IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control ,
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Correspondence Acoustic Waves in a Structure Containing Two Piezoelectric Plates Separated by an Air (Vacuum) Gap Irina A. Borodina, Boris D. Zaitsev, Senior Member, IEEE, Iren E. Kuznetsova, Member, IEEE, and Andrey A. Teplykh Abstract—This paper presents experimental results for the characteristics of acoustic waves propagating in a structure containing two parallel piezoelectric plates (I and II) separated by an air gap. Plate I, made of Y-X lithium niobate, contained two interdigital transducers that excited and received an acoustic wave with shear-horizontal polarization. Piezoelectric plate II, made of lithium niobate, was placed above and between the transducers, separated by a fixed gap. For its certain orientation, the amplitude-frequency characteristic showed sharply defined resonant attenuation peaks, which were situated at an equidistant separation from each other. The depth of the peaks was observed to decrease with a wider gap between the plates. It has been stated that these peaks are associated with the resonant reflections of a slot acoustic wave across the width of plate II. Experimentally determined phase velocities and electromechanical coupling coefficient for the slot wave in the structure under study are in a good agreement with theoretical values for various crystallographic orientations of plate II. A comparison between the experimental and theoretical results has allowed us to state two conditions for the slot wave to exist. The structures described may be employed for noncontact excitation of acoustic waves in the plates and for the development of various liquid, gas, and temperature sensors.
I. Introduction
S
lot waves propagating in the structure of two piezoelectric elements separated by an air (vacuum) gap have been theoretically investigated in detail [1]–[4]. The investigated structures contained 1) two semi-infinite media [1]–[3], 2) a semi-infinite medium and a piezoplate [4], and 3) two piezoplates [4]. The characteristics of these slot waves, such as phase velocity, electromechanical coupling coefficient, and temperature coefficient of delay as a function of gap between the piezoelectrics and their material properties, were studied. The waves propagating in the structure of two piezoelectrics separated by the liquid layer [3] have also been theoretically analyzed. The prospect of the use of these waves for the development of gas,
Manuscript received June 3, 2013; accepted September 13, 2013. The work is partially financially supported by the Ministry of Education and Science of Russian Federation (contract 8400) and the Russian Foundation of Basic Research (12-02-01057a, 12-02-31757mol-a, and 13-0200596a). I. A. Borodina, B. D. Zaitsev, and A. A. Teplykh are with the Institute of Radio Engineering and Electronics of the Russian Academy of Sciences, Saratov Branch, Saratov, Russia (e-mail: [email protected]). I. E. Kuznetsova is with the Institute of Radio Engineering and Electronics of the Russian Academy of Sciences, Moscow, Russia. DOI http://dx.doi.org/10.1109/TUFFC.2013.2867 0885–3010/$25.00
liquid, and temperature sensors has been shown [5], [6]. It has been demonstrated that the existence of the slot waves is connected with piezoeffect and that waves’ polarization depends on the crystallographic orientation of the piezoelectrics. The surface slot waves propagating in a structure containing two piezoelectrics have been studied experimentally [7]. The slot waves in the structure containing two piezoelectric plates were not investigated experimentally, although it is common knowledge that acoustic waves propagating in piezoelectric plates being thin compared with the wavelength exhibit higher electromechanical coupling coefficient than that of surface acoustic waves [8]. Because electric fields accompanying such waves greatly penetrate into air (vacuum), we can significantly vary wave characteristics by affecting these fields. It has been, for example, demonstrated that the phase of acoustic wave may be varied over a wide range by bringing the plate near a conducting plane [9]. The acoustic wave phase velocity would be affected by placing a dielectric sample at a certain distance from the plate and the dielectric permittivity of the sample can be obtained from the known calibration curve [10]. One can also change the characteristics of acoustic wave in a structure containing two piezoelectric plates separated by a gap. Phase velocity and electromechanical coupling coefficient of the slot wave in this structure is altered by varying the distance between the plates [4]. It has been shown that the study of the slot waves is not only of fundamental, but also of practical interest, particularly for the development of acoustic sensors [5], [6]. Therefore, this paper reports detailed experimental results for the slot acoustic wave propagating in a structure containing two piezoelectric plates separated by the gap, and compares the results with the data from theoretical analysis. II. Experimental Results For carrying out the experiments, a device was fabricated that included a Y-X LiNbO3 plate with lateral dimensions of 22 × 52 mm placed on a special support. The support was a rectangular frame of acrylic glass with thickness of 6 mm with outside and inside dimensions of 60 × 80 mm and 18 × 48 mm, respectively. The lithium niobate plate carrying two interdigital transducers (IDTs) on the lower side was glued by epoxy to the frame so that both sides of plate between the IDTs were mechanically free (Fig. 1). The initial plate thickness was 500 μm. To be able to reduce the thickness of the plate in the course of the experiments while preserving its flatness, ten reference silicon samples of greater hardness than lithium niobate were glued along the perimeter of the frame. These samples had the initial thickness of 500 μm and lateral dimensions of 8 × 8 mm. The lithium niobate plate and the
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Fig. 1. The scheme of the delay line under study: 1 = piezoelectric plate I (Y-X LiNbO3); 2 = IDT; 3 = acrylic glass support; 4 = piezoelectric plate II; 5 = the reference silicon samples; 6 = reflection-reducing edge geometry of plate I.
