- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
Advances in Materials Science and Engineering
Volume 2013 (2013), Article ID 125634, 7 pages
Dielectric and Ferroelectric Properties of Lead-Free Ceramic System
1Department of Physics and Material Science & Engineering, Jaypee Institute of Information Technology, Noida 201307, India
2Electroceramics Group, Solid State Physics Laboratory, Timarpur, Delhi 110054, India
Received 31 May 2013; Revised 20 July 2013; Accepted 22 July 2013
Academic Editor: Amit Bandyopadhyay
Copyright © 2013 Vijayeta Pal et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Lead-free specimens of [ -BaTiO3] (BLNLT-BT, where , , and , 0.02, 0.04, and 0.06) ceramic system were synthesized by a semiwet technique. In the present study, we have investigated the effect of Ba on the structure, morphology, and dielectric, ferroelectric, and piezoelectric properties of BLNLT system. The XRD patterns of all the specimens showed rhombohedral structure at room temperature. Field emission scanning electron microscopy images (FE-SEM) showed grain growth inhibition with Ba content in BLNLT system. The temperature dependence of dielectric constant revealed that the temperature of maximum dielectric constant “” and depolarization temperature “” decreased for the sample and showed high value of dielectric constant with low dielectric loss. These samples exhibited nonlinear behaviour of hysteresis loop. The values of dielectric constant (), dissipation factor (tan δ), piezo charge coefficient (), remnant polarization (), and coercive field () for the composition were 1495, 0.06, 20 pC/N, 5 μC/cm2, and 10.5 kV/cm, respectively.
Lead-free piezoelectric ceramics were studied extensively over the last few decades due to environmental concern as well as government regulations against the use of hazardous substances . Bismuth sodium titanate, Bi0.5Na0.5TiO3 (BNT), was considered to be a promising lead-free material, and discovered by Smolenskii et al. in 1961 . BNT is a ferroelectric material having Bi3+ and Na+ ions on the A-sites of ABO3 type perovskite structure with a rhombohedral symmetry. It has high Curie temperature ( ~ 320°C) and strong ferroelectric nature at room temperature . However, the shortcoming of this material is its high conductivity and high coercive field ( kV/mm) [4, 5]. Therefore, pure BNT ceramic usually exhibits weak piezoelectric properties. Among the studied materials, solid solutions between a rhombohedral (Bi1/2Na1/2)TiO3 (BNT) and a tetragonal BaTiO3 (BT) have been of particular interest largely because of morphotropic phase boundary (MPB). A morphotropic phase boundary (MPB) exists at 6-7 mol% BT. The BNT-BT system was firstly reported by Takenaka et al. . To improve the electrical properties of material, a number of BNT-based ceramics have been usually produced by the convectional solid state method and various chemical methods, such as hydrothermal process , citrate method , sol-gel, and autocombustion . Recently, a lot of efforts have been made to improve their densification behaviour and electrical properties through doping elements [10, 11] and few studies revealed that there were many possibilities to further enhance the piezoelectric properties of KNN-based and Bi- based ceramics even through simple Li doping [12–14]. Due to volatile nature of Bi2O3 at high sintering temperature (>1200), Li was often used in BLNT compositions to achieve enhanced dielectric, ferroelectric, and piezoelectric properties . In order to get highly dense ceramic, this sample was sintered at 1200°C for 2 hours. To avoid the volatility of Bi2O3 and getting high density at low temperature, we have substituted La/Li on A-site in BNT system. As we know that La acts as modifier and enhances the electrical properties  and Li improves the densification with reduced sintering temperature . In the present work, we demonstrate the influence on crystal structure, dielectric, ferroelectric, and piezoelectric properties of Ba substitution in (BLNLT)-(BT) system where , 0.02, 0.04, and 0.06. To the best of our knowledge, the specimens of [(BLNLT)-(BT) system, ] were synthesized and studied in detail for the first time using semiwet technique. The potential advantages of semiwet technique over sol-gel and solid state reaction technique are controlled size and shape, atomic level homogeneity of doping elements at A-site and B-site in ABO3 perovskite structure and it is a promising technique to produce fine multicomponent oxide ceramic powders in a very simple and economic way. This technique was found to be very useful in improving the properties .
