Spontaneous Growth of CaBi 4 Ti 4 O 15 Piezoelectric Crystal Using Mixed Flux Agents

: The bismuth layer-structured ferroelectrics (BLSFs) materials have potential for high-temperature piezoelectric applications. Among these piezoelectric materials, the CaBi 4 Ti 4 O 15 (CBT) piezoelectric ceramic with a high decomposition temperature of about 1250 ◦ C attracts a lot of attention. Achieving a CBT single crystal is a signiﬁcant way to improve its piezoelectric properties. For this purpose, the ﬂux system for growing CBT crystal was explored in this study. The optimum ﬂux composition ratio was found to be PbO:B 2 O 3 :CBT = 3:3:1 in mol%, where the PbO–B 2 O 3 mixtures were used as a ﬂux system. Millimeter size ﬂake-shaped CBT crystals were obtained using the spontaneous growth process for the ﬁrst time. The relationship between the crystal structure and ﬂake growth habit was analyzed. In addition, the bandgap was evaluated by the combination of transmittance spectrum and ﬁrst-principle calculations. Besides, the piezoelectric property was predicted from the perspective of polyhedral distortion, which indicated the potential of CBT crystal for piezoelectric applications.


Introduction
Since the discovery of the piezoelectric effect, piezoelectric materials have been widely explored as sensors, transducers, actuators, energy harvesting devices, etc. Recently, piezoelectric materials that can maintain the electromechanical and piezoelectric properties at high temperatures and even harsh environments are needed, especially in aerospace industries, oil exploitation, and power plant fields [1][2][3]. The ever-increasing demands on operational temperature have stimulated a great deal of research effort on exploring piezoelectric materials with a high curie temperature (T C ) or high melting point, prior to which the electromechanical and piezoelectric properties should be maintained.
To date, several kinds of piezoelectric crystals with high melting points have been studied as the candidates for high-temperature piezoelectric applications [4][5][6]. For example, the modified langasite type crystal Ca 3 Ta(Ga 1−x Al x ) 3 Si 2 O 14 (CTGAS) with a melting point above 1400 • C was determined to possess a relatively high piezoelectric coefficient (d 11 = 4.6 pC/N) and electromechanical coupling factor (k 12 = 14.4%) [4]. The low-cost calcium aluminate silicate Ca 2 Al 2 SiO 7 (CAS) crystal with moderate piezoelectric activity was explored for high-temperature pressure sensing [5]. Furthermore, the RECa 4 O(BO 3 ) 3 (ReCOB) crystals with good temperature stability and high electrical resistivity were studied for high-temperature vibration sensing applications [6]. Through the success fabrication of different prototypes of piezoelectric sensors, the sensitivity is expected to be further enhanced, which encourages the exploration of new piezoelectric crystals with strong piezoelectric response. Bismuth layer-structured To avoid the introduction of impurities, we first consider the self-melting system. Hence, Bi 2 O 3 was selected and used as the flux agent. The prepared CBT polycrystalline powders with the extra added Bi 2 O 3 flux agent were mixed in different mole proportions (Bi 2 O 3 :CBT = 3:1, 4:1 and 5:1), heated, and melt at 1000-1100 • C for 20 h and then slowly cooled down to room temperature. In addition to the Bi 2 O 3 flux agent, PbO-B 2 O 3 was chosen as the mixed flux system for crystallizing CBT crystal. PbO and B 2 O 3 have their own merits for crystal growth using the flux method; reports indicate that PbO is an effective solvent used for many oxides and complex perovskites [18][19][20][21][22][23][24]. The B 2 O 3 can reduce the melting temperature, increase the solubility of the melt, and create an optimum degree of complex formation and optimum viscosity [25]. Besides, because of its low melting point and high viscosity, B 2 O 3 can also form a sealing layer to prevent the evaporation of PbO in the molten state at elevated temperatures. Based on the above considerations, the PbO-B 2 O 3 mixed flux system was attempted for CBT single crystal growth. Firstly, the prepared CBT polycrystalline powders were mixed with the PbO-B 2 O 3 flux systems in different mole proportions (PbO:B 2 O 3 :CBT = 2:2:1, 3:3:1, 4:4:1, 5:1:1, and 5:3:1) to perform the comparative experiments. Secondly, the mixed compounds were heated and melt at 1000-1100 • C for 20 h; then, they were slowly cooled down to room temperature to find the expected crystal phase.
In this study, the CBT crystal was finally grown by the spontaneous nucleation method using PbO-B 2 O 3 as flux. The CBT polycrystalline powders, high-purity PbO (4N, Aladdin, Shanghai, China) and B 2 O 3 (4N, Alfa Aesar, Haverhill, MA, USA), were weighed in a certain mole proportion (the proportion for CBT and PbO-B 2 O 3 mixed flux was PbO:B 2 O 3 :CBT = 3:3:1). The powders were mixed thoroughly, ground, and placed into platinum crucibles in a growth furnace, after which the crucible was slowly heated to 1000 • C and maintained at this temperature for 20 h to make the solution melt completely and mix homogeneously. After that, the crucible was cooled slowly to 500 • C with a very low rate of 2-5 • C/h and then to room temperature at 10 • C/h. When the spontaneous crystallization process was finished, the crucible was boiled with nitric acid to separate the flux from the crystallized CBT crystals.

