Enhanced electromechanical response of ferroelectret ultrasonic transducers under high voltage excitation

Introduction

Air coupled ultrasonic (ACUS) transducers are welcome in a broad range of applications in industry, medicine, non-destructive testing, etc. The main challenge of all ACUS techniques is the enormous acoustic impedance Z_A mismatch between air and transducers, which is responsible for the high attenuation of the information carrying signal between transmitter and receiver. One of the ways to overcome the problem is the use of piezoelectrics with low Z_A. Recently developed ferroelectrets (FEs), which are charged polymer foams,1^–3 possess the lowest known acoustic impedance among piezoelectric materials. Although several polymers were proposed,4,5 FEs based on the internally charged cellular polypropylene (PP) films are the mainly used ones. Their piezoelectric activity originates from macroscopic dipoles formed by the charges located at walls of the lens-like voids1,2 and provides, in combination with low density and extreme softness, a promising solution for the ACUS transducers.6^–8 Polypropylene FEs have 2–3 order of magnitude lower Z_A than ceramic, polymer and ceramic polymer composite piezoelectric materials (Table 1). Consequently, replacement of a ceramic piezoelement by the FE one allows reducing the attenuation of sound energy at transducer/air interface by ∼50 dB.

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Table 1

Piezoelectric materials in comparison

Materials	FE film	Ferroelectric polymer film	Ceramic (PZT) polymer composite	Ceramics
Property	PP FE	Polyvinylidene fluoride		PZT
Density ρ/kg m−3	∼330	1780	1000–5000	4000–8000
Dielectric permittivity /10 kHz	1·12–1·23	12	50–500	150–3500
Dielectric losses tan δ/10 kHz	∼0·001	0·01–0·1	0·001–0·1	0·001–0·1
Coupling factor K33	0·04–0·12	0·11–0·15	0·65	0·35–0·55
Quasi-static piezoelectric coefficient	25–1200	20–25	50–300	70–600
d33/pC N−1	80–400
Sound velocity V3/m s−1	50–85	2200	∼3000	4000–6000
Acoustic impedance ZA/MRayl	∼0·03	3·9	6·5	25–37
	100–3000	0·19	42	∼0·6
Operating temperature/°C	−20…+50	…+80	…+150	…+300

*Values of the piezoelectric coefficient from literature.

Ferroelectrets differ essentially from the ceramic based piezoelectrics not only due to their density but also softness. They are nearly ideal dielectrics with a very low permittivity (∼1·1), low losses1,5 and high breakdown voltage.3,6,7 Unusually for electrets but similar to ferroelectrics, they can be repolarised by electric field demonstrating ferroelectric and piezoelectric hysteresis loops.1 Ferroelectrets are anisotropic materials: they are extremely soft (Young's modulus9 Y∼1·5 MPa) and elastic only along the direction of remanent polarisation, i.e. perpendicular to the film surface. Therefore, only the longitudinal piezoelectric coefficient d₃₃ is large, comparable with that of piezoceramics1,2 and can be practically used.

Two parameters characterise efficiency of piezoelectric materials for ACUS applications: coupling factor K₃₃, which defines an efficiency of the energy transformation by the ultrasonic transducers, and acoustic impedance Z_A, which defines the transmission energy attenuation due to the impedance mismatch between the transducers and air. Consequently, ACUS figure of merit was derived6,7 (1) Low K₃₃ of PP FEs is compensated by their extremely low Z_A and advantages of FE PP are clearly seen in comparison (Table 1). Efficiency and high sensitivity of the PP FE transducers was proved in the ultrasonic experiment.7 Scanned images of the inhomogeneous relief object (Fig. 1a), taken by PP FE transducers in both pulse echo (Fig. 1b) and transmission (Fig. 1c) modes, demonstrated that non-contact ultrasonic testing and imaging with FE transducers is possible. To make it real, efficiency, sensitivity and construction of the FE transducers should be further improved.

