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Surface load induced electrical impedance shift in relaxor-PbTiO3 crystal piezoelectric Kyungrim Kim, Shujun Zhang, and Xiaoning Jiang

Citation: Appl. Phys. Lett. 100, 253501 (2012); doi: 10.1063/1.4729766 View online: http://dx.doi.org/10.1063/1.4729766 View Table of Contents: http://apl.aip.org/resource/1/APPLAB/v100/i25 Published by the American Institute of Physics.

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Downloaded 28 Jul 2012 to 152.14.119.97. Redistribution subject to AIP license or copyright; see http://apl.aip.org/about/rights_and_permissions APPLIED PHYSICS LETTERS 100, 253501 (2012)

Surface load induced electrical impedance shift in relaxor-PbTiO3 crystal piezoelectric resonators Kyungrim Kim,1 Shujun Zhang,2 and Xiaoning Jiang1,a) 1Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, North Carolina 27695, USA 2Materials Research Institute, Pennsylvania State University, University Park, Pennsylvania 16802, USA (Received 13 April 2012; accepted 1 June 2012; published online 18 June 2012)

The effect of surface loads on Pb(Mg1/3Nb2/3)O3-PbTiO3 single crystal piezoelectric resonators was studied. Electrical impedance shifts at both resonance and anti-resonance due to surface loads were recorded for comparison among face-shear mode, thickness-shear mode, and thickness mode resonators. It was observed that electrical impedances of face shear mode resonators exhibited significantly higher sensitivity to surface load changes comparing with other resonators with similar dimensions, because of enhanced energy dissipation in face shear mode resonators, indicating a promising innovative face-shear mode single crystal piezoelectric sensing mechanism. VC 2012 American Institute of Physics.[http://dx.doi.org/10.1063/1.4729766]

Relaxor-PbTiO3 (PT) single crystals, including Pb(Mg1/3 prepared crystal samples, the , resonant fre- Nb2/3)O3-PT (PMN-PT) and Pb(In0.5Nb0.5)O3-Pb(Mg1/3Nb2/3) quency, and anti-resonant were measured using an O3-PT (PIN-PMN-PT), are known with advanced properties impedance analyzer (HP4294A, Agilent). According to the 8,9 such as higher piezoelectric coefficients (e.g., d33 > 1500 pC/ IRE standards, properties of the face-shear PMN-PT single E 2 N), elastic constants (e.g., s33 > 50 pm /N), and electrome- crystals can be calculated. Similarly, thickness-shear (10 mm chanical coupling factors (e.g., k33 > 0.9) when compared to 10 mm 1 mm) and thickness (10 mm 10 mm 0.5 mm) Pb(Zr,Ti)O3 (PZT) and other piezoelectric polycrystalline mode PMN-PT crystals were prepared and characterized for materials.1–3 These crystals have been deployed successfully the following surface load experiments. The poling direction, in piezoelectric sensors, actuators, and transducers for a broad electrodes, and vibration mode for prepared single crystal range of applications.4–6 More recently, the face-shear mode resonators in three different modes were shown in Fig. 1. relaxor-PT crystals have drawn research attention due to their Both acoustic surface load and surface force load experi- high piezoelectric coefficients (e.g., d36 of 1600-2800 pC/N) ments were performed using the prepared resonators. In E 2 and ultrahigh elastic compliances (s66 > 120 pm /N). More order to apply different surface acoustic loads, alumina importantly, unlike thickness shear mode crystals, the face (Al2O3) powders in different percentages by weight were shear mode crystals were found to possess much higher me- mixed with the liquid silicone rubber (Sylgard 170, Dow chanical quality factor Qm (>120, compared to 30 for thick- Corning Corp.). The liquid silicone rubber (about 2 mm ness shear mode crystals) and can be easily repolarized since thick) with and without Al2O3 powders (10%, 20%, 30%, the poling electrodes are the same as the active electrodes.7 and 40% of the silicone rubber by weight) was applied to These unique properties suggest the need of further study on one large surface (10 mm 10 mm) of each crystal resonator face shear mode single crystals for potential advanced appli- plate and cured for 24 h in a vacuum desiccator. Acoustic cations. This letter investigates the effect of surface load on impedances of rubber mixtures were characterized by meas- the face-shear mode PMN-PT single crystal resonators. The uring sound velocity and density of rubber mixtures. The electrical impedance changes induced by the applied surface longitudinal sound speed of rubber mixtures was measured loads were measured and then the sensitivity or the ratio of using the ultrasonic pulse-echo method. The time of flight of electrical impedance change to the surface load variations echo waves received by a 30 MHz transducer from the top was calculated and compared among thickness mode, and bottom surfaces of rubber samples (2 mm thick) was thickness-shear mode, and face-shear mode single crystal pie- recorded and the longitudinal sound velocity was then calcu- 10 zoelectric resonators. Finally, the experimental results were lated. The shear velocity (vs) of rubber mixtures was verified by an analytical model, followed by discussions. For face shear resonators, [011] poled rhombohedral PMN-PT single crystals were used, which possess the macro- scopic symmetry mm2. Face-shear mode plates (10 mm 10 mm 1 mm) were prepared by rotating a 45 angle about the Z-axis [011] direction. Cr/Au electrodes were deposited on (011) surface of each resonator plate. The 10 cm co-ax wires (AWG 25) were bonded to electrode surfaces using silver epoxy for electrical connection. For the FIG. 1. The poling direction, electrodes, and vibration mode for (a) thick- ness mode, (b) thickness-shear mode, and (c) face-shear mode PMN-PT a)Electronic mail: [email protected]. crystals.

