Stabilization of Size-Controlled BaTiO3 Nanocubes via Precise Solvothermal Crystal Growth and Their Anomalous Surface Compositional Reconstruction.

Crystal growth of barium titanate (BaTiO3) using a wet chemical reaction was investigated at various temperatures. BaTiO3 nanoparticles were obtained at an energy-efficient temperature of 80 °C. However, BaTiO3 nanocubes with a preferred size and shape could be synthesized using a solvothermal method at 200 °C via a reaction involving titanium tetraisopropoxide [(CH3)2CHO]4Ti for nucleation and fine titanium oxide (TiO2) nanoparticles for crystal growth. The BaTiO3 nanocubes showed a high degree of dispersion without the use of dispersants or surfactants. The morphology of BaTiO3 was found to depend on the reaction medium. The size of the BaTiO3 particles obtained using water as the reaction medium was the largest among the particles synthesized using various reaction media. In the case of alcohol reaction media, the BaTiO3 particle size increased in the order methanol, ethanol, 1-propanol, 1-butanol, and 1-pentanol. Furthermore, BaTiO3 powder obtained using alcohol reaction media resulted in cubic shapes as opposed to the round shapes obtained when water was used as the medium. We found that the optimal condition for the synthesis of BaTiO3 nanocubes involved the use of 1-butanol as the reaction medium, resulting in an average particle size of 52 nm, which is the average distance of the cubes measured diagonally from corner to corner, and gives an average side length of 37 nm, and a tetragonal crystal system as evidenced by the powder X-ray diffraction pattern obtained using high-energy synchrotron X-rays. The origin of the spontaneous polarization of the BaTiO3 tetragonal crystal structure was clarified by a pair distribution function analysis. In addition, surface reconstruction of BaTiO3 nanocubes led to an outermost surface comprising two layers of Ti columns.

Introduction

Barium titanate (BaTiO3) is widely used in ceramic capacitors because of its ferroelectric and piezoelectric properties.[1,2] In addition, it exhibits high relative permittivity, enabling its use in sensors, actuators, power transmission devices, memory devices, and high energy storage devices.[1,3] However, further improvements to BaTiO3 particles are necessary in order to enhance their dielectric constant. BaTiO3 is generally synthesized at temperatures greater than 1000 °C via a solid-phase reaction although such a reaction makes controlling the morphology of the obtained powders difficult. However, a wet chemical reaction enables control of the morphology; moreover, it is a more energy-efficient process than a solid-phase reaction. Highly energy-efficient processes are those that can be performed at room temperature. A previous study demonstrated the synthesis of sub-10 nm BaTiO3 nanocrystals at room temperature via the vapor diffusion sol–gel method and their subsequent characterization by Rietveld analysis of synchrotron X-ray diffraction (XRD) data, Raman spectroscopy, and a pair distribution function (PDF) analysis, which revealed non-centrosymmetric regions arising from the off-centering of Ti atoms.[4] By contrast, a different reaction occurred at 200 °C using a novel nonaqueous route for the preparation of nanocrystalline BaTiO3.[5] The authors of this second paper reported obtaining nearly spherical BaTiO3 nanoparticles with diameters ranging from 4 to 5 nm.

The ideal BaTiO3 morphology is a single nano-sized crystal with a cubic shape.[6−10] A densely assembled ceramic can be created if uniform BaTiO3 nanocubes are used as a base substance. The authors of previous studies have reported using platinum (Pt)[11] and palladium (Pd)[12] nanocubes as a base substance; however, the strain between the BaTiO3 nanocubes led to a high dielectric constant in the densely assembled ceramic.[13] That is, BaTiO3 nanocubes are necessary for the material design because of the surface properties of the particles. The synthesis of BaTiO3 nanoparticles requires three key points: (1) a method to control the particle size because nanoscale materials are desirable as a consequence of their large specific surface area; (2) a method to control the particle shape because cubes are desirable as a consequence of the wide contract area between nanocubes; and (3) a method to control the particle surface as strain between nanocubes is desirable because it eliminates the need for a dispersant or surfactant.

Controlling BaTiO3 nucleation and crystal growth is essential[14,15] for the formation of BaTiO3 nanocubes. One technique for morphological control is a wet chemical reaction using a bottom-up approach that enables atomic-level control. Researchers have reported synthesizing BaTiO3 with various morphologies, including cube-like,[16] nanorod,[17] nanowire,[18] acicular,[19] and hollow[20] shapes, using wet chemical reactions. In the present study, we chose a solvothermal method as a wet chemical reaction method; this technique involves using reaction media at high temperatures and under high saturated vapor pressures in an autoclave. Specifically, we used the solvothermal method, which is a solvothermal method in which water is used as the reaction medium. We selected this method because it enables the dissolution of raw materials such as titanium oxide (TiO2) while maintaining control of nucleation and crystal growth at ∼200 °C. From the viewpoint of morphological control, surface modification is not used in BaTiO3 synthesis because the surface properties of BaTiO3 particles directly affect their dielectric constant.

We used electron microscopy to investigate the surface of the obtained BaTiO3 nanocubes. In particular, surface reconstruction was examined in detail. Surface reconstruction, where the atomic column arrangement at a crystal’s surface differs from the regular atomic column arrangement within the crystal, often occurs in one or two layers at the surface of metal oxide or oxynitride crystals. Previous studies have reported the occurrence of surface reconstruction on TiO2,[21−23] SrTiO3,[24−26] and LaTiO2N[27] crystals. These studies have provided important information about the function expression. In the present study, we primarily focused on the size, shape, and surface of BaTiO3 particles as well as on controlling their morphology during synthesis without modifying their surface.

Results and Discussion

Raw Materials and Reaction Media

The type and concentration of raw material, reaction temperature and time, and reaction medium are important factors for morphological control; these parameters determine the solubility of the raw material, nuclei formation, and crystal growth of the obtained powders. In the present study, we used TiO2 and/or [(CH3)2CHO]4Ti and Ba(OH)2·8H2O as raw materials and water, methanol, ethanol, 1-propanol, 1-butanol, and 1-pentanol as the reaction media.

Although TiO2 is difficult to dissolve in all the chosen reaction media, [(CH3)2CHO]4Ti is hydrolyzed in water and can be dissolved in methanol, ethanol, 1-propanol, 1-butanol, or 1-propanol. Ba(OH)2·8H2O can dissolve in water but not in the alcohol media. Additionally, the relative permittivity at room temperature differs among the media used, with water having the largest relative permittivity, followed by methanol, ethanol, 1-propanol, 1-butanol, and 1-pentanol. The relative permittivity of the reaction medium is closely related to the solubility of the raw material.

