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Dec 12, 2006 - c66. D. 17.3987 21.1639. 11.4275. 29.8217. 12.5014. 14.6292. 6.5360. 0.4065. 7.1000. Elastic compliance coefficients: sE and sD (10−12 m2 ...
APPLIED PHYSICS LETTERS 89, 242908 共2006兲

Complete set of elastic, dielectric, and piezoelectric coefficents of 0.93Pb„Zn1/3Nb2/3…O3 – 0.07PbTiO3 single crystal poled along †011‡ Rui Zhang Department of Physics, Harbin Institute of Technology, Harbin, Heilongjiang 150080, China

Bei Jiang, Wenhua Jiang, and Wenwu Caoa兲 Materials Research Institute, The Pennsylvania State University, University Park, Pennsylvania 16802

共Received 12 September 2006; accepted 30 October 2006; published online 12 December 2006兲 The authors report a complete set of elastic, dielectric, and piezoelectric coefficients of rhomboheral phase 0.93Pb共Zn1/3Nb2/3兲O3 – 0.07PbTiO3 single crystal poled along 关011兴 measured at room temperature. It was found that the electromechanical coupling coefficients k32 and k33 of this domain engineered single crystal can reach 0.86 and 0.87, respectively, and the piezoelectric coefficients d32 and d15 are −1460 and 1823 pC/ N, respectively. This complete set of data can meet the urgent need of device designers using these super piezoelectric crystals and also provide important information for fundamental studies on domain engineering. © 2006 American Institute of Physics. 关DOI: 10.1063/1.2404613兴 It has been demonstrated that relaxor based 共1 共PZN-PT兲 and 共1 − x兲Pb共Zn1/3Nb2/3兲O3 – xPbTiO3 − x兲Pb共Mg1/3Nb2/3兲O3 – xPbTiO3 共PMN-PT兲 ferroelectric single crystal systems with composition near the morphotropic phase boundary 共MPB兲 exhibit superior electromechanical properties at room temperature when being poled along the 关001兴 of cubic coordinates.1–5 For theoretical studies and for device designs, knowing the complete set of material properties is crucial. By using a hybrid technique that combines ultrasonic and resonance methods,6 we were able to measure several complete sets of material constants of 关001兴 poled PMN-PT and PZN-PT single crystals with composition near the MPB.7–11 These data have greatly facilitated the use of these super piezoelectric crystals and provided important input data for the fundamental studies of the domain engineering method. The small d33 and k33 values of single-domain 0.67Pb共Mg1/3Nb2/3兲O3 – 0.33PbTiO3 共PMN-33%PT兲 crystals but large effective d33 and k33 values of multidomain PMN-33%PT crystals poled along 关001兴 demonstrated that functional properties can be drastically improved through the orientation effect.12 For single-domain crystals poled along the polar direction of 关111兴, the d15 value is as high as 4100 pC/ N even under electrical bias. Part of this large d15 is converted to the effective d33 in the 关001兴 poled crystal. It is possible to obtain other effective piezoelectric coefficients if the crystals are being poled along other directions. In fact, in recent years, trying to improve specific material properties using domain engineering methodology has become a new trend in functional materials research.13–24 Different poling directions can produce different domain patterns that will define the macroscopic symmetry of the multidomain system. Experimental results showed that the 关011兴 direction is another promising poling direction to engineer better multidomain piezoelectric materials, which can produce very large 兩d32兩. In order to facilitate engineers to use such large d32 values and provide more information to study the domain orientation principle, we report here a a兲

Electronic mail: [email protected]

complete set of elastic, dielectric, and piezoelectric coefficients of a 关011兴 poled 0.93Pb共Zn1/3Nb2/3兲O3 – 0.07PbTiO3 共PZN-7%PT兲 single crystal. At room temperature, the PZN-7%PT crystal is in the rhombohedral phase with 3m crystal symmetry, and the dipoles in each unit cell is pointing along one of the eight 具111典 directions of the cubic phase 关Fig. 1共a兲兴. There are two remaining energetic degenerate dipole orientations after poling along 关011兴 关Fig. 1共b兲兴. Statistically, the remaining two types of domains have equal possibilities to form, so that the macroscopic symmetry is orthorhombic mm2.24,25 We take the poling direction as the x3 direction, which is along 关011兴 of ¯ 1兴 and 关100兴 are defined as the cubic coordinates, and the 关01 the x1 and x2 axes, respectively, for defining the macroscopic property matrices. The single crystals used in this work were grown by a modified Bridgman method using a Pt crucible supported at its bottom by a conical insulator stand.14 The crystals were

FIG. 1. 共a兲 Eight polarization directions in PZN-7%PT single crystals before poling. 共b兲 Two remaining polarization directions after being poled along 关011兴.

