IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control ,
vol. 58, no. 12,
December
2011
2753
Correspondence Temperature Dependence of Elastic Properties and Piezoelectric Applications of BaTeMo2O9 Single Crystal Zeliang Gao, Xin Yin, Weiguo Zhang, Shanpeng Wang, Minhua Jiang, and Xutang Tao Abstract—BaTeMo2O9 (BTM) single crystal, as a lead-free piezoelectric material, belongs to the monoclinic system, space group P21. We report the temperature dependence of the elastic constants by the transmission method over the range −50°C to 150°C. The first-order temperature coefficients of the elastic constant s44 is about 180 × 10−6/°C. Piezoelectric resonators based on BTM crystal using the thickness-stretching vibration and the shear vibration modes were designed and evaluated, which eliminated or minimized the influence of the off-principal axis coefficients. The Qm of one of the resonators is about 600. Our results show that the elastic constants have good temperature stability, and the resonators have already met the requirements for some piezoelectric applications. This study on the BTM crystal has revealed the application for the low-symmetry crystal.
I. Introduction
P
iezoelectric devices play an important role in electronics for information processing, sensing, and automation [1]–[3]. Continuous efforts are being paid to developing new materials to replace hazardous lead-containing piezoelectrics [4], [5]. Currently, the most widely used piezoelectric crystals are SiO2, LiNbO3, and LiTaO3. Lead-free crystals such as BaTiO3 and Na0.5Bi0.5TiO3 [6]– [9] have been the subject of intense research. However, these crystals are usually high-symmetry crystals. To our knowledge, only a few piezoelectric devices based on low-symmetry crystals have been reported [10], although many piezoelectric crystals are actually of low symmetry. BaTeMo2O9 (BTM), a new lead-free crystal first synthesized by P. S. Halasyamani and grown by our group from TeO2-MoO3 flux system [11], [12], shows great potential for piezoelectric and nonlinear optical applications [13]. Our previous studies showed that BTM crystal contains Te-O4 tetrahedrons and Mo-O6 octahedrons. Both the Mo6+ and Te4+ cations are in asymmetric coordination environments because of the second-order Jahn-Teller distortions, which makes the crystal exhibit strong piezoelectric and electro-optic properties [11]–[17]. In particular, its excellent piezoelectric properties (d34 = 30.25 pC/N) Manuscript received May 10, 2011; accepted September 6, 2011. This work was supported by the State National Natural Science Foundation of China (grant numbers 50721002, 50590403, and 50802054) and the 973 Program of the People’s Republic of China (grant number 2010CB630702). The authors are with the State Key Laboratory of Crystal Materials, Shandong University, Jinan, China (e-mail:
[email protected]). Digital Object Identifier 10.1109/TUFFC.2011.2139 0885–3010/$25.00
imply that it has great potential for fabricating lead-free piezoelectric devices. However, the crystal belongs to the monoclinic system with many off-principal axis coefficients in its piezoelectric and elastic matrix, which causes extreme difficulties in piezoelectric applications. In addition, the temperature dependence of the elastic constants is a very important parameter for frequency devices based on piezoelectric crystals with relatively small piezoelectric constants. In this paper, we have reported the temperature dependence of the elastic constants, and realized piezoelectric resonators by the coordinate rotation method which can eliminate the negative effects of the off-principal-axis coefficients. The parameters and temperature stability of the piezoelectric resonators have been investigated. Our experiments indicated that the BTM devices can meet the requirements for piezoelectric applications. II. Temperature Dependence of Elastic Properties To determine all of the thirteen elastic constants of the BTM crystal, we have prepared thirteen samples following the method in the literature [8]. The samples were coated with silver in the direction in which the alternating current electric field was applied. The elastic properties were investigated by resonance technique using an Agilent 4294A impedance network analyzer (Agilent Technologies Inc., Santa Clara, CA) and a self-designed experimental setup [18]. All of the samples were first placed into a container filled with dry ice and then the container was put into a furnace. This system enabled the