in Fig. 8(a)–(d). During the first sin-
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growth of many grains at a temperature higher than the conventional sintering temperature appears to reduce the broadening of the grain size distribution compared with the change in the grain size distribution in conventional sintering, as previously calculated for a two-phase system [20]. 4. Conclusions Grain growth behavior in 89Na1/2 Bi1/2 TiO3 -11BaTiO3 was studied at 1100 and 1200 ◦ C, and also under two-step sintering at these two temperatures. At the low temperature, distinctive abnormal grain growth was observed after the initial growth of many grains. At the high temperature, the grain growth behavior was quite normal, followed by indistinctive abnormal grain growth behavior. The grain growth behavior at the two different temperatures, including the differences, can be explained in terms of the coupling effect of the maximum driving force for the growth of the largest grain and the critical driving force for appreciable migration of the grain boundary. The two-step sintering at 1200 and 1100 ◦ C suppressed further growth of grains after the first sintering step at 1200 ◦ C. From the measured grain size distributions of the two-step sintered and conventionally sintered samples, it was found that the beneficial effect of two-step sintering for grain growth suppression is related to a narrower grain size distribution than that of the conventionally sintered sample, and hence a reduction of the maximum driving force for the growth of the largest grain. Our experimental results of conventional and two-step sintering support the general applicability of the recently deduced principle of microstructural evolution in polycrystals [53,59,60] to understanding grain growth in polycrystalline materials. Acknowledgements
Fig. 9. (a) Grain size distributions and the estimated maximum driving forces in the sample conventionally sintered at 1100 ◦ C for 1 h and that in the sample immediately after the first sintering step at 1200 ◦ C for 0 h. (b) Schematic showing the growth rate of grains together with the maximum driving forces in the two different samples in (a).
tering step, grains growth took place rapidly, similar to the case of the conventional sintering at 1200 ◦ C. However, as the temperature was decreased to 1100 ◦ C after the first sintering step, no significant grain growth occurred at 1100 ◦ C during the second sintering step and no apparent abnormal grains formed even after sintering of 10 h, unlike in the case of the conventional sintering at 1100 ◦ C (Fig. 3). This observation shows the beneficial effect of the twostep sintering in the NBT-BT system for suppressing grain growth, including AGG. The measured grain size distributions of the sample conventionally sintered at 1100 ◦ C for 1 h and that first-step sintered at 1200 ◦ C for 0 h are shown in Fig. 9(a). Although the average grain sizes are similar, 0.57 m for the conventional sintering case and 0.60 m for the two-step sintering case, the grain size distributions are quite different from each other. The grain size distribution in the first-step sintered sample is much narrower than that in the conventionally sintered sample at 1100 ◦ C. The estimated gmax from the measured grain size distribution of the sample immediately after the first sintering step is 2.1 × 106 J m−3 . This value is distinctly smaller than that (2.7 × 106 J m−3 ) in the sample conventionally sintered at 1100 ◦ C for 1 h and the estimated critical driving force for appreciable migration of the boundary at 1100 ◦ C, as schematically shown in Fig. 9(b). Our experimental observations and estimation indicate that the beneficial effect of two-step sintering for grain growth suppression is related to a change in the grain size distribution and a reduction of gmax below gc . Rapid
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