Issue 
Eur. Phys. J. Appl. Phys.
Volume 88, Number 1, October 2019
Materials for energy harvesting, conversion, storage and environmental engineering (Icome 2018)



Article Number  10901  
Number of page(s)  10  
Section  Physics of Energy Transfer, Conversion and Storage  
DOI  https://doi.org/10.1051/epjap/2019190085  
Published online  17 December 2019 
https://doi.org/10.1051/epjap/2019190085
Regular Article
Sensors and energy harvesters based on (1–x)PMNxPT piezoelectric ceramics^{★}
^{1}
Chouaib Doukkali University, Ecole Nationale des Sciences Appliqués (ENSA), Laboratoire des Sciences d'Ingénierie pour l'Énergie (LabSIPE), El Jadida, Maroc
^{2}
Chouaib Doukkali University, Faculté des sciences, Laboratoire de physique et des techniques nucléaires, atomiques et moléculaires, El Jadida, Maroc
^{*} email: lifihouda@gmail.com
Received:
18
March
2019
Received in final form:
4
August
2019
Accepted:
1
October
2019
Published online: 17 December 2019
With recent advancements in energy conversion mechanisms, piezoelectric ceramics (1–x)PbMg_{1/3} Nb_{2/3}Ο_{3}xPbTiΟ_{3} (1–x)PMNxPT have demonstrated their abilities for converting mechanical vibrations into electricity. Three (1–x)PMNxPT compositions were used in the present work with (x = 0.25, 0.31 and 0.33). The purpose of this paper is to investigate their piezoelectric performance as generators for energy harvesting applications. The energy harvester is numerically analyzed in this work. It consists of a piezoelectric bimorph clamped at one end to vibrating machinery, and a proof mass mounted on its other end. The energy harvester is also analyzed and experimental measurements of the harvested power are compared to the simulation results. A good agreement was observed between the experimental and the simulations results. According the application to exploit the vibrations of a hot air extractor, the results show that the harvested energy density of solid ceramics (1–x)PMNxPT is 0.043 W/m^{2}.
© EDP Sciences, 2019
1 Introduction
A growing need of selfpower devices, especially the development of microelectronic systems, the inconvenience of replacing batteries and the limited capacities of finite power sources, has been noticed during the last decades [1–5]. Harvesting energy from ambient environment has become an emerging technology for many applications, ranging from portable electric devices to renewable energy. Converting mechanical energy to electrical energy using piezoelectric materials has been the choice for many energy harvesting applications [6–8]. They have the ability of producing electrical charge when deformed, known by the direct piezoelectric effect. Deformation can be applied on the piezoelectric materials using ambient mechanical energy such as undesirable vibrations or human's permanent movements and then converted into electric power supply for wireless autonomous devices [4,9–14]. Piezoelectric energy harvesters are used because of their fast response when subjected to a mechanical charge and their facility to be used in portable applications [5,15–18]. Lead magnesium niobatelead titanate ((1–x)PbMg_{1/3}Nb_{2/3}Ο_{3}xPbTiΟ_{3}), shortly known as (1–x)PMNxPT, are piezoelectric materials which have aroused the interest of several researchers, due to their excellent properties such as great dielectric response and high electromechanical coupling coefficients (k) is greater than 90% near to the morphotropic phase boundary (MPB) [19–22].
Piezoelectric harvesters can generally be categorized into two types: (1) directly coupled and (2) indirectly coupled (or seismic). For a directly coupled piezoelectric harvester, the active material is directly bonded onto the host structure, so that the stress is directly applied to the piezoelectric material without any intermediate storage of energy in mechanical form. With such a configuration, there is no resonance frequency tuning requirement as the piezoelectric element experiences the same strain as the host structure. However, the mechanical to mechanical coupling effect would indeed result in an additional damping of the host structure due to the energy conversion between the host structure and the harvester (Fig. 1), and thus a decreased output power [23].
The purpose of this paper is therefore to study the mechanical backward coupling of seismic energy harvesting. It has to be noted the direct piezoelectric conversion using different (1–x)PMNxPT compositions with (x = 0.25, 0.31 and 0.33). Numerical simulation using finite element calculating software and an experimental study were carried out. The evolution of the resonance frequency of the system and the voltage and harvested power depending on the seismic mass added to its end was presented. An Experimental measurement of the power harvested, by exploiting the vibrations of a hot air extractor, using 0.65PMN–0.35PT pellets were presented, too depending on different resistive charges.
Fig. 1 The energy flow in the whole system. 
2 Theoretical background of piezoelectric cantilever configuration