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Figure 1

Non-contact ultrasonic imaging with PP FE transducers7:

Essential improvement of the important parameters of PP FEs such as piezoelectric coefficient, coupling factor and FOM was achieved by optimisation of the film mesostructure and softness using the inflation process.9,10 The optimisation results in the increase in d₃₃ and K₃₃ by a factor of 2, while Z_A does not change essentially. The FOM increase by more than order of its magnitude is demonstrated (Fig. 2). Furthermore, FE PP transducers were better adjusted to the ultrasonic system. Integration of a preamplifier with high electric impedance matching increases sensitivity of the receiver by ∼40 dB.10 As a way of further progress, the authors propose to use non-linear electromechanical properties of the PP FE transmitter.

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Figure 2

Optimisation of PP FE properties by inflation process:9,10 a coupling coefficient K₃₃, b acoustic impedance Z_A, c figure of merit FOM and d piezoelectric coefficient d₃₃ of differently inflated PP FE films versus their density; symbols correspond to experimental points; dash lines denote reference values of standard not optimised PP FE film; for comparison, dash–dot lines denote values achieved by high voltage excitation of PP1 film with rather low sensitivity (see the section ‘Non-linear electromechanical response of FE transmitter’)

Non-linear electromechanical response of FE transmitter

Non-linear behaviour is a natural feature of a soft and sensitive material. One can suppose a considerable non-linear contribution to the electromechanical properties of FEs, more pronounced than in hard ceramic or composite piezoelectrics. Low dielectric losses1,5 and high breakdown voltage3,6,7 of PP FEs enable application of a high electric field to increase the expected non-linear contribution.

Indeed, ultrasonic transmission between two air coupled PP FE transducers in dependence on the amplitude of the high voltage exciting pulse V₁ revealed a strongly non-linear electromechanical response of the FE transmitter.11 The same experimental set-up is used for extended investigations. Short rectangular electric pulses of both polarities with amplitude V₁ from −3500 V to +3500 V and a length of 1 μs were applied to the FE transmitter with a rate of 15 pulses per second. The acoustic decaying sine burst generated at the thickness resonance frequency of the FE film propagates through 15 cm air path to the FE receiver where it is further transformed into the electric decaying sine burst with a peak to peak amplitude V₂. The pulse amplitude V₁ is considered as positive if the applied voltage polarity is the same as that of remanent polarisation P_r and as negative if the applied voltage polarity is opposite to that of P_r. Several kinds of the commercially available EMFIT PP FE films12 were used as an active part of FE transducer, including the less sensitive PP1 (nominal d₃₃∼70–80 pC N⁻¹) and more sensitive PP3 and PP4 (d₃₃∼200 pC N⁻¹). Polypropylene films of the same type were used in the transmitter–receiver pair.

Transmission characteristics V₂(V₁) of all studied transducers are significantly non-linear and asymmetric regarding polarity of the exciting pulse (Fig. 3). The second zero transmission point at positive exciting voltage (V₁∼+1200 V for PP3 and PP4 transducers) evidences a compensation of the contributions of competing mechanisms. The authors describe these transmission characteristics by promotion and competition of the piezoelectric and electrostriction contributions following the simple model used in Ref. 11. Thickness change of the transmitter FE film Δh₁ due to application of the exciting voltage V₁ consists of the piezoelectric Δh_1d and electrostriction Δh_1α contributions (see Fig. 4a) (2) where is an inverse electromechanical transducer constant of the transmitter, d₃₃ and α₃₃ are piezoelectric coefficient and electrostriction constant respectively. Then is dependent on the exciting voltage (3) Accounting for different signs of d₃₃ and α₃₃ (d₃₃>0 and α₃₃<0), electrostriction enhances piezoelectric effect at negative V₁ and competes with it at positive V₁ (Fig. 4). Consequently, a compensation point corresponding to Δh₁ = 0 at V_C = −d₃₃/α₃₃ is observed.

