Properties Of Piezoelectric Materials Research Articles

Thermodynamic potential construction and biaxial stress analysis of K0.4Na0.6NbO3 single crystals

The macroscopic properties of piezoelectric materials can be profoundly influenced by stress. In this research, thermodynamic potential parameters of K0.4Na0.6NbO3 (KNN) single crystals have been experimentally quantified to assess the effects of stress. Leveraging the Landau thermodynamic potential theory, it has been identified that the application of biaxial tensile stress causes a significant elevation in both the piezoelectric property and phase transition temperature in KNN crystals. This transition remarkably extends their working range and improves the material's applicated potential. The coherence between these computational outcomes and experimental data—from the strategic growth of KNN single crystals with internal stress—underscores the reliability of our findings (dielectric constant from 213 to 1274, TO-T from 180 to 234 °C). Additionally, theoretical calculation predicts a potential enhancement in the piezoelectric capabilities of KNN single crystals. This study provides valuable insights for the growth of high-quality piezoelectric crystals and further promotes the application of lead-free piezoelectric materials.

Compressive stress reduction in sputter-deposited yttrium aluminum nitride (Y0.2Al0.8N) thin films for BAW resonators with high electromechanical coupling

In the past decade, rare earth elements have found increasing interest in enhancing the piezoelectric coefficient of aluminum nitride (AlN) thin films. Until now, scandium has been the most successful rare earth element to enhance the piezoelectric coefficient (d33) up to 600 %. In this research paper, we present a 250 % increase in d33 to 12.5 pC/N for sputter-deposited yttrium alloyed aluminum nitride (Y0.2Al0.8N) thin films compared to pure AlN. However, this increase in d33 comes with a substantial increase in compressive layer stress well above 1 GPa. Therefore, a chamber pressure sweep technique is introduced, resulting in a 40 % reduction in the stress level without significantly affecting the crystallographic film parameters to facilitate device integration. Even more, high compressive stress in thin films is a critical concern in piezoelectric MEMS devices such as bulk acoustic wave (BAW) resonators, as it can adversely affect the piezoelectric material properties and hence, the electromechanical performance. For this purpose, we demonstrate that the pressure sweep technique improves the electromechanical coupling factor of Y0.2Al0.8N to 7.02 %, being substantially above the reference value of 6.02 % set by pure AlN. In summary, the findings from this study may stimulate further effort to integrate YxAl1-xN thin films in BAW filter devices for future telecommunication applications.

Two-scale asymptotic homogenization analysis of piezoelectric composite materials in generalized curvilinear coordinates

This paper presents a comprehensive study on applying the two-scale asymptotic homogenization method to derive the effective properties of piezoelectric composite materials characterized by generalized periodicity in curvilinear coordinates. The methodology involves formulating the homogenization problem in a general curvilinear framework suitable for materials with complex geometric configurations. By systematically deriving the homogenized equations and effective coefficients, the paper provides a robust theoretical foundation for understanding the macroscopic behavior of piezoelectric composites under various loading conditions. The model’s versatility is demonstrated through its application to specific curvilinear coordinate systems, including the helix coordinate system and cylindrical coordinates with wavy geometry. These examples highlight the potential of the proposed approach in analyzing and designing piezoelectric materials with intricate geometries. The state-of-the-art numerical homogenization methods have also validated the proposed homogenization method, ensuring its accuracy and robustness.

A simple measurement method for in-situ temperature-dependent piezoelectric coefficient d 33 of piezoelectric materials

Piezoelectric materials have been widely used in sensors, actuators, and transducers due to their positive and inverse piezoelectric effects, which can convert electrical and mechanical energy into one another. The most important parameter to evaluate the piezoelectric properties of materials is their piezoelectric coefficient (d 33). The value of d 33 varies with temperature. The measurement of temperature-dependent d 33 is a difficult task and at present, the equipment used to measure the temperature-dependent d 33 has many limitations. To overcome these limitations, the current study proposes an in situ temperature-dependent d 33 measuring method based on the inverse piezoelectric effect of piezoelectric materials. The newly developed measuring equipment contains a laser vibrometer, and automatic detection program including data processing. Moreover, the image is displayed on LabVIEW program. Compared with the quasi-static temperature-dependent d 33 measurement method, the KNN- based piezoelectric material demonstrated the reliability of this measurement method.