When the piezoelectric materials are deformed or stressed, a voltage appears across the material. The electrical and mechanical behavior can be modeled by two constitutive equation (1) of longitudinal mode [23]:(1)where S is the strain, T is the applied mechanical stress, E is the Electric field, D is the electric displacement, ε is dielectric permittivity tensor (Fm^{−1}), sE is the matrix of elasticity under conditions of constant electric field, T is the stress, and d is the piezoelectric coefficient.
The second term in the right side of first equation represents the piezoelectric coupling term, which provides the mechanism for energy conversion. The property variable like (d) has 2 prefix i, j → d_{i,j}, where i is polarization direction (usually 3) and j is strain direction.
Typically, two different modes can be used in the design of a piezoelectric harvester. The first one is longitudinal mode (d_{33}) where the polarization of the beam is laterally developed in the deposited film. The second mode, which is commonly used, is transversal (d_{31}) where the polarization of the beam is perpendicular to the deposited film.
Οne of the most important design parameters in designing a vibration energy harvesting device is the resonant frequency. The electrical output energy attains a peak value if the vibration frequency of the environment matches the resonant frequency of the cantilever, and dies out dramatically when it deviates from the resonant frequency of the device. A lower resonant frequency is desirable to be closer to most of environmental vibration sources.
A cantilever beam can have many different modes of vibration, each with a different resonant frequency. The first mode of vibration has the lowest resonant frequency, and typically provides the most deflection and therefore the most electric energy [24]. A description of the system is given in Figure 2.
The resonant frequency (fn) can be calculated by following equation (2) [25].(2)where(3) m is the mass per unit area which is calculated by the thicknesses and densities, ρp and ρs are the densities of the piezoelectric and substrate, material respectively. The bending modulus (Dp) is a function of Young's modulus and thickness and is expressed by equation (4) [19].(4)where E_{p} and E_{s} are Young's modules of piezoelectric and substrate materials and their thicknesses, tp and ts, on the tip of the cantilever [19].
Fig. 2 model geometry, showing the major components of the energy harvested, including the piezoelectric bimorph, proof mass and supporting structure. 
3 Experimentals
3.1 Materials and preparation
We selected for our study the three (1–x)PMNxPT compositions were used with x taking the values of 0.31, 0.33 and 0.35 belonging to the morphotropic zone. There has been considerable interest in the perovskitetype solid solutions of (1–x)Pb(Mg_{1/3}Nb_{2/3})Ο_{3}xPbTiΟ_{3} due to their excellent dielectric, piezoelectric and electromechanical properties by combining the advantages of both the relaxor Pb(Mg_{1/3}Nb_{2/3}) and its solid solution with the normal ferroelectric PbTiΟ_{3} [26–29]. Moreover, it was proven that these properties were maximum at the morphotropic phase boundary (MPB) which marks the transition from rhombohedral to tetragonal (1–x)PMNxPT compositions.
The method of synthesis of (1–x)PMNxPT ceramics consists of the preparation of the columbite MgNb_{2}Ο_{6}, by mixing metal oxides MgΟ (0.99 Aldrich) and Nb_{2}Ο_{5} (0.99 Sigma) followed by a heat treatment for 3 h at 1100 °C [30]. Columbite is then grounded with titanium oxide (TiΟ_{2}) (0.99 Merck) and lead oxide (PbΟ) (Penox) in adequate proportions to obtain solid solutions (1–x)PMNxPT. The solid solution obtained is subjected to a heat treatment for 4 h at 825 °C with a heating rate of 2 (°C/min). The MnO_{2} manganese oxide (0.99 Merck) is introduced in the current synthesis step in order to obtain the doped solid solution. A slight excess of MgO is used to obtain an almost pure perovskite phase, avoiding leaving free Nb_{2}O_{5} during the formation of the columbite. The crystalline powder of perovskite structure is mixed with an organic binder to facilitate the shaping of the mixture by uniaxial pressing. The mixture was calcinated for 6 h at temperatures ranging from 1200 to 1250 °C (Fig. 3).
Phase analysis was performed in a step scanning mode using a standard Xray powder diffraction (Bruker D8 Advanced diffractometer). Which confirmed the successful growth and showed that: samples with x = 0.31, x = 0.33 and x = 0.35 exhibit a morphotropic phase boundary (MPB). The Xray diffraction spectrum of the investigated solid ceramics are reported in Figure 4.
Figure 4 shows the Xray diffractogram of the 0.69PMN–31PT, 0.67PMN–33PT and 0.65PMN–35PT powder. It indicates a pure perovskite phase and no pyrochlore phase was detected within the sensitivity of the Xray diffraction, meaning that Pb(Mg_{1/3}Nb_{2/3})O_{3} and PbTiO_{3} have formed a perfect solid solution with the perovskite structure. It also shows a mixture phase (rhombohedral and tetragonal phases) which is normal since that this formulation belongs to the morphotropic boundary MPB.