2. Experimental Procedure
Lead-free specimens of (BLNLT)-(BT), were prepared by semi-wet technique using AR-grade metal oxides or nitrate powders (Sigma Aldrich) as raw materials like Bi2O3 (99%), NaNO3 (99%), La2O3 (99.9%), LiNO3 (99.9%), TiO2 (99.9%), and ethylene glycol. All the raw materials were weighed in appropriate amount according to their chemical compositions. The BLNLT and BT compositions were synthesized separately. The A-site of BLNLT system was prepared by using ethylene glycol precursor solution, in which ethylene glycol was expected to distribute the cations in atomic level forming a polymeric complex which was combusted at appropriate temperature ( ~ 150–200°C) in the form of ash powders. The ash, highly fine, homogeneous, and highly reactive, was mixed thoroughly with appropriate amount of TiO2 powder in ethanol media for 2 hrs. The details of synthesis process were described elsewhere . Dried powders for these compositions were calcined at 750°C for 2 hours. In order to get highly dense ceramic, sintering was done at 1100°C for 2 hours. To avoid the volatility of Bi2O3 and getting high density at low sintering temperature, we had substituted La/Li on A-site in BNT system separately. Thereafter, the specimens of [(BLNLT)-(BT) complex system with compositions 0.04/0.025/0–0.06] were synthesized by semiwet method and calcined at temperature that is, 800–900°C for 2 hours. After calcination, powder were reground with binder (polyvinyl alcohol) and pressed into pellets of diameter 10 mm and thickness ≤1.5 mm using hydraulic press. These pellets were kept at 400°C for 4 hours to burn off the binder, and temperature was raised to 1100–1150°C and kept at this temperature for 2 hours for sintering.
The crystalline structure of the sintered samples was examined using X-ray diffraction analysis with Cu-Kα radiation (XRD-6000, Shimadzu, Japan). The surface morphology of sintered samples was studies by field emission scanning electron microscopy (FE-SEM, Quanta 200 FEG, FEI, Netherlands). Bulk density of the sintered sample was measured by the Archimedes method. The relative density was determined using bulk density (calculated by taking mass and dimensions of the pellet) and theoretical density (determined using XRD data). Silver paste was coated on both sides of these sintered and polished samples as electrodes for the purpose of electrical measurements, and cured at 500°C for 20 min. The dielectric constant and dielectric loss (tan δ) of these samples at 1 kHz, 10 kHz, and 100 kHz were measured as a function of temperature over the temperature range from room temperature to 500°C using LCR meter (Hioki 3522); P-E loop tracer (Marine India), based on modified Sawyer-Tower circuit, was used to trace polarization versus electric field loops at 50 Hz. Piezoelectric charge constant () was measured after poling using Piezometer (Take Control, PM 35) for all the specimens. Poling was done under 3 kV/mm DC electric field at 50°C for 1 hour duration.
3. Results and Discussion
Figure 1 shows the X-ray diffraction pattern of lead free [(BLNLT)-(BT), ] system. It was observed from the diffraction patterns that all the specimens exhibited single-phase formation with rhombohedral structure and no secondary phase(s) were observed within detection limit of XRD. It implied that La3+, Li+, and Ba2+ have diffused into BNT lattice to form a solid solution. Even though many investigations have been carried out on the symmetry of BNT-based ceramics; yet, there is still controversy in crystallographic symmetry. A large number of researcher reported that BNT has rhombohedral structure [19–21]. However, few reports suggested that the BNT has a lower symmetry with monoclinic phase [22, 23]. In the present system, we found that the symmetry of the solid solution became more complex for BLNLT-BT solid solution. In order to confirm the structure and symmetry, further study had been carried out through some structural software, which will be presented later. The bulk density of the sintered specimens was measured by the Archimedes method. The relative density was determined using bulk density (calculated by taking mass and dimensions of the pellet) and theoretical density (determined using XRD data). The bulk density observed in [(BLNLT)-(BT), = 0.04/0.025/0] system was 5.8 gm/cc which is 97% of theoretical density, and the bulk density observed in [(BLNLT)-(BT), = 0.04/0.025/0.06] system was 5.7 gm/cc which is 95% of theoretical density.
