Polymorphic Phase Transition and Piezoelectric Performance of BaTiO 3 -CaSnO 3 Solid Solutions

: BaTiO 3 -based piezoelectric ceramics have attracted considerable attention in recent years due to their tunable phase structures and good piezoelectric properties. In this work, the (1 − x )BaTiO 3 − x CaSnO 3 (0.00 ≤ x ≤ 0.16, abbreviated as BT − x CS) solid solutions, were prepared by traditional solid-state reaction methods. The phase transitions, microstructure, dielectric, piezoelectric, and ferroelectric properties of BT- x CS have been investigated in detail. The coexistence of rhombohedral, orthorhombic, and tetragonal phases near room temperature, i.e., polymorphic phase transition (PPT), has been conﬁrmed by X-ray diffraction and temperature-dependent dielectric measurements in the compositions range of 0.06 ≤ x ≤ 0.10. The multiphase coexistence near room temperature provides more spontaneous polarization vectors and facilitates the process of polarization rotation and extension by an external electric ﬁeld, which is conducive to the enhancement of piezoelectric response. Remarkably, the composition of BT-0.08CS exhibits optimized piezoelectric properties with a piezoelectric coefﬁcient d 33 of 620 pC/N, electromechanical coupling factors k p of 58%, k t of 40%, and a piezoelectric strain coefﬁcient d 33 * of 950 pm/V. previous investigations, (Ba, Ca)(Ti 1 − x M x )O 3 based ceramics are good piezoelectric ceramic materials operating at room temperature. Therefore, the investigations on the enhanced piezoelectric properties of (Ba, Ca)(Ti 1 − x M x )O 3 solid solutions are of great interest for BaTiO 3 -based ceramics. the coexistence of R , O , T phases at x = 0.08 provides more spontaneous polarization vectors [41,42,50], resulting in the increase of piezoelectricity. On the other hand, the low energy barriers in the region of phase boundaries can greatly facilitate the process of polarization rotation and extension under an external electric ﬁeld [16–18], which can be responsible for the signiﬁcant enhancement of piezoelectric response. Meanwhile, there are similar variation tendencies of k p and k t , and the values of k p and k t increase initially as the x content increases from 0.00 to 0.08, and then decreases with the x content further increasing to 0.16. The composition with x = 0.08 exhibits optimal piezoelectric properties, with the maximum d 33 value of 620 pC/N, k p of 58%, and k t of 40%.

