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Materials Chemistry and Physics 125 (2011) 718–722

Contents lists available at ScienceDirect

Materials Chemistry and Physics

journa l homepage: www.e lsev ier .com/ locate /matchemphys

ryogenic transverse and shear mode properties of1 − x)Pb(Mg1/3Nb2/3)O3–xPbTiO3 single crystal with theptimal crystallographic direction

eifei Wanga,∗, Wangzhou Shia, Siu Wing Orb, Xiangyong Zhaoc, Haosu Luoc

Key Laboratory of Optoelectronic Material and Device, Mathematics & Science College, Shanghai Normal University, Shanghai 200234, ChinaDepartment of Electrical Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong KongInformation Materials and Devices Research Center, Shanghai Institute of Ceramics, Chinese Academy of Sciences, Shanghai 201800, China

r t i c l e i n f o

rticle history:eceived 19 June 2010eceived in revised form 5 September 2010ccepted 25 September 2010

a b s t r a c t

The cryogenic transverse extensional and thickness shear properties of the(1 − x)Pb(Mg1/3Nb2/3)O3–xPbTiO3 (PMN–xPT) single crystal with the optimal crystallographic directionswere investigated in present work. With the temperature down to 78 K, a characteristic decreasein piezoelectric strain constants (d , 2020–831 pC N−1 and d , 4114–2823 pC N−1) and compliance

eywords:lectronic materialsiezoelectricitylectrical properties

31 15

coefficients (sE11, 95.3–50.6 × 10−12 m2 N−1 and sE

55, 227–184 × 10−12 m2 N−1) was demonstrated. Incomparison, the piezoelectric voltage constant (g31 and g15) and electromechanical coupling coefficient(k31 and k15) exhibits an almost temperature-independent behavior. Even at 78 K, high values ofg31 ∼ 0.045 Vm N−1, g15 ∼ 0.057 Vm N−1, k31 ∼ 0.86, and k15 ∼ 0.94 can be obtained. Such superior lowtemperature piezoelectric performance is favorable for the cryogenic device designs and applications,

hones

especially for the hydrop

. Introduction

Ferroelectric materials are widely used as sensors and actuatorsor their electro-mechanical properties, and in electronic applica-ions for their dielectric properties. Most piezoelectric devices areomposed of Pb(Zr, Ti)O3 (PZT)-based solid solution due to theirxcellent electromechanical properties [1] and various modifica-ions were performed to further enhance the piezoelectric activities2,3]. In comparison, the subsequently discovered relaxor-based1 − x)Pb(Mg1/3Nb2/3)O3–xPbTiO3 (PMN–xPT) single crystals wereegarded as another important type of piezoelectric material forew electromechanical devices due to more superior piezoelectricroperties of piezoelectric strain constant d33 > 2500 pC N−1 andlectromechanical coupling coefficient k33 ∼ 0.94 [4]. The ultrahighiezoelectricity has been theoretically attributed to polarizationotations between tetragonal and rhombohedral phases throughntermediate monoclinic or orthorhombic symmetries [5]. Recentlyhis crystal with the composition x around MPB has also been

emonstrated to own excellent transverse (d31 ∼ 2500 pC N−1,31 ∼ 0.94) and thickness shear (d15 ∼ 5000 pC N−1, k15 ∼ 0.95) per-ormances in certain crystallographic directions [6,7]. Based onhis, various prototype piezoelectric devices have been designed

∗ Corresponding author. Fax: +86 21 64328894.E-mail address: f f w@sohu.com (F. Wang).

254-0584/$ – see front matter © 2010 Elsevier B.V. All rights reserved.oi:10.1016/j.matchemphys.2010.09.067

with high gij needed.© 2010 Elsevier B.V. All rights reserved.

and fabricated [8–11]. A Rosen-type PMN–xPT single-crystal trans-former exhibited a high step-up ratio of 137 at 37 kHz with ahigh efficiency of 95% when driving a LCD backlight [11]. Novelmagnetoelectric (ME) and converse ME composite sensors andtransducers with giant response as high as 57.3 V/Oe and 11.9 G/Vwere designed from the combination of the ME composites andPMN–xPT transformer [12,13]. These configurations own the out-standing advantages of high efficiency, no power consumption andshort response time, indicating potential applications in the mag-netic field sensors and electrically controlled magnetic memorydevices [14]. Besides, utilizing the “soft” feature of PMN–xPT, avibration energy harvesting device was also suggested recentlywith a high output voltage of 45.7 V at 500 Hz, exhibiting a potentialin low-power portable electronics and wireless sensors [15].

