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Article

Evolution Characteristics of Electric Field-Related Properties in Polymorphic Piezoceramics with Temperature-Impelled Phase Transition

by
Chunlin Zhao
1,*,†,
Haopeng Feng
1,†,
Yanli Huang
2,
Xiao Wu
1,
Min Gao
1,
Tengfei Lin
1 and
Cong Lin
1,*
1
College of Materials Science and Engineering, Fuzhou University, Fuzhou 350108, China
2
College of Photonic and Electronic Engineering, Fujian Normal University, Fuzhou 350117, China
*
Authors to whom correspondence should be addressed.
†
These authors contributed equally to this work.
Crystals 2023, 13(9), 1324; https://doi.org/10.3390/cryst13091324
Submission received: 9 August 2023 / Revised: 24 August 2023 / Accepted: 28 August 2023 / Published: 30 August 2023
(This article belongs to the Special Issue Advanced Ferroelectric, Piezoelectric and Dielectric Ceramics)
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Abstract

:
In this work, to systematically investigate the evolution characteristics of electrical properties in polymorphic piezoceramics, the Ba(Ti0.92Zr0.08)O3 ceramics are selected as a paradigm that possesses all the general phase structures above room temperature. It is found that the evolution of electrical properties with temperature change can be divided into three stages based on phase structure transforming: high ferroelectric and stable strain properties at R and R-O, high ferroelectric and enhanced strain/converse piezoelectric properties at O, O-T, and T phase, and the rapidly decreased ferroelectric and strain properties in T-C and C phase. However, the ferroelectric and strain properties all increase with rising electric field and their evolution can be divided into two parts based on phase structures. The high property and slow increase rate are present at R, R-O, O, and O-T, while the poor property but a high increase rate is present around T-C. Similar results can be found in the evolution of electrostrictive property. Finally, the highest d33* of ~1240 pm/V and Q33 of ~0.053 m4/C2 are obtained at O-T due to the high ferroelectricity but easy domain switching. This work affords important guidance for the property optimization of polymorphic piezoceramics.

1. Introduction

Piezoelectric materials can convert mechanical and electrical energy and are extensively used as sensors, actuators, etc. [1,2,3,4,5,6]. Nowadays, the most used piezoceramics are lead-based ceramics, such as Pb(Zr, Ti)O3 [7]. Lead-free piezoceramics, representing an environmentally friendly alternative to replace toxic lead-based piezoceramics, have been widely investigated in recent years. The most studied lead-free piezoelectric ceramics include BaTiO3 (BT)- and (K, Na)NbO3 (KNN)-based ceramics, which show high electrical properties after phase structure regulation or chemical modification [8,9,10]. Unlike the temperature-insensitive morphotropic phase boundary in lead-based piezoceramics, most of the lead-free piezoelectric ceramics exhibit the polymorphic phase transition (PPT), showing the temperature-impelled phase transition, resulting in the temperature-sensitive phase structure and electrical properties [10,11,12].
Polymorphic BT- and KNN-based piezoceramics belong to ABO3 perovskite ferroelectrics. These piezoceramics have the same types of phase structure and a similar phase transition process when the temperature changes. For example, BT-based piezoceramics usually have four possible phase structures. From low temperature to high temperature, the phase structure sequentially transforms from ferroelectric rhombohedral (R) phase to ferroelectric orthorhombic (O) phase, then to ferroelectric tetragonal (T) phase, and finally to paraelectric cubic (C) phase [9,10]. The corresponding phase transition process is R-O, O-T, and T-C and the corresponding phase transition temperature can be defined as TR-O, TO-T, and TC (Curie temperature), respectively. Previous works have carried out lots of investigations on chemical modification, property optimization, mechanism interpretation, and preparation study, especially focusing on property optimization by phase structure regulation [3,9,10,11,12,13,14]. It has been extensively proved that the electrical properties are directly dependent on the phase structure of piezoceramics. The different phase structures can bring about different polarization, phase stability, and domain switching/polarization rotation behavior, thus contributing to different electrical properties and evolution characteristics of properties. However, there are few works to systematically investigate the evolution characteristics of electrical properties for polymorphic piezoceramics between all possible phase structures and phase transitions, especially under different electric fields [3,8,10].
In this work, a BT-based piezoceramic (Ba(Ti0.92Zr0.08)O3) is selected as the paradigm, which possesses all possible phase structures and phase transitions above room temperature. Zr4+ has a similar ionic radius and the same valence as Ti4+, thus Zr4+ can be well-doped into the BT matrix. The addition of Zr4+ can decrease TC and elevate the TR-O and TO-T of BT ceramics [8]. Then, the evolution of electrical properties with temperature and electric field change is systematically investigated. It is found that the evolution of electrical properties with temperature can be divided into three stages based on phase structure transforming, while the evolution of electrical properties with the electric field can be divided into two stages based on different phase structures. The best overall electrical properties are observed around the O-T phase transition because of the high ferroelectricity and easy domain switching/polarization rotation. These discoveries give more cognitions on the relationships between phase structures and electrical properties and can guide the future investigations on polymorphic piezoceramics.