reference silicon samples were lapped by aluminum oxide abrasive powders of sizes 14, 10, and 5 μm on a glass polishing pad down to 200 μm [11]. To prevent of the abrasive powder from spilling over onto the plate surface carrying the IDTs, the window was covered by Scotch tape (Nova Roll Ltd., Moscow, Russia). Control of the plate thickness and flatness was performed by vertical optimeter with the scale division of 2.5 μm. Each IDT contained five pairs of split electrodes with an aperture of 8 mm and a period of 1.2 mm. The spacing between the IDTs was 27 mm. The transducers excited and received an SH0 wave that propagated along the X-axis. The operating frequency band of the delay line was 2.5 to 3.9 MHz. The opposite edges of the plate were wave-shaped with the depth of ~λ/2 (where wavelength λ = 1.2 mm) to prevent reflections (Fig. 1). At first, we studied the delay line parameters under pulsed operation in the absence of the upper plate II. Measurements demonstrated the insertion loss to be 25 dB at a central frequency of 3.3 MHz. The power of the main signal exceeded that of all spurious signals by more than 30 dB. This enabled us to carry out the measurements in a continuous regime by using the Agilent E5071C meter of S-parameters (Agilent Technologies Inc., Santa Clara, CA). Figs. 2(a) and 2(b) demonstrate frequency dependencies for the insertion loss and phase of the delay line under study, respectively. Then, we placed the plate II onto the delay line. For the upper plate, we used lithium niobate plates with thicknesses ~500 μm with the following crystallographic orientations: Z-X, Y-X, Y-X+155°, Y-X+140°, and 128° Y-X. In all cases discussed, excluding the structure (Y-X)–(128° Y-X) LiNbO3, the frequency dependence of insertion loss
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showed sharp peaks of resonant attenuation. As an example, the insertion loss dependences are indicated in Figs. 3(a), 3(b), and 3(c) for the (Y-X)–(Z-X) LiNbO3 structure with gaps of 0, 20, and 31 μm, respectively. The gap between plates I and II was controlled by using a set of aluminum foil strips with thicknesses of 7, 20, and 31 μm and lateral dimensions of 10 × 10 mm. These strips were set on the edges of the lower LiNbO3 plate and the upper plate was placed on the strips. To flatten the strips, the upper plate was pressed by a load of ~15 g. It was observed that the value of resonant peaks decreased with a wider gap. To excite the deep resonant peaks, two conditions should be met: 1) the edges of the upper plate II of lithium niobate must be parallel, and 2) they must be parallel to the acoustic wave-fronts. Therefore, when the upper plate is rotated, all resonances disappeared. We next found frequencies corresponding to the resonant attenuation peaks, assuming that N and N + 1 are the numbers of half-waves stacking across the width of the plate II for two neighboring peaks, where N ≫ 1. In this case, it may be shown that the wave velocity value for the structure under study V = 2L( f2 − f1), where L is plate II width and f1 and f2 are the frequencies of two neighboring
Fig. 2. The frequency dependencies of the (a) insertion loss and (b) phase of the delay line under study without plate II.
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resonant peaks. For all plates II under study, L = 20 mm. Two values Vfr and Vsh of acoustic wave velocity with different values of the gap between the plates were found for all of the aforementioned structures. Here, Vfr is the wave velocity in the structure when all surfaces of plates are electrically free and Vsh is the wave velocity in the structure when the upper surface of plate II is electrically shorted. The electrical shorting was performed by deposition of thin layer of aluminum in vacuum. This allowed us to determine the electromechanical coupling coefficient as K2 = 2(Vfr − Vsh)/Vfr. To reduce the effect of random measurement errors, we averaged the frequency differences over all attenuation peaks observed. It has been found that the error of the measurement of f2 − f1 does not exceed ±3%. Therefore, the precision of the velocity determination is equal to ±3%. III. Theoretical Analysis and Comparison With Experimental Results
Fig. 3. The frequency dependencies of the insertion loss for the (Y-X)– (Z-X) LiNbO3 structure for three values of the gap: (a) 0 μm, (b) 20 μm, and (c) 31 μm.
