Ferroelectric/piezoelectric domains

Fig. 3. An overview of atomistic mechanisms involved in electroceramic components and the corresponding uses (a) ferroelectric domains capacitors and piezoelectrics, PTC thermistors (b) electronic conduction NTC thermistor (c) insulators and substrates (d) surface conduction humidity sensors (e) ferrimagnetic domains ferrite hard and soft magnets, magnetic tape (f) metal—semiconductor transition critical temperature NTC thermistor (g) ionic conduction gas sensors and batteries and (h) grain boundary phenomena varistors, boundary layer capacitors, PTC thermistors.

Finally, ferroelectricity is manifest in asymmetrical crystals producing domains of spontaneous polarization whose polar axis direction can be reversed in an electric field directed opposite the total dipole moment of the lattice. The two (or more) directions can coexist in a crystal as domain structures comprising millions of unit cells which contain the same electric orientation. The symmetry elements are temperature sensitive in ferroelectric materials [27]. At a particular temperature called the Curie Point the values of the piezoelectric coefficients reach particularly high values. Above the Curie Point the crystal transformation is to a less polar form and the ferroelectric nature disappears. 

Figure 2.1 Schematic illustrations of intrinsic and extrinsic contributions to the piezoelectric constant of perovskite ferroelectrics. (a) and (b) correspond to the intrinsic unit cell shape (a) without and (b) with applied electric field, (c) and (d) correspond to the extrinsic response associated with the change in position of a non-180° domain wall (shown as a black line) (c) before and (d) after an electric field is applied. Note that both intrinsic and extrinsic responses lead to a change in shape of the material due to application of an electric field (and hence to a piezoelectric response). In both cases, the actual distortions are significantly exaggerated to make visualization easier.

In many ferroelectric materials, the net piezoelectric effect is a result of both intrinsic and extrinsic responses. Here, intrinsic refers to the response that would result from an appropriately oriented single crystal (or ensemble thereof, in a polycrystalline sample). The extrinsic response is typically the result of motion of non-180° domain walls. The principle of these... 

Piezoelectric coefficients are also temperature dependent quantities. This is true for both the intrinsic and the extrinsic contributions. Typically, the piezoelectric response of a ferroelectric material increases as the transition temperature is approached from below (See Figure 2.3) [3], Where appropriate thermodynamic data are available, the increase in intrinsic dijk coefficients can be calculated on the basis of phenomenology, and reflects the higher polarizability of the lattice near the transition temperature. The extrinsic contributions are also temperature dependent because domain wall motion is a thermally activated process. Thus, extrinsic contributions are lost as the temperature approaches OK [4], As a note, while the temperature dependence of the intrinsic piezoelectric response can be calculated on the basis of phenomenology, there is currently no complete model describing the temperature dependence of the extrinsic contribution to the piezoelectric coefficients. 

Finally, while the piezoelectric d, e, g, and h constants are typically reported as real numbers, there is increasing use of the fact that the material response is not always in phase with the applied field. This can be due to a variety of factors, including domain wall motion in ferroelectrics [5]. Thus, coefficients can be described as complex quantities. Discussions of how to measure these constants are given in [6-10],... 

Figure 2.4 Strain-field curves for < 001 > oriented 0.91PbZn1/3Nb2/303-0.09PbTi03 single crystals. The sample in (a) was poled at room temperature, where the resulting domain state is unstable (due to induction of tetragonal material associated with the curved morphotropic phase boundary), yielding substantial hysteresis. In (b) the crystal was poled at low temperatures to keep it in the rhombohedral phase. When measured at room temperature, the piezoelectric response is much more linear and non-hysteretic, due to the improved stability of the ferroelectric domain state. Data courtesy of S. E. Park.

In such a measurement, the sample is clamped as lightly as possible, and the displacement of the surface in monitored. The amount of sample clamping is important, because the mechanical constraints can impact the ferroelastic response of the sample. That is, in samples where the mechanical coercive stress is low, it is possible to change the domain state of the material by improperly clamping it in the sample fixture. This is especially important in elastically soft piezoelectrics, such as many of the relaxor ferroelectric PbTiC>3 single crystals. 

Two types of contributions to dielectric and piezoelectric properties of ferroelectric ceramics are usually distinguished [6], [9-12], One type is called an intrinsic contribution, and it is due to the distortion of the crystal lattice under an applied electric field or a mechanical stress. The second type is called an extrinsic contribution, and it results from the motion of domain walls or domain switching [8], To provide an understanding of material properties of pzt, several methods to separate the intrinsic and extrinsic contributions were proposed. These methods are indirect, and are based on measurements of the dielectric and piezoelectric properties of ferroelectric ceramics [8], [10-12], In the experiments reported in this paper a different approach is adopted, which is based on measurements of high-resolution synchrotron X-ray powder diffraction. The shift in the positions of the diffraction peaks under applied electric field gives the intrinsic lattice deformation, whereas the domain switching can be calculated from the change in peak intensities [13,14],... 

The major trends in ferroelectric photonic and electronic devices are based on development of materials with nanoscale features. Piezoelectric, electrooptic, nonlinear optical properties of fe are largely determined by the arrangement of ferroelectric domains. A promising way is a modification of these basic properties by means of tailoring nanodomain and refractive index superlattices. 

Another frequently reported high-resolution tool for observing ferroelectric domains is piezoelectric response imaging using sfm [8,9], From the viewpoint of resolution for ferroelectric domains, sndm will surpass the piezo-response imaging because sndm measures the nonlinear response of a dielectric material which is proportional to the square of the electric field,... 

Electrostrictive materials offer important advantages over piezoelectric ceramics in actuator applications. They do not contain domains (of the usual ferroelectric type), and so return to their original dimensions immediately a field is reduced to zero, and they do not age. Figure 6.24(a) shows the strain-electric field characteristic for a PLZT (7/62/38) piezoelectric and Fig. 6.24(b) the absence of significant hysteresis in a PMN (0.9Pb(Mg1/3Nb2/303-0.1 PbTi03) electrostrictive ceramic. 

What are the nonzero piezoelectric coefficients for a single domain of the ferroelectric tetragonal phase of PZT (class 4mm) ... 

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