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Figure 3

Transmission characteristics V₂(V₁) of PP1, PP3 and PP4 FE transducers: symbols denote experimental points; lines correspond to fits to equation (5) accounting for piezoelectric and electrostriction contributions

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Figure 4

Schematic presentation of piezoelectric and electrostriction contributions to electromechanical response of FE transducer:

The V₂(V₁) relation can be written as following11 (4) where and are inverse and direct electromechanical transducer constants of the transmitter and receiver, a>0 is a parameter accounting for the signal attenuation due to the acoustic impedance mismatch at transducer/air interfaces, absorption in the air path, experiment imperfections (relative transducer orientation, etc.) and difference in the V₁ and V₂ definition (rectangular pulse amplitude and peak to peak burst amplitude respectively). In the first approach a is considered to be independent on V₁. The absolute value in equation (4) reflects the definition of V₂ as a peak to peak burst amplitude. The phase of the received signal is not taken into account and the V₂ value is always positive, independent on the sign of Δh₁ and . The FE receiver works in a linear (low strain/low field) regime, at least for sound pressure below 3000 Pa.11,13 Therefore, , accounting that coefficients of the inverse and direct piezoelectric effect are equal14,15 for identical PP FE films of transmitting and receiving transducers. Then equation (4) can be rewritten as (5) Consequently, the V₂(V₁) characteristic caused by piezoelectric and electrostriction contributions contains a zero transmission point at V_C (Fig. 4b) and is similar to the experimentally observed ones (Fig. 3). Experimental data for all studied FE transducers can be fitted well to the equation (5), at least under the moderate exciting voltage between −1500 and +2000 V. In this range, the electromechanical response of PP FE transducers and transmission characteristics can be completely described by piezoelectric and electrostriction effects.

The piezoelectric contribution dominates only at a low exciting voltage; the electrostriction contribution should be taken into account at abs{V₁}>100 V (Fig. 5a). In this case an amplitude transmission coefficient is defined by the voltage dependent inverse transducer constant (3) (6) In the low excitation limit (V₁→0), and . Then the normalised amplitude transmission coefficient T_V(V₁)/T_V(0) is equal to the absolute value of the normalised inverse transducer constant (7) In the case of negative exciting pulse amplitude V₁, α₃₃V₁/d₃₃>0 provides a monotonic, linear increase in the normalised inverse transducer constant with the increasing pulse amplitude (Fig. 5b). While in the case of positive exciting pulse amplitude, α₃₃V₁/d₃₃<0 and the electrostriction contribution compensates the piezoelectric one and results in reduction of the normalised inverse transducer constant. At the compensation point V_C = −d₃₃/α₃₃ (V_C∼+1200 V for PP3 and PP4 transducers), .

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Figure 5

Piezoelectric (dash line) and electrostriction (dash–dot line) contributions to electromechanical response of PP1, PP3 and PP4 FE transducers: symbols denote experimental points; solid lines correspond to fits to equations (5) and (7):

The electrostriction contribution to t₃₃ in PP FEs can be attributed to the electrostatic force between electrodes14 and Maxwell stress effect.16 Both mechanisms are particularly important in soft dielectrics with a low Young's modulus of elasticity and can provide essential contributions. Similarity of the dc bias effect3 and high voltage excitation11 supports attribution of the electrostriction effect to the electrostatic force between two electrodes, while the relation between electrostriction and piezoelectric coefficients11 supports presence of the Maxwell stress contribution in the electrostrictive response. In the case of PP FEs, the electrostriction constant α₃₃ describes probably contributions of both mechanisms mentioned above.