The schematic diagrams of phase transitions of pure BaTiO 3 in the temperature range from −90 • C to 130 • C are shown in Figure 1. There are four phases: rhombohedral (R) phase, orthorhombic (O) phase, tetragonal (T) phase, and cubic (C) phase; and three phase transitions: ferroelectric-ferroelectric phase transitions of R to O phase with T R-O of~−90 • C and O to T phase with T O-T of~5 • C, and the ferroelectric-paraelectric phase transition T to C phase with T R-O of~130 • C. Great efforts have been made to adjust phase transitions of BaTiO 3 -based ceramics in order to enhance their dielectric, ferroelectric, and piezoelectric properties. For example, the strontium-doped BaTiO 3 ceramics exhibit diffused phase transitions due to compositional inhomogeneity [31][32][33]; the BaTiO 3 -BiMO 3 transitions due to compositional inhomogeneity [31][32][33]; the BaTiO3-BiMO3 (where M represents Sc 3+ , In 3+ , etc.) solid solutions present phase transition from normal ferroelectrics to relaxor ferroelectrics by compositional design, and the hysteresis loop characteristics of relaxor ferroelectrics are conducive to the enhancement of energy storage properties [34][35][36]; the (Ba, Ca)(Ti1−xMx)O3 (where M represents Zr 4+ , Hf 4+ , Sn 4+ , etc.) ceramics are the most widely investigated BaTiO3-based ceramics with enhanced piezoelectric properties in recent years due to their tunable phase transitions with the variation of M concentration [37][38][39][40][41][42][43]. A high piezoelectric constant d33 of 485 pC/N with electromechanical coupling coefficient kp of 39% and mechanical quality factor Qm of 191 was achieved in the (Ba0.95Ca0.05)(Ti0.90Sn0.10)O3 ceramics with 3 mol% Li2CO3 by constructing the phase coexistence of R and T phases at room temperature (RT) [37]. The improved piezoelectric and dielectric properties, with a d33 of 407 pC/N, dielectric constant εr of 5,500, and dielectric loss tanδ of 0.3%, have been obtained in the (1 − x)Ba0.98Ca0.02Ti0.94Sn0.06O3-xBa0.85Ca0.15Ti0.9Zr0.1O3 ceramics, where the phase coexistence of orthorhombic and tetragonal phases is identified with x = 0.40 [38]. Significantly enhanced piezoelectric properties with a d33 of 515 pC/N and a field-induced strain d33* of 1,293 pm/V at 10 kV were acquired in the ternary system BaTiO3-CaTiO3-BaSnO3, where the several phase transitions (R-O, O-T and T-C) are designed near RT [39]. As indicated in previous investigations, (Ba, Ca)(Ti1−xMx)O3 based ceramics are good piezoelectric ceramic materials operating at room temperature. Therefore, the investigations on the enhanced piezoelectric properties of (Ba, Ca)(Ti1−xMx)O3 solid solutions are of great interest for BaTiO3-based ceramics. Note that the B-site doping cations of Zr 4+ , Hf 4+ , Sn 4+ have similar effects on inducing the phase transitions in the (Ba, Ca)(Ti1−xMx)O3 ceramics, while the Sn 4+ ion has a significant impact on the construction of phase boundary [41]. Additionally, it has been confirmed that the introduction of CaSnO3 decreases the c/a ratio of BaTiO3 [44], and the distortion of lattice structure may have great influence on the piezoelectric properties. However, few reports on the dielectric, piezoelectric, and ferroelectric properties of the CaSnO3 modified BaTiO3 ceramics exist in the literature. Therefore in this work, (1 − x)BaTiO3-xCaSnO3 (BT-xCS) solid solutions have been prepared by the conventional solid-state reaction method. The microstructure, phase structure, dielectric, ferroelectric, and piezoelectric properties have been investigated in detail.

Materials and Methods
(1 − x)BaTiO3-xCaSnO3 (abbreviated as BT-xCS, x = 0.00, 0.02, 0.04, 0.06, 0.08, 0.10, 0.12, 0.14, and 0.16) ceramics were prepared by conventional solid-state reaction method. Analytical-grade BaCO3 (>99.5%), TiO2 (>99.8%), CaCO3 (>99.5%), and SnO2 (>99.5%) were used as raw materials. The powders were weighed according to the stoichiometric compositions, and then wet-milled in polyethylene bottles with ZrO2 balls for 12 h in ethanol. Note that the B-site doping cations of Zr 4+ , Hf 4+ , Sn 4+ have similar effects on inducing the phase transitions in the (Ba, Ca)(Ti 1−x M x )O 3 ceramics, while the Sn 4+ ion has a significant impact on the construction of phase boundary [41]. Additionally, it has been confirmed that the introduction of CaSnO 3 decreases the c/a ratio of BaTiO 3 [44], and the distortion of lattice structure may have great influence on the piezoelectric properties. However, few reports on the dielectric, piezoelectric, and ferroelectric properties of the CaSnO 3 modified BaTiO 3 ceramics exist in the literature. Therefore in this work, (1 − x)BaTiO 3 -xCaSnO 3 (BT-xCS) solid solutions have been prepared by the conventional solid-state reaction method. The microstructure, phase structure, dielectric, ferroelectric, and piezoelectric properties have been investigated in detail.