Crafting very low frequency magnetoelectric antenna via piezoelectric and electromechanical synergic optimization strategy

A boom in exploration for marine geology and ocean resources has resulted in a huge demand for radio navigation or special environment communications, in turn spurring the rapid development of portable underwater wireless communication technology. State of the art acoustic communication methods used today are plagued by substantial transmission delays, multipath effects, and doppler frequency shifts, among other challenges, thus impeding the advancement of underwater wireless communication technology. Low-frequency electromagnetic transmission has proven to be a prospective solution for underwater communication, but the conventional electrical antennas is too large for portable underwater wireless communication. Emergent magnetoelectric (ME) antennas driven by piezoelectric materials have become a promising solution for miniaturizing very low frequency (VLF) communication systems. Here, a theoretical model between the radiation performance and piezoelectric material properties of the ME antenna was conducted. Guide by the theory analysis, Pb(In1/2Nb1/2)O3-Pb(Mn1/3Sb2/3)O3-Pb(Zr0.49Ti0.51)O3 (PIN-PMS-PZT) piezoelectric ceramic simultaneous with high d33 and Qm (d33 ∼ 401, Qm ∼ 1510) has been designed to enhance the magnetoelectric radiation of the VLF ME antenna. The PIN-PMS-PZT based ME antenna achieves a large converse magnetoelectric response 1.78 Gs·cm/V in EMR, which is almost doubled to commercial PZT based ME antenna. More importantly, a VLF communication system was built based on the VLF antenna, which successfully transmitted digital signals using Amplitude-Shift-Keying (ASK) modulation. It is believed that the presented work could provide a theoretical basis and feasible technical path for the employment of ME antennas in the future.

Theoretical study on multi-physics coupling problems of functionally-graded lead-free piezoelectric rectangular thin plates

This paper carried out a theoretical research on multi-physics coupling problems of functionally-graded lead-free piezoelectric rectangular thin plates. Firstly, the perturbation theory was used to study the bending problem of functionally-graded lead-free piezoelectric rectangular thin plates, and the nonlinear governing equations for this bending problem were established. Then, the three piezoelectric coefficients reflecting the piezoelectric property were taken as the perturbation parameters, and the nonlinear governing equations were transformed into multiple sets of linear equations by the multi-parameter perturbation method. Finally, the solutions of these linear equations were solved by the semi-inverse solving method. Based on the finite element simulations, the effectiveness of the perturbation solutions obtained here was verified. The research results showed that it was reasonable to choose three piezoelectric coefficients as perturbation parameters, which was accord with the basic idea of perturbation theory. The analysis results indicated that there was a cross transfer relationship between external loads and perturbation solutions of every order, which could be used to simplify the perturbation expansion. Moreover, the deformation of the functionally-graded lead-free piezoelectric thin plate was less than that of the functionally-graded thin plate, that is, piezoelectric properties in lead-free piezoelectric materials had a piezoelectric enhancement effect.

Effects of doping with selected rare-earth elements (Eu3+, Dy3+, Eu3+/Dy3+) on the structural characteristics as well as electrical and luminescent properties of K0.5Na0.5NbO3

The effects of adding Eu3+, Dy3+, and Eu3+/Dy3+ rare-earth elements on the microstructural, optical and electrical properties of lead-free piezoelectric materials based on K0.5Na0.5NbO3 (KNN) were investigated. A series of fine powders were synthesized via a modified Pechini route utilizing citric acid. Relatively large amounts of rare-earth elements were successfully incorporated into the crystal lattice of KNN. A combination of X-ray diffraction, X-ray absorption spectroscopy, energy-dispersive X-ray and scanning electron microscopy were used to characterize the structure and chemical composition of the powders and sinters. XRD patterns indicated the formation of a single-phase orthorhombic structure in the co-doped sinter. X-ray absorption spectroscopy revealed the nominal 3+ valence states of Eu and Dy in KNN ceramic sinters. The Mott model and group symmetry theory were used to discuss the characteristics of Raman spectra obtained for the EuDy:KNN ceramics. The ceramics exhibited good dielectric permittivity (ε≃1300) and low dielectric loss (tan δ=0.03) in the temperature range of 170–240°C. The electrical properties of the ceramics showed that the basic mechanism of conduction and relaxation was thermal activation, and that small polaron hopping was responsible for charge carrying. The Eu3+ and Dy3+ ions displayed characteristic red and orange emissions in sinters when excited with light in the wide ultraviolet spectra range (380–420 nm).

