Jahn-Teller effect phase properties

Some metal oxide structures are unstable when over-delithiated, and as a consequence, the crystal lattice collapses to form a new phase that is electrochemically inactive. Examples are the so-called Jahn—Teller effect for spinel cathodes and similar behavior for LiNi02 and LiCo02 materials as well. These irreversible processes are considered to be caused by the intrinsic properties of the crystalline materials instead of electrolytes and are, therefore, beyond the scope of the current review. See ref 46 for a detailed review. 

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]. 

DMBE III calculation, permutational symmetry, dynamic Jahn-Teller and geometric phase effects, 699—711 Double degeneracy, geometric phase theory, Jahn-Teller models, 2-4, 31-33 Dynamic phase, properties, 210... 

Geometric phase effect (GPE) (Continued) adiabatic states, conical intersections invariant operators, 735-737 Jahn-Teller theorem, 733-735 antilinear operator properties, 721-723 degenerate/near-degenerate vibration levels, 728-733... 

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