Effects of annealing on particle size and pore size distribution of hydrothermally synthesized BaTiO3 nanopowders and their grain-growth kinetics during sintering

With an increase in the annealing temperature, the hydrothermally synthesized BaTiO3 nanopowders increased in particle sizes from 100 to 260 nm and decreased in pore volume from 7.2 to 2.82 cm3 g−1, while the pore size remained constant at 3.06 nm. Samples with different initial particle sizes were sintered in the temperature range of 1210 °C–1300 °C and for periods of 0.5–48 h at 1270 °C. The kinetic grain-growth exponent of the sintered BaTiO3 samples, n, was proportional to the increase of an initial particle size and the decrease of pore volume, and the grain growth obeyed the Arrhenius equation. The activation energies for the grain growth of the sintered BaTiO3 samples with initial particle size of 100, 155 and 260 nm were 737, 702 and 755 kJ mol−1, respectively, indicating that the activation energy was independent of the initial particle size in the range of 100–300 nm under identical purity conditions, and pore volume was supposed to be attributed to the velocity of grain growth.


Introduction
BaTiO 3 is a perovskite-type electroceramic material that has been extensively studied and utilized owing to its high dielectric constant and low tangent loss. They are often used as basic ferroelectric materials in various electronic components, such as multilayer ceramic capacitors (MLCC), positive temperature coefficient (PTC) thermistors, optoelectronic devices, memory applications, sensors and actuators. Additionally, BaTiO 3 can be used as a chemical sensors owing to its surface sensitivity for gas adsorption [1][2][3][4][5]. Prototype BaTiO 3 is used as the ferroelectric additive for fabricating high-performance ferroelectric-based composites, which are used for advanced energy conversion and storage applications [6]. BaTiO3 has proven to be a promising photocatalyst because of its low cost, low toxicity, environmental friendliness, and perovskite structure [7]. The ferroelectric phase transitions of BaTiO 3 involve the macroscopic polarizations. At the lowest temperature (< -110°C), the polarization of the rhombohedral phase is parallel to the 〈111〉 crystal axis. Upon heating BaTiO 3 , it undergoes transitions to orthorhombic (<3°C), tetragonal (<120°C), and cubic phases, wherein the macroscopic polarization is parallel to the orthorhombic 〈011〉 aixs, then to the tetragonal 〈001〉 aixs, and subsequently vanishes in the cubic phase [8].
Previously, BaTiO 3 was prepared using a high-temperature (>1100°C) solid-state reaction between BaCO 3 and TiO 2 , which yielded large crystal grains (>3 μm) with various shapes and sizes, thereby reducing chemical homogeneity [9]. In contrast, wet chemical methods, such as a novel tartaric acid coprecipitation [10], microwave-assisted microemulsion [11], and sol-gel hydrothermal synthesis of hollow nanoparticles [12], offer the advantages of phase purity and homogeneity. In this study, hydrothermal synthesis is used for BaTiO 3 preparation because of the production of fine particles with a narrow size distribution, direct preparation of crystalline BaTiO 3 without high-temperature calcination, and the generation of powders that do not need to be milled before sintering, thus avoiding contamination and producing spherical particles [13,14]. Additionally, hydrothermal powders are highly reactive during sintering [15].
Barium hydroxide reacts with titania under hydrothermal conditions to form barium titanate. The stoichiometric reaction is written as follows: Barium hydroxide is present as barium ions, whereas titania exists as a solid phase that dissolves into the liquid phase to participate in the reaction of equation (1). The hydrothermally synthesized BaTiO 3 powders initially contain H 2 O and OH − , which are eliminated by an annealing process that transforms the crystalline structure from cubic to tetragonal [16]. Notably, the hydrothermal technology has also been used to synthesize BaTiO 3 single crystals and thin films [17,18]. The electrical properties of BaTiO 3 are governed by grain size, density, and morphology of the materials, which depending on the grain-growth kinetics.
Regarding the grain growth of BaTiO 3 ceramics, previous studies have mainly focused on primary abnormal grain growth, secondary abnormal grain growth, and microstructural evolution without considering the kinetics of the process. The kinetics of the process can be classified as normal or abnormal grain growth. During normal grain growth, the grain size distribution remains constant. In contrast, during abnormal grain growth, a few abnormal grains grow at the expense fine matrix grains, which related to the presence of a second phase [19,20]. This study focuses on normal grain growth because the synthesized BaTiO 3 is of very high purity, and the powders used for the sintering process are fabricated by an annealing process.