Materials and Methods
(1 − x)BaTiO 3 -xCaSnO 3 (abbreviated as BT-xCS, x = 0.00, 0.02, 0.04, 0.06, 0.08, 0.10, 0.12, 0.14, and 0.16) ceramics were prepared by conventional solid-state reaction method. Analytical-grade BaCO 3 (>99.5%), TiO 2 (>99.8%), CaCO 3 (>99.5%), and SnO 2 (>99.5%) were used as raw materials. The powders were weighed according to the stoichiometric compositions, and then wet-milled in polyethylene bottles with ZrO 2 balls for 12 h in ethanol. The milled powders were dried and calcined at 1200 • C for 3 h. Afterwards, the calcined powders were milled, dried, grinded, and granulated with polyvinyl alcohol (PVA) binder and subsequently pressed into discs with diameters of 12.0 mm and thicknesses of 2.0 mm at a pressure of 150 MPa. After binder burn-out at 650 • C, the green compacts were placed in Al 2 O 3 crucibles with self-source. The samples were sintered at 1380 • C for 3 h, and then furnace-cooled down to room temperature.
The phase structure was characterized by an X-ray diffractometer (Smartlab SE, Rigaku Corporation, Tokyo, Japan) with Cu K α radiation in the 2θ range of 20-80 • . The natural surface morphology of the sintered ceramics was carried out by field-emission scanning electron microscopy (Helios G4 UC, Thermo Fisher Scientific, Hillsboro, OR, USA), and the intercept method was used to measure the grain size using the software of ImageJ. Before the electrical measurements, both sides of the sintered ceramics were polished, and fired at 600 • C for 30 min after the silver electrodes were screen-printed on both polished surfaces of ceramics. The dielectric properties were tested by an impedance analyzer (E4990A, Keisight Technologies, Santa Rosa, CA, USA). Hysteresis loops were measured by a ferroelectric analyzer (TF Analyzer 2000, aixACCT Systems GmbH, Aachen, Germany). The piezoelectric constant d 33 was measured using a d 33 meter (YE2730A, Sinocera Piezotronics, Inc., Yangzhou, China) after the sample was poled in silicone oil under a direct-current (DC) electric field of 40 kV/cm at room temperature. The electromechanical coupling factor k t and k p were determined by the IEEE resonance method with E4990A impedance analyzer.  Figure 2a, all the BT-xCS compositions exhibit pure perovskite structure without any trace of secondary or impure phases detected. In terms of Shannon's work, the effective ionic radius of XII Ba 2+ , VI Ti 4+ , XII Ca 2+ , and VI Sn 4+ are 161 pm, 60.5 pm, 134 pm, and 69 pm, respectively. According to the fundamentals of radius matching rule, Ca 2+ ions and Sn 4+ ions occupy the A-site (Ba-site) and B-site (Ti-site) of BaTiO 3 lattice, respectively. Additionally, the tolerance factor of perovskite structure is usually used to evaluate the stability of crystal structure, which can be determined by the following equation:

Phase Structure
where R A , R B , and R O represent the ionic radius of the A-, B-site, and O 2in ABO 3 structure, respectively. It is commonly recognized that the perovskite structure is stable with 0.77 < t < 1.09, and the value of t locates between 1.062 and 1.039 for BT-xCS (0.00 ≤ x ≤ 0.16), indicating the stable structure of BT-xCS solid solutions in this work. The enlarged (200) diffraction peaks with angles from 44.6 • to 47.0 • are given in Figure 2b to clearly show the phase evolutions. It is clear that the diffraction peaks of the compositions with x < 0.04 are assigned to the T phase, and those of the compositions with x > 0.12 correspond to the C phase. Note that the diffraction peaks of the compositions with 0.06 ≤ x ≤ 0.10 are not separately matched well with those four R, T, O, and C phases, which can be described as phase coexistence. Similar results have been reported in other elements modified BT-based ceramics [38][39][40][41][42]. Furthermore, the (200) peak shifts slightly towards higher degrees with the increase of x content, indicating the shrinkage of the lattice parameters, and this can be ascribed to the decrease of the ionic radius in A-site, 134 pm for Ca 2+ compared with 161 pm for Ba 2+ in 12-fold coordination.

