induced _ electric _ field = = = = σ V

Transcription

1 The Figure shows that the open-circuit voltage V (an hence the fiel strength ) is proportional to compressive stress T up to a maximum of 5 kv, which occurs at a stress of 50 MPa. Inuce electrical fiel 5000 V V. m 0.0m g inuce _ electric _ fiel mechanical _ stress _ applie g V. m Pa V Pa m

2 The piezoelectric charge constant, (), polarization generate per unit of mechanical stress (irect), or, mechanical strain experience by a piezoelectric per unit of electric fiel applie (converse). The piezoelectric voltage constant, (g), is the electric fiel generate by a piezoelectric material per unit of mechanical stress applie or, alternatively, is the mechanical strain experience by a piezoelectric material per unit of electric isplacement applie. Definitions of frequent use g P g D Inuce _ Polarization Mechanical _ Stress _ applie mechanical _ strain _ obtaine electric _ fiel _ applie inuce _ electric _ fiel mechanical _ stress _ applie mechanical _ strain obtaine electric _ isplacement _ applie g r O

3 xample (Piezoelectric) The piezoelectric spark generator as use in various applications such as lighters an car ignitions, operates by stressing a piezoelectric crystal to generate a high voltage which is ischarge through a spark gap in air (see (a) F figure below). The breakown fiel for air is 3x10 6 V.m -1. If you consier a gap of 1mm it is about 3000V. L A F Piezoelectric V Piezoelectric Piezoelectric F F (b) Fig. 7.39: The piezoelectric spark generator From Principles of lectronic Materials an Devices, Secon ition, S.O. Kasap ( McGraw-Hill, 00)

4 Aitional Notes The ratio of strain to electric fiel is calle the constant for a piezoelectric. The ratio of electric fiel generate to stress applie is calle the g constant (piezoelectric voltage coefficient) for a piezoelectric, where (V/m) is the electric fiel, is the strain, is the stress (Pa) The g an are relate to the ielectric constant as follows: where r is the ielectric constant an O is the permittivity uner vacuum (8.85x10-1 F/m). g strain electric _ fiel _ generate electric _ fiel _ generate stress g r O

5 Consier a piezoelectric sample in the form of a cyliner (see figure). Suppose that the piezoelectric coefficient 50x10-1 m.v -1 an r The piezoelectric has a length of 10mm an a iameter of 3mm. The spark gap is in air an has a breakown voltage of about 3.5kV. What is the force require to spark the gap? Is this a realistic force? Solution g r O m. V 1 ( ) ( F. m ) A F g m.( V. F) 1 L Piezoelectric V V V. m L 0. 01m 3500 V 5 1 F

6 g g V. F. m Force Area F N V. m ( V. F) F A F m N. m A Fara F units (kg -1 m - s 4 A ) VoltsV units (kg m s -3 A -1 ) NewtonN units (kg m s -) π This force (about 9kg-f) can be applie by squeezing by han an appropriate lever arrangement. The force must be applie quickly because the piezoelectric charge generate will leak away (become neutralize). The voltage generate can be increase (or the force neee reuce) by using two piezoelectric crystals back to back.

7 Piezoelectric Constants Because a piezoelectric is anisotropic, its physical constants (elasticity, permittivity, etc.) are tensor quantities an relate to both the irection of the applie stress or electric fiel an the irections perpenicular to these. ach constant generally has two subscripts that inicate the irections of the two relate quantities, such as stress an strain for elasticity. Piezoelectric Ceramics: The irection of positive polarization is mae to coincie with the Z-axis of a orthogonal system of X, Y, an Z axes. Direction X, Y, or Z is represente by the subscript 1,, or 3, respectively, an shear about one of these axes is represente by the subscript 4, 5, or 6, respectively.