In situ electric field-dependent structural changes in (Ba,Ca)(Zr,Ti)O3 with varying grain size

The functional properties of piezoelectric ceramic materials, such as barium titanate, are highly dependent on grain size. Lead-free polycrystalline Ba0.85Ca0.15Zr0.1Ti0.9O3 (BCZT) samples were prepared with a combination of the hydrothermal method and spark plasma sintering to achieve grain sizes from 100 nm to 10 μm by varying the maximum sintering temperature. In this range, a transition from a nearly linear dielectric to a ferroelectric response can be seen in macroscopic electromechanical measurements, demonstrating the importance of grain size on functional properties in BCZT. Furthermore, in situ electric field-dependent synchrotron x-ray diffraction measurements were performed to quantify the intrinsic and extrinsic strain contributions and their variations with grain size. At lower grain sizes, the data revealed a significant loss of extrinsic contributions in the piezoelectric behavior, limiting the response to intrinsic contribution associated with lattice strain. For BCZT, a critical grain size between approximately 0.08 and 0.18 μm is proposed, below which no piezoelectric response was observed.

Temperature-dependent dielectric response of free standing PVDF-MoS2 nanocomposite films

Poly(vinylidene fluoride) (PVDF) and its copolymers are known for possessing the highest electroactive response including dielectric constant, piezoelectric and ferroelectric effects which has a wide range of applications such as in energy transfer, energy generation and storage, monitoring and control, and include the development of capacitors, sensors, actuators and so on. We report an enhancement in dielectric properties in PVDF generated by the addition of MoS2 nanosheets. The addition of 1 wt% MoS2 nanosheets as a filler in PVDF, stabilize its beta phase over the alpha phase, resulting in a significant increase in dielectric constant (ε’) across a wide range of frequencies (100 Hz to 1 MHz) and temperatures (140 K- 340 K). The high dielectric constant was achieved by the PVDF-MoS2 nanocomposite while maintaining a relatively low tangent loss factor of 0.94. Such properties in soft polymer-based piezoelectric materials were previously challenging and unachievable. The nanocomposite exhibits excellent ferroelectric properties with 11 times enhancement in remnant polarization compared to pristine PVDF in ambient conditions. The stored energy density (Us) is 39.43 mJ/cm3 for the PVDF-MoS2 film. These lead-free and soft polymer-based nanocomposites can bring remarkable advances in various flexible sensors, data storage, and energy harvesting applications.

Relaxor ferroelectricity and elevated thermal expansion behaviour of (1−x)Bi0.5Na0.5TiO3-xBaSnO3 lead-free piezoelectric ceramics

The study on piezoelectric and ferroelectric properties of sodium bismuth titanate-based materials is essential for piezoelectric electronic components. In this study, a series of lead-free relaxor ferroelectric (1−x)Bi0.5Na0.5TiO3-xBaSnO3 (BNT-xBS) ceramics were prepared by a conventional solid-state reaction method. The phase performance, fracture morphologies, permittivity, ferroelectricity, piezoelectricity, and thermal expansion for various BS contents (x) were systematically studied. With an increase in x, the phase transition from R3c to P4bm, and the grain size marginally decreased from 1.79 to 1.51 μm. Meanwhile, the degree of dielectric relaxor and diffused phase transition improved, and the ferroelectricity and piezoelectricity initially increased and then decreased. The optimal electrical properties of Pr = 41.6 μC/cm2, d33 = 167.8 pC/N, and kp = 0.318 were observed at x = 0.06. The paper discusses how site disorder, long-range electric dipole ordering, and grain size influence various electrical properties. The mechanism of the thermal expansion behaviour was investigated based on Born-Lande theory. This study could serve as a landmark for studying multifunctional BNT-based piezoelectric materials for potential energy-harvesting devices.

