Print version ISSN 1516-1439
Mat. Res. vol.15 no.4 São Carlos July/Aug. 2012 Epub July 17, 2012
Ronaldo Santos da SilvaI; Antonio Carlos HernandesII; Jean-Claude M'PekoII,*
IGrupo de Materiais Cerâmicos Avançados, Departamento de Física, Universidade Federal de Sergipe UFS, Campus Universitário, CEP 49100-000, São Cristóvão, SE, Brasil
IIGrupo Crescimento de Cristais e Materiais Cerâmicos, Instituto de Física de São Carlos, Universidade de São Paulo USP, CP 369, CEP 13560-970, São Carlos, SP, Brasil
Ba0.77Ca0.23TiO3 ceramics were produced in this work starting from nanopowders synthesized via a polymeric precursor method. By adjusting the pH values of the precursor solutions above 7, it was possible to prepare powders weakly aggregated and with a smaller particle size, both facts which traduced into an enhanced nanopowders' sintering process at comparatively lower temperatures. Irrespective of the initial pH value, highly-dense and second phase-free ceramics were obtained following optimal sintering parameters (temperature and time) extracted from dilatometric and density measurements. By considering these and other sintering conditions, moreover, polycrystalline materials with an average grain size varying from 0.35 to 8 mm were produced, the grain growth process involving liquid phase-assisted sintering for heat treatments achieved at 1320 °C. The study of grain size effects on the ferroelectric properties of these materials was conducted, the results being discussed in the light of previous debates, including grain size-dependent degree of tetragonal distortion in such materials, as verified in this work.
Keywords: barium calcium titanate, nanopowders synthesis, sintering, microstructures, dielectric properties
Barium calcium titanate (BCT) is a perovskite-structured ferroelectric system, with tetragonal 4 mm point group. In particular, the Ba0.77Ca0.23TiO3 (BCT23) composition is the only congruently melting compound in this system1. Single crystals from this compound present a Curie temperature (denoting the temperature of paraelectric-to-ferroelectric phase transition upon cooling) at 98 °C, and do not show, in contrast to undoped BaTiO3 (BT), any further structural transition down to -120 °C1. BCT compounds have been reported as promising materials for the manufacture of multi-layer ceramic capacitors (MLCC), with the main advantages of showing good dielectric performance on cheap electrode (such as nickel) and, as mentioned above, an increasing temperature range of ferroelectric tetragonal phase. Moreover, addition of calcium is known to inhibit the formation of undesirable non-ferroelectric hexagonal BT secondary phase, as sometimes found in BT-based systems2. Due to all these and other attractive properties, considerable efforts have been devoted to optimize preparation, (micro)structural and dielectric properties of BCT ceramics.
Theoretically, highly-dense ceramic materials may be prepared at a lower cost (thermal energy viewpoint, at least) from compacts with nano-sized particles, as they present higher effective area and surface energy, implying an increased grain boundary mobility and, thus, enhanced sinterability when compared to compacts formed by micrometric particles. In practice, nevertheless, elimination of large pores from green compacts is often the common problem when dealing with sintering of nanopowders, these pores being created due to the propensity of such powders to form agglomerates during their synthesis by chemical methods3,4. It is well known that green compacts showing particle agglomeration normally require higher sintering temperatures than compact with well deagglomerated particles; otherwise, significantly reduced final densities of the prepared ceramics may be unfortunately obtained.
To address the above problem, adjustment of the pH value of the precursor solutions prepared via chemical synthesis-based methods has often been used as an alternative way to nearly prevent agglomerates formation and to control morphology of the powders planed to be produced4-8. In a preceding paper4, we showed that the pH values of the starting solutions effectively influenced the physical properties of BCT23 nanocrystalline powders that were synthesized by a modified polymeric precursor method. That is, increasing the pH values to alkaline conditions allowed the production of highly-reactive powders with very fine and homogeneous particles. For samples with pH value equal to or higher than 7 and calcined up to 600 °C, nevertheless, the observation was that a small amount of secondary BaCO3 phase remained stable, even after 5 hours of heat treatment. Traces of this undesirable phase disappeared after calcination, for instance, at 700 °C for 2 hours, but accompanied by an increase in the average particle size of the powders finally synthesized. In any case, considering that the particle size of powders, morphology and presence of spurious phases, if any, normally have significant effects on the sintering process of materials, the present work was focused on performing the study of pH influence on BCT23 synthesis, with a special attention paid to the sintering dynamics, microstructures and dielectric properties of the ceramic bodies prepared from such nanopowders.
