Study on Polarization Characteristics of Piezoelectric Ceramics

As a new material that has emerged in recent years, piezoelectric ceramics are widely used in the manufacture of electronic products and laboratory research. The variation of the dielectric constant of piezoelectric ceramics is closely related to its structural characteristics and polarization mode. Therefore, studying the characteristics of its polarization mode has a high reference for a deeper understanding and research on the new materials such as piezoelectric ceramics. The polarization mode of piezoelectric ceramics was analyzed by experiments, and the polarization mode of piezoelectric ceramics was predicted under the condition of external alternating electric field. The dielectric spectrum was measured by an electric spectrometer, and the previously prediction was verified by the measuring dielectric spectrum and analyzed.

Polarization and dielectric parameters of piezoelectric ceramics crystals is mostly dielectric crystals, also known as dielectrics. Under the action of an external electric field, the dielectrics will react to the external electric field in the inductive manner. A certain amount of charge appears in the body or on the surface. This phenomenon is called on polarization. Electrodeization is represented by a macroscopic polarization vector P, which is equal to the vector sum of the electric dipole moments per unit volume. If the equal number charges which leaves a distance under the action of an electric field, which represents the electric dipole moment of the charge system, and the direction of l is directed by the negative charge to the positive charge. The essence of the polarization of the dielectric in the external electric field is that the charge is constituting the dielectric which has a macroscopic displacement under the action of the external electric field. The positive charge will be displaced along the power line, and the negative charge will shift the reverse power line, it is causing the dielectric to generate a macro-electric dipole moment. Within a certain range, the polarization P is proportional to the external electric field E P = ε0xE, and x is called the polarization rate. From the microscopic mechanism analysis, there are three ways to generate dielectric polarization, namely electron displacement polarization is used for displacement polarization and orientation polarization of polar molecules.regardless of the polarization actually is occurring, the result can be attributed to the formation of an electric dipole in the medium, which can be characterized by the electric dipole momentμof the molecule or atom. The size of μ is determined not only by the macroscopic electric field E, but also by the electric field generated by the adjacent molecules. The sum of the two is called the effective field Ei. In the formula μ = αEi, α is called the polarizability of a molecule or an atom, and it is a microscopic physical quantity describing the polarization characteristics of a molecule.

1.1Electron displacement polarization

Under the action of an external electric field, the electron cloud in the atoms and ions that make up the dielectric will be distorted,which causes the electron cloud to move relative to the nucleus, thus generating an electric dipole moment. This polarization is called the displacement polarization of electrons. Electron displacement polarization is a form of polarization that all dielectrics have. The displacement polarization of an electron indicates that due to the influence of the external electric field, the electron will have a certain probability of absorbing energy and transitioning between the corresponding energy levels. Since the outer electrons are weakly bound by atoms, the electron displacement of atoms is mainly derived from valence electrons. The displacement polarizability of the electron is represented by αe, and it is assumed that the molecule under consideration is a sphere, which is calculated by a point-charge sphere piezo ceramic model and a circular orbit model.

Ion displacement polarization

Orientation polarization of the intrinsic electric dipole moment

If the molecule is constituting the dielectric which is a polar molecule ,whose positive charge center does not coincide with the center of the negative charge, it has an inherent electric dipole moment. In the absence of an external electric field, since the electric dipole moment of the thermal motion dielectric molecules of piezoelectric ceramic component is spatially disordered, the probability of pointing in all directions is the same, and the molecular electric dipole moments cancel each other out. Therefore, the dielectric as a whole has no electric dipole moment. When an external electric field is applied, the positive and negative charges of the molecular electric dipole are affected by the electric field force, and there is a tendency to point toward the direction of the external electric field, or they must be kept in a stable state, so that the energy of the system is minimized, and it is necessary to point to the direction of the external electric field. Or precession around an external electric field. According to statistical theory, the number of particles at energy E is proportional to e=-EkT. According to this, the polarizabilityαd of the orientation polarization of the dielectric molecule can be calculated. Dd=μ2 .In the 3kT formula, μ is the molecular intrinsic electric dipole moment, k is the Boltzmann constant, and T is the temperature.

The total polarizability α of the molecule can be considered as the sum of the polarizabilities of various mechanisms α = αe + αa + αd. If the number of molecules per unit volume is N, the macroscopic polarization vector P can be correlated with the microscopic molecular polarizability α. P=NαEiP=ε0(εr-1)E=NαEi, so the effective electric field Ei perceived by each molecular polarization in the dielectric constant medium is different from the macroscopic average electric field E. For a molecule, it is not only affected by E, but also by the electric field generated by other polarizations. It is envisaged that the molecular model examined is a sphere, and the radius of the sphere is much larger than the spacing of the atoms. The influence of molecular polarization outside, the ultrasonic piezoelectric transducer can be treated as a continuous polarized medium in a macroscopic way. The degree responses to the change of the external field during the polarization of the medium is represented by the relaxation time τ. The physical meaning of τ is adding a constant electric field to the dielectric, removing the electric field after the polarization is stabilized, and passing the time τ, the polarization P .The sum of the electric dipole moment vectors in the volume is reduced to 1/e of the original pm, ie P=Pmetτ. Since there is relaxation in the polarization process, D (displacement vector), P and E changes are not in phase. D, P will lag behind the phase of E. The sinusoidal alternating electric field is represented by a complex number. In order to measure the dielectric spectrum of the piezoelectric ceramic, in this experiment, a buzzer made of piezoelectric ceramic is placed between two circular electrode sheets, and the angular frequency is added to the electrode sheet and sinusoidal voltage of ω.