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Piezoelectric and Pyroelectric Dielectrics

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Piezoelectric and Pyroelectric Dielectrics Lecture 5.8: Piezoelectric and Pyroelectric Dielectrics 1) Piezoelectric Ceramics Piezoelectric effect was discovered by Jacques and Pierre Curie in 1888. Direct piezoelectric effect is the ability of some materials to create an electric potential in response to applied mechanical stress. The applied stress changes the polarization density within the material's volume leading to the observed potential. As a requirement, only materials with non- centrosymmetric crystal structure can exhibit piezoelectric effect. Some of the commonly used/known piezoelectric materials are quartz (SiO2), zinc oxide (ZnO), polyvinylidenefluoride (PVDF) and lead zirconate titanate, (PZT or Pb(Zr,Ti)O3). An oscillating applied stress on a piezoelectric material can give rise to the field which can be applied to an electrical load such as a bulb. Another example can be charging of your mobile or any other device in your backpack while you walk. You could not achieve the same while standing. For a detailed discussion on the piezoelectric properties, materials, and applications, readers are referred to the book titled Electroceramics by A.J. Moulson and J.M. Herbert. 2) Direct Piezoelectric Effect Direct effect occur when applied stress to material gives rise to a change in the polarization density which in turn can be detected as electric field or potential across the sample. Here, the polarization is directly proportional to the stress applied, as described by the equation P = d. σ (33) where P is polarization, is applied stress and d is piezoelectric coefficient (actually a third rank tensor). 3) Reverse or Converse Piezoelectric Effect Reverse is true is when an electric field is applied to the material and as a result, a strain is induced expressed as ε = d. E (34) where is strain induced, d is piezoelectric coefficient and E is the applied electric field. The direct piezoelectric effect is used as the basis for force, pressure, vibration and acceleration sensors while converse effect is used as a basis for actuator and displacement devices. F F Direct Piezoelectric Effect P A A F F - Converse Piezoelectric + E E + Effect - Contraction Expansion Figure 1 Direct and Converse Piezoelectric Effects 4) Poling of Piezoelectric Materials As obvious from the previous sections (1 and 2), there are some piezoelectrics such as quartz which are not spontaneously polarized but get polarized upon application of stress while ferroelectric which are anyway piezoelectric in nature are spontaneously polarized and show a change of polarization upon application of stress. The values of piezoelectric coefficient of some materials are given below: Material Piezoelectric Constant, d (pm/V) Quartz 2.3 Barium Titanate 100-149 Lead Niobate 80-85 Lead zirconate titanate 250-365 So, you can observe from this table that the level of strain generated is not so massive but is still important because of preciseness and reversibility of the effect. Most ferroelectrics have to be poled to be useful as a piezoelectric. In the unpoled virgin state of the material, the ferroelectric domains of single polarization direction are randomly distributed across the material and in such a situation the net polarization would be zero. Application of stress to such a material would not achieve any change in the net polarization thus making it useless as a piezoelectric. Poling i.e. application of a large electric field near Tc (just below Tc) orients the domains along the field and when field is removed, the domain structure does not get back to original condition giving rise to a net polarization along a certain direction. Now, when a stress is applied to such a crystal, noticeable change in the polarization can be observed. E PR Before poling, PR = 0 After poling, PR = 0 Polarization increases Polarization decreases Figure 2 Poling of ferroelectrics and application of stress on poled material 5) Depolarization of Piezoelectrics Just like a ferroelectric material can be poled, opposing polarity high electric field or thermal cycling close to Tc or application of large mechanical stresses can lead to disappearance of polarization or rather result in alignment of dipoles gets lost. 6) Common Piezoelectric Materials a) Barium Titanate (BaTiO3) This was the first piezoelectric material which was developed commercially for application in the generation and detection of acoustic and ultrasonic energy. We discussed its structure and transitions in the previous section (2.6). The transition temperature can be modified by chemical substitutions: Ba substitution by Pb and Ca lowers the Tc of tetragonal to orthorhombic transition. This has been used to control the piezoelectric properties around 0C, important for