Antiferrodistortive ordering

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... 

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

In this case the interaction constant at k = 0 is negative, i.e. the phonons tend to establish the antiferrodistortive ordering. 

Fig. 5 Antiferrodistortive ordering of tetragonal elementary cells with rhombic JT instabdity of E b g type (z axis view of the ay plane), (a) The case when elementary cells do not share common atoms, (b) Same when elementary cells share common vertices. (From [16,17])...

Fig. 6 Antiferrodistortive order of tetragonal elementary cells with rhombic JT instability of the E b g type (similar to Fig. 3b). (a) In the traditional approach, ligands are explicitly included. Orientation of central-atom orbitals is determined by formation of chemical bonds with nearest-neighbor ligands, (b) In the OOA ligands are omitted. Central-atom orbitals point toward next-neighbor sites...

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

A unit cell with an antiferrodistortive order of tetragonaUy elongated octahedra can be described by consisting of two ferrodistorthre sublattices which are rotated... 

Equation (26) is again valid only for large values of x. 27 = 90° describes the undisturbed antiferrodistortive order (Fig. 9b) and changes Eq. (26) into Eq. (25). An extension to o-rhombic sublattices A and B with 4 120° is easily possible. 

Flgi 17. Cooperative Jahn-Teller ordering in complexes A2PbCu(N02)g (a) Antiferrodistortive order of elongated CuNg octahedra (small o-rhombic component) in 7-modifications [(001) planes, z = 0 z = 1/2 rotation of (z = 0) plane around [001 ] by 90° " )j (b) Incommensurate p-phase of K complex [from )] (c) Antiferrodistortive order in 7-phase and spatial disorder in p nodification of K complex ). 

In general the antiferrodistortive pattern is more stable than the ferrodistortive order in a 3-dimensional frame-work of comer-connected octahedra (jperov tes, lead nitrocomplexes). As discussed just before the antiferrodistortive order leads to appreciable deformations of those octahedral sites which are occupied by non-Jahn-Teller ions in elpasolite-type stmctuies. Thus the ferrodistortive order may be stabilized also (oxidic elpasolites, alkaline earth nitrocomplexes). The lower transition temperatures of the lead compared to the alkaline earth compounds indicate weaker cooperative-elastic interactions and are possibly caused by the less distinct distortion of the CuNg polyhedra (Table 3). Finally it should be mentioned that the g tensor in the (001) planes of the 7-modifications has an orientation [K 15° ... 

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). 

Fig. 22. Orbital ordering in (001) planes of structures with comer-connected TLg polyhedra [T d cations] (a) compressed octahedra in ferrodistortive order (b) elongated octahedra in antiferrodistortive order...

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