A picture describes in detail the manufactured process (sample diameter and thicknesss) of (1–x)PMNxPT is shown in Figure 5 and Table 3.
Fig. 3 Elaboration of (1–x)PMNxPT samples. 
Fig. 4 Xray diffraction spectra of the (1–x)PMNxPT. 
Fig. 5 A picture of a manufactured (16 mm x 1 mm) (1–x)PMNxPT piezoelectric ceramic on an alumina substrate. 
3.2 Experimental setup
This work is based on the evolution of piezoelectric direct conversion using (1–x)PMNxPT, x taking the values of 0.31, 0.33 and 0.35. Accordingly, in this section, an experimental setup with a mass ratio will be presented to expose the mechanical to mechanical coupling effect on the host structure. For the purposes of convenience, the host structure is taken as a cantilever beam, although it can be any other structure (e.g., rotating machinery, car engine, wing, etc.).
The harvester is composed of a bimorph ceramic and it is attached to the host beam through a support and magnets. Two small magnets are also placed at the freeend of the harvester to form a proof mass. The external excitation is applied at the freeend of the host structure with an electromagnet. The experimental setup is depicted in Figure 6.
The goal is to study the operating frequency effect of frequency, the structure mass and the (1–x)PMNxPT composition on the output voltage and the generated power [31,32]. A description of the system is given in Figure 2. Vibration frequencies are visualized via the oscilloscope. The resonance frequency corresponds to the pic of the maximum output voltage (Fig. 2).
Fig. 6 The experimental setup. 
4 Results and discussions
The aim of this section is to present our experimental measurements of the micropiezoelectric generators and demonstrate its capability to convert mechanical vibrations into electrical energy. The experimental performs two analyses; first, the voltage harvested (Ν_{rms}) and the effect of the masse is analyzed as a function of vibration frequency of three compositions of (1–x)PMNxPT. A conversion techniques amplifying the energy delivered was proposed by Guyomar et al. [20], who developed it, to damp out the sinusoidal vibrations of a vibrating structure, using patch' S piezoelectric positioned on the structure. The energy harvester consists of a piezoelectric (1–x)PbMg_{1/3}Nb_{2/3}Ο_{3}xPbTiΟ_{3} (1–x)PMNxPT which provides interesting ferroelectric and dielectric properties, clamped at one end to the vibrating machinery with a different proof mass mounted on the other end.
Table 1 summarizes the characteristics of different samples (1–x)PMNxPT as a function of x, and it also compares these values of conventional piezoelectric materials. The increases in dielectric constant are attributed to the composition variations that shift Tc significantly from ∼165 °C to ∼190 °C with increasing x, ε in (1–x)PMNxPT were in the range of 1821.12–2318.06, and the piezoelectric coefficient d_{33} of (1–x)PMNxPT ceramics increases with increasing PT content, from 307 pC/N for 0.69PMN–0.31PT to 383 pC/N for 0.65PMN0.35PT. In comparison with other materials such as PZT, the PMNxPT exhibit much more important properties depending on the composition and the used technological methods. Piezoelectric coefficient d_{33} and dielectric constant are 5–10 times greater than that of the PZT; electromechanical coupling coefficients (k) is greater than 90% [33,34], which can give a significant increase in the performance of the devices based on these materials.
The piezoelectric charge constant d_{33} is defined as the electric polarization generated in a material per unit mechanical stress applied to it. Alternatively, it is the mechanical strain experienced by the piezoelectric material per unit electric field applied to it. The Cantilever type vibration energy harvesting has a simple structure, and can produce a large deformation. The cantilever model can be used in the 33 mode; this mode means the electric field produced is on the same axis as the applied strain. The method to measure d_{33} is to apply a force static 1N to the samples (1–x)PMNxPT at a frequency of 100Hz and measure the corresponding charge [35]. Theoretically, d_{33} is the relationship ratio between the charge density and the stress: (5)
Summary of property parameters of (1–x)PMN–xPT.
4.1 The output voltage
The evolution of the output voltage harvested is analyzed as a function of vibration frequency in order to determine the resonance frequency of the different structure mass (Fig. 7a–c).
Figure 7a–c shows the experimental results of the evolution of the voltage harvested as a function of the vibration frequency, for the three (1–x)PMNxPT compositions, for the different masses. The graphs are parabolic and have a maximum corresponding to the resonance frequency as showed in Table 2 decrease when the mass increase. We can observe that the voltage harvested of the (1–x)PMNxPT is very influenced by the addition of PT. it is noted that the voltage harvested for both samples PMN–0.31PT, PMN–0.33PT, and PMN–0.35PT shows an increase with the increase of the mass and the percentage of the lead titanate (PT).
