Ferroelectric,dielectric and pyroelectric properties of Sr and Sn codoped BCZT lead free ceramics

Abstract

The 1 mol.-%Sr and 1 mol.-%Sn codoped (Ba_0·84Ca_0·15Sr_0·01)(Ti_0·90Zr_0·09Sn_0·01)O₃ (BCSTZS) ceramics were synthesised by the normal solid state sintering method. The electric field and temperature dependence of the ferroelectric properties of the BCSTZS ceramics were investigated. Their energy storage density depending on electric field and temperature was determined from the polarisation–electric field (P–E ) hysteresis loops. According to the dielectric analysis, the BCSTZS ceramics experience three-phase transitions upon cooling. At room temperature, the pyroelectric coefficient p calculated from the remnant polarisation–temperature (P_r–T ) curve is 1116·7 μC K^− 1 m^− 2, and the figures of merit F_d is 18·1 μPa^− 1/2, F_v is 0·013 m² C^− 1 and F_i is 479·3 pm V^− 1 respectively. The pyroelectric figures of merit exhibit high frequency stability over a wide range from 100 to 2000 Hz, whereas these values vary gradually with the increase in temperature, which deserves further research to improve their stability. The excellent pyroelectric property of the BCSTZS ceramics is considered as correlating with a polymorphic phase transition occurring around room temperature. The present study demonstrates that the lead free BCSTZS ceramics are promising candidate for replacing the lead zirconate titanate based ceramics.

Keywords

Doping Polymorphic phase transition Ferroelectric property Pyroelectric property

Introduction

Lead based ferroelectric ceramics, such as lead zirconate titanate, have dominated transducer and actuator devices due to the superior piezoelectric properties and the adjustability of properties via doping.¹ Lead zirconate titanate based ceramics are chemically and mechanically stable, which are low cost to achieve in mass production by the traditional oxide mixing method.² However, the containing lead element in the lead zirconate titanate based ceramics is harmful to the environment and human health.³ Hence, much attention has been attracted to seek high performance lead free piezoelectric ceramics.^4–6

Recently, a lead free Ba(Zr_0·2Ti_0·8)O₃–x(Ba_0·7Ca_0·3)TiO₃ (BZT-BCT, BCZT) system with superhigh d₃₃ (∼620 pC N^− 1) around the morphotropic phase boundary (MPB) composition was reported by Liu and Ren,⁷ which could be regarded as a breakthrough in the research of lead free piezoceramics. The high piezoelectric performance was considered as a result of the MPB characterised by a cubic–tetragonal–rhombohedral tricritical triple point, which induced the instability of the polarisation.⁷ Such result has attracted a significant interest and motivated further researches on the microstructure morphology and macroscale properties of the BZT–BCT/BCZT ceramics.^8–11 The electrical properties of the BZT–BCT ceramics could be adjusted by many factors, including elements doping, altering the compositions, changing the temperature range of the polymorphic phase transition, tailoring sintering conditions, etc.^7,12 Various dopants have been researched to enhance the piezoelectric properties of the BZT–BCT ceramics. Tan et al. investigated the effects of LiF on the structure and piezoelectric properties of the BCZT ceramics. They found that the LiF doped BCZT ceramics exhibit enhanced piezoelectric properties due to a polymorphic phase transition around room temperature.¹² Cui et al. investigated the effects of additives CuO,¹³ CeO₂ (Ref. 14) and Y₂O₃ (Ref. 15) on improving density, piezoelectric and ferroelectric properties of the BCZT ceramics. Their researches showed that appropriate addition of these dopants into the BCZT ceramics could improve the electrical properties.

In this work, SrCO₃ and SnO₂ were used to adjust electrical properties of the (Ba_0·85Ca_0·15)(Ti_0·90Zr_0·10)O₃ ceramics. Such composition was chosen since it corresponds to the MPB composition where the orthorhombic and tetragonal ferroelectric phases coexist around room temperature.¹⁶ The ferroelectric, dielectric and pyroelectric properties of the Sr²⁺ and Sn⁴⁺ codoped (Ba_0·84Ca_0·15Sr_0·01)(Ti_0·90Zr_0·09Sn_0·01)O₃ (BCSTZS) ceramics were discussed.

