Ferroelectrics displacive type

According to the concept of the displacive-type ferroelectric phase transition [10], an increase in the dielectric constant corresponds directly to the softening of the IR-active transverse phonon. When the crystal can be regarded as an assembly of the vibrators of normal coordinates, the soft phonon... 

Recently, perfect softening of the ferroelectric TO mode was confirmed by Takesada et al., so ST018 is considered to be a displacive-type ferroelectric [11]. Kvyakovskii [ 12] gave an explanation for the phase transition mechanism. Part of the theory is summarized below. 

Figure 14 shows the result of a Brillouin scattering experiment in the vicinity of Tc [11]. Closed circles and open circles below Tc indicate the modes split from the doubly degenerated ferroelectric soft mode. The closed circles above Tc denote the frequency of the doubly degenerated soft u mode in the paraelectric phase. The results clearly show a softening of the soft mode toward zero frequency at Tc following the Curie-Weiss law. The soft mode remains underdamped even at Tc. Generally, a soft mode is heavily damped in the vicinity of Tc, e.g., as for PbTiOs, which are typical displacive-type... 

Gradient coefficients > 0 and q > 0 the expansion coefficient an>0 for the second order phase transitions. Coefficient ai(T) = ar T — Tc), E is the transition temperature of a bulk material. Note, that the coefficient flu for displacement type ferroelectrics does not depend on T, while it is temperature dependent for order-disorder type ferroelectrics (see corresponding reference in [117]). Eq is the homogeneous external field, the term Ed (P3) represents depolarization field, that increases due to the polarization inhomogeneity in confined system. Linear operator Ed P3) essentially depends on the system shape and boundary conditions. Below we consider the case when depolarization field is completely screened by the ambient free charges outside the particle, while it is nonzero inside the particle due to inhomogeneous polarization distribution (i.e., nonzero divP 0) (see Fig. 4.35b). 

Ferroelectricity is caused by a cooperative interaction of molecules or ions in condensed matter. The transition to ferroelectricity is characterized by a phase transition. Depending on the mechanism of how the molecules or ions interact in the material, we can classify the ferroelectric phase transitions and also the ferroelectric materials themselves into three categories (I) order-disorder type, (II) displacive type, and (III) indirect type. In the order-disorder type (I), the spontaneous... 

SbSI (LB Number 20A-7). SbSI is ferroelectric below 20 °C. The phase transition is of the displacive type, a relatively rare characteristic in nonoxide materials. The crystal is photoconductive (Figs. 4.5-47 and 4.5-48). 

Ferroelectric substances perovskites exhibit no permanent dielectric dipoles in the p electric phase (which belongs to the centrosymmetrical symmetry group /w3/w). The dipole moments appear in ferroelectric phase as a result of the spontaneous displacements of ions. Such phase transition is therefore called displacement-type phase transition. 

Resonant behavior of the dielectric dispersion in ferroelectric crystals of the displacement-type appears usually in the far infrared frequency range. For the ferroelectrics of the order-disorder type it appears in the microwave frequency range. 

Another class of ferroelectrics is the perovskites such as the titanates (BaTiOs, PbTiOs, SrTiOs, CaTiOs), the niobates (KNbOs, NaNbOs), the ilmentites, (LiNbOs, LiTaOs)), the ternary lead zirconate titanate (PZT), and the quaternary lead lanthanum zirconate titanate (PLZT). These materials undergo a displacive-type phase transformation at their Curie temperature. 

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 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. 

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

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