Synthesis of BaTiO3 Particles Below 80 °C

Figure shows XRD patterns for powders produced via solvothermal synthesis using TiO2 as a raw material and different reaction temperatures. TiO2 (10 mmol) and Ba(OH)2·8H2O (20 mmol) were the raw materials reacted for 72 h in water (40 mL) at room temperature, 40, 60, or 80 °C. The XRD pattern was assigned to a single phase of anatase-type TiO2. No peaks attributable to BaTiO3 were observed in the pattern for the product obtained after reaction at room temperature [Figure (a-1)]. However, the XRD pattern for the product obtained at 40 °C [Figure (b-1)] shows the formation of both anatase-type TiO2 and BaTiO3, with single phases of BaTiO3 also confirmed in the products obtained at 60 and 80 °C [Figure (c-1),(d-1)]. The XRD peaks were assigned to BaTiO3 with a tetragonal crystal system (JCPDS file: 5-0626). In addition, the full width at half-maximum of the XRD peaks assigned to BaTiO3 decreased with increasing reaction temperature, suggesting that the BaTiO3 crystallite became larger with increasing temperature.

Figure 1

XRD and ND patterns for powders produced via the hydrothermal method using TiO2 as a raw material at different reaction temperatures. TiO2 (10 mmol), Ba(OH)2·8H2O (20 mmol) for 72 h, with a reaction medium of water (40 mL) at (a-1) room temperature, (b-1, b-2, b-3) 40 °C, (c-1, c-2, c-3) 60 °C, and (d-1, d-2, d-3) 80 °C. ○: BaTiO3, ▲: TiO2.

XRD measurements with high-energy synchrotron X-rays and Rietveld refinement were performed to confirm the formation temperature of a single phase of BaTiO3. Rietveld refinement of the P4mm model of BaTiO3 in the tetragonal crystal system was executed using the RIETAN-FP[37,38] and Z-Rietveld[39−41] software packages for XRD and neutron diffraction (ND) patterns, respectively. The R-weighted pattern (Rwp) and R-pattern (Rp) are shown in Tables and 2.

Table 1

Rietveld Refinement of the Structural Parameters of the High-Energy Synchrotron XRD Pattern for the Same Sample Shown in Figure

BaTiO3, P4mm model
synthesis temperature (°C)	a/Å	c/Å	Rwp/%	Rp/%
40	4.00671(63)	4.01753(110)	1.66	1.07
60	4.01129 (43)	4.02317(78)	0.86	0.65
80	4.00643(39)	4.02050(71)	0.83	0.64

Table 2

Rietveld Refinement of the Structural Parameters of the High-Energy Synchrotron ND Pattern for the Same Sample Shown in Figure

BaTiO3, P4mm model
synthesis temperature (°C)	a/Å	c/Å	Rwp/%	Rp/%
40	4.03033(3)	4.03804(5)	4.08	3.19
60	4.02464(9)	4.04024(11)	5.21	3.79
80	4.02259(8)	4.04132(11)	3.11	2.42

The XRD pattern for the product obtained at 40 °C [Figure (b-2)] indicates that the principal component was BaTiO3 and that the peak intensity of anatase-type TiO2 decreased. Notably, we obtained BaTiO3 at 40 °C, which is an extremely low reaction temperature. When the synthesis temperature was increased, the amount of BaTiO3 obtained increased [Figure ]. The high-energy synchrotron XRD pattern for the product obtained at 80 °C [Figure (d-2)] clearly confirmed a single phase of BaTiO3.

A shortcoming of XRD is its poor ability to detect light elements such as oxygen (O) because an element’s atomic scattering factor depends on its atomic number; that is, the atomic scattering factor increases with increasing atomic number. ND has an advantage in detecting light elements such as oxygen because the coherent neutron scattering length varies by element. Therefore, ND measurements and Rietveld refinement were performed to confirm the presence of oxygen defects in BaTiO3. The corresponding Rwp and Rp values are shown in Figure . All the Rwp and Rp values from the Rietveld analysis were satisfactory [Figure (b-3,c-3,d-3)]. The ND pattern for the product obtained at 40 °C [Figure (b-3)] indicates that the principal component was BaTiO3 and the intensity of the anatase-type TiO2 decreased. When the synthesis temperature increased, the amount of BaTiO3 increased [Figure (c-3,d-3)]. The ND pattern for the product obtained at 80 °C [Figure (d-3)] shows that a single phase of BaTiO3 was obtained.

Tables and 2 show the Rietveld refinement structural parameters corresponding to the high-energy synchrotron XRD and ND pattern for the samples [Figure (b-1,c-1,d-1)]. The lattice constants obtained from refinement of the high-energy synchrotron XRD data and ND data were approximately the same. In addition, the ND analysis revealed no oxygen defects.

Figure shows secondary electron (SE) images of powders produced via solvothermal synthesis using TiO2 as a raw material and different reaction temperatures. Fine particles with diameters of tens of nanometers were observed in the product synthesized at room temperature [Figure a]. Fine particle agglomeration occurred at 40 °C [Figure b]. Moreover, the particle morphology revealed aggregated fine particles in the products obtained at 60 and 80 °C, where the particles increased in size and acquired a cubic shape at the higher temperature [Figure c,d].

Figure 2

SE images of powders produced via the hydrothermal method using TiO2 as a raw material and different reaction temperatures. TiO2 (10 mmol), Ba(OH)2·8H2O (20 mmol) for 72 h, with a reaction medium of water (40 mL) at (a)room temperature, (b) 40 °C, (c) 60 °C, and (d) 80 °C.

Transmission electron microscopy (TEM) observations and its nano-beam electron diffraction were conducted for two BaTiO3 nanoparticles (sample 1 and sample 2 as shown in the TEM image of Figure ); the nano-beam electron diffraction confirmed a single-crystalline structure (Figure ). Figure shows high-angle annular dark-field scanning transmission electron microscopy (HAADF–STEM) and annular bright-field scanning transmission electron microscopy (ABF–STEM) observations with electron energy loss spectroscopy (EELS) analysis for two BaTiO3 nanoparticles (sample 1 and sample 2 as shown in the TEM image of Figure ) in the direction of [001] incidence. EELS is an effective method for elemental analysis of BaTiO3 because characteristic X-rays for Ba and Ti cannot be distinguished in energy-dispersive X-ray spectroscopy (EDX). Figure shows observations of atomic columns in BaTiO3 produced via the solvothermal method at 80 °C from the direction of [001] incidence. Figure a,b shows different BaTiO3 particles. Atomic arrangement of Ba and Ti were observed in detail from HAADF–STEM and ABF–STEM. Also, elemental analyses of Ba and Ti were conducted using EELS peaks. Ba and Ti are indicated by green and red, respectively. Ti atomic columns were arranged in line with the surface of the BaTiO3 nanoparticle. Surface reconstruction of the BaTiO3 nanoparticle was confirmed from STEM observations and EELS analyses. In addition, EELS analysis of another BaTiO3 nanoparticle is shown in Figure S1. The surface reconstruction of the BaTiO3 nanoparticle is indicated in Figure S1.