Experimental

The 1 mol.-%Sr and 1 mol.-%Sn codoped BCSTZS ceramics were synthesised by the traditional oxide mixing method. All the stoichiometric raw carbonates and oxides, BaCO₃ (99%), CaCO₃ (99%), SrCO₃ (99%), TiO₂ (99·97%), ZrO₂ (99%) and SnO₂ (99·5%), were well mixed and calcined at 1250°C for 4 h. The calcined powders were dry pressed into discs after conglomeration using 8 wt-% polyvinyl alcohol aqueous solution as the binder. After removing the polyvinyl alcohol, the discs were sintered at 1550°C for 4 h in air.

Specific heat C_p of the BCSTZS ceramics was tested using a differential scanning calorimeter (Pyris DSC 8500, PerkinElmer Co. Ltd, USA). Silver paste was fired on upper and bottom surfaces of the ceramics at 600°C for 15 min to form electrodes. Polarisation–electric field (P–E ) hysteresis loops of the BCSTZS ceramics were measured by a Radiant Precision Premier LC ferroelectric measurement system (Radiant Technologies Inc., USA). Strain–electric field (S–E ) hysteresis loops were tested by a TF analyser 1000 test system (aixACCT Systems GmbH, Germany). Dielectric properties of the unpoled and poled BCSTZS ceramics were measured by a Novocontrol GmbH Concept 40 broadband dielectric spectrometer (Novocontrol Technologies GmbH & Co. KG, Germany) and a computer controlled TH2818 automatic component analyser (Changzhou Tonghui Electronic Co. Ltd, China) under a weak oscillation level of 1 V_rms respectively. Detailed procedures of electrical performance tests were expatiated elsewhere.¹⁷

Results and discussion

Before the systematic discussion of the phase transition characteristic and electrical properties, the fundamental physical performances of the BCSTZS ceramics were determined. The fabricated BCSTZS ceramics exhibit densified microstructure and excellent piezoelectric properties, in which the relative density exceeds 94%, and piezoelectric constant d₃₃ and electromechanical coupling coefficient K_p reaches 514 pC N^− 1 and 52·62% respectively.

Figure 1 shows the electric field dependence of the P–E hysteresis loops of the BCSTZS ceramics measured at 5–30 kV cm^− 1 and 1 Hz. With the increase in the electric field, the P–E hysteresis loops become more saturated together with the increase in the values of remnant polarisation P_r and coercive field E_c as shown in Fig. 2a and b. The P_r and E_c values reach 10·39 μC cm^− 2 and 2·99 kV cm^− 1 respectively at 30 kV cm^− 1. The unipolar strain–E curve and bipolar strain–E curve are shown in Fig. 1a and b respectively. The typical butterfly-like curve reflects the ferroelectric domains switching during the bipolar external electric field drive. A maximum strain value of 0·13% is reached at E = 20 kV cm^− 1. Such strain can even be comparable to some lead based piezoelectric ceramics.^17,18

Electric field dependence of P–E hysteresis loops of BCSTZS ceramics measured at 5–30 kV cm^− 1 and 1 Hz; inset shows a unipolar strain–E curve and b bipolar strain–E curve measured at 20 kV cm^− 1 and 1 Hz

Electric field dependence of a remnant polarisation P_r, b coercive field E_c and c energy storage density W of BCSTZS ceramics

The energy storage density of the BCSTZS ceramics can be obtained by integrating the area between the polarisation axis and the hysteresis loops: , where E is the applied electric field and P is the polarisation.¹⁹ By measuring the polarisation response from the P–E loops and excluding the dissipated energy, the stored energy can be estimated. According to the previous reports, higher energy densities can be achieved either by enlarging the difference between the saturated polarisation and the remnant polarisation in the P–E loops or by enhancing the dielectric breakdown strength.^20–22 As shown in Fig. 2c, the values of energy storage density W increase nearly linear as the electric field increases, which reaches 0·134 J cm^− 3 at E = 30 kV cm^− 1. Such value of the energy storage density can be comparable to some other BCZT based ceramics.²³ The low energy storage efficiency can be attributed to the low coercive field, remnant polarisation and small electric field, or the early saturation polarisation of the BCZT based ceramics.²³

