Ferroelectric order

The ferroelectricity usually disappears above a certain transition temperature (often called a Curie temperature) above which the crystal is said to be paraelectric this is because thermal motion has destroyed the ferroelectric order. Occasionally the crystal melts or decomposes before the paraelectric state is reached. There are thus some analogies to ferromagnetic and paramagnetic compounds though it should be noted that there is no iron in ferroelectric compounds. Some typical examples, together with their transition temperatures and spontaneous permanent electric polarization P, are given in the Table. 

Ferroelectric ordering in certain infinite two-dimensional lattices is due to the long-range contribution of dipole forces. Thus, it is not surprising that in limited two-dimensional lattices numerical calculations of dipole interactions lead to the replacement of ferroelectric states with macrovortex states64 which approximate to ferroelectric states far from the center of the limited lattice (coinciding with the center of the macrovortex). 

Here we focus on the effect of dipolar dispersion laws for high-frequency collective vibrations on the shift and width of their spectral line, with surface molecules inclined at an arbitrary angle 6 to the surface-normal direction. For definiteness, we consider the case of a triangular lattice and the ferroelectric ordering of dipole moments inherent in this lattice type.56,109 Lateral interactions of dynamic dipole moments p = pe (e = (sin os, sin6fcin , cos )) corresponding to collective vibrations on a simple two-dimensional lattice of adsorbed molecules cause these vibrations to collectivize in accordance with the dispersion law 121... 

Keywords Hydrogen-bonded ferroelectrics Order/disorder-displacive effects ... 

Keywords Anharmonic effects Displacive phase transition Isotope effects KDP-type ferroelectrics Order-disorder phase transition... 

It was assumed that values of other model parameters (A, B, K, and M) are the same for both KDP and DKDP. These values were chosen to reproduce some experimental results for KDP. More precisely, KDP and DKDP systems have the Hamiltonian defined by Eqs. 5-7. In the case of classical PO4 dipoles both systems show a ferroelectric ordered state at T = 0 K where /u, = yu, holds for each PO4 dipole. It follows from Eq. 6 that the potential energy per dipole in this state is given by ... 

By analogy to the SDPC model, the parameters A, Aj, K, K , M, and M of the MSDPC model have the same value for KDP and DKDP. For the KDP and DKDP system of classical PO4 dipoles in ferroelectric ordered state at T = 0 K, all PO4 dipoles have components fit = (0> F-)- The potential energy per dipole and the ferroelectric-mode frequency in this state are given by the same relations from the SDPC model (Eq. 8 and fe = ( ( (/Usl/Af) / ), where B = 0. To reproduce the same saturated dipole value Fs = and the same saturated force value Fs = 2Kfs = 0.6 evA for KDP, the constants A and K have the same values as do the constants A + B and K in the SDPC model, respectively. Therefore, the isotope effect on Fs and Fs has the same... 

G. Ayton and G. N. Patey, Phys. Ref. Lett., 76, 239 (1996). Ferroelectric Order in Model Discotic Nematic Liquid Crystals. 

Already in the seminal paper of Bednorz and Muller [1], the guide to look for systems with a high superconductive transition temperature (Tc), has been the presence of strong electron-phonon interactions. Such interaction has been known to exist in a wide class of perovskite type oxides. The authors mention [1] the vibronic Jahn-Teller polaron effect [2] in this context. They also emphasize the fact that the Cu2+-ion is a well-known Jahn-Teller system and this circumstance preserves significance in the physics of cuprate superconductors [3-7]. As a microscopic cause for ferroelectric ordering the interband vibronic hybridisation has been supposed [8-11] enlargening the view on perovskites as Jahn-Teller systems. 

Fig. 7. Mean-field phase diagram of the four-state Ising-Potts model (A/kB = 90 K, J lkB = 125 K). The high-spin (HS) phase, the low-spin (LS) phase, and the ferroelectric-ordered (FO) phase are shown. The arrow line corresponds to Jo/kB = — 36 K, appropriate to the [Mn(taa)] system.

Tyunina M, Narkilahti J, Plekh M, Qja R, Nieminen RM, Dejneka A, Trepakov V (2010) Evidence for strain-induced ferroelectric order in epitaxial thin-film KTa03. Phys Rev Lett 104 227601... 

The low temperature anti-ferroelectrically ordered polymorph of ice VI with a ten molecule unit cell, and a sixteen-molecule super-cell for ice VIII, were also used. Both ice VII(A) and ice VII(B) consist of identical eight molecule sub-lattices anti-parallel to one another. Ice VII(A) consists of six C and two D type-hydrogen bonds respectively, while ice VII(B) contains four C and D type hydrogen bonds. The structure of these phases is considered in detail. 

We have been able to compare the difference that full anti-ferroelectric ordering present in ice VIII has with the incomplete anti-ferroelectric ordering in two ice VII structures in terms of bond stiffness Xi As and charge movement The ability of the O—O... 

Szafrahski, M., Katrusiak, A. and McIntyre, G.J. (2002). Ferroelectric order of parallel bistable hydrogen bonds. Phys. Rev. Lett. 89, 215507-1-4. 

Szafrahski, M. and Katrusiak, A. (2004). Short-range ferroelectric order induced by proton... 

Calamitic metallomesogens forming a chiral smectic C phase (SmC ) are ferroelectric materials. Due to the low symmetry of this phase when the helix is unwound (C2) the molecular dipoles are aUgned within the layers of the SmC phase, giving rise to ferroelectric order in the layers. Because the SmC phase has a helical structure, there is no net macroscopic dipole moment for the bulk phase. However, it is possible to unwind the helix by application of an external electric field or by surface anchoring in thin cells. Under such conditions, a well-aligned film of the ferroelectric liquid crystal can exhibit a net polarisation, called the spontaneous polarisation (Ps). Ferroelectric liquid crystals are of interest for display applications because the macroscopic polarisation can be switched very fast by an... 

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