8 Piezoelectric Charge Constant (): ab xample: P Inuce Mechanical Polarization Stress _ applie a inicates the irection of inuce polarization of the material when the electric fiel is zero or the irection of the applie electric fiel b inicates the irection of the applie stress or the irection of the strain. 13 inuce polarization voltage measure in the irection 1 (perpenicular to the poling irection) when a stress is applie in a irection 3 or or inuce strain in the irection 3 when an electric fiel is applie in the irection 1 (perpenicular to the poling irection). mechanical _ strain _ obtaine electric _ fiel _ applie

9 ab 33 inuce polarization in irection 3 (parallel to irection in which ceramic element is polarize) per unit stress applie in irection 3 or inuce strain in irection 3 per unit electric fiel applie in irection 3 15 inuce polarization in irection 1 (perpenicular to irection in which ceramic element is polarize) per unit shear stress applie about irection (irection perpenicular to irection in which ceramic element is polarize) or inuce shear strain about irection per unit electric fiel applie in irection 1

10 Piezoelectric Voltage Constant (g) g ab g g D inuce _ electric _ fiel mechanical _ stress _ applie mechanical _ strain obtaine electric _ isplacement _ applie a inicates the irection of the inuce electric fiel on the material or the irection of the applie electric isplacement. b inicates the irection of the applie stress or the irection of the obtaine strain. xample: g 31 inuce electric fiel in irection 3 (parallel to irection in which ceramic element is polarize) per unit stress applie in irection 1 (perpenicular to irection in which ceramic element is polarize) or inuce strain in irection 1 per unit electric isplacement applie in irection 3.

11 g ab g 33 inuce electric fiel in irection 3 (parallel to irection in which ceramic element is polarize) per unit stress applie in irection 3 or inuce strain in irection 3 per unit electric isplacement applie in irection 3 g 15 inuce electric fiel in irection 1 (perpenicular to irection in which ceramic element is polarize) per unit shear stress applie about irection (irection perpenicular to irection in which ceramic element is polarize) or inuce shear strain about irection per unit electric isplacement applie in irection 1

12 If T j is the applie mechanical stress along some j irection an P i is the inuce polarization along some i irection, we relate them via P i ij T j where ij are calle piezoelectric coefficients an T can represent either tensile or shear stresses. An equivalent relation between the strain S j along the j irection an the electric fiel i along the i irection is given by S j ij i

13 ffect of Stress on Tetraheral groups in Piezoelectrics (e.g. Quartz)

14 Piezoelectric crystals are essentially electromechanical transucers as they convert electrical signals to mechanical signals, strain or vice versa. Typical engineering applications: ultrasonic transucers, microphones, sonar etectors, accelerometers, frequency control of oscillators an filters, monitoring of thin film eposition. g. In phonographic pick-ups; stylus traverses grooves of recor pressure variation impose on a piezoelectric material locate in cartrige transforme into electrical signal amplifie an broacaste through speaker. fficiency of conversion between electrical an mechanical energy is given by the electromechanical conversion factor K efine in terms of K by K mechaniucal _( electrical) _ energy _ output electrical _( mechanical) _ energy _ input

15 Characteristics: Light weight an compact. Inexpensive Relative linear fiel-strain relations at low rive levels. Broaban rive capabilities Very high set-point accuracy Actuator an sensor capabilities Due to the non-centrosymmetric nature of ferroelectric materials they exhibit hysteresis an constitutive non-linearities at all rive levels. For low rive regimes these effects can be mitigate through feeback mechanisms. For high rive regimes, it is necessary to employ charge or current control. lectrostatic transucers constructe from relaxors ferroelectric materials are avantageous ue to the fact that they exhibit minimal hysteresis. Unlike piezoelectric materials, electrostrictive compouns are not pole an hence exhibit few aging effects.

16 Direct piezoelectric effect: In this effect an electric polarization P arises as a result of an applie stress. The applie stress is in reality a stress tensor given by Then, the polarization in the i irection (axis), is relate to the stress jk by the coefficient ijk. For example: τ τ P xx xy xz τ τ yx yy yz τ τ i ijk jk P P P zx zy zz D (C/m ) Ε ο (electric fiel V/m) D Ε ο P Dielectric isplacement jk The 7 ijk are the piezoelectric mouli an form a thir rank tensor. As ijk ikj, there are up to 18 inepenent mouli.