0003-6951/2012/100(25)/253501/4/$30.00 100, 253501-1 VC 2012 American Institute of Physics

Downloaded 28 Jul 2012 to 152.14.119.97. Redistribution subject to AIP license or copyright; see http://apl.aip.org/about/rights_and_permissions 253501-2 Kim, Zhang, and Jiang Appl. Phys. Lett. 100, 253501 (2012) calculated from the longitudinal velocity using the Poisson’s TABLE I. Properties of relaxor-PT single crystals for the calculation. ratio of rubbers (t ¼ 0.5). The density of the rubber mixtures C0 ZC (q) was calculated using measured volume and weight. 3 PMN-PT Dim. (mm ) fa kij (nF) (Mrayl) Finally, the shear (Zs) of rubber mix- tures, or surface loads, was calculated (Zs ¼ qvs), which was Thickness mode (d33)10 10 0.5 5.0 MHz 0.58 (kt) 1.6 40.5 found to increase with weight percentages of Al2O3 powders Thickness-shear mode (d15)10 10 1 1.2 MHz 0.90 1.1 19.4 in rubber mixtures. Face-shear mode (d36)10 10 1 93.5 kHz 0.76 1.1 15.2 The electrical impedance spectra for face-shear, thick- ness-shear, and thickness mode resonators under different surface loads were measured using an impedance analyzer. thickness and thickness-shear mode resonators with similar In order to verify the measured electrical impedance results, sizes. In specific, the ratio of electrical impedance shift to electrical impedances (ZAB) for loaded and unloaded piezo- the applied acoustic impedance of the face-shear mode reso- electric crystal resonators were also estimated using the nator was found to be at least 20 times and 90 times higher Krimholtz, Leedom, and Matthaei model 11,12 than those of thickness-shear mode and thickness mode res- (KLM model) as follows: onators, respectively. Table I indicates the properties of "# three different PMN-PT crystals used for the calculation. 1 k2 2 tan a j ZL 2 Zc The slight difference between the measured and calculated ZAB ¼ 1 Z ; (1) jxC0 a 1 j L cot a Zc results is likely due to the fact that the effect of additional surface loads from the wires and silver epoxy used for the where x, C0, k, a, and Zc represent the angular frequency, wire bonding was not considered in the simulation. Figures clamped capacitance of the crystal plate, electromechanical 3(a) and 3(b) show measured electrical impedances under coupling factor, the complex acoustic wave shift different surface forces for resonators in three modes, at the (¼px/x0, x0 is anti-resonant frequency), and the acoustic resonant frequency and anti-resonant frequency, respec- impedance of the piezoelectric crystal (¼Aqv, A is the aper- tively. Again, significantly higher electrical impedance shift ture area, q is the density, and v is the sound speed of the sensitivity (SF) under applied surface forces was observed crystal), respectively. The ratio (Sz) of electrical impedance from the face-shear mode resonator at both resonance and shift (DZAB) of crystal resonators to the applied surface load anti-resonance frequencies, comparing with SF observed change or acoustic impedance change (DZL) can be consid- from thickness mode and thickness shear mode resonators. ered as the electrical impedance sensitivity to surface acous- These findings (Figs. 2 and 3) can be supported by the na- tic load for the studied crystal resonators. ture of advanced properties of face-shear mode crystals. For resonator tests under various applied forces, a layer The crucial factors which determine the electrical imped- of pure silicone rubber was applied to both large surfaces of ance characteristic of piezoelectric resonators are the fre- crystal resonator plates. Weight forces were then applied to quency (x), clamped capacitance C0, acoustic load (ZL), the rubber layer through a steel cylinder. Similarly, the ratio and acoustic impedance of resonators (ZC) as shown in Eq. (SF) of electrical impedance shift (DZAB) to applied force (1). The anti-resonant frequency (x0 ¼ pv/t or pv/l) and the change (DFS) can be considered as the electrical impedance static capacitance (C0 ¼ eA/t) are related with the resonator sensitivity to surface force loads for the studied crystal dimension (t and l), and the product of them (¼ x0C0) resonators. affects resultant electrical impedance at resonance and anti- Figures 2(a) and 2(b) present the results of measured resonance. As the magnitude of x0C0 decreases, the slope and calculated electrical impedance changing with acoustic (jDZAB/DZLj) of electrical impedance shift over acoustic load impedance for PMN-PT resonators in three different load increases as shown in Figs. 4(a) and 4(b), indicating modes at resonant frequency and anti-resonant frequency, that electrical impedance shift of face shear mode resona- respectively. One can observe that for the face-shear mode tors is significantly more sensitive to surface load changes resonator, the electrical impedance increases and decreases comparing with resonators in other two modes. The small rapidly with the increasing acoustic impedances of surface inset in Fig. 4(b) indicates the relationship between x0C0 loads at the resonant frequency and anti-resonant frequency, and the crystal aspect ratio for three different modes. In respectively. This is in stark contrast to the findings from square plate (dimensions: l l t) resonators, the frequency

