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Piezoelectricity

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The piezoelectricity of minerals refers to medium Of single crystal , can make the crystal perpendicular to stress The property of having an equal amount of opposite charges on the surfaces of both sides of the. If the stress direction reverses charge Change number.

crystal Such single crystals are piezoelectric.

Chinese name: Piezoelectricity
Object: single crystal

Characters: P. Curie and the J. Curie brothers
Discovery time: 1880

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seven Piezoelectric effect

Historical evolution

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The property that a dielectric polarizes under pressure, resulting in a potential difference between the surfaces at both ends.

In 1880, French brothers P. Curie and J. Curie discovered quartz crystal Under pressure, some of its surfaces will generate electric charges, Charge quantity Is proportional to the pressure; This phenomenon is called Piezoelectric effect ； Objects with piezoelectric effect are called Piezoelectric body 。

The Curie brothers also confirmed that piezoelectric materials have Inverse piezoelectric effect That is, the piezoelectricity will deform under the action of an external electric field. Piezoelectric crystals have low symmetry. When they are deformed by external forces Monad The relative displacement of positive and negative ions makes the center of positive and negative charges move unequally, leading to the macroscopic polarization of the crystal; And crystal Surface charge density be equal to Polarization intensity The projection on the surface normal direction, so the surface charge appears when the crystal is deformed under pressure.

Piezoelectric constant

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Fang Cheng 1

External electric field Crystalline Polarization intensity Are vectors in Rectangular coordinate system Whose components are respectively recorded as Eα and pα ; α =1、2、3。 Strain of crystal s It's a second-order symmetry tensor , only six independent components, recorded as S i; i =1. 2 and 3 correspond to three longitudinal strain components; i =4. 5 and 6 correspond to three shear strain components. When the deformation is not too large Piezoelectric effect Is linear,

The equation set can be described as (1)

about Inverse piezoelectric effect Yes (2)

Formula 2

call eα I is piezoelectric constant, also called piezoelectric stress coefficient. call dα I is piezoelectric modulus, also called piezoelectric strain coefficient. e and d It's all third-order tensor , commonly known as piezoelectric tensor, can generally have 18 independent components each. The symmetry of the crystal can further reduce the number of non-zero independent components of the piezoelectric tensor.

Crystal point group

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In 32 crystal point groups (see Symmetry of crystal ）11 of them have Symmetrical center ； Piezoelectric crystal with symmetric center tensor All components of are equal to zero, and none of them are Piezoelectric body 。 Although the crystal belonging to point group 432 has no symmetry center, it has high symmetry and no piezoelectricity. Piezoelectric crystals can only belong to 20 point groups (see the table below):

Dielectric crystals (32 kinds)
Crystals without symmetry center (21 kinds) Among them, piezoelectric crystals (20 kinds)	Polar crystals (pyroelectric crystals) (10 kinds)	1，2，3，4，6， m，mm2，4mm，3m，6mm
	Non polar crystals (11 kinds)	222，-4，422，-42m，32，-6，622，-6m2，23，-43m 432 (not piezoelectric)
Crystals with symmetrical center (11 kinds)		-1，2/m， mmm，4/m，4/mmm， -3，-3m，6/m，6/mmm，m3m，m3

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ZnS with sphalerite structure belongs to point group 嬄 3 m , its piezoelectricity tensor Only one non-zero independent component d 14= d 25= d 36。 The piezoelectric tensor of crystals belonging to point group 1 can have 18 non-zero independent components.

e and d They are not independent of each other. Their components are linked by the elastic coefficient of the crystal, and the relationship between them can be obtained from the thermodynamic theory. The value of the piezoelectric tensor component is related to the direction of the coordinate system relative to the crystal axis. Since the 1950s, the IRE standards in general use in the world Rectangular coordinate system 。 When Piezoelectric body When the strain of is large, Piezoelectric effect appear Nonlinear 。

Piezoelectric material

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definition

Piezoelectric material Ferroelectric single crystals and ferroelectric ceramics (see Ferroelectricity ）After artificial polarization Piezoelectric body 。 Non ferroelectric piezoelectric body can be single crystal or Polymer 。 For the main properties of piezoelectric materials used in technology Elastic constant 、 Dielectric constant , piezoelectric constant and Electromechanical coupling coefficient These parameters are often simply called the electroelastic constants of piezoelectric bodies. The electromechanical coupling coefficient is determined by Piezoelectric effect The ratio of the converted energy to the total energy input into the piezoelectric body marks the efficiency of the piezoelectric body when it converts mechanical energy into electrical energy. Dielectric and mechanical properties of piezoelectric materials Loss tangent The reciprocal of is called electrical quality factor and mechanical quality factor respectively.

Natural piezoelectric materials

Natural piezoelectric materials include quartz, tourmaline, etc. Synthetic materials include Potassium sodium tartrate 、 Ammonium dihydrogen phosphate , artificial quartz Piezoelectric ceramics 、 Lithium iodate 、 lithium niobate , zinc oxide and polymer piezoelectric film, etc. Since the 1950s, Chinese academies of science, universities, industrial and mining enterprises and other units have extensively synthesized artificial piezoelectric materials. They have achieved good results and large-scale production in most aspects of the above materials, solved domestic needs, and gained international attention.

