Antiferrodistortive phase transition

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. 

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. 

In one respect the antiferrodistortive order in the lead nitrocomplexes is different from the one found in the perovskite lattice. While the molecular field in the perovskite compounds is determined by a large Qe component which shifts the sublattices appreciably from tp = 120°, 240° towards

deviate from 120° and 240° towards 180° (Table 3). This observation may possibly be related with the first order nature of the phase transitions (Table 4). 

It should be noted that in the last years EuTiOs attracts a lot of attention of scientists. For instance, the comparative analysis of EuTiOs and SrTiOs has been performed recently. This analysis is based upon specific heat and soft phonon mode measurements. Refs. [23] and [24, 25] respectively. The obtained results made it possible for authors to ascribe new 282 K instability of EuTiOs to antiferrodistortive phase transition. 

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