Figure 3 shows the ferroelectric properties dependence on temperature of the BCSTZS ceramics. The P–E loops are saturate and symmetric, which become slimmer with increasing environmental temperature accompanied by the gradual decrease in P_r and E_c as indicated in Fig. 3b and c. The non-linear hysteresis loop could be observed even at 120°C. The existence of limited P–E hysteretic loop above the Curie temperature is mainly attributed to the residual polar microregions or ferroelectric clusters.²⁴ According to the previous reports, the degradation of piezoelectric and ferroelectric properties with the increase in temperature is mainly due to the lattice distortion (intrinsic contribution) and the domain walls motion (extrinsic contribution).^25,26 However, the energy storage density remains stable with increasing temperature as indicated in Fig. 3d, which may be attractive for capacitor applications.²⁰

Temperature dependence of a P–E hysteresis loops, and b P_r, c E_c and d W of BCSTZS ceramics measured at 2 kV mm^− 1 and 1 Hz; inset shows SEM image of free surface of BCSTZS ceramics after 2%HF etching

Temperature dependence of dielectric properties of the BCSTZS ceramics measured at several frequencies are shown in Fig. 4. It is interesting that the dielectric peaks are broad around the Curie temperature, indicating the diffusion characteristic of the relaxor ferroelectrics. However, the maximum dielectric constant ε_m keeps nearly unchanged with the variation of frequency, indicating that the BCSTZS ceramics are close to normal ferroelectrics. A polymorphic phase transition appearing near 20°C as indicated by the black arrows is a common phenomenon in the BCZT based ceramics, representing the orthorhombic phase transforming to tetragonal phase.^16,27–29 Another dielectric anomaly appearing around − 17°C as indicated by the red arrow on the dielectric loss curves may be the rhombohedral–orthorhombic phase transition. Recently, Keeble et al. revised the phase diagram of the BCZT ceramics by high resolution synchrotron X-ray powder diffraction. They proposed that the MPB composition (Ba_0·85Ca_0·15)(Ti_0·90Zr_0·10)O₃ ceramics undergo the successive phase transitions: cubic → tetragonal → orthorhombic → rhombohedral upon cooling.¹⁶ Tian et al. investigated the phase evolution of the BCZT ceramics using in situ X-ray diffraction and dielectric analysis. They also suggested that the (Ba_0·85Ca_0·15)(Ti_0·90Zr_0·10)O₃ ceramics experience an orthorhombic–tetragonal phase transition around room temperature and a rhombohedral–orthorhombic phase transition below room temperature.²⁷ Further researches on the structure evolution and phase transition characters of the BCSTZS ceramics are required.

Temperature dependence of a dielectric constant and b loss tangent of unpoled BCSTZS ceramics measured at several frequencies

Figure 5 shows temperature and frequency dependence of dielectric properties of the BCSTZS ceramics poled at 25 kV cm^− 1. As shown in Fig. 5a, the dielectric anomaly appearing around room temperature in the tan δ–T curve represents the polymorphic ferroelectric phase transition upon heating.²⁷ As compared to the unpoled samples, the dielectric frequency dispersion characteristic does not change, i.e. the poled BCSTZS ceramics still approach to the normal ferroelectrics. At 100 Hz, the Curie temperature T_C, maximum dielectric constant ε_m and maximum loss tangent tan δ_m at T_C of the unpoled BCSTZS ceramics are 77·3°C, 13 000 and 0·0224 respectively. After poling, the values of ε_m and tan δ_m decrease to 12 500 and 0·0191 respectively, while the T_C temperature increases to 82·7°C. Such phenomena occur since polarisation stabilises the ferroelectric domains, leading to the increase in T_C.³⁰ The growth and orientation of the ferroelectric domains induced by the poling process decrease the contribution of the movement of domain walls on dielectric response, leading to the decrease in ε_m and tan δ_m.³⁰ At 100 Hz, the room temperature values of ε and tan δ are 4200 and 0·0189 respectively, as shown in Fig. 5b, which keep almost unchanged between 100 and 2000 Hz. Such outstanding frequency stability of the dielectric properties shows the promising potential of the BCSTZS ceramics in the applications of electronic ceramic industries.

a temperature and b frequency (room temperature) dependence of dielectric properties of BCSTZS ceramics poled at 25 kV mm^− 1

Temperature dependences of specific heat C_p and pyroelectric coefficient p of the BCSTZS ceramics upon heating are given in Fig. 6. The value of room temperature C_p is 0·431 J g^− 1 °C^− 1, which increases slightly to 0·444 J g^− 1 °C^− 1 at 119°C. The increase in specific heat with temperature may cause the fluctuation of the pyroelectric detecting performance. The bulk density of the BCSTZS ceramics is 5·40 g cm^− 3 at ambient temperature, which keeps almost unchanged in the temperature range for the pyroelectric property measurement. Therefore, the calculated room temperature volume specific heat C_v = C_p × ρ_v is 2·33 × 10⁶ J m^− 3 °C^− 1, where ρ_v is the bulk density.