Discussion

Increase in the input signal amplitude V₁ in ∼10 times (from the standard 300 to ∼3000 V) results in the tenfold (20 dB) increase in the output signal amplitude V₂ in the case of linear electromechanical response (t₃₃ = d₃₃). Electrostriction enhances piezoelectric effect (in the case of negative pulse amplitude) and provides significant enlargement of the transducer constant, e.g. by a factor of 4 comparatively to d₃₃ for the PP1 transducer (Fig. 5b). It corresponds to increase in the transmission coefficient T_V by a factor of 4 (in 12 dB). Added together, the output signal and the signal to noise ratio of the PP–FE based ACUS system can be increased by a factor of 40 (by 32 dB). Let us note that high voltage excitation of the FE film with a rather low sensitivity (such as PP1) enlarges its transducer constant to the d₃₃ level of the best high sensitive films (Fig. 2d). Therefore, the use of high voltage exciting pulses with negative amplitude is strongly recommended for effective application of PP FE transmitters.

The non-linear electromechanical properties of the PP FE result in a strong increase in its ACUS figure of merit under the high voltage excitation11 which exceeds results of the PP FE technological optimisation (Fig. 2c). The FOM enlargement can be related to the increase in coupling factor and to the decrease in acoustic impedance. Acoustic impedance is defined by the FE film density ρ and sound velocity v (Ref. 15) (8) where m, S and h are mass, surface and thickness of the film and F_R is the frequency of its thickness resonance. Consequently, the decrease in acoustic impedance under high voltage excitation is proportional to the decrease in F_R. The experimentally observed decrease in F_R does not exceed 5% even for the more sensitive FE film PP4 (Fig. 6), and thus Z_A depends weakly on the applied voltage. Therefore, it can be concluded that the strong increase in FOM under high voltage excitation is mainly related to the increase in coupling factor K₃₃. In the case of less sensitive FE film PP1, the high voltage excitation results in the FOM increase in 256 times11 and in the correspondent K₃₃ increase in ∼4 times (Fig. 2a).

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Figure 6

Frequency dependences of normalised transmission amplitude of PP4 transducers near their thickness resonance frequency at a negative and b positive excitation voltage V₁ obtained by Fourier transformation of transmitted burst

The FOM enlargement describes improvement of transmitter parameters only, while the receiver parameters remain unchanged by the high voltage excitation. Therefore, a real benefit of the ACUS system from the non-linear electromechanical response of the FE transmitter should be described correctly by the square root of its normalised FOM enlargement11 where FOM₀ is a figure of merit at low excitation voltage (e.g. estimated by the impedance measurements). That is, the ACUS system power transmission coefficient T_W increases by a factor of 16 (in 12 dB) for the PP1 FE transducer. It corresponds to the amplitude transmission coefficient T_V increase by a factor of 4 caused by the t₃₃ enlargement.

Summarising, non-linear properties of PP FEs are very useful for their applications utilising an inverse piezoelectric effect. The high voltage excitation provides a significant (in a few times) enhancement of the FE actuator and transmitter efficiency. We recommend using the non-contact FE PP transmitters with a high voltage excitation in non-destructive testing and other ACUS applications. Enhanced efficiency of the FE transducers without matching layers allows realisation of their advantage of broad band response. This exactly meets the requirements of the pulse echo technique. The electromechanical non-linearity of PP FE transducers can additionally expand their bandwidth. These and other aspects the FE non-linear response will be the subject of our further study.

Conclusion

A strongly non-linear electromechanical response of the PP FEs was revealed and described by promotion and competition of the piezoelectric and electrostriction contributions. The non-linear electromechanical properties are proposed to be used for efficiency increase in the FE transmitter. Enlargement of the inverse transducer constant of the PP FE film by a factor of 4 was demonstrated. The non-linear EM properties of the PP FEs result in a strong increase in their ACUS figure of merit under the high voltage excitation which exceeds results of the technological optimisation. Consequently, enhancement of the ACUS system transmission in 12 dB and signal to noise ratio in 32 dB was achieved. The non-contact FE PP transmitters with a high voltage excitation are recommended for non-destructive testing and other ACUS applications.