Analysis of piezoelectric ceramic performance parameters

Views: 10 Author: Site Editor Publish Time: 2018-11-28 Origin: Site

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The manufacture of excellent piezoelectric ceramic components usually requires requirements for the performance of piezoelectric ceramics. Because the performance of piezoelectric ceramics has a decisive influence on the quality of components. Therefore, to discuss and understand the components of piezoelectric ceramics, we must first understand the performance parameters and measurement methods of piezoelectric ceramics. Piezoelectric ceramics have piezoelectric properties in addition to the dielectric and elastic properties of general dielectric materials. Piezoelectric ceramics have anisotropy after polarization treatment, and each performance parameter has different values in different directions, which makes the performance parameters of piezoelectric ceramics much more than the general isotropic dielectric ceramics. . The numerous performance parameters of piezoelectric ceramics are an important basis for its widespread use.

(1) Dielectric constant
The dielectric constant is a reflection of the dielectric properties of a piezo cylinde piezoceramic, or the nature of polarization, and is usually expressed byε. Piezoelectric ceramic components for different purposes have different dielectric constant requirements for piezoelectric ceramics. For example, an audio component such as a piezoelectric ceramic speaker requires a ceramic is having a large dielectric constant, and a high frequency piezoelectric ceramic component requires a material is having a low dielectric constant. The relationship between the dielectric constant ε and the capacitance C of the element, the electrode area A and the distance t between the electrodes is ε=C·t/A .where the unit of each parameter is the capacitance C is F, and the electrode area A is M2, the electrode spacing t is m, and the dielectric constant ε is F/m. Sometimes the relative permittivity εr (or κ) is used, which is related to the absolute permittivity ε. εr=ε/εo where εo is the dielectric constant of vacuum (or free space), εo=8.85×10- 12 (F/m), while εr has no unit and a value.

(2) The polarization of piezo tubes transducer is preceded by an isotropic polycrystal, which has the same dielectric constant along the 1(x), 2(y), and 3(z) directions, that is, only one dielectric constant. After the polarization treatment, an anisotropic polycrystal is formed due to the remnant polarization generated in the polarization direction. At this time, the dielectric properties in the polarization direction are different from those in the other two directions. Let the polarization direction of the ceramic be in the 3 direction: ε11 = ε22 ≠ ε 33. The polarized piezoelectric ceramic has two dielectric constants ε11 and ε33. Due to the piezoelectric effect of piezoelectric ceramics, the measuring dielectric constants of the samples are different under different mechanical conditions. Under mechanically free conditions, the measured dielectric constant is called the free dielectric constant, and in εT, the upper corner T represents the mechanical free condition. Under mechanical clamping conditions, the measuring dielectric constant is referred to as the clamping dielectric constant, expressed as εS, and the upper reference S is the mechanical clamping condition. Since there is an additional electric field generated by deformation under the mechanical conditions, and there is no such effect under mechanical clamping conditions, the values of the dielectric constants measurement under the two conditions are different. According to the above, the piezoelectric ceramic polarized in the three directions has four dielectric constants, namely ε11T, ε33T, ε11S, ε11S.

(3) dielectric loss
Dielectric loss of underwater piezoceramic transducer is one of the important quality indicators of any dielectric material including piezoelectric ceramics. Under an alternating electric field, the charge is accumulated in the medium has two parts: one is the active part (in phase), which is caused by the conductance process; and the other is the reactive part (heterogeneous), which is caused by the relaxation process of the medium. The ratio of the out-of-phase component to the in-phase component of the dielectric loss, Ic is the in-phase component, IR is the out-of-phase component, the angle between Ic and the total current I is δ, ω is the angular frequency of the alternating electric field, and R is the loss resistance, C is dielectric capacitor. It can be seen from the formula (1-4) that when the IR is large, the tan δ is also large; the IR hour tan δ is also small. The dielectric loss usually expressed by tan δ is called the dielectric loss tangent or loss factor, or it is called dielectric loss. The loss of dielectric in an electrostatic field is derived from the conductance process in the medium. The dielectric loss in an alternating electric field is derived from the dielectric loss caused by the conductance process and polarization relaxation. In addition, the dielectric loss of ferroelectric piezoelectric ceramics is also related to the motion process of domain walls, but the situation is more complicated.

(4) Elastic constant

Piezoelectric ceramics are an elastomer in the range of elastic limits, stress should be proportional. Let the stress be T, applied to the piezoelectric ceramic sheet with the cross-sectional area A, and the strain generated by S. According to Hooke's law, the relationship between the stress T and the strain S is as follows, where S is the elastic smoothness constant. The unit is m2/N; C is the elastic stiffness constant in N/m2. However, any material is three-dimensional, that is, when stress is applied in the longitudinal direction, strain is generated not only in the longitudinal direction but also in the width and thickness directions. There is a thin piece as shown, the length of which is in one direction and the width in two directions. Applying the stress T1 in the direction of 1 causes the sheet to generate the strain S1 in the 1 direction and the strain S2 in the direction 2, and it is not difficult to obtain the S1=S11T1 from the equation (1-5); S2=S12T1. The above two elastic compliance constants S11 compared with S12.

(5) Piezoelectric constant

For a typical solid, the stress T only causes a proportional strain S of Pzt piezoelectric tubular transducer, which is related by the elastic modulus, that is, T = YS; the piezoelectric ceramic has piezoelectricity, that is, an additional charge can be generated when stress is applied. The charge generated is proportional to the applied stress. For pressure and tension, the sign is opposite. The dielectric displacement D (charge area) and stress T (force area) are expressed as follows: D=Q/A=dT where d is in coulomb/newton (C/N). This is the positive piezoelectric effect. There is also an inverse piezoelectric effect that produces a strain S proportionally when an electric field E is applied, and the resulting strain is either expanded or contracted depending on the polarization direction of the sample.In the formula S=dE, the unit of d is meters/volt (m/v). The proportionality constant d in the above two equations is called the piezoelectric strain constant. For positive and inverse piezoelectric effects, d is numerically the same,

(6)Frequency constant:

The frequency constant is the product of the resonant frequency and the dimension that determines the resonance. If the applied electric field is perpendicular to the vibration direction, the resonant frequency is the series resonant frequency; if the electric field is parallel to the vibration direction, the resonant frequency is the parallel resonant frequency. Therefore, for the resonance of the 31 and 15 modes and the resonance for the planar or radial mode, the corresponding frequency constants are NE1, NE5 and NEP, and the resonance frequency constant of the 33 mode is ND3. For a longitudinally polarized long rod, the frequency constant of the longitudinal vibration is usually expressed by ND3; for a thin wafer of any size that is resistant to linear polarization, the frequency constant of the thickness stretching vibration is usually expressed by NDT. The NDT and NDP of the wafer are important parameters. Except for the frequency constant NDP, the other frequency constants are equal to half of the main sound velocity in the piezoceramic body, that is, ND = 1/2 (SDpm) - 1/2 and NE = 1/2 (SEpm) - 1/2, where SD =SE(1-K2), each frequency constant has a corresponding lower corner.