Lattice dimerization

Spin-Peierls Compounds. - A good review of the properties of the spin-Peierls compound CuGe03 has been given recently.82 A lattice dimerization,... 

Lattice dimerization in the course of the spin-Peierls-like transition leads to the appearance of new optically active modes folded from a boundary of the Brillouin zone to its center. Charge ordering results in a dielectric anomaly observable in the far-infrared spectral region. 

Below Tc, the magnetic susceptibility decreases isotropically, thus showing a spin gap formation, the lattice dimerizes and, as follows from the 51V NMR data [22], a charge ordering into the V44 and V5+ states occurs. According to the theoretical consideration of Ref [23], Coulomb repulsion... 

CuGeO, is the first known inorganic spin-Peierls material [35], A lattice dimerization, which is one of the most characteristic features in the spin-... 

Flere, as in metal model wave number k — 2%jjNax (j — 0, +1,..., .N/2), Pi, and p2 are exchange integrals for short and long bonds in the lattice dimer unit, respectively, and it was obvious that Pi > p2. As is shown in Figure 10.2 ji orbital levels form two bands divided by the band gap AE. The minimal value of gap AE (Afs0) between highest occupied molecular orbitals... 

A (somewhat reduced) neutral-to-ionic first-order-like transition has been reported for another material TMB-TCNQ (TMB = 3,3, 5,5 -te-tramethylbenzidine) [79]. At room temperature p = 0.6, cr = 10-4 S/cm, and 2A = 0.2 eV. At ambient pressure, the transition is at Tc = 205 K and in this case p goes only from = 0.6 to = 0.7. At ambient temperature, the transition occurs at a pressure of 4.3 kbar. In contrast to the case of TTF-p-chloranil, the high-temperature phase is not really a neutral phase (p = 0.6) and the low-temperature phase is found to consist of both ionic and neutral molecules. Lattice dimerization also occurs in this compound below 205 K [79]. 

Metals when cooled may undergo what is known as the Peierls transition, which denotes lattice dimerization and band gap formation. In this way, the system changes from a metal to a semiconductor or insulator. This transition corresponds to the Jahn-Teller effect in molecules. 

He is the one-electron Hamiltonian of a molecular chain exhibiting a lattice dimerization, wnose amplitude is specified by the longitudinal displacement Uq of the molecules from their location in die undistorted chain. The electrons are also subjected to a potential, say from the inorganic anion chains and from some mean-field electron correlation, of period twice the regular chain spacing d, acting on the bonds (i.e. between sites) with an amplitude B. ... 

Polymerization in solution. Using the lattice dimerization model (see Figure 16.17), derive the equilibrium constant for creating a chain of m monomers of type A in a solvent s. 

For sufficiently small u, the negative term — lu will always dominate any term that is just proportional to u. The elastic energy cost of the lattice dimerizing - the atoms forming pairs so that the distance between atoms alternates on going along... 

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