Transmission Spectra Measurement and Phase Characterization
The transmission spectra of polycrystalline CBT were measured with a Nicolet IS 10 (Thermo Fisher, Waltham, MA, USA) over the wavelength range of 400 to 4000 nm at room temperature. The crystal phase of the solidified CBT solution obtained by using different flux systems and different proportions was identified by using the Bruker AXS D8 Advance X-ray diffractometer (XRPD, Bruker-axs, Karlsruhe, Germany) at room temperature.

Theoretical Calculations
The band structure calculations of CBT compound employed the Vienna ab initio Simulation Package (VASP 5.3.5) [26,27] implementation of density functional theory (DFT) in conjunction with the projector-augmented wave (PAW) [28] method. Thereby, the Ca 4s 2 , Bi 6s 2 6p 3 , Ti 3d 2 4s 2 , and O 2s 2 2p 4 states were treated as valence electrons. The electronic wave functions were expanded in plane waves using an energy cutoff of 400 eV. The electron exchange and correlation (XC) within the General Gradient Approximation (GGA) of the Perdew, Burke, and Ernzerhof (PBE) [29] functional was used to optimize the configurations, and the force convergence criterion for the structural relaxation was set to 0.01 eV/Å. The electronic properties were performed by the screened hybrid functional of Heyd, Scuseria, and Ernzerhof (HSE06) [30,31]. 4 × 4 × 4 and 2 × 2 × 2 Monkhorst-Pack [32] k-point meshes were employed to sample the Brillouin zones for PBE and HSE06 calculations, respectively.

