# The Piezoelectric Effects and Its Applications

## Introduction

Have you ever wondered how most of the appliances and gadgets you use at home, workplace, or those used in the industries operate? To a large extent, the principles of the piezoelectric effect are applied in most of these devices, from your car to your phone.

The piezoelectric effect in Quartz was discovered by the Curie brothers – Pierre and Jacques Curie — in 1880. They demonstrated this effect with natural crystals; to this effect, they combined their knowledge about the pyroelectric effect and the structures of crystals.

The reverse piezoelectric effect was discovered in 1881 by Gabriel Lippmann through his understanding of the mathematical model of the piezoelectric effect [1]. These discoveries were of no practical use till a French Professor, P. Langevin, in 1917 used the plates of a Quartz crystal to detect acoustic waves in water; this eventually leads to the development of sonar [2]. In 1927 [1], A Meissner proposed an explanatory model of the piezoelectric effect.

This article presents a detailed explanation of the piezoelectric effect, the general piezoelectric materials, their process of fabrication, the applications of the piezoelectric effects in the development of piezoelectric nanomaterials (PN), energy harvesting devices, piezoelectric sensors, and actuators.

## The Piezoelectric Effect

The term “piezoelectric” is a compound word that is derived from the Greek words: piezein, which means to press or squeeze; and elektron, which means amber and basically describes electrostatic charges. Therefore, in simple terms, the piezoelectric effect describes the production of electric charges when a piezoelectric material is subjected to elastically deformational stress.

The piezoelectric effect is produced in a crystalline structured material when the structure is disturbed. The materials are normally polarized: this means there are finely aligned electric dipoles inside the material and the disturbance causes a misalignment of the dipoles – depolarization.

The initial polarization causes a stable electric field, while the change in polarization results in a change in the dielectric field. The piezoelectric effect is an A.C phenomenon.

This effect is described mathematically by the equations shown below. The simultaneous equation uses tensor parameters to describe mechanical behaviors and the electric field.

The first equation depicts the transformation of an electric field into mechanical stress. Therefore, in the absence of an electric field, it becomes  . This shows the relationship between the distortion and the applied stress for an elastic material, that is the Hooke’s law.

The second equation depicts how the application of mechanical strain is transformed into an electric field. Therefore, in the absence of a mechanical stress, it becomes ; for a dielectric substance, this depicts the relationship between the electric displacement and the electric field strength.

Now, the charge coefficient for the direct piezoelectric effect  and that of the reverse piezoelectric effect  are nearly equal for the same material, hence they can both be taken as equal to d. with this in mind, manipulating both equations give:

Where K is called the electromechanical coupling coefficient. It shows the efficiency of the material in converting electric energy into mechanical energy and vice-versa. That is the materials efficiency for a piezoelectric effect and for a reverse piezoelectric effect.

## The General Piezoelectric Materials

From [3], piezoelectric materials can be classified into two categories.

• First, the naturally occurring crystals such as Quartz, Topaz, Tourmaline, Rochelle salt, and cane sugar.
• Second, the man-made materials such as lithium sulfhate, polarized ferroelectric ceramics such as the lead zirconate titanate (PZT), polyvinylidene fluoride (PVDF).

## The General Fabrication Process

The synthetically made piezoelectric materials are generally fabricated through the process called Poling. It involves [4].

• First, the fine PZT powder of the different metal oxides are mixed in specific proportions and then heated to form a powder. The formed piezoelectric powder is then mixed with an organic binder and is formed into structural elements of the desired shape – discs, rods, plates, etc. The element is then heated to a temperature above the Curie point, where the ferromagnetic properties of the crystal break down.
• Second, the heated material is then allowed to cool under a strong DC electric field. This ensures the alignment of all the dipoles in the material. The direction of alignment is determined by the direction of the applied electric field and the field strength

## Applications of the Piezoelectric Effect

There is a wide range of application of the piezoelectric effect. Some of these applications are in the areas of the development of piezoelectric nanomaterials, design of energy harvesters, piezoelectric sensors, and actuators. The next sections of this article explores the details of these applications.

## Piezoelectric Nanomaterials

Different research works have been conducted in the application of the piezoelectric effect at the nanoscale. This has birthed what is called the piezoelectric nanomaterial (PN) [5].

PNs are a class of nanomaterials and are the basis for the design of smart nanodevices and nanoelectronics. According to [6], the PNs are potential elements in making smart nanopiezoelectronics such as nanoresonators, nanosensors, nanoactuators, and nanogenerators.