2. Experimental Procedure

Ba(Ti1−xZrx)O3 (x = 0.04, 0.08, 0.10, 0.12, and 0.15) ceramics were prepared by the conventional solid-state method. The BaCO3 (0.99), ZrO2 (0.99), and TiO2 (0.98) (all from Sinopharm Chemical Reagent Co., Ltd., Shanghai, China) were the raw materials, then these materials were weighted and ball-mixed (200 r/min) in ethanol for 24 h using the zirconium balls as the ball mill medium. The mixed powders were calcined at 1240 °C for 3 h and then were pressed into the circle pellets under ~200 MPa after adding 8 wt% polyvinyl alcohol (PVA) as the binder. The PVA was burned out at 800 °C. After that, the green pellets were sintered at 1400 °C for 3 h. The phase structure and phase transition of ceramics were analyzed via X-ray diffraction (XRD) with Cu Kα radiation (Rigaku Ultima III, Rigaku Corporation, Japan) and temperature-dependent relative dielectric permittivity (εr-T) and dielectric loss (tan δ-T) curves using a dielectric meter (TH2816A, Tonghui Electronic, Changzhou, China) from room temperature to 200 °C and 100–100 kHz. The ceramic surface was observed via field-emission scanning electron microscopy (FE-SEM, Zeiss Supra 55, Carl Zeiss, Oberkochen, Germany) after polishing and thermally etching the ceramics. Temperature- and electric field-dependent ferroelectric hysteresis (P-E) loops, current (J-E) loops, and bipolar strain (S-E) curves were measured using a ferroelectric tester (TF Analyzer 2000E, aixACCT Systems GmbH, Aachen, Germany). Detailed preparation and measurement information are afforded in previous reports [15,16,17].

