D system

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

Fig 1 shows the situation, at some time after the start of detonation, for a 1-D system consisting of a semi-infinite expl slab, initially in contact with a metal plate on one side and vacuum on the other side, with detonation started simultaneously all along the original HE-vacuum boundary As indicated, the plate moves to the right at a velocity V and product gases expand into vacuum (in Appendix A it is shown that expansion into air is negligibly different from expansion into vacuum) at velocity -U. The coordinate system used assigns x = 0 to the product/vacuum boundary and x = 2 to the position of the plate at time t. Then, as taken directly from Ref 14 ... 

Although conceptually one can make the systems described by Eqns 2—6 one-dimensional, in practice this would be difficult to achieve because of the simultaneous initiation requirement We now turn to pseudo-1-D systems, namely a hollow cylinder filled with expl which is initiated simultaneously all along its central axis. This configuration is sketched below (Fig 2) and the derivation of the Gurney formula follows ... 

Studies at Lawrence Radiation Laboratory (LRL) (Kury et al (Ref 7) quoting Wilkins) indicate that in 1-D systems a twofold volume expansion of the detonation products is sufficient to transfer the maximum amount of energy to a metal in contact with these detonation products, but for tangential incidence (2-D systems) a sevenfold volume expansion is required. They state that for explosively driven cylinders observations of the early stages of expansion are expected to provide information on 1-D systems, and measurements of the later stages of expansion are expected to characterize 2-D systems. We will consider their hypothesis in Section IV... 

In Section III we quoted LRL s suggestion that the early stages of expansion of an explosively driven cylinder behave like a 1-D system (called head-on detonation in Ref 7). The results of Table 3 support this idea. In Table 3 we compare LRL s relative /2E values with the relative values we have computed from the average /2E s of Table 1. Agreement between the two sets of relative values is excellent... 

Suppose we want to know the mass per unit area mg, momentum g(x) of the detonation products expanding in the direction of the metal plate in a 1-D system. The Gurney assumption of linear distribution of gas velocities enables us to compute all these quantities. The derivations of the necessary equations are given in Appendix G. Here we present only the final results, namely ... 

With regard to 1-D systems, it can be clearly stated that, in contrast to 2-D systems where a 2-D phase transition has been considered by Stanley and Kaplan among others28,78), the 1-D short-range order = 3-D long-range order transition only shows 3-D properties7). 

In 2-D and 1-D systems even in non-uniaxial materials, the Neel model can still be used since the anisotropic field in the plane where the moments can rotate is small compared with the exchange field in the perpendicular direction. After first considering the particular case of CsNiF3, we will described several 2-D and 1-D Heisenberg fluorides showing spin-flop behavior. 

U of Eq. (5), but here it is a two-particle on-site energy), and V is the nearest-neighbor Coulomb interaction energy. These two Hamiltonians cannot be solved for the general case. They have been solved exactly for 1-D systems and for the 2-state system, and numerically for some restricted conditions. Details are given elsewhere in this volume [206]. 

Instabilities in a 1-D system, driven by a strong on-site electron-electron Coulomb repulsion U, lead to a Mott-Hubbard insulator [161], particularly for p = 1 systems this causes charge localization, and the crystal becomes insulating. For a chemist, a Mott-Hubbard insulator is like a NaCl crystal, where the energy barrier to moving a second electron onto the Cl site is prohibitively high, as is the cost of moving an electron off a Na site. 

In analogy to the layered 2-D semiconductors, it is also possible to produce onedimensional (1-D) systems i.e., nanostructures with quantum confinement in two dimensions). This results in quantum wires (nanowires), quantum rods (nanorods) or nanotubes. Over the past decade this field has experienced exponential growth with about 1250 papers published in 2005 compared with none in 1994. Many important advances in the growth, characterisation and applications of 1-D systems have occurred and these are described in several reviews (Law et al, 2004 Rao et al, 2006 Lieber et al, 2007 Robertson, 2007). 

For 1-D systems (which are confined along two directions), the exciton binding energy increases further. The effect of confinement on the electron s eigenspectrum, within a tight-binding approximation, is given by (Coulson et al, 1962 Brus, 1986)... 

A Peierls distorsion at zero Kelvin on purely 1 D system is a second order phase transition. The observed transition (Figure 4) might be of weakly first order transition it is interesting to note that the specific heat anomaly increases with the transition temperature in the three considered compounds. We suppose that this critical temperature increases in relation with the 3-D and the disorder effects. 

Nonstoichiometry can be assessed by precise elemental analysis. Extreme care must be taken to ensure that reproducible nonstoichiometry is characterized. For example, absorption spectra, x-ray fluorescence, neutron activation, and mass spectral analysis were used to determine the 0.300 0.006 1 Br Pt ratio for K2Pt(CN)4Bro.3oo 3H2O (10). The errors associated with routine elemental analysis allow significant differences in the stoichiometry of nonstoichiometric materials. In order to understand fully the physics of 1-D systems, it is imperative that the exact stoichiometry be known as this relates directly to the band filling which, in general, cannot be obtained by alternative techniques. 

Fig. 9.9 Electron-phonon scattering in a one-dimensional (1-d) and in a two-dimensional (2-d) metallic system. Since the Fermi energy is always large compared to the phonon energies, the single-phonon scattering processes are limited to the immediate neighbourhood of the Fermi surface. In the 1-d system, the Fermi surface consists of only two points and the conduction electrons can be scattered only from kp to -kp. In the (isotropic)...

Fig. 9.10 The density-response function x-x q) describes the redistribution Sn q) of the electron density by a periodic modulation Vq q) of the potential as a function of the wavevector q (cf. also Fig. 9.8). In a 1-d system, x has a singularity atq = 2kf. This singularity does not exist in 2-d- and 3-d systems. From [9] and [M4], Chap. 2.

In the mean-field approximation for the description of the Peierls transition, all the lattice fluctuations except those with the wavevector q = lkp are neglected. Fluctuations are however particularly effective in highly onedimensional systems in contrast to 3-d systems, phase transitions in 1-d systems are seriously influenced by fluctuations. The relation between the real phase-transition temperature Tp and the experimentally observable ground-state energy gap 2A(T = 0) is, taking the fluctuations in onedimensional metals into account ... 

PEDOT PSS nanowire (Figure 10.41) [101,102]. The temperature dependence of the resistance indeed followed Mott VRH for a 1-D system, i.e., p T) oc exp (TMott/T). Tiviott was determined to be 1900 K, which is similar to that of PEDOT PSS thin films. 

The density of states is depicted in Figure 2.6. In 1-D systems the density of states has a E -dependence, and thus exhibits singularities near the band edges 17]. Each of the hyperbolas contains a continuous distribution of fe states, but only one... 

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