We also performed numerical calculations of phase velocity and electromechanical coupling coefficient of acoustic waves for these structures by using a calculation procedure for the characteristics of acoustic waves propagating in piezoelectric plates which has been detailed in [4]. The calculations have shown that there should propagate waves which may be divided into three groups. The first group may involve nonpiezoactive waves propagating independently of one another in each of the plates. These waves are not coupled with each other. The second group includes waves that are piezoactive in one plate and nonpiezoactive in the other one. They are also independent. The third group consists of slot or coupled waves that are tied together by electric fields penetrating through the gap. Comparison between the calculated data and experimental results has been conducted. This comparison has shown the experimentally observed peaks to correlate with the slot waves in the considered structures. The phase velocity and electromechanical coupling coefficient values calculated for the (Y-X)–(Z-X) LiNbO3 structure are tabulated in Table I as an example. The values found experimentally are also indicated here. A good agreement between theory and experiment is seen for the slot wave with the shear-horizontal polarization (SH0). Similar situation was observed for all of the aforementioned investigated structures. Tables II, III, and IV present the calculated and measured results for the slot waves for other orientations of plate II.
TABLE I. Theoretical and Experimental Values of the Velocity and Electromechanical Coupling Coefficient of a Slot Wave in the (Y-X)–(Z-X) LiNbO3 Structure. Theory Gap = 0 μm, freq = 3.3 MHz Gap = 7 μm, freq = 3.3 MHz
Vfr (m/s)
Vsht (m/s)
4314.01 4322.33
4240.07 4275.44
Experiment K2
(%)
3.4 2.2
Vfr (m/s)
Vsht (m/s)
K2 (%)
4340 4320
4290 4290
2.5 1.4
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TABLE II. Theoretical and Experimental Values of the Velocity and Electromechanical Coupling Coefficient of Slot Wave in the (Y-X)–(Y-X) LiNbO3 Structure. Theory Gap = 0 μm, freq = 3.3 MHz Gap = 7 μm, freq = 3.3 MHz
Experiment
Vfr (m/s)
Vsht (m/s)
4446.43 4446.57
4117.98 4226.65
K2
(%)
14.2 9.6
Vfr (m/s)
Vsht (m/s)
K2 (%)
4490 4460
4220 —
11.7 —
TABLE III. The Theoretical and Experimental Values of the Velocity and Electromechanical Coupling Coefficient of Slot Wave in the (Y-X)–(Y-X+155°) LiNbO3 Structure. Theory Gap = 0 μm, freq = 3.3 MHz Gap = 7 μm, freq = 3.3 MHz
Experiment
Vfr (m/s)
Vsht (m/s)
4274.35 4294.32
4116.24 4225.42
K2
(%)
7.3 3.2
Vfr (m/s)
Vsht (m/s)
K2 (%)
4200 4220
4090 4090
5.2 6.2
TABLE IV. The Theoretical and Experimental Values of the Velocity and Electromechanical Coupling Coefficient of Slot Wave in the (Y-X)–(Y-X-140°) LiNbO3 Structure. Theory Gap = 0 μm, freq = 3.3 MHz Gap = 7 μm, freq = 3.3 MHz
Experiment
Vfr (m/s)
Vsht (m/s)
K2 (%)
Vfr (m/s)
Vsht (m/s)
K2 (%)
4140.79 4061.15
4106.47 4016.36
1.7 2.2
4090 4050
3970 3940
6 5.4
The obtained results have demonstrated two conditions which must be fulfilled to excite the slot wave in the structure of two parallel piezoelectric plates separated by the gap: 1) the waves propagating in each of the plates should be piezoactive; and 2) the velocities of the waves should be of nearly the same value. This conclusion was confirmed with an additional experiment in which the 128 Y-X LiNbO3 plate was used as plate II. It is obvious from Table V that there are no piezoactive waves in this plate which have the velocities on the order of 4200 to 4500 m/s. The velocity of the only piezoactive wave A0 is substantially lower. No resonant peaks were therefore observed at the amplitude-frequency characteristic of the structure under study in this case (Fig. 4). The only peak marked at the
characteristics is appropriate to excitation of a shear bulk wave propagating normally to the plate surface. IV. Conclusion This paper deals with the experimental investigation of acoustic waves propagating in a structure composed of two parallel piezoelectric plates separated by a vacuum (air) gap. It has been shown that the frequency dependencies of insertion loss may show equidistant resonant peaks of attenuation under certain conditions. These resonant peaks are observed for the structures containing a piezoplate II made of lithium niobate ~500 μm thick with the following crystallographic orientations: Z-X, Y-X, Y-X+155°, and Y-X+140°. The theoretical analysis has been undertaken for acoustic waves propagating in the structure. It has demonTABLE V. The Theoretical Values of the Velocity and Electromechanical Coupling Coefficient of a Plate Wave in the Plate of 128°Y-X LiNbO3 (Plate Thickness = 0.5 mm). Vfr (m/s)
Fig. 4. The frequency dependency of the insertion loss for the (Y-X)– (128°Y-X) LiNbO3 structure.