3. Results and Discussion

Figure 1a shows the phase diagram of Ba(Ti1−xZrx)O3 ceramics. It can be seen that the TR-O and TO-T of ceramics gradually move to high temperature and TC shifts to low temperature when the doping Zr content is elevated. With further increasing x, TR-O, TO-T, and TC become quite close. When x arrives at 0.08, both TR-O and TO-T move to the temperature that exceeds room temperature, while these three-phase transition temperatures still maintain a relatively wide temperature distance from each other, as shown in Figure 1b. Therefore, all the possible phase structures and phase transitions of BT-based piezoceramics can be obtained in Ba(Ti0.92Zr0.08)O3 ceramics over room temperature. Thus, this ceramic is selected as the paradigm to study the electric field-dependent electrical properties in polymorphic piezoceramics with different phase structures and temperature-impelled phase transition. Figure 1c displays the XRD pattern of Ba(Ti0.92Zr0.08)O3 ceramics at room temperature. This ceramic shows the pure perovskite structure, indicating the well-doped Zr in the BT matrix. According to the expanded XRD peak in Figure 1d, this ceramic has the pure R phase at room temperature, which is consistent with the result of εr-T and tan δ-T curves. Figure 1e displays the surface morphology and grain size distribution of Ba(Ti0.92Zr0.08)O3 ceramics. This ceramic shows large grains, with an average grain size of ~180 μm.
The ferroelectric, strain, and converse piezoelectric properties as a function of temperature are investigated to figure out the property evolution in BT-based polymorphic piezoceramics with different phase structures. Figure 2a and Figure 2b, respectively, show the P-E and J-E loops of Ba(Ti0.92Zr0.08)O3 ceramics with different phase structures impelled by temperature change. This ceramic shows the typical and saturated P-E loops with high maximum polarization (Pmax) and high remnant polarization (Pr) at room temperature (R phase). With the rising temperature, the phase structure changes from R to O, then to T, and finally to C phases. In this process, the P-E loop gradually becomes a soft shape with decreased Pmax, rapidly declined Pr, and coercive field (Ec). A similar phenomenon can be also observed in the evolution of J-E loops. As shown in Figure 2b, the sharp current peak (Jm) gradually becomes low and broad. The current peak in the J-E loop is the current induced by ferroelectric domain switching [18]. The high and sharp current peak indicates the strong and rapid domain switching process of large domains, while the low and broad current peak implies the weak and gradual domain switching process of small domains [19,20].
Figure 2c shows the evolution of Pmax and Pr with phase structure transition impelled by temperature change. From R phase to R-O, Pmax (21.64 to 20.88 μC/cm2) and Pr (15.11 to 14.00 μC/cm2) change a little. When the phase structure transforms to O phase, O-T, and T phase, the decrease rate of Pmax and Pr becomes fast, to 19.74, 19.09, 17.79 μC/cm2 and to 12.09, 10.42, 7.67 μC/cm2, respectively. When the phase structure further transforms to T-C and C phase, Pmax and Pr decrease fast to 15.31, 13.59 μC/cm2 and to 3.70, 1.34 μC/cm2, respectively. It is also found that the decrease rate of Pr is much faster than Pmax when the phase structure transforms to a high-temperature phase. A similar change tendency can be found in Ec evolution (Figure 2d). Furthermore, the evolution of Jm also shows a similar change tendency before the T-C phase transition. However, when the phase structure is C phase, Jm and Pr become quite low since there is little domain switching process over TC, while a high Pmax is still present in this structure. This mainly results from the obvious electric field-induced polarization over TC [21,22]. Based on the evolution of ferroelectric parameters, three stages of phase structure evolution can be divided. The high polarization with “hard” ferroelectric characteristics is shown in R phase and R-O phase transition. The high polarization but “soft” ferroelectric characteristics (easy domain switching) are present in O phase, O-T phase transition, and T phase. The slim ferroelectric loop with low polarization and weak domain switching behavior is displayed in T-C phase transition and C phase.
Figure 3a displays a general schematic of bipolar S-E curve for piezoceramics. The positive strain (Spos), negative strain (Sneg), and poling strain (Spol = Spos + Sneg) can be obtained. Sneg indicates the sample contraction when the domain switches from the opposite direction with the electric field. Spos indicates the sample stretch with the domain switching and extension along the electric field direction. Spol indicates the sample deformation in the whole domain switching process [23]. Figure 3b shows the bipolar S-E curves of Ba(Ti0.92Zr0.08)O3 ceramics with different phase structures. The typical butterfly S-E curves are present in all the phase structures. However, with phase structure transforming impelled by temperature rising, Sneg gradually decreases, while Spos first increases and then decreases (Figure 3c). With the rising temperature, the phase structure changes from R phase to R-O and Spos slightly increases from 0.120% to 0.125% (under 30 kV/cm). After that, Spos fast increases to 0.133% (O phase), and reaches the highest value of 0.151% at O-T. Then, Spos begins to decrease to 0.132% at T phase and rapidly decreases to 0.104% at T-C, then to 0.084% at C phase. The obvious