Figure 3

TEM image and the corresponding nano-beam electron diffraction pattern for BaTiO3 produced via the solvothermal method at 80 °C, from the direction of [001] incidence. The accelerating voltage was 80 kV. TiO2 (10 mmol), Ba(OH)2·8H2O (20 mmol) for 72 h in 40 mL of water as a reaction medium. (a) Nano-beam diffraction of sample 1 and (b) nano-beam diffraction of sample 2.

Figure 4

Observation of atomic columns in BaTiO3 produced via the solvothermal method at 80 °C from the direction of [001] incidence. STEM images were observed at an accelerating voltage of 80 kV on an instrument equipped with a Cs corrector. (a) and (b) STEM observations of sample 1 and sample 2 of BaTiO3 particles shown in the TEM image of Figure , respectively. Ba and Ti are indicated by green and red of EELS elemental mapping, respectively. Scanning direction was only inverted for (b).

One explanation for the formation of BaTiO3 at temperatures above 40 °C is the inclusion of larger TiO2 particles and their solubility characteristics. In general, TiO2 does not dissolve in water at room temperature; however, fine TiO2 particles can dissolve in water with a basic pH. Therefore, when Ba(OH)2·8H2O was dissolved more readily in water at higher temperatures, the solution acquired a basic pH that promoted solvation of the fine TiO2 particles.

Synthesis of BaTiO3 Particles at Above 80 °C

Solvothermal Synthesis Using TiO2 as a Ti Raw Material

Following the solvothermal reaction of TiO2 and Ba(OH)2·8H2O between 100 and 200 °C for 72 h, the XRD pattern for the products revealed BaTiO3 with a tetragonal crystal system (JCPDS file: 5-0626). (Figures S2 and S3 in the Supporting Information). Regarding the effect of acetic acid treatment, the product remained unchanged at 200 °C for 72 h when compared with after the treatment [Figure S2 (f)] and before (Figure S3). Rietveld refinement of the P4mm model of BaTiO3 in the tetragonal crystal system was performed using the Z-Rietveld[39−41] software packages for the XRD pattern (Figure S3). Rietveld refinement revealed a single phase of BaTiO3 before acetic acid treatment. The R-weighted pattern (Rwp) and R-pattern (Rp) are shown in Table S1. All the Rwp and Rp values from the Rietveld analysis were satisfactory (Figure S3, Table S1). The SE images in Figure reveals that the synthesized particles were smallest at 100 °C [Figure a] and became larger with increasing reaction temperatures [Figure b–f]. Furthermore, the particles acquired a cubic shape with increasing temperature, with BaTiO3 cubes forming at 200 °C [Figure f]. It was found that the reaction temperature was important for synthesis of BaTiO3 nanocubes. Regarding the previous reports, a metal based on one element such gold (Au)[28−35] and palladium (Pd)[12] can be synthesized with the use of dispersants or surfactants below 80 °C (at a low temperature). On the other hand, cesium lead halide (CsPbX3) is given as an example with a perovskite structure being necessary below 160 °C (high temperature) for the nanocube synthesis.[36] Therefore, the reaction temperature is the key point for the nanocube synthesis.

Figure 5

SE images of obtained powders produced via the hydrothermal method using TiO2 as a raw material and different reaction temperatures. TiO2 (10 mmol), Ba(OH)2·8H2O (20 mmol) for 72 h, with a reaction medium of water (40 mL) at (a) 100 °C, (b) 120 °C, (c) 140 °C, (d) 160 °C, (e) 180 °C, and (f) 200 °C.

We next examined the effect of varying the Ba(OH)2·8H2O concentration on the solvothermal synthesis of BaTiO3. XRD patterns were assigned to the same tetragonal crystal system (JCPDS file: 5-0626) (Figure S4, Supporting Information); however, the shape changed dramatically as the Ba(OH)2·8H2O concentration was varied. Figure shows SE images indicating that formless particles were synthesized from low-concentration Ba(OH)2·8H2O [Figure a], whereas the shape gradually became cube-like as the Ba(OH)2·8H2O concentration increased [Figure b,c]. We found that cube-shaped BaTiO3 particles formed when the amount of Ba(OH)2·8H2O was greater than 20 mmol [Figure d–f], with no significant difference in shape, although their sizes were on the order of several hundred nanometers. Therefore, subsequent solvothermal syntheses were performed using 20 mmol of Ba(OH)2·8H2O as a raw material.

Figure 6

SE images of powders produced via the hydrothermal method using TiO2 as a raw material and different amounts of Ba(OH)2·8H2O as a raw material. TiO2 (10 mmol) at 200 °C for 72 h, with a reaction medium of water (40 mL) using Ba(OH)2·8H2O: (a) 5 mmol, (b) 10 mmol, (c) 15 mmol, (d) 20 mmol, (e) 25 mmol, and (f) 30 mmol.

We next evaluated the effect of reaction time on the solvothermal synthesis. The XRD patterns were assigned to BaTiO3 with a tetragonal crystal system (JCPDS file: 5-0626) (Figure S5, Supporting Information). Figure shows SE images revealing aggregated particles resulting from a relatively short reaction time [Figure a–c], where the shape of the BaTiO3 powder particles became gradually more cube-like as the reaction time was increased to 72 h [Figure d,e]. Moreover, we found no substantial difference in the shape of the BaTiO3 products at reaction times longer than 72 h [Figure e,f], where the particle size was on the order of several hundred nanometers. Therefore, subsequent solvothermal syntheses were performed at a reaction time of 72 h.

Figure 7

SE images of powders produced via the hydrothermal method at 200 °C using TiO2 as a raw material and different reaction times. TiO2 (10 mmol), Ba(OH)2·8H2O (20 mmol) at 200 °C, with a reaction medium of water (40 mL) for (a) 6 h, (b) 12 h, (c) 24 h, (d) 48 h, (e) 72 h, and (f) 96 h.

