Piezoelectric charge coefficient

The piezoelectric effect entails a linear coupling between electrical and mechanical energies. Numerous piezoelectric coefficients are in use, depending on the electrical and mechanical boundary conditions imposed on the part under test. Each of the piezoelectric d, e, g, and h coefficients can be defined in terms of a direct and a converse effect the two sets of coefficients are related by thermodynamics. For example, the piezoelectric charge coefficient, dkjk, can be defined via [1] ... 

Because of the very large differences in mechanical compliance between the two phases, the hydrostatic pressures experienced by the polymer phase transfer forces to the rods magnifying the stress in them in the poled direction. This magnified stress increases the charge induced on to the electrode tending to compensate for the inactive polymer. As a result, in typical practical cases, the piezoelectric charge coefficient fi/13) is not very sensitive to volume fraction of PZT . 

The piezoelectric charge coefficient is improved, and the materials is more difficult to depole. A typical composition is Pbo,94 Sro.oeCZro.sa Tio.47)03.o. 

The piezo effect produced after the poling is quantified by the tensor coefEcients of the piezoelectric charge coefficients d.33, dis and d.15. For a clear indexing the Cartesian xs-coordinate (i. e. the -axis) is applied as a reference axis in parallel direction to the polarization vector in general [90-92]. 

Here D is the vector of the dielectric displacement (size 3x1, unit C/m ), S is the strain (size 6x1, dimension 1), E is a vector of the electric field strength (size 3x1, unit V/m) and T is a vector of the mechanical tension (size 6x1, unit N/m ). As the piezoelectric constants depend on the direction in space they are described as tensors e- is the permittivity constant also called dielectric permittivity at constant mechanical tension T (size 3x3, unit F/m) and 5 , is the elastic compliance matrix (size 6x6, unit m /N). The piezoelectric charge coefficient df " (size 6x3, unit C/N) defines the dielectric displacement per mechanical tension at constant electrical field and (size 3x6, unit m/V) defines the strain per eiectric fieid at constant mechanical tension [84], The first equation describes the direct piezo effect (sensor equation) and the second the inverse piezo effect (actuator equation). 

The piezoelectric charge coefficients are generally expressed by using condensed subscripts, such as djj and c/jj, where the first subscript refers to the electric field direction or direction of polarization and the second subscript refers to the stress or strain direction. The piezoelectric charge coefficients g j. are also expressed in condensed form and are related to the charge coefficients via the dielectric constant K,... 

Thus, for polymer films with symmetry type 2mm (i.e. uniaxially stretched PVDF), the components of the piezoelectric charge coefficient are expressed in matrix form as... 

Temperature-dependence observations for PVDF [33] and the copolymers [25] showed an increase in piezoelectric charge coefficient... 

Polymer electrets can be operated as sensors or actuators. Their operation is very similar to that of a piezoelectric material and their direct piezoelectric transducer coefficient (d33) is higher than that of solid PVDF ferroelectric polymers [97]. If a compressive force is apphed to the film, the pores will deform preferentially with respect to the polymer material. Unlike charges within the polymer will be pushed closer together and the potential measured at the contacts will change accordingly. Similarly, the application of a voltage across the electrodes will yield a change in thickness in the material. 

Here the coefficients 7e, 7s = 7a, and 7m correspond to the small-signal capacitance C, the effective piezoelectric charge constant dp and the inverse of the small-signal stiffness cp for a piezoelectric transducer and to the small-signal inductance L, the effective magnetostrictive constant du and the inverse of the small-signal stiffness cm for a magnetostrictive transducer, respectively. 

Sensitivity. The sensitivity of a piezoelectric material is taken to be equal to the generated open-circuit voltage that drop>s across to the contact with the distance t (= thickness) divided by the applied stress or the product g t, where g is the relevant piezoelectric voltage coefficient. The voltage coefficient g is connected with the charge coefficient d via the dielectric permittivity = CrCo according to... 

Equation 6 is an approximate expression for die piezoelectric thickness coefficient 33 = dP I Fii — / At)NqulD/YM + / At)Nq[)lD/YD that describes the longitudinal direct piezoelectricity in die diickness direction of a slab or film. If the combined charge Nqp on all dipoles per area A is replaced by the bipolar interfacial charge density o, die second line of Eq. 6 yields the expression 33 ([Pg.496]

FEP layers. After eharging, the FEP layers, separated by flie ePTFE layer, form macroscopic dipoles, leading to strong piezoelectricity of flic sample. The piezoelectric 33 coefficient is thermally stable if flie sample is charged at elevated temperatures. However, the 33 decays from 800 to 400 pC/N under atmospheric pressures within 6 days, and repeated mechanical loading leads to a similar loss of piezoelectricity, apparently related to mechanical fatigue in the highly porous ePTFE. 

In this eontext, ferroelectrets actually represent a third elass of piezoelectric polymers in the sense that these cellular materials share features of charge electrets (real eharges) with those of ferroelectric polymers (hysteresis-type ED characteristics) (Bauer et al. 2004 Lekkala et al. 1996). Moreover, ferroelectrets are characterized by extremely high piezoelectric 33 coefficients as well as an extreme anisotropy in their mechanical and electromechanical properties, which partially require speeifie characterization techniques (Dansachmiiller et al. 2005). 

Here the symbols po, L, y, and e(x) denote the density, the sample thickness, the electrostriction coefficient, and the piezoelectric strain coefficient. From Eqs. 24 and 25, one sees that from the current response J t) of the pressure pulse experiment, the direct image of the space-charge distribution p x) or the gradient of the piezoelectric coefficient can be deduced by using the simple transformation x = ct. 

Theoretical estimations and experimental investigations tirmly established (J ) that large electron delocalization is a perequisite for large values of the nonlinear optical coefficients and this can be met with the ir-electrons in conjugated molecules and polymers where also charge asymmetry can be adequately introduced in order to obtain non-centrosymmetric structures. Since the electronic density distribution of these systems seems to be easily modified by their interaction with the molecular vibrations we anticipate that these materials may possess large piezoelectric, pyroelectric and photoacoustic coefficients. 

Because the piezoelectric coefficients can each be expressed in two ways, there are in general two different approaches to measuring the piezoelectric response approaches based on measurement of charge (or current), and those based on measurements of displacement (or strain). Choice of which coefficient to measure is often a matter of convenience. 

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