electro-strain can be still observed in the C phase, which should be original from the electrostrictive effect [24]. In this process, Sneg maintains at ~0.047% from R phase to R-O, then begins to decrease to 0.039% (O phase), 0.025% (O-T), and 0.01% (T phase). Finally, there is barely any negative strain for T-C and C phase. Because of the obvious negative strain and gradually enhanced positive strain, the poling strain Spol exhibits a high and stable value of ~0.168–0.175% from R phase to O-T, while linearly decreases from O-T to C phase due to the declined Spos and gradually vanished Sneg. On the other hand, the converse piezoelectricity of ceramics can be evaluated via the converse piezoelectric coefficient d33* (Smax/Emax). As shown in Figure 3d, a high d33* of ~400 pm/V (under 30 kV/cm) is obtained in R phase, then d33* further increases to ~500 pm/V at O-T, then decreases to ~280 pm/V at C phase. Before the T-C phase transition, the high converse piezoelectric property is mainly contributed by the piezoelectric effect. Above the T-C phase transition, the converse piezoelectric property all comes from the electrostrictive effect [25]. According to the evolution of strain property, three stages of phase structure transforming can be also divided, that is, the stable Spos and Sneg from R phase to R-O, the improved Spos but decreased Sneg around O-T due to the high ferroelectricity but easy domain switching, and the fast declined Spos and Sneg from T-C phase to C phase.
To investigate the evolution differences of electric field-dependent electrical properties in polymorphic BT-based piezoceramics with different phase structures, the electric field-related ferroelectric, strain, and electrostrictive properties are measured. Figure 4a–g shows the P-E loops measured at 5–40 kV/cm. The relatively “hard” P-E loops with high ferroelectricity can be observed for the low-temperature phases, while the P-E loops gradually become slim for the high-temperature phases, which show weak ferroelectricity. It is also observed that the low electric field cannot achieve the saturated P-E loops for the low-temperature phases (see Figure 4(a2)), while the saturated P-E loops can be easily obtained for the high-temperature phases. The above results indicate that the low-temperature phase structures have large domains but are difficult to switch and the high-temperature phase structures possess small domains that can be easily switched.
Figure 5a–c shows the evolution of Pmax, Pr, and Ec as a function of electric field for Ba(Ti0.92Zr0.08)O3 ceramics with different phase structures. All these three parameters increase with an elevating electric field and all decrease when the phase structure transforms from R phase to C phase. However, the increase rate with the electric field and decrease rate with temperature is different for the ceramics with different phase structures. Firstly, with phase structure transforming impelled by temperature improvement, the decrease rate of Pmax and Pr becomes fast under each electric field. Especially for Pr evolution, its decrease rate is much faster than Pmax and the decrease rate of Pr becomes more rapid for the high-temperature phases compared with low-temperature phases. For Ec evolution shown in Figure 5c, the decrease rate can be divided into three stages as discussed in Figure 2d, that is, the slight decrease of Ec from R phase to R-O, rapid decrease from R-O to O phase, slight decrease again from O phase to T phase, then rapid decrease again from T phase to T-C and C phase. This result indicates that the difficulty of domain switching shows step descent and is similar between R and R-O, between O, T, and O-T, or between T-C and C phase, respectively. On the other hand, the evolution of ferroelectric property with electric field increase can be divided into two stages based on phase structure transformation. The increase rate of Pmax, Pr, and Ec with an electric field exhibits a similar change tendency, as shown in Figure 5d–f. The increase rate is quite similar for R phase, R-O, O phase, and O-T. However, when the phase structure transforms to T phase, which closes to TC peak, the Pmax, Pr, and Ec all become small under a low electric field and then increase obviously when an electric field is elevated. With phase structure further transforming to T-C and C phase, the smaller values are obtained under low electric field and increase more obviously under high electric field. This result implies that the ferroelectric characteristics here are mainly contributed by the high electric field-induced polarization rather than the intrinsic ferroelectric polarization.
Figure 6a–g shows the bipolar S-E curves measured at 5–40 kV/cm for Ba(Ti0.92Zr0.08)O3 ceramics with different phase structures. The butterfly S-E loops are observed for all the phase structures, while the S-E curves gradually become slim and linear when the phase structure transforms into high-temperature phases. The apparent negative strain is present in the low-temperature phases, while the negative strain gradually decreases to near zero when the phase structure transforms to T-C and C phase. The negative strain results from the switching of non-180° domains, therefore the high negative strain means the more or larger domains and the obvious non-180° domain switching process [17,26]. The decreased negative strain implies that the number or size of domains becomes small and domain switching behavior is weak. All the phenomena are well consistent with the results of P-E loops. The high-temperature strain response is mainly contributed by the electrostrictive effect rather than the piezoelectric/domain switching effect.
