Electromechanical coefficients

Anomalous slope of x or e in the vicinity of the phase transition is a reason for the anomalous behavior also for quantities d,e,c, s (tensor indexes are omitted for simplicity) measured at constant electric field. It follows from the thermodynamic relations between the electromechanical coefficients shown in Table 4.3. On the contrary, no anomaly in the temperature dependencies for quantities g,h,cP,P measured at constant electric displacement D (or constant polarization P) is observed. 

Book content is otganized in seven chapters and one Appendix. Chapter 1 is devoted to the fnndamental principles of piezoelectricity and its application including related histoiy of phenomenon discoveiy. A brief description of crystallography and tensor analysis needed for the piezoelectricity forms the content of Chap. 2. Covariant and contravariant formulation of tensor analysis is omitted in the new edition with respect to the old one. Chapter 3 is focused on the definition and basic properties of linear elastic properties of solids. Necessary thermodynamic description of piezoelectricity, definition of coupled field material coefficients and linear constitutive equations are discussed in Chap. 4. Piezoelectricity and its properties, tensor coefficients and their difierent possibilities, ferroelectricity, ferroics and physical models of it are given in Chap. 5. Chapter 6. is substantially enlarged in this new edition and it is focused especially on non-linear phenomena in electroelasticity. Chapter 7. has been also enlarged due to mary new materials and their properties which appeared since the last book edition in 1980. This chapter includes lot of helpful tables with the material data for the most today s applied materials. Finally, Appendix contains material tensor tables for the electromechanical coefficients listed in matrix form for reader s easy use and convenience. 

With regard to the electromechanical coefficients of the beam, two different cases need to be distinguished. For schemes / and II of Table 10.2 with consistent electric conditions aroimd the cross-section, given by Eqs. (10.8), the following coefficients are applicable ... 

For scheme III with changes in the electric sign between adjacent quadrants, as described by Eqs. (10.9), the electromechanical coefficients of the beam become... 

The semiconducting properties of the compounds of the SbSI type (see Table XXVIII) were predicted by Mooser and Pearson in 1958 228). They were first confirmed for SbSI, for which photoconductivity was found in 1960 243). The breakthrough was the observation of fer-roelectricity in this material 117) and other SbSI type compounds 244 see Table XXIX), in addition to phase transitions 184), nonlinear optical behavior 156), piezoelectric behavior 44), and electromechanical 183) and other properties. These photoconductors exhibit abnormally large temperature-coefficients for their band gaps they are strongly piezoelectric. Some are ferroelectric (see Table XXIX). They have anomalous electrooptic and optomechanical properties, namely, elongation or contraction under illumination. As already mentioned, these fields cannot be treated in any detail in this review for those interested in ferroelectricity, review articles 224, 352) are mentioned. The heat capacity of SbSI has been measured from - 180 to -l- 40°C and, from these data, the excess entropy of the ferro-paraelectric transition... 

The class of ferroelectric materials have a lot of useful properties. High dielectric coefficients over a wide temperature and frequency range are used as dielectrics in integrated or in smd (surface mounted device) capacitors. The large piezoelectric effect is applied in a variety of electromechanical sensors, actuators and transducers. Infrared sensors need a high pyroelectric coefficient which is available with this class of materials. Tunable thermistor properties in semiconducting ferroelectrics are used in ptcr (positive temperature coefficient... 

The electromechanical coupling coefficient (k) is a measure of the ability of a piezoelectric material to transform mechanical energy into electrical energy, and vice versa. It is defined [5] by... 

Table 1.1. Abundance of the metal in the earths s crust, optical band gap Es (d direct i indirect) [23,24], crystal structure and lattice parameters a and c [23,24], density, thermal conductivity k, thermal expansion coefficient at room temperature a [25-27], piezoelectric stress ea, e3i, eis and strain d33, dn, dig coefficients [28], electromechanical coupling factors IC33, ksi, fcis [29], static e(0) and optical e(oo) dielectric constants [23,30,31] (see also Sect. 3.3, Table 3.3), melting temperature of the compound Tm and of the metal Tm(metal), temperature Tvp at which the metal has a vapor pressure of 10 3 Pa, heat of formation AH per formula unit [32] of zinc oxide in comparison to other TCOs and to silicon...

The stiffness parameter C55 has, in effect, been increased by the factor (1 + K ) — an effect known as piezoelectric stiffening. The factor is the electromechanical coupling coefficient for the jt-propagating, z-polarized plane wave ... 

The last term is approximately equal to K when <4 1. Thus, the electromechanical coupling coefficient K ) has a second interpretation is approx-... 

The electrical impedance of the IDT depends on a variety of factors including the electromechanical coupling coefficient (K ), the dielectric permittivity of the substrate (e ), and the geometry of the IDT electrode width, spacing, number of finger pairs, and acoustic aperture (i.e., IDT finger overiap length). Table... 

For low frequency electromechanical applications in which the acoustic wavelength is much larger than the scale of component phases, some of the ceramic-polymer composites have piezoelectric voltage coefficients orders of magnitude larger than solid PZT. Such materials have obvious applications in hydrophones and other listening devices. 

As a consequence, the joins for (Pbi. (Bajc)Ti03 at low temperature and for Pb(Zri cTy03 at room temperature are interrupted by a morphotropic phase boundary (MPB), which separates tetragonal and rhombohedral phases (Fig. 14). The structural state of the oxides in the vicinity of the MPB is a subject of active inquiry, because many of the physical properties of PBZT ferroelectrics are maximized at the MPB. These include the dielectric constant, the piezoelectric constant, and the electromechanical coupling coefficients (Jaffe 1971, Thomann and Wersing 1982, Heywang and Thomann 1984). For industrial purposes, this behavior is exploited by annealing PBZT ferroelectrics with compositions near the MPB close to the Curie temperature in an... 

Activation and conductivity at room temperature are problems that can be addressed by the incorporation of other electronic structures that increase carrier transport. Crystal morphology is an important parameter in the boron doping process to determine uncompensated acceptors (Aa-Ad) for different crystal facets as a function of doping concentration. The temperature coefficient of resistance for a CVD diamond film can be changed by boron doping. As conductivity depends on the crystal phase, the combined electromechanical properties can be exploited in sensor applications both for resistive temperature detectors and for pressure transdu-cers. " As electrical conductivity is related linearly with boron concentration, a better-controlled process may allow for the development of better semiconductor devices improving crystal quality and operating limits. ... 

The electromechanical analogy provides for simple equivalents of a resistor, an inductance, and a capacitance, which are the dashpot (quantified by the drag coefficient, p), the point mass (quantified by the mass, mp), and the spring (quantified by the spring constant, /cp). The ratio of force and speed is the mechanical impedance, Z - For a dashpot, the impedance by definition is... 

If the film cannot be freely deformed in its plane, the piezoelectric current is called t/33 or dj. If the variation in the electric field is measured per unit of stress, g coefficients are obtained that are connected by the correlation of g = d/e where e is the dielectric constant depending on the film thickness. Constants g and tf are most widely used in the design of electromechanical transducers. The yield from the conversion of mechanical energy into electrical energy is represented by the electromechanical coupling coefficient ATjby Eq. (3.3). 

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