Figure 2 showed microstructure of all the sintered samples of [(BLNLT)-(BT), = 0.04/0.025/0, 0.04/0.025/0.02 & 0.04/0.025/0.06] system taken for polished and etched surfaces. The microstructures of all the sintered samples were homogeneous, dense, and pore free. From the micrographs, it was evident that average grain size was found to decrease with Ba substitution in BLNLT system, which was consistent with the reported results . In the present system, grain growth was slightly inhibited with the substitution of Ba2+ and small grains were formed, which may be due to the reduction in the mobility of the grain boundary. Thus, the mass transportation was weakend after the addition of Ba2+ . The linear intercept method was used to determine the average grain size of these samples (See Table 1).
Figure 3 illustrated the temperature dependence of dielectric constant and dielectric loss of BLNLT-BT ceramics at different frequencies (1, 10, and 100 kHz). The temperature dependence of showed that increased upto certain temperature and exhibited broad dielectric maxima around , which decreased gradually with further increase in temperature above . In general, two broad dielectric anomalies were obtained in BNT system, which is known to be and where “” referred as depolarization temperature, corresponding the transition from ferroelectric to antiferroelectric transition, and it can also be derived from the peak in the temperature dependence plot of tan δ , and “” referred as the temperature of maximum dielectric constant which corresponds to the transition from antiferroelectric to paraelectric phase transition. It was observed that dielectric plots of specimen exhibited slight frequency dependence above (near ) and for specimens , the dielectric constant was frequency dependent especially at low frequency and at higher temperature, and it seemed to be common feature in ferroelectric materials associated with ionic conductivity, and generally referred as low frequency dielectric dispersion . The relative effect of ionic conductivity became small with increasing frequency. As a result, the frequency dependence of becomes weak. However, tan δ showed variation with frequency in a different manner, tan δ increased with increasing frequency and the increment was ascribed to the ionic conductivity. The retardation in polarization caused from ionic conductivity was enhanced with an increase in frequency that led to an increase of tan δ [28, 29], Figures 3(b) and 3(c). The dielectric constant decreased whereas slightly increased with increase in frequency [30, 31].
As evident from Figure 3, the values of dielectric constant and dielectric loss were decreased at higher frequencies, with the addition of Ba in BLNLT system. It was observed that the phase transition at is a diffuse type phase transition as there was no dispersion between versus frequency in the BLNLT-BT system. The phase transitions (blue circle) and (red circle) shifted towards low temperature with increasing Ba content in BLNLT system (see Figure 3), which was expected owing to low Curie temperature ( ~ 130°C as compared with that of BLNT ~ 355°C) of Barium titanate. The maximum dielectric constant and low value of dielectric loss were observed for the specimen at room temperature. For all the specimens, the values of dielectric constant and dielectric loss were listed in Table 1.
The diffuseness of BLNLT- BT ceramics can be expressed by equation, proposed by modified Curie-Weiss law , where, is Curie coefficient, is degree of diffuseness, and the maximum value of dielectric constant at . The exponent “” can have a value ranging from 1 (for normal ferroelectric) to 2 (for an ideal relaxor ferroelectric). A linear relationship was observed in all the samples above from versus plots, which is shown in Figure 4. For present system, the values of “” lie in the range of 1.58–1.79, which indicated that the material is highly disordered and diffuse phase transition was observed in BLNLT-BT system. The diffuseness was attributed mainly to the structural disordering and compositional fluctuations in the arrangement of cations in one or more crystallographic sites of the structure.
Figure 5 showed the room temperature hysteresis (P-E) loops for the sample at different frequencies. It was found that the sample with exhibited saturation polarization under an applied electric field of 50–60 kV/cm at 50 Hz with high and low . The value of polarization was observed to decrease with increasing frequency. This may be due to the fact that the contributions of all type of polarization are present at low frequency. As the frequency is increased, this type of contribution is decreased. The variations of and for all the samples were listed in Table 1.