3230.76 4140.79 4030.78 4030.65 4649.32 6267.61 6547.31 6547.31
Vsht (m/s)
K2 (%)
3157.27 4106.47 4030.78 4027.24 4649.32 6258.45 6547.31 6547.31
4.5 1.7 0 0.2 0 0.3 0 0
borodina et al.: acoustic waves in a structure containing two plates separated by a gap
strated the resonant nature of the frequency dependencies of insertion loss to be related to the propagation of slot acoustic waves. It has been shown that the slot waves in the structure consisting of two piezoelectric plates separated by a gap can exist under certain conditions, namely: 1) the acoustic waves propagating in each of the plates must be piezoactive, and 2) velocities of the waves must be close in value. The structures described may be employed for noncontact excitation of acoustic waves in piezoelectric plates. An electric field of a piezoactive wave propagating in one of the plates will penetrate through the vacuum into the other plate and excite an acoustic wave traveling in the same direction. In this case, the electric field of the initial wave will act as an interdigital transducer. The structure under study may be used for the development of liquid and gas sensors. It has been shown in [6] that the velocity of a slot wave depends on the permittivity of the medium filling the gap. Therefore, a change in the medium composition will cause a change in the wave velocity and frequencies of the resonant peaks of wave attenuation. This effect may allow monitoring of the composition of a gas or liquid medium. Finally, the aforementioned structure may also be used for measuring the temperature. It is obvious that variations of the temperature will cause change in wave velocity and frequencies of the resonant attenuation peaks. The availability of an appropriate calibration curve will allow for monitoring of the temperature.
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References [1] Y. V. Gulyaev and V. P. Plesskii, “Acoustic gap waves in piezoelectric materials,” Sov. Phys. Acoust., vol. 23, no. 5, pp. 410–413, 1977. [2] M. K. Balakirev and A. V. Gorchakov, “Coupled surface waves in piezoelectrics,” Sov. Phys. Solid State, vol. 19, no. 2, pp. 355–356, 1977. [3] C. Mayerfild and P. Tornois, “Pure shear elastic wave guided by the interface of the two semi-infinite media,” Appl. Phys. Lett., vol. 19, no. 4, pp. 117–121, 1971. [4] M. Yu. Dvoesherstov, V. I. Cherednik, S. G. Petrov, and A. P. Chirimanov, “Numerical analysis of the properties of slot electroacoustic waves,” Acoust. Phys., vol. 50, no. 6, pp. 670–676, 2004. [5] P. A. Pyatakov, “Shear horizontal acoustic waves at the boundary of two piezoelectric crystals separated by a liquid layer,” Acoust. Phys., vol. 47, no. 6, pp. 739–745, 2001. [6] M. Veleekoop, “Acoustic wave sensors and their technology,” Ultrasonics, vol. 36, no. 1–5, pp. 7–14, 1998. [7] M. Yu. Dvoesherstov and V. I. Cherednik, “Plate and gap acoustic waves for highly sensitive gas and liquid sensors,” in IEEE Ultrasonics Symp., 2004, vol. 2, pp. 1553–1556. [8] M. K. Balakirev, S. V. Bogdanov, A. V. Gorchakov, and A. E. Chakushin, “Experimental study of gap waves in LiIO3,” Sov. Phys. Solid State, vol. 21, no. 8, pp. 1448–1450, 1979. [9] I. A. Borodina, S. G. Joshi, B. D. Zaitsev, and I. E. Kuznetsova, “Acoustic waves in thin plates of lithium niobate,” Acoust. Phys., vol. 46, no. 1, pp. 33–37, 2000. [10] B. D. Zaitsev, S. G. Joshi, and I. E. Kuznetsova, “Characteristics of quasi-shear horizontal (QSH) acoustic waves in thin piezoelectric plates,” in IEEE Ultrasonics Symp., 1998, vol. 1, pp. 138–141. [11] B.D. Zaitsev, A.M. Shikhabudinov, A.A. Teplykh, and I.E. Kuznetsova, “The method of noncontact measurement of the permittivity,” Russian Federation Patent 2 442 179, Apr. 21, 2009. [12] B. D. Zaitsev, S. G. Joshi, and I. E. Kuznetsova, “Investigation of quasi-shear-horizontal acoustic waves in thin plates of lithium niobate,” Smart Mater. Struct., vol. 6, no. 6, pp. 739–744, 1997.