samples to be cooled down to −50°C. The temperature of the samples was measured by a Pt-Rh thermocouple and controlled by a Shimaden FP23 controller/programmer (Shimaden Co. Ltd., Tokyo, Japan) connected to a thyristor. To obtain a uniform temperature distribution and avoid current influence, the heating rate was maintained at 0.5°C/min. The enactment temperature was maintained at each measurement point for 2 min. The resonance frequencies were recorded, and the fitting curves for sij are shown in Fig. 1. Considering that the off-diagonal matrix components of sij were influenced by more than one elastic constant, we have only given the first-, second-, and third-order temperature coefficients of sij (i = j), and they are listed in Table I using the following equations [19]:
Ts(ij1) =
1 ∂s ij ⋅ s ij 0 ∂T
Ts(ij2) =
1 ∂s ij ⋅ 2s ij 0 ∂T
T =T0
Ts(ij3) =
1 ∂s ij ⋅ 6s ij 0 ∂T
T =T0
© 2011 IEEE
T =T0
(1) (2)
, (3)
2754
IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control ,
vol. 58, no. 12,
December
2011
rotation method, the negative coefficients of piezoelectric and elastic constants resulting from the low symmetry of BTM crystal can be eliminated as follows: After a coordinate rotation, the piezoelectric constants ′ ′ ′ ′ ′ d 34 , d 16 , d 35 and elastic constants s 46 and s 44 can be expressed as follows: ′ d 34 = d 14 sin θ cos θ + d 34 cos 2 θ + d 16 sin 2 θ + d 36 sin θ cos θ (4) ′ d 16 = −d 14 sin θ cos θ − d 34 sin 2 θ + d 16 cos 2 θ (5) + d 36 sin θ cos θ
+ d 36 cos 2 θ
where sij0 is the elastic coefficient at the temperature T = T0. III. Piezoelectric Resonator Designs Table I indicates that the s44 has the best temperature stability. Fortunately, the piezoelectric constant d34 is the largest, which is beneficial to the applications. Because of the low symmetry of the crystal (monoclinic system, space group P21), the piezoelectric matrix (dij) is complex, and the valuable piezoelectric constants for applications may be affected by the other constants. 0 0 d 14 0 d 16 0 d 21 d 22 d 23 0 d 25 0 0 0 0 d 34 0 d 36 0 7.46 0 0 12.04 0 = −2.7 10.8 −3.21 0 0 pC//N −0.64 0 0 0 30.25 0 12.83
For the piezoelectric resonators, samples perpendicular to b and a axis can induce thickness stretching and shear vibrations, respectively [20]. When the mode was stimulated by d22, the other two constants d21 and d23 would also stimulate vibrations. The interferential frequencies were much lower than the target frequency and can be ignored. For the mode stimulated by d34, the interferential frequency is stimulated by d36. According to coordinate
′ s 46 = (s 66 − s 44) sin θ cos θ − s 46(sin 2 θ − cos 2 θ) (7)
′ s 44 = s 44 cos 2 θ + 2s 46 sin θ cos θ + s 66 sin 2 θ, (8)
′ 1) The largest d 34 has been obtained and the influence ′ ′ of d 16 and d 14 has been reduced. From (4)–(6), we can see that d16 and d36 contribute ′ to d 34 in the new coordinate system. In this design, ′ not only has the largest d 34 been obtained, but the ′ ′ d 16 and d 14 which give negative influences on the property have also been minimized. In fact, in the new coordinate system, the electric field was only ′ applied in the direction of z ′, so the coefficients d 16 ′ and d 14 cannot stimulate vibrations. The largest val′ ue of d 34 appeared at the angle θ = 23.5°, and it was marked as (zxω) 23.5°. ′ 2) Elimination of the influence of d 35 . In the new coordinate system, the frequency excited ′ by d 35 was a low frequency, because the vibration mode was face shear. The elimination of influence of ′ d 35 happened at the angle θ = 24.5°, and it was marked as (zxω) 24.5°.
′ . According to 3) Elimination of the influence of s 46 Hooke’s law, strain (Si) and stress (Ti) can be expressed with elastic constants (sij) as
S1 s 11 S 2 s 12 S 3 s 13 = S 4 0 S 5 s 15 S 6 0
s 12 s 22 s 23 0 s 25 0
s 13 0 s 23 0 s 33 0 0 s 44 s 35 0 0 s 46
s 15 0 T1 s 25 0 T2 s 35 0 T3 × . (9) 0 s 46 T4 s 55 0 T5 T6 0 s 66
TABLE I. The Temperature Coefficients of Elastic Constants. Ts(ij1) (ppm/°C) Ts(ij2) (ppb/°C) Ts(ij3) (ppt/°C)
Ts(11n) 274 25 680
(6)
where θ is the rotation angle. By this coordination rotation, several effects are realized:
Fig. 1. Temperature dependence of elastic constants.
′ d 36 = −d 14 sin 2 θ − d 34 sin θ cos θ + d 16 sin θ cos θ
Ts(22n) 265 634 −7208
Ts(33n) 205 262 −1428
Ts(44n) 181 337 −921
Ts(55n) 236 240 −1639
Ts(66n) 271 −44.3 352
gao et al.: properties and applications of BaTeMo2O9 single crystal
2755
Fig. 2. Orientations of all of the samples in the piezoelectric coordinate system.