During the practical applications, the temperature stability ofthe device performance is one of the key parameters. It is alwaysrequired that the piezoelectric materials could work within a widetemperature range. Up to now, most of the previous studies focusedon the piezoelectric and dielectric properties at or above roomtemperature (RT) [7,16,17]. For the transverse and thickness shearmode the service temperature was determined to be 80 ◦C and

93 ◦C, respectively [7]. In comparison, investigations on PMN–xPTcrystals at low temperature have been primarily about the phasetransition behavior, dielectric properties, and thermal properties[18,19]. It is only quite recently that the piezoelectric activity ofthe crystals was investigated to explore the application viability

F. Wang et al. / Materials Chemistry and Physics 125 (2011) 718–722 719

ique: (a) transverse extensional sample and (b) thickness shear mode sample.

itaplwtsas

ebtoi

2

met

t

6Ttap

(taecaf

s

d

g

wd

k

s

d

g

Fig. 2. Temperature (T) dependence of the free relative permittivity (εT33/ε0) and

loss tangent (tan ı) for the poled transverse extensional sample with T from 78 K to300 K at 1 kHz.

Fig. 1. Schematic diagram of sample orientations in the resonance techn

n cryogenic fields. The study on the thickness extensional vibra-ion mode revealed that piezoelectric stress constant e33 reachedbout 5.1–5.7 C/m2 even at 4.2 K, indicating an extraordinarily largeiezoelectric effect compared with other materials even at such a

ow temperature [20]. Nevertheless, systematic study to determinehether and to what extent the cryogenic temperature influence

he transverse and thickness shear piezoelectric behavior is stilleldom reported. Therefore, it is quite necessary for us to performsystematic characterization so as to evaluate the applications of

uch excellent working modes at low temperature.In this paper, we aim to study the cryogenic transverse

xtensional and thickness shear piezoelectric properties of rhom-ohedral PMN–xPT (x around 0.28–0.29) single crystals foremperature down to 78 K, so as to reveal the temperature stabilityf these two vibration modes for instructing practical applicationsn potential cryogenic fields.

. Experimental

In present work, PMN–xPT single crystal with x around 0.28–0.29, grown by aodified Bridgman method [21], was used due to its excellent piezoelectric prop-

rties [7]. The as-grown ingot was oriented using an X-ray diffractometer andhen diced to prepare plate-shaped single crystals with two different sets of crys-

allographic orientations: 13[0 0 1]L × 4[1 1 0]W × 1[1 1 0]T mm3 and 13[1 1 1]L ×

[1 1 2]W × 1[1 1 0]

Tmm3 (L: length, W: width, T: thickness), as shown in Fig. 1.

he arrows indicate the polarization direction. They were used for the piezoelec-ric measurements due to the optimal crystal cuts for the transverse extensionalnd thickness shear vibration mode, respectively [6,7,22,23]. The samples wereolarized in a silicon oil bath under an electric field of 1 kV mm−1 at 100 ◦C for 15 min.

During the test, the temperature (T) dependence of relative permittivityεT

33/ε0 and εT11/ε0), loss tangent (tan ı), and impedance spectrum for the poled crys-

als were measured for every 10 ◦C with 5 min stabilization using an impedancenalyzer (Agilent 4294A) with the liquid-nitrogen bath cryostat (Oxford DN1704)quipped with the temperature controller (Oxford ITC601). Then the electrome-hanical coupling coefficients (k31 and k15), piezoelectric coefficients (d31, g31, d15,nd g15), elastic compliance coefficients (sE

11 and sE55) can be determined from the

ollowing formula based on the IEEE standards [24].For the transverse extensional vibration sample,

k231 − 1

k231

= tan[(�/2)(fa/fr )](�/2)(fa/fr )

(1)

E11 = [�(2lfr )2]

−1(2)

31 = k31(εT33sE

11)1/2

(3)

31 = d31

εT33

(4)

here fr , fa , �, l represent the resonance frequency, anti-resonance frequency, theensity, and the length of the transverse mode sample, respectively.

For the thickness shear vibration sample,

215 = �fr

2fatan

[�(fa − fr )

2fa

](5)

E55 = 1

(6)

�(2tfa)2(1 − k2

15)

15 = k15(εT11sE

55)1/2

(7)

15 = d15

εT11

(8)

Fig. 3. Temperature (T) dependence of the free relative permittivity (εT11/ε0) and

loss tangent (tan ı) for the poled thickness shear mode sample with T from 78 K to300 K at 1 kHz.

where fr , fa , �, t represent resonance frequency, anti-resonance frequency, thedensity, and the thickness of the shear mode sample, respectively.