The piezoelectric measurements of the poled BLNLT-BT system, sintered at 1150°C, for 2 hour, measured at room temperature were included in Table 1. With Ba2+ substitution, the piezoelectricity was reduced. According to thermodynamic theory of ferroelectricity, piezoelectric charge constant () is greatly dependent on the relative permittivity and polarization, which is directly proportional to dielectric permittivity () and remnant polarization (), as per the following equation :
where , , and , are the vacuum/relative permittivity and electrostrictive coefficient, respectively, where should not change significantly by the doping for perovskite ceramics. Thus, value of had been found to decrease due to weak ferroelectricity in BLNLT-BT system. Electrical properties of BLNLT-BT system had been compared with reported results (shown in Table 2). There were few reports, which are available on grain size, in which grain size played an important role to affect piezoelectric properties. The piezoelectric properties were expected to degrade with smaller grain size and improved the dielectric strength and mechanical strength , which may be explained on the basis of several models including the presence of internal stress in fine-grained ceramics, which was due to the absence of 90° domain walls, increased domain-wall contributions to the dielectric response in fine-grained ceramics, shift in phase transition temperatures with grain size, and so forth .
In summary, the complex BLNLT-BT system with compositions was synthesized at temperature 1150°C by semiwet technique. The substitution of La/Li/Ba had shown a significant effect on the microstructure, phase transition temperatures ( & ), dielectric, ferroelectric, and piezoelectric properties in BLNLT-BT system. Microstructure of all the specimens exhibited homogeneous grain growth, and the grain size was found to decrease with substitution of Ba in BLNLT-BT system. The temperature dependence of dielectric constant confirmed diffuse phase transition behaviour in BLNLT-BT system. There was a significant influence of the reduced grain size on the dielectric and piezoelectric properties of present system with Ba substitution.
One of the authors, Ms. Vijayeta Pal, is thankful to JIIT for providing teaching assistan ship and other research facilities to carry out her research work at JIIT, Noida, India.
- J. Rödel, W. Jo, K. T. P. Seifert, E.-M. Anton, T. Granzow, and D. Damjanovic, “Perspective on the development of lead-free piezoceramics,” Journal of the American Ceramic Society, vol. 92, no. 6, pp. 1153–1177, 2009.
- G. A. Smolenskii, V. A. Isupov, A. I. Agranovskaya, and N. N. Kainik, “New ferroelectrics of complex composition,” Soviet Physics: Solid State, vol. 2, no. 11, pp. 2651–2654, 1961.
- H. Nagata and T. Takenaka, “Additive effects on electrical properties of (Bi1/2Na1/2)TiO3 ferroelectric ceramics,” Journal of the European Ceramic Society, vol. 21, no. 10-11, pp. 1299–1302, 2001.
- D. M. Lin and K. W. Kwok, “Dielectric and piezoelectric properties of (Bi1−x−yNdxNa1−y)0.5BayTiO3 lead-free ceramics,” Current Applied Physics, vol. 10, pp. 422–427, 2010.
- Z. W. Chen and J. Q. Hu, “Piezoelectric and dielectric properties of (Bi0.5Na0.5)0.94Ba0.06TiO3–Ba(Zr0.04Ti0.96)O3 lead-free piezoelectric ceramics,” Ceramics International, vol. 35, no. 1, pp. 111–115, 2009.
- T. Takenaka, K. Maruyama, and K. Sakata, “(Bi1/2Na1/2)TiO3–BaTiO3 system for lead-free piezoelectric ceramics,” Japanese Journal of Applied Physics, vol. 30, pp. 2236–2239, 1991.
- P. Pookmanee, G. Rujijanagul, S. Ananta, R. B. Heimann, and S. Phanichphant, “Effect of sintering temperature on microstructure of hydrothermally prepared bismuth sodium titanate ceramics,” Journal of the European Ceramic Society, vol. 24, no. 2, pp. 517–520, 2004.
- D. L. West and D. A. Payne, “Preparation of 0.95Bi1/2Na1/2TiO3·0.05BaTiO3 ceramics by an aqueous citrate-gel route,” Journal of the American Ceramic Society, vol. 86, no. 1, pp. 192–194, 2003.
- J. G. Hou, Y. F. Qu, W. B. Ma, and D. Shan, “Synthesis and piezoelectric properties of (Na0.5Bi0.5)0.94Ba0.06TiO3 ceramics prepared by sol-gel auto-combustion method,” Journal of Materials Science, vol. 42, no. 16, pp. 6787–6791, 2007.
- C. Y. Kim, T. Sekino, and K. Niihara, “Synthesis of bismuth sodium titanate nanosized powders by solution/sol-gel process,” Journal of the American Ceramic Society, vol. 86, no. 9, pp. 1464–1467, 2003.