0003-6951/2006/89共24兲/242908/3/$23.00 89, 242908-1 © 2006 American Institute of Physics Downloaded 15 Dec 2006 to 146.186.113.76. Redistribution subject to AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp

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TABLE I. Complete set of electromechanical coefficients of PZN-7%PT single crystal poled along 关011兴. Density: ␳ = 8038.4 kg/ m3. Elastic stiffness coefficients: c␭E␮ and c␭D␮ 共1010 N / m2兲 cE11

cE12

cE13

cE22

cE23

cE33

cE44

cE55

cE66

14.5000

15.3160

12.6660

18.0240

15.0000

14.1000

6.4720

0.3430

7.1000

cD11 17.3987

sE11 67.5153 sD11 59.4003

cD12

cD13

cD22

cD23

cD33

cD44

cD55

cD66

21.1639

11.4275

29.8217

12.5014

14.6292

6.5360

0.4065

7.1000

sE12

Elastic compliance coefficients: s␭E␮ and s␭D␮ 共10−12 m2 / N兲 sE13 sE22 sE23 sE33 sE44

sE55

sE66

−60.1637

3.3551

102.0024

−54.4683

62.0233

15.4512

291.5452

14.0845

sD12

sD13

sD22

sD23

sD33

sD44

sD55

sD66

−35.3773

−16.1684

26.2949

5.1644

15.0523

15.2998

245.9933

14.0845

Piezoelectric coefficients: ei␭, 共C / m 兲, di␭ 共10 and hi␭ 共108 V / m兲 e31 e32 e33 2

e15 6.2529

e24 3.2360

−8.6446

−17.4399

3.6935

d15

d24

d31

d32

d33

1823

50

478

−1460

1150

g15

g24

g31

g32

g33

3.0280

16.9770

−51.8545

40.8443

h24

h31

h32

h33

1.9791

−33.5315

−67.6476

14.3266

24.9873 h15 1.0158 ␧S11 6953

␤S11 1.4383

C / N兲, gi␭ 共10 V m / N兲,

−12

Dielectric coefficients: ␧ij共␧0兲 and ␤ij共10−4 / ␧0兲 ␧S22 ␧S33 ␧T11 ␧T22

␧T33

1847

291

8240

1865

3180

␤S22

␤S33

␤T11

␤T22

␤T33

5.4150

34.3440

1.2136

5.3619

3.1440

k15

k24

0.40

0.10

Electromechanical coupling coefficients k31 k32 k33 0.35

0.86

0.87

orientated using the Laue method with an accuracy of ±0.5°. Each sample was cut and polished with three pairs of parallel surfaces perpendicular to each other. Gold electrodes were ¯¯1兴 faces of each sample. sputtered onto the 关011兴 and 关01 Then an external electric field ⬃0.4 MV/ m was applied to pole these samples at room temperature. For the lengthextensional resonance measurements, the aspect ratio of the resonators should exceed 5:1 in order to yield nearly pure resonance modes.26 For orthorhombic symmetry, there are in total 17 independent material coefficients to be determined, i.e., nine elastic, five piezoelectric, and three dielectric coefficients.27 In ultrasonic pulse-echo measurements, a 15 MHz longitudinal wave transducer 共Ultran Laboratories, Inc.兲 and a 20 MHz shear wave transducer 共Panametrics Com.兲 were used. The electric pulses used to excite these transducers were generated by a 200 MHz pulser/receiver 共Panametrics Com.兲, and the time of flight between echoes was measured

−3

kt 0.19

using a Tektronix 460A digital oscilloscope. The phase velocities of the longitudinal and shear waves were measured ¯ 1兴, and along the three pure mode directions, 关100兴, 关01 关011兴, to obtain eight independent combinations of different material coefficients.28 Three length-extensional and one thickness resonance measurements were conducted using an HP 4194A impedance/gain-phase analyzer. From the resonance and antiresonance frequencies we can calculate corresponding piezoelectric coefficients d31 and d32, the elastic compliance E E E D 26 , s22 , and s33 , and the elastic stiffness c33 . Dielectric s11 measurements were carried out at 1 kHz using a Stanford Research System SR715 LCR meter. From capacitance meaT T T , ␧22 , and ␧33 were surements, the dielectric permittivity ␧11 obtained. In addition, the piezoelectric strain coefficients d33 can be directly measured by quasistatic method using a ZJ-2 piezo d33 meter.

