The Synthesis and Domain Structures of Single-Crystal-Like Mesoscale BaTiO3 Plates

Abstract

The (001) plate-like BaTiO₃ piezoelectric micromaterials are synthesized by topochemical microcrystal conversion technique. BaTiO₃ plates with a length of 2~10 μm and thickness of 0.5~1.3 μm are obtained. The dependence of morphology on synthesis conditions is discussed in detail. The crystal symmetry and multiscale domain structures of BaTiO₃ plates are systematically investigated by various characterizations. X-ray diffraction (XRD) and Raman spectra analyses demonstrate the tetragonal symmetry of the (001) oriented BaTiO₃ plates at room temperature. The domain configurations of the micron BaTiO₃ are investigated with a polarized light microscope (PLM) and piezoresponse force microscopy (PFM). The single-crystal-like quality and uniformity are supported by PLM observations. More importantly, the classical 90° banded ferroelectric domains of ~125 nm width are observed for the first time in such BaTiO₃ plates. The domain features in the mesoscale BaTiO₃ plate are discussed and compared with its bulk counterparts. The results may provide insights into understanding and designing the mesoscale BaTiO₃ functional materials.

1. Introduction

Barium titanate (BaTiO₃) is a classical lead-free ferroelectric/piezoelectric material that was first discovered in the early 1940s [1]. BaTiO₃ exhibits a cubic perovskite structure, which transforms into a tetragonal symmetry at the Curie point around 120 °C [2]. At room temperature, BaTiO₃ was widely investigated in various material forms including single crystal and ceramics since its discovery, due to its excellent piezoelectric/ferroelectric/dielectric performances at room temperature.

Materials can display very distinct and interesting properties when the dimensions change from three-dimension bulk [3,4,5] to low-dimension nanoscale [6]. Generally, microscale and nanoscale refer to 1–100 μm and 1–100 nm, respectively, whereas mesoscale is somewhere in between. Significant advantages could be expected from those materials. Piezoelectric micro-/nano- materials and related devices have attracted more and more interest in recent years due to their small size and easy integration [7,8,9]. Two-dimensional ZnO platelet and the array assembled by ZnO platelets show great advantages as integrated piezotronic transistors [7]. Nanostructured piezoelectrics, for example, BaTiO₃ were combined with polymer to form composite porous foam [8], which enhanced piezocatalysis due to the nanomaterial and the specific surface area. Moreover, nano- or mesoscale BaTiO₃ materials can also be used as templates for piezoelectric ceramic texturing [10,11], which can enhance piezoelectric performance significantly. As a piezoelectric catalyst, nano- and micro-BaTiO₃ particles were successfully utilized in wastewater degradation and H₂ production [12,13].