- J. Hao, X. Wang, R. Chen, and L. Li, “Synthesis of (Bi0.5Na0.5)TiO3 nanocrystalline powders by stearic acid gel method,” Materials Chemistry and Physics, vol. 90, no. 2-3, pp. 282–285, 2005.
- H. L. Du, W. C. Zhou, F. Luo, D. M. Zhu, B. Qu, and Z. B. Pei, “An approach to further improve piezoelectric properties of (K0.5Na0.5)NbO3-based lead-free ceramics,” Applied Physics Letters, vol. 91, no. 20, Article ID 202907, 3 pages, 2007.
- D. M. Lin, D. Xiao, J. Zhu, P. Yu, H. Yan, and L. Li, “Synthesis and piezoelectric properties of lead-free piezoelectric [Bi0.5(Na1−x−yKxLiy)0.5]TiO3 ceramics,” Materials Letters, vol. 58, pp. 615–618, 2004.
- K. H. Lam, M. S. Guo, D. M. Lin, K. W. Kwok, and H. L. W. Chan, “Lead-free piezoelectric BNKLT 1−3 composites,” Journal of Materials Science, vol. 43, no. 5, pp. 1677–1680, 2008.
- Y. Zhang, R. Chu, Z. Xu, Q. Chen, Y. Liu, and G. Zhang, “Effects of Li2CO3 on the sintering behavior and piezoelectric properties of Bi2O3-excess (Bi0.5Na0.5)0.94Ba0.06TiO3 ceramics,” Current Applied Physics, vol. 12, no. 1, pp. 204–209, 2012.
- A. Herabut and A. Safari, “Processing and electromechanical properties of (Bi0.5Na0.5)(1−1.5x)LaxTiO3 ceramics,” Journal of the American Ceramic Society, vol. 80, no. 11, pp. 2954–2958, 1997.
- V. Pal and R. K. Dwivedi, “Effect of rare earth Gadolinium substitution on the structural, microstructure and dielectric properties of lead free BNT ceramics,” Advanced Materials Research, vol. 585, pp. 200–204, 2012.
- V. Pal, R. K. Dwivedi, and O. P. Thakur, “Effect of processing on synthesis and dielectric behavior of bismuth sodium titanate ceramics,” Journal of Ceramics, vol. 2013, Article ID 261914, 6 pages, 2013.
- T. Zhou, R. Huang, X. Shang, et al., “Lead-free In2O3-doped (Bi0.5Na0.5)0.93Ba0.07TiO3 ceramics synthesized by direct reaction sintering,” Applied Physics Letters, vol. 90, no. 18, Article ID 182903, 2007.
- X. Zhou, H. Gu, Y. Wang, W. Y. Li, and T. S. Zhou, “Piezoelectric properties of Mn-doped (Na0.5Bi0.5)0.92Ba0.08TiO3 ceramics,” Materials Letters, vol. 59, no. 13, pp. 1649–1652, 2005.
- G. O. Jones and P. A. Thomas, “Investigation of the structure and phase transitions in the novel A-site substituted distorted perovskite compound Na0.5Bi0.5TiO3,” Acta Crystallographica B, vol. 58, pp. 168–178, 2002.
- S. Gorfman and P. A. Thomas, “Evidence for a non-rhombohedral average structure in the lead-free piezoelectric material Na0.5Bi0.5TiO3,” Journal of Applied Crystallography, vol. 43, pp. 1409–1414, 2010.
- E. Aksel, J. S. Forrester, J. L. Jones, P. A. Thomas, K. Page, and M. R. Suchomel, “Monoclinic crystal structure of polycrystalline Na0.5Bi0.5TiO3,” Applied Physics Letters, vol. 98, no. 15, Article ID 152901, 2011.
- D. Lin and K. W. Kwok, “Structure, ferroelectric and piezoelectric properties of (Bi0.98−x La0.02Na1−x )0.5Bax TiO3 lead-free ceramics,” Applied Physics A, vol. 97, no. 1, pp. 229–235, 2009.
- K. Ramam and M. Lopez, “Ferroelectric and piezoelectric properties of Ba modified lead zirconium titanate ceramics,” Journal of Physics D, vol. 39, no. 20, p. 4466, 2006.
