Rayleigh analysis of domain dynamics across temperature induced polymorphic phase transitions in lead-free piezoceramics (1−x)(BaTi_0.88Sn_0.12)–x(Ba_0.7Ca_0.3)TiO₃

Increased environmental concerns have led to great interest in lead-free piezoceramics [1, 2]. Among others, Zr, Sn, and Hf modified BaTiO₃ are interesting systems which increase the piezoelectric coefficient d₃₃ of BaTiO₃ from 190 pC N⁻¹ (for unmodified BaTiO₃) to ~400 pC N⁻¹ in the vicinity of the tetragonal (P4mm)–orthorhombic (Amm2) polymorphic phase boundaries [3–6]. A remarkable breakthrough however was the discovery of ultra high d₃₃ (~600 pC N⁻¹) in Ca-modified Ba(Ti, Zr)O₃ [7]. Since then, Ca modified Ba(Ti, Zr/Sn/Hf) have attracted considerable attention [6, 8–22]. Liu and Ren argued that the extraordinary piezoelectric response of the Ca-modified systems is due to the close proximity of the polymorphic phase boundary to the tricritical point [7]. This significantly flattens the free energy profile and drastically reduces the polarization anisotropy, enabling ease of polarization rotation and domain wall motion. Acosta et al pointed out that, in addition to the reduction in the polarization anisotropy, the high value of the small-signal piezoelectric response (d₃₃) requires the system to exhibit large remanent/spontaneous polarization and increased elastic softening [12]. A comparative study of the Ca-free and Ca-modified Ba(Ti, Sn)O₃ by Abebe proved that Ca modification decreases the spontaneous lattice strain without compromising the spontaneous polarization [13]. The authors argued that the reduction in the spontaneous lattice strain enhanced the domain wall contribution to the piezoelectric response.

In general, the dielectric and piezoelectric response of piezoceramics has contributions from the lattice (intrinsic) and domain wall motion (extrinsic). While the lattice contribution is reversible in nature, the domain wall has both reversible and irreversible components. The irreversibility increases with increasing amplitude of the applied field. Rayleigh analysis is one of the conventional methods used to analyze the contribution of domain wall motion to the measured dielectric and piezoelectric response in piezoceramics in the subcoercive field regime [23, 24]. As per this formalism, the domain walls move in a medium comprising of pinning centers (defects) or varying strengths [24]. In the Rayleigh regime, the dielectric response is proportional to the amplitude of the field as given below.

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle \varepsilon ={{\varepsilon}_{{\rm r}}}+{{\alpha}_{\varepsilon}}*{{E}_{{\rm o}}},\nonumber \end{align} \tag{ 1 }$$

where E_o is the amplitude of the cyclic field below the coercive field of the material. ${{\varepsilon}_{{\rm r}}}$ and αE_o represent the reversible and the irreversible contributions, respectively, to the measured dielectric response. The validity of this relationship has been tested for a large variety of piezoceramics such as Pb(Zr, Ti)O₃ [23–29], PbTiO₃–BiScO₃ [30, 31], (Na, K)NbO₃ (KNN)-based [32–35], and BaTiO₃-based piezoceramics [16, 36, 37]. A systematic study of how the Rayleigh parameters varies vis-à-vis structural changes in BaTiO₃-based high performance piezoceramics has not received detailed attention, as it is difficult to ascertain the nature of the subtle structural distortions in (Ba, Ca)(Ti, Zr/Sn/Hf)O₃. In the present paper we have investigated the possible correlation between Rayleigh parameters and structural changes both as a function of composition and temperature. The investigation was carried out on Ca-modified Ba(Ti, Sn)O₃ system, i.e. (Ba, Ca)(Ti, Sn)O₃ (BCTS). Similar to the (Ba, Ca)(Ti, Zr)O₃ (BCTZ), the group of Ren et al has shown large piezoelectricity in the BCTS series [9]. We synthesized BCTS series as per the nominal formula (1−x)Ba(Ti_0.88Sn_0.12)O₃–(x)Ba_0.7Ca_0.3TiO₃ [9]. We found that the orthorhombic phase shows the highest irreversible Rayleigh parameter. We also found a correlation between the irreversible Rayleigh parameter α and the coercive field, and discuss the proximity of the Curie point on the temperature evolution of the Rayleigh parameters.