Dielectric Properties
In order to further investigate the phase transition behavior of BT-xCS ceramics, the temperature-dependent dielectric constant ε r and dielectric loss tanδ measured at 100 kHz in the temperature range from −50 • C to 150 • C are shown in Figure 3. The room Actuators 2021, 10, 129 4 of 12 temperature dielectric constant ε r and dielectric loss tanδ of BT-xCS measured at 100 kHz are listed in Table 1. The value of ε r increases initially from 1966 to 10,811 as the x content increases from 0.00 to 0.14, and then decreases to 8,803 at x = 0.16. Meanwhile, the dielectric loss tanδ of BT-xCS ceramics is low (tanδ < 0.06) within the investigated temperature range. The variation of ε r is mainly due to the evolution of phase transitions around room temperature. As shown in Figure 3, there are two significant dielectric anomalies for the compositions of x = 0.00 and 0.02 within the investigated temperature range, and the dielectric anomalies correspond to the ferroelectric-ferroelectric phase transition (O-T) at T O-T and the paraelectric-ferroelectric phase transition (T-C) at T C , respectively. For the compositions of 0.04 ≤ x ≤ 0.10, another ferroelectric-ferroelectric phase transition (R-O) at T R-O arises. With the increase of x content, the T R-O and T O-T shift to higher temperature, while the T C shifts to lower temperature, resulting in the merging of three phase transition peaks into one broad peak at T C for the composition of x = 0.12, and the R-O and O-T phase transitions disappear gradually with x ≥ 0.12. The phase transition temperatures (T R-O , T O-T , and T C ) of BT-xCS are also summarized in Table 1. The T R-O increases from −26.1 • C to 5.2 • C as the x content increases from 0.04 to 0.10, the T O-T increases from 16.6 • C to 24.5 • C as the x increases from 0.00 to 0.10, and the T C decreases from 126.9 • C to −4.3 • C as the x increases from 0.00 to 0. 16

Dielectric Properties
In order to further investigate the phase transition behavior of BT-x temperature-dependent dielectric constant εr and dielectric loss tanδ meas

Phase Transition
The phase diagrams of BT-xCS are established according to the temperature-dependent dielectric results, as shown in Figure 4a. The phase diagrams consist of three ferroelectric phase regions, R, O, and T phases and one paraelectric phase region, C phase, which visually demonstrates the phase transitions. The T C decreases almost linearly with the increase of x content, which is mainly influenced by the substitution of Sn 4+ for Ti 4+ ions, as the Ca 2+ in A-site of BT generally has little effects on the T C [45]. However, the substitution of Sn 4+ for Ti 4+ significantly affects the stability of BO 6 octahedron and decreases the tetragonality c/a. Similar results have been reported in Sn 4+ -modified BaTiO 3 [46,47]. The T R-O and T O-T increase at different rising rate as the x content increases from 0.00 to 0.10, and merge into T C around room temperature for the composition of x = 0.12. Herein the shadow area represents the phase components around room temperature. Figure 4b presents the lattice parameters as a function of x content based on the refining PXRD data. The composition-dependent lattice parameters are considered as the further evidence of phase evolution. As indicated by the yellow symbols (lattice parameters of T phase), the c decreases but the a increases as the x content increases from 0.00 to 0.10, which means that the ratio of c/a decreases and also suggests that the structure tends to be an R or C phase. Furthermore, combining the PXRD results, the phase structure for the compositions of 0.06 ≤ x ≤ 0.10 cannot be simply identified as the T phase, and thereby the lattice parameters of these compositions are also given based on the R and O phases. As shown in Figure 4a

Phase Transition
The phase diagrams of BT-xCS are established according to the temperature-dependent dielectric results, as shown in Figure 4a. The phase diagrams consist of three ferroelectric phase regions, R, O, and T phases and one paraelectric phase region, C phase, which visually demonstrates the phase transitions. The TC decreases almost linearly with the increase of x content, which is mainly influenced by the substitution of Sn 4+ for Ti 4+ ions, as the Ca 2+ in A-site of BT generally has little effects on the TC [45]. However, the substitution of Sn 4+ for Ti 4+ significantly affects the stability of BO6 octahedron and decreases the tetragonality c/a. Similar results have been reported in Sn 4+ -modified BaTiO3 [46,47]. The TR-O and TO-T increase at different rising rate as the x content increases from 0.00 to 0.10, and merge into TC around room temperature for the composition of x = 0.12. Herein the shadow area represents the phase components around room temperature. Figure 4b presents the lattice parameters as a function of x content based on the refining PXRD data. The composition-dependent lattice parameters are considered as the further evidence of phase evolution. As indicated by the yellow symbols (lattice parameters of T phase), the c decreases but the a increases as the x content increases from 0.00 to 0.10, which means that the ratio of c/a decreases and also suggests that the structure tends to be an R or C phase. Furthermore, combining the PXRD results, the phase structure for the compositions of 0.06 ≤ x ≤ 0.10 cannot be simply identified as the T phase, and thereby the lattice parameters of these compositions are also given based on the R and O phases. As shown in Figure  4a

