Ferroelectric Domain-Walls

Ferromagnetic and ferroelectric materials are only two examples of a wider group that contains domains built up from switchable units. Such solids, which are called ferroic materials, exhibit domain boundaries in the normal state. These include ferroelastic crystals whose domain structure can be switched by the application of mechanical stress. In all such materials, domain walls act as planar defects running throughout the solid. 

Domain wall polarization plays a decisive role in ferroelectric materials and contributes to the overall dielectric response. The motion of a domain wall that separates regions of different oriented polarization takes place by the fact that favored oriented domains with respect to the applied field tends to grow. 

When a ferroelectric single crystal is cooled below the phase transition temperature the electrical stray field energy caused by the non-compensated polarization charges is reduced by the formation of ferroelectric domains, see Figure 1.19. The configuration of the domains follows a head-to-tail condition in order to avoid discontinuities in the polarization at the domain boundary, VP = a. The built-up of domain walls, elastical stress fields as well as free charge carriers counteract the process of domain formation. In addition, an influence of vacancies, dislocations and dopants exists. 

The ferroelectric hysteresis originates from the existence of irreversible polarization processes by polarization reversals of a single ferroelectric lattice cell (see Section 1.4.1). However, the exact interplay between this fundamental process, domain walls, defects and the overall appearance of the ferroelectric hysteresis is still not precisely known. The separation of the total polarization into reversible and irreversible contributions might facilitate the understanding of ferroelectric polarization mechanisms. Especially, the irreversible processes would be important for ferroelectric memory devices, since the reversible processes cannot be used to store information. 

For ferroelectrics, mainly two possible mechanisms for irreversible processes exist. First, lattice defects which interact with a domain wall and hinder it from returning into its initial position after removing the electric field that initiated the domain wall motion ( pinning ) [16]. Second, the nucleation and growth of new domains which do not disappear after the field is removed again. In ferroelectric materials the matter is further complicated by defect dipoles and free charges that also contribute to the measured polarization and can also interact with domain walls [17]. Reversible contributions in ferroelectrics are due to ionic and electronic... 

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],... 

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],... 

Fp, as observed. At lower T, non-linearity in the free energy functional is expected to favor sharp domain walls [21], The transition to the monodomain ferroelectric phase F1 has been predicted by treating the ferroelectric as a semiconductor, in which carriers can be created by the field effect [16]. This transition can be calculated to occur at Tc - T = 325 K for d = 10 nm [4], in qualitative agreement with our observations. The rich phase diagram we have observed in this simple system makes it an excellent test case for more quantitative development of these concepts. 

Ferroelectric domains have been visualized in the ferroelectric phase in sbn with high resolution piezo-response force microscopy (see Figure 15.8) [23], The domains are found to be needlelike with lengths in the range of 10 to 500 nm and are oriented along the polar c-axis. The dynamics of the domain walls under externally applied electric fields or heating are expected to influence the polarization especially at low frequencies (see domain wall polarization, Chapter 1) [24],... 

Several studies have examined the thickness of the domain wall in ferroelectric materials [17]. The 90° a-c domain wall thickness has been measured using a transmission electron microscope (tem), [14] but distinguishing the positive and negative domains in 180° opposite polarization areas is difficult because these methods are used to observe the strain of arrangements of molecules. Direct clarification of the domain wall thickness is important with respect to both scientific and engineering aspects. 

A further unusual characteristic of ferroelectric materials is that their properties change with time in the absence of either external mechanical or electrical stresses or temperature changes. This ageing is due to a diminution of domain wall mobility through the gradual build-up of inhibiting causes. These may be internal fields due to the alignment of dipoles formed from lattice defects... 

In ferroelectrics the major contributor to tan 3 is domain wall movement which diminishes as the amplitude of the applied field diminishes the value applicable to pyroelectric detectors will be that for very small fields. The permittivity is also very sensitive to bias field strength, as is its temperature coefficient. The properties of some ferroelectrics - the relaxors - are also frequency dependent. It is important, therefore, to ensure that when assessing the suitability of a ferroelectric for a particular application on the basis of measured properties that the measurements have been made using values of the parameters (frequency, field strength etc.) appropriate to the application. This is not always done. 

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