The (1−x)Ba(Ti_0.88Sn_0.12)O₃−(x)Ba_0.7Ca_0.3TiO₃ (BCTS) with x  =  0.10, 0.21, and 0.25 piezoceramics were prepared by the solid state reaction method. These compositions correspond to rhombohedral, orthorhombic and tetragonal perovskite phases, respectively, at room temperature. The raw materials BaCO₃ (99.8%; Alfa Aesar), CaCO₃ (99.99%; Alfa Aesar), TiO₂ (99.8%; Alfa Aesar), and SnO₂ (99.99%; Alfa Aesar) were thoroughly mixed in zirconia jars with zirconia balls and acetone as the mixing medium using a planetary ball mill (Fritsch P5). The slurry was dried and then calcined at 1100 °C for 4 h and milled again in acetone for 5 h for better homogenization. After drying the powder was mixed with 2% polyvinyl alcohol (PVA) as a binder and then pressed uniaxially into a 15 mm diameter disk at 10 ton. The sintering was carried out under ambient conditions at 1300 °C for 4 h and 1500 °C for 6 h. High temperature x-ray powder diffraction (XRD) was done using a Rigaku SmartLab with a Johansson monochromator in the incident beam to remove the Cu-Kα₂ radiation. Dielectric measurement was carried out using a Novocontrol (Alpha AN) impedance analyzer. The polarization–electric field hysteresis loop was measured with a Precision premier II loop tracer at 1 Hz. The density of the sintered pellets was measured by the Archimedes' method. The microstructure of the sintered pellets was recorded by scanning electron microscopy (ESEM, Quanta) after gold sputtering the pellets for 6 min. Rietveld analysis was carried out using Fullprof software [38]. A pseudo-Voigt function was chosen to fit the Bragg profiles. The background was accounted for by linear interpolation between data points.

3.1. Structural evolution as a function of composition

Figure 1 shows scanning electron microscopy images of the sintered pellets of some representative compositions of the series. The average grain size for all the compositions are ~12, 80, 90, and 13 µm for x  =  0.10, 0.13, 0.21, and 0.25, respectively. The absence of pores suggests good density, which was also confirmed by the ~95% density measured using the liquid displacement method. For the XRD studies, sintered pellets were ground to powder and annealed at 500 °C for 6 h to get rid of the effect of residual stress which might have been incurred during the grinding process. Figure 2 shows the compositional evolution of the representative pseudo cubic x-ray Bragg profiles. With increasing x, drastic notable changes can be seen first at x  =  0.13 and then at x  =  0.21. These compositions are polymorphic phase boundary compositions of this series. The splitting of the {4 0 0}_pc profile, with nearly equal intensity for x  =  0.13 is consistent with orthorhombic (Amm2) distortion of the perovskite cell [9–11]. The shape of the Bragg profiles in the composition range 0.13  <  x  <  0.21 do not vary much suggesting the stability of the orthorhombic Amm2 phase in the range at room temperature. For x  ⩾  0.22, an abrupt increase in the separation of the doublet of the {4 0 0}_pc profile along with the intensity ratio ~1:2, indicates the onset of a tetragonal (P4mm) distortion. Accurate structural analysis was carried out by the Rietveld method, figure 3. The diffraction patterns of the intermediate compositions 0.13  ⩽  x  ⩽  0.21 could be fitted satisfactorily with a single phase Amm2 structure. The compositions x  =  0.10 and x  =  0.25 could be nicely fitted with rhombohedral (R3m) and tetragonal (P4mm) structural models The refined structural parameters of compositions exhibiting single phase tetragonal, orthorhombic, and rhombohedral structures are given in table 1.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Table 1. Refined structural parameters and agreement factors for annealed powder of (1  −  x)(BaTi_0.88Sn_0.12)–x(Ba_0.7Ca_0.3)TiO₃ using (a) for the x  =  0.10 (R3m), (b) for the x  =  0.21 (Amm2), and (c) for the x  =  0.25 (P4mm) phase models.