2. Experimental Procedure
Ba0.77Ca0.23TiO3 nanocrystalline powders were synthesized by a modified polymeric precursor method, using titanium isopropoxide (Ti[OCH(CH3)2]4 Alfa Aesar, 97%), barium acetate (C4H6BaO4 Synth, 99%) and calcium carbonate (CaCO3 Alfa Aesar, 99.95 %) as precursor materials, while varying the solutions' pH value in the range of 1.5 to 11. Adjustment of the pH value of the resins was achieved through addition of ammonium hydroxide, followed by heating up to 120-150 °C in order to eliminate the water excess and promote the polyesterification reaction. As presented in the previous report4, Table 1 summarizes some of the properties of interest for the powders calcined at 600 °C for 5 hours, the data showing an evident influence of the pH value of the resin on the powder characteristics finally observed. Instead of those BaCO3-free powders calcined, for instance, at 700 °C for 2 hours, the present ones (Table 1) were selected as starting powders for developing this study because of their comparatively smaller average particle size, according to powders' analysis performed through field emission scanning electron microscopy, FE-SEM (FEG-VP Zeiss Supra 35 equipment). This fact is theoretically expected to promote sintering effectiveness at relatively lower temperatures.
In the present work, these powders (synthesized at 600 °C for 5 hours) were mixed with a binder solution of polyvinyl alcohol in a concentration of 0.1 g mL1, and uniaxially compacted at about 120 MPa into 4 mm-diameter disk-shaped samples. Shrinkage measurements of the pressed powders were carried out by using a Netzsch DIL 402 PC dilatometer equipment, in the range of 25 to 1350 °C, under a constant heating rate of 10 °C/min and synthetic air (O2/N2 1/4) flow. Achievement of these measurements was considered in order to evaluate the sintering temperature to be ideally applied for each material so as to produce highly-dense bodies. After sintering, density of the ceramics was determined by the Archimedes' method using distilled water. Moreover, the microstructures of these ceramics were examined by scanning electron microscopy, SEM (in a Zeiss-DSM960 microscope equipment), after which the average grain size was in each case evaluated following the intercept length method9. The structural investigation of these materials was performed through powder X-ray diffraction, XRD (in a Rigaku Rotaflex RU-200B diffractometer), using CuKa1 radiation. The measurements were carried out at room temperature in continuous mode, in the 2θ range from 20 to 60°, with a step of 0.02°. Finally, electric contacts were fabricated out on both major surfaces of polished ceramic samples by applying Pt paste, followed by firing at 700 °C for 30 minutes. Subsequently, permittivity data of these samples were recorded at 1 kHz using a Solartron 1260 Impedance Analyzer controlled by a personal computer. The measurements were carried out during cooling from 200 to 25 °C, with a cooling rate of 0.5 °C/min and an applied electric potential of 100 mV.
3.1 Dilatometric and densification analyses
Figure 1 shows the results of linear shrinkage ΔL/L0 and shrinkage rate d(ΔL/L0)/dT for all the prepared samples as a function of temperature. As can be seen, the inflection point in each linear shrinkage curve (Figure 1a), which corresponds to the temperature of maximum shrinkage rate (i.e., d(ΔL/L0)/dT peak, Figure 1b), decreases when the pH value increases. In general, in terms of thermal dynamics, differences in the results shown in this Figure 1 involve the effect expected from variations of both starting particle size and agglomeration level in the powders when synthesized from precursor solutions with different pH values (see Table 1). Following these results, different values of sintering temperature were adopted in order to produce all the ceramic bodies with high densities. These values are summarized in Table 2, together with the relative density (relative to BCT23 theoretical density, TD = 5.55 g.cm3)10 measured for each material. For the sake of comparison, BCT23_03 (pH = 3.5) and BCT23_07 (pH = 7.0) compacts were also sintered at 1250 °C for 3 hours, the corresponding density data being as well included in this Table (the two last rows).
