Domain, hysteresis switching

When a critical field (Ec) is reached, which is near to the coercive field, the domains switch direction as a whole involving considerable hysteresis loss. This loss is proportional to the area of the loop, so that for the single crystal in Fig 2.46(a) it amounts to about 0.1 MJm-3. At 100Hz the power dissipated as heat would be 100 MW m-3, which would result in a very rapid rise in temperature. The dissipation factor (tan (5) is also very high at high field strengths, but becomes small at low field strengths, as described above. Modifications to the composition diminish the loss still further. 

As mentioned above, domain switching in ferroelectrics is accompanied by domain nucleation, moving domain walls and restructuring of dipoles and charges. A characteristic feature of this irreversible process is the appearance of a hysteresis loop in the dependence of dielectric displacement... 

In addition to resulting in very large k at Tq, spontaneous polarization will result in hysteresis loops, as shown in Fig. 15.14. At low applied fields, the polarization is reversible and almost linear with the applied field. At higher field strengths, the polarization increases considerably due to switching of the ferroelectric domains. Further increases in the electric field continue to increase the polarization as a result of further distortions of the TiOf, octahedra. ... 

In general a ferroelectric perovskite single crystal will be composed of a roughly equal number of domains oriented in all the equivalent directions allowed by the crystal symmetry. The overall polarisation of the crystal will be zero. The application of an electric field will cause a polarisation switch and lead to a classical hysteresis loop in which the important values are P, (the remanent or residual polarisation when the electric field is reduced to zero), and E, (the coercive field, which is the reverse field required to reduce the polarisation to zero). Extrapolation of the high-field portion of the curve to =0 gives the value of the spontaneous polarisation P (Figure 6.9a). 

In low-temperature phase, the order parameter is a sum of field-induced and spontaneous parts so that it becomes nonlinear function of external field due to domain structure influence. As a result, the field dependence of order parameters in the ferroics is described by hysteresis loops, schematically depicted in Fig. 1.1. The shape of these loops is close to those observed in specially prepared (e.g. by application of external field during the crystal growth) monodomain ferroics. One can see from Fig. 1.1 that order parameter in the ferroics contains spontaneous part (at zero field, where two opposite values of order parameter exist) and field-induced one, that saturates at large fields. Under the field decrease, order parameter first decreases and at some field called coercive, it becomes zero and then changes sign (so-called switching phenomenon) accompanied by strong nonlinearity. 

Another distinguishing feature of ferroelectric behavior is the polarization versus electric field P—B) hysteresis loop. The hysteresis loop results from the domain reorientation which occurs as the electric field direction is varied. The size and shape of the loop is determined by the magnitude of the dipole moment of the unit cell and the domain-switching characteristics of the material. Hysteresis loop behavior is measured using either a Sawyer—Tower circuit or a Diamant—Pepinsky bridge. Details of the construction and operation of a Sawyer—Tower circuit are given in Reference 24. Thin film properties have also been measmed with these two devices, and in addition, a commercially available measurement system has been widely used. ... 

Plotting the polarization against the electric field strength yields the typical hysteresis loop of a ferroelectric material (Figure 8.5 see also Figure 8.10). After switching off the field, a part of the preferential domain orientation will be retained (remanent polarization). To remove this remanent polarization, a reverse electric... 

Ferroelectricity is an electrical phenomenon and also an important property in solids. It arises in certain crystals in terms of spontaneous dipole moment below Curie temperature [1], The direction of this moment can be switched between the equivalent states by the application of an external electric field [2-4], It is observed in some crystal systems that undergo second-order structural changes below the Curie temperature, which results in the development of spontaneous polarization. This can be explained by Landau-Ginzburg free energy functional [3, 4, 9]. The ferroelectric behavior is commonly explained by the presence of domains with uniform polarization. This behavior is nonlinear in terms of hysteresis of polarization (P) and electric field (E) vectors. Phenomenological models of ferroelectrics have been developed for engineering computation and for various applications. 

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