It is believed that the ferroelectricity/piezoelectricity of BaTiO₃ is critical to the desired functionalities, and how to synthesize good-quality mesoscale BaTiO₃ with good performances is therefore in high demand. In contrast to bulk BaTiO₃ and nanoscale BaTiO₃ materials, mesoscale BaTiO₃ is far less investigated. Single crystalline mesoscale BaTiO₃ thin plates were first reported by Remeika in 1954 [14]. These clear, large size crystals have desired ferroelectric characteristics [15]. However, the potassium fluoride flux used during the growth of BaTiO₃ single crystal is environmentally harmful and will cause the corrosion of furnace refractories. An eco-friendly and commonly used approach to obtain plate-like BaTiO₃ is the topochemical microcrystal conversion (TMC) technique, which was first reported by Liu et al. [16]. In the TMC process, bismuth layer structure precursors transform to perovskite structure BaTiO₃ in molten salt. There are two TMC methods reported on the synthesis of BaTiO₃ plates, including the one-step TMC and the two-step TMC. The one-step TMC converts the Bi₄Ti₃O₁₂ precursor to BaTiO₃ directly. The two-step TMC converts Bi₄Ti₃O₁₂ to BaBi₄Ti₄O₁₅ first, and then obtains BaTiO₃ from the BaBi₄Ti₄O₁₅ precursor. With the topochemical reactions, the Ba²⁺ ions completely replace the Bi³⁺ ions in the precursor. Moreover, the plate-like morphology of the precursor, meanwhile, is maintained in the final products. BaTiO₃ plates synthesized by the TMC method show a quadrate shape and a high aspect ratio. The obtained BaTiO₃ particles are either single crystalline or polycrystalline, which is determined by the initial alignment after nucleation and the recrystallization process [17]. Much work has been focused on controlling the morphology of mesoscale BaTiO₃ plates, which is mainly related to the following three factors. The first important factor is the choice of a suitable Aurivillius precursor. The morphology of the precursor directly affects the morphology of the final product during topochemical conversion. The morphology of BaTiO₃ can be optimized by using a suitable precursor with a high aspect ratio, regular shape, and clean surface. Liu et al. utilized polycrystalline BaBi₄Ti₄O₁₅ as a precursor for the preparation of BaTiO₃ [16]. The plate-like and rectangular Aurivillius precursor of about 6~10 μm in length successfully converts to 5~10 μm perovskite BaTiO₃ micrometer plates. Fan et al. found the exfoliation of BaTiO₃ during TMC when they used Bi₄Ti₃O₁₂ precursor or polycrystalline BaBi₄Ti₄O₁₅ precursor [18]. The exfoliation resulted in irregular shape BaTiO₃ plates and some fine particles among the plates. As a result, single-crystalline BaBi₄Ti₄O₁₅ precursor [18] was reported to achieve uniform BaTiO₃ plates. The size of BaTiO₃ plates was also found to be closely related to the size of the precursor [19]. Micrometer and sub-micrometer BaTiO₃ can be derived from a micro- or sub-micro-precursor, respectively. The second factor is the suitable molten salts. NaCl, KCl, and BaCl₂ salts are the commonly used molten salts in the synthesis of BaTiO₃ plates by the TMC method [16,17,18,19]. BaCl₂-KCl molten salts systems are used in the transformation from Bi₄Ti₃O₁₂ to BaBi₄Ti₄O₁₅, because of their higher Ba²⁺ concentration to accelerate the growth of BaBi₄Ti₄O₁₅ [16]. The NaCl-KCl molten salt system is used in the conversion from BaBi₄Ti₄O₁₅ to BaTiO₃. The last factor is the removal process of the salts and the byproducts. The resultant of the two-step TMC reaction includes BaTiO₃ plate-like particles, salts, and residual Bi₂O₃. Salts can be easily removed after washing with deionized water several times. In order to remove the Bi₂O₃, an acid-washing process is needed with the reaction between Bi³⁺ and nitric acid (HNO₃). Zuo et al. [20] compared two different washing methods. It was found to be better to first remove the salts by deionized water, and then eliminate the residual Bi³⁺ by HNO₃.

On the one hand, potential applications are highly reliant on physical properties, such as piezoelectric and dielectric performances. On the other hand, the polar domain structures and corresponding dynamics can serve as an important extrinsic contribution to obtained electric properties. Therefore, the investigation of domain features is critical to the understanding of physical behaviors. However, the domain structure of BaTiO₃ within the mesoscale is rarely reported. Wu et al. [13] reported PFM results of individual BaTiO₃ plates. Though the amplitude butterfly loop and phase hysteresis loop were obtained along the out-of-plane direction, no obvious domains can be seen. Kržmanc et al. [19] found irregular domains in the PFM results of BaTiO₃ plates, but the plates were stacked and the influence of polishing treatment cannot be ruled out.

In this work, we have optimized the synthesis of BaTiO₃ plates by the TMC method, which guarantees the obtainment of single-crystal-like BaTiO₃ materials in mesoscale. The crystal structure and microstructure of BaTiO₃ plates are determined using X-ray diffraction (XRD), Raman spectra, and field-emission scanning electron microscope (FE-SEM). More importantly, direct observation of the domain structures in the BaTiO₃ plates is performed by polarized light microscope (PLM) and piezoresponse force microscopy (PFM). The good quality sample enables the observation of clear domain configurations. The domain features of BaTiO₃ materials in mesoscale are discussed by comparing them with their bulk counterparts. The results may provide new insights into understanding and designing the mesoscale BaTiO₃ functional materials.