To complete the analysis of the sintering process, the densification behavior of the calcined and compressed BCT23_01 and BCT23_11 powders was also closely studied in real time, the results being illustrated in Figure 2. In this case, the temperature was varied at a constant heating rate of 10 °C/min up to reach the sintering temperature selected (in each case) from the dilatometric (DIL) analysis, that is, 1320 °C and 1250 °C, respectively. From the observed results, it is clear that both samples show a similar densification behavior, reaching the same final density of 97 ± 1% TD after sintering for 3 hours at these two but different temperatures. These results allow concluding that the influence of the pH value and, thus, particle size and agglomeration level on the final density of the ceramics is negligible when the green compacts are sintered following the appropriate conditions established from the dilatometric study. This observation is further supported by Figure 3, which shows the pH dependence of density of all the samples under 3 different conditions, namely (i) as-compacted powders (green compacts prepared under equal pressing conditions), on the one hand, and sintering for 3 hours (ii) at 1250 °C and (iii) at the temperatures established by the DIL analysis, on the other hand. For the samples sintered at 1250 °C for 3 hours, there is a significant increase in materials' relative density with raising the pH value. As may be realized, these samples reach their maximum density when the applied sintering conditions coincide with the pH-modified DIL ones (data summarized in Table 2), the latter conditions allowing a similar maximum reachable density for all these materials, that is, irrespective of the pH value considered.
3.2 (Micro)structural (SEM and XRD) analyses
Examination of the microstructures of all the ceramics was achieved in this work by using the SEM analysis technique. Figure 4 shows, for instance, the SEM images of the ceramics after sintering at two different conditions: at 1250 °C for 3 hours for all of them (Figure 4a-e) and, in addition, at 1320 °C for 3 hours for BCT23_01 (Figure 4f). Under identical sintering conditions (1250 °C/3 h), a decrease of porosity was indeed noted as the pH value increased (that is, when various SEM images from different regions of the samples were compared). In terms of behavior, this result remains in accordance with that obtained from the DIL analysis (Figure 1) and density measurements (Figure 3). For a quantitative comparison, values estimated from the SEM images for the average grain size (AGS) of all the ceramics have been included in Table 2. Accordingly, Figure 4a-e involves a reduction of AGS toward the acid conditions (compare in Table 2 the AGS values of the ceramics, from pH = 11 to 3.5, after sintering at 1250 °C for 3 hours), certainly because the samples prepared from solutions with the lower pH values still were in a somewhat intermediate sintering stage at 1250 °C, as could be concluded from the DIL results (Figure 1). This means that a significant grain growth process may be still expected for these samples at higher sintering temperatures11. In fact, when the BCT23_01 compact was sintered applying the corresponding DIL condition (1320 °C/3 h), so as to achieve full density, the ceramic body presented an anomalous grain growth with a size distribution ranging from 1 to 25 µm (Figure 4f and Table 2).
The XRD patterns obtained for the BCT23_01, BCT23_07 and BCT23_11 samples sintered applying the DIL conditions (given in Table 2) are illustrated in Figure 5. Qualitatively, the same results applied to the other ceramic samples. That is, only the BCT23 phase was observed in all the XRD spectra, revealing that the initial pH value did not show any important influence on synthesizing ceramics with the stoichiometric (second phase-free) BCT23 composition envisaged. This result was expected provided that, as briefly commented in the introduction, all the powders (even those prepared from the precursor solutions with the higher pH values, and showing small amounts of a BaCO3 phase after solution heating at 600 °C for 5 hours) resulted free of BaCO3 traces after calcination at 700 °C and above4. Taking as reference, for instance, the tetragonal double (002)/(200) peak appearing in these XRD spectra just above 2θ = 45°, as magnified in the Figure 5 inset, the only difference applying to all these ceramic samples is the observation of a clear trend of the double peak resolution and, thus, structure tetragonality to increase with diminishing the pH value. Indeed, this apparent structure tetragonality-pH value connection must be here considered being, of course, only indirect, the real justification being, in reality, the increase of AGS when the starting precursor solutions' pH value was reduced.
