Order ferroelectrics

Ferroelectric-paraelectric transitions can be understood on the basis of the Landau-Devonshire theory using polarization as an order parameter (Rao Rao, 1978). Xhe ordered ferroelectric phase has a lower symmetry, belonging to one of the subgroups of the high-symmetry disordered paraelectric phase. Xhe exact structure to which the paraelectric phase transforms is, however, determined by energy considerations. 

Watts (KWW) relaxation function. At a=l expression (1.20) transforms into conventional exponent leading to Debye law for dynamic dielectric permittivity of ordered ferroelectrics [11] ... 

L and dependence on temperature and film thickness in Fig. 3.24. It follows from Fig. 3.24a, c, that at fixed temperature the average polarization L decreases for the film thinning (compare curves 1-5). Built-in field smears the temperature of phase transition and susceptibility maximum its influence increases with the films thinning (see Fig. 3.24b, d). Moreover, the order parameter behavior for the thinnest possible films resembles that for thin films of ordered ferroelectrics with the thickness less than critical one (compare the curves 5 in Fig. 3.24c, d with Fig. in the paper [54]). Built-in field induces order parameter in the film with maximal disorder, see dotted curves 5 in Fig. 3.24a, b. However hysteresis loops is absent on these curves so that the behavior resembles that of electret state. 

Recently an indication of two-dimensional ferroelectricity in ultrathin Langmuir-Blodgett (LB) films as thin as two molecular monolayers (about Inm) was discovered [1, 2] for a copolymer vinylidene fluoride with trifluoroethylene P(VDF-TrFE). The observations of the spontaneous polarization of the order of Ps 0.1 cW, the first order ferroelectric phase transition [2], a critical point [3], a surface phase transition and electric switching [1,2, 5] were reported. 

Multiferroics materials that have, at least, two of the three ferroic orders ferroelectricity -ferromagnetism and ferroelasticity. For example, perovskites - BlFeOs, Bii La FeOa, Bii Nd . FeOa, Aurivillius - Bi7Ti3Fe302i... 

The second-order ferroelectric transitions can be modeled using the Curie-Weiss theory of ferromagnetism. It is assumed that there is a local field that is proportional to the polarization or E-Loc = E + yP/so, where y is the constant of proportionality. For T>Tq, Equation 23.28 gives P = Np Eux /kT and the susceptibility is given by... 

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