17 P P P P

18 Converse piezoelectric effect: In this effect a strain arises as a result of an applie electric fiel. The mouli are the same as for the irect effect jk i ijk i

19 In a matrix form

20 Crystal Orientation The irection in which tension or compression evelops polarization parallel to the strain is calle the piezoelectric axis. In quartz, this axis is knows as the "Xaxis", an in pole ceramic materials such as PZT the piezoelectric axis is referre to as the "Z-axis". From ifferent combinations of the irection of the applie fiel an orientation of the crystal it is possible to prouce various stresses an strains in the crystal. For example, an electric fiel applie perpenicular to the piezoelectric axis will prouce elongation along the axis as shown. If, however, the electric fiel is applie parallel to the piezoelectric axis, a shear motion is inuce.

21

22 Neumann s Principle This is the most important concept in crystal physics. It states;... the symmetry of any physical property of a crystal must inclue the symmetry elements of the point group of the crystal. This means that measurements mae in symmetry-relate irections will give the same property coefficients. xample: NaCl belongs to the m3m group. The [100] an [010] irections are equivalent. Since these irections are physically the same, it shoul be expecte that measurements of permittivity, elasticity or any other physical property will be the same in these two irections.

23 Piezoelectric Symmetry Groups In 0 out of the 1 acentric point groups (only the 43 is exclue) the application of a stress ( hk ) along a suitable irection generates an electric ipole (P).

24 The relationship between the ipole Pi an the stress ( hk ) is P i ihk h, k hk The ihk are the components of a thir rank tensor known as piezoelectric tensor. 7 components are expecte for a thir rank tensor ihk. However, the stress tensor is symmetrical so ihk ikh an the number of components reuces to 18 (triclinic crystals). Crystal symmetry constrain the 18 components in triclinic crystals to 10 or 8 in monoclinic crystals, 9 in orthorhombic, 7-6 in tetragonal, 6-4 or in trigonal, 4- or 1 in hexagonal an 1 in cubic.

25 Quartz (Point Group 3)

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28 Applications of ferroelectrics The worl market for ferroelectric materials an evices is in the range $0-30billion per annum. Capacitors The wiest application of ferroelectrics (not making use of ferroelectricity but simply the high ielectric constant) is in capacitors. BaTiO 3 has cornere more than 50% of the ceramic capacitor market. For a given volume, a BaTiO 3 capacitor has times the capacitance of a linear ielectric. Ferroelectric memories (FeRAM) Ferroelectrics exhibit bi-stable polarization (±Pr when Ε 0). Hence, binary memory systems can be esigne base on the ifferent polarization states, Pr 0, -Pr 1. e.g. computer RAM. In FeRAM ata (in the form of polarization state Pr 0, -Pr 1) is recore on the material an is non-volatile (NV-RAM) it is retaine when the voltage is turne off.

29 Square hysteresis loops are require for memory evices since it is easier to istinguish between the remanent polarization states of the material ± Pr. Hysteresis loops have ifferent shapes. Psat Ps for a strongly sigmoial loop, whereas Psat Ps Pr for a square loop.

30 The applie fiel (i.e. rea / write operations) is controlle by fiel effect transistors (millions on a chip). They aress the ferroelectric cells an isolate them from their neighbors. Switching occurs by omain wall motion must be fast to compete with Si-base memories where switching occurs by electron motion. The materials requirements for FeRAM are high κ, high Psat (an Pr), small an high Tc (operable at RT an slightly above). xamples are LiNbO 3, PbTiO 3, Pb(ZrxTi 1-x )O 3 (PZT) SrBi Ta O 9 (SBT). The materials nee to be mae in thin film form (few hunre nm) in orer to minimize switching voltage. The wie scale application of FeRAM evices will epen on the successful materials science, namely optimization of composition, microstructure, interface quality with the electroes, an controlling the nano-scale omain wall pinning efects. Target applications of FeRAM inclue cell phones, smart cars, vieo games.