Characterization and calibration of a piezo-energetic composite film as a reactive gauge

The field of multifunctional energetics encompasses a range of materials including propellants, explosives, and pyrotechnics that possess the ability to be manipulated through various characteristics that can be switched between go and no-go, or those that have controllable energy release levels or have additional functions beyond energetic output. The development of multifunctional energetics harnessing electromechanical or piezoelectric properties of polymeric materials or binder systems has garnered increasing interest in recent years. Among polymers, fluoropolymers such as poly(vinylidene fluoride) (PVDF) and copolymers such as poly(vinylidene fluoride-trifluoroethylene) [P(VDF-TrFE)], which are used as the binder and oxidizer in the energetic formulations, have demonstrated the highest piezoelectric coefficients. In this study, we fabricated piezo-energetic composite films using aluminum nanopowders (10 wt. % active content) as fuel and P(VDF-TrFE) (70/30) as an oxidizer and investigated the piezoelectric response using a small-scale drop weight setup. Additionally, we employed a shaker setup to investigate the response of the films to vibrations. Our findings demonstrate that these piezo-energetic films can replicate the behavior of a commercial PVDF gauge at relatively low-pressure impacts, indicating their potential use as shock or pressure sensors in various fields, as well as an accelerometer gauge. Additionally, aging studies of up to one year indicated minimal loss in the energetic content of the created films, enabling the use of energetic gauges for an extended period. Our findings support the effectiveness of piezo-energetic composite films as pressure sensors or accelerometers and highlight their potential for energetic applications.

Effect of temperature on dislocation-tuned dielectricity and piezoelectricity in single-crystal BaTiO3

The pinning-controlled mobility of ferroelectric/ferroelastic domain walls is an important part of managing polarization switching and determining the final properties of ferroelectric and piezoelectric materials. Here, we assess the impact of temperature on dislocation-induced domain wall pinning as well as on dislocation-tuned dielectric and piezoelectric response in barium titanate single crystals. Our solid-state nuclear magnetic resonance spectroscopy results indicate that the entire sample exclusively permits in-plane domains, with their distribution remaining insensitive to temperature changes below the Curie temperature (TC). The domain wall pinning field monotonically decreases with increasing temperature up to TC, as evidenced by a combination of experimental observations and phase-field simulations. Our work highlights the promising potential of dislocation engineering in controlling domain wall mobility within bulk ferroelectrics.

Numerical analysis of functionally graded piezoelectric bionic fishtail based on Hermite element-free method

Piezoelectric bionic fishtails have good flexibility, response speed, anti-interference ability, and have great application prospects in ocean exploration. However, the inherent drawbacks of the mechanical properties of traditional homogeneous piezoelectric materials significantly affect the propulsion performance and reliability of the piezoelectric bionic fishtails. To fill this gap, this paper develops a functionally graded piezoelectric bionic fishtail (FGPBF) by imitating the tail characteristics of groupers. The geometric structure and working principle of the FGPBF are introduced in detail. Based on the first-order shear deformation theory and Hermite element-free method, an element-free model for the FGPBF is established. The effects of gradient factor, substrate material, substrate thickness and electrical load on the propulsion performance of the FGPBF are addressed. The results show that the current results are in good agreement with the finite element results. The deformation of the FGPBF is negatively correlated with the thickness and stiffness of the substrate and linearly positively correlated with the electrical load. As the gradient factor increases, the deflection of the FGPBF first increases and then decreases. When the gradient factor is 2, the potential is 200 V, the dimensionless aluminum substrate thickness is 1, the propulsion performance of the FGPBF is improved by 28% compared to the homogeneous piezoelectric bionic fishtail.

Exploring the electric and Superior Piezoelectric Properties of Two-Dimensional PH-SiX Materials for High-Performance Silicon-Based Devices

The search for advanced two-dimensional materials with exceptional piezoelectric properties has led to the investigation of PH-SiX (X = Cd, Zn, Bi, Ga, and Al) semiconductors, which is compatible with...

Review of Piezoelectric Properties and Power Output of PVDF and Copolymer-Based Piezoelectric Nanogenerators.

The highest energy conversion efficiencies are typically shown by lead-containing piezoelectric materials, but the harmful environmental impacts of lead and its toxicity limit future use. At the bulk scale, lead-based piezoelectric materials have significantly higher piezoelectric properties when compared to lead-free piezoelectric materials. However, at the nanoscale, the piezoelectric properties of lead-free piezoelectric material can be significantly larger than the bulk scale. The piezoelectric properties of Poly(vinylidene fluoride) (PVDF) and Poly(vinylidene fluoride-co-trifluoroethylene) (PVDF-TrFE) lead-free piezoelectric nanomaterials are reviewed and their suitability for use in piezoelectric nanogenerators (PENGs) is determined. The impact of different PVDF/PVDF-TrFE composite structures on power output is explained. Strategies to improve the power output are given. Overall, this review finds that PVDF/PVDF-TrFE can have significantly increased piezoelectric properties at the nanoscale. However, these values are still lower than lead-free ceramics at the nanoscale. If the sole goal in developing a lead-free PENG is to maximize output power, lead-free ceramics at the nanoscale should be considered. However, lead-free ceramics are brittle, and thus encapsulation of lead-free ceramics in PVDF is a way to increase the flexibility of these PENGs. PVDF/PVDF-TrFE offers the advantage of being nontoxic and biocompatible, which is useful for many applications.