Microstructural Properties
Previous investigations have shown that the BaTiO3-based ceramics exhibit an enhanced dielectric response as the grain size decreases to micron level due to the grain size

Microstructural Properties
Previous investigations have shown that the BaTiO 3 -based ceramics exhibit an enhanced dielectric response as the grain size decreases to micron level due to the grain size effect [48,49]. The SEM images and grain distributions of BT-xCS (0.02 ≤ x ≤ 0. 16) ceramics are shown in Figure 5. All the samples are densely sintered with distinctive grain boundaries, and the relative density of each composition is over 95%. The insets of Figure 5 are the distributions of grain size and the average grain size corresponding to each composition. It is obvious that the microstructure of BT-xCS is dependent on the substitution of CS. The grain distributions are inhomogeneous in the compositions of x < 0.06, which are similar to the grain morphology of pure BT [36]. For example, the grain size of large grains in the composition of x = 0.02 is approximately 20 µm and that of small grains is only about 4 µm. The variation of grain growth in the range of 0.06 ≤ x ≤ 0.10 may be ascribed to the phase transition around room temperature induced by composition. With further increase of x content, the grain tends to distribute homogeneously and the grain size is nearly unchanged in the compositions of x > 0.08. However, further doping of CS (x = 0.16) leads to the decrease in grain size, which may be attributed to the excess doping of CS concentrates near grain boundaries and inhibits the grain growth of BT-xCS ceramics.
Actuators 2021, 10, x FOR PEER REVIEW 7 of 12 effect [48,49]. The SEM images and grain distributions of BT-xCS (0.02 ≤ x ≤ 0.16) ceramics are shown in Figure 5. All the samples are densely sintered with distinctive grain boundaries, and the relative density of each composition is over 95%. The insets of Figure 5 are the distributions of grain size and the average grain size corresponding to each composition. It is obvious that the microstructure of BT-xCS is dependent on the substitution of CS. The grain distributions are inhomogeneous in the compositions of x < 0.06, which are similar to the grain morphology of pure BT [36]. For example, the grain size of large grains in the composition of x = 0.02 is approximately 20 μm and that of small grains is only about 4 μm. The variation of grain growth in the range of 0.06 ≤ x ≤ 0.10 may be ascribed to the phase transition around room temperature induced by composition. With further increase of x content, the grain tends to distribute homogeneously and the grain size is nearly unchanged in the compositions of x > 0.08. However, further doping of CS (x = 0.16) leads to the decrease in grain size, which may be attributed to the excess doping of CS concentrates near grain boundaries and inhibits the grain growth of BT-xCS ceramics.    Figure 6 shows the composition-dependent piezoelectric constant d 33 , planar electromechanical coupling factor k p , and thickness electromechanical coupling factor k t of BT-xCS ceramics. The d 33 values are summarized in Table 2; the values of d 33 increases initially from 350 pC/N for pure BaTiO 3 to 620 pC/N for the composition of x = 0.08, and then decreases rapidly to 130 pC/N at x = 0.16. There are two reasons for the enhancement of piezoelectric response. According to the polarization deflection theory proposed by Fu and Cohen [18], the coexistence of R, O, T phases at x = 0.08 provides more spontaneous polarization vectors [41,42,50], resulting in the increase of piezoelectricity. On the other hand, the low energy barriers in the region of phase boundaries can greatly facilitate the process of polarization rotation and extension under an external electric field [16][17][18], which can be responsible for the significant enhancement of piezoelectric response. Meanwhile, there are similar variation tendencies of k p and k t , and the values of k p and k t increase initially as the x content increases from 0.00 to 0.08, and then decreases with the x content further increasing to 0.16. The composition with x = 0.08 exhibits optimal piezoelectric properties, with the maximum d 33 value of 620 pC/N, k p of 58%, and k t of 40%. ors 2021, 10, x FOR PEER REVIEW Figure 6 shows the composition-dependent piezoelectric con mechanical coupling factor kp, and thickness electromechanical c xCS ceramics. The d33 values are summarized in Table 2; the values from 350 pC/N for pure BaTiO3 to 620 pC/N for the compositio decreases rapidly to 130 pC/N at x = 0.16. There are two reasons piezoelectric response. According to the polarization deflection and Cohen [18], the coexistence of R, O, T phases at x = 0.08 prov polarization vectors [41,42,50], resulting in the increase of piezo hand, the low energy barriers in the region of phase boundaries process of polarization rotation and extension under an extern which can be responsible for the significant enhancement of piezo while, there are similar variation tendencies of kp and kt, and the va initially as the x content increases from 0.00 to 0.08, and then decr further increasing to 0. 