BaTiO tetragonality

Fig. 3. Crystal structure and lattice distortion of the BaTiO unit ceU showiag the direction of spontaneous polarization, and resultant dielectric constant S vs temperature. The subscripts a and c relate to orientations parallel and perpendicular to the tetragonal axis, respectively. The Curie poiat, T, is also shown.

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. 

Fig. 4 (Color online) Angular dependencies of the second moment of the Ti spectra shown in Fig. 2 for cubic BaTiOs at 450 K. Best fits (solid lines) are obtained with i.e., with the tetragonal displacements scenario...

Figure 6.27 View of (a) the tetragonal unit ceU of BaTiOs and (b) the ionic positions projected in a [100] direction onto a (100) face. From K. M. Rails, T. H. Courtney, and J. Wulff, Introduction to Materials Science and Engineering. Copyright 1976 by John Wiley Sons, Inc. This material is used by permission John Wiley Sons, Inc.

Figure 6.55 Distortion of TiOg octahedron in the tetragonal BaTiOs (top) and possible orientations of the polar axis when an electric field is applied along the pseudo-cubic (001) direction of BaTi03 (middle). Polar axes are shown by arrows inside each cube. Phase transitions in BaTiOj accompanied by changes in (a) dielectric constant (b) spontaneous polarization (c) heat capacity and (d) lattice dimensions (bottom).

Phase transitions. Examples BaTiO (> 120°C, cubic perovskite type) -y BaTiOj (< 120°C, tetragonal), cf. Fig. 19.5, p. 230 CaCl2 (> 217°C, rutile type) CaCl2 (< 217°C), cf. Fig. 4.1, p. 33. For second-order phase transitions it is mandatory that there is a group-subgroup relation between the involved space groups (Section 18.4). 

Figure 1.1 Unit cell of cubic BaTiOs. The arrow schematically indicates one of the possible displacement of the central Ti4+ ion at the transition to the tetragonal ferroelectric structure that leads to a spontaneous polarization, in reality all ions are displaced against each other.

IR spectroscopy can be used to distinguish several different phases characterized by the stoichiometry ABO3 (Table 3.4), such as cubic, tetragonal, orthorombic and rhombohedral perovskites (such as SrTiOs, BaTiOs, LaFeOs and LaMnOs, respectively [56, 64, 65]), from ilmenites and lithium niobate structures. In Figure 3.10 the spectrum of LaFeOs is reported. It shows some of the 26 IR active modes expected. 

The Bravais lattice of BaTiOs at room temperature is primitive tetragonal but because the distortion from cubic is small, the structure can be considered to be primitive cubic with a(pc) = a = 6 c 0.4 nm. 

Studying the temperature evolution of UV Raman spectra was demonstrated to be an effective approach to determine the ferroelectric phase transition temperature in ferroelectric ultrathin films and superlattices, which is a critical but challenging step for understanding ferroelectricity in nanoscale systems. The T. determination from Raman data is based on the above mentioned fact that perovskite-type crystals have no first order Raman active modes in paraelectric phase. Therefore, Raman intensities of the ferroelectric superlattice or thin film phonons decrease as the temperature approaches Tc from below and disappear upon ti ansition into paraelectric phase. Above Tc, the spectra contain only the second-order features, as expected from the symmetry selection rules. This method was applied to study phase transitions in BaTiOs/SrTiOs superlattices. Figure 21.3 shows the temperature evolution of Raman spectra for two BaTiOs/SrTiOa superlattices. From the shapes and positions of the BaTiOs lines it follows that the BaTiOs layers remain in ferroelectric tetragonal... 

Raman spectra as a function of temperature are shown in Fig. 21.6b for the C2B4S2 SL. Other superlattices exhibit similar temperature evolution of Raman spectra. These data were used to determine Tc using the same approach as described in the previous section, based on the fact that cubic centrosymmetric perovskite-type crystals have no first-order Raman active modes in the paraelectric phase. The temperature evolution of Raman spectra has indicated that all SLs remain in the tetragonal ferroelectric phase with out-of-plane polarization in the entire temperature range below T. The Tc determination is illustrated in Fig. 21.7 for three of the SLs studied SIBICI, S2B4C2, and S1B3C1. Again, the normalized intensities of the TO2 and TO4 phonon peaks (marked by arrows in Fig. 21.6b) were used. In the three-component SLs studied, a structural asymmetry is introduced by the presence of the three different layers, BaTiOs, SrTiOs, and CaTiOs, in each period. Therefore, the phonon peaks should not disappear from the spectra completely upon transition to the paraelectric phase at T. Raman intensity should rather drop to some small but non-zero value. However, this inversion symmetry breakdown appears to have a small effect in terms of atomic displacement patterns associated with phonons, and this residual above-Tc Raman intensity appears too small to be detected. Therefore, the observed temperature evolution of Raman intensities shows a behavior similar to that of symmetric two-component superlattices. 

BaTiOs are suppressed by biaxial compressive strain, which stabilizes the tetragonal c phase. Similar behavior was also observed in compressively strained BaTiOs/SrTiOs superlattices described in Sect. 4.1. 

The tetragonal perovskite phase is the stable polymorph of BaTiOs and KNbOs, in a temperature range between the cubic and orthorhombic modifications (393K>T>278 K in BaTiOg [100], 708K>T>498 K in KNbOs [101]). 

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