Recently, a number of electrical and thermal properties for BaTiO 3 were evaluated based on only the particle size of the cubic and the tetragonal structures [21][22][23]. To the best of our knowledges, reports on the variation in particle size, pore volume, and pore size distribution are limited, whereas those on the phase transition induced by annealing and its effect on the grain-growth kinetics of hydrothermal BaTiO 3 nanopowders during sintering are not. Therefore, this study aims to analyze the morphology and pore size distribution of hydrothermal BaTiO 3 nanopowders obtained by annealing and elucidate the grain-growth exponent and activation energy for the isothermal grain growth of pre-annealed BaTiO 3 powder.

Material and methods
The hydrothermally synthesized BaTiO3 nanopowders with a mean particle size of ∼100 nm, purity of 99.95%, and cubic crystal structure (Shandong Sinocera Functional Material Co., Ltd, China) were synthesize and annealed at 600°C and 750°C for 5 h to increase the particle size without transforming the crystal structure from cubic to tetragonal, which is based on empirical research that the phase transition of hydrothermally synthesized BaTiO 3 occurs at annealing temperatures higher than 850°C [16]. Three powders with different particle sizes were prepared by the annealing process and compressed into a cylindrical shape with a diameter of 6 mm and thickness of 2 mm at 60 MPa for 5 min at room temperature. The compressed samples were dried at 150°C in an oven for 2 h prior to sintering. The BaTiO 3 samples were sintered in the temperature range of 1210°C-1300°C for 2 h and for different holding times in the range of 0.5-48 h at 1270°C under N 2 atmosphere.
The specific surface area (SSA), pore size, and pore volume measurements of the BaTiO 3 nanopowders before and after annealing were determined using an automatic adsorption instrument (Quanta chrome Corp. Quadrasorb evo, USA). Sample degassing was performed at 170°C for 13 h, before the absorption and desorption of liquid N 2 at 77 K. The MicroActive 4.0 software (TriStar II 3020 version 2.0) was used to generate the Brunauer-Emmett-Teller (BET) surface area and the Barrrett-Joyner-Helenda (BJH) pore size distribution of the activated carbons. The microstructure and morphology of the powders and sintered samples were characterized by scanning electron microscopy (SEM) at an accelerating voltage of 15 kV (SU5000, Hitachi). The sintered samples were mechanically ground using grinding papers and then polished in a vibratory polishing machine with 0.05 μm for 1 h. To prevent specimen charging, a layer of platinum was sputter-coated onto the powder and sintered samples for 10 s. The particle and grain sizes of the powders and sintered samples were calculated using image analysis software (Image-Pro, Media Cybernetics Inc.).

Results
The morphology of the annealed BaTiO 3 powders was characterized by the electron microscopy technique SEM. Figures 1(a)-(c) show the SEM images of the BaTiO 3 nanopowders before and after annealing at 600°C and 750°C, and figures 1(a′)-(c′) show the corresponding particle size distribution histograms for the samples. The as-received BaTiO 3 powders increased in particle size with an increase in annealing temperature up to 750°C, while the approximately spherical particle morphology was retained after the annealing process. As shown in figures 1(a′)-(c′), the mean particle sizes of the three samples were approximately 100, 155 and 260 nm, respectively, and the standard deviation increased slightly with an increase in particle sizes.
As shown in figure 2, the BET isotherms for nitrogen adsorption by the BaTiO 3 powder with particle sizes of 100, 155, and 260 nm were measured to evaluate the pore structure. The distinctive hysteresis loop was mainly observed at a higher pressure, that is, P/P0 = 0.0-1.0, indicating a type IV isotherm, which is indicative of a typical mesoporous material [24]. The SSA of the BaTiO 3 powders with particle sizes of 100, 155 and 260 nm, determined from the N 2 adsorption-desorption isotherm using the BET method, were 22.28, 18.23, and 12.63 m 2 g −1 , respectively. The SSA decreased as the particle size increased, which was consistent with the trend of the adsorption capacity of the tested BaTiO 3 samples with increasing pore volume. The pore volume of the samples with particle sizes of 100, 155, and 260 nm were 7.2, 4.01 and 2.82 cm 3 g −1 , respectively.
