Transition ferroelectric

Relaxor Ferroelectrics. The general characteristics distinguishing relaxor ferroelectrics, eg, the PbMg 2N b2 302 family, from normal ferroelectrics such as BaTiO, are summari2ed in Table 2 (97). The dielectric response in the paraelectric-ferroelectric transition region is significantly more diffuse for the former. Maximum relative dielectric permittivities, referred to as are greater than 20,000. The temperature dependence of the dielectric... 

Single crystal and bulk BaTiOs exhibits a sharp paraelectric-to-ferroelectric transition at 393K. In the presence of submicron grains, the transition becomes diffuse and can be absent for polycrystalline BaTiOs. Twin boundaries along the four crystallographically equivalent 11 planes constitute the main lattice defects. Junctions between such twin boundaries can be frequently observed within a grain. The local atomic arrangement of the core of twin intersections was studied by focal-series reconstruction (Jia etal. 1999). 

Witzel, F Sill, GA Hall, WK. The selective reduction of NO and combustion of paraffins over MFI zeolites. Stud. Surf. Sci. Catal, 1994, Volume 84, 1531-1536. Parravano, G. Ferroelectric transitions and heterogenous Catalysis, J. Chem. Phys., 1952, Volume 20,342-343. 

In order to understand these extreme changes in physical and chemical properties of hydrogen-bonded systems, first attempts to model their dynamics were related to rather simple structures, as exhibited by the KDP family or squaric acid and its analogues. The isotope effects on their ferro- or anti-ferroelectric transition temperatures are listed in Table 1 together with the corresponding isotope exponent. 

Table 1 Isotope effects and exponent a various hydrogen-bonded systems on the ferroelectric transition temperatiu es for...

Abstract This chapter describes the experimentai compiement of theoretical models of the microscopic mechanism of ferroelectric transitions. We use the hydrogen-bonded compounds as examples, and attempt to show that the new experimental data obtained via recently developed high resolution nuclear magnetic resonance techniques for solids clearly support the hypothesis that the transition mechanism must involve lattice polarizability (i.e. a displacive component), in addition to the order/disorder behaviour of the lattices. 

Similar data have also been observed for the isotropic chemical shift and the line width for ADP in the authors laboratory. We noted that a fully deuterated DKDP crystal, which is known to exhibit no ferroelectric transition, showed an essentially flat chemical shift response over the 200-280 K range [25]. 

Displacive ferroeiectrics where a discrete symmetry group is broken at Tc and the ferroelectric transition can be described as the result of an instability of the anharmonic crystal lattice against soft polar lattice vibration (e.g., BaTiOs). 

Whereas the first microscopic theory of BaTiOs [1,2] was based on order-disorder behavior, later on BaTiOs was considered as a classical example of displacive soft-mode transitions [3,4] which can be described by anharmonic lattice dynamics [5] (Fig. 1). BaTiOs shows three transitions at around 408 K it undergoes a paraelectric to ferroelectric transition from the cubic Pm3m to the tetragonal P4mm structure at 278 K it becomes orthorhombic, C2mm and at 183 K a transition into the rhombohedral low-temperature Rm3 phase occurs. 

In a recent letter the first NMR observation of quadrupole coupling induced Ti and Ti satellites in the cubic phase of an ultrapure BaTiOs single crystal above the ferroelectric transition was presented [8]. 

As shown in Fig. 13a, An for the (llO)c face is composed of two contributions from the antiferrodistortive phase transition and the ferroelectric transition (see data for 7 x 2 x 0.3 mm ). On the other hand, only the ferroelectric transition is seen for the (OOl)c face. The inequality Px 7 Py means the breaking of symmetry in the (OOl)c plane. Therefore, the symmetry of the ferroelectric phase is below orthorhombic. 

Measurements of NMR for Ti, Ti [33], and Sr [34,35] were carried out for STO 16 and STO 18-96. Ti and Sr nuclear magnetic resonance spectra provide direct evidence for Ti disorder even in the cubic phase and show that the ferroelectric transition at Tc = 25 K occurs in two steps. Below 70 K, rhomb ohedral polar clusters are formed in the tetragonal matrix. These clusters subsequently grow in concentration, freeze out, and percolate, leading to an inhomogeneous ferroelectric state below Tc. This shows that the elusive ferroelectric transition in STO 18 is indeed connected with local symmetry lowering and impHes the existence of an order-disorder component in addition to the displacive soft mode [33-35]. Rhombohedral clusters, Ti disorder, and a two-component state are found in the so-called quantum paraelectric... 

In hydrogen-bonded ferroelectrics, the Curie temperature and permittivity alter when deuterium is substituted for hydrogen. What does this suggest about the origin of the ferroelectric transition in these compounds ... 

The crystal structure of colemanite has been shown to contain [B.O4(OH)3]"n polyanion chains. The structural relationships between colemanite and the other minerals of the series 2CaO, 3B203 t/H20 (n = 1, 5, 7, 9,13), and structural changes accompanying the ferroelectric transition of colemanite have been outlined (134). 