(a) $x=0.10$	space group: R3m
Atoms	x	y	z	B(Å2)
Ba/Ca	0.000	0.000	0.000	0.14(5)
Ti/Sn	0.000	0.000	0.516(2)	0.39(8)
O	0.355(3)	0.222(2)	0.687(3)	0.08(6)
a  =  5.678(5) Å, c  =  6.955(9) Å
Rp: 7.72, Rwp: 9.56, Rexp: 5.51, ${{\chi}^{2}}=2.02$
(b) $x=0.21$	space group: Amm2
Atoms	x	y	z	B(Å2)
Ba/Ca	0.000	0.000	0.000	0.12(3)
Ti/Sn	0.500	0.000	0.479(4)	0.68(4)
O1	0.000	0.000	0.540(9)	0.29(6)
O2	0.500	0.273(3)	0.253(6)	0.37(7)
a  =  4.0044(8) Å, b  =  5.675(2) Å, c  =  5.670 25(2) Å
Rp: 8.18, Rwp: 10.2, Rexp: 5.30, ${{\chi}^{2}}=1.48$
(c) $x=0.25$	Space group: P4mm
Atoms	x	y	z	B(Å2)
Ba/Ca	0.000	0.000	0.000	0.79(3)
Ti/Sn	0.500	0.500	0.532(3)	0.64(8)
O1	0.500	0.500	0.032(2)	0.11(1)
O2	0.500	0.000	0.506(2)	0.60(6)
a  =  4.0022(5) Å, c  =  4.0143(4) Å
Rp: 9.00, Rwp: 11.9, Rexp: 5.44, ${{\chi}^{2}}=1.55$

3.2. Structural changes with temperature

Figure 4 shows the temperature evolution of the XRD profiles of the pseudocubic {2 2 2}_pc and {4 0 0}_pc reflections for x  =  0.10, 0.21, and 0.25. For x  =  0.10, the {4 0 0}_pc at T ~ 25 °C appears singlet and there is noticeable asymmetry on the left side of the {2 2 2}_pc suggesting a rhombohedral structure. The splitting of {4 0 0}_pc with nearly equal intensity at T ~ 35 °C suggests the onset of the orthorhombic (Amm2) phase. At 40 °C, the {4 0 0}_pc is split in the ratio ~1:2 suggesting a tetragonal P4mm structure. The {4 0 0}_pc abruptly changed to singlet at T ~ 45 °C indicating the cubic (Pm3m) phase.

Zoom In Zoom Out Reset image size

For x  =  0.21, the splitting of the {4 0 0}_pc peak with nearly equal intensity at 25 °C suggests an orthorhombic structure. At 30 °C the orthorhombic phase (Amm2) transformed to the tetragonal (P4mm) phase as is evident from the 1:2 ratio of the split peaks of the {4 0 0}_pc profile. The P4mm structure persists in the temperature range of 35 °C  ⩽  T  ⩽  55 °C. For T  ⩾  60 °C, the structure becomes cubic. The successful Rietveld fitting of the patterns at 25 °C, 50 °C, and 70 °C with the Amm2, P4mm, and Pm3m structures, shown in figure 5, confirms our visual inspection based conjectures.

Zoom In Zoom Out Reset image size

3.3. Dielectric measurements

We corroborated the results of the temperature dependent structural phase transformations with a temperature dependent dielectric study. Figure 6 shows the temperature dependence of the real part and imaginary parts of the relative dielectric permittivity at 1 kHz. The compositions x  =  0.10 (rhombohedral) and x  =  0.25 (tetragonal) show only one anomaly in the real part of the permittivity at 40 °C and 65 °C, respectively. The orthorhombic composition x  =  0.21, on the other hand, shows two anomalies in the real part of the permittivity. The number of phase transitions above room temperature were, however, best determined from the peaks in the loss tangent (tanδ) versus temperature data, figure 6(b). For x  =  0.10, the highly slanted nature of the tanδ peak profile on the low temperature side of the maximum suggests a series of transformation occurring in quick succession. As evident from the XRD data presented above for this composition, the quick succession of transformations in this small temperature window correspond to R3m-Amm2 and Amm2-P4mm on heating. For x  =  0.21, which exhibits an orthorhombic Amm2 structure at room temperature, the two anomalies at 30 °C and 60 °C in the temperature dependence of tanδ are associated with the Amm2-P4mm and P4mm-Pm3m, respectively. For x  =  0.21, we see only one peak in tanδ at 65 °C, corresponding to the tetragonal-cubic, Curie point. The temperature dependent structural and dielectric measurements are therefore consistent with each other.