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Correspondence Acoustic Waves in a Structure Containing Two Piezoelectric Plates Separated by an Air (Vacuum) Gap Irina A. Borodina, Boris D. Zaitsev, Senior Member, IEEE, Iren E. Kuznetsova, Member, IEEE, and Andrey A. Teplykh Abstract—This paper presents experimental results for the characteristics of acoustic waves propagating in a structure containing two parallel piezoelectric plates (I and II) separated by an air gap. Plate I, made of Y-X lithium niobate, contained two interdigital transducers that excited and received an acoustic wave with shear-horizontal polarization. Piezoelectric plate II, made of lithium niobate, was placed above and between the transducers, separated by a fixed gap. For its certain orientation, the amplitude-frequency characteristic showed sharply defined resonant attenuation peaks, which were situated at an equidistant separation from each other. The depth of the peaks was observed to decrease with a wider gap between the plates. It has been stated that these peaks are associated with the resonant reflections of a slot acoustic wave across the width of plate II. Experimentally determined phase velocities and electromechanical coupling coefficient for the slot wave in the structure under study are in a good agreement with theoretical values for various crystallographic orientations of plate II. A comparison between the experimental and theoretical results has allowed us to state two conditions for the slot wave to exist. The structures described may be employed for noncontact excitation of acoustic waves in the plates and for the development of various liquid, gas, and temperature sensors.
I. Introduction
S
lot waves propagating in the structure of two piezoelectric elements separated by an air (vacuum) gap have been theoretically investigated in detail [1]–[4]. The investigated structures contained 1) two semi-infinite media [1]–[3], 2) a semi-infinite medium and a piezoplate [4], and 3) two piezoplates [4]. The characteristics of these slot waves, such as phase velocity, electromechanical coupling coefficient, and temperature coefficient of delay as a function of gap between the piezoelectrics and their material properties, were studied. The waves propagating in the structure of two piezoelectrics separated by the liquid layer [3] have also been theoretically analyzed. The prospect of the use of these waves for the development of gas,
Manuscript received June 3, 2013; accepted September 13, 2013. The work is partially financially supported by the Ministry of Education and Science of Russian Federation (contract 8400) and the Russian Foundation of Basic Research (12-02-01057a, 12-02-31757mol-a, and 13-0200596a). I. A. Borodina, B. D. Zaitsev, and A. A. Teplykh are with the Institute of Radio Engineering and Electronics of the Russian Academy of Sciences, Saratov Branch, Saratov, Russia (e-mail: [email protected]). I. E. Kuznetsova is with the Institute of Radio Engineering and Electronics of the Russian Academy of Sciences, Moscow, Russia. DOI http://dx.doi.org/10.1109/TUFFC.2013.2867 0885–3010/$25.00
liquid, and temperature sensors has been shown [5], [6]. It has been demonstrated that the existence of the slot waves is connected with piezoeffect and that waves’ polarization depends on the crystallographic orientation of the piezoelectrics. The surface slot waves propagating in a structure containing two piezoelectrics have been studied experimentally [7]. The slot waves in the structure containing two piezoelectric plates were not investigated experimentally, although it is common knowledge that acoustic waves propagating in piezoelectric plates being thin compared with the wavelength exhibit higher electromechanical coupling coefficient than that of surface acoustic waves [8]. Because electric fields accompanying such waves greatly penetrate into air (vacuum), we can significantly vary wave characteristics by affecting these fields. It has been, for example, demonstrated that the phase of acoustic wave may be varied over a wide range by bringing the plate near a conducting plane [9]. The acoustic wave phase velocity would be affected by placing a dielectric sample at a certain distance from the plate and the dielectric permittivity of the sample can be obtained from the known calibration curve [10]. One can also change the characteristics of acoustic wave in a structure containing two piezoelectric plates separated by a gap. Phase velocity and electromechanical coupling coefficient of the slot wave in this structure is altered by varying the distance between the plates [4]. It has been shown that the study of the slot waves is not only of fundamental, but also of practical interest, particularly for the development of acoustic sensors [5], [6]. Therefore, this paper reports detailed experimental results for the slot acoustic wave propagating in a structure containing two piezoelectric plates separated by the gap, and compares the results with the data from theoretical analysis. II. Experimental Results For carrying out the experiments, a device was fabricated that included a Y-X LiNbO3 plate with lateral dimensions of 22 × 52 mm placed on a special support. The support was a rectangular frame of acrylic glass with thickness of 6 mm with outside and inside dimensions of 60 × 80 mm and 18 × 48 mm, respectively. The lithium niobate plate carrying two interdigital transducers (IDTs) on the lower side was glued by epoxy to the frame so that both sides of plate between the IDTs were mechanically free (Fig. 1). The initial plate thickness was 500 μm. To be able to reduce the thickness of the plate in the course of the experiments while preserving its flatness, ten reference silicon samples of greater hardness than lithium niobate were glued along the perimeter of the frame. These samples had the initial thickness of 500 μm and lateral dimensions of 8 × 8 mm. The lithium niobate plate and the
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Fig. 1. The scheme of the delay line under study: 1 = piezoelectric plate I (Y-X LiNbO3); 2 = IDT; 3 = acrylic glass support; 4 = piezoelectric plate II; 5 = the reference silicon samples; 6 = reflection-reducing edge geometry of plate I.
