Ferroelectric phase state

A from the surface the density is typically constant and equal to the bulk value. In strong unscreened electric fields several authors [137-140] report a phase transition towards a ferroelectric crystalline state in their simulations. However, it should be kept in mind that these systems, because of the absence of ionic screening, are rather unphysical in nature. 

Application of a field to the ShiCaPa phase causes switching by precession of the director around the tilt cone in alternate layers, to give a ferroelectric ShiCsPf state with uniform tilt. In this case, there can be no domains of opposite tilt since such domains would necessarily have their polarization opposing the applied field. This leads to a uniform SmC-like texture with a green birefringence color. The extinction brushes in the cylindrical focal conic rotate counterclockwise when the net tilt rotates clockwise, as indicated in Figure 8.25. As anticipated, the chiral rotation of the brushes is a direct manifestation of the chirality of the phase. Elsewhere in the sample there must be ShiCaPa domains of opposite handedness, which would possess the opposite sense of tilt for the same sign of the applied field. 

A schematic phase diagram summarizing the three temperature regions (Ff, Fnf and melt) is shown in Fig. 9. For VF2 compositions below 82%, at room temperature, one observes the predominant ferroelectric phase. With increasing temperature, the paraelectric phase appears and at higher temperatures one obtains the molten state of the paraelectric crystallites. The Tm values of the copolymers are considerable lower than those of both homopolymers and show... 

Tc a phase transition to a state with spontaneous polarization takes place (ferroelectric phase transition). The mechanism becomes clearer considering Figure 1.11 (b). At the zone center (k = 0) the wavelength of the to mode is infinite (A —> oo), i.e the region of homogeneous polarization becomes infinite. In the case of the softening of the to mode the transverse frequency becomes zero and no vibration exists anymore ( frozen in ). 

Figure 2.4 Strain-field curves for < 001 > oriented 0.91PbZn1/3Nb2/303-0.09PbTi03 single crystals. The sample in (a) was poled at room temperature, where the resulting domain state is unstable (due to induction of tetragonal material associated with the curved morphotropic phase boundary), yielding substantial hysteresis. In (b) the crystal was poled at low temperatures to keep it in the rhombohedral phase. When measured at room temperature, the piezoelectric response is much more linear and non-hysteretic, due to the improved stability of the ferroelectric domain state. Data courtesy of S. E. Park.

Section 4 is entirely devoted to ferroelectric and H-bonded systems. It also provides a nice illustration of results that always maintained the utility of proton NMR in solid state, even wideline, or how the old question of the order disorder or displacive nature of some ferroelectric phase transitions were reopened by progresses in NMR resolution. A number of structural phase transition is discontinuous, but the examples of coexistence in solid-state and kinetic studies are rather scarce this is the object of Section 5. Section 6 is devoted to single-crystal studies that allow very precise comprehension of subtle phase transition mechanisms. Section 7 introduces the salient features of NQR that represent an interesting alternative to NMR in some cases. The section ends with a table of miscellaneous phase transitions that complete the references given in the text. Section 8 concludes and presents some perspectives in NMR phase transition studies. 

In most papers referenced above, the standard molecular formulation of the B3LYP functional has been employed, and its results graded against a set of other Hamiltonians available in CRYSTAL. These usually include at least HP, LDA and one GGA functional (PW or PBE), and thus enable a critical appraisal of the B3LYP performance compared to other well established Hamiltonians in solid-state chemistry. Several observables have been examined, such as the equilibrium structure, elastic constants and bulk moduli, thermochemical data, electric field gradients, phonon spectra and vibrational frequencies, polarisation of the ferroelectric phases, magnetic coupling in open-shell transition metal oxides. We shall comment on each observable separately. 

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