It is also observed, the voltage harvested reaches a maximum value for a titanium content of 0.35, the (1–x)PMNxPT has a morphotropic phase boundary (MPB), Between the rhombohedral and tetragonal phases occurs at approximately x = 0.35 where both phases coexist [4]. These relaxors are widely used to their extremely high excellent piezoelectric coefficients and high dielectric and ferroelectric properties (Tab. 1 and Fig. 8).
Figure 8 shows the recovered voltage is analyzed as a function of proof mass, for the three compositions (0.69/0.31, 0.67/0.33 and 0.65/0.35) of (1–x)PMNxPT. We can observe that the recovered voltage of the PMN is very influenced by the addition of PT. It is noted that the recovered voltage for both samples PMN–0.31PT, PMN–0.33PT, and PMN–0.35PT shows an increase with the increase of the mass (Fig. 8). To reach a relationship between the proof mass and the resonance frequency, the equation (2) gives this relationship between them. According to Figure 7, we can conclude that fact of increasing the mass decreases the frequency of resonance, for the three compositions of (1–x)PMNxPT (0.69/0.31, 0.67/0.33, and 0.65/0.35), that respects the trend given by equation (2).
Fig. 7 (a) The voltage harvested as a function for three masses for the sample PMN0.31PT. (b) The voltage harvested as a function for three masses for the sample PMN0.33T. (c) The voltage harvested as a function for three masses for the sample PMN0.35PT. 
The resonance frequency range of three samples.
Fig. 8 The recovered voltage as a function of the masse for the different samples. 31PT, 33PT, 35PT with f = Fr. 
5 Generator simulation
The development of extremely wireless systems and low power electronics has led to a strong interest in the field of energy harvesting – the development of miniature generators. The energy harvesting in the micropiezoelectric generators depends on the electromechanical coupling. A conversion techniques amplifying the energy delivered was proposed by Guyomar et al. [20], who developed it, to damp out the sinusoidal vibrations of a vibrating structure, using patch'S piezoelectric positioned on the structure.
In this section, modeling of the harvester and host structure system based on the finite element method is proposed in the frequency domain as an alternative method and to validate the experimental results using piezoelectric devices module as 2D configuration as shown in detail in Figure 9. The goal is to study the power harvested and the voltage of piezoelectric (1–x)PMNxPT.
With the plane strain assumption and based on the material constitutive equations, for the beams (host structure and harvester substrate), the longitudinal stress T_{1} is linked with the strain S_{1} by:(6)where Φ, the Young's modulus; ϑ, the Poisson's ratio of the beam.
The general expression of the electrical displacement D_{3} and the strains S_{1} and S_{2} in the piezoelectric elements along the x_{1} and x_{2} axes can be linked using the piezoelectric constitutive equations considering isotropic material as:(7)where , the mechanical compliance tensor of the piezoelectric element in shortcircuit conditions, dkl, the piezoelectric constants, , defined as the permittivity under constant stress, E_{3}, the electric field in the x_{3} direction.
With the plane strain condition, S_{2} = 0, and with the pure bending assumption, T_{3} = 0. Hence, the longitudinal stress of the piezoelectric element is obtained as(8)
In bimorph configuration and according to the polarization direction in the piezoelectric materials, the electric field for the upper element is E_{3up} = ϑ/t_{p} and that for the lower element is E_{3low} = − ϑ/t_{p} as the voltage is referenced to the substructure.
The energy harvester simulated in this model consists of a piezoelectric (1–x) PbMg_{1/3}Nb_{2/3}Ο_{3}xPbTiΟ_{3} (1–x)PMNxPT solid ceramic, clamped at one end to the vibrating machinery by a various proof mass mounted on the other end, and make a comparison between the experimental and simulated results.
The objective of the first part is to analyze the resonance frequency to analyze the voltage harvested for the different proof masses of the composition 0.65PMN35PT. the Second part is to determine the power harvested from the device a function of frequency and the load resistance for three deferent masses (0.31 g, 0.63 g, and 1.042 g) of 0.65PMN35PT ceramics.
The load dependence of the bimorph in the frequency range from the resonance can be computed by using the equivalent circuit representation shown in Figure 10. The voltage across the load can then be expressed as:(9) where (RS) is the series resistance, and (C) is the damped capacitance of the bimorph. The average power delivered to the load can then be found using the expression (9) (Fig. 10).
Fig. 9 2D model geometry, showing the major components of the energy harvester. 
Fig. 10 Equivalent circuit representation of the piezoelectric generator. 
5.1 Subdomain setting