Temperature dependence of C_p and p of BCSTZS ceramics upon heating

Based on the P–E hysteresis loops upon heating, the values of P_r with increasing temperature are determined. In this work, the pyroelectric coefficient p is calculated using a static method: .¹¹ It must be pointed out that the main drawback of the static method is the offset of the P–E hysteresis loops. Such offset indicates the existence of defects or internal bias field, which may pin down the domain walls and stabilise the domains, leading to the deviation of p extracted from the measured P–E loops.³¹ However, the internal bias field of the BCSTZS ceramics reported here can be negligible due to the high symmetry of the P–E loops, revealing that the calculated value of p is accurate. The calculated room temperature value of p is 1116·7 μC K^− 1 m^− 2, considerably exceeding that of the widely used LiTaO₃ (230 μC K^− 1 m^− 2).^32,33 The value of p decreases gradually as the temperature increases to 40°C. Such p extremum is a manifestation of the polymorphic phase transition, demonstrating that the orthorhombic and tetragonal phases coexist around room temperature.^16,27–29 The coexistence of two ferroelectric phases significantly decreases the energy barrier of polarisation rotation, leading to the nearly vanishing of the polarisation anisotropy. Accordingly, the ferroelectric domains show high mobility, and the electrical properties are improved.⁷ The p peak appearing ∼80°C in the p–T curve may be correlated with the tetragonal–cubic ferroelectric phase transition.

Pyroelectric figures of merit are calculated by three equations: current responsivity , voltage responsivity and detectivity .^34,35 Figures 7 and 8 show the F_d and F_v values of the BCSTZS ceramics dependence on frequency and temperature. At 100 Hz, the values of room temperature F_d and F_v of the BCSTZS ceramics are 18·1 μPa^− 1/2 and 0·013 m² C^− 1 respectively. The F_d and F_v performances exhibit excellent frequency stability between 100 and 2000 Hz, whereas the gradual variation of F_d and F_v with increasing temperature is unfavourable to the pyroelectric applications.

Room temperature frequency dependence of F_d and F_v of BCSTZS ceramics

Temperature dependence of F_d and F_v of BCSTZS ceramics

Table 1 summarises the pyroelectric parameters of the BCSTZS ceramics and LaTiO₃ for comparison.^32,33 Of particular interest is that the pyroelectric properties of the BCSTZS ceramics are rather excellent, which shows promising potential for the uncooled infrared detectors.

Table 1

Pyroelectric parameters of BCSTZS ceramics and LaTiO₃ for comparison

Composition	ε_r	tan δ (100 Hz)	C_v/ × 10⁶ J m^− 3 K^− 1	p/μC K^− 1 m^− 2	F_i/pm V^− 1	F_v/m² C^− 1	F_d/μPa^− 1/2
LiTaO₃	47 (10 Hz)	10^− 4–5 × 10^− 3 (10 Hz)	2·212	230	…	0·17	35·2–49
BCSTZS	4200 (100 Hz)	0·0189 (100 Hz)	2·33	1116·7	479·3	0·013	18·1

Conclusions

In conclusion, the 1 mol.-%Sr and 1 mol.-%Sn codoped BCSTZS ceramics were prepared by the conventional solid state sintering method. The values of remnant polarisation P_r, coercive field E_c, maximum strain S_max and energy storage density W of the BCSTZS ceramics reaches 10·39 μC cm^− 2, 2·99 kV cm^− 1, 0·13% and 0·134 J cm^− 3 respectively. Dielectric analysis indicates that the BCSTZS ceramics undergo three-phase transitions upon cooling, whereas further researches are required to clarify the nature of these phase transitions. The BCSTZS ceramics exhibit exceptional pyroelectric properties, the pyroelectric parameters p, F_d, F_v and F_i are 1116·7 μC K^− 1 m^− 2, 18·1 μPa^− 1/2, 0·013 m² C^− 1 and 479·3 pm V^− 1 respectively. Such excellent pyroelectric properties are correlated with the polymorphic phase transition around room temperature.