From (9), it can be seen that the vibration excited by ′ s44 would undergo interference from s46 except when s 46 = ′ 0. Two angles which make s 46 = 0 could be deduced. However, for the angle in the forth quadrant, the correspond′ ing coefficients d 34 and k ij′ were too small for practical applications, so the appropriate rotation angle should be θ = 16.5°, and it was marked as (zxω) 16.5°. All of the samples were cut using the piezoelectric coordinates [8], and they are shown in Fig. 2. IV. Experiments and Results In our experiments, three kinds of rotated samples were ′ designed to obtain the largest d 34 and to eliminate the ′ ′ influences caused by d 35 and s 46. They can be marked as (zxω) 23.5°, (zxω) 24.5°, and (zxω) 16.5°, respectively. Based on the coordinate rotation method, five kinds of BTM samples were fabricated as squares with dimensions of 4 × 4 mm. The surfaces of the samples were sputtercoated with gold, and the samples were packaged in an iron box with two antennae. The resonant frequencies were measured by an Agilent 4294A impedance network analyzer. The k ij′ can be calculated according to
k ij′ =
d ij′ εii′ s jj′
, (10)
where εii′ is the dielectric coefficient. The corresponding coefficients d ij′ , s ij′ , and k ij′ are shown in Fig. 3. The quality factor (Qm) was evaluated according to the following equation:
Qm =
f1/2
fs , (11) − f −1/2
where fs is the resonant frequency, f1/2 and f−1/2 are the frequencies at the half-power point.
Fig. 3. Distributions of corresponding coefficients with rotation angle (−90° to 90°): (a) d ij′ , (b) s ij′ , and (c) k ij′ .
The parameters for the five types of the resonances were listed in Table II. As a resonator, the temperature coefficients are especially important, because they indicate the frequency stability with regard to temperature. The experimental setup and process are the same as those used for the determina-
2756
IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control ,
vol. 58, no. 12,
December
2011
TABLE II. Parameters for Five Types of Resonance Devices. Sample y square z square (zxω) 23.5° (zxω) 24.5° (zxω) 16.5°
t (mm)
f (MHz)
Qm
kij
dij (pC/N)
sij (pm2/N)
0.58 0.61 0.56 0.5 0.48
4.93 1.78 2.08 2.21 2.31
250 256 344 300 600
0.228 0.351 0.362 0.360 0.364
10.8 30.25 35.72 35.70 35.21
10.96 36.46 37.24 37.19 37.35
Fig. 5. A graph showing the resonator working.
TABLE III. The Temperature Coefficients of ∆f /fT0 . Sample y square z square (zxω) 23.5° (zxω) 24.5° (zxω) 16.5°
Fig. 4. (a) Temperature dependence of resonant frequencies, and (b) temperature dependence of ∆f /fT0 (T0 = 25°C).
tion of the elastic constants temperature coefficients. The fitting curves of resonance, the frequencies, and ∆f /fT0 (T0 = 25°C) were obtained, as shown in Fig. 4. Similar to the temperature coefficients of the elastic constants, the temperature coefficients of ∆f /fT0 were obtained, as listed in Table III. A graph of a working resonator is shown in Fig. 5. V. Discussion From Table II, we can see that large effective piezoelectric coefficients, electromechanical coupling coefficients, and mechanical quality factors have been realized for all the designs. The electromechanical coupling coefficients are over 30%, and most of the mechanical quality factors
a1 (ppm/°C)
a2 (ppb/°C)
a3 (ppt/°C)
−121 −101 −120 −104 −99
36 417 −440 −19 −101
26.5 −3555 −2138 1418 2369
are large enough to be suitable for practical applications. The design (zxω) 23.5° has the largest piezoelectric coefficients and the electromechanical coupling coefficients in this design are larger than those of the z square sample. In Table I, the first-order temperature coefficient of s44 is the smallest, therefore we can obtain a high-quality device by using it. From Table III and Fig. 4, it is obvious that all the values of ∆f /fT0 are less than 1% in the range from −50°C to 100°C. Extraordinarily, the sample (zxω) 16.5° has the smallest frequency shift Δf and ∆f /fT0, indicating that this design has the best temperature stability among these three designs. The design of y square has the largest Δf and ∆f /fT0; the fitting curves are approximately linear, and it can be used in temperature detection applications. VI. Conclusions In summary, we have investigated the temperature dependence of the elastic properties of the low-symmetry