2. Materials and Methods

2.1. The Synthesis of the Precursors and the BaTiO₃ Plates

The BaTiO₃ plates were prepared by the TMC method in three steps. First, a stoichiometric amount of Bi₂O₃ (99%) and TiO₂ (98%) with respect to the Bi₄Ti₃O₁₂ precursor were mixed by ball milling in ethanol for 15 h. The mixture was then dried and calcined under 1080~1160 °C using an equal weight of molten salts. The molar ratio of NaCl (99.5%) and KCl (99.5%) salts was 1:1. Subsequently, BaBi₄Ti₄O₁₅ precursor particles were synthesized in 1:1 mol BaCl∙2H₂O (99.5%) and KCl (99.5%) salts. The salts, BaCO₃ (99%) and TiO₂ (98%), were ball milled for 15 h. Then, the Bi₄Ti₃O₁₂ particles obtained in the first step were added and magnetically stirred with ethanol for 8 h. After drying, the mixture was calcined at 1040~1080 °C. An excess of BaCO₃ and TiO₂, equivalent to 10 mol% were added prior to the ball-milling process. Finally, BaTiO₃ was synthesized from the mixture of BaBi₄Ti₄O₁₅ and BaCO₃ (99%) with an equal weight of NaCl (99.5%) and KCl (99.5%) salts. The salts and BaCO₃ were ball milled, and then magnetic stirred with BaBi₄Ti₄O₁₅ particles for 8 h in ethanol. The mixture was dried at 90 °C. The calcined temperature was 925~975 °C. The heating rate was 4 °C/min throughout the calcination process. The salts of each step were removed by washing them several times in deionized water. Especially, in the third step, an acid-washing process was needed to remove the Bi₂O₃ byproduct. The calcined powder of the third step was washed in HNO₃ solution for 2 h, and then washed in deionized water several times.

2.2. Characterization

The phase structure was determined using a high-resolution X-ray diffractometer (XRD, PANalytical Empyrean, PANalytical, Almelo, the Netherlands) with Cu Kα1 radiation. The Raman spectra were collected by Raman spectrometer (RTS2-501-SMSXS, Zolix, Beijing, China) with a 532 nm laser at room temperature. The morphology of the BaTiO₃ and the precursor particles were examined using field-emission scanning electron microscopy (FE-SEM, FEI Quanta 250 FEG, FEI, Minato, Japan). Energy dispersive spectroscopic (EDS) mapping was carried out on the BaTiO₃ plates. A polarized light microscope (PLM, Olympus BX-51, Olympus, Tokyo, Japan) was used to investigate the extinction angle and the domain structure of the BaTiO₃. The domain structures of the BaTiO₃ plates were characterized by a piezoresponse force microscope (PFM, Dimension ICON, Bruker, Billerica, MA, USA).

3. Results and Discussion

The structure of Aurivilius compounds can be described as the intergrowth of (Bi₂O₂)²⁺ layers and (A_n−1B_nO_3n+1)²⁻ layers, where n (n = 1–6) is the number of octahedral layers between two neighboring bismuth oxides layers [21]. Aurivilius-structured Bi₄Ti₃O₁₂ was chosen as the precursor, and was obtained by the reaction between Bi₂O₃ and TiO₂ according to Equation (1). In the second step of the TMC process, Ba²⁺ partially substituted Bi³⁺ in the Bi₄Ti₃O₁₂ precursor and formed BaBi₄Ti₄O₁₅ (Equation (2)). In the final step, Ba²⁺ substituted all the residual Bi³⁺ in the BaBi₄Ti₄O₁₅, resulting in the formation of the final product BaTiO₃ (Equation (3)).

(1)$2{\mathrm{Bi}}_2{\mathrm{O}}_3+3{\mathrm{TiO}}_2\to {\mathrm{Bi}}_4{\mathrm{Ti}}_3{\mathrm{O}}_{12}$

(2)${\mathrm{Bi}}_4{\mathrm{Ti}}_3{\mathrm{O}}_{12}+{\mathrm{BaCO}}_3+4{\mathrm{TiO}}_2\to {\mathrm{BaBi}}_4{\mathrm{Ti}}_4{\mathrm{O}}_{15}+{\mathrm{CO}}_2$

(3)${\mathrm{BaBi}}_4{\mathrm{Ti}}_4{\mathrm{O}}_{15}+{\mathrm{BaCO}}_3\to 2{\mathrm{BaTiO}}_3+2{\mathrm{Bi}}_2{\mathrm{O}}_3+{\mathrm{CO}}_2$

Figure 1 shows the FE-SEM images of the Bi₄Ti₃O₁₂, BaBi₄Ti₄O₁₅ precursor particles and the BaTiO₃ plates synthesized at different temperatures. The results revealed that all the particles possess a plate-like shape. The morphology of the Bi₄Ti₃O₁₂ particles is shown in Figure 1a–c.