Figure 7a–c shows the evolution of Spos, Sneg, and d33* as a function of the electric field. Spos and Sneg increase with the rising electric field. However, the evolution of Spos and Sneg with phase structure transforming is different. Firstly, the variation of Sneg is quite similar to the evolution of ferroelectric parameters displayed in Figure 5a–c, showing a decreased tendency when phase structure transforms from R to C phase. The decrease rate exhibits an analogical trend with three change stages divided by different phase structures. Nevertheless, Spos at different electric fields show the same change tendency, firstly increasing when phase structure changes from R phase to O-T and then decreasing when phase structure transforms from O-T to C phase. This result indicates the O-T phase transition can bring about the highest strain and converse piezoelectric properties than other ferroelectric single phase or phase transition. Furthermore, the single O or T phase exhibits a higher strain value than R-O, implying that not all the multiphase coexistence can contribute to the optimized strain or piezoelectric property than the single phase. The evolution of d33* with phase structure is the same as Spos variation. However, d33* displays a decreasing tendency with increasing electric field, except for C phase. This change is opposite to the variation of Spos and ferroelectric properties. That is, the highest d33* is obtained at a low electric field rather than a high one. For example, the maximum d33* of ~1240 pm/V is obtained at O-T under 5 kV/cm, while this high property rapidly decreases to ~400 pm/V when an electric field is elevated to 40 kV/cm. Secondly, as shown in Figure 7d–f, the increase rate of Spos and Sneg and the decrease rate of d33* with electric field exhibit similar behavior. The increase or decrease rate is quite similar for R phase, R-O, O phase, and O-T. However, when the phase structure transforms to T phase, T-C, or C phase, the Spos, Sneg, and d33* all become low and then increase obviously for Spos and Sneg or decrease slowly for d33*. Therefore, the evolution of strain property with an electric field can be also divided into two stages based on different phase structures, similar to the evolution of ferroelectric property (Figure 5d–f). In addition, this result indicates that the strain and converse piezoelectric response are mainly contributed by the electrostrictive effect when domain switching is clamped under a high electric field [27].
It has been proved that all the piezoelectric materials show the electrostrictive effect that describes the ions shifting of materials under an electric field [24]. According to the above measured P-E loops and S-E curves, the electrostrictive S-P curves of Ba(Ti0.92Zr0.08)O3 ceramics with different phase structures can be obtained, as displayed in Figure 8a–g. It can be seen that all the S-P curves show a low hysteresis and quadratic-curve-like shape. With increasing electric field, the polarization and strain are simultaneously improved and the high polarization and O-T phase coexistence can stimulate the higher strain response. In addition, when the phase structure transforms to T-C or C phase, the S-P curves become quite slim with nearly vanished hysteresis. Based on the quadratic fitting of S-P curves (Figure 8h), the electrostrictive effect Q33 can be obtained, which is equivalent to the quadratic coefficient of quadratic fitting on S-P curves [25,28]. The obtained Q33 of Ba(Ti0.92Zr0.08)O3 ceramics with different phase structures is shown in Figure 9a. The evolution of Q33 is quite similar to the variation of Spos, which increases with the rising electric field and reaches the highest value at O-T under each electric field. In addition, when the electric field is elevated, the increase rate of Q33 for R, R-O, O, and O-T is much higher than that of T, T-C, and C phase, that is, the evolution of electrostrictive property with electric field can be also divided into two stages based on different phase structures, as shown in Figure 9a,b. The obvious domain extension behavior before T phase should contribute to this phenomenon. The domain extension under a high electric field can contribute a higher electrostrictive strain than the strain induced by the pure electrostrictive effect with only ions shifting around T-C (here T and C phases are included) [29,30]. On the other hand, it can be seen that Q33 gradually becomes a constant when the electric field is elevated to a high value. This is because the highest electrostrictive property of each phase is limited and can be only obtained under a high electric field. It is also found that the highest electrostrictive effect is achieved at ferroelectric O-T phase transition rather than T-C or C phase reported by many previous works. According to the above results, the O-T phase transition exhibits the highest strain and converse piezoelectric properties, which should be contributed by the high ferroelectricity but unstable ferroelectric phase structure. Therefore, under a high electric field, this unstable phase structure contributes to the high electrostrictive effect [31,32]. As a result, the maximum Q33 of ~0.053 m4/C2 is obtained in the O-T phase transition under a high electric field, which is higher than the Q33 (~0.046 m4/C2) of C phase with no piezoelectric contribution.