- K. Yoshii, Y. Hiruma, H. Nagata, and T. Takenaka, “Electrical properties and depolarization temperature of (Bi1/2Na1/2)TiO3–(Bi1/2K1/2)TiO3 lead-free piezoelectric ceramics,” Japanese Journal of Applied Physics, vol. 45, pp. 4493–4496, 2006.
- S. P. Yordanov, I. Ivanov, and C. P. Carapanov, “Dielectric properties of the ferroelectric Bi2Ti2O7 ceramics,” Journal of Physics D, vol. 31, no. 7, pp. 800–806, 1998.
- X. X. Wang, C. L. Choy, X. G. Tang, and H. L. W. Chan, “Dielectric behavior and microstructure of (Bi1/2Na1/2)TiO3–(Bi1/2K1/2)TiO3–BaTiO3 lead-free piezoelectric ceramics,” Journal of Applied Physics, vol. 97, no. 10, Article ID 104101, 4 pages, 2005.
- C. Zhou, X. Liu, W. Li, and C. Yuan, “Dielectric and piezoelectric properties of Bi0.5Na0.5TiO3–Bi0.5K0.5TiO3–BiCrO3 lead-free piezoelectric ceramics,” Journal of Alloys and Compounds, vol. 478, no. 1-2, pp. 381–385, 2009.
- S. Said and J. P. Mercurio, “Relaxor behaviour of low lead and lead free ferroelectric ceramics of the Na0.5Bi0.5TiO3–PbTiO3 and Na0.5Bi0.5TiO3–K0.5Bi0.5TiO3 systems,” Journal of the European Ceramic Society, vol. 21, no. 10-11, pp. 1333–1336, 2001.
- Y. M. Li, W. Chen, Q. Xu, J. Zhou, X. Gu, and S. Fang, “Electromechanical and dielectric properties of Na0.5Bi0.5TiO3–K0.5Bi0.5TiO3–BaTiO3 lead-free ceramics,” Materials Chemistry and Physics, vol. 94, no. 2-3, pp. 328–332, 2005.
- K. Uchino and S. Nomura, “Critical exponents of the dielectric-constants in diffused-phase-transition crystals,” Ferroelectrics Letters Section, vol. 44, no. 11, pp. 55–61, 1982.
- D. Damjanovie, “Ferroelectric, dielectric and piezoelectric properties of ferroelectric thin films and ceramics,” Reports on Progress in Physics, vol. 61, no. 9, p. 1267, 1998.
- M. Cernea, B. S. Vasile, C. Capiani, A. Ioncea, and C. Galassi, “Dielectric and piezoelectric behaviors of NBT-BT0.05 processed by sol-gel method,” Journal of the European Ceramic Society, vol. 32, no. 1, pp. 133–139, 2012.
- M. Cernea, E. Andronescu, R. Radu, F. Fochi, and C. Galassi, “Sol-gel synthesis and characterization of BaTiO3-doped (Bi0.5Na0.5)TiO3 piezoelectric ceramics,” Journal of Alloys and Compounds, vol. 490, no. 1-2, pp. 690–694, 2010.
- M. Cernea, C. Galassi, B. S. Vasile et al., “Structural, dielectric, and piezoelectric properties of fine-grained NBT-BT0.11 ceramic derived from gel precursor,” Journal of the European Ceramic Society, vol. 32, no. 10, pp. 2389–2397, 2012.
- P. Jarupoom, K. Pengpat, N. Pisitpipathsin et al., “Development of electrical properties in lead-free bismuth sodium lanthanum titanate-barium titanate ceramic near the morphotropic phase boundary,” Current Applied Physics, vol. 8, no. 3-4, pp. 253–257, 2008.
- B. H. Kim, S. J. Han, J. H. Kim, J. H. Lee, B. K. Ahn, and Q. Xu, “Electrical properties of (1−x)(Bi0.5Na0.5)TiO3−xBaTiO3 synthesized by emulsion method,” Ceramics International, vol. 33, no. 3, pp. 447–452, 2007.
- M. P. McNeal, S.-J. Jang, and R. E. Newnham, “The effect of grain and particle size on the microwave properties of barium titanate (BaTiO3),” Journal of Applied Physics, vol. 83, no. 6, pp. 3288–3297, 1998.