BaBi₄Ti₄O₁₅ nucleation initiates on the Bi₄Ti₃O₁₂ precursor and further grows by Ostwald ripening during the heating and holding stages. Generally, smaller particle size Bi₄Ti₃O₁₂ leads to smaller BaBi₄Ti₄O₁₅ after the topochemical reaction. Notably, the Bi₄Ti₃O₁₂ reaches a larger particle size at higher temperatures but shows obvious agglomeration in Figure 1c. The thickness of Bi₄Ti₃O₁₂ is about 0.2~1 μm. The length distributions are shown in Figure 2a–c. The average length of the Bi₄Ti₃O₁₂ synthesized at 1080 °C, 1120 °C, and 1160 °C are about 4.43 μm, 7.54 μm, and 12.51 μm, respectively. The Bi₄Ti₃O₁₂ obtained at 1080 °C in Figure 1a is too small and not suitable as a precursor. Bi₄Ti₃O₁₂ particles that grew at 1120 °C were selected as the precursor for the second step. BaBi₄Ti₄O₁₅ obtained at 1040 °C, 1060 °C, and 1080 °C are 6.23 μm, 7.73 μm, and 8.91 μm in length, respectively. The distribution curves show better uniformity at 1040 °C and 1060 °C temperature conditions, according to Figure 2d–f.

The FE-SEM images in Figure 1g–i show the plate-like shaped BaTiO₃ plates converted from the optimized BaBi₄Ti₄O₁₅ of the second step. The morphology of BaTiO₃ synthesized at 925 °C and 950 °C are similar. Figure 1g shows the BaTiO₃ synthesized at 925 °C with an average particle size of 6.18 μm. The particles possess suitable size in the range of 3–10 μm, but are not uniformly distributed. Moreover, the BaTiO₃ in Figure 1i contains many irregular shape particles with poor uniformity, which is also evidenced by Figure 2i. The BaTiO₃ plates obtained at 950 °C in Figure 1h are approximately 6.79 μm in length with a relatively regular square shape. The particles in Figure 1h are about 2~10 μm in length and about 0.5~1.3 μm in thickness. As shown in Figure 1h and Figure 2h, the plates show good uniformity without obvious agglomeration. The products with the optimized condition of the three steps show no obvious changes in length between the precursors and BaTiO₃ plates, which means minimized exfoliation. These mesoscale BaTiO₃ particles exhibit a clean surface, and no obvious crack or hole was found. Note the obtained large anisotropic morphology and high aspect ratio are important for BaTiO₃ as templates in ceramic texturing applications. Moreover, the large specific surface area is also in favor of potential piezocatalysis applications.

Figure 3a shows the XRD patterns of the BaTiO₃ plates synthesized at 950 °C. Phase-pure BaTiO₃ particles were obtained. The diffraction pattern in Figure 3a can be well indexed with a standard PDF card (No. 81-2202) with a P4mm space group. Moreover, the lattice parameter of the BaTiO₃ plates is calculated to be a ≈ 4.00 Å and c ≈ 4.04 Å, which agree well with the reported value in standard PDF card, i.e., a = b = 3.99 Å, c = 4.04 Å. Figure 3b displays the Raman spectra measured in the frequency range of 100 cm⁻¹ − 900 cm⁻¹. The inset is the photograph of the measured plate on a platinum substrate. The Raman spectra show peaks at 183 cm⁻¹, 301 cm⁻¹, 510 cm⁻¹, and 721 cm⁻¹, which is consistent with the literature [22,23,24,25]. The peak at ~180 cm⁻¹ is related to the decoupling of the A₁(TO) phonons [19]. A weak peak at 301 cm⁻¹ suggests the [B₁, E(TO + LO)] mode related to the TiO₆ octahedra [13,26]. The peaks at 510 cm⁻¹ and 721 cm⁻¹ correspond to the Raman active mode of [E(TO),A₁(TO)] and [E(LO),A₁(LO)], respectively.

