Antiferroelectrics temperature dependence

Fig. 12 Temperature dependence of the average MAS peaks at 14.1 Tesla in the vicinity of the antiferroelectric transition at 372 K. Note that the value above the transition differs considerably from its value below the transition temperature, thus yielding clearer evidence for the role of the displacive component in the transition mechanism [26]...

Fig. 18 Temperature dependence of the CPMAS spectra of NH4H2ASO4 around the antiferroelectric phase transition temperature. The peaks corresponding to the paraelec-tric and antiferroelectric phases are labelled P and AF, respectively...

The temperature dependence of 1/Ti for is shown in Fig. 21. The discontinuity in the l/Ti data near Tn 216 K (highhghted by the arrow) appears at the onset of the antiferroelectric phase transition. Below Tn l/Ti increases abruptly from about 370 ms to 700 ms. 

A difference between ferro- and antiferroelectrics may also be discussed in terms of the soft elastic mode [3], In the infinite ferroelectric crystal, there is no spatial modulation of the spontaneous polarization (only dipole density is periodic). Therefore, at the transition from a paraelecttic to the ferroelectric phase, both the wavevector q for osciUatimis of imis responsible for polarization and the correspondent oscUlatimi frequency co = Kef tend to zero. We may say that the soft elastic mode in ferroelecttics condenses at q 0. In antiferroelectrics, the sign of the local polarization Pq alternates in space with wavevector qo = 2nl2l = n/l and the corresponding imi oscillation frequency is finite, m = Kqf = Kn ll. It means that in antiferroelectrics the soft mode condenses at a finite wavevector n/l and rather high frequency. As a result, in the temperature dependence of the dielectric permittivity at low frequencies, the Curie law at the phase transitimi between a paraelecttic and antiferroelectric phases is not well pronounced. 

As we will show below, the obtained expression for the free energy (3.60) with the coefficients dependent on temperature, film thickness and other material parameters, simplifies a lot the calculations of physical properties of antiferroelectric... 

Fig. 3.21 Free energy dependence on electric field. Solid curves correspond to antiferroelectric phase, dotted ones to paiaelectric phase and dashed ones to the regions of ferroelectric phase stability. The parameters values = 0.9, Pp/t) =0.9, g/p,2A = 0.1, /8 = — 1, /fr = 3, / /, = 0.5, X = 1, h = 3, 10, 30, 100 (curves 1, 2, 3, 4) lattice constants, temperatures T/Ta = 0.25 (a) and 0.5 (b) [70]...

The two polarizations Pp and Pap may be taken as secondary order parameters coupled with the genuine order parameters. As a result, depending of the model, the theory predicts transitions from the smectic A phase into either the synclinic ferroelectric phase at temperature Tp or into an anticlinic antiferroelectric phase at Tap- One intermediate ferrielectric phase is also predicted that has a tilt plane in the i + 1 layer turned through some angle

tilt plane in the i layer. The models based on the two order parameters are of continuous nature (9 may take any values) and, although conceptually are very important, caimot explain a variety of intermediate phases and their basic properties. 

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