4. Conclusions

The evolution of electric field-dependent electrical properties in polymorphic piezoceramics with different phase structures was systematically investigated based on BT-based ceramics. The evolution of electrical properties with temperature change can be divided into three stages, while the property evolution with electric field change is divided into two parts based on phase structure transformation. It is also found that the O-T phase transition has the highest strain and converse piezoelectric properties than other ferroelectric single phase or phase transition, while not all the multiphase coexistence can contribute to the higher strain/piezoelectric properties than single phase. For all the possible phase structures, the high ferroelectric polarization but low coercive field, highest strain/converse piezoelectric, and electrostrictive properties are obtained around the O-T phase transition.

Author Contributions

Conceptualization, C.Z. and C.L.; methodology, C.Z. and H.F.; formal analysis, C.Z. and H.F.; resources, C.Z., Y.H., X.W., M.G., T.L. and C.L.; writing—original draft preparation, C.Z. and H.F.; writing—review and editing, H.F., Y.H., X.W., M.G. and T.L.; visualization, C.Z.; supervision, Y.H., X.W., M.G. and T.L.; project administration, C.Z. and C.L. All authors have read and agreed to the published version of the manuscript.

Funding

The authors appreciate the support of the National Natural Science Foundation of China (No. 12104093, 12204104, 52072075, and 52102126), the Natural Science Foundation of Fujian Province (No. 2021J05122, 2021J05123, 2022J01087, and 2022J01552), and Qishan Scholar Financial Support from Fuzhou University (GXRC-20099).

Data Availability Statement

The data and materials that support the findings of this study are available from the corresponding author upon reasonable request.

Conflicts of Interest

The authors declare no conflict of interest.