3. Results and discussion

Figs. 2 and 3 illustrate the dielectric data for the [1 1 0] – (alsothe poled direction) and [1 1̄ 0] – (poled along [1 1 1] direction) ori-ented crystals at the frequency of 1 kHz, respectively. For the twosamples, with the T decreased from 300 to 78 K both the dielectricresponses of εT

33/ε0 and εT11/ε0 decrease gradually from 5910 to

2110 (Fig. 2) and 9314 to 5548 (Fig. 3), respectively. According to

the phase diagram of PMN–xPT single crystal, the present compo-sition with x of 0.28–0.29 locates in the rhombohedral region nearthe morphotropic phase boundary (MPB) [17]. This crystal is dom-inated by the ferroelectric microdomains. After poled, most of the

720 F. Wang et al. / Materials Chemistry and Physics 125 (2011) 718–722

Fs

mtioisdiuu

vdfnrfsrtBhHobewts

Fu

Fig. 6. Temperature (T) dependence of transverse piezoelectric constants (d31 andg31) for the poled [1 1 0]-oriented crystals with the optimal crystal cut.

ig. 4. The impedance spectrum (1–110 kHz) of the transverse mode sample mea-

ured at 77 K, 150 K, and 300 K.

icrodomains are merged into macrodomains. With the tempera-ure decreasing to low temperature, the reduced dielectric constantn the two samples should be originated from the normal freezingf the ferroelectric macrodomains, which has also been observedn other ferroelectric systems [25]. For the dielectric loss tan ı ofhear mode sample (Fig. 3), it increases slightly to 0.027 with the Town to 78 K. In comparison, the tan ı of the transverse one (Fig. 2)

ncreases also slightly with the T down to 120 K and however annexpected increase is observed for T between 120 and 78 K. Thisnexpected dielectric loss response will be discussed later.

Fig. 4 shows the impedance spectrum (1–110 kHz) of the trans-erse mode sample at 77 K, 150 K, and 300 K. With the temperatureecreasing, both the resonance frequency fr and antiresonancerequency fa move to the higher frequencies, indicating simulta-eous increase of the frequency constant N31. One well-knowneason responsible for temperature response of the resonancerequency should be the crystal lattice shrinkage, which induceslight lattice distortion with the temperature decreasing. Anothereason may also ascribe to the frozen effect of the ferroelec-ric macrodomains at low temperature as presented above [25].esides, during impedance spectrum measurement process, theolder always has great influence on the piezoelectric resonance.ere the influence of the holder (at RT and cryogenic temperature)n the impedance is also examined as shown in Fig. 5. The red and

lack dot lines correspond to impedance spectrum of the transversextensional sample under the free and partially clamped conditionsith the frequency from 1 to 100 kHz, respectively. The stress on

he holder creates a clamping effect on the sample, leading to twopurious vibrations at around 30 kHz and 60 kHz. This clamping

ig. 5. The impedance spectrum of the transverse extensional sample measurednder free and partially clamped conditions with the frequency from 1 to 100 kHz.

Fig. 7. Temperature (T) dependence of transverse electromechanical coupling coef-ficient and elastic compliance coefficient (k31 and sE

11) for the poled [1 1 0]-orientedcrystals with the optimal crystal cut.

effect becomes weaker with the temperature decreasing as can beseen in Fig. 4. The derived transverse piezoelectric constants andelastic coefficient d31, g31, k31, and sE

11 from formula (1)–(4) areillustrated in Fig. 6 and Fig. 7, respectively. It can be observed thatthe cryogenic temperature induced a stiffening effect on the crys-tals, resulting in a characteristic decrease in d31, sE

11 and an increaseE

in the elastic stiffness constant c11. In comparison, the variation of

k31 and g31 on the T is insignificant and high values of k31 ∼ 0.86and g31 ∼ 0.045 Vm N−1 can be achieved even at 78 K.

Fig. 8 shows the impedance spectrum of the shear mode samplesunder different holder measured at room temperature. Different

Fig. 8. The impedance spectrum of the thickness shear mode sample measuredunder free and partially clamped conditions with the frequency from 50 kHz to 2MHz.

F. Wang et al. / Materials Chemistry and Physics 125 (2011) 718–722 721

Fig. 9. The impedance spectrum (50 kHz to 2 MHz) of the thickness shear modesample measured at 95 K, 140 K, 260 K, and 300 K.

