Ferroic phase transitions

Moya X, Kar-Narayan S, Mathur ND Caloric materials near ferroic phase transitions. Nat. Mater., 2014 13 439 50. DOI 10.1038/nmat3951... 

More generally, the dynamic behavior of domain walls in random media under the influence of a periodic external field gives rise to hysteresis cycles of different shape depending on various external parameters. According to a recent theory of Nattermann et al. [54] on disordered ferroic (ferromagnetic or fe) materials, the polarization, P, is expected to display a number of different features as a function of T, frequency, / = iv/2tt, and probing ac field amplitude, E0. They are described by a series of dynamical phase transitions, whose order parameter Q = uj/2h) Pdt reflects the shape of the P vs. E loop. When increasing the ac... 

Characteristic feature of ferroics is the existence of at least two equivalent states which differ only in their orientations (either of some structural units or spontaneous electric/magnetic moment, or both) called orientation states. The term prototype phase means real or hypothetical phase of crystal where all of the orientational states are the same. It is clear that the prototype phase has higher point symmetry group, than real ferroic. Therefore there is a phase transition in a ferroic if [2] ... 

It is known that the crystal symmetry defines point symmetry group of any macroscopic physical property, and this symmetry cannot be lower than corresponding point symmetry of a whole crystal. The simplest example is the spontaneous electric polarization that cannot exist in centrosymmetric lattice as the symmetry elements of polarization vector have no operation of inversion. We remind that inversion operation means that a system remains intact when coordinates x, y, z are substituted by —x, —y, —z. If the inversion center is lost under the phase transition in a ferroic at T < 7), Tc is the temperature of ferroelectric phase transition or, equivalently, the Curie temperature), the appearance of spontaneous electrical polarization is allowed. Spontaneous polarization P named order parameter appears smoothly... 

The above considered core-shell model gives an approximate description of radiospectroscopy spectra size effects in the cases, when it is difficult to find the coordinate dependence of resonant field. For the ferroics this problem can be solved more accurately. Really, the phase transitions, which are characteristic for ferroics (see Chap. 1), generate the order parameter. This parameter depends on the new phase symmetry, its crystalline field consfanfs and nanoparticles size. In the majority of cases, the latter constants determine the resonant fields and size effects in the corresponding spectra of ferroics. Below we calculate the EPR spectra for this case on the example of nanosize ferroelectric BaTiOs powders. 

Among different (like flexoelectric, flexomagnetic etc.) flexoeffects, the influence of flexoelectric effect on the nanosystem properties had been studied in most details. One can conclude that even rather moderate flexoelectric effect significantly renormalizes all the polar, piezoelectric and dielectric properties and the correlation radius in particular. The effect also suppresses the size-induced phase transition from ferroelectric to paraelectric phase and thus stabilizes the ordered phase in ferroic nanoparticles. 

If the adaptronic structure requires temperature stability, active functional materials must be used since they can have a flat temperature response away from the phase transition and are controllable with external fields. Most materials in this category are ferroic materials, i. e., ferroelectric, ferromagnetic and ferroelastic materials. 

AH of these materials have at least two phase transitions that can be described in terms of thermodynamic functions with two ordering parameters (see Appendix B). Ferroic materials are operated near an instabiUty to make domain walls with their associated dipoles and strains moveable, as encountered in PZT or Terfenol . On the other hand, a second type of material involves a partially ordered phase, as in PMN or the shape memory alloys. These materials are operated near a diffuse phase transition with two coexisting phases, a high-temperature austenite-like phase and a low-temperature martensite-Uke phase. A third type of smart... 

At high temperatures, ferroelectric materials transform to the paraelectric state (where dipoles are randomly oriented), ferromagnetic materials to the paramagnetic state, and ferroelastic materials to the twin-free normal state. The transitions are characterized through order parameters (Rao Rao, 1978). These order parameters are characteristic properties parametrized in such a way that the resulting quantity is unity for the ferroic state at a temperature sufficiently below the transition temperature, and is zero in the nonferroic phase beyond the transition temperature. Polarization, magnetization and strain are the proper order parameters for the ferroelectric. 

Equating the expression in the brackets (1.3) to zero, we obtain the order parameter in the low-temperature phase of a ferroic. Before doing so, we analyze the behavior of the coefficients. Keeping in mind that ho = 0 at T = 7), one finds in the transition point... 

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