3.3 Dielectric properties
According to the microstructure characteristics of the ceramic samples prepared here, as summarized in Table 2, it was in this work possible to achieve a study of average grain size (AGS) influence on the dielectric properties of these materials. Figure 6 illustrates the temperature dependence of dielectric constant (ε) of these BCT23 ceramics, for the measurements performed at 1 kHz. As expected, each curve shows a dielectric peak denoting the ferroelectric-to-paraelectric phase transition at the called Curie temperature (Tc). The main observations are that both Tc as well as dielectric constant at room temperature, εRT = ε(RT), and at Tc, εm = ε(Tc), reveal to be grain size dependent, as can be clearly seen in Figures 7 and 8. In particular, on the one hand, Tc and εm decrease with diminishing AGS, especially below 0.77 µm (Figure 7). Similar results have been reported elsewhere for perovskite-structured undoped BT and PbTiO3 (PT) ceramics12-14, being here also found in BCT ceramics. On the other hand, εRT peaks at a grain size of about 0.55 µm (Figure 8). This behavior is to date indeed exclusively characteristic of BT ceramics (i.e., when compared with other perovskite-structured parent materials), with a peak classically developing around 0.7-1 µm15-17. We note that the value of εRT(0.55 µm) = 1280 found in Figure 8 remains among the higher ones presented in literature for BCT ceramic materials2,18-20.
According to Figure 1, a large shrinkage process was noted to occur at about 1320 °C for the BCT23_01 (pH = 1.5) and BCT23_03 (pH = 3.5) samples, this temperature being adopted as the minimum one necessary to achieve effectively sintering in these materials. Nevertheless, a close inspection of the dilatometric data shown in this figure suggests, moreover, occurrence of another contraction process, modest in appearance (i.e., of seemingly lower intensity), toward a lower temperature range of ~1150-1250 °C. As summarized in Table 1, it was shown in our preceding work4 that, for those starting precursor solutions prepared with the lower pH values (pH = 1.5 and 3.5), the synthesized BCT23 powders revealed to be significantly agglomerated. In consequence, green compacts from such powders are expected to most likely exhibit two distributions of pores, as it is also straightforward from the FE-SEM images we previously presented for such samples4: large inter-agglomerate voids that communicate throughout the samples, besides the intra-agglomerate ones which are comparatively smaller in size. Development of two contraction processes in these materials is therefore attributed to this pore size distributions' feature21. In particular, the shrinkage process toward lower temperatures should correspond to expulsion of the intra-agglomerate porosity, while that at the higher temperature is to be associated with expulsion of the inter-agglomerate porosity. In any case, the following two comments can be formulated. That is, resolution of the two agglomeration-related contraction processes for BCT23_01 and BCT23_03 indicates that, firstly, the agglomerates were, of course, but not broken during samples' compaction before sintering and that, secondly, intra- and inter-agglomerate sintering do not occur both simultaneously.
Also, the fact of starting with green compacts showing agglomerated-like particles (with a bimodal pore distribution) should lead, during heat treatment, to locally inhomogeneous sintering dynamics of the compacts, as may be concluded, for instance, for the BCT23_01 ceramic sample whose SEM image is shown in Figure 4a (sintering at 1250 °C/3 h and ρrel = 90% TD). Two regions 1 and 2 are indicated in this figure, representing completely dense and porous regions of the sample, respectively. In those areas like region 1, absence of porosity is expected to favor grain boundary migration through solid/solid interfaces and, thus, grain growth if performing sample heat treatment at higher temperatures. In contrast, densification dynamics in those areas like region 2 should be comparatively prejudiced due to the presence of solid/gas interfaces22,23. The microstructure of the above BCT23_01 material, but now after sintering at 1320 °C/3 h (ρrel = 96% TD), was shown in Figure 4f. Accordingly, it is observed that areas like region 1 clearly show a larger AGS than those areas like region 2 that were initially less dense (i.e., with formerly solid/gas interfaces). For this ceramic sample, the estimated AGS is about 8 mm, quite above the range of AGS < 2 mm normally found for solid-state sintering in BT-based ceramics24. We just recall that the temperature of 1320 °C basically coincides with the eutectic point (1322 °C) found in the phase diagram of BaO-TiO2 mixtures25 for stoichiometric Ba/Ti ratios close to but below 1. Accordingly, therefore, development of a liquid phase-assisted sintering mechanism should be responsible for the expressive grain growth finally found in the BCT23_03 and, especially, BCT23-01 ceramic samples (see values of AGS summarized in Table 2), as it is common in BT-based ceramics slightly rich in Ti and sintered at temperatures close to and above 1300 °C24.