The research in this area of material science necessitates the development of new fabrication techniques and theories other than those applicable to normal piezoelectric effects. The reason is that the characteristics of the piezoelectric effect at the macroscale are different at the nanoscale. These new theories are so that the behavior of the PN at the nanoscale can be interpreted.

The various piezoelectric properties have been studied using the following methods [5]

• Experimental techniques such as piezoelectric force microscope and direct tensile testing
• Atomistic simulations such as the molecular dynamics simulations, quantum mechanics calculations and computational simulations.

The various factors affecting the effective piezoelectric coefficients (EPC) or properties of the PNs include the small-scale effects, crystal orientation effects, temperature effect, surface adsorption, and finite strain.

The types of PNs, their applications, and methods of fabrication are as follows [5]:

1.Three-Dimensional PNs: These materials are available at both the macroscale and the nanoscale. They include

• Perovskite: The PNs with Perovskite crystal structures are made from materials like PZT and are majorly macroscale, with applications such as electromechanical sensors, actuators, and energy generators. There are also Perovskite Nanostructures that exhibit both piezoelectricity and ferroelectricity. This makes them applicable in phased-array radars and ferroelectric memories .The Perovskite nanostructures can be fabricated using techniques such as the Sol-gel template method, electrospinning, and sheet casting.
• The Wurtzite Structure: These PNs are made from materials such as ZnO, GaN, Indium Nitride, Zinc Sulfide etc. They exhibit less piezoelectric effects than the Perovskite types. They possess a synergy of piezoelectric and semiconducting properties called the nanopiezotronic effects. This makes them useful in making piezoelectric nanogenerators, nanotransistors , and nanodiodes.

The fabrication technique applied in their design is the hydrothermal method.

2. Two-Dimensional PNs: These materials are available only at the nanoscale and are classified into three groups.

• The single-atom layer of boron nitride nanotubes that can be used in developing smart nanomaterials. Its fabrication method includes arc discharge and laser-ablation.
• The family of trigonal-prismatically coordinated transition metal dichalcogenide crystals. They possess strong piezoelectric effects than Wurtzite materials. Their fabrication techniques include mechanical exfoliation and chemical vapor deposition.
• Chemically modified graphene which is basically carbon nanosheets. They have a zero band gap semi-metallic behavior and excellent mechanical responses, but they are intrinsically non-piezoelectric. To induce piezoelectricity in these materials, the fabrication is performed such that the graphene sheets are made to adsorb atoms on one of its sides.

## Energy Harvesting Applications

There are research works and prototypes on the extraction of the waste energy from the environment using the principles of the piezoelectric effect; in actual sense, they employ the reverse piezoelectric effect. Some of these works involved the collection of vibration energy produced by the movement of vehicles on the road, vibrational energy of fixed mechanical equipment, and from waste heat sources such as electronic chips.

Most piezoelectric energy harvesting devices are operated in mainly two modes [7]

• The 33-mode as shown in figure 1 below, where the direction of the applied stress and that of the generated voltage are the same.
• The 31-mode, as shown in figure 2, where the direction of the applied axial stress is orthogonal to that of the generated voltage.

Furthermore, the common structural design of these devices are stacked, cantilever beam, and cymbals  as shown in figure 3,4, and 5 respectively [7].

The research work in [7] successfully built a piezoelectric transducer box that was embedded experimentally in roads. Also according to [7], a road energy harvesting system that produces 250kW of electric power was invented in Israel in 2008.

A piezoelectric floor that lights up office LEDs exist in Japan. In [8], a thermal energy harvester that combines the piezoelectric effect and pyroelectric effect has been developed.

The device produced 0.54uW at a load resistance of 610Kohms.The major components of the device are the PZT arranged in a cantilever beam structure, a bimetal beam, a heat resonator, a linear slide, and two neodymium magnets.

## Piezoelectric Sensors

These are macro scale level devices that employ the piezoelectric effect in providing solutions to industrial practical problems. It should be noted that these devices are passive – they are powered only through the applied input stimulus.

Some of these sensors, their principle of operation, structural design, and applications are listed below

1.Piezoelectric Tactile Sensors: These can be fabricated from PVDF and can be made to operate in either passive or active modes depending on the application.