Footnotes

Acknowledgement

The authors thank the Priority Academic Program Development of Jiangsu Higher Education Institutions for financial support.

References

Shannigrahi

S. R.

, Tay

F. E. H.

, Yao

and Choudhary

R. N. P.

: ‘Effect of rare earth (La, Nb, Sm, Eu, Gd, Dy, Er and Yb) ion substitutions on the microstructural and electrical properties of sol–gel grown PZT ceramics’, J. Eur. Ceram. Soc., 2004, 24, 163–170. doi: 10.1016/S0955-2219(03)00316-9

Guggilla

, Batra

A. K.

, Currie

J. R.

, Aggarwal

M. D.

, Alim

M. A.

and Lal

R. B.

: ‘Pyroelectric ceramics for infrared detection applications’, Mater. Lett., 2006, 60, 1937–1942. doi: 10.1016/j.matlet.2005.05.086

Rödel

, Jo

, Seifert

K. T. P.

, Anton

E. M.

and Granzow

: ‘Perspective on the development of lead-free piezoceramics’, J. Am. Ceram. Soc., 2009, 92, 1153–1177. doi: 10.1111/j.1551-2916.2009.03061.x

Chen

T. T.

, Fu

M. S.

, Jia

B. W.

, Wu

Y. J.

, Liu

X. Q.

and Chen

X. M.

: ‘Dielectric and ferroelectric properties of Ba_1 − xSr_xTiO₃ ceramics: effects of grain size and ferroelectric domain’, Adv. Appl. Ceram., 2013, 112, 270–276. doi: 10.1179/1743676112Y.0000000070

Chen

Y. L.

and Yang

S. F.

: ‘PTCR effect in donor doped barium titanate: review of compositions, microstructures, processing and properties’, Adv. Appl. Ceram., 2011, 110, 257–269. doi: 10.1179/1743676111Y.0000000001

Yang

W. G.

, Zhang

B. P.

, Ma

and Zhao

: ‘High piezoelectric properties of BaTiO₃–xLiF ceramics sintered at low temperatures’, J. Eur. Ceram. Soc., 2012, 32, 899–904. doi: 10.1016/j.jeurceramsoc.2011.10.054

Liu

and Ren

: ‘Large piezoelectric effect in Pb-free ceramics’, Phys. Rev. Lett., 2009, 103, 257602. doi: 10.1103/PhysRevLett.103.257602

Liu

, Liu

, Wang

, Chen

, Fang

, Ding

, Zhao

, Xu

and Luo

: ‘Improving piezoelectric property of BaTiO₃–CaTiO₃–BaZrO₃ lead-free ceramics by doping’, Ceram. Int., 2014, 40, 9881–9887. doi: 10.1016/j.ceramint.2014.02.082

Liu

, Zhu

, Chen

, Fang

, Ding

, Zhao

, Xu

and Luo

: ‘Structure and electrical properties of Li-doped BaTiO₃–CaTiO₃–BaZrO₃ lead-free ceramics prepared by citrate method’, J. Alloys Compd., 2014, 613, 219–225. doi: 10.1016/j.jallcom.2014.06.046

10.

Fang

B. J.

, Wang

W. W.

, Ding

J. N.

, Zhao

X. Y.

, Xu

H. Q.

and Luo

H. S.

: ‘Preparation and electrical properties of pseudoternary BaTiO₃–CaTiO₃–BaZrO₃ lead-free piezoelectric ceramics’, Adv. Appl. Ceram., 2013, 112, 257–262. doi: 10.1179/1743676112Y.0000000068

11.

Yao

, Ren

, Ji

, Wu

, Shi

, Xue

, Ren

and Ye

Z. G.

: ‘High pyroelectricity in lead-free 0·5Ba(Zr_0·2Ti_0·8)–0·5(Ba_0·7Ca_0·3)TiO₃ ceramics’, J. Phys. D, 2012, 45D, 195301. doi: 10.1088/0022-3727/45/19/195301

12.