We subsequently evaluated the effects of different media on the BaTiO3 solvothermal synthesis. The XRD results indicate that the products crystallized in the same crystal system as those synthesized under the previously studied conditions (Figure S6, Supporting Information); however, the SE images indicate that the dielectric constant of the solvent affected the size and shape of the particles (Figure ). Water is a hydrophilic solvent with the largest room-temperature dielectric constant among the tested solvents. By contrast, the alcohol-based solvents are hydrophobic, with small room-temperature dielectric constants that vary with the number of carbon atoms (i.e., methanol < ethanol < 1-propanol < 1-butanol < 1-pentanol). We found that cube-like BaTiO3 crystals were obtained with particle sizes > 100 nm in water [Figure a], whereas the particle size was dramatically decreased in the alcohol-based solvents, with the smallest size observed in methanol and increasing according to the number of carbon atoms in the solvent (methanol < ethanol < 1-propanol < 1-butanol) [Figure b–e]. The particle shape was approximately the same between products synthesized in 1-butanol and 1-pentanol [Figure e,f]. Moreover, the shape became increasingly cubic under the same conditions in the alcohol solvents. Furthermore, electron microscopy observations were conducted at an acceleration voltage of 200 kV. The shape of nanocubes was clearly observed from the SE and bright-field transmission electron microscopy (BF–TEM) images [Figure a,b]. A single crystal of BaTiO3 was confirmed from the selected area electron diffraction (SAED) pattern for the BF–TEM image [Figure c].

Figure 8

SE images of powders produced via the solvothermal method using various reaction media. TiO2 (10 mmol), Ba(OH)2·8H2O (20 mmol) at 200 °C for 72 h in 40 mL of reaction medium of (a) water, (b) methanol, (c) ethanol, (d) 1-propanol, (e) 1-butanol, (f) and 1-pentanol.

Figure 9

SE images, BF–TEM image from the direction of [001] incidence, and the corresponding SAED pattern for powders produced via the solvothermal method using TiO2 (10 mmol) and Ba(OH)2·8H2O (20 mmol) as raw materials at 200 °C for 72 h in 40 mL of reaction medium of water. (a) SE image, (b) BF–TEM image, and (c) SAED image of (b).

Solvothermal Synthesis Using [(CH3)2CHO]4Ti and/or TiO2 as the Raw Material for Ti

The solubility of the raw material is an important factor for morphological control because of its effect on nucleation and crystal growth. We aimed to enable the formation of a large number of BaTiO3-nuclei to obtain nanoscale BaTiO3. We used [(CH3)2CHO]4Ti and TiO2 as raw materials. The [(CH3)2CHO]4Ti is soluble in methanol, ethanol, 1-propanol, 1-butanol, and 1-pentanol at room temperature; however, TiO2 cannot dissolve in alcohol-based solvents at room temperature but rather requires heat treatment to enable Ti-related crystal growth. We found that using a mixture of [(CH3)2CHO]4Ti and TiO2 under solvothermal conditions led to BaTiO3-nucleation and crystal growth, respectively, with the number of nuclei determining the particle size (a large number of nuclei resulted in small particles and vice versa) and crystal growth determining the particle shape. We therefore conducted solvothermal synthesis using [(CH3)2CHO]4Ti and TiO2 as raw materials to obtain BaTiO3 nanocubes.

We predicted that the size of the obtained particles would increase in the alcohol-based solvents because of the high solubility of [(CH3)2CHO]4Ti decreasing the dielectric constant of the solvent. XRD patterns were assigned to BaTiO3 with a tetragonal crystal system (JCPDS file: 5-0626) (Figure S7, Supporting Information), and the SE images revealed cube-like shapes under all solvent conditions [Figure a–f]. However, the sizes of the products varied greatly according to each solvent, with water producing the largest particles [Figure a]. Hydrolysis of [(CH3)2CHO]4Ti in water resulted in its precipitation, whereas the alcohol-based solvents dissolved [(CH3)2CHO]4Ti. Similar to the results of solvothermal synthesis using TiO2 as a raw material, we found that the sizes of the cube-like BaTiO3 crystals decreased in the alcohol-based solvents, with the smallest size observed in methanol increasing with increasing the number of carbon atoms in the solvent (methanol < ethanol < 1-propanol < 1-butanol < 1-pentanol) [Figure b–f]. The morphology of the particles synthesized in 1-butanol and 1-pentanol was approximately the same [Figure e,f].

Figure 10

SE images of powders produced via the solvothermal method using [(CH3)2CHO]4Ti as a raw material and various reaction media. [(CH3)2CHO]4Ti (10 mmol), Ba(OH)2·8H2O (20 mmol) at 200 °C for 72 h in 40 mL of reaction medium of (a) water, (b) methanol, (c) ethanol, (d) 1-propanol, (e) 1-butanol, and (f) 1-pentanol.

We next evaluated the result of using equal parts of [(CH3)2CHO]4Ti and TiO2 as raw materials in different media for solvothermal synthesis of BaTiO3. The XRD patterns showed the same tetragonal crystal system (JCPDS file: 5-0626) (Figure S8, Supporting Information). The SE images revealed cube-like shapes and large particles when water was used as the reaction medium [Figure a]. In addition, the BaTiO3 products displayed substantially smaller particle sizes when methanol, ethanol, 1-propanol, 1-butanol, and 1-pentanol were used as solvents [Figure b–f]. Moreover, the particle sizes for the BaTiO3 powders increased as the solvent was varied from methanol to ethanol, 1-propanol, and 1-butanol, with the powders obtained using 1-butanol and 1-pentanol showing similar particle sizes [Figure e,f]. We found that the morphology from the reaction with 1-butanol was optimal for the synthesis of BaTiO3 nanocubes [Figure e].

Figure 11

SE images of powders produced via the solvothermal method using equal parts [(CH3)2CHO]4Ti and TiO2 as raw materials and various reaction media. [(CH3)2CHO]4Ti (5 mmol), TiO2 (5 mmol), Ba(OH)2·8H2O (20 mmol) at 200 °C for 72 h in 40 mL of reaction medium of (a) water, (b) methanol, (c) ethanol, (d) 1-propanol, (e) 1-butanol, and (f) 1-pentanol.

We subsequently investigated the effects of different ratios of [(CH3)2CHO]4Ti and TiO2 in 1-butanol for the solvothermal synthesis of BaTiO3. The XRD patterns were again assigned to a tetragonal crystal system (JCPDS file: 5-0626) (Figure S9, Supporting Information), and SE images showed fine particles with cubic shapes [Figure a–e]. Regarding the effect of acetic acid treatment as shown in Figure d, there was a second phase of barium carbonate (BaCO3) before acetic acid treatment (Figure S10). Rietveld refinement of the P4mm model of BaTiO3 in the tetragonal crystal system was performed using the Z-Rietveld[39−41] software packages for XRD patterns. Rietveld refinement revealed the products of BaTiO3 and BaCO3 before acetic acid treatment. The R-weighted pattern (Rwp) and R-pattern (Rp) are shown in Table S2. All of the Rwp and Rp values from the Rietveld analysis were satisfactory. However, acetic acid treatment removed the second phase of BaCO3 and a single phase of BaTiO3 was obtained after acetic acid treatment [Figure d]. The BaTiO3 morphology changed to uniform-sized particles upon addition of [(CH3)2CHO]4Ti to TiO2 [Figure b–d], with the optimal solvothermal condition for the BaTiO3 nanocubes determined to be 7.5 mmol TiO2 and 2.5 mmol [(CH3)2CHO]4Ti [Figure d]. The average particle size of BaTiO3 nanocubes which were synthesized with the optimal solvothermal condition was 52 nm, which is the average distance of the cubes measured diagonally from corner to corner, and the average side length was 37 nm.