The structure is composed of two subdomains, the first is piezoelectric ceramic made of lead magnesium niobatelead titanate 0.65PMN0.35PT, and the second is substrate layer which is chosen to be steel, the properties of the material are: relative permittivity = 2318.06, density = 8100 kg/m^{3}, Poisson's ratio = 0.37, Young's modulus = 72 GPa.
The dimension and physical properties are given in Table 3. However, the maintenance issues associated with this approach for replacing the piezoelectric material in case of malfunction, indirectly coupled piezoelectric harvesters are frequently choose. In this approach, the energy conversion is performed by an additional mechanical system (cantilever beam) featuring piezoelectric inserts bonded onto the host structure. Because of this mechanical separation from the host structure, maintenance is facilitated as the additional electromechanical system can be easily replaced. However, the resonance frequency has to be matched with the host structure to optimize its performance.
The beam characteristics.
5.2 Boundary conditions
The energy harvester is numerically analyzed in this work. It consists of a piezoelectric bimorph clamped at one end to vibrating machinery, and a proof mass mounted on its other end. The fixed constraint condition is applied to the vertical faces of both ceramic, while all other faces are free of displacement.
The mode d_{33} attach vertical face and freely suspended vertical face are chosen as floating and ground potential respectively, while all other faces of the piezoelectric layer are preserved as zero chargeSymmetry constraint. The body load F (0.1N) is applied as an input to the piezoelectric layer to get a strain.
5.3 The voltage harvested
An experimental measurement of the harvested power has been compared with the simulation behavior predicted by the proposed model. Then, we can conclude that the experimental results agree with the simulations with proof masses (0.31 g, 0.63 g, and 1.042 g) of the sample PMN35PT (Fig. 11a–c).
Figure 11a–c gives the evolution of the voltage for the different masses (0.31 g, 0.63 g, and 1.042 g) of the sample PMN0.35PT, and this is valid for all the three samples, the graphs are parabolic and have a maximum corresponding to the resonance frequency. This voltage harvested increases when increasing the masses. Then, observed the resonance frequency range of three masses between [150; 250].
Fig. 11 (a) The voltage harvested as a function for the masse 0.31g for the PMN0.35PT ceramic. (b) The voltage harvested as a function for the masse 0.63g for the PMN0.35PT ceramic. (c) The voltage harvested as a function for the masse 1.042 g for the PMN0.35PT ceramic. 
5.4 The power harvested
Harvested power for three masses different masses of PMN35PT related to the frequency that has been presented in Figure 12. It is observed that the value of maximum power is dependent on mass. Also, the optimum value of harvested power increases with the increase of mass.
Figure 12 presents the power harvested (in mW) as a function of frequency for the different masses (0.31 g, 0.63 g, and 1.042 g) of the composition PMN35PT, when the power harvester is excited by a local vibration. The electrical load is 10 kΩ. The response of the system shows a peak at 219 Hz, close to the computed resonant frequency of the cantilever at 215 Hz (Fig. 12).
Figure 13 shows the harvested power from the device as a function of the load resistance at 219 Hz. The maximum power is about (0.07 MW, 0.30 MW, and 0.82 MW) for (0.31 g, 0.63 g, and 1.042 g) respectively of PMN35PT ceramics. The peak in energy harvested corresponds to an electrical load of 100 kΩ, then increases by increasing the masses.
The piezoelectric ceramics (1–x)PbMg_{1/3}Nb_{2/3}Ο_{3}x PbTiΟ_{3} (1–x)PMNxPT have demonstrated their abilities for converting mechanical vibrations into electricity. The power harvesting in the micro piezoelectric generators depends heavily on the electromechanical coupling. It is noted that the PMN–0.35PT represent good electromechanical coupling constant 90% near to the morphotropic phase boundary compared to PMN–0.31PT and PMN–0.33PT, hence the choice of their use in the application of a piezoelectric generator in an extractor application.
Fig. 12 Harvested power (in mW) related to frequency for three deferent masses (0.31g, 0.63g, and 1.042 g) of PMN35PT ceramics. 
Fig. 13 Power harvested from the device as a function of the electrical load resistance at 219Hz for three deferent masses (0.31 g, 0.63 g, and 1.042 g) of PMN35PT ceramics. 
6 Application: hot air extractor
The recuperation system associated with the piezoelectric system plays a significant role. The power harvesting in the micro piezoelectric generators depends heavily on the electromechanical coupling. Typically these devices are used to power sensors and wireless communication systems [36,37], It is a way in addition to other controls of vibrations, for example using viscoelastic materials or using magnetic actuators [18,38,39]. As an application, we did a study on a hot air extractor in a room of electric ovens laboratory for cooling (Fig. 14). The purpose of this section is to use the direct piezoelectric effect to harvested energy from a hot air extractor to power resistors of different values and hence determine the optimal resistance. The 0.65PMN–0.35PT which provides interesting electromechanical properties was used in this study, it's attached to the extractor, deformation can be applied on the piezoelectric 0.65PMN–0.35PT by vibration of hot air though an extractor and then converted into electric power. The general concept of the proposed application is illustrated in Figure 14.