gao et al.: properties and applications of BaTeMo2O9 single crystal
BTM crystals. By using the large piezoelectric coefficients and highly temperature-stable elastic constants, we have designed and studied five piezoelectric resonators. Our results have demonstrated real applications of the BTM crystals. Moreover, our designs have successfully minimized the negative influence caused by the low symmetry of the crystal, and this can give direction for the piezoelectric application of other low-symmetry crystals. References [1] A. Talbi, F. Sarry, L. Le Brizoual, O. Elmazria, and P. Alnot, “Sezawa mode SAW pressure sensors based on ZnO/Si structure,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol. 51, no. 11, pp. 1421–1426, 2004. [2] D. Parenthoine, L. Haumesser, F. Vander Meulen, M. Lethiecq, and L. P. Tran-Huu-Hue, “Nonlinear constant evaluation in a piezoelectric rod from analysis of second harmonic generation,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol. 56, no. 1, pp. 167–174, 2009. [3] A. Novell, M. Legros, N. Felix, and A. Bouakaz, “Exploitation of capacitive micromachined transducers for nonlinear ultrasound imaging,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol. 56, no. 10, pp. 2733–2743. [4] L. E. Cross, “Lead-free at last,” Nature, vol. 432, no. 7013, pp. 24–25, 2004. [5] J. Ravez and A. Simon, “Some solid state chemistry aspects of leadfree relaxor ferroelectrics,” J. Solid-State Chem., vol. 162, no. 2, pp. 260–265, 2001. [6] K. Datta, K. Roleder, and P. A. Thomas, “Enhanced tetragonality in lead-free piezoelectric (1−x)BaTiO3-xNa1/2Bi1/2TiO3 solid solutions where x = 0.05–0.40,” J. Phys. D, vol. 106, no. 12, art. no. 123512, 2009. [7] W. W. Ge, H. Liu, and X. Y. Zhao, “Crystal growth and high piezoelectric performance of 0.95Na0.5Bi0.5TiO3-0.05BaTiO3 lead-free ferroelectric materials,” J. Appl. Phys., vol. 41, no. 11, pp. 115403, 2008.
2757
[8] D. Fu, M. Itoh, and S. Y. Koshihara, “Crystal growth and piezoelectric of BaTiO3-CaTiO3 solid solution,” Appl. Phys. Lett., vol. 93, no. 1, art. no. 012904, 2008. [9] Q. H. Zhang, Y. Y. Zhang, and F. F. Wang, “Enhanced piezoelectric and ferroelectric properties in Mn-doped Na0.5Bi0.5TiO3-BaTiO3 single crystals,” Appl. Phys. Lett., vol. 95, no. 10, art. no. 102904, 2009. [10] MasonW. P., “Properties of monoclinic crystals,” Phys. Rev., vol. 70, no. 9–10, pp. 705–728, 1946. [11] H. S. Ra, K. M. Ok, and P. S. Halasyamani, “Combining secondorder Jahn-Teller distorted cations to create highly efficient SHG materials: Synthesis, characterization, and NLO properties of BaTeM2O9 (M = Mo6+ or W6+),” J. Am. Chem. Soc., vol. 125, no. 26, pp. 7764–7765, 2003. [12] W. G. Zhang, X. T. Tao, C. Q. Zhang, and Z. L. Gao, “Bulk growth and characterization of a novel nonlinear optical crystal BaTeMo2O9,” Cryst. Growth Des., vol. 8, no. 1, pp. 304–307, 2008. [13] Z. L. Gao, X. T. Tao, X. Yin, W. G. Zhang, and M. H. Jiang, “Elastic, dielectric, and piezoelectric properties of BaTeMo2O9 single crystals,” Appl. Phys. Lett., vol. 93, no. 25, art. no. 252906, 2008. [14] P. S. Halasyamani and K. R. Poeppelmeier, “Noncentrosymmetric oxides,” Chem. Mater., vol. 10, no. 10, pp. 2753–2769, 1998. [15] N. S. P. Bhuvanesh and J. Gopalakrishnan, “Solid-state chemistry of early transition-metal oxides containing d0 and d1 cations,” J. Mater. Chem., vol. 7, no. 12, pp. 2297–2306, 1997. [16] Z. L. Gao, X. Yin, W. G. Zhang, S. P. Wang, M. H. Jiang, and X. T. Tao, “Electro-optic properties of BaTeMo2O9 single crystals,” Appl. Phys. Lett., vol. 95, no. 15, art. no. 151107, 2009. [17] W. G. Zhang, X. T. Tao, C. Q. Zhang, H. J. Zhang, and M. H. Jiang, “Structure and thermal properties of the nonlinear optical crystal BaTeMo2O9,” Cryst. Growth Des., vol. 9, no. 6, pp. 2633–2636, 2009. [18] Z. L. Gao, Y. X. Sun, X. Yin, S. P. Wang, M. H. Jiang, and X. T. Tao, “Growth and electric-elastic properties of KTiAsO4 single crystal,” J. Appl. Phys., vol. 108, no. 2, art. no. 024103, 2010. [19] WangH.XuB.HanJ. R.LiT. J.HuoL. Y., “The thermal behavior of elastic constants of berlinite (α-AlPO4),” Acta Phys. Sin., vol. 35, no. 7, pp. 889–895, 1986. [20] P. Zhang and Z. Zhang, Piezoelectric Measurement. Jinan, China: Shandong University Press, 1983, ch. 3.