The pore size distribution, determined from the adsorption-desorption curve using the BJH method, was analyzed as a function of the pore diameter of the BaTiO 3 powders, as shown in figure 3. Figure 3 shows the pore size distribution for pore diameters ranging from 1 to 200 nm. The macropore (50 nm) volume decreased with an increase in particle sizes from 100 nm (figure 3(a)) to 260 nm ( figure 3(c)), indicating that the annealing process is effective for decreasing the macropore volume in the BaTiO 3 powders. The overall pore size decreased because elevated temperatures allow atoms and molecules within the powder to diffuse and migrate during annealing. The distinct peak in the pore size (5 nm) distribution curve confirmed the presence of very narrow pores in the annealed BaTiO 3 powders. Most of the pores were in the range of 1-10 nm, and the maximum  number of pores had a diameter of 3 nm. The compressed samples with different particle sizes and pore volumes were sintered at different temperatures and holding times in an N 2 atmosphere, and their microstructural evolution were observed. Figure 4 shows the images of the sintered BaTiO 3 samples with different particle sizes and holding times at the sintering temperature of 1270°C. The observed plane was perpendicular to the compression direction. All the samples were composed of approximately equiaxed grains, and the grain size increased with increasing holding time at the set sintering temperature. The pore volume between the grains in the sintered samples decreased significantly, and the grain sizes rapidly increased with an increase in the holding time from 0.5 to 12 h. The thermodynamic driving force for grain growth is assumed to be the difference in the interfacial energy between the large and small grains. Typically, small grains exhibit higher activity because of their large surface energies. Thus, they were easily absorbed by the large grains to reduce the surface energy, as shown in figures 4(d)-(f). After sintering for 12 h, more pores were observed in matrix of the sample with an initial particle size of 100 nm than in the matrix of the sample with an initial particle size of 260 nm, suggesting that the growth velocity of the sample with a lower pore volume is larger than that of the sample with a higher pore volume. Figure 5 shows the SEM images of the BaTiO 3 samples with different particle sizes and sintering temperature at the holding time of 2 h. Similar to figure 4, all samples were composed of almost equiaxed grains, and the grain sizes increased with increasing annealing temperature from 1210°C to 1300°C for 2 h. The small grains observed in figures 5(a)-(c) were not detected in the samples annealed at 1300°C, as shown in figures 5(d)-(f), indicating that grain growth occurs at the expense of these small grains owing to the reduction in the surface  energy. The larger the initial particle size of the sample, the larger the resulting grain size obtained at all the sintering temperatures.
The evolution of the mean grain size of the samples with initial particle size in the range of 100 to 260 nm under different sintering conditions in terms of sintering time and temperature in the range of 1210°C-1300°C is shown in figure 6, and the error bars represent the standard deviation of the grain-size measurement. Based on the obtained graph, the mean grain size increased with the sintering time and temperature. As shown in figure 6(a), grain growth was clearly faster in the sample with an initial particle size of 260 nm than in that with an initial particle size of 110 nm. Generally, during the initial stages of heating, the grain-growth rate increases rapidly because a significant amount of energy is available to promote the movement of atoms and the merging of neighbouring grains. However, as the grains increase in size, they begin to hinder grain growth, and thus the growth rate decreases. Eventually, the growth rate decreases until it is effectively negligible [25]. As shown in figure 6(b), above a sintering temperature of 1270°C, grain growth occurred more rapidly, and the mean grain sizes of the samples with relatively larger initial particle sizes were greater than those of samples with relatively smaller initial particle sizes.  To determine the grain-growth kinetics, the data from figure 6(a) were fitted to the equation for classical grain-growth kinetics [26,27], which is commonly described as follows: where G is the grain size at time t, G 0 is the initial grain size, K is a constant, and n is the grain-growth exponent representing the grain-growth behavior. The grain-growth exponent, n, was calculated from the inverse of the slope of the ln G versus ln t plot at a constant sintering temperature, as followed as [28]: Figure 7(a) shows the mean grain size as a function of the holding time at a sintering temperature of 1270°C. For the samples with initial particle sizes of 100, 155, and 260 nm, the slopes of the ln G versus ln t plots were 0.263, 0.301 and 0.309, and thus the grain-growth exponents n calculated from equation (2) were approximately 3.79, 3.31, and 3.23, respectively. As shown in figure 7(a), the R values, which represent the Pearson's correlation coefficients, were greater than 0.95, indicating that the data for all samples lies on an approximately straight line with a positive slope. When the initial particle sizes of the sintered samples were large, the samples had a low n value. At a constant n value, the activation energy Q for the grain-growth process can be calculated using the standard assumption that K can be expressed in the Arrhenius form as follows [29]: where Q is the activation energy; T is the temperature in Kelvin; K 0 is the pre-exponential value, which is assumed to be constant over the investigated temperature range; R is the gas constant. By integrating equations (1) and (3), the activation energy for grain growth can be determined from the slope of the Arrhenius plot of ln (G n /t) versus 1/T at a constant sintering times [18]: Figure 7(b) shows an Arrhenius plot for the samples sintered at temperatures between 1210 and 1300°C. Thus, the activation energy for the grain growth can be obtained from the average slopes of the graphs and were calculated to be 737, 702, and 755 kJ mol −1 for the sintered samples with initial particle size of 100, 155, and 260 nm, respectively.

