材料物理性能3.ppt

单击此处编辑母版标题样式,,单击此处编辑母版文本样式,,第二级,,第三级,,第四级,,第五级,,,,*,7.8 Piezoelectricity, Ferroelectricity, and Pyroelectricity,7.8.1 Piezoelectricity,,Certain crystals, for example, quartz( crystalline SiO2) and BaTiO3, become polarized when they are mechanically stressed.,,1,,The piezoelectric effect.,,(a) A piezoelectric crystal with no applied stress or field.,,(b) The crystal is strained by an applied force that induces polarization in the crystal and generates surface charges.,,(c) An applied field causes the crystal to become strained. In this case the field compresses the crystal.,,(d) The strain changes direction with the applied field and now the crystal is extended.,Only certain crystals can exhibit piezoleectricity because the phenomen requires a special crystal structure,2,,A NaCl-type cubic unit cell has a,center of symmetry,.,,In the absence of an applied force, the centers of mass for positive and negative,,ions coincide.,,(b) This situation does not change when the crystal is strained by an applied force.,,,If we,graw,a vector from O to any charge and draw the reverse vector, we will find the same type of charge.,3,,(a) In the absence of an applied force the centers of mass for positive and negative ions coincide.,,(b) Under an applied force along y the centers of mass for positive and negative ions are shifted which results in a net dipole moment P along y.,,(c) When the force is along a different direction, along x, there may not be a resulting net dipole moment in that direction though there may be a net P along a different direction (y).,,A hexagonal unit cell has,no center of symmetry,.,,,If we graw a vector from O to any charge and draw the reverse vector, we will find an opposte charge.,4,,Piezoelectric Effect,P,i,= induced polarization along the,i,direction,,d,ij,= piezoelectric coefficients,,T,j,= mechanical stress along the,j,direction,P,i,= d,ij,T,j,Converse Piezoelectric Effect,S,j,= induced stain along the,j,direction,,d,ij,= piezoelectric coefficients,,E,i,= electric field along the,i,direction,S,j,= d,ij,E,i,5,,6,,Electro-Mechanical Coupling Factor,k,= electromechanical coupling factor,Electro-Mechanical Coupling Factor,k,= electromechanical coupling factor,7,,8,,The piezoelectric spark generator.,9,,Piezoelectric Voltage Coefficient,E,= electric field,,,g,,= piezoelectric voltage coefficient,T,= applied stress,E,=,g,T,Mechanical standing waves are formed in the piezoelectric crystal,n,= an integer,,,= wavelength of crystal vibrations,,,l,,= crystal (sample) length along which the waves are traveling,10,,7.8.2 Piezoelectricity:Quartz Oscillators and Filters,When a suitably cut quartz crystal with electrodes is excited by an ac voltage as (a), it behaves as if it has the equivalent Circuit in (b).,,(c) and (d),,The magnitude of the,,impedances Z and reactance (both between A and B) versus frequency, neglecting losses.,11,,Mechanical Resonant Frequency,f,s,= mechanical resonant frequency,,L,= mass of the transducer,,C,= stiffness,Antiresonant Frequency,f,a,= antiresonant frequency,,L,= mass of the transducer,,C,,is,C,o,and,C,in parallel, where,C,o,is the normal parallel plate capacitance between electrodes,12,,Piezoelectric transducers,,|SOURCE: Photo by SOK,13,,14,,(a) In the absence of an applied force the centers of mass for positive and negative ions coincide.,,(b) Under an applied force along y the centers of mass for positive and negative ions are shifted which results in a net dipole moment P along y.,,(c) When the force is along a different direction, along x, there may not be a resulting net dipole moment in that direction though there may be a net P along a different direction (y).,,A hexagonal unit cell has,no center of symmetry,.,,,If we graw a vector from O to any charge and draw the reverse vector, we will find an opposte charge.,15,,7.8.3 Ferroelectric and Pyroelectric Crystals,Ferroelectric Crystals,,Certain crystals are permanently polarized even in the absence of an applied field. The crystal already possesses a finite polarization vector due to the separation pf positive and negative charges in the crystal.,,These crystals are called ferroelectric.,,Example BaTiO3,16,,BaTiO,3,has different crystal structures above and below 130,,C that lead to different dielectric,,properties.,Above approximately 130℃,the crystal structure of BaTiO3 has a cubic unit cell,.The centers of mass of the negative charges （O2-）and the positive charges ,Ba2+and Ti4+ coincide at the Ti4+ ion .There is therefore no net polarization and P=0.,below 130℃, the structure of barium titanate is tetragonal, in which the Ti4+ atom is not located at the center of mass of the negative charges.,,The crystal is therefore polarized by the separation of the centers of mass of the negative and positive charges.,,The crystal possesses a finite polarization vector P and is ferroelectric.,,17,,An important and technological useful characteristic of a ferroelectric crystal is its ability to be poled.,,Above 130℃, there is no permanent polarization in the crystal. If we apply temporary field E and let the crystal cool to below 130℃, we can induce the spontaneous polarization P to develop along the field direction. In other words, we should define the c axis by imposing a temporary external field.,,This process is called poling. The c axis is the polar axis along which P develops. It also called the ferroelectric axis.,18,,All ferroelectric crystals are also piezoelectric, but the reverse is not true: not all piezoelectric crystals are ferroelectric.,,,When a,stress,along y is applied to the BaTiO3 crystal in Figure 7.45a, the crystal is stretched along y, as a result of which the Ti4+ atom becomes displaced, as shown in Figure 7.45b. There is, no shift in the center of mass of the negative charges, which means that there is a change △P in the polarization vector along y. Thus, the applied stress induces a change in the polarization, which is a piezoelectric effect.,,,If the stress is along x, as illustrated in Figure 7.45c, then the change in the polarization is along y. In both cases, △P is proportional to the stress, which is a characteristic of the piezoelectric effect.,19,,The barium titanate crystal is also said to be pyroelectric because when the temperature increases, the crystal expands and the relative distances of ions change.,,The Ti4+ ion becomes shifted, which results in a change in the polarization. Thus, a temperature change δT induces a change δP in the polarization of the crystal. This is called,pyroelectricity,, which is illustrated in Figure 7.46.,20,,The magnitude of this effect is quantized by the,pyroelectric coefficient,p, which is defined by,,A few typical pyroelectric crystals and their pyroelectric coefficients are listed in Table 7.9.,,Very small temperature changes, even in thousandths of degrees, in the material can develop voltages that can be readily measured.,21,,For example, for a PZT-type pyroelectric ceramic in Table 7.9, taking δT=10-3 K and p≈380*10-6 ，we find δP=3.8*10-7 Cm-2. From,,δP = εo(εr-1) δE,,with εr=290, we find,,δE=148Vm-1,,If the distance between the faces of the ceramic where the charges are developed is 0.1mm, then,,δV=0.0148 or 15mV,22,,1 Piezoelectricity: Certain crystals, become polarized when they are mechanically stressed.,,2. Certain crystals are permanently polarized even in the absence of an applied field. The crystal already possesses a finite polarization vector due to the separation pf positive and negative charges in the crystal.,,3. A temperature change δT induces a change δP in the polarization of the crystal. This is called,pyroelectricity,,7.8 Piezoelectricity, Ferroelectricity, and Pyroelectricity,23,,24,,25,,26,,27,,Piezoelectric transducers are widely used to generate ultrasonic waves in solids and also to detect such mechanical waves. The transducer on the left is excited from an ac source and vibrates mechanically. These vibrations are coupled to the solid and generate elastic waves. When the waves reach the other end they mechanically vibrate the transducer on the right which converts the vibrations to an electrical signal.,28,,。