Figure 12

SE images of powders produced via the solvothermal method using different ratios of Ti raw materials. Ba(OH)2·8H2O (20 mmol) at 200 °C for 72 h in reaction medium of 1-butanol (40 mL). Ti raw material: [(CH3)2CHO]4Ti: (a) 10 mmol, (b) 7.5 mmol, (c) 5 mmol, (d) 2.5 mmol, (e) 0 mmol. TiO2: (a) 0 mmol, (b) 2.5 mmol, (c) 5 mmol, (d) 7.5 mmol, and (e) 10 mmol.

Figure illustrates the formation mechanism for BaTiO3 nanocubes using mixtures of the raw materials [(CH3)2CHO]4Ti and TiO2. Before solvothermal synthesis, [(CH3)2CHO]4Ti was dissolved in the reaction medium, whereas TiO2 was not. After solvothermal synthesis, nuclei of BaTiO3 were formed from the dissolved [(CH3)2CHO]4Ti, whereas the TiO2 nanoparticles became smaller because they slowly dissolved into the reaction medium as a consequence of their stability. Subsequently, the BaTiO3 crystals grew into a cubic shape. [(CH3)2CHO]4Ti and TiO2 participate in nucleation and crystal growth, respectively. We obtained BaTiO3 nanocubes by controlling these processes.

Figure 13

Formation mechanism of BaTiO3 nanocubes using mixtures of the raw materials [(CH3)2CHO]4Ti and TiO2.

XRD and ND Analyses of the BaTiO3 Nanocubes

Figure shows high-energy synchrotron X-ray and neutron crystal structures of the BaTiO3 nanocubes. The high-energy synchrotron XRD pattern [Figure a] and ND pattern [Figure b] were collected, and Rietveld refinement of the P4mm model of BaTiO3 in the tetragonal crystal system was performed using the RIETAN-FP[37,38] and Z-Rietveld[39−41] software packages for XRD and ND patterns, respectively. The BaTiO3 nanocube used for analysis is shown in Figure d. The wavelength of the high-energy synchrotron radiation was 0.2015 Å, allowing acquisition of high-resolution XRD data. On the basis of the XRD and ND data, we confirmed a single phase of BaTiO3 assigned to a tetragonal crystal system of the P4mm space group. In addition, Rietveld refinement showed highly similar estimated lattice constants between the XRD and ND data, with no oxygen-related defects in the BaTiO3 nanocubes according to analysis of the ND pattern (Table ).

Figure 14

High-energy synchrotron X-ray and neutron crystal structure analysis of BaTiO3 nanocubes. (a) High-energy synchrotron XRD pattern and its Rietveld refinement at a wavelength of 0.02015 nm. (b) ND pattern and its Rietveld refinement using the TOF method with a white neutron source. Regarding the Rietveld refinement, the recorded spectrum is shown as red cross marks and the light-blue solid line is the fit to the model for the BaTiO3 phase. Red cross marks, light-blue solid lines, and blue solid lines represent observed, calculated, and differing intensities, respectively. Green ticks represent positions of the calculated Bragg reflections of the BaTiO3 phase.

Table 3

Rietveld Refinement of the Structural Parameters of the High-Energy Synchrotron XRD and ND Patterns for the Same Sample Shown in Figure da

atom	site	x	y	z	occupancy	Biso	x	y	z	occupancy	Biso
BaTiO3, P4mm model
		high-energy synchrotron XRD					ND
Ba	1a	0	0	0	1	1.297(14)	0	0	0	1	0.127(14)
Ti	1b	1/2	1/2	Z1	1	0.642(38)	1/2	1/2	Z4	1	0.011(14)
O1	1b	1/2	1/2	Z2	1	0.642	1/2	1/2	Z5	1	0.392(32)
O2	2c	1/2	0	Z3	2	0.642	1/2	0	Z6	2	0.467(17)
a/Å		3.99243(18)					4.00685(4)
c/Å		4.01542(23)					4.02502(5)
Rwp/%		9.34					5.79
Rp/%		7.41					4.68

Z1 = 0.46851(96), Z2 = 0.98840(487), Z3 = 0.46557(177), Z4 = 0.46693(68), Z5 = -0.00955 (65), and Z6 = 0.50577(65).

The PDF method was performed to analyze the radial distribution from disordered materials via the powder XRD pattern and to obtain information about the interatomic distances. Figure shows a PDF analysis of the XRD pattern obtained using high-energy synchrotron X-rays [Figure a]. The PDF analysis of XRD data confirmed Ti–O interatomic distances of 1.9 and 2.1 Å, a Ba–O interatomic distance of 2.9 Å, a Ba–Ti interatomic distance of 3.5 Å, and a Ba–Ba interatomic distance of 4.0 Å. These results suggest displacement of the Ti atom from the center of the BaTiO3 unit cell, which caused spontaneous polarization of the BaTiO3 tetragonal crystal structure.[42]

Figure 15

PDF analysis of the XRD pattern obtained using high-energy synchrotron X-rays and shown in Figure a. Regarding the PDF analysis, the recorded spectrum is shown as a black solid line and red circles are the fit to the recorded spectrum. The black solid line, red circle marks, and blue solid lines represent observed, calculated, and differing intensities, respectively.