16    3.6. Ferroelectric Properties Figure 7a shows the polarization-electric field (P-E) loops of BT-xCS (0.04 ≤ x ≤ 0.16) under the driven electric field of 40 kV/cm. The P-E loops tend to become "slim" with the increase of x content. The loop for the composition of x = 0.16 presents a "curve", demonstrating that the BT-0.16CS ceramic is transformed to the paraelectric phase [51]. The maximum polarization P m , remnant polarization P r and coercive field E c , derived from P-E loops, are displayed in Figure 7b as a function of x content, and the corresponding values are summarized in Table 2. It is clear that the P m , P r , and E c exhibit the similar decline tendency with the increase of x content. Note that the value of E c decreases from 2.57 kV/cm to 0.57 kV/cm as the x content increases from 0.00 to 0.16, leading to an easier domain switching under the external electric field. The reduction of E c can be attributed to the instability of the ferroelectric domains. It has been well established that the stability of ferroelectric domain is determined by the coupling of A-site cations and BO 6 octahedron with ferroelectric properties for an ABO 3 type perovskite structure, and the distortion of lattice structure induced by the substitution of Ca 2+ and Sn 4+ weakens the coupling between A-site cation and BO 6 octahedron of BT-xCS, resulting in the instability of the ferroelectric domains and thereby decreasing the value of E c [52,53]. Meanwhile, P m and P r decrease from 25.4 µC/cm 2 and 11.40 µC/cm 2 to 13.2 µC/cm 2 and 0.29 µC/cm 2 as the x content increases from 0.00 to 0.16, respectively. Figure 7c exhibits the bipolar field-induced strain as a function of electric field of BT-xCS (0.04 ≤ x ≤ 0.16) ceramics under the electric field of 40 kV/cm. Butterfly-shape S-E loops are observed in the compositions of x < 0.10, and this type loop is intrinsically determined by their ferroelectric phase structure. The loops tend to be slender in the compositions of x > 0. 10. The values of positive strain S pos and negative strains S neg increase initially to 4.02% and 0.75% at x = 0.08, and then decrease to 0.67% and almost zero at x = 0.16, respectively. Since the external electric field is much higher than E c , the values of S pos are very close to that of the maximum strain induced by the unipolar electric field (S uni ) [54]. The unipolar field-induced strain of BT-0.08CS is presented in Figure 7d, and the maximum value of S uni reaches 0.38% under the electric field of 40 kV/cm. The derived piezoelectric strain coefficient d 33 * as a function of x content is shown in the inset of Figure 7d. The values of d 33 * are calculated according to the following equation:

Piezoelectric Properties
where S max and E max are the maximum values of strain and electric field obtained from the unipolar strain loops, as d 33 * calculated from unipolar S-E loops are more representable than that from bipolar loops [45]. As shown in Table 2, the excellent piezoelectric response with large d 33 * value of 950 pm/V is obtained for the BT-0.08CS, which is caused by the PPT around the room temperature [39].

Conclusions
The (1 − x)BaTiO 3 -xCaSnO 3 (0.00 ≤ x ≤ 0.16) solid solutions have been prepared by the traditional solid-state reaction methods. The coexistence of R, O, T phases in the compositions with 0.06 ≤ x ≤ 0.10 is revealed by the PXRD results, and also confirmed by the temperature-dependent dielectric measurements. The composition of BT-0.08CS exhibits optimized piezoelectric properties, which is attributed to the polymorphic phase transition. A high piezoelectric coefficient d 33 of 620 pC/N and a large piezoelectric strain coefficient d 33 * of 950 pm/V are achieved, demonstrating the enhanced piezoelectric properties of BT-xCS ceramics.

Conflicts of Interest:
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.