In generator mode, the proposed device converts all vibration into electrical energy. Νibration sources are numerous and easily present in the environment. This intelligent generator can be placed near sensors and wireless communication systems. The electrical energy produced by the piezoelectric conversion via the (1–x)PMNxPT, will be stored or used directly to supply the acquisition system of sensor (Fig. 15).
To determine the harvested power, The microgenerator was prepared from a cutting a support 1 mm width and 16 mm in length, second part is to measure of the resonance frequency of extractor using a generator vibration supplied 3Ν connected to the laser cutting we find Fr = 240 Hz (resonance frequency), then fix the micro generator on the extractor, regulate the resonance frequency of device contain the microgenerator and the extractor such that it be equal to 240 Hz. Connect an internal resistance with the micro generator to measure the effective value of the voltage harvested. The power harvested delivered to the load can than be found using the equation (10):(10)
Figure 16 presents the harvested power versus the electric load; the value of power density is 43 (mW/m^{2}), this data suggested the existence of an optimal load resistance R = 635 KΩ⋅
We will use the proposed technique and the results obtained to develop a smart sensorgenerator device based on (1–x)PMNxPT, able to detect vibration, convert it in electrical energy and use it to ensure its own supply. According the application, the results show that the harvested energy of solid ceramics is 43 (mW/m^{2}). According the application, this type of energy has been considered as the most available ambient energy source which allows a high level of harvested energy. We want, through this work, valorize the mechanical energy and exhibit that it is one of the ambient energy sources applicable everywhere and which provides a very high harvested energy compared to what is obtained using thermal energy [40–42].
Fig. 14 Hot air extractor in a room of electric ovens laboratory for cooling. 
Fig. 15 Schematic illustration of the application. 
Fig. 16 The evolution of power harvested as a function of the resistance. 
7 Conclusion
In this work, we presented a model piezoelectric power harvesting, to supply an electronic device. The piezoelectric ceramics (1–x)PMNxPT with diﬀerent volume fraction of solid ceramics are fabricated and characterized. We reports on measurements of the mechanicaltoelectrical energy harvesting by the effect of adding a seismic mass and frequency of the voltage harvested of a piezoelectric materials (1–x)PMNxPT. The modeling of the harvested power has been developed and has also shown that optimization of harvested voltage and power for greater electromechanical conversion. An experimental measurement of the harvested power has been compared with the simulation behavior predicted by the proposed model. Then, we can conclude, the experimental results agree with the simulations. The piezoelectric materials (1–x)PMNxPT are potential candidates for certain applications with low frequency of vibration, that occur, for example; when a wireless sensor is mounted on a vibrating piece of machinery. Piezoelectric ceramics (1–x)PMNxPT are investigated for energyharvesting applications. To make use of the highenergy density, while maintaining mechanical integrity, (1–x)PMNxPT is a preferred form for the solid ceramics to be utilized for energy harvesting. According to the application of exploiting the vibration of a hot air extractor, we have designed a piezoelectric generator and installed it on a hot air extractor; the power density harvestable measured achieved 0.043 W/m^{2} of solid ceramics (1–x)PMNxPT, power that is sufficient to power low consumption devices.
Author contribution statement
Houda Lifi: make experimental measurements from the intrinsic to validate and write the document. Chouaib Ennawaoui and Said Laasri: perform planning and supervision experiences. Abdelowahed Hajjaji and Samira Touhtouh (supervisor): carry out the analysis of the document. Madiha Yessari and Mohammed Benjelloun (codirector): project supervision, contribution of the analysis tool.
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Cite this article as: Houda Lifi, Chouaib Ennawaoui, Abdelowahed Hajjaji, Samira Touhtouh, Said Laasri, Madiha Yessari, Mohammed Benjelloun, Sensors and energy harvesters based on (1–x)PMNxPT piezoelectric ceramics, Eur. Phys. J. Appl. Phys. 88, 10901 (2019)
All Tables
All Figures
Fig. 1 The energy flow in the whole system. 

