Peierls temperature

Peierls showed 74 [41,42] that an instability in a one-dimensional chain, with one electron per site, driven by electron-phonon interactions, can lead to a subtle structural distortion and to a first-order Peierls phase transition, at and below a finite temperature TP (the Peierls temperature) [42], For instance, at and below Tp either a dimerization into two sets of unequal interparticle distances d and d" (such that d + d" = 2d) or some other structural distortion must occur. The electronic energy of the metallic chain may also be lowered by the formation of a charge-density wave (CDW) of amplitude p(x) ... 

As one approaches the Peierls temperature from above, the restoring force for a distortion which has the symmetry that would create a gap at the Fermi surface gets smaller and smaller, until at the Peierls temperature it goes to zero and the lattice distorts spontaneously to the new structure. Thus phonons with the symmetry of this distortion become soft as one approaches this temperature and the amplitude of thermal excitation of the mode grows enormous. These effects show up in x-ray studies of such compounds and allow the identification of the instability. 

The temperature dependence of the spin susceptibility is one of the most intriguing problems of the conducting charge transfer salts. Basing their arguments on T measurements, some authors maintain that the large decrease of observed between room temperature and the metal-insulator transition temperature is related to the development of a pseudo-gap in the density of states at the Fermi level, as temperature becomes smaller than a mean-field Peierls temperature /3o,... 

A couple of theoretical studies [5,19] have hitherto attempted to estimate the Peierls transition temperature (Tp) for metallic CNT. A detailed theoretical check with respect to the stability of metallic wavefunction in tube (5, 5) has also... 

It will be intriguing to theoretically examine the possibility of superconductivity in CNT prior to the actual experimental assessment. A preliminary estimation of superconducting transition temperature (T ) for metallic CNT has been performed considering the electron-phonon coupling within the framework of the BCS theory [31]. It is important to note that there can generally exist the competition between Peierls- and superconductivity (BCS-type) transitions in lowdimensional materials. However, as has been described in Sec. 2.3, the Peierls transition can probably be suppressed in the metallic tube (a, a) due to small Fermi integrals as a whole [20]. 

SN)x are free to move under the influence of an applied potential difference and thus conduction occurs along the polymer chain. The S-N distances in the chain are essentially equal, consistent with a delocalized structure. The increase in conductivity with decreasing temperature is characteristic of a metallic conductor. The predicted Peierls distortion is apparently inhibited by weak interactions between the polymer chains (S—S = 3.47-3.70 A S—N = 3.26-3.38 A.). ... 

For the deformation of NiAl in a soft orientation our calculations give by far the lowest Peierls barriers for the (100) 011 glide system. This glide system is also found in many experimental observations and generally accepted as the primary slip system in NiAl [18], Compared to previous atomistic modelling [6], we obtain Peierls stresses which are markedly lower. The calculated Peierls stresses (see table 1) are in the range of 40-150 MPa which is clearly at the lower end of the experimental low temperature deformation data [18]. This may either be attributed to an insufficiency of the interaction model used here or one may speculate that the low temperature deformation of NiAl is not limited by the Peierls stresses but by the interaction of the dislocations with other obstacles (possibly point defects and impurities). 

The (110) dislocations are from our calculations not expected to contribute significantly to the plastic deformation in hard oriented NiAl because of the very high Peierls stresses. Experimentally, these dislocations do not appear unless the temperature is raised to about 600 K [18]. At this temperature the experimental data strongly suggest a transition from (111) to (110) slip. 

Excellent agreement between experiment and onr calculations is obtained when considering the low temperature deformation in the hard orientation. Not only are the Peierls stresses almost exactly as large as the experimental critical resolved shear stresses at low temperatures, but the limiting role of the screw character can also be explained. Furthermore the transition from (111) to (110) slip at higher temperatures can be understood when combining the present results with a simple line tension model. 

An important property of the dimerized Peierls stale is the existence of gaps in the spectra of spin and charge excitations. For free electrons (//ci-ci=0) both gaps are equal, while in the presence of Coulomb repulsion the spin gap is smaller than the charge gap [23, 24]. In what follows, we will assume the temperature to be much smaller than these two gaps, so that we can neglect electronic excitations and replace Hcl [ A (.v)] by its ground state expectation value. 

Poly(4-phenoxybenzoyl-1,4-phenylene) (PPBP), sulfonated, 23 718 Polyacetal, antioxidant applications, 3 121 Polyacetaldehyde, 1 103 Polyacetal fiber, 13 392 Polyacetylene, 7 514-515 26 953 conduction in, 7 527 22 208 molecular structure of, 22 211 optical band gap, 7 529t Peierls distortion in, 22 203, 208 room temperature conductivity, 7 532 synthesis of, 22 213... 

After publication of the X-ray study, the charge transfer was obtained from the reciprocal-space position of the satellite reflections, which occur in the diffraction pattern at temperatures below the Peierls-type metal-insulator transition at 53 K (Pouget et al. 1976). Assuming that the gap in the band structure occurs at twice the Fermi wavevector, that is, at 2kF, the position of the satellite reflections corresponds to a charge transfer of 0.59 e, in excellent agreement with the direct integration. The agreement confirms the assumption that the gap in the band structure occurs at 2kF. 

As already discussed in Chapter 1, this kind of mixed valence salt becomes conductive due to the transfer of one electron from two BEDT-TTF molecules to the anion layers. However, at the surface, the charge can become unbalanced, resulting is an incomplete CT. This leads to differentiated surface vs. bulk nesting vectors and to the existence of surface CDWs (Ishida et al, 1999). The Peierls transition has also been observed on the a -planes of single crystals of TTF-TCNQ with a variable temperature STM (Wang et al, 2003) and will be discussed in Section 6.1. 

Figure 6.36. Detail of the /o(T ) curve for 3 showing the Peierls transition. The dashed line corresponds to a linear interpolation of the higher temperature region. Reprinted from Journal of Solid State Chemistry, Vol. 168, J. Fraxedas, S. Molas, A. Figueras, I. Jimenez, R. Gago, R Auban-Senzier and M. Goffman, Thin films of molecular metals TTF-TCNQ, 384-389, Copyright (2002), with permission from Elsevier.

The phase transition consists of a cooperative mechanism with charge-ordering, anion order-disorder, Peierls-like lattice distortion, which induces a doubled lattice periodicity giving rise to 2 p nesting, and molecular deformation (Fig. 11c). The high temperature metallic phase is composed of flat EDO molecules with +0.5 charge, while the low temperature insulating phase is composed of both flat monocations... 

Highly conducting 1-D system. Undergoes a Peierls transition at low temperature. Nearly superconducting. Stack of super-positioned, square-planar Pt(CN)4 groups. 

The trisulphides (and triselenides) of Ti, Zr, Hf, Nb and Ta crystallize in onedimensional structures formed by MSg trigonal prisms that share opposite faces. Metal atoms in these sulphides are formally in the quadrivalent state, and part of the sulphur exists as molecular anions, M S2 S . TaSj shows a metal-insulator transition of the Peierls type at low temperatures (Section 4.9). NbSj adopts a Peierls distorted insulating structure suggesting the possibility of a transformation to a metallic phase at high temperatures, but does not transform completely to the undistorted structure. Electronic properties and structural transitions of these sulphides have been reviewed (Rouxel et al, 1982 Meerschaut, 1982 Rouxel, 1992). 

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