Different from all the results discussed above, the powders synthesized from the precursor solutions with the higher pH values (especially pH = 8.5 and 11) presented weakly agglomerated particles. This fact allowed preparing highly-homogeneous green compacts that resulted in slightly-higher starting (green) densities (see Figure 3) and a more narrow grain size distribution in the sintered ceramic samples (see Figure 4 and AGS distribution data given in Table 2). Here, of course, values of grain size are lower (all below 1 µm in average) also because sintering was achieved at temperatures (1250 and 1280 °C) below the eutectic point. In any case, the main observation to be here highlighted is that the increase of the starting precursor solutions' pH value traduced into powders with a decreased particle size and, especially, diminished particle aggregation level after calcination. As expected, this fact allowed a much more effective process of densification of the materials at comparatively lower temperatures (Figures 1-3). This is a right consequence of the higher surface energy involved in such nanopowders, its reduction remaining essentially the driving force of sintering processes of materials, as well established in the literature22,23.
In terms of dielectric properties (Figures 6-8), moreover, what is seen is that the reduction of the average grain size (AGS from 8 to 0.38 mm) results in three main alterations, namely a decrease of both Tc and εm = ε(Tc), while εRT shows a somewhat complex but typical dependence upon grain size variations. Similar results have been reported in literature for undoped BT ceramics, and some verifiable explanations have been proposed to account for these effects12,13,17,26. According to Frey et al.26, the decrease of permittivity with diminishing grain size may respond to the increasing density of a low-permittivity non-ferroelectric phase (called dead layer) associated with grain boundaries. Nevertheless, from achievement of structural and local piezoresponse force microscopy measurements (on BT and PT), some authors have concluded that, far to be exclusively caused only by the above extrinsic-like size effect (surface contribution), a complete interpretation of permittivity depression with decreasing grain size requires that intrinsic size effects (bulk phenomenon) be also considered. According to Zhao et al.12, with decreasing grain size the crystal structure of BT ceramics at room temperature becomes progressively less tetragonal and the heat of the tetragonal (ferroelectric) to cubic (paraelectric) phase transition is gradually reduced. Therefore, Curie temperature is shifted to lower values, while the magnitude of permittivity is reduced, as found here for Tc, εm and εRT (below AGS = 0.55 µm, in the latter case). In the present work, the partial loss of tetragonality is verified in the Figure 5 inset, manifesting as a partial loss of the double (002)/(200) peak resolution with decreasing grain size.
With respect now to the behavior of room temperature permittivity, in particular, the pronounced maximum of eRT for AGS values approaching 0.55 µm (Figure 8), that is, close to the 0.7-1 µm AGS range of manifestation in undoped BT15-17, has been discussed elsewhere. By combining theory and experiment, this behavior has been attributed to an increase of the mobility of ferroelectric 90° domain walls, their width showing to decrease proportionally with the square root of AGS, as was determined by considering the equilibrium between elastic field and domain wall energies in such materials17. In general, although behaving like BT, the present dielectric results on BCT ceramics may be considered to be important, provided that quite different trends of grain size dependence of permittivity may be, and have been in fact, surprisingly found in even parent compounds. That is, different from BT samples, the permittivity of PT, Pb(Mg,Nb)O3 and Pb(Zr,Ti,Nb)O3 has been found to instead decrease monotonously with diminishing AGS, these materials revealing as well a different behavior when compared with (Pb,La)(Zr,Ti)O3, whose permittivity has shown an apparent minimum value at an AGS of about 1.7 µm15-17,27-30. In other words, similarity between compounds is not necessarily a guarantee of similar behaviors to be expected for grain size effects on the ferroelectric properties of these materials. We in fact believe that further studies are needed to clarify observation of such so different behaviors even in comparatively parent compounds.