Zoom In Zoom Out Reset image size

3.4. Rayleigh analysis

Figure 7 shows the temperature dependence of the P–E hysteresis loops for representative compositions under selected temperatures in the sub coercive field region (0.2–0.8 kV cm⁻¹). The dielectric coefficient was calculated and obtained using the expression

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle \varepsilon ={{P}_{{\rm p}-{\rm p}}}/2{{E}_{{\rm o}}},\nonumber \end{align} \tag{ 2 }$$

where ${{P}_{{\rm p}-{\rm p}}}$ is peak-to-peak polarization measured for the applied electric field amplitude ${{E}_{{\rm o}}}$. The linearity of $-{{E}_{{\rm o}}}$ confirms the validity of the Rayleigh approach in the chosen field region, figure 7. The reversible (ε_r) and the irreversible (α) Rayleigh coefficients were determined using relation (1). Figure 8 shows the temperature variation of both coefficients for the three compositions x  =  0.10, 0.21, and 0.25. For all the three compositions ε_r is maximum at their respective Curie points. For x  =  0.10, the irreversible Rayleigh parameter α increases from 2.1 mm V⁻¹ at 25 °C to 3.2 mm V⁻¹ at 30 °C. This temperature corresponds to rhombohedral–orthorhombic transformation. On further increase of the temperature to 35 °C, α decreases to 1.7 mm V⁻¹. This temperature corresponds to Amm2-P4mm transformation. This decrease continues as the Curie point (~45 °C) is approached. For x  =  0.21, i.e. the composition exhibiting an orthorhombic (Amm2) phase at room temperature, $\alpha$ is 5.98 mm V⁻¹ at 25 °C. This value is nearly retained on heating up to 30 °C, the temperature corresponding to the orthorhombic-tetragonal transition. It decreased to 4.77 mm V⁻¹ at 35 °C, and to further lower values as the Curie point is approached. For the composition exhibiting a tetragonal structure at room temperature (x  =  0.25), the value of $\alpha$ continues to decrease monotonically on heating above room temperature. This composition exhibits only tetragonal (P4mm)–cubic (Pm3m) transition at the Curie point (65 °C) on heating above room temperature.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Enhanced domain wall contribution to dielectric and piezoelectric response appears to be a common feature at polymorphic phase boundaries [36, 39, 40]. Our study confirms that at room temperature, the irreversible Rayleigh parameter α is highest (5.9 mm V⁻¹) for the orthorhombic composition, x  =  0.21. A similar observation was also reported by Acosta et al [37] on (Ba, Ca)(Ti, Zr)O₃. This view is further corroborated from the thermal evolution of α for x  =  0.10 which shows an increase of α from 2.1–3.2 mm V⁻¹ as the rhombohedral phase transforms to orthorhombic at ~30 °C. The non-monotonic temperature variation of the irreversible Rayleigh parameter observed by us is analogous to that recently reported by Gao et al for 0.675Ba(Zr_0.2Ti_0.8)O₃–0.325(Ba_0.7Ca_0.3)TiO₃, a composition in the vicinity of the convergence region [16]. The fact that x  =  0.21 also exhibits the highest piezoelectric response in this series [13], seems to confirm that the enhanced piezoelectric response is also associated with the enhancement in the irreversible Rayleigh parameter α. In another lead-free piezoelectric system Li_x(Na_0.5K_0.5)_1−xNbO₃, Kobayashi et al [34] reported the maximum irreversible contribution in the orthorhombic phase in the immediate vicinity of orthorhombic–monoclinic phase boundary. The enhancement of α in this case has been attributed to the occurrence of the largest number of domain variants and availability of easy pathways for domains to switch collectively, and couple across the randomly oriented grains in the piezoceramic. A slightly different result was reported by Ochoa et al [35] on a Li, Ta, and Sb modified (K, Na)NbO₃. The authors reported α to exhibit the maximum in the temperature region showing the coexistence of tetragonal and orthorhombic phases. α drops drastically in the temperature region showing a single phase Amm2 phase, which happens to occur below room temperature. Ochoa et al also reported that the reversible component of the Rayleigh parameter decreases as the system enters the tetragonal phase region while heating [35]. This contrasts with our result which show that the reversible parameter continues to increase until the Curie point (figure 8), irrespective of whether the room temperature phase is rhombohedral (x  =  0.10), orthorhombic (x  =  0.21), or tetragonal (x  =  0.25). Our results are rather consistent with Gao et al who reported an increase in the reversible Rayleigh parameter as the Curie point is approached in the BCTZ system [16]. Similar to our observation, Peng et al also reported that their orthorhombic composition in a LiTaO₃ modified KNN (KNN-LT) shows a monotonic decrease in α with increasing temperature, even while the system passes through the orthorhombic–tetragonal transformation [32]. The authors attributed this to self clamping of the tetragonal domain walls as the system changes from the orthorhombic to tetragonal phase while heating [32]. Keeping in view the fact that the Curie point of the KNN-LT system is 400 °C, and the precursor effect associated with the Curie point is not likely to set in up to ~200 °C, the argument of Peng et al appears plausible. However, the same argument may not hold when the Curie point is approached. The Curie point of our orthorhombic composition (x  =  0.21) is ~60 °C. The decrease in the irreversible component of the Rayleigh parameter in our case is therefore most likely due to the decrease in the domain wall density as the Curie point is approached [16]. In view of this, the small increase in α from 2.1–3.2 mm V⁻¹ as the temperature of the rhombohedral composition (x  =  0.10) increases from 25 °C–30 °C assumes significance. It suggests that, in spite of the proximity of the system to the Curie point (45 °C), the domain wall contribution to the dielectric response is still considerably high at ~30 °C. From the above, it becomes apparent that although the domain wall contribution is maximized in the orthorhombic phase region, it is equally important to consider how far this phase is from the Curie point.