Tan

C. K. I.

, Yao

and Ma

: ‘Effects of LiF on the structure and properties of Ba_0·85Ca_0·15Zr_0·1Ti_0·9O₃ lead-free piezoelectric ceramics’, Int. J. Appl. Ceram. Technol., 2013, 10, 701–706. doi: 10.1111/j.1744-7402.2012.02771.x

13.

Cui

, Liu

, Jiang

, Hu

, Su

and Wang

Hua

: ‘Lead-free (Ba_0·7Ca_0·3)TiO₃–Ba(Zr_0·2Ti_0·8)O₃–xwt% CuO ceramics with high piezoelectric coefficient by low-temperature sintering’, J. Mater. Sci., Mater. Electron., 2012, 23, 1342–1345. doi: 10.1007/s10854-011-0596-2

14.

Cui

, Liu

, Jiang

, Zhao

, Shan

, Li

, Yuan

and Zhou

: ‘Lead-free (Ba_0·85Ca_0·15)(Ti_0·9Zr_0·1)O₃–CeO₂ ceramics with high piezoelectric coefficient obtained by low-temperature sintering’, Ceram. Int., 2012, 38, 4761–4764. doi: 10.1016/j.ceramint.2012.02.063

15.

Cui

, Yuan

, Liu

, Zhao

and Shan

: ‘Lead-free (Ba_0·85Ca_0·15)(Ti_0·9Zr_0·1)O₃–Y₂O₃ ceramics with large piezoelectric coefficient obtained by low-temperature sintering’, J. Mater. Sci., Mater. Electron., 2013, 24, 654–657. doi: 10.1007/s10854-012-0785-7

16.

Keeble

D. S.

, Benabdallah

, Thomas

P. A.

, Maglione

and Kreisel

: ‘Revised structural phase diagram of (Ba_0·7Ca_0·3TiO₃)–(BaZr_0·2Ti_0·8O₃)’, Appl. Phys. Lett., 2013, 102, 092903. doi: 10.1063/1.4793400

17.

Fang

, Qian

, Chen

, Yuan

, Ding

, Zhao

, Xu

and Luo

: ‘Large strain and pyroelectric properties of Pb(Mg_1/3Nb_2/3)–PbTiO₃ ceramics prepared by partial oxalate route’, Funct. Mater. Lett., 2014, 7, 1450059. doi: 10.1142/S1793604714500593

18.

Kumar

, Prakash

and Goel

T. C.

: ‘Dielectric, electrostrictive properties of PMNT near MPB’, Sci. Technol. Adv. Mater., 2007, 8, 463–468. doi: 10.1016/j.stam.2007.05.007

19.

Chu

, Zhou

, Ren

, Neese

, Lin

, Wang

, Bauer

and Zhang

Q. M.

: ‘A dielectric polymer with high electric energy density and fast discharge speed’, Science, 2006, 313, 334–336. doi: 10.1126/science.1127798

20.

Ogihara

, Randall

C. A.

and Mckinstry

S. T.

: ‘Mckinstry, High-energy density capacitors utilizing 0·7BaTiO₃–0·3BiScO₃ ceramics’, J. Am. Ceram. Soc., 2009, 92, 1719–1724. doi: 10.1111/j.1551-2916.2009.03104.x

21.

Puli

V. S.

, Pradhan

D. K.

, Riggs

B. C.

, Chrisey

D. B.

and Katiyar

R. S.

: ‘Investigations on structure, ferroelectric, piezoelectric and energy storage properties of barium calcium titanate (BCT) ceramics’, J. Alloys Compd., 2014, 584, 369–373. doi: 10.1016/j.jallcom.2013.09.108

22.

Puli

V. S.

, Pradhan

D. K.

, Riggs

B. C.

, Chrisey

D. B.

and Katiyar

R. S.

: ‘Structure, ferroelectric, dielectric and energy storage studies of Ba_0·70Ca_0·30TiO₃, Ba(Zr_0·20Ti_0·80)O₃ ceramic capacitors’, Integr. Ferroelectr., 2014, 157, 139–146. doi: 10.1080/10584587.2014.912939

23.