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Crystals 13 01324 g001
Figure 1. (a) Phase diagram of Ba(Ti1−xZrx)O3 ceramics. (b) εr-T and tan δ-T curves under different frequencies, (c) XRD pattern and (d) expanded XRD peak, (e) surface FE-SEM image, grain size distribution, and density of Ba(Ti0.92Zr0.08)O3 ceramics.
Figure 1. (a) Phase diagram of Ba(Ti1−xZrx)O3 ceramics. (b) εr-T and tan δ-T curves under different frequencies, (c) XRD pattern and (d) expanded XRD peak, (e) surface FE-SEM image, grain size distribution, and density of Ba(Ti0.92Zr0.08)O3 ceramics.
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Figure 2. Temperature dependence of (a) ferroelectric P-E and (b) J-E loops for Ba(Ti0.92Zr0.08)O3 ceramics with different phase structures under 30 kV/cm. Evolution of (c) Pmax and Pr, (d) Ec, and (e) Jm for Ba(Ti0.92Zr0.08)O3 ceramics with different phase structures impelled by temperature change.
Figure 2. Temperature dependence of (a) ferroelectric P-E and (b) J-E loops for Ba(Ti0.92Zr0.08)O3 ceramics with different phase structures under 30 kV/cm. Evolution of (c) Pmax and Pr, (d) Ec, and (e) Jm for Ba(Ti0.92Zr0.08)O3 ceramics with different phase structures impelled by temperature change.
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Figure 3. (a) Schematic of bipolar S-E curve showing Spos, Sneg, and Spol. (b) Temperature dependence of bipolar S-E curves for Ba(Ti0.92Zr0.08)O3 ceramics with different phase structures under 30 kV/cm. Evolution of (c) Spos, Sneg, and Spol and (d) d33* for Ba(Ti0.92Zr0.08)O3 ceramics with different phase structures impelled by temperature change.
Figure 3. (a) Schematic of bipolar S-E curve showing Spos, Sneg, and Spol. (b) Temperature dependence of bipolar S-E curves for Ba(Ti0.92Zr0.08)O3 ceramics with different phase structures under 30 kV/cm. Evolution of (c) Spos, Sneg, and Spol and (d) d33* for Ba(Ti0.92Zr0.08)O3 ceramics with different phase structures impelled by temperature change.
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Figure 4. Electric field dependence of ferroelectric P-E loops at 5–40 kV/cm for Ba(Ti0.92Zr0.08)O3 ceramics with (a1) R phase, (b) R-O phase transition, (c) O phase, (d) O-T phase transition, (e) T phase, (f) T-C phase transition, and (g) C phase impelled by temperature change. (a2) The expanded P-E loops in the first quartile for R phase.
Figure 4. Electric field dependence of ferroelectric P-E loops at 5–40 kV/cm for Ba(Ti0.92Zr0.08)O3 ceramics with (a1) R phase, (b) R-O phase transition, (c) O phase, (d) O-T phase transition, (e) T phase, (f) T-C phase transition, and (g) C phase impelled by temperature change. (a2) The expanded P-E loops in the first quartile for R phase.
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Figure 5. Evolution of (a) Pmax, (b) Pr, and (c) Ec as a function of electric field for Ba(Ti0.92Zr0.08)O3 ceramics with different phase structures. Comparison of change rate for (d) Pmax, (e) Pr, and (f) Ec compared with their values at 40 kV/cm in Ba(Ti0.92Zr0.08)O3 ceramics with different phase structures.
Figure 5. Evolution of (a) Pmax, (b) Pr, and (c) Ec as a function of electric field for Ba(Ti0.92Zr0.08)O3 ceramics with different phase structures. Comparison of change rate for (d) Pmax, (e) Pr, and (f) Ec compared with their values at 40 kV/cm in Ba(Ti0.92Zr0.08)O3 ceramics with different phase structures.
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Figure 6. Electric field dependence of bipolar S-E curves at 5–40 kV/cm for Ba(Ti0.92Zr0.08)O3 ceramics with (a1) R phase, (b) R-O phase transition, (c) O phase, (d) O-T phase transition, (e) T phase, (f) T-C phase transition, and (g) C phase impelled by temperature change. (a2) The expanded S-E loops in the first quartile for R phase.
Figure 6. Electric field dependence of bipolar S-E curves at 5–40 kV/cm for Ba(Ti0.92Zr0.08)O3 ceramics with (a1) R phase, (b) R-O phase transition, (c) O phase, (d) O-T phase transition, (e) T phase, (f) T-C phase transition, and (g) C phase impelled by temperature change. (a2) The expanded S-E loops in the first quartile for R phase.
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Figure 7. Evolution of (a) Spos, (b) Sneg, and (c) d33* as a function of electric field for Ba(Ti0.92Zr0.08)O3 ceramics with different phase structures. Comparison of change rate for (d) Spos, (e) Sneg, and (f) d33* compared with their values at 40 kV/cm in Ba(Ti0.92Zr0.08)O3 ceramics with different phase structures.
Figure 7. Evolution of (a) Spos, (b) Sneg, and (c) d33* as a function of electric field for Ba(Ti0.92Zr0.08)O3 ceramics with different phase structures. Comparison of change rate for (d) Spos, (e) Sneg, and (f) d33* compared with their values at 40 kV/cm in Ba(Ti0.92Zr0.08)O3 ceramics with different phase structures.
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Figure 8. Electric field dependence of bipolar S-P curves for Ba(Ti0.92Zr0.08)O3 ceramics with (a) R phase, (b) R-O phase transition, (c) O phase, (d) O-T phase transition, (e) T phase, (f) T-C phase transition, and (g) C phase structure impelled by temperature change. (h) Schematic showing the quadratic fitting of the S-P curve.
Figure 8. Electric field dependence of bipolar S-P curves for Ba(Ti0.92Zr0.08)O3 ceramics with (a) R phase, (b) R-O phase transition, (c) O phase, (d) O-T phase transition, (e) T phase, (f) T-C phase transition, and (g) C phase structure impelled by temperature change. (h) Schematic showing the quadratic fitting of the S-P curve.
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Figure 9. (a) Temperature dependence of Q33 for Ba(Ti0.92Zr0.08)O3 ceramics with different phase structures impelled by temperature change. (b) Comparison of change rate for Q33 compared with their values at 40 kV/cm with different phase structures.
Figure 9. (a) Temperature dependence of Q33 for Ba(Ti0.92Zr0.08)O3 ceramics with different phase structures impelled by temperature change. (b) Comparison of change rate for Q33 compared with their values at 40 kV/cm with different phase structures.
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MDPI and ACS Style