reference silicon samples were lapped by aluminum oxide abrasive powders of sizes 14, 10, and 5 μm on a glass polishing pad down to 200 μm [11]. To prevent of the abrasive powder from spilling over onto the plate surface carrying the IDTs, the window was covered by Scotch tape (Nova Roll Ltd., Moscow, Russia). Control of the plate thickness and flatness was performed by vertical optimeter with the scale division of 2.5 μm. Each IDT contained five pairs of split electrodes with an aperture of 8 mm and a period of 1.2 mm. The spacing between the IDTs was 27 mm. The transducers excited and received an SH0 wave that propagated along the X-axis. The operating frequency band of the delay line was 2.5 to 3.9 MHz. The opposite edges of the plate were wave-shaped with the depth of ~λ/2 (where wavelength λ = 1.2 mm) to prevent reflections (Fig. 1). At first, we studied the delay line parameters under pulsed operation in the absence of the upper plate II. Measurements demonstrated the insertion loss to be 25 dB at a central frequency of 3.3 MHz. The power of the main signal exceeded that of all spurious signals by more than 30 dB. This enabled us to carry out the measurements in a continuous regime by using the Agilent E5071C meter of S-parameters (Agilent Technologies Inc., Santa Clara, CA). Figs. 2(a) and 2(b) demonstrate frequency dependencies for the insertion loss and phase of the delay line under study, respectively. Then, we placed the plate II onto the delay line. For the upper plate, we used lithium niobate plates with thicknesses ~500 μm with the following crystallographic orientations: Z-X, Y-X, Y-X+155°, Y-X+140°, and 128° Y-X. In all cases discussed, excluding the structure (Y-X)–(128° Y-X) LiNbO3, the frequency dependence of insertion loss
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showed sharp peaks of resonant attenuation. As an example, the insertion loss dependences are indicated in Figs. 3(a), 3(b), and 3(c) for the (Y-X)–(Z-X) LiNbO3 structure with gaps of 0, 20, and 31 μm, respectively. The gap between plates I and II was controlled by using a set of aluminum foil strips with thicknesses of 7, 20, and 31 μm and lateral dimensions of 10 × 10 mm. These strips were set on the edges of the lower LiNbO3 plate and the upper plate was placed on the strips. To flatten the strips, the upper plate was pressed by a load of ~15 g. It was observed that the value of resonant peaks decreased with a wider gap. To excite the deep resonant peaks, two conditions should be met: 1) the edges of the upper plate II of lithium niobate must be parallel, and 2) they must be parallel to the acoustic wave-fronts. Therefore, when the upper plate is rotated, all resonances disappeared. We next found frequencies corresponding to the resonant attenuation peaks, assuming that N and N + 1 are the numbers of half-waves stacking across the width of the plate II for two neighboring peaks, where N ≫ 1. In this case, it may be shown that the wave velocity value for the structure under study V = 2L( f2 − f1), where L is plate II width and f1 and f2 are the frequencies of two neighboring
Fig. 2. The frequency dependencies of the (a) insertion loss and (b) phase of the delay line under study without plate II.
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resonant peaks. For all plates II under study, L = 20 mm. Two values Vfr and Vsh of acoustic wave velocity with different values of the gap between the plates were found for all of the aforementioned structures. Here, Vfr is the wave velocity in the structure when all surfaces of plates are electrically free and Vsh is the wave velocity in the structure when the upper surface of plate II is electrically shorted. The electrical shorting was performed by deposition of thin layer of aluminum in vacuum. This allowed us to determine the electromechanical coupling coefficient as K2 = 2(Vfr − Vsh)/Vfr. To reduce the effect of random measurement errors, we averaged the frequency differences over all attenuation peaks observed. It has been found that the error of the measurement of f2 − f1 does not exceed ±3%. Therefore, the precision of the velocity determination is equal to ±3%. III. Theoretical Analysis and Comparison With Experimental Results
Fig. 3. The frequency dependencies of the insertion loss for the (Y-X)– (Z-X) LiNbO3 structure for three values of the gap: (a) 0 μm, (b) 20 μm, and (c) 31 μm.