The atomic column arrangement and surface reconstruction phenomenon were observed using Cs-corrected HAADF–STEM and ABF–STEM. The contrast in HAADF–STEM depends on the atomic number of the observed elements, where the contrast of heavy elements is brighter than that of light elements, making the detection of light elements difficult. By contrast, ABF–STEM enables the detection of light elements such as oxygen; therefore, using both HAADF–STEM and ABF–STEM enables a more complete observation that overcomes the shortcomings of each detection method. Figure shows atomic column observations of a BaTiO3 nanocube from the [001] incidence direction, as observed in the corresponding scanning electron microscopy (SEM) image used for analysis [Figure d]. The left-hand side of the pair is the HAADF–STEM image and the right-hand side is the ABF–STEM image. In Figure (a-1),(a-2), in the middle of the array is an overall view of the BaTiO3 nanocube. The particle size of the BaTiO3 nanocube was approximately 40 nm. Figure (b-1),(b-2),(d-1),(d-2),(h-1),(h-2),(f-1),(f-2) shows images of the four corners of the BaTiO3 nanocube. Figure (c-1),(c-2),(i-1),(i-2),(e-1),(e-2),(g-1),(g-2) shows images corresponding to the top, left, right, and bottom of the BaTiO3 nanocube, respectively. In the HAADF–STEM images, we observe two lines of atomic columns of differing contrast intensities: one line of spots is bright, and the other line of spots is very bright. Compared with the atomic number of 22Ti, that of 56Ba is greater, suggesting that the bright spots indicate 22Ti columns and that the very bright spots indicate 56Ba columns. Columns associated with O were not visible because of their poor contrast. The ABF–STEM images also show two lines of atomic columns although the Ti atomic columns were obscured by the O atomic columns. However, the ABF–STEM images also show O atomic columns between the Ba atomic columns.

Figure 16

Atomic column observations of a BaTiO3 nanocube in the direction of [001] incidence. STEM images at an accelerating voltage of 200 kV, obtained with an instrument equipped with a Cs corrector. HAADF–STEM images: (a-1) whole particle, (b-1) top left-hand corner of the particle, (c-1) top of the particle, (d-1) top right-hand corner of the particle, (e-1) right-hand side of the particle, (f-1) bottom right-hand corner of the particle, (g-1) bottom of the particle, (h-1) bottom left-hand corner of the particle, and (i-1) left-hand side of the particle. ABF–STEM images: (a-2) whole particle, (b-2) top left-hand corner of the particle, (c-2) top of the particle, (d-2) top right-hand corner of the particle, (e-2) right-hand side of the particle, (f-2) bottom right-hand corner of the particle, (g-2) bottom of the particle, (h-2) bottom left-hand corner of the particle, and (i-2) left-hand side of the particle.

Examination of the atomic column arrangements of the surface of the BaTiO3 nanocubes revealed a homogeneous internal structure although not at the surface, where surface reconstruction was clearly observed. If the BaTiO3 nanocrystal had been homogeneous throughout, the surface arrangement would have ended at the Ba or Ti atomic columns. However, our observations of the nanocrystal’s surface indicated the existence of atomic columns, which we theorized to be Ti layers, and a lack of Ba atomic columns; therefore, we examined the composition of the surface of the BaTiO3 nanocrystal in greater detail. Figure shows an atomic observation of a BaTiO3 nanocube from the [001] incidence direction, which was used for analysis [Figure (i-1),(i-2)]. A regular arrangement of Ba and Ti columns was clearly observed inside the BaTiO3 nanocube from HAADF–STEM and ABF–STEM. However, the atomic arrangement at the outermost surface of the BaTiO3 nanocube clearly differed from that inside the BaTiO3 nanocube. Specific atomic columns were arranged at equal distances and built by surface reconstruction. We can understand the arrangement detail from the histogram. From the HAADF–STEM contrast results, Figure a,b shows the histograms representing Ti atomic columns and Ba atomic columns inside a BaTiO3 nanocube, respectively. From the results of the histogram, we confirmed that the Ti atomic columns and the Ba atomic columns were arranged at equal distances inside BaTiO3 nanocubes. However, the atomic column arrangement at the outermost surface of the BaTiO3 nanocube clearly differed from that inside the BaTiO3 nanocube. In addition, the peaks of the histogram were in the same positions for the Ba atomic columns [Figure a] and the Ti atomic columns [Figure b] at the outermost surface of the BaTiO3 nanocube. Furthermore, the intensities in the histogram corresponding to the outermost surface of the BaTiO3 nanocube were weak. That is, even though atomic columns were arranged with regularity at the outermost surface of the BaTiO3 nanocube, lattice defects did exist. EELS analysis was performed to clarify the component elements of the outermost surface of the BaTiO3 nanocube.

Figure 17

Observations of atomic columns in a BaTiO3 nanocube in the direction of [001] incidence. STEM images were observed at an accelerating voltage of 200 kV using an instrument equipped with a Cs corrector. (a,b) Histogram of the areas surrounded by dotted lines of HAADF–STEM image of the left-hand side of the BaTiO3 nanocube.

Surface reconstruction was investigated from the point of view of elemental analysis. BaTiO3 comprises three elements (Ba, Ti, and O). Analysis of Ba and O is possible, whereas analysis of Ti is more difficult because the Lα lines of Ba overlap the Kα lines of Ti. However, EELS enables elemental analysis of Ti because its peaks do not overlap those of Ba in EELS spectra. Therefore, elemental analysis of the surface of a BaTiO3 nanocube was conducted using EELS.

The surface of a BaTiO3 nanocube before acetic acid treatment was also examined with electron microscopy. Figure S11 shows observations of a BaTiO3 nanocube from the direction of [001] incidence before acetic acid treatment. A single crystal of BaTiO3 was confirmed from the results of TEM and its nano-beam diffraction [Figure S11]. Figure S12 shows atomic column observations of a BaTiO3 nanocube from the [001] incidence direction before acetic acid treatment, as observed in the corresponding TEM image used for analysis [Figure S11a]. Figure (a-1) is the HAADF–STEM image and Figure S12(a-2) is the ABF–STEM image. In Figure S12(a-1), (a-2), in the middle of the array is an overall view of the BaTiO3 nanocube. Figure S12(b-1), (b-2), (d-1), (d-2), (h-1), (h-2), (f-1), and (f-2) shows images of the four corners of the BaTiO3 nanocube. Figure S12(c-1), (c-2), (i-1), (i-2), (e-1), (e-2), (g-1), and (g-2) shows images corresponding to the top, left, right, and bottom of the BaTiO3 nanocube, respectively.

Atomic column observations of HAADF–STEM and their EELS analyses of the top, right-side, bottom, and left-side of the BaTiO3 nanocube before acetic acid treatment, as observed in corresponding pairs of TEM images used for analysis [Figure S11a], were performed as shown in Figures S12, S13. Ba and Ti are indicated by green and red, respectively. Each EELS spectrum is shown in Figure S14. A regular arrangement of Ba and Ti columns was clearly observed inside the BaTiO3 nanocube, along with surface reconstruction comprising Ti columns without Ba columns at the outermost surface on all sides of the BaTiO3 nanocube.