Figure 4 exhibits the EDS mapping results on the surface of BaTiO₃ plates. The measured single plate is square in shape with a length of about 7 μm as shown in Figure 4a. The dotted lines in Figure 4b–d mark the boundary of the plate. Elements distribution of Ba, Ti, and O elements are shown in red, green, and yellow colors, respectively. Generally, Ba, Ti, and O elements are homogeneously distributed in the plates, suggesting good uniformity of the sample. Note in Figure 4d, a lower content of O elements was detected beyond the region of the plate, which may originate from the surrounding circumstance.

PLM images of the (001) face of BaTiO₃ plates are depicted in Figure 5. The white arrow marks the direction of [100] along the edge of the BaTiO₃ plate. The images with crossed polarizer (P) and analyzer (A) are shown in Figure 5b–d at different intersection angles of 0°, 45°, and 90° between the analyzer and [100] direction. As shown in Figure 5b–d, the mesoscale BaTiO₃ plate reveals an extinction angle of 90 degrees, which is consistent with the tetragonal symmetry evidenced by XRD characterization in Figure 3. Moreover, the complete extinction characteristics observed not only indicate the good uniformity of symmetry in the sample, but also suggest the unified orientation, i.e., the geometry of the template is coincident with the microscale perovskite unit cell. This also supports the single-crystal-like quality of the sample. The sample becomes color at 45° (the brightest position), reflecting the effect of a-domains in tetragonal BaTiO₃. However, no obvious regular domain patterns can be clearly seen. One possible reason is that the domain size is too small to be detected, as PLM cannot detect sub-micrometer scale domains. Another reason could be the domain overlapping, which may also make the PLM observation difficult.

To further investigate the local domain structure in the micro-scale BaTiO₃ plates, PFM was performed on an individual plate. It can be seen that the out-of-plane as well as the in-plane amplitude images exhibit distinct contrast of about 180°, which is also revealed in the corresponding phase images. Figure 6a shows an out-of-plane PFM image recorded on the (001) surface of the plate, whereas the normal edge of the plate is oriented parallel to <001>-axis or <010>-axis. Figure 6c–f are the enlarged view of the region marked in Figure 6a. The roughness of this enlarged region extracted from the surface morphology image is ~43.5 nm. The rough surface is consistent with the FE-SEM results observed in Figure 1 and Figure 4, which may be caused by the variation in growth rate in the different regions of the plate. Out-of-plane and in-plane images in the region of 6 μm × 6 μm area were recorded. The bright and dark stripes show the in-plane polarization with opposite directions along the <100>-axis (or <010>-axis), respectively. In the out-of-plane images, the bright and dark stripes indicate polarization with opposite directions along the <001>-axis. The BaTiO₃ plate shows a group of regular 90° ferroelectric banded domains with an average domain width of ~125 nm. In Figure 6b, a 3D schematic domain structure is sketched according to the possible orientation of the domains in the T phase (001) plate. Arrows indicate the orientation of spontaneous polarization (P_s). In the a₁/a₂-domain, the P_s is parallel with the surface of the plate, marked as P₁. In the c-domain, the P_s is perpendicular to the plate surface, marked as P₂. The green stripes mark the c-domains while pink stripes represent the a-domains as illustrated in Figure 6b. The walls between 90° a/c domains intersect with the (001) plane by an angle of 45°. In the in-plane images, the bright and dark stripes correspond to P₁ and P₂, respectively. Meanwhile, in the out-of-plane images, the P₁ and P₂ regions also show distinct contrast. However, the bright and dark stripes indicate the P₂ and P₁, which are opposite to the in-plane signals. In previous studies, only irregularly shaped domain patterns were reported in mesoscale BaTiO₃ plates [19]. The results in Figure 6 show the first observation of typical 90° banded domains in such BaTiO₃ plates in mesoscale.