We also performed numerical calculations of phase velocity and electromechanical coupling coefficient of acoustic waves for these structures by using a calculation procedure for the characteristics of acoustic waves propagating in piezoelectric plates which has been detailed in [4]. The calculations have shown that there should propagate waves which may be divided into three groups. The first group may involve nonpiezoactive waves propagating independently of one another in each of the plates. These waves are not coupled with each other. The second group includes waves that are piezoactive in one plate and nonpiezoactive in the other one. They are also independent. The third group consists of slot or coupled waves that are tied together by electric fields penetrating through the gap. Comparison between the calculated data and experimental results has been conducted. This comparison has shown the experimentally observed peaks to correlate with the slot waves in the considered structures. The phase velocity and electromechanical coupling coefficient values calculated for the (Y-X)–(Z-X) LiNbO3 structure are tabulated in Table I as an example. The values found experimentally are also indicated here. A good agreement between theory and experiment is seen for the slot wave with the shear-horizontal polarization (SH0). Similar situation was observed for all of the aforementioned investigated structures. Tables II, III, and IV present the calculated and measured results for the slot waves for other orientations of plate II.
TABLE I. Theoretical and Experimental Values of the Velocity and Electromechanical Coupling Coefficient of a Slot Wave in the (Y-X)–(Z-X) LiNbO3 Structure. Theory Gap = 0 μm, freq = 3.3 MHz Gap = 7 μm, freq = 3.3 MHz
Vfr (m/s)
Vsht (m/s)
4314.01 4322.33
4240.07 4275.44
Experiment K2
(%)
3.4 2.2
Vfr (m/s)
Vsht (m/s)
K2 (%)
4340 4320
4290 4290
2.5 1.4
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TABLE II. Theoretical and Experimental Values of the Velocity and Electromechanical Coupling Coefficient of Slot Wave in the (Y-X)–(Y-X) LiNbO3 Structure. Theory Gap = 0 μm, freq = 3.3 MHz Gap = 7 μm, freq = 3.3 MHz
Experiment
Vfr (m/s)
Vsht (m/s)
4446.43 4446.57
4117.98 4226.65
K2
(%)
14.2 9.6
Vfr (m/s)
Vsht (m/s)
K2 (%)
4490 4460
4220 —
11.7 —
TABLE III. The Theoretical and Experimental Values of the Velocity and Electromechanical Coupling Coefficient of Slot Wave in the (Y-X)–(Y-X+155°) LiNbO3 Structure. Theory Gap = 0 μm, freq = 3.3 MHz Gap = 7 μm, freq = 3.3 MHz
Experiment
Vfr (m/s)
Vsht (m/s)
4274.35 4294.32
4116.24 4225.42
K2
(%)
7.3 3.2
Vfr (m/s)
Vsht (m/s)
K2 (%)
4200 4220
4090 4090
5.2 6.2
TABLE IV. The Theoretical and Experimental Values of the Velocity and Electromechanical Coupling Coefficient of Slot Wave in the (Y-X)–(Y-X-140°) LiNbO3 Structure. Theory Gap = 0 μm, freq = 3.3 MHz Gap = 7 μm, freq = 3.3 MHz
Experiment
Vfr (m/s)
Vsht (m/s)
K2 (%)
Vfr (m/s)
Vsht (m/s)
K2 (%)
4140.79 4061.15
4106.47 4016.36
1.7 2.2
4090 4050
3970 3940
6 5.4
The obtained results have demonstrated two conditions which must be fulfilled to excite the slot wave in the structure of two parallel piezoelectric plates separated by the gap: 1) the waves propagating in each of the plates should be piezoactive; and 2) the velocities of the waves should be of nearly the same value. This conclusion was confirmed with an additional experiment in which the 128 Y-X LiNbO3 plate was used as plate II. It is obvious from Table V that there are no piezoactive waves in this plate which have the velocities on the order of 4200 to 4500 m/s. The velocity of the only piezoactive wave A0 is substantially lower. No resonant peaks were therefore observed at the amplitude-frequency characteristic of the structure under study in this case (Fig. 4). The only peak marked at the
characteristics is appropriate to excitation of a shear bulk wave propagating normally to the plate surface. IV. Conclusion This paper deals with the experimental investigation of acoustic waves propagating in a structure composed of two parallel piezoelectric plates separated by a vacuum (air) gap. It has been shown that the frequency dependencies of insertion loss may show equidistant resonant peaks of attenuation under certain conditions. These resonant peaks are observed for the structures containing a piezoplate II made of lithium niobate ~500 μm thick with the following crystallographic orientations: Z-X, Y-X, Y-X+155°, and Y-X+140°. The theoretical analysis has been undertaken for acoustic waves propagating in the structure. It has demonTABLE V. The Theoretical Values of the Velocity and Electromechanical Coupling Coefficient of a Plate Wave in the Plate of 128°Y-X LiNbO3 (Plate Thickness = 0.5 mm). Vfr (m/s)
Fig. 4. The frequency dependency of the insertion loss for the (Y-X)– (128°Y-X) LiNbO3 structure.