Many ferroelectric materials were found in the past. However, there is a limited number of structures that are adopted by the majority of the commercially important ferroelectric materials. In each of these structures, the ferroelectricity is tied to distortion of the coordination polyhedra of one or more of the cations in the structure. One example is the perovskite structure. Cations that seem to be especially susceptible to forming such distorted polyhedra include Ti, Zr, Nb, Ta, and Hf. All of these ions lie near crossover points between the stability of different electronic orbitals, and so may be likely to form distorted coordination polyhedra [5], Polarizable cations such as Pb and Bi are also common to many ferroelectric materials. In this case, it has been suggested that the lone pair electrons may play an important role in stabilizing ferroelectric structures. Thus the ferroelectric transition temperature and spontaneous distortion of PbTiC>3 is much larger than that of BaTiC>3. 

A primary focus of our work has been to understand the ferroelectric phase transition in thin epitaxial films of PbTiOs. It is expected that epitaxial strain effects are important in such films because of the large, anisotropic strain associated with the phase transition. Figure 8.3 shows the phase diagram for PbTiOs as a function of epitaxial strain and temperature calculated using Landau-Ginzburg-Devonshire (lgd) theory [9], Here epitaxial strain is defined as the in-plane strain imposed by the substrate, experienced by the cubic (paraelectric) phase of PbTiOs. The dashed line shows that a coherent PbTiOs film on a SrTiOs substrate experiences somewhat more than 1 % compressive epitaxial strain. Such compressive strain favors the ferroelectric PbTiOs phase having the c domain orientation, i.e. with the c (polar) axis normal to the film. From Figure 8.3 one can see that the paraelectric-ferroelectric transition temperature Tc for coherently-strained PbTiOs films on SrTiOs is predicted to be elevated by 260°C above that of... 

Figure 8.7 Upper plot Ferroelectric transition temperature versus film thickness. Lower plot Stripe period versus film thickness. Diamonds phase Fp at T = Tc — 250 K. Triangles phase Fa at T = TC — 50 K. Lines fits to parabolic dependece.

These layered perovskite compounds are ferroelectric, with fairly high Curie temperatures (Schmid 1975 Subbarao 1974). Some ambiguity still attaches to the interpretation of paraelectric/ferroelectric transitions, but it is clear that ionic... 

Fig. 19. Antiferroelectric to ferroelectric transition in a columnar mesophase made of molecules with a cone-shaped core...

At temperatures below 300° K. deviations from linear p vs. T behavior may appear, particularly when the ratio of M to W03 is below 0.3. This has been observed on single crystals of copper-doped WOs (36), silver-doped WOs (5), and low-sodium Na WOs (20). It is postulated that a second-order transition occurs, which is related to the ferroelectric transition in W03. This transition which occurs in the neighborhood of 220° K. (it is spread over roughly 50°, probably because it occurs piecemeal as a domain-growth phenomenon), shows up in pure W03 in its resistivity behavior, its Hall coefficient, and its thermoelectric power (7). The carrier mobility drops significantly as the temperature is lowered through the transition, so it is probable that the rather steep rise in resistivity... 

Ordering of orthophosphate anions results in ferroelectricity in K2Bi30(P04)2 whereas in AM2(P04)3 types (A = Li-Cs, Ag, Cn M = Ce, Th, U) it results from the alignment of A cation displacements from the center of AOg polyhedra. A m P04 materials (e.g. A = Rb, Cs M = Mg, Co, Zn) containing tetrahedral MPO4 frameworks can undergo ferroelectric transitions due to the coupled rotations of the tetrahedra. 

Relaxation near a ferroelectric transition. Ferroelectridty includes a range of diverse phenomena. There is a broad distinction between ferroelectrics in which the structural units are dipolar, but disordered, at temperatures well above the transition temperature, and those in which the units seem to be non-polar at such temperatures, the ordering and displadve classes, respectively. ... 

In a crystal of polar molecules it may well be as easy to reverse a molecule in its site as to form any other defect. This reversal will cost less in energy the more disorder is already present, and this co-operative effect may give rise to a dear order-disorder transition. The ordered phase may in particular be ferro- or antiferro-electric. The ferroelectric transition in thiourea is essentially of this nature. 

Rabe KM, Waghmare UV (1996) Strain coupling in the PbTiOs ferroelectric transition. Philos Trans R Soc Lond A354 2897... 

Deuterium Isotope Effect. Ubbelohde and co-workers have done much work on the effect of deuterium substitution on the structures of H bonded crystals (1729, 2067, 1728, 1727, 2071, 522, 739, 2068). The results are reviewed in the summary paper, 2068. In most crystals the D bond is slightly longer than the H bond. Furthermore, in those crystals which are ferroelectric, the deuterated crystal has a higher ferroelectric transition temperature (upper Curie temperature). Some of the results summarized by Ubbelohde and Gallagher are... 

The presence of an isotropic ferroelectric transition is also reflected by the total configm-ational potential energy per particle U /N plotted in the inset of Fig. 6.6. Increasing P from the initial smaller values, U) /N first increases, but then begins to decrease at a transverse pressure of about 7 11 2.0 where Pi begins to rise rather sharply. Clearly, the decrease of (/) /N can only be caused by the dipolar interactions, because the short-range fluid fluid and the fluid substrate potentials are purely repulsive. 

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