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From these measurements we can obtain 17 independent E E D E E D D E E E E T , c22 , c33 , c44 , c55 , c44 , c55 , c66 , s11 , s22 ,s33, ␧11 , coefficients: c11 T T , ␧33 , d31, d32, and d33. In order to check matrix consis␧22 tency, we need to explicitly derive nine independent elastic coefficients c␭E␮ or s␭D␮, five independent piezoelectric coefficients ei␭ or di␭, and three independent dielectric permittivity ␧Tij or ␧Sij 共i , j = 1 , 2 , 3; ␭ , ␮ = 1 – 6兲. The basic relationships to calculate them from the measured data are E s11 =

E E E 2 c22 c33 − 共c23 兲 , C

共1兲

E = s22

E E E 2 c33 − 共c13 兲 c11 , C

共2兲

E = s33

E E c22 c11 −

E 2 共c12 兲

C

共3兲

,

E E E 2 E E E E E E E E E c22 − 共c12 兲 兲c33 − c13 共c22 c13 − c12 c23兲 − c23 共c11 c23 where C = 共c11 E E E − c12 c13兲, and c33 is given by E D = c33 共1 − k2t 兲, c33

d15 =

d24 =

冑 冉 冑 冉 T ␧11

T ␧22

1 E c55

1 E c44

共4兲 −



1 D c55

1 D c44

冊 冊

,

共5兲

.

共6兲

An iteration procedure is implemented while trying to determine the independent data set within the error limits. Using this procedure, we have derived a complete coefficient set of a 关011兴 poled PZN-7%PT single crystal, as listed in Table I. These properties are quite different from those of 关001兴 poled PZN-7%PT.10 For example, the piezoelectric coefficient d15 of this system is 1823 pC/ N, while for 关001兴 poled crystal, d15 is only 176 pC/ N. Moreover, the d24 of 关011兴 poled crystal is only 50 pC/ N but the d24 and d15 of 关001兴 poled crystal are the same.10 It is worth mentioning that the shear anisotropy is very large in the 关011兴 poled PZN-7%PT E crystal, there is almost a 20 times difference between c44 E E D E D and c55. Moreover, c44 / c44 and c55 / c55 also exhibit a large difference, which is directly linked to the large difference between k24 and k15. Most importantly, unlike 关001兴 poled PZN-7%PT, there is a very large difference between the piezoelectric coefficients d32 and d31 in 关011兴 poled PZN-7%PT crystals. In summary, we have shown that 关011兴 direction poled PZN-7%PT single crystals can produce a superlarge transverse d32 piezoelectric coefficient. Using a hybrid characterization technique, we have measured a complete set of material coefficients, including elastic, dielectric, and piezoelectric coefficients, based on macroscopic orthorhombic mm2 symmetry. The full matrix data allowed us to compre-

hensively evaluate the 关011兴 direction poled multidomain crystal and compare the properties with that of 关001兴 poled crystals. The largest improvement compared to 关001兴 poled PZN-7%PT are the d32 and d15, which can reach −1460 and 1823 pC/ N, respectively. The electromechanical coupling coefficient k32 共0.86兲 is also very impressive, making the 关011兴 poled PZN-7%PT an excellent candidate for transverse mode sensors, actuators and other electromechanical devices. From both the results of 关001兴 and 关011兴 poled crystals we also verified a general rule in domain engineered crystals: larger piezoelectric coefficients always correspond to lower elastic stiffness coefficients or larger elastic compliance coefficients along the corresponding direction. This research was sponsored by the NIH Grant for the Ultrasonic Transducer Engineering Resource 共Grant No. P41-EB2182-07兲. 1

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