Puli

V. S.

, Kumar

, Chrisey

D. B.

, Tomozawa

, Scott

J. F.

and Katiyar

R. S.

: ‘Barium zirconate–titanate/barium calcium–titanate ceramics via sol–gel process: novel high-energy-density capacitors’, J. Phys. D, 2011, 44D, 395403. doi: 10.1088/0022-3727/44/39/395403

24.

Yan

, Inam

, Viola

, Ning

, Zhang

, Jiang

, Zeng

, Gao

and Reece

M. J.

: ‘The contribution of electrical conductivity, dielectric permittivity and domain switching in ferroelectric hysteresis loops’, J. Adv. Dielectr., 2011, 1, 107–118. doi: 10.1142/S2010135X11000148

25.

Hajjaji

, Pruvost

, Sebald

, Lebrun

, Guyomar

and Benkhouja

: ‘Mechanism of depolarization with temperature for < 001> (1 − x)Pb(Zn_1/3Nb_2/3)O₃–xPbTiO₃ single crystals’, Acta Mater., 2009, 57, 2243–2249. doi: 10.1016/j.actamat.2009.01.029

26.

Davis

, Damjanovic

and Setter

: ‘Temperature dependence of the direct piezoelectric effect in relaxor-ferroelectric single crystals: intrinsic and extrinsic contributions’, J. Appl. Phys., 2006, 100, 084103. doi: 10.1063/1.2358408

27.

Tian

, Chao

, Jin

, Wei

, Liang

and Yang

: ‘Polymorphic structure evolution and large piezoelectric response of lead-free (Ba,Ca)(Zr,Ti)O₃ ceramics’, Appl. Phys. Lett., 2014, 104, 112901. doi: 10.1063/1.4868414

28.

Zhang

, Glaum

, Groh

, Ehmke

M. C.

, Blendell

J. E.

, Bowman

K. J.

and Hoffman

M. J.

: ‘Correlation between piezoelectric properties and phase coexistence in (Ba,Ca)(Ti,Zr)O₃ ceramics’, J. Am. Ceram. Soc., 2014, 97, 2885–2891. doi: 10.1111/jace.13047

29.

Acosta

, Novak

, Jo

and Rödel

: ‘Relationship between electromechanical properties and phase diagram in the Ba(Zr_0·2Ti_0·8)O₃–x(Ba_0·7Ca_0·3)TiO₃ lead-free piezoceramic’, Acta Mater., 2014, 80, 48–55. doi: 10.1016/j.actamat.2014.07.058

30.

Fang

, Du

, Zhou

, Zhao

, Xu

and Luo

: ‘Structural phase transition and physical properties of tetragonal 0·85Pb(Zn_1/3Nb_2/3)O₃–0·15PbTiO₃ single crystals’, J. Appl. Phys., 2009, 106, 074110. doi: 10.1063/1.3238249

31.

Xiao

, Avrutin

, Liu

, Özgür

Ü.

, Morkoc

and Lu

: ‘Large pyroelectric effect in undoped epitaxial Pb(Zr, Ti)O₃ thin films on SrTiO₃ substrates’, Appl. Phys. Lett., 2008, 93, 052913. doi: 10.1063/1.2969778

32.

Whatmore

R. W.

: ‘Pyroelectric devices and materials’, Rep. Prog. Phys., 1986, 49, 1335–1386. doi: 10.1088/0034-4885/49/12/002

33.

Tang

, Zhao

, Feng

, Jin

and Luo

: ‘Pyroelectric properties of [111]-oriented Pb(Mg_1/3Nb_2/3)O₃–PbTiO₃ crystals’, Appl. Phys. Lett., 2005, 86, 082901. doi: 10.1063/1.1865337

34.

Tang

, Luo

, Jia

, Luo

, Zhao

, Xu

, Lin

, Sun

, Meng

, Zhu

and Es-Souni

: ‘Mn-doped 0·71Pb(Mg_1/3Nb_2/3)O₃–0·29PbTiO₃ pyroelectric crystals for uncooled infrared focal plane arrays applications’, Appl. Phys. Lett., 2006, 89, 162906. doi: 10.1063/1.2363149

35.

Zhao

, Wu

, Liu

, Luo

, Neumann

and Yu

: ‘Pyroelectric performance of relaxor-based ferroelectric single crystals and related infrared detectors’, Phys. Status Solidi A, 2011, 208A, 1061–1067. doi: 10.1002/pssa.201000051