Symmetry random distortions

So-called ternary or mixed oxide systems based on the rock salt structure are well established. Thus LiFe02 exists both in a disordered form in which Li and Fe are randomly distributed on the metal sites, and as an ordered variant with tetragonal symmetry. Rhombohedral distortions are found for LiNi02, LiV02, and NaFe02 in which the cations are ordered on different sublattices. The HCP counterpart of the sodium chloride structure, the so-called Nickel Arsenide stucture (5ee Chalcogenides Solid-state Chewistr, is found only for the heavier members of the Oxygen family. 

It was pointed out independently by Williams (1967) and Culvahouse et al. (1967) that for a non-Kramers ion at a site lacking in full inversion symmetry, terms linear in an electric held may exist for a doublet state. Thus for Cj, symmetry (but not for C y) the system may have a permanent electric dipole moment, and its interaction with an electric held may be represented by additional terms of the form -I- SyEy). Transitions then occur with an RF electric held normal to the z-axis, even in the absence of a distortion from axial symmetry. As before, random distortions again produce an asymmetrical line shape, but with a maximum corresponding to the point for zero distortion, unlike the magnetic transitions referred to above. The asymmetry is present because in each case the distortions move the transitions to higher frequency at constant applied held, or to lower held at constant frequency. Such electric dipole moments also give rise to electric interactions between the ions (see section 5.6). 

The cores of 406 and 407 are each 3/4/3 stacks (alternatively described as a bi-octahedron with a broken shared edge or as two distorted fused trigonal prisms) with idealized symmetry C2h which encloses a C2 unit. The Co and Ni atoms cannot be distinguished and are probably distributed randomly. The carbides are in distorted seven-vertex cages (capped trigonal prisms) with M-C distances between 1.90-2.15 A (mean 2.07 A). 

Going from the molecular picture to that of collective properties in a solid means adding translational symmetry to the point group symmetry. The theoretical description does this by introducing a phase of the distortion throughout the material, which is determined by the spatial variation of the variously distorted molecules. If, as is usual in a classical crystal, the phase of the distortion shows the translational symmetry of the solid, the so-called cooperative Jahn-Teller effect appears where the shape of one molecule and the space group determines the shape of all the others. If the distortions are not correlated, however, the phase is random and the situation is not different from that of isolated molecules. This is the dynamic Jahn-Teller effect where the distortions cannot be detected but the solid-state consequences still appear in the electronic structure [16]. 

Some recent papers report on the metal ion binding at homo- and copolymers of maleic acid a) Insoluble polymer metal complexes have been prepared from Cu(II), Co(II), Ni(II) and Zn(II) with poly(maleic acid) in water. For Ni(II) and Co(II) complexes a distorted octahedral symmetry has been proposed (see Section 5.4, Experiment 5-5) [39]. b) The kinetics and equilibrium of the complexation of Al(III) with a random copolymer of maleic acid and acrylic acid has been studied [40]. In the first step of complexation an outer sphere complex is formed, followed in the second rate-determining step by the formation of an inner sphere complex, c) Insoluble complexes have been obtained from poly(maleic acid-co-olefin) with Cu(II), Co(II), Ni(II) and Zn(II) [41], For the Zn(II) complexes a distorted octahedral geometry has been proposed. 

In practice, many phases are disordered and contain random or partly ordered wider or narrower bands of perovskite-like stracture corresponding to different n values. Non-stoichiometry is common for phases containing Co, Mn or Fe as the B-site cation. In addition, octahedral tilting and distortion are present in the perovs-kite slabs, and these both lower the symmetry of the structures and influence their physical properties. 

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