Antiferrodistortive

Figure 13 shows the optical birefringence measured on the (OOl)c and (llO)c faces [19]. According to the indicatrix deformation approach [25], the optical birefringence, An, for the (llO)c face can detect the antiferrodistortive transition, the square of long-range order (P>, and its fluctuation term (SP) in STO by ... 

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. 

An interesting aspect of many structural phase transitions is the coupling of the primary order parameter to a secondary order parameter. In transitions of molecular crystals, the order parameter is coupled with reorientational or libration modes. In Jahn-Teller as well as ferroelastic transitions, an optical phonon or an electronic excitation is coupled with strain (acoustic phonon). In antiferrodistortive transitions, a zone-boundary phonon (primary order parameter) can induce spontaneous polarization (secondary order parameter). Magnetic resonance and vibrational spectroscopic methods provide valuable information on static as well as dynamic processes occurring during a transition (Owens et ai, 1979 Iqbal Owens, 1984 Rao, 1993). Complementary information is provided by diffraction methods. 

KCuFj is a ID antiferromagnet (A type) with the spins lying in the ab plane. The magnetic behaviour is again a consequence of antiferrodistortive ordering of distorted octahedra. Interaction between two half-filled orbitals occurs along the c axis... 

Figure 34 ESR spectra for axial environment involving (a) ferrodistortive order and (b) antiferrodistortive order396...

The high temperature (O-orthorhombic) phase can be described as a dynamical locally distorted phase with the strong antiferrodistortive first neighbour coupling [20],... 

Fig. 8. Ferrodistortive and antiferrodistortive orderings of corner-connected (CuFs) octahedra...

The structure of KCrF3 is derived from the perovskite structure by a tetragonal distortion4. An antiferrodistortive coupling occurs between half-filled dz orbitals and empty d 2 yj orbitals. The superexchange interaction d°z y2 - p - dz2 leads to ferromagnetic layers, antiferromagnetically bound via the empty dx2 y2 orbitals. 

A tolerance factor [9,10] can be used to determine the phase transition in AB03 perovskite oxides, as given by t — (rA + > o )/V2(J b + ro), where rA, rB, and rQ are the ionic radii [11] of the A, B, and O ions, respectively. This indicates that the spatial margin relates to the type of phase transition. However, the atomistic explanation has not been given for the factor in order to distinguish between ferroelectric and antiferrodistortive phase transitions in AB03 perovskite oxides. 

Because of the fixed cubic lattice, in this study, the Ti06 octahedron is slightly elongated in the directions of the x- and y-axes by TiOf, rotation. But, it is believed that such a distortion of TiOg octahedron does not affect the probability of the antiferrodistortive phase transition. 

The changes in the four A-0 + covalent interactions were evaluated as a function of the rotation of TiOg octahedron around the z-axis in the three perovskite oxides, and it was concluded that the probability of the antiferrodistortive phase transition is higher in SrTi03 than in PbTi03, and lower in BaTi03 than in PbTi03. 

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