Figure shows observations of a BaTiO3 nanocube after acetic acid treatment from the direction of [001] incidence. A single crystal of BaTiO3 was confirmed from the results of TEM and its nano-beam diffraction, HAADF–STEM, and ABF–STEM observation [Figure a–d]. Figure e shows a BaTiO3 nanocube as shown in sample 3 of Figure a,c,d. Atomic column observations of HAADF–STEM and their EELS analyses of the top, right-side, bottom, and left-side of BaTiO3 nanocube were performed as shown in Figure e. Ba and Ti are indicated by green and red, respectively. Each EELS spectrum is shown in Figure S15. A regular arrangement of Ba and Ti columns was clearly observed inside the BaTiO3 nanocube, along with surface reconstruction comprising Ti columns without Ba columns at the outermost surface on all sides of the BaTiO3 nanocube. In addition, EELS analysis of another BaTiO3 nanocube is shown in Figure S16. Figure S16a shows the observed atomic columns in a BaTiO3 nanocube from the direction of [001] incidence. Elemental analyses of Ba and Ti were conducted using the EELS peaks at Ti: 457.8–461.1 and Ba: 782.4–785.6 eV [Figure S16 (b-1, b-2)] and at Ti: 458.4–461.1 and Ba: 798.1–800.9 eV [Figure S16 (c-1, c-2)], respectively. As a result, the surface reconstruction of the BaTiO3 nanoparticle is indicated in Figure S16.

Figure 18

Observations of a BaTiO3 nanocube in the direction of [001] incidence. TEM and the corresponding nano-beam electron diffraction pattern and STEM images were observed at an accelerating voltage of 80 kV using an instrument equipped with a Cs corrector. (a) TEM image of a BaTiO3 nanocube; (b) nano-beam diffraction of sample 3; (c,d) HAADF–STEM and ABF–STEM images; (e) HAADF–STEM observations of atomic columns in a BaTiO3 nanocube the direction of [001] incidence and their EELS elemental mapping. Ba and Ti are indicated by green and red of EELS elemental mapping, respectively.

Comparing before and after acetic acid treatments, the surface reconstruction was clearly observed after acetic acid treatment. Therefore, further investigation is necessary to identify the mechanism for the formation of the surface reconstruction of the BaTiO3 nanocube.

Figure shows observations of a BaTiO3 nanocube from the direction of [110] incidence. A single crystal of a BaTiO3 nanocube was obtained from the results of TEM and its nano-beam diffraction. Figure shows HAADF–STEM and ABF–STEM observations of a BaTiO3 nanocube from the direction of [110] incidence. Note that one of the atomic positions of O overlaps on the atomic position of Ti in the direction of [001] incidence (Figures –18), whereas one of them overlaps on the atomic position of Ba in the direction of [110] incidence (Figure ). Thus, we can clearly observe different atomic positions of some O atoms between the images in the direction of [001] and [110].

Figure 19

Observations of a BaTiO3 nanocube in the direction of [110] incidence. TEM and the corresponding nano-beam electron diffraction pattern were observed at an accelerating voltage of 200 kV using an instrument equipped with a Cs corrector. (a) TEM image and (b) nano-beam diffraction.

Figure 20

Atomic column observations in a BaTiO3 nanocube in the direction of [110] incidence. STEM images at an accelerating voltage of 200 kV, obtained with an instrument equipped with a Cs corrector. HAADF–STEM images: (a-1) whole particle, (b-1) top left-hand corner of the particle, (c-1) top of the particle, (d-1) top right-hand corner of the particle, (e-1) right-hand side of the particle, (f-1) bottom right-hand corner of the particle, (g-1) bottom of the particle, (h-1) bottom left-hand corner of the particle, and (i-1) left-hand side of the particle. ABF-STEM images: (a-2) whole particle, (b-2) top left-hand corner of the particle, (c-2) top of the particle, (d-2) top right-hand corner of the particle, (e-2) right-hand side of the particle, (f-2) bottom right-hand corner of the particle, (g-2) bottom of the particle, (h-2) bottom left-hand corner of the particle, and (i-2) left-hand side of the particle.

In this study, the internal structure of a BaTiO3 nanocube was confirmed to be homogeneous. However, we discovered that surface reconstruction resulted in two Ti layers (Figure ). This phenomenon was theorized to be a consequence of the solvothermal method used to synthesize the BaTiO3 nanocubes. Surface reconstruction is dependent on ionic radius and/or binding energy forces. Ti4+ has an ionic radius of approximately one-half that of Ba2+, which enables easier arrangement of Ti4+ on the BaTiO3 nanocube surface. Ti has a higher binding-energy force than Ba, thus making the surface harder to split apart. The field of atomic arrangement is important and intriguing. In the present study, we confirmed the atomic arrangement of a BaTiO3 nanocube. Identifying an atomic arrangement, especially on the surface of a BaTiO3 nanocube, is challenging; however, our results are informative.

Figure 21

BaTiO3 surface reconstruction which is composed of Ti atomic columns. The green circles are Ba and the red circles are Ti.

Conclusions

In summary, we described a wet chemical method for synthesizing BaTiO3 without dispersants of surfactants. This approach involves mixing fine TiO2 nanoparticles with Ba(OH)2·8H2O to form a single phase of BaTiO3 at 80 °C. Additionally, we obtained a high dispersion of BaTiO3 nanocubes using a solvothermal method at 200 °C. Moreover, we mediated BaTiO3 nanocube synthesis by controlling nucleation and crystal growth by altering the ratio of [(CH3)2CHO]4Ti and TiO2 as raw materials where the role of [(CH3)2CHO]4Ti promoted nucleation and the fine TiO2 nanoparticles promoted crystal growth. [(CH3)2CHO]4Ti was dissolved in a reaction medium of alcohol before the solvothermal reaction. Thereafter, uniform nuclei formed under the solvothermal reaction conditions. Uniform nuclei led to a narrow particle size distribution. In addition, the large number of nuclei resulted in fine nano-sized particles. On the other hand, fine TiO2 nanoparticles dissolved slowly in the reaction medium compared with [(CH3)2CHO]4Ti. The fine TiO2 nanoparticles led to crystal growth when the solvothermal synthesis was carried out at 200 °C.

The shape of the obtained powders in the present study depended on the crystal system of BaTiO3, which, in this case, is a tetragonal crystal system. During the solvothermal reaction, the crystals of BaTiO3 that grew depended on the crystal system. BaTiO3 particle sizes obtained using different reaction media increased in the order methanol, ethanol, 1-propanol, 1-butanol, 1-pentanol, water. The optimum condition for synthesizing BaTiO3 nanocubes was achieved with 1-butanol as the reaction medium. The average particles size was 52 nm, which is the average distance of the cubes measured diagonally from corner to corner, and the average side length was 37 nm, and the crystal system of BaTiO3 nanocubes was a tetragonal crystal system. In addition, the origin of the spontaneous polarization of the BaTiO3 tetragonal crystal structure was clarified from a pair PDF analysis.