Figure 6 below shows the design of an active piezoelectric tactile sensor. The structural design is such that the PVDF film is placed between a central compression film made of silicon rubber. The amplifier and the demodulator setup can also be seen from the figure.

The operating principle is such that, if a mechanical compressing force is applied to the upper film, it generates a voltage that is sent to the input of the amplifier. Simultaneously, the compression is transmitted through the silicone rubber to the bottom film; a voltage signal is generated from this bottom film and it is sent to the demodulator so that the appropriate output AC voltage is produced.

These devices are used in electronic musical instruments such as electronic pianos. They are also applicable in robotics for detecting colliding motions.

2. Piezoelectric Accelerometers: This is a type of linear accelerometer that works by being attached to a moving platform; it does not require a stationary coordinate system. The basic mathematical principle it employs is the one that describes Newton’s second law of motion. These piezoelectric accelerometer devices are structured such that a piezoelectric material is sandwiched between the supporting structure and a proof mass; the proof mass s directly coupled to the piezoelectric material and exerts a force proportional to the acceleration.

There are various configurations for mounting the piezoelectric material and the proof mass on the accelerometer housing. These configurations are the compression coupling (a), the flexural coupling (b), and the shear coupling (c); all these are shown in figure 7 below.

3. Piezoelectric Force Sensors: These are also called piezoelectric force transducers. They basically transform an applied force into a varying electrical charge output. There are quite a few ways through which the output can be detected and measured.

• The output can be amplified using a charge amplifier.
• The output can be integrated as a resonator in an electronic oscillator

There is more information about the design, fabrication, and principle of operation of these devices in [9]. They find applications in pinball machines as a roll-over type switch, shaft rotation counter in natural gas meters, gear tooth counters in electric utility metering, and in textile plants for thread breakage monitoring.

## Piezoelectric Actuators

These are devices that use the principle of the reverse piezoelectric effect. Their applications can be grouped into three classes of smart actuators systems, which are [10]:

• Positioners,
• Motors, and
• Vibration suppressors

Some of the most common designs for these devices are the multilayer, bimorph, and moonie structures. These designs are shown in figure 7 below.

### Conclusion

This article successfully discussed the piezoelectric effect and its various applications cutting across nanoscience, energy harvesting, force sensing, and actuator systems.

There are still lots of applications of the piezoelectric effect that was not discussed, some of which include piezoelectric cables, ultrasonic sensors, airbag sensors, ceramic filters and resonators, piezoelectric buzzers, piezoelectric transformers, etc.

However, they all follow the same working principles as most of the devices listed in this article — there are only variances in their structural design.

### References

 [1] A. Ledoux, “Theory of Piezoelectric Materials and Their Applications in Civil Engineering,” Massachusetts Institute of Technology, 2011. [2] Jacob Fraden, Handbook of Modern Sensors, Springer, 2015. [3] T. Systems, “Comparng strain gauges to piezoelectric sensors,” Tacuna Systems, 2019. [Online]. Available: https://tacunasystems.com/knowledge-base/force-measurement-tips/comparing-strain-gauges-to-piezoelectric-sensors/. [4] Chapman and Hall, Electroceramics: Materials, Properties, and Applications, New York, 1990. [5] Jin Zhang, Chengyuan Wang, and Chris Bowen, “Piezoelectric Effects and Electromechanical Theories at The Nanoscale,” Nanoscale, vol. 6, no. 22, pp. 13314 – 13327, 2014. [6] Wang ZL, Song J., “Piezoelectric nanogenerators based on zinc oxide nanowire arrays,” Science, vol. 312, no. 5771, pp. 242-246, 2006. [7] Xiaochen Xu, Dongwei Cao, Hailu Yang, Ming He, “Application of Piezoelectric Transducer in Energy Harvesting in Pavement,” International Journal of Pavement Research and Technology, vol. 11, pp. 388-395, 2018. [8] Miwon Kang and Eric M. Yeatman, “Thermal Energy Harvesting Using Pyroelectric and Piezoelectric Effect,” Journal of Physics: Conference Series, vol. 773, no. 012073, 2016. [9] T. Systems, “Installing and Mounting Piezoelectric Force Transducers,” Tacuna Systems, 2019. [Online]. Available: https://tacunasystems.com/knowledge-base/force-measurement-tips/installing-and-mounting-piezoelectric-force-transducers/. [10] Kenji Uchino, “Introduction to Piezoelectric Actuators and Transducers,” International Center for Actuators and Transducers, Penn State University, 2003.