XRPD Analysis and Crystallization
The polycrystalline CBT compounds were synthesized in a stoichiometric ratio with an excess amount of Bi 2 O 3 (1 mol%) added for compensating the evaporation of Bi 2 O 3 during the solid-state Crystals 2020, 10, 698 4 of 10 reaction process. There were individual impurity peaks (TiO 2 component) observed in the compounds obtained by sintering the stoichiometric raw materials using the solid-state reaction method, as shown in Figure 1a. In addition, experimental results proved that the CBT crystalline phase was difficult to obtain solely using Bi 2 O 3 or PbO as flux agents. When using Bi 2 O 3 as the flux agent (Bi 2 O 3 :CBT = 3:1, 4:1 and 5:1), the main compound was Bi 12 TiO 20 , and no CBT phase was detected using XRPD (Figure 1b). Similarly, when using PbO as the flux agent (PbO:CBT = 2:1, 3:1 and 4:1), the impurity phase is mainly Pb x Bi y Ti z O (2x + 3y + 4z)/2 (x, y, z ≥ 0) compounds (Figure 1c). In contrast, when using the mixed PbO-B 2 O 3 flux system and selecting the ratio of PbO:B 2 O 3 to be 1:1, the CBT single crystal phase could be achieved. However, when the ratio deviated from 1:1, the impurity phases such as the Pb 5 B 8 O 17 and Bi 12 TiO 20 might be formed, as presented in Figure 1d.
contrast, when using the mixed PbO-B2O3 flux system and selecting the ratio of PbO:B2O3 to be 1:1, the CBT single crystal phase could be achieved. However, when the ratio deviated from 1:1, the impurity phases such as the Pb5B8O17 and Bi12TiO20 might be formed, as presented in Figure 1d.
Considering that the PbBi4Ti4O15 (PBT) compound has the same symmetry with CBT crystal, further XRPD analysis was performed to identity the crystalline CBT phase. Figure 2a gives the XRPD patterns of crystalline CBT with different flux ratios and compared with the PBT phase. It is observed that the diffraction angle of the main peak at approximately 30.54° for CBT is higher than that of PBT (ICSD No.173544). However, the main peaks in the patterns of crystalline CBT with different flux ratios (PbO:B2O3:CBT = 2:2:1, 3:3:1 and 4:4:1) are kept the same with standard CBT (ICSD No. 99500), supporting that the obtained crystal phase is CBT rather than PBT. Experimental results indicate that when the flux ratio is 2:2:1, the mixed compounds are difficult to solute, while when the ratio is 4:4:1, the solubility is relatively low. Therefore, the optimum flux ratio was obtained to be PbO:B2O3:CBT = 3:3:1. In order to evaluate the purity of crystalline CBT compounds obtained by using the mixed PbO-B2O3 flux agents (PbO:B2O3:CBT = 3:3:1), the refined crystal structure by the Rietveld method for the powder X-ray diffraction was performed. Results are shown in Figure 2b. It is indicated that the differences between the pristine data and the refined data are very small, showing a good agreement with the measurements.  Considering that the PbBi 4 Ti 4 O 15 (PBT) compound has the same symmetry with CBT crystal, further XRPD analysis was performed to identity the crystalline CBT phase. Figure 2a gives the XRPD patterns of crystalline CBT with different flux ratios and compared with the PBT phase. It is observed that the diffraction angle of the main peak at approximately 30.54 • for CBT is higher than that of PBT (ICSD No.173544). However, the main peaks in the patterns of crystalline CBT with different flux ratios (PbO:B 2 O 3 :CBT = 2:2:1, 3:3:1 and 4:4:1) are kept the same with standard CBT (ICSD No. 99500), supporting that the obtained crystal phase is CBT rather than PBT. Experimental results indicate that when the flux ratio is 2:2:1, the mixed compounds are difficult to solute, while when the ratio is 4:4:1, the solubility is relatively low. Therefore, the optimum flux ratio was obtained to be PbO:B 2 O 3 :CBT = 3:3:1. In order to evaluate the purity of crystalline CBT compounds obtained by using the mixed PbO-B 2 O 3 flux agents (PbO:B 2 O 3 :CBT = 3:3:1), the refined crystal structure by the Rietveld method for the powder X-ray diffraction was performed. Results are shown in Figure 2b. It is indicated that the differences between the pristine data and the refined data are very small, showing a good agreement with the measurements. The CBT single crystals with millimeter dimensions were successfully grown by using the spontaneous nucleation process using the mixed PbO-B2O3 flux agents (PbO:B2O3:CBT = 3:3:1). The crystalline state in the platinum crucible and the photographs of as-grown flake-shaped CBT crystals are shown in Figure 3a,b, respectively.

