Domain wall motions

This class of smart materials is the mechanical equivalent of electrostrictive and magnetostrictive materials. Elastorestrictive materials exhibit high hysteresis between strain and stress (14,15). This hysteresis can be caused by motion of ferroelastic domain walls. This behavior is more compHcated and complex near a martensitic phase transformation. At this transformation, both crystal stmctural changes iaduced by mechanical stress and by domain wall motion occur. Martensitic shape memory alloys have broad, diffuse phase transformations and coexisting high and low temperature phases. The domain wall movements disappear with fully transformation to the high temperature austentic (paraelastic) phase. 

Dynamic domain imaging or Kerr microscopy of low coercivity thin films at MHz domain-switching frequencies allows one to examine domain wall motion in detail. ... 

Figure 6 Scanning Karr image of the magnetization changes in the indirection for a thin-film head having a 1-MHz, 5-mA p-p coil current, and the magnetic domain pattern deduced for this head from the observed domain wall motion. ...

Figure 20.1. The magnetization process (a) demagnetized state (b) unsaturated state (c) saturated state. When an external magnetic field is applied, domain rotation and domain wall motion occur simultaneously or sequentially. Domain configuration can be found by minimizing the total energy related to magnetization. (From Ref 1, with permission from Elsevier.)...

A metallic glass containing 80% Fe and 20% B is an excellent soft magnetic material because there are no grain boundaries to obstruct domain wall motion. 

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... 

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],... 

This is valid under relatively small signal excitation conditions, and describes the motion of domain walls in local random fields, a describes the irreversibility of the domain wall motion. Under the conditions where the Rayleigh model holds, the hysteresis in the piezoelectric... 

A number of transition ions (Fe3+, Ni2+, Co3+) that can occupy Ti4+ sites reduce that part of the dissipation factor due to domain wall motion. 

It is easily shown from Eq. (5.45) that, while the domain wall area per grain is proportional to g5 2, the domain wall area per unit volume of ceramic is approximately 5000g /2. The part of the permittivity due to domain wall motion will be proportional to the domain wall area and so increases as the grain size diminishes from 10 pm to 1 pm. 

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