Pyroelectricity, 238 defined

The unique piezoelectric and pyroelectric properties of semicrystalline films of PVDF arise from changes in the polarization imparted to the overall film by the crystalline P-phase. The polar nature of the P-phase is, in turn, a direct result of the parallel alignment of the dipole moment of the repeat units in the unit cell (Figure 11.1). The crystal polarization is defined as the dipole moment density of the crystal ... 

Equations (6) and (7) express these relationships. are the elastic compliance constants OC are the linear thermal expansion coefficients 4 and d jj,are the direct and converse piezoelectric strain coefficients, respectively Pk are the pyroelectric coefficients and X are the dielectric susceptibility constants. The superscript a on Pk, Pk, and %ki indicates that these quantities are defined under the conditions of constant stress. If is taken to be the independent variable, then O and are the dependent quantities ... 

The material properties appearing in Eqs. (6)-(9) are defined by the partial derivatives of the dependent variables (P, c, e) with respect to the independent variables. At this point, to maintain consistency with the literature on the P-phase of PVDF, we label c as the 1 axis, a as the 2 axis, and, b as the 3 axis. In evaluating the piezoelectric and pyroelectric responses we consider changes in polarization along the 3 axis only polarization along the 1 and 2 axes remains zero, by symmetry, for all the cases considered here. The direct piezoelectric strain 03 , pC/N) and stress (gaj, C/iiE) coefficients are defined in Eqs. (10) and (11),... 

When the film is short-circuited and heated to high temperatures at which the molecules attain a sufficiently high mobility, a current is observed in the external circuit. This phenomenon is called pyroelectric effect, thermally stimulated current, or, when the film has been polarized by a static field prior to measurement, depolarization current. The conventional definition of pyroelectricity is the temperature dependence of spontaneous polarization Ps, and the pyroelectric constant is defined as dPJdd (6 = temperature). In this review, however, the term will be used in a broader definition than usual. The pyroelectric current results from the motion of true charge and/or polarization charge in the film. Since the piezoelectricity of a polymer film is in some cases caused by these charges, the relation between piezoelectricity and pyroelectricity is an important clue to the origin of piezoelectricity. 

Among the 20 crystal classes lacking a center of symmetry ten of them contain a unique polar axis and exhibit pyroelectricity in addition to piezoelectricity, i.e. in the unstrained dipolar network of these crystals the dipole moment components remain and add to a resultant polar-axis moment. The term pyroelectricity is assigned because thermal expansion will expand or contract the dipole. The pyroelectric constant is defined by ... 

The difference between the two definitions rests with the fact that a pyroelectric crystal must possess an overall (observable) permanent electric dipole. Thus a pyroelectric crystal is built from unit cells, each of which must contain an overall electric dipole, (Figure 4.11b). The pyroelectric effect will only be observed, however, if all of these dipoles are aligned throughout the crystal, (Figure 4.11c). [Note that a ferroelectric crystal is defined in a similar way. The difference between a pyroelectric crystal and a ferroelectric crystal lies in the fact that the direction of each overall electric dipole in a ferroelectric crystal can be altered by an external electric field.]... 

Piezoelectricity is defined as an electric polarization that occurs in certain crystalline materials at mechanical deformation [69]. The polarization is proportionate to the deformation and the polarity changes with change in deformation. In reverse, electric polarization produces mechanical deformation in piezoelectric crystals. The piezoelectric materials also possess pyroelectric properties, i.e., electric polarization is generated at temperature change. 

At times, particularly with amorphous materials, the term electret is used instead of piezoelectric to describe a material the term was introduced as an electric counterpart to the magnet, defined as all materials that are able to retain at least a quasi-permanent electric polarization within and perhaps trap charge on the surface (or within in a porous material). Polytetrafluor-ethylene (PTFE) is a powerful electret material. The critical difference among the terms is that electrets retain polarization in thermod3mamic wowequilibrium, pyroelectric materials retain polarization in equilibrium, ferroelectrics permit... 

In summary, pyroelectric materials have found applications in a wide range of fields. For device applications and the convenience of application engineers, several figures of merit criteria are defined. Most of these can be calculated using the thermal, electrical, and optical characteristics of the materials available in the literature and various handbooks on the physical constants of materials. 

A ferroelectric crystal is defined as a crystal which belongs to the pyroelectric family (i. e. shows a spontaneous electric polarization) and whose direction of spontaneous polarization can be reversed by an electric... 

The base vectors of an elementary cell in a translation lattice together with one lattice point define a crystollogrophic coordinote system, which is suitable for description of crystallographic planes and directions by means of vectors with integer components. But for description of crystal pltysical properties (e.g. elastic, dielectric or pyroelectric properties, etc.) rising material constants another coordinate system, so called the Cortesion system, is preferred. 

The pyroelectric coefficient (p) of a material under constant stress and electric field is defined hy the following expression ... 

Pyroelectric currents are proportional to the time derivative of the temperature and, in case of infrared (IR) detectors, to the changes of IR radiation. In order to assess stationary IR sources as well, a chopper is used to modulate the IR radiation. Signals thus exhibit a well-defined angular chopping frequency a>. The smallest detectable temperature change is limited to the terr5>erature fluctuation of the detector system, the electronics or the intrinsic noise current jn of the p)Toelectric element, given here for a thin film by the expression... 

The pyroelectric effect may be defined as the change in spontaneous polarisation, s, as a function of temperature. The symmetry requirements for pyroelectricity are far more restrictive compared with SHG and piezoelectricity. To exhibit a spontaneous polarisation, the material in question must crystallise in one of ten polar crystal classes (1, 2, 3, 4, 6, m, mm2, 3m, 4mm, or 6mm). Thus, polarity is required for pyroelectric behaviour. Determining the pyroelectric coefficient may be done two ways - either measuring the pyroelectric current or the pyroelectric charge. Both techniques will be described. 

A ferroelectric is formally defined as a pyroelectric material that has a reversible, or switchable , polarisation.Thus, for a material to be ferroelectric, the compound must be polar, i.e. must possess a permanent dipole moment, and must be capable of having this moment... 

The pyroelectric effect is defined as the change in spontaneous polarisation, s, as a function of temperature, T. The pyroelectric coefficient, p, is mathematically defined as shown in equation 1.4. 

The extent of piezoelectric activity depends upon the poling time, field strength, and temperature. The dipoles are aligned relative to the direction of the field during the poling process. The constants that characterize the activity of piezoelectric and pyroelectric films have been listed in Table 14.14. The axes are defined as length 1, width 2, and thickness 3. Two numeric subscripts are used to respectively denote the axis of polarization (applied electrical field) and the axis of mechanical strain or applied stress. 

The ferroelectric property of PVDF form I (and its copolymers) reflects diractly on the hi sl piezo- and pyroelectric effects among the synlh ptri3rmets. Piezoelect strain or stress constant tensor, d or e, are defined, respectively, as follows for the polarization change AP caused by stress a or strain c under the oonditioo of constant temperature and zero electric field ... 

Pyroelectricity is defined as the reversible change in polarization with temperature, and the pyroelectric coeCBcients p, are defined by... 

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