Barium titanate piezoelectric ceramics

Barium titanate piezoelectric ceramics were discovered in the 1940s, and then a series of other piezoelectric ceramics were made. Because ceramics are insoluble in water, have high working temperature, high mechanical strength, and are easy to be made into various required geometric shapes at low cost Piezoelectric body Its application has been greatly developed. Piezoelectric ceramics are ferroelectric Polycrystal 。

Ferroelectric ceramics generally do not have piezoelectricity, but after artificial polarization Electric moment The orientation is dominant along the direction of the external electric field during polarization, resulting in a macroscopic surplus with an average of non-zero Polarization intensity p R and become piezoelectric ceramics. Usually ceramic p R is higher than the same material single crystal Of Spontaneous polarization p S is much smaller. The macroscopic properties of piezoelectric ceramics The directional symmetry belongs to Point group ∞ m Its infinite symmetry axis is along the direction of the applied electric field during artificial polarization. The number of non-zero independent components of its piezoelectric tensor is equal to 6 mm Same, i.e

d 31= d 32， d 33， d 15= d 24。

Lead zirconate titanate binary piezoelectric ceramics

The most widely used is lead zirconate titanate binary piezoelectric ceramics, referred to as PZT. This series of materials Homomorphic phase boundary It has high piezoelectric property nearby, and the performance can be adjusted by changing the composition and doping. Its Curie point is above 350 ℃, Electromechanical coupling coefficient Up to 0.7, p R can reach 0.4C/m2, d15 can reach 7 × 10-10C/N, d33 can reach 5 × 10-10C/N, and d31 can reach - 2 × 10-10C/N. Piezoelectric resonator Piezoelectric crystal is usually cut into a certain geometric shape in a special way, and then a pair of appropriate electrodes are added on the surface, using its mechanical resonance performance and Piezoelectric effect Phase coupling becomes piezoelectric resonator. The normal direction of the thin slice vibrator along the x, y or z axis is called X cut, Y cut and Z cut respectively; See Figure 1, where the relationship between the coordinate system and the crystal axis is specified in IRE standard. There are many special cutting methods for different piezoelectric crystals according to the requirements of application.

equation

Quartz crystal is β Type, genus Point group 622； When the temperature drops to 573 ℃ α Type, belonging to point group 32. Usually used α Quartz, commonly known as crystal in China, or quartz for short. its z Shaft and tertiary Axis of symmetry Parallel is the optical axis; x The axis is along the quadratic symmetry axis, which is a Polar axis , called electric shaft; y Axis perpendicular to zx Plane, called mechanical shaft. Figure 1 also shows two special orientation cutting methods of quartz, called AT cutting and GT cutting; The resonant frequencies of these two kinds of chips are independent of temperature in the room temperature range. Piezoelectricity of α quartz tensor Only two non-zero independent components

equation

In the formula, a positive sign is used for left-handed quartz data and a negative sign is used for right-handed quartz data.

Piezoelectric oscillators with various resonant modes can be designed. For example, an X-cut quartz sheet with electrodes on both sides (Fig. 2a) can excite various modes of mechanical resonance with AC voltage at different frequencies according to the design shape of the sheet. Figure 2b shows the utilization of d 11 excited thickness resonance. Figure 2c shows the utilization of d 12 excited longitudinal length resonance, Figure 2d shows the use of d 14 Excited shear resonance. Piezoelectric vibrators made of different materials can also excite other more ways of resonance, such as radial resonance of the disk, bending resonance of the strip, and so on.

Piezoelectric resonator

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Piezoelectricity

The frequency characteristics of the piezoelectric resonator near the resonance region can be described by the equivalent circuit of Figure 3. It has a series connection resonant frequency And a parallel resonant frequency. By equivalent circuit The measurement of various electrical performance parameters can calculate the Elastic constant , dielectric constant, piezoelectric constant Electromechanical coupling coefficient Isoelectric elastic constants and the Q Value.

Application of piezoelectric body

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Piezoelectricity

Single crystal and ceramic piezoelectric resonators are widely used as frequency stabilizing elements and Bandpass filter 。 Quartz crystal has good chemical, mechanical and aging properties; Quartz oscillator Q Up to 105; The oscillation circuit composed of AT or GT cut quartz oscillator can achieve long-term low frequency Stability Not more than 1/109; It can be used for quartz clock and is a modern time standard.

Piezoelectric body is used as Electroacoustic transducer It is very effective in generating or receiving sound waves, and is widely used in sonar, ultrasonic nondestructive testing, power ultrasonic and buzzer. The theoretical maximum intensity of ultrasonic wave generated by quartz in water can reach 2000W/cm2. utilize Piezoelectric effect Excitable Mechanical wave The highest frequency has reached 1011Hz or even 1012Hz, that is, microwave frequency band or even far infrared frequency band. Used in recent years lithium niobate When the single crystal is made Surface acoustic wave device , widely used in TV IF filters.

Piezoelectric effect

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Piezoelectricity

Piezoelectric effect can produce high voltage for ignition and detonating devices. from inertia force adopt Piezoelectric effect Generated electrical signal It can be used to measure acceleration and navigation. piezoelectricity single crystal And transparent piezoelectric ceramics are widely used in laser technology. Piezoelectrics also have many unique applications in information processing and electronic computers.

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