Displacive ferroelectrics

Figure 6 shows the influence of the pressure of e T) on both ST018-92(a) and SCT(0.007) [21]. We first note the large shift in the transition to lower temperature for STO 18. The initial slope is dTcdP = - 20 K/kbar, a large effect. Second, there is a large decrease in the ampHtude of the peak with pressure. At 0.70 kbar, the transition is completely suppressed, and the e (T) response closely resembles that of STO 16 at 1 bar. These pressure effects are characteristic of displacive ferroelectrics in the quantum regime and can be understood in terms of the soft-mode theory. The situation is similar for SCT(0.007), as shown in Fig. 6b. In the case of SCT(0.007), ferroelectricity completely disappears at 0.5 kbar.

Tani discusses the dynamics of displacive ferroelectrics and obtains a damped-resonant response. 

Of central importance for understanding the fundamental properties of ferroelec-trics is dynamics of the crystal lattice, which is closely related to the phenomenon of ferroelectricity [1]. The soft-mode theory of displacive ferroelectrics [65] has established the relationship between the polar optical vibrational modes and the spontaneous polarization. The lowest-frequency transverse optical phonon, called the soft mode, involves the same atomic displacements as those responsible for the appearance of spontaneous polarization, and the soft mode instability at Curie temperature causes the ferroelectric phase transition. The soft-mode behavior is also related to such properties of ferroelectric materials as high dielectric constant, large piezoelectric coefficients, and dielectric nonlinearity, which are extremely important for technological applications. The Lyddane-Sachs-Teller (LST) relation connects the macroscopic dielectric constants of a material with its microscopic properties - optical phonon frequencies ... 

Fig. 8. Simple model of order-disorder or displacive ferroelectric phase transition. Left, ferroelectricity by relative displacement of the anion and cation sublattices (a) displacive model, where r — 0 in the HTP and the atoms are translated by r/0 in the LTP. The order parameter is r. (b) Order-disorder model in the high-temperature phase, the ions are symmetrically disordered with equal probabilities p+ — p — 1/2 over two positions r — +rQ. In the low-temperature phase, the occupancies of the sites become unequal with probabilities p p +. The order parameter is the difference Ap — p+—p. The spontaneous polarization Psocr and PsccAp for the displacive model and order-disorder model, respectively. Right, ferroelectricity by alignment of molecular dipoles (c) displacive model in the HTP, all the molecules are aligned with a = 0 in the LTP, the molecules are rotated around the center of inversion with angles +a/0, the order parameter is a. (d) Order-disorder model. The spontaneous polarization Ppx ct and PsccAp for the displacive model and order-disorder model, respectively.

Barium titanate BaTi03 is usually considered as the prototype of compounds having a purely displacive ferroelectric phase transition, which exhibits a soft mode describable by an anharmonic phonon. The nonferro-electric compound NH4C1 is another example of compound with pure order-disorder phase transition, with two phases that differ from the ordering of the ammonium (NH/) cation in the unit cell. 

In second-order or nearly second-order phase transitions, the dielectric dispersion is observed to show a critical slowing-down a phenomenon in which the response of the polarization to a change of the electric field becomes slower as the temperature approaches the Curie point. Critical slowing-down has been observed in the GHz region in several order-disorder ferroelectrics (e.g. Figs. 4.5-8 and 4.5-9) and displacive ferroelectrics (e.g. Fig. 4.5-10). The dielectric constants at the Curie point in the GHz region are very small in order-disorder... 

Typical dielectric susceptibility of a displacive ferroelectric transition versus the ratio of temperature to the Curie temperature. 

The dynamics of atoms in solids is responsible for many phenomena which cannot be explained within the static lattice model. Examples are the specific heat of crystals, thermal expansion, thermal conductivity, displacive ferroelectric phase transitions, piezoelectricity, melting, transmission of sound, certain optical and dielectric properties and certain aspects of the interaction of radiation such as X-rays and neutrons with crystals. The theory of lattice vibrations, often called lattice dynamiosy and its implications for many of the above mentioned phenomena is the subject of this two-volume book. 

