Ferroelectric/piezoelectric extrinsic ferroelectricity

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... 

It is also important to realize that piezoelectricity implies a linear coupling between dielectric displacement and strain, for example. However, in many ferroelectric materials, this response is linear only over a relatively limited field range (See for example, Figure 2.2). Non-linearity is especially important in ferroelectric materials which show a strong extrinsic contribution to the piezoelectric response [5], In addition, it is quite common for the response to be hysteretic. The amount of hysteresis that is observed depends strongly on the measurement conditions. Larger amplitude excitations often result in larger extrinsic contributions to the coefficients, and more non-linearity and hysteresis in the response. 

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. 

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],... 

An understanding of hardening-softening properties can be achieved through the analysis of the domain wall contribution to the polarization response of ferroelectrics. It should be noted here that this is not the only contribution to the polarization response rather, the intrinsic polarization response as well as surface, boundary, and interface effects may also contribute significantly to the total polarization of a ferroelectric material, especially in thin films. However, the dominant contribution to the dielectric, elastic, and piezoelectric properties in ferroelectric materials is extrinsic, and typically originates from displacement of the domain walls [59]. 

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