Structure-Morphology Relationships
The crystal structures of the four-layer ferroelectric Aurivillius phases ABi4Ti4O15 (A = Ca, Sr, Ba, and Pb) were reported by B.J. Kennedy et al. [33], but they lack descriptions in detail about the CBT crystal with a bismuth-layered structure. The relationship between the crystal structure and morphology was analyzed based on the refined structure data by the Rietveld method. The results are shown in Figure 4. The CBT crystal structure is composed of Bi2O2 layers and TiO6 octahedrons arranged alternately along the crystallographic c-axis, where 0.6Bi(2)/0.4Ca(1) and 0.7Bi(3)/0.3Ca (3) atoms are occupied in the intervals among TiO6 octahedrons. The flake-shaped morphology is closely related to the bismuth layer structure of CBT crystal. It is believed that the flake-shaped morphology is associated with the Bi2O2 layer in the CBT crystal. Generally speaking, the bonding strength decreases with the increase of bond length, and large bond lengths are easy to break. It is found that the bond distance of the Bi(1)-O is about 2.55 Å and 2.69 Å , which is much longer than that of the Ti-O bond (1.77 Å and 1.89 Å ), as presented at Figure 4b. Therefore, the CBT crystal is relatively difficult to grow along the crystallographic c-axis due to the weak chemical bonding, but it is relatively easy to grow along the a-and b-axes. In addition, it is found that the axis ratio c/a for CBT crystal reached 7.5065, exhibiting strong structural anisotropy. There are the reasons why the CBT crystal grown along the crystallographic c-axis shows a flake growth habit.  The CBT single crystals with millimeter dimensions were successfully grown by using the spontaneous nucleation process using the mixed PbO-B2O3 flux agents (PbO:B2O3:CBT = 3:3:1). The crystalline state in the platinum crucible and the photographs of as-grown flake-shaped CBT crystals are shown in Figure 3a,b, respectively.

Structure-Morphology Relationships
The crystal structures of the four-layer ferroelectric Aurivillius phases ABi4Ti4O15 (A = Ca, Sr, Ba, and Pb) were reported by B.J. Kennedy et al. [33], but they lack descriptions in detail about the CBT crystal with a bismuth-layered structure. The relationship between the crystal structure and morphology was analyzed based on the refined structure data by the Rietveld method. The results are shown in Figure 4. The CBT crystal structure is composed of Bi2O2 layers and TiO6 octahedrons arranged alternately along the crystallographic c-axis, where 0.6Bi(2)/0.4Ca(1) and 0.7Bi(3)/0.3Ca (3) atoms are occupied in the intervals among TiO6 octahedrons. The flake-shaped morphology is closely related to the bismuth layer structure of CBT crystal. It is believed that the flake-shaped morphology is associated with the Bi2O2 layer in the CBT crystal. Generally speaking, the bonding strength decreases with the increase of bond length, and large bond lengths are easy to break. It is found that the bond distance of the Bi(1)-O is about 2.55 Å and 2.69 Å , which is much longer than that of the Ti-O bond (1.77 Å and 1.89 Å ), as presented at Figure 4b. Therefore, the CBT crystal is relatively difficult to grow along the crystallographic c-axis due to the weak chemical bonding, but it is relatively easy to grow along the a-and b-axes. In addition, it is found that the axis ratio c/a for CBT crystal reached 7.5065, exhibiting strong structural anisotropy. There are the reasons why the CBT crystal grown along the crystallographic c-axis shows a flake growth habit.

Structure-Morphology Relationships
The crystal structures of the four-layer ferroelectric Aurivillius phases ABi 4 Ti 4 O 15 (A = Ca, Sr, Ba, and Pb) were reported by B.J. Kennedy et al. [33], but they lack descriptions in detail about the CBT crystal with a bismuth-layered structure. The relationship between the crystal structure and morphology was analyzed based on the refined structure data by the Rietveld method. The results are shown in Figure 4. The CBT crystal structure is composed of Bi 2 O 2 layers and TiO 6 octahedrons arranged alternately along the crystallographic c-axis, where 0.6Bi(2)/0.4Ca(1) and 0.7Bi(3)/0.3Ca (3) atoms are occupied in the intervals among TiO 6 octahedrons. The flake-shaped morphology is closely related to the bismuth layer structure of CBT crystal. It is believed that the flake-shaped morphology is associated with the Bi 2 O 2 layer in the CBT crystal. Generally speaking, the bonding strength decreases with the increase of bond length, and large bond lengths are easy to break. It is found that the bond distance of the Bi(1)-O is about 2.55 Å and 2.69 Å, which is much longer than that of the Ti-O bond (1.77 Å and 1.89 Å), as presented at Figure 4b. Therefore, the CBT crystal is relatively difficult to grow along the crystallographic c-axis due to the weak chemical bonding, but it is relatively easy to grow along the aand b-axes. In addition, it is found that the axis ratio c/a for CBT crystal reached 7.5065,