Decoupling the roles of mechanical stretching and piezoelectrical stimulation in calcium signal mediated osteogenic differentiation of MSCs on biomimetic nanofibers

Piezoelectric materials implanted in vivo will be affected by physiological stress, leading to the generation of dynamic piezoelectrical signals. The cells identify both piezoelectrical and mechanical stimuli, and the way they behave is regulated through an electromechanical coupling process. Understanding the specific functions of individual stimulation on the osteogenic differentiation of mesenchymal stem cells (MSCs) would aid the development of ideal biomaterials for bone tissue engineering. In this work, by utilizing the controllable piezoelectric properties of polylactic acid materials, we prepared biomimetic piezoelectric poly (L-lactic acid) nanofibers and its non-piezoelectric isomer poly (D, l-lactide) nanofibers using the electrospinning technology. The dynamic piezoelectric and mechanical stimuli on the nanofibers were theoretically and experimentally investigated. A home-made in-situ mechanical loading platform was used to apply predetermined tensile loading on the nanofibers under cell culture conditions. The results indicated that piezo-potential ranging from 11 to 103 μV could be produced by cell adhesion forces varied between 1 and 15 nN, while mechanical loading ranging from 1 % to 15 % strain resulted in piezoelectrical signals in the magnitude of several volts. These piezoelectric signals could influence cell adhesion through enhancing cell aspect ratio and cell area. During the process of cell contraction and re-spreading caused by the mechanical loading, the piezoelectric signals were capable of accelerating the recovery of spreading and adhesion. Furthermore, individual piezoelectric and mechanical signals could modulate intracellular calcium signals, and significantly promote osteogenic differentiation of MSCs. Specifically, the mechanical stimulation could activate PIEZO signaling pathway, resulting in a greater upregulation of early osteogenic differentiation markers of Collagen type I and Bone morphogenetic protein-2 compared to the piezoelectric signal. However, the combination of the two stimuli could obviously and effectively enhance osteogenic differentiation of MSCs in a synergistic manner. These findings offer fresh understandings regarding the electromechanical influences in the process of bone tissue regeneration, which afford additional possibilities for optimizing piezoelectric biomaterials for biomedical applications in a more reasonable manner.

A unified treatment of axisymmetric adhesive contact for piezoelectric materials

Nanoindentation technique has been widely applied to characterize the electromechanical properties of piezoelectric materials, where the adhesion effect induced by different surface forces becomes very prominent. The indenter tip should have more general profile rather than just three common simple shapes (flat, cone and sphere) in practical testing. In this study, the classical Johnson-Kendall-Roberts (JKR) and Maugis-Dugdale (M-D) models are extended to investigate the adhesion behaviors of a piezoelectric half-space indented by the power-law shaped punches with different electric properties, whose shape index is denoted as n. The JKR-n and M-D-n adhesion models for both the electrically conducting and electrically insulating punches are set up by means of Griffith energy balance. The Derjaguin-Muller-Toporov-n (DMT-n) adhesion solutions are derived from the corresponding M-D-n adhesion models as the limiting cases. The generalized Tabor parameter and interfacial adhesion strength applicable to piezoelectric materials are defined for the first time, with the former being used to describe the transition behavior from JKR-n model to DMT-n model. The impacts of the electric loading and the shape index on adhesion behaviors are discussed in detail. It is found that the pull-off force increases with the electric potential, which reveals the adhesion strengthening effect caused by electric loading. The shape index has a prominent influence on the pull-off force, interfacial adhesion strength, contact radius at pull-off moment, indentation depth and contact radius at self-equilibrium state, and the transition behavior from JKR-n model to DMT-n model. The results derived from this work not only are helpful to understand the contact behaviors of piezoelectric materials at micro/nano scale, but also provide a theoretical basis for nanoindentation technique in evaluating material properties of piezoelectric mediums.

