Solids Peierls distortions

The model of the chain of hydrogen atoms with a completely delocalized (metallic) type of bonding is outlined in the preceding section. Intuitively, a chemist will find this model rather unreal, as he or she expects the atoms to combine in pairs to give H2 molecules. In other words, the chain of equidistant H atoms is expected to be unstable, so it undergoes a distortion in such a way that the atoms approach each other in pairs. This process is called Peierls distortion (or strong electron-phonon coupling) in solid-state physics ... 

The Peierls distortion is not the only possible way to achieve the most stable state for a system. Whether it occurs is a question not only of the band structure itself, but also of the degree of occupation of the bands. For an unoccupied band or for a band occupied only at values around k = 0, it is of no importance how the energy levels are distributed at k = n/a. In a solid, a stabilizing distortion in one direction can cause a destabilization in another direction and may therefore not take place. The stabilizing effect of the Peierls distortion is small for the heavy elements (from the fifth period onward) and can be overcome by other effects. Therefore, undistorted chains and networks are observed mainly among compounds of the heavy elements. 

Figure 9 (Top) schematic of bistability in 1,3,2-dithiazolyl radicals arising from a solid-solid phase transition between regular and Peierls distorted n-stacks (bottom) free energy diagram of the two structural phases present...

Besides magnetic perturbations and electron-lattice interactions, there are other instabilities in solids which have to be considered. For example, one-dimensional solids cannot be metallic since a periodic lattice distortion (Peierls distortion) destroys the Fermi surface in such a system. The perturbation of the electron states results in charge-density waves (CDW), involving a periodicity in electron density in phase with the lattice distortion. Blue molybdenum bronzes, K0.3M0O3, show such features (see Section 4.9 for details). In two- or three-dimensional solids, however, one observes Fermi surface nesting due to the presence of parallel Fermi surface planes perturbed by periodic lattice distortions. Certain molybdenum bronzes exhibit this behaviour. 

However, there is another distortion that the polyene can and does undergo. This is double-bond localization, an example of the very important Peierls distortion, i.e., the solid state analogue of theJahn-Teller effect. 

The Peierls distortion plays a crucial role in determining the structure of solids in general. The one-dimensional pairing distortion is only one simple example of its workings. Let s move up in dimensionality. 

The details of what actually happens are presented elsewhere.16 The situation is intricate the observed structure is only one of several likely ways for the parent structure to stabilize—there are others. Diagram 95 shows some possibilities suggested by Hulliger et al.72 CeAsS chooses 95c.75 Nor is the range of geometric possibilities of the MAB phases exhausted by these. Other deformations are possible many of them can be rationalized in terms of second order Peierls distortions in the solid.16... 

Fig. 26. Computed energy difference curves for Peierls distortions. The solid and dashed lines correspond to dimerization and trimerization respectively (37, 38)...

An important aim of the book is then to show how common orbital situations arise throughout the whole chemical spectrum. For example, there are isomorphisms between the electronic structure of CHj, Fe(CO)4, and Ni(PRj)s and between the Jahn-Teller instability in cyclobutadiene and the Peierls distortion in solids, These relationships will be highlighted, and to a certain extent, we have chosen problems that allow us to make such theoretical connections across the traditional boundaries between the subdisciplines of chemistry,... 

Peierls distortions occur in other systems, and in fact they are fairly common in solid state physics. A common situation in which a Peierls distortion might be expected is in a crystal of relatively flat molecules that stack on each other along one crystal axis. Rather than... 

In conducting solids, the conduction electron density is spatially modulated, forming charge density waves (CDW) the periodic distortion accompanying the CDW (due to interaction between the conduction electron and the lattice) is responsible for the incommensurate phase (Overhauser, 1962 Di Salvo Rice, 1979 Riste, 1977). The occurrence of CDW and the periodic distortion can be understood in terms of the model proposed by Peierls and Frdhlich for one-dimensional metals. Let us consider a row of uniformly spaced chain of ions (spacing = a) associated with conduction electrons of energy E k) and a wave vector k. At 0 K, all the states are filled up to the Fermi energy, = E(kp). If the electron density is sinusoidally modulated as in Fig. 4.15 such that... 

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