Piezoelectric Activity Evaluation
CaBi4Ti4O15 crystal belongs to the 2 mm point group; thus, it has a non-centrosymmetric structure, which determines that the CBT crystal has piezoelectric properties. In order to explore its potential applications in piezoelectric fields, preliminary evaluations were conducted.

Transmission Spectra
For high-temperature piezoelectric application, the electrical conductivity is an important factor that influences the dielectric loss and temperature stability of the electro-elastic properties. Usually, the electrical conductivity at high temperatures is associated with the bandgap. In this study, the transmittance for CBT polycrystalline sample was measured at room temperature, and the band structure was calculated. As shown in Figure 5, the transmittance from 910 to 4000 nm is about 90% and gradually decreases below the wavelength of 910 nm and reaches zero at about 400 nm, indicating that the transmission cut-off edge of the CBT is about 400 nm, which corresponds to the bandgap of 3.11 eV and is very close to calculated bandgap 3.17 eV. These results are basically consistent with the value reported by Tanwar et al. (3.36 eV) [34].

Piezoelectric Activity Evaluation
CaBi 4 Ti 4 O 15 crystal belongs to the 2 mm point group; thus, it has a non-centrosymmetric structure, which determines that the CBT crystal has piezoelectric properties. In order to explore its potential applications in piezoelectric fields, preliminary evaluations were conducted.

Transmission Spectra
For high-temperature piezoelectric application, the electrical conductivity is an important factor that influences the dielectric loss and temperature stability of the electro-elastic properties. Usually, the electrical conductivity at high temperatures is associated with the bandgap. In this study, the transmittance for CBT polycrystalline sample was measured at room temperature, and the band structure was calculated. As shown in Figure 5, the transmittance from 910 to 4000 nm is about 90% and gradually decreases below the wavelength of 910 nm and reaches zero at about 400 nm, indicating that the transmission cut-off edge of the CBT is about 400 nm, which corresponds to the bandgap of 3.11 eV and is very close to calculated bandgap 3.17 eV. These results are basically consistent with the value reported by Tanwar et al. (3.36 eV) [34].

Piezoelectric Activity Evaluation
CaBi4Ti4O15 crystal belongs to the 2 mm point group; thus, it has a non-centrosymmetric structure, which determines that the CBT crystal has piezoelectric properties. In order to explore its potential applications in piezoelectric fields, preliminary evaluations were conducted.

Transmission Spectra
For high-temperature piezoelectric application, the electrical conductivity is an important factor that influences the dielectric loss and temperature stability of the electro-elastic properties. Usually, the electrical conductivity at high temperatures is associated with the bandgap. In this study, the transmittance for CBT polycrystalline sample was measured at room temperature, and the band structure was calculated. As shown in Figure 5, the transmittance from 910 to 4000 nm is about 90% and gradually decreases below the wavelength of 910 nm and reaches zero at about 400 nm, indicating that the transmission cut-off edge of the CBT is about 400 nm, which corresponds to the bandgap of 3.11 eV and is very close to calculated bandgap 3.17 eV. These results are basically consistent with the value reported by Tanwar et al. (3.36 eV) [34].