FIG. 2. Comparison of measured electrical impedance (ZAB) and sensitivity (Sz) under different surface loads for face-shear mode (FS), thickness-shear mode (TS), and thickness mode (T) resonators. (a) Measured electrical impedance at the resonant frequency. (b) Measured electrical impedance at the anti-resonant frequency. (Calculated sensitivities at the resonant frequency for three different mode resonators: Sz, FS ¼ 88 X/Mrayl, Sz, TS ¼ 2.1 X/Mrayl, and Sz, T ¼ 0.7 X/Mrayl. Calculated sensitivities at the anti- resonant frequency: Sz, FS ¼ 46 kX/Mrayl, Sz, TS ¼ 0.8 kX/Mrayl, and Sz, T ¼ 0.3 kX/Mrayl).

Downloaded 28 Jul 2012 to 152.14.119.97. Redistribution subject to AIP license or copyright; see http://apl.aip.org/about/rights_and_permissions 253501-3 Kim, Zhang, and Jiang Appl. Phys. Lett. 100, 253501 (2012)

FIG. 3. Comparison of measured electrical impedance (ZAB) and sensitivity (SF) under different surface forces (0.2 N–10 N) for FS mode, TS mode, and thickness mode (T) resonators. (a) Measured electrical impedance at the resonant frequency. (b) Measured electrical im- pedance at the anti-resonant frequency.

FIG. 4. (a) Calculated electrical impedance (ZAB)asa function of acoustic load (ZL) at the resonant frequency and (b) calculated electrical impedance at the anti- resonant frequency. The small inset in (b) indicates the relationship between xC0 and the aspect ratio (l/t)of crystal dimensions. For the calculation, electromechani- cal coupling factor (k) and (ZC) are 0.8 and 30 Mrayl, respectively.