It was shown that controlling the pH values of the precursor solutions is an effective way to prevent particle aggregation in Ba0.77Ca0.23TiO3 powders synthesized through chemical methods. In particular, this was possible via using here pH values above 7, resulting in strongly reactive powders that allowed preparing fairly homogeneous green compacts and producing highly-dense ceramics at comparatively lower sintering temperatures. Such ceramic bodies specifically showed a relatively narrow distribution of grain sizes. By applying sintering conditions extracted from dilatometric and density analyses, moreover, ceramics with an average grain size varying from 0.38 to 8 µm were prepared, the grain growth process involving most likely liquid phase-assisted sintering mechanism for those samples heat treated at 1320 °C. A strong effect of grain size on the ferroelectric properties of these materials was verified, and includes a decrease of both Curie temperature and maximum permittivity with decreasing grain size, as a consequence of a decrease of the unit cell tetragonality distortion in these materials, implying a transition trend to the non-ferroelectric cubic phase. On the other hand, the materials' room temperature permittivity showed a complex behavior with a peak at a grain size of about 0.55 µm, a result that is typical of undoped BaTiO3 ceramics (for which the peak classically locates at about 0.7-1 µm) and may be accounted for by considering, particularly, contribution from the ferroelectric 90° domain walls mobility.
The authors gratefully acknowledge financial support from FAPESP, FAPITEC and CNPq, three Brazilian funding agencies.
1. Kuper C, Pankrath R and Hesse H. Growth and dielectric properties of congruently melting Ba1-xCaxTiO3 crystals. Applied Physics A: Materials Science & Processing. 1997; 65:301-305. http://dx.doi.org/10.1007/s003390050583 [ Links ]
2. Mazon T, Hernandes AC, Souza AG, Moraes APA., Ayala AP, Freire PTC et al. Structural and dielectric properties of Nd3+-doped Ba0.77Ca0.23TiO3 ceramics. Journal of Applied Physics. 2005; 97:104113. http://dx.doi.org/10.1063/1.1901834
4. Silva RS, Bernardi MIB and Hernandes AC. Synthesis of nonagglomerated Ba0.77Ca0.23TiO3 nanopowders by a modified polymeric precursor method. Journal of Sol-Gel Science and Technology. 2007; 42:173-179. http://dx.doi.org/10.1007/s10971-007-1554-6 [ Links ]
6. Jesus FAA, Silva RS, Hernandes AC and Macedo ZS. Effect of pH on the production of dispersed Bi4Ge3O12 nanoparticles by combustion synthesis. Journal of the European Ceramic Society. 2009; 29:125-130. http://dx.doi.org/10.1016/j.jeurceramsoc.2008.05.048 [ Links ]
7. Yue Z, Guo W, Zhou J, Gui ZL and Li LT. Synthesis of nanocrystilline ferrites by sol-gel combustion process: the influence of pH value of solution. Journal of Magnetism and Magnetic Materials. 2004; 270:216-223. http://dx.doi.org/10.1016/j.jmmm.2003.08.025 [ Links ]
8. Fang TT and Tsay JD. Effect of PH on the chemistry of the barium titanium citrate gel and its thermal decomposition behavior. Journal of the American Ceramic Society. 2001; 84:2475-2478. http://dx.doi.org/10.1111/j.1151-2916.2001.tb01038.x [ Links ]
9. American Society for Testing and Materials ASTM. E1382: Standard test methods for determining average grain size using semiautomatic and automatic image analysis. ASTM; 1991. Annual Book of ASTM Standards, v. 03.01. [ Links ]
10. Barbosa LB, Ardila DR and Andreeta JP. Crystal growth of congruent barium calcium titanate by LHPG. Journal of Crystal Growth. 2001; 231:488-492. http://dx.doi.org/10.1016/S0022-0248(01)01455-5 [ Links ]
11. Shaw NJ. Densification and coarsening during solid-state sintering of ceramics - A review of the models 2. Grain-growth powder metallurgy international. Powder Metallurgy International. 1989; 21:31-33. [ Links ]