Detailed observations of a BaTiO3 nanocube were carried out using electron microscopy. The surface reconstruction of the BaTiO3 nanocube clarified that the outermost surface of the BaTiO3 nanocube was composed of Ti columns. Two layers of Ti columns at the surface of the BaTiO3 nanocubes were identified. By comparing the atomic ratio of Ba and Ti, we found that Ti was slightly richer than Ba. These data were reflected in the observation of surface reconstruction of Ti atomic columns.

To reiterate, BaTiO3 nanocubes were synthesized using a solvothermal method and the occurrence of surface reconstruction of Ti columns was revealed in the present work.

Experimental Section

Raw Materials

We used the following raw materials for BaTiO3 synthesis: anatase-type TiO2 (particle size: <25 nm; 99.7% purity; Sigma-Aldrich, St. Louis, MO, U.S.A.); titanium tetraisopropoxide {[(CH3)2CHO]4Ti; >97.0% purity; Kanto Chemical Co., Inc., Tokyo, Japan}; barium hydroxide octahydrate [Ba(OH)2·8H2O; 99% purity; Kojundo Chemical Laboratory Co., Ltd., Saitama, Japan]; acetic acid (CH3COOH; 99.7% purity; Kanto Chemical Co., Inc., Tokyo, Japan); acetone [CH3COCH3; 99.5% purity; Kanto Chemical Co., Inc., Tokyo, Japan]; methanol (CH3OH; 99.8% purity; Kanto Chemical Co., Inc., Tokyo, Japan); ethanol (C2H5OH; 99.5% purity; Kanto Chemical Co., Inc., Tokyo, Japan); 1-propanol (1-C3H7OH; 99.5% purity; Kanto Chemical Co., Inc., Tokyo, Japan); 1-butanol (1-C4H9OH; 99.0% purity; Kanto Chemical Co., Inc., Tokyo, Japan); and 1-pentanol (1-C5H11OH; 98.5% purity; Kanto Chemical Co., Inc., Tokyo, Japan).

Acetic Acid Treatment

Acetic acid treatment was performed to remove the second phase. The concentration of the acetic acid aqueous solution was first adjusted to 0.69 mol·dm–3; 50 mL of this solution was then combined with 2 g of the product, and the resultant mixture was stirred at 350 rpm for 5 min.

Synthesis of BaTiO3 Particles Below 80 °C

BaTiO3 particles were synthesized at temperatures below 80 °C. First, 20 mmol of Ba(OH)2·8H2O and 10 mmol of fine anatase-type TiO2 (particle size: < 25 nm) were stirred in a Teflon reactor in 40 mL of water for 5 min, after which the Teflon reactor was placed in a stainless-steel autoclave with an internal volume of 100 mL, and a heat treatment was performed from room temperature to 80 °C for 72 h. After the autoclave cooled to room temperature, the product was collected using a centrifugal separator at 10,000 rpm, rinsed with water for three cycles and acetone for two cycles, and then dried at room temperature. An acetic acid treatment was then performed, after which the product was again collected by centrifugation using a centrifugal separator at 10,000 rpm, rinsed with water for three cycles and then acetone for two cycles, and dried overnight at room temperature.

Synthesis of BaTiO3 Particles Above 80 °C

BaTiO3 nanocubes were synthesized using a solvothermal method. First, the raw materials were added to a Teflon reactor and stirred at 350 rpm for 5 min; the resultant mixture was placed into a stainless-steel autoclave with an internal volume of 100 mL. Solvothermal synthesis was then performed at 200 °C for 6 to 96 h, after which the autoclave was cooled to room temperature. The product was collected by centrifugation at 10,000 rpm, rinsed with water for three cycles and ethanol for two cycles, and then dried at 80 °C in a dryer. An acetic acid treatment was then performed, after which the product was collected using a centrifugal separator at 10,000 rpm, rinsed with water for three cycles and ethanol for two cycles, and then dried overnight at 80 °C in a dryer.

Characterization of the Obtained Powders

XRD measurements were performed using an Ultima IV diffractometer (Rigaku Co., Tokyo, Japan) equipped with a Cu Kα radiation source (wavelength: 0.15418 nm) operating at 40 kV and 30 mA; samples were scanned at room temperature over the 2θ range from 10 to 80°. High-energy synchrotron XRD measurements were carried out at SPring-8 (Hyogo, Japan); data were collected in transmission mode at the SPring-8 BL22XU beamline using high-energy X-rays with a wavelength of 0.02015 nm. Short- and long-range structural parameters were refined using the Rietveld technique and the RIETAN-FP program.[37,38] An ND pattern was obtained by the time-of-flight (TOF) method using white neutrons at J-PARC (Ibaraki, Japan). ND data were collected in a high-resolution bank (150° ≤ 2θ ≤ 175°) at beamline BL20 (iMATERIA) using neutron beams produced at the Materials and Life Science Experimental Facility (J-PARC) from megawatt-class high-power pulsed proton beams generated by a 3 GeV rapid-cycling synchrotron.[39−41] The use of a white pulsed neutron source enabled ND measurement.

SE images of the powders were obtained by SEM using an instrument (SU-5000; Hitachi High-Tech Corporation, Tokyo, Japan) operating at an accelerating voltage of 3 kV and by STEM using an instrument (HD-2700; Hitachi High-Tech Corporation, Tokyo, Japan) operated at a 200 kV acceleration voltage. BF–TEM observations were conducted and SAED patterns were obtained by TEM using an instrument (Tecnai Osiris; FEI; Thermo Fisher Scientific, Waltham, MA, U.S.A.) operating at an accelerating voltage of 200 kV. The BaTiO3 surface was analyzed by HAADF–STEM and ABF–STEM using a JEM-ARM200CF (JEOL Ltd., Tokyo, Japan) operating at an accelerating voltage of 80 and 200 kV and equipped with a cold field emission gun and a Cs corrector to observe atomic columns of BaTiO3. Elemental analysis was carried out using a JEOL JEM-ARM200CF transmission electron microscope equipped with an electron energy loss spectroscope. Regarding the accelerating voltage, 200 kV has a higher resolution for the atomic column observation compared with 80 kV. On the other hand, 80 kV is suitable for EELS elemental mapping because it can be performed over a long period of time. A long duration observation time causes damage to the BaTiO3 nanocube if observed at an accelerating voltage of 200 kV. Therefore, in the STEM observations including the EELS elemental mapping, we used 80 kV with an accelerating voltage due to the lowered damage to the BaTiO3 nanocube.