Dipole Moment Calculation
The piezoelectric activity is closely related to the polyhedron distortion and net dipole moment. As for the polyhedron distortion in CBT crystal, there are several types of polyhedron distortions (Figure 6a), among which the distortion ∆d for Bi(1)O 6 octahedron was calculated by using the following formula [35]: where the O1-O6 are coordination oxygen atoms of the Bi(1)O 6 octahedron, and θ 1 , θ 2 , and θ 3 are bond angles. The distortion ∆d for the Bi(1)O 6 octahedron was found to be 1.37 Å, which can be identified as strong distortions according to the fourth category defined by Halasyamani [35]. Generally, the larger the polyhedron distortion, the stronger the piezoelectric activity of the crystals. Besides the polyhedron distortion, the net diploe moments in CBT crystal were studied, according to the bond-valence theory [36][37][38][39][40]. Table 1 summarizes the dipole moments of each polyhedron in CBT crystal. It was found that the magnitude of the net dipole moment in the unit cell of the CBT crystal was about 37 Debye, which is comparable with the α-BiB 3 O 6 single crystal (35 Debye), of which the piezoelectric charge coefficient d 22 was determined to be in the order of 40 pC/N [41]. Additionally, the directions of the dipole moment for the polyhedral and unit cell of the CBT crystal are identified and shown in Figure 6b, where the net dipole moment direction of the CBT unit cell was negative along the crystallographic c-axis. The calculated results indicated that the Bi(1)O 6 octahedron showed a larger distortion and contributed to the piezoelectric activity of the CBT crystal. Hence, it is predicted that the CBT single crystal has excellent piezoelectric performances.

Dipole Moment Calculation
The piezoelectric activity is closely related to the polyhedron distortion and net dipole moment. As for the polyhedron distortion in CBT crystal, there are several types of polyhedron distortions (Figure 6a), among which the distortion ∆d for Bi(1)O6 octahedron was calculated by using the following formula [35]: where the O1-O6 are coordination oxygen atoms of the Bi(1)O6 octahedron, and θ1, θ2, and θ3 are bond angles. The distortion ∆d for the Bi(1)O6 octahedron was found to be 1.37 Å , which can be identified as strong distortions according to the fourth category defined by Halasyamani [35]. Generally, the larger the polyhedron distortion, the stronger the piezoelectric activity of the crystals. Besides the polyhedron distortion, the net diploe moments in CBT crystal were studied, according to the bond-valence theory [36][37][38][39][40]. Table 1 summarizes the dipole moments of each polyhedron in CBT crystal. It was found that the magnitude of the net dipole moment in the unit cell of the CBT crystal was about 37 Debye, which is comparable with the α-BiB3O6 single crystal (35 Debye), of which the piezoelectric charge coefficient d22 was determined to be in the order of 40 pC/N [41]. Additionally, the directions of the dipole moment for the polyhedral and unit cell of the CBT crystal are identified and shown in Figure  6b, where the net dipole moment direction of the CBT unit cell was negative along the crystallographic c-axis. The calculated results indicated that the Bi(1)O6 octahedron showed a larger distortion and contributed to the piezoelectric activity of the CBT crystal. Hence, it is predicted that the CBT single crystal has excellent piezoelectric performances.

Conclusions
In summary, the flake-shaped CBT crystals in the millimeter range were grown by the flux method using the mixed PbO-B 2 O 3 agents for the first time. The optimum flux composition mole ratio was found to be PbO:B 2 O 3 :CBT = 3:3:1. The flake-shaped growth habit of the CBT crystal was analyzed from the perspective of a microcrystal structure. The structural distortions and the net dipole moment of the CBT crystal were found to be 1.37 Å (Bi(1)O 6 octahedron) and 37 Debye, respectively. The Bi(1)O 6 octahedron showed the larger distortion and believed to contribute to the piezoelectric activity of the CBT crystal. In addition, the transmittance spectrum of the CBT crystal was measured and found to show a broad transmission range, where the bandgap was found to be near 3.11 eV. However, the main problem encountered in CBT growth is the observed flake growth habit. In the following studies, the large-size single crystal growth by using the top-seeded method with mixed PbO-B 2 O 3 fluxes will be performed.