Octahedra tilting

The main structural changes occurred in LSGT-8 at the phase transition become apparent in anion sublattice and result in the different character of the octahedra tilting in LT and HT structures. In terms of Glaser notations... 

Another type of deformation of the perovskite structure is known to occur among the LT modifications of cerium and praseodymium aluminates and solid solutions based on them. In the orthorhombic Imma structures, 12 nearest distances in the RO12 polyhedra split into a set of five imique R-O distances, typically grouped as 1-4-2-4-1. The six Al-O bonds within the octahedra split into two shorter and four longer distances, but this deformation is very weak and octahedra are distorted mainly due to considerable deviations of the O-Al-O angles from 90° (see Table 28). Moreover, the octahedra tilt either about the twofold [110]p axis or about both [010]p and [001]p pseudo-axes of the perovskite cell, which corresponds to the tilt system a% b (Figure 39C). 

FIGURE 43 Octahedra tilt angles as functions of R-cation radius. tetragonal structures rhombohedral structures. For orthorhombic structures, the average tilt angles are shown as well. 

Here we took into account that the charge susceptibility is the response of the system to the external potential. In Eq. (22) we allowed also for low oscillation frequency of the octahedron tilts [44]. The potential depends on the coordinates and 0 y,of these... 

Figure 21 The La2Cu04 structure, a) Structure showing distorted octahedron and puckered CuOz planes, b) Illustration of the tilted octahedra (0 = 4.5°), and rotation about the b axis = 1°). From Reference 108.

There are three kinds of Mn-0 distances within each oxygen octahedron surrounding a central manganese ion two of them are shorter (0.191 and 0.195 nm for PrMnOj, and 0.194 and 0.190 for TbMnOj) and the other is a little longer (0.222 nm for PrMnOj and 0.223 nm for TbMnOj). Thus each oxygen octahedron distorts and tilts each other, which are caused by the Jahn-Teller effect of trivalent manganese ion. Each rare... 

It is more common to see the octahedron as shown in Figure 12, where the polyhedron in Figure 11 is tilted up until two spheres from the top layer and two from the bottom layer are perpendicular to the plane of the paper. 

The comer connectivity of the BX octahedra means that the tilt of one octahedron completely determines the tilting in the plane perpendicular to the tilt axis... 

Figure 1.10 Tilt axes of an octahedron (a) one of three tetrad axes (b) one of six diad axes (c) one of four triad axes...

Figure 1.11 Tilting of a plane of corner-linked octahedra about a tetrad axis perpendicular to the plane of the figure through one octahedron (a) no tilt (b) a tilt...

In the simplest case, and considering only a two-octahedron repeat along each of the cubic or pseudocubic axes, 10 possible tilt combinations are possible ... 

As a matter of fact, the tolerance factor is a rather complex crystaUo-chemical parameter, which can reflect the structural distortion, force constants of binding, rotation and tilt of the BOg octahedrons. These in turn affect the dielectric properties, transition temperature, temperature coefficient of the dielectric constant of material, and even the dielectric loss behavior in a perovskite dielectric. 

Fig. 13.2 Proton traces sampled by quantum molecular dynamics simulations involving intraoctahedron transfer (a) and inter-octahedra proton transfer (b) [24, 25], The transition state configurations for proton transfer are shown for both cases In the case of intra-octahedron transfer, this is characterized by B-O bond elongations and strong contraction of the OH-O separation in the case of inter-octahedra transfer, severe tilting of the participating octahedra is involved (see text)...

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