The paraelectric-ferroelectric transition is usually accompanied by small permanent relative displacements of ions or molecular groups from the symmetry positions in the paraelectric phase. Local electric dipoles result from the ion displacements and these crystals are referred to as displacive ferroelectrics. The structural instability may be associated with highly temperature-dependent low-frequency transverse optical phonons in the paraelectric phase which predominate at the Curie temperature (see, for example. Refs. 214-216 and Volume 2, Chapter 3). The nature and magnitude of the ion displacements determine many of the properties of ferroelectric crystals. 

Ferroelectrics can be placed into two main classes. The first comprise the displacive ferroelectrics. Typical representatives of this class have the perovskite or a perovskite-like structure. The transition is usually related to the low-frequency optical lattice vibrations in the paraelectric phase. 

Discussions of the ionic nature of displacive ferroelectrics usually utilize formal charges, i.e., consider complete electron transfer to the anion and this suggests complete ionic bonding. For example, one can consider LiNbOj as Li Lithium-7 NMR studies and... 

Since niobates and tantalates belong to the octahedral ferroelectric family, fluorine-oxygen substitution has a particular importance in managing ferroelectric properties. Thus, the variation in the Curie temperature of such compounds with the fluorine-oxygen substitution rate depends strongly on the crystalline network, the ferroelectric type and the mutual orientation of the spontaneous polarization vector, metal displacement direction and covalent bond orientation [47]. Hence, complex tantalum and niobium fluoride compounds seem to have potential also as new materials for modem electronic and optical applications. 

The main source of spontaneous polarization in crystals is the relative freedom of cations that fit loosely into the crystal s octahedral cavities. The number of degrees of freedom of the octahedrons affects the spontaneous polarization value and hence influences the crystal s ferroelectric properties. Abrahams and Keve [389] classified ferroelectric materials into three structural categories according to their atomic displacement mechanisms onedimensional, two-dimensional and three-dimensional. 

The phase transiton from a paraelectric to a ferroelectric state, most characteristic for the SbSI type compounds, has been extensively studied for SbSI, because of its importance with respect to the physical properties of this compound (e.g., J53, 173-177, 184, 257). The first-order transition is accompanied by a small shift of the atomic parameters and loss of the center of symmetry, and is most probably of a displacement nature. The true structure of Sb4S5Cl2 106), Bi4S5Cl2 194), and SbTel 108,403) is still unknown. In contrast to the sulfides and selenides of bismuth, BiTeBr 108) and BiTel (JOS, 390) exhibit a layer structure similar to that of the Cdl2 structure, if the difference between Te, Br, and I (see Fig. 36) is ignored. 

Burrows AD (2004) Crystal Engineering Using Multiple Hydrogen Bonds 108 55-96 Bussmann-Holder A, Dalai NS (2007) Order/Disorder Versus or with Displacive Dynamics in Ferroelectric Systems. 124 1-21... 

Dalai NS, Gunaydin-Sen O, Bussmann-Holder A (2007) Experimental Evidence for the Coexistence of Order/Disorder and Displacive Behavior of Hydrogen-Bonded Ferroelectrics and Antiferroelectrics. 124 23-50 Dalai NS, see Bussmann-Holder A (2007) 124 1-21 Daul CA, see Atanasov M (2003) 106 97-125... 

Liquid Crystal Displays (LCD). Liquid crystal displays, once limited to small devices such as calculators, are now displacing color CRT (cathode ray tube) displays in commercial quantities. The ability to fabricate these display devices at high quality and at low cost is partially due to the wider spread use of photopolymer-based materials. Photopolymer technology is being used for the alignment of liquid crystal (LC) elements (49), the orientation of ferroelectric materials (50), the synthesis of LC polymers (57) and the manufacture of color filters for liquid crystal display applications (52). 

In lead zirconate, PbZr03, the larger lead ions are displaced alternately from the cube comer sites to produce an antiferroelectric. This can readily be converted to a ferroelectric by the substitution of Ti4+ ions for some of the Zr4+ ions, the maximum value of permittivity occurring at about the 50 50 mixture of PbZrC>3 and PbTiC>3. The resulting PZT ceramics are used in a number of capacitance and electro-optic applications. The major problem in the preparation of these solid solutions is the volatility of PbO. This is overcome by... 

Order/Disorder Versus or with Displacive Dynamics in Ferroelectric Systems 3... 

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