In the text 
Fig. 2 model geometry, showing the major components of the energy harvested, including the piezoelectric bimorph, proof mass and supporting structure. 

In the text 
Fig. 3 Elaboration of (1–x)PMNxPT samples. 

In the text 
Fig. 4 Xray diffraction spectra of the (1–x)PMNxPT. 

In the text 
Fig. 5 A picture of a manufactured (16 mm x 1 mm) (1–x)PMNxPT piezoelectric ceramic on an alumina substrate. 

In the text 
Fig. 6 The experimental setup. 

In the text 
Fig. 7 (a) The voltage harvested as a function for three masses for the sample PMN0.31PT. (b) The voltage harvested as a function for three masses for the sample PMN0.33T. (c) The voltage harvested as a function for three masses for the sample PMN0.35PT. 

In the text 
Fig. 8 The recovered voltage as a function of the masse for the different samples. 31PT, 33PT, 35PT with f = Fr. 

In the text 
Fig. 9 2D model geometry, showing the major components of the energy harvester. 

In the text 
Fig. 10 Equivalent circuit representation of the piezoelectric generator. 

In the text 
Fig. 11 (a) The voltage harvested as a function for the masse 0.31g for the PMN0.35PT ceramic. (b) The voltage harvested as a function for the masse 0.63g for the PMN0.35PT ceramic. (c) The voltage harvested as a function for the masse 1.042 g for the PMN0.35PT ceramic. 

In the text 
Fig. 12 Harvested power (in mW) related to frequency for three deferent masses (0.31g, 0.63g, and 1.042 g) of PMN35PT ceramics. 

In the text 
Fig. 13 Power harvested from the device as a function of the electrical load resistance at 219Hz for three deferent masses (0.31 g, 0.63 g, and 1.042 g) of PMN35PT ceramics. 

In the text 
Fig. 14 Hot air extractor in a room of electric ovens laboratory for cooling. 

In the text 
Fig. 15 Schematic illustration of the application. 

In the text 
Fig. 16 The evolution of power harvested as a function of the resistance. 

In the text 
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