3230.76 4140.79 4030.78 4030.65 4649.32 6267.61 6547.31 6547.31
Vsht (m/s)
K2 (%)
3157.27 4106.47 4030.78 4027.24 4649.32 6258.45 6547.31 6547.31
4.5 1.7 0 0.2 0 0.3 0 0
borodina et al.: acoustic waves in a structure containing two plates separated by a gap
strated the resonant nature of the frequency dependencies of insertion loss to be related to the propagation of slot acoustic waves. It has been shown that the slot waves in the structure consisting of two piezoelectric plates separated by a gap can exist under certain conditions, namely: 1) the acoustic waves propagating in each of the plates must be piezoactive, and 2) velocities of the waves must be close in value. The structures described may be employed for noncontact excitation of acoustic waves in piezoelectric plates. An electric field of a piezoactive wave propagating in one of the plates will penetrate through the vacuum into the other plate and excite an acoustic wave traveling in the same direction. In this case, the electric field of the initial wave will act as an interdigital transducer. The structure under study may be used for the development of liquid and gas sensors. It has been shown in [6] that the velocity of a slot wave depends on the permittivity of the medium filling the gap. Therefore, a change in the medium composition will cause a change in the wave velocity and frequencies of the resonant peaks of wave attenuation. This effect may allow monitoring of the composition of a gas or liquid medium. Finally, the aforementioned structure may also be used for measuring the temperature. It is obvious that variations of the temperature will cause change in wave velocity and frequencies of the resonant attenuation peaks. The availability of an appropriate calibration curve will allow for monitoring of the temperature.
2681
References [1] Y. V. Gulyaev and V. P. Plesskii, “Acoustic gap waves in piezoelectric materials,” Sov. Phys. Acoust., vol. 23, no. 5, pp. 410–413, 1977. [2] M. K. Balakirev and A. V. Gorchakov, “Coupled surface waves in piezoelectrics,” Sov. Phys. Solid State, vol. 19, no. 2, pp. 355–356, 1977. [3] C. Mayerfild and P. Tornois, “Pure shear elastic wave guided by the interface of the two semi-infinite media,” Appl. Phys. Lett., vol. 19, no. 4, pp. 117–121, 1971. [4] M. Yu. Dvoesherstov, V. I. Cherednik, S. G. Petrov, and A. P. Chirimanov, “Numerical analysis of the properties of slot electroacoustic waves,” Acoust. Phys., vol. 50, no. 6, pp. 670–676, 2004. [5] P. A. Pyatakov, “Shear horizontal acoustic waves at the boundary of two piezoelectric crystals separated by a liquid layer,” Acoust. Phys., vol. 47, no. 6, pp. 739–745, 2001. [6] M. Veleekoop, “Acoustic wave sensors and their technology,” Ultrasonics, vol. 36, no. 1–5, pp. 7–14, 1998. [7] M. Yu. Dvoesherstov and V. I. Cherednik, “Plate and gap acoustic waves for highly sensitive gas and liquid sensors,” in IEEE Ultrasonics Symp., 2004, vol. 2, pp. 1553–1556. [8] M. K. Balakirev, S. V. Bogdanov, A. V. Gorchakov, and A. E. Chakushin, “Experimental study of gap waves in LiIO3,” Sov. Phys. Solid State, vol. 21, no. 8, pp. 1448–1450, 1979. [9] I. A. Borodina, S. G. Joshi, B. D. Zaitsev, and I. E. Kuznetsova, “Acoustic waves in thin plates of lithium niobate,” Acoust. Phys., vol. 46, no. 1, pp. 33–37, 2000. [10] B. D. Zaitsev, S. G. Joshi, and I. E. Kuznetsova, “Characteristics of quasi-shear horizontal (QSH) acoustic waves in thin piezoelectric plates,” in IEEE Ultrasonics Symp., 1998, vol. 1, pp. 138–141. [11] B.D. Zaitsev, A.M. Shikhabudinov, A.A. Teplykh, and I.E. Kuznetsova, “The method of noncontact measurement of the permittivity,” Russian Federation Patent 2 442 179, Apr. 21, 2009. [12] B. D. Zaitsev, S. G. Joshi, and I. E. Kuznetsova, “Investigation of quasi-shear-horizontal acoustic waves in thin plates of lithium niobate,” Smart Mater. Struct., vol. 6, no. 6, pp. 739–744, 1997.