determining factor of thickness and thickness-shear mode is the resonant frequency shift but not the magnitude of elec- the crystal thickness (t), while that of face-shear-mode is trical impedance change. Besides, a in Eq. (1) does not play 2 the lateral length (l). x0C0 can be expressed by pev(l/t) for a significant role in determining the electrical impedance thickness and thickness-shear mode, and pev(l/t) for face- change since a is constant near the resonant frequency shear mode. As a result, face-shear mode resonator is fea- (a ¼ pxr/x0) and the anti-resonance frequency (a ¼ px0/x0). tured with lower x0C0 than other modes with the same as- For surface force tests, the applied force (FS) through the pect ratio (l:t) and thus its electrical impedances at both rubber layer on top of the resonator surface can be consid- resonance and anti-resonance frequencies shift more rapidly ered as a clamping force leading to vibration energy losses. under surface loads. On the other hand, the low acoustic im- As high clamping force is applied, more energy is dissipated, pedance of the loaded crystal (ZC) can to a significant resulting in decreased Qm and electrical impedance changes change in electrical impedance at the resonant frequency, in crystal resonators. Unlike thickness and thickness-shear while no significant change was found at the anti-resonant mode, the particle vibration of the face-shear mode resonator frequency, as can be seen in Figs. 5(a) and 5(b). This also occurs along the diagonal axis on the large surfaces (or can affects the load sensitivity of resonators at the resonant loaded surfaces). Therefore, when the face-shear resonator is frequency since ZC of each resonator is different (Table I). clamped by applied surface force (FS), relatively high Nevertheless, the load sensitivity of face-shear mode reso- energy dissipation occurs on its surface which can result in nator is affected dominantly by the product of the angular the large reduction of mechanical quality factor (Qm) of the frequency and the static capacitance at both resonance and resonator. Consequently, the electrical impedance (ZAB) anti-resonance, due to more than two orders of magnitude increases at the resonance and decreases at the anti- difference in x0C0 between face-shear mode and other resonance, with weak resonance peaks corresponding to the modes. The electromechanical coupling factor (k) affects reduced Qm.

FIG. 5. (a) Calculated electrical impedance (ZAB) with different characteristic impedance of the resonator at the resonant frequency and (b) calculated electrical im- pedance with different characteristic impedance at the anti-resonant frequency. For the calculation, electrome- chanical coupling factor (k) and the value of xC0 are 0.8 and 0.01 F/s, respectively.

Downloaded 28 Jul 2012 to 152.14.119.97. Redistribution subject to AIP license or copyright; see http://apl.aip.org/about/rights_and_permissions 253501-4 Kim, Zhang, and Jiang Appl. Phys. Lett. 100, 253501 (2012)

In summary, the effect of surface loads on PMN-PT comments. The work is partially supported by NC State ca- single crystal piezoelectric resonators was investigated. reer development fund provided to XJ. Different acoustic surface loads were applied to the thick- ness mode, thickness-shear mode, and face-shear mode res- 1S. Zhang and F. Li, J. Appl. Phys. 111, 031301 (2012). 2 onators with similar dimensions. The highest sensitivity of D. Zhou, J. Chen, L. Luo, X. Zhao, and H. Luo, Appl. Phys. Lett. 93, 073502 (2008). electrical impedance to the surface loads, including rubber 3S. Zhang, F. Li, N. P. Sherlock, J. Luo, H. J. Lee, R. Xia, R. J. Meyer, Jr., mixtures with different acoustic impedances and applied W. Hackenberger, and T. R. Shrout, J. Cryst. Growth 318, 846 (2010). forces, was obtained from the face-shear resonator. The ex- 4K. C. Cheng, H. L. W. Chan, C. L. Choy, Q. Yin, H. Luo, and Z. Yin, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 50, 1177 (2003). perimental results were in general agreement with the ana- 5 P. A. Wlodkowski, K. Deng, and M. Kahn, Sens. Actuators, A 90, 125 lytical estimations. These findings suggest that more (2001). energy dissipation occurs in face shear resonators under 6S. Dong, L. Yan, N. Wang, D. Viehland, X. Jiang, P. Rehrig, and W. surface loads. The newly revealed characteristic of high Hackenberger, Appl. Phys. Lett. 86, 053501 (2005). 7S. Zhang, F. Li, W. Jiang, J. Luo, R. J. Meyer, W. Cao, and T. R. Shrout, sensitivity of electrical impedance to surface loads for face Appl. Phys. Lett. 98, 182903 (2011). shear mode resonators can be favorable for a number of 8IRE Standards on Piezoelectric Crystals, Proc. IRE 46, 764 (1958). applications, including smart artificial skins, biological sen- 9S. Zhang, W. Jiang, R. J. Meyer, F. Li, J. Luo, and W. Cao, J. Appl. Phys. sors, chemical sensors, touch screen, and other tactile 110, 064106 (2011). 10I. Y. Kuo, B. Hete, and K. K. Shung, J. Acoust. Soc. Am. 88, 1679 (1990). based sensors. 11R. Krimholtz, D. A. Leedom, and G. L. Matthaei, Electron. Lett. 6, 398 (1970). The author would like to thank their lab members, Sau- 12R. W. Cernosek, S. J. Martin, A. R. Hillman, and H. L. Bandey, IEEE rabh Bakshi, Laura Tolliver, and Sijia Guo, for the insightful Trans. Ultrason. Ferroelectr. Freq. Control 45, 1399 (1998).

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