The features of the domain in mesoscale BaTiO₃ plates compared with bulk BaTiO₃ are worth further discussion. Different from the randomly oriented grains in BaTiO₃ ceramics, the BaTiO₃ plates possess a preferred orientation and much smaller sample thickness. The dimensions have a notable influence on the domain size. Though BaTiO₃ in the T phase is known to display typical 180° and 90° ferroelectric domain features [27], domain size can vary significantly with different microstructures. In the case of ceramics with different grain sizes, 90° domains of sub-micrometer scale were reported in the BaTiO₃ ceramics with 8.61 μm grains, whereas nanodomains (10~30 nm) were found in the ceramics of grain size <1 μm [28]. Also in BaTiO₃ single crystals, multiscale domain patterns covering a wide range from nanometers to several tenths of micrometers [29,30,31] are observed. Kittel’s law shows the relation between the domain width w and the sample thickness t in ferroelectrics, ferromagnetics, and ferroelastics [32,33]. The domain width decreases with the decreasing thickness, i.e., w² = kt. The theoretical constant of proportionality k in this relation is reported to be 8.5 × 10⁻⁹ m for BaTiO₃ single crystals [34]. Adopted with the same parameter k, the calculated domain width w is in the range of 65~105 nm based on experimental thickness data. This is in the same order as our measured results ~125 nm, indicating the size dependence in mesoscale BaTiO₃ plate generally coincides with bulk single crystals.

4. Conclusions

The mesoscale plate-like BaTiO₃ was synthesized by the TMC technique in three steps. The Bi₄Ti₃O₁₂, BaBi₄Ti₄O₁₅ precursor, and the final product BaTiO₃ prepared at different processing temperatures in each step were compared. The length distribution of the Bi₄Ti₃O₁₂, BaBi₄Ti₄O₁₅, and BaTiO₃ particles were analyzed based on the FE-SEM results. The dependence of morphology on synthesis conditions were discussed in detail. Micron-size plate-like BaTiO₃ plates with near square shape and high aspect ratio were obtained. The BaTiO₃ plates show good uniformity without obvious agglomeration. The average length of these (001) oriented plates is 6.79 μm. EDS results demonstrate the homogeneously distributed Ba, Ti, and O elements in the plates. XRD patterns, Raman spectra, and PLM results indicate that as-obtained BaTiO₃ plates possess a tetragonal phase structure at room temperature. Single-crystal-like extinction behavior and good uniformity are supported by PLM observations. The typical a-c domains are demonstrated by PFM, which is the first observation of typical 90° banded domains in such BaTiO₃ plates in mesoscale. The width of banded domains (~125 nm) generally satisfies Kittel’s law of bulk single crystal. Moreover, there are regions with extremely weak signals in comparison with the banded 90° domain regions, which may have potential influences on applications used in the surface performance. The results may provide a new understanding of the domain structure of BaTiO₃ mesoscale materials and are helpful for promoting related applications.

Author Contributions

Conceptualization, J.Z. (Jian Zhuang), L.W. and W.R.; Methodology, K.Z. and Y.Q.; Formal analysis, Y.Q., J.Z. (Jinyan Zhao), L.W. and Z.W.; Investigation, K.Z., J.Z. (Jinyan Zhao) and L.W.; Resources, Z.W.; Writing—original draft, K.Z.; Writing—review and editing, J.Z. (Jian Zhuang) and W.R.; Funding acquisition, W.R. All authors have read and agreed to the published version of the manuscript.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Not applicable.

Conflicts of Interest

The authors declare that they have no known competing financial interest or personal relationships that could have appeared to influence the work reported in this paper.

Footnotes

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Figures

Figure 1. FE-SEM images of (a–c) Bi4Ti3O12 precursor, (d–f) BaBi4Ti4O15 precursor, and (g–i) BaTiO3 mesoscale particles synthesized at different temperatures.

Figure 2. Length distributions of (a–c) Bi4Ti3O12 precursor, (d–f) BaBi4Ti4O15 precursor, and (g–i) BaTiO3 mesoscale particles synthesized at different temperatures.

Figure 3. (a) XRD patterns and (b) the Raman spectra of BaTiO3 plates synthesized at 950 °C. The inset in (b) indicates the measuring region in a single template with the light spot marked by a green cross.

Figure 4. The EDS mapping results of the BaTiO3 plates synthesized at 950 °C. (a) The FE-SEM image of the scanning area of EDS mapping includes a single BaTiO3 plate. The distribution of (b) Ba element, (c) Ti element, and (d) O element in the scanning area.

Figure 5. (a) The photograph of BaTiO3 plates. The PLM images of BaTiO3 micron plates with the crossed polarizers at (b) 0°, (c) 45°, and (d) 90°.

Figure 6. Domain structures of BaTiO3 plate. (a) Out-of-plane PFM image of the whole plate. (b) 3D schematic domain structure. Out-of-plane (c) amplitude and (d) phase image, in-plane (e) amplitude, and (f) phase image of a 6 μm × 6 μm square region.

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