Further, in view of the fact that higher α is a manifestation of the enhanced contribution of the domain walls (figure 9), it is tempting to correlate it with the trend in the coercive field (E_c) measured from a conventional P–E hysteresis loop. Seeking such a correlation is justified since specimens of different compositions were made under identical synthesis conditions, and the pellets' dimensions and the electrodes used in the P–E measurements were also identical. Figure 9 shows the variation of the coercive field as a function of an irreversible Rayleigh parameter (α) at room temperaure for the three compositions x  =  0.10, 0.21, and 0.25. The composition x  =  0.21, exhibiting the highest α (~6 mm V⁻¹) shows the lowest coercive field (figure 9). The decrease in E_c with increasing α confirms that higher α is a manifestation of an easy domain wall motion, and this happens in the Amm2 phase. For x  =  0.10, the coercive field decreases from 2.7 kV cm⁻¹ at 25 °C to 2.2 kV cm⁻¹ as the system approaches at 30 °C, the rhombohedral–orthorhombic transformation temperature. While this is consistent with the increase in α from 2.1–3.2 mm V⁻¹ (figure 10), the coercive field and α start to decrease with increasing temperature above 30 °C. Evidently, the decrease in the coercive field in this temperature region cannot be attributed to the enhanced domain wall motion. In fact, the monotonic decrease in E_c and α with increasing temperature is evident in x  =  0.25, the tetragonal composition which shows only a ferroelectric–paraelectric transition above room temperature, figure 6. The important point to note is that the saturation polarization also decreases noticeably with increasing temperature, as can be seen from the P–E loops shown in figure 10 for x  =  0.21 and 0.25. The decrease in saturation polarization is indicative of the decrease in the spontaneous polarization as the Curie point is approached. For x  =  0.21, we may however note that it also goes through an orthorhombic–tetragonal phase change, before approaching the Curie point while heating. It is interesting to note that for x  =  0.10, the saturation polarization does not decrease significantly when heating from x  =  0.25 and 30 °C. In view of the fact that this composition also shows an increase in the irreversible Rayleigh parameter α when the temperature is increased from 25 °C–30 °C, suggests that the decrease in the coercive field with increasing temperature in this temperature interval, is most likely due to enhanced domain wall mobility. On further heating, the effect associated with the proximity to the Curie point dominates in determining the coercive field and the Rayleigh parameters.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

We carried out temperature evolution of the dielectric function Rayleigh parameters in conjunction with thermal evolution of the structure on the lead-free piezoceramic (1− x)Ba(Ti_0.88Sn_0.12)O₃–(x)Ba_0.7Ca_0.3TiO₃. Experiments carried out on three representative compositions x  =  0.10, 0.21, and 0.25 corresponding to rhombohedral, orthorhombic, and tetragonal structures at room temperature confirm that the orthorhombic phase exhibits a large irreversible Rayleigh parameter. We showed that a correspondence exists between the enhanced irreversible Rayleigh parameter and a reduction in the coercive field. This correspondence is broken when the system approaches the Curie point. In the latter scenario, the saturation polarization, coercive field, and the irreversible Rayleigh parameter decrease with increasing temperature. We hope our findings will help in understanding the complex relationship of structure and Rayleigh parameters in other analogous piezoceramics.

K Brajesh gratefully acknowledges the Science and Engineering Research Board (SERB) of the Department of Science and Technology, Government of India, for the award of the National Post Doctoral Fellowship. R Ranjan is grateful to the SERB for financial assistance (Grant No. EMR/2016/001457) and for financial assistance from the IISc-ISRO STC cell.