underwater detection and echo sounding. Ti substitution by Zr or Sn increases the transition temperature for both the tetragonal– orthorhomic and orthorhomic–rhombohedral transitions and enhances piezoelectric properties. Ti substitution by 1-2 at% Co3+ leads to much reduced losses as high fields useful in ultrasonic applications. Care must be taken during processing to avoid reduction of Co3+ to Co2+ which occurs very easily. b) Pb(Zr,Ti)O3 or PZT PZT is one of the most used piezoelectric in a variety of applications due to its excellent properties and high enough transition temperatures. It has a perovskite structure with B sites randomly occupied by either of isovalent Ti and Zr ions. The phase diagram of PZT is shown below. © DoITPoMS, University of Cambridge 800 TC Cubic 700 ) K Rotational ( phase e 600 r u t Ferroelectric a r Ferroelectric Tetragonal e 500 Rhombohedral p High-temperature m e T 400 Morphotropic phase Ferroelectric boundary or MPB Rhombohedral 300 Low-temperature 0 20 40 60 80 100 PbZrO3 PbTiO3 Mol % PbTiO 3 Figure 3 Phase diagram of PZT (Courtesy: © DoITPoMS, University of Cambridge, http://www.doitpoms.ac.uk/tlplib/piezoelectrics/images/img017.gif ) The typically used composition is about Zr:Ti::50:50 which gives excellent properties. The reason for this is that this is closed to morphotropic phase boundary and here rhombohedral and tetragonal structures co-exist. As we know that Ps vector is along [001]-direction in tetragonal phase and <111>-direction in rhombohedral phase, it permit material to be poled easily as there are quite a few poling directions available making it a useful piezoelectric. Donor doping in PZT such as La3+ on Pb site reduces the concentration of oxygen vacancies. This in turn reduces the concentration of defect pairs which otherwise impede the domain wall motion. This leads to noticeable increases in the permittivity, dielectric losses, elastic compliance and coupling coefficients, and reduction in the coercivity. 7) Measurement of Piezoelectric Properties Piezoelectric measurements are usually made to measure the displacement of the material when an electric field is applied. These techniques are resonance or subresonance techniques. In the resonance methods, one conducts the measurement of the characteristic frequencies of the materials upon the application of alternating electric field and is widely used for bulk samples. To a first approximation, the electromechanical response of a piezoelectric material close to the characteristics frequency can represented by the electrical equivalent circuit as shown in the figure 24. Simplest measurements are conducted by poling a piezoelectric long rod of length ~6 inch and diameter ~¼ inch along its length. Mechanical part Electrical part (Figure to be drawn) Figure 4 Schematic representation of (a) equivalent electrical circuit of a piezoelectric sample close to its characteristic frequency (b) Plot of electrical reactance os the sample a function of frequency The coupling coefficient, k33, is expressed in terms of series and parallel resonance frequencies (fs and fp respectively) as 2 휋 푓푠 휋 (푓푝−푓푠) 푘33 = 푡푎푛 ( ) (35) 2 푓푝 2 푓푝 퐸 Using this relation along with elastic compliance 푠33 and low frequency dielectric constant 푋 휀33, the piezoelectric coefficient, d33, can be calculated by using the following relation: 1 퐸 푋 푑33 = 푘33. (푠33 × ε33)2 (36) Measurements are limited to the specific frequencies determined by the fundamental vibration modes of the sample. In the case of piezoelectric thin films, the thickness resonance occurs in the GHz range in which the measurements involve considerable difficulties. In such cases, the resonance in the substrate driven by a thin film could be used to determine the piezoelectric coefficient of a thin film. The disadvantage of this method is that measurements are limited by the number of characteristics frequencies determined by the electromechanical response of a material. One can use subresonance techniques for the measurement of piezoelectric properties at the frequencies which are much below the characteristics fundamental resonance frequencies. This includes measurement of direct effect i.e. charge developed on a piezoelectric material under application of an external mechanical stress and measurement of converse effect i.e. measurement of electric field induced displacements. Although displacements can be rather small to measure accurately, technological advances have allowed accurate measurements using techniques like strain gauges or linear variable differential transformers (LVDTs) or optical interferometers or atomic force microscopes. Appropriate electrical circuits needs to drawn and modeled to clearly elucidate the material properties. 8) Applications of Piezoelectric Ceramics Piezoelectric ceramics are used in a variety of applications
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