Discussion
Hydrothermally synthesized BaTiO 3 nanopowders with a mean particle size of 100 nm were annealed at 600°C and 750°C, and the variation in particle size, SSA, pore volume, and pore size distribution were investigated. By increasing the annealing temperature, the nanopowders increased in particle size (up to 260 nm), and decreased in SSA (up to 12.6 m 2 g −1 ) and pore volume (up to 2.8 cm 3 g −1 ), while the mean pore size remained constant at 3 nm and the pore shape was unchanged. In the case of capillary condensation in the mesopores and macropores, the desorption pathway is different from that of adsorption, resulting in the formation of a hysteresis loop (figure 2) [30]. Because the loop type is mainly associated with the pore shape, the pore shapes of Figure 7. (a) ln G (grain size) versus ln t (sintering time) at 1270°C and (b) the Arrhenius plot of ln (G n /t) versus 1/T as a function of sintering temperature for the samples with different initial particle sizes the nanopowders before and after annealing were approximately analogues [31]. Furthermore, the number of the macropores in the as-received BaTiO 3 nanopowders decreased with increasing annealing temperature ( figure 3). Thus, it is proposed that the annealing process is effective for increasing the particle size of BaTiO 3 nanopowders, while decreasing the pore volume and quantity of macropores.
Various growth processes are distinguished based on their mechanisms of grain boundary migration, and the growth rate is directly proportional to the instantaneous average rate v¯of grain boundary migration in the structure [32]: where Ḡ is the mean grain size. Comparing equations (2) and (6), the larger the grain-growth exponent, n, the lower the grain boundary migration rate. In this study, when the BaTiO 3 samples with different initial particles sizes from 100 to 260 nm were sintered at various time and temperature, the grain-growth kinetics were determined by observing their microstructural evolution, as shown in figures 4 and 5. Based on the results of equation (3), the n value of the sintered samples increased as the initial particle size decreased, while the pore volume increased. The n value ranged from 2 to 4. If n = 1, the grain linearly increases in size with time as G-G 0 = Kt, that is, where denotes the abnormal grain growth assuming that the atomic structure of the boundary is unchanged [33]. The n value of 2, 3 and 4 are classified based on the control mechanism of boundary migration, which occurs by boundary diffusion in a pure single-phase system, defects such as vacancies, and pore migration involving the surface diffusion of atoms in impure single-phase systems [34,35]. In this study, the n values are in the range of 3-4, these results may indicate differences in the initial particle size and pore volume of the sintered samples. Generally, if grain growth is inhibited, the n value is large. The growth of the sample with an initial particle size of 100 nm was smaller than that of matrix, resulting in a larger n value for the sample with an initial size of 260 nm. This is because the presence of macropores (>50 nm) in the former powder inhibits grain boundary migration during sintering, resulting in the decreased grain-growth rate shown in figure 7(a). Although the sintered samples with different initial particle sizes had various n values, the activation energies for BaTiO 3 grain growth were similar (approximately 730 kJ mol −1 ) over a wide temperatures and grain sizes. The activation energy for the grain growth in BaTiO 3 has been reported to be approximately 750 kJ mol −1 [28], which is similar to the results obtained in this study. A similar activation energy (approximately 800 kJ mol −1 ) was reported for fine-grained BaTiO 3 in a superplastic flow [35]. Compared with the activation energies reported for BaTiO 3 grain growth in these previous studies, the activation energy of approximately 730 kJ mol −1 observed in this study may be related to the grain boundary diffusion mechanism of grain growth, despite the large difference in the initial particle size of the starting materials. The findings of this study demonstrate that the initial particle sizes in the range of 100 nm to 260 nm for the BaTiO 3 powder have little effect on the activation energy for grain growth. However, the pore volume of the powder impedes the rate of grain growth.

Conclusion
The microstructural evolution of hydrothermally synthesized BaTiO 3 nanopowders was investigated in the sintering time range of 0.5-48 h and the temperature range of 1210°C-1300°C using various initial particle sizes fabricated by the annealing process. Annealing the powders in the temperature range of 600°C-750°C increased the particle size and decreased the pore volume, while the pore size and shape remained unchanged. The pore volume of the powder significantly influences the rate of grain growth, because of the variation in the grain-growth exponent n. The n value of the sintered sample with an initial particle size of 100 nm was higher than that of the sample an initial particle size of 260 nm, indicating a slower growth rate for the former sample. The activation energy for grain growth was approximately 730 kJ mol −1 for the sintered samples, independent of the initial particle size.