12. Zhao Z, Buscaglia V, Viviani M, Buscaglia MT, Mitoseriu L, Testino A et al. Grain-size effects on the ferroelectric behavior of dense nanocrystalline BaTiO3 ceramics. Physical Review B. 2004; 70:024107. http://dx.doi.org/10.1103/PhysRevB.70.024107 [ Links ]
13. Buscaglia MT, Buscaglia V, Viviani M, Petzelt J, Savinov M, Mitoseriu L et al. Ferroelectric properties of dense nanocrystalline BaTiO3 ceramics. Nanotechnology. 2004; 15:1113-1117. http://dx.doi.org/10.1088/0957-4484/15/9/001 [ Links ]
14. Jiang Q, Cui XF and Zhao M. Size effects on Curie temperature of ferroelectric particles. Applied Physics A: Materials Science & Processing. 2004; 78:703-704. [ Links ] http://dx.doi.org/10.1007/s00339-002-1959-6
15. Jonker GH and Noorlander W. Grain Size of Sintered Barium Titanate. In: Stewart GH. Science of Ceramics 1. London and New York: Academic Press; 1962. p. 255 [ Links ]
16. Sharma NC and McCartney ER. The dielectric properties of pure barium titanate as a function of grain size. Journal Australasian Ceramic Society. 1974; 10:16-20. [ Links ]
18. Jayanthi S and Kutty TRN. Extended phase homogeneity and electrical properties of barium calcium titanate prepared by the wet chemical methods. Materials Science and Engineering: B. 2000; 110:202-212. http://dx.doi.org/10.1016/j.mseb.2004.03.008 [ Links ]
20. Tiwari VS, Singh N and Pandey D. Structure and properties of (Ba,Ca)TiO3 ceramics prepared using (Ba,Ca)CO3 precursors. 1. Crystallographic and microstructural studies. Journal of the American Ceramic Society. 1994; 77:1813-1818. http://dx.doi.org/10.1111/j.1151-2916.1994.tb07055.x
21. Tai LW and Lessing PA. Modified resin intermediate processing of perovskite powders. 1. Optimization of polymeric precursors. Journal of Materials Research. 1992; 7:502-510. http://dx.doi.org/10.1557/JMR.1992.0502 [ Links ]
22. Chiang Y-M, Birnie DP and Kingery WD. Physical Ceramics: principles for ceramic science and engineering. New York: John Wiley & Sons; 1997. [ Links ]
23. German RM. Sintering Theory and Practice. New York: John Wiley & Sons; 1996. [ Links ]
24. Lin TF, Hu CT and Lin IN. Influence of stoichiometry on the microstructure and positive temperature coefficient of resistivity of semiconducting barium titanate ceramics. Journal of the American Ceramic Society. 1990; 73:531-536. http://dx.doi.org/10.1111/j.1151-2916.1990.tb06549.x
25. Jaffe B, Cook WR and Jaffe H. Piezoelectric Ceramics. London and New York: Academic Press Inc.; 1971. 317 p. [ Links ]
26. Frey MH, Xu Z, Han P and Payne DA. The role of interfaces on an apparent grain size effect on the dielectric properties for ferroelectric barium titanate ceramics. Ferroelectrics. 1998. 206:337-357. http://dx.doi.org/10.1080/00150199808009168 [ Links ]
27. Papet P, Dougherty JP and Shrout TR. Particle and grain-size effects on the dielectric behavior of the relaxor ferroelectric Pb(Mg1/3Nb2/3)O3. Journal of Materials Research. 1990; 5:2902-2909. http://dx.doi.org/10.1557/JMR.1990.2902 [ Links ]
28. Yamamoto T. Optimum preparation methods for piezoelectric ceramics and their evaluation. American Ceramic Society Bulletin. 1992; 71:978-985. [ Links ]
29. Uchino K, Sadanaga E and Hirose T. Dependence of the crystal structure on particle size in barium titanate. Journal of the American Ceramic Society. 1992; 72:1555-1558. http://dx.doi.org/10.1111/j.1151-2916.1989.tb07706.x
30. Sato Y, Kanai H and Yamashita Y. Grain-size dependence of dielectric-constant for modified (Pb0.63Ba0.37)(Zr0.7Ti0.3)O3 ceramic material. Japanese Journal of Applied Physics. 1994; 33:1380-1384. http://dx.doi.org/10.1143/JJAP.33.1380
Received: September 27, 2011
Revised: April 3, 2012