Dielectric materials polarization domains

In dielectric materials there can be both permanent and induced polarization domains. The walls between these domains may also act as barriers to dislocation motion. They tend to have larger energies than magnetic domain walls so they may have more effect on hardness (McColm, 1990). 

The contribution E(ds/dT) (Eq. (7.3)) can be made by all dielectrics, whether polar or not, but since the temperature coefficients of permittivity of ferroelectric materials are high, in their case the effect can be comparable in magnitude with the true pyroelectric effect. This is also the case above the Curie point and where, because of the absence of domains, the dielectric losses of ferroelectrics are reduced, which is important in some applications. However, the provision of a very stable biasing field is not always convenient. 

This chapter concentrates on the results of DS study of the structure, dynamics, and macroscopic behavior of complex materials. First, we present an introduction to the basic concepts of dielectric polarization in static and time-dependent fields, before the dielectric spectroscopy technique itself is reviewed for both frequency and time domains. This part has three sections, namely, broadband dielectric spectroscopy, time-domain dielectric spectroscopy, and a section where different aspects of data treatment and fitting routines are discussed in detail. Then, some examples of dielectric responses observed in various disordered materials are presented. Finally, we will consider the experimental evidence of non-Debye dielectric responses in several complex disordered systems such as microemulsions, porous glasses, porous silicon, H-bonding liquids, aqueous solutions of polymers, and composite materials. 

As indicated above, exponential relaxation does not generally provide a satisfactory description of experimental data. The response of dielectric materials is instead generally found to be characterized by certain power laws, both in the time and frequency domains (95,96). As observed by Curie and von Schweidler, a long time ago (97,98), the polarization current following the application of a constant electric field typically decays as a power function of time. The same is true for the dielectric response function, since it is proportional to the current oc l/t , where a is a positive constant. This response... 

The fact that an electric field can reverse the direction of spontaneous polarization by the cooperative movement of domain walls-that is, the collective ordering of local dipole moments-requires an energy contribution that the dielectric material takes from the surrounding electric field. In an oscillating a.c. field, the phase... 

The most important materials among nonlinear dielectrics are ferroelectrics which can exhibit a spontaneous polarization PI in the absence of an external electric field and which can spHt into spontaneously polarized regions known as domains (5). It is evident that in the ferroelectric the domain states differ in orientation of spontaneous electric polarization, which are in equiUbrium thermodynamically, and that the ferroelectric character is estabUshed when one domain state can be transformed to another by a suitably directed external electric field (6). It is the reorientabiUty of the domain state polarizations that distinguishes ferroelectrics as a subgroup of materials from the 10-polar-point symmetry group of pyroelectric crystals (7—9). 

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. 

The polarizability of the individnal molecules is also frequency dependent, but the characteristic values are of the order of lO Vs and lO Vs for the rotational and electronic polarization, respectively. " Therefore, in the typical frequency domain for investigation of dispersions (1/s < co < 10 /s) the polarizability, e, of the material building up the particles is frequency independent. On the other hand, the disperse medium (which is usually an electrolyte solution) has a dielectric permittivity, Ej, for which the freqnency dependence can be described by the Debye-Falkenhagen theory. Besides, the characteristic relaxation time of the bulk electrolyte solutions is also given by Eqnation 5.385. ... 

Swelling. If water (or any polar solvent) can penetrate the bulk of the polymer, it should be preferentially located in the ionic domains, thereby, creating domains with a high dielectric constant. It could, therefore, produce a morphology of the ionic aggregates different from that of the anhydrous material. 

The observation of optical properties in an applied electric field, which are similar to those of a collection of oriented uniaxial crystallites, suggests that within each domain the molecules are cooperatively oriented. It remains to be determined whether or not the observed domains present a net spontaneous polarization. Previous experiments with nematic p-azoxyani-sole indicated that dielectric peculiarities did accompany the formation of domains which appear when thin samples of this material are subjected to an electric field (4). 

A given field strength produces a polarization proportional to the number of dipoles per unit volume, and to the degree to which the charges in the material can be induced to move. Said another way, the wider the domain in which the changes can swing, the greater the effective dielectric constant of the material. 

The divergences of dielectric permittivity and correlation radius at the critical value of the flexoelectric coefficient (related to the critical radius) give new possibilities to control the physical properties of ferroelectric materials. The effect of the correlation radius renormalization by the flexoelectric effect alters the intrinsic width of domain walls. The predicted effects are useful for design of ferroelectric nanowires with radius up to several nanometers, which have ultra-thin domain walls and reveal polar properties close to those in bulk samples. 

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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