Obtaining and Characterizing the Dielectric and Ferroelectric Properties of the PZT-Pms Complex System Through Solid State Reactions and Spark Plasma Sintering

Abstract In this paper B-oxide sintering process and Spark plasma Sintering (SPS) method is used to synthesize 0.88Pb(Zr0.52Ti0.48)O3 – 0.12Pb(Mn1/3Sb2/3)O3 – x at%Pr complex system where x = 0 and 0.02. The sintering temperature used in the SPS technique is considerably lower than that used in the B-oxide method (200 to 400oC) with significant decrease of the duration of the sintering route, arriving to some minutes instead of some hours. The aim of the study is the investigation of the effect of sintering technique on the dielectric and ferroelectric properties of such piezoelectric materials. The properties of the developed ceramic materials were determined: the development of crystalline phases was investigated by X-ray diffraction technique and the microstructural behavior by scanning electron microscopy was observed. The composition obtained by the SPS technique shows a lower remnant polarization and maximum strain, as well as a higher coercive field, compared to the those obtained using the same composition produced by B-oxide method.

A cascaded Nitinol Langevin transducer for resonance stability at elevated temperatures

Across power ultrasonics and sensing, piezoelectric ultrasonic transducers commonly experience degradation in mechanical, electrical, and dynamic performance due to the relatively high sensitivity of piezoelectric materials to changes in temperature. These changes, arising for example through high excitation voltages or environmental conditions, can lead to nonlinear dynamic behaviours which compromise device performance. To overcome this, the excitation signal to the piezoelectric material is often pulsed, mitigating the influence of temperature rises. However, there remain constraints on suitable candidate piezoelectric materials for power ultrasonic devices. As a novel approach to mitigating the influence of temperature on the properties of piezoelectric materials, the phase-transforming shape memory alloy Nitinol is incorporated into the piezoelectric stack of a Langevin power ultrasonic transducer, in a cascade formation. The underlying principle is that the nonlinear hardening response of Nitinol to rising temperature can be used to dynamically compensate for the nonlinear softening of the piezoelectric materials. Thus, the dynamic response of the transducer can be linearised at elevated excitation levels. In this study, two configurations of Langevin transducer are designed and characterised. One transducer incorporates a Nitinol middle mass, and in the second, titanium. A combination of electrical and thermomechanical characterisation is undertaken, where it is demonstrated that the nonlinear softening of the piezoelectric stack can be mitigated through control of the Nitinol microstructure. The vibration amplitudes of the Nitinol-middle cascaded transducer are higher and more stable when the Nitinol is austenite rather than a combination of martensite and austenite at room temperature. It has also been shown that the vibration amplitude and resonance frequency of Nitinol-middle cascaded transducer remain stable as temperature changes from 20 °C to 45 °C, dependent of the excitation voltage. Moreover, the self-heating experiment demonstrates the resonance stability of the Nitinol-middle cascaded transducer for continuous operation.

The enhanced vertical piezoelectricity in Janus C3HFX (X = Si and Ge) monolayers based on the born effective charges dipole-moment

Recently, two-dimensional (2D) piezoelectric materials are widely studied, and the vertical piezoelectric properties of 2D materials are highly required to be known in the related theory research works and experiments, so it becomes very important to explore the intrinsic mechanism of piezoelectricity in the 2D materials. Herein, we systematically study the piezoelectricity of Janus C3HFX (X = Si and Ge) monolayers with semiconductor property, which are carbon-based 2D materials, using the first-principles calculation. The remarkable enhancements on the absolute values of the vertical piezoelectric coefficient of C3HFSi-1 (e33 = 11.27 × 10−10 C/m) and C3HFGe-4 (e33 = −12.78 × 10−10 C/m) are larger than that of C4HF (e33 = −2.28 × 10−10 C/m) by 5 and 6 times, respectively. It indicates that the atom replacement at appropriate positions in the multiatomic monolayer can significantly enhance the vertical piezoelectric properties based on the appropriate distribution of polarization charge. We define the concepts, the Born effective charges center (BECs-center) and the BECs-dipole-moment in this work, to explain these large vertical piezoelectric coefficients’ variation. The larger BECs-dipole-moment will enhance the vertical piezoelectricity for these C3HFX monolayers than that of the C4HF monolayer. These concepts defined in this work will deepen the understanding of the internal physical mechanism about the piezoelectricity.