Zhao, C.; Feng, H.; Huang, Y.; Wu, X.; Gao, M.; Lin, T.; Lin, C. Evolution Characteristics of Electric Field-Related Properties in Polymorphic Piezoceramics with Temperature-Impelled Phase Transition. Crystals 2023, 13, 1324. https://doi.org/10.3390/cryst13091324

AMA Style

Zhao C, Feng H, Huang Y, Wu X, Gao M, Lin T, Lin C. Evolution Characteristics of Electric Field-Related Properties in Polymorphic Piezoceramics with Temperature-Impelled Phase Transition. Crystals. 2023; 13(9):1324. https://doi.org/10.3390/cryst13091324

Chicago/Turabian Style

Zhao, Chunlin, Haopeng Feng, Yanli Huang, Xiao Wu, Min Gao, Tengfei Lin, and Cong Lin. 2023. "Evolution Characteristics of Electric Field-Related Properties in Polymorphic Piezoceramics with Temperature-Impelled Phase Transition" Crystals 13, no. 9: 1324. https://doi.org/10.3390/cryst13091324

APA Style

Zhao, C., Feng, H., Huang, Y., Wu, X., Gao, M., Lin, T., & Lin, C. (2023). Evolution Characteristics of Electric Field-Related Properties in Polymorphic Piezoceramics with Temperature-Impelled Phase Transition. Crystals, 13(9), 1324. https://doi.org/10.3390/cryst13091324

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