Fsc

fihfmitapt

Fc[

ig. 10. Temperature (T) dependence of thickness shear mode piezoelectric con-tants (d15 and g15) for the poled [1 1̄ 0]-oriented crystals with the optimal crystalut.

rom that observed in the transverse sample, much weaker clamp-ng effects are detected. This indicates that the influence of theolder structure on the shear mode sample is weaker. The reason

or this observed phenomenon should be related to the shear-ode vibration direction and higher resonance frequency. The

mpedance spectrums (50 kHz ∼ 2 MHz) at four different tempera-

ures are illustrated in Fig. 9. During the cooling process, the fr and f˛lso move rightwards. Figs. 10 and 11 show the derived shear modeiezoelectric properties of d15, g15, k15, and sE

55, respectively. Similaro the transverse sample, a stiffening effect is also observed. The d15

ig. 11. Temperature (T) dependence of thickness shear mode electromechani-al coupling coefficient (k15) and elastic compliance coefficient (sE

55) for the poled1 1̄ 0]-oriented crystals with the optimal crystal cut.

Fig. 12. The X-ray diffraction patterns with the 2� range of 35–48◦ at 298 and 103 K.

and sE55 exhibit a characteristic decrease from 4114–2823 pC N−1

to 227–184 × 10−12 m2 N−1, respectively. The g15 and k15 exhibit anearly temperature-independent behavior with the values about0.057 Vm N−1 and 0.94, respectively.

From Figs. 2–11 it can be observed that the parameters ofεij, dij, gij, kij, SE

ijfor the PMN–xPT single crystal exhibit differ-

ent temperature dependent behaviors. Unexpected dielectric lossresponse between 120 and 78 K is also confusing. It is gener-ally known that the dielectric and piezoelectric activities at lowtemperature strongly depends on the phase structure. Systemati-cal investigations have been performed in PMN–xPT piezoelectricceramics to reveal the low temperature structure to clarify theelectrical properties [26]. Therefore, in order to give an insightinto the underlying mechanism of this unusual cryogenic dielec-tric behavior, X-ray diffraction analyses were performed under thetemperature of 298 K and 103 K, with the 2� range of 35–48◦ shownhere in Fig. 12, corresponding to the (1 1 1) and (2 0 0) diffractionpeaks, respectively. For the tetragonal phase is characterized bythe splitting of the (2 0 0) and (0 0 2) peaks, from Fig. 12 no observ-able split can be observed in (2 0 0) peaks. It demonstrates that therhombohedra are still the dominant phase at low temperature andno ferroelectric phase transition happened. Here, the unexpecteddielectric loss peak in Fig. 2 is suggested to originate from collectivepinning of randomly distributed point defects (actually existing inmany ferroelectrics) to the macrodomain walls at low tempera-tures [26,27]. With the temperature down to 78 K, the motion ofmacrodomain walls becomes difficult owing to collective pinningof these point defects, thereby causing the decrease of the εij, dijand sE

ij. Besides, due to the simultaneous decrease of dij and εij, the

piezoelectric voltage constant gij vary little with temperature. Fromthe application prospect, the temperature dependent character-istics for εij, dij and sE

ijare not encouraged due to poor stability.

In comparison, the parameters of gij and kij hold up large valueseven at 78 K and exhibit a nearly temperature-independent behav-ior during the whole range (the variation of kij ∼ 5% and gij ∼ 15%).Such properties make them very attractive for applications to pas-sive transducers and sensors in many cryogenic fields, such as thespace, the South Pole, and the North Pole.

4. Conclusions

In summary, the cryogenic transverse extensional and thick-ness shear properties of the PMN–xPT (x: 0.28–0.29) single crystal

with the optimal crystallographic directions were investigated.The εT

33, εT11, d31, d15, SE

11, and SE55 exhibited a more temperature-

dependent behavior and decrease obviously with the temperaturedown to 78 K. In comparison, good temperature stability wasrevealed in g31, g15, k31, and k15. Even at 78 K, high values of

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31 ∼ 0.045 Vm N−1 and g15 ∼ 0.06 Vm N−1 can be achieved andhe coupling coefficients kept around 0.9. Such superior cryo-enic piezoelectric performances are favorable for the cryogenicevice designs and applications, especially for the passive trans-ucers such as underwater hydrophones where high gij and kij areequired.

cknowledgements

This work was supported by the Science and Technologyommission of Shanghai Municipality (Grant Nos. 10ZR1422300nd 09520501000), National Natural Science Foundation of ChinaGrant No. 60807036), the Natural Science Foundation of Ningbo2009A610103), and Condensed Physics of Shanghai Normal Uni-ersity (Grant No. DZL712).

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