Electron phases

A simple VB approach was used in [75] to describe the five structures. Only the lowest energy spin-pairing structures I (B symmehy) of the type (12,34,5 were used (Fig. 21). We consider them as reactant-product pairs and note that the transformation of one structure (e.g., la) to another (e.g., Ib) is a thr ee-electron phase-inverting reaction, with a type-II transition state. As shown in Figure 22, a type-II structure is constructed by an out-of-phase combination of... 

Phase transitions are involved in critical temperature thermistors. Vanadium, VO2, and vanadium trioxide [1314-34-7] V2O3, have semiconductors—metal transitions in which the conductivity decreases by several orders of magnitude on cooling. Electronic phase transitions are also observed in superconducting ceramics like YBa2Cu30y but here the conductivity increases sharply on cooling through the phase transition. 

The continuum electron-phase shifts induced by the short-range scattering off the chiral molecular potential are most conveniently introduced by a third choice of continuum function, obtained by diagonalizing the K-matrix by a transformation U, resulting in a set of real eigenchannel functions (apart from normalization) [41] ... 

Fig. 10.6. 2D CALDER simulations for UHC experimental parameters FWD and BWD proton energy distributions (a) and related electron phase space plot (b) at the laser peak...

According to Girgis (1983) the existence field of the electron phases may be especially related to the combinations of d elements with the elements of the Periodic Table columns from 11 to 14 (from the Cu to Si groups). It can also be observed that, for several alloy systems, the dependence of the structures (structure types) on the electron concentration (instead of on the composition) may be clearly illustrated by well-known diagrams such as those shown in Fig. 4.39. 

Figure 4.40. Valence electron (s,p, d) concentration ranges for different types of phases as reported by Lee and Hoistad (1995). Experimental average values are compared with those computed. (For the conventional names of the phases, compare with Table 4.6.) On the left transition metal binary alloys, on the right the Hume-Rothery electron phases are shown.

Viologen salts act as one-electron phase-transfer agents and, in conjunction with sodium dithionite which regenerates the bipyridinium radical cation, they have been used for the debromination of 1,2-dibromoalkanes to yield alkenes in variable yields [13-15]. Nitroarenes are reduced to anilines in high yield (>90%) under similar conditions [16], whereas conjugated nitroalkenes are converted into the oximes of the saturated ketones [17] saturated aliphatic nitro compounds are not reduced by this process. 

The identification and study of colossal magnetoresistance (CMR) materials could be amenable to combinatorial-style searches. Such approaches could be useful for elucidating the structural and electronic phase diagrams of these fascinating materials. Ultimately this could help sort out the apparently complex physics that underlies their behavior. An indication of the value of these approaches was recently provided by Xiang et al. [21]... 

Let us finally discuss to what extent the MFT method is able to (i) obey the principle of microreversibility, (ii) account for the electronic phase coherence, and (iii) correctly describe the vibrational motion on coupled potential-energy surfaces. It is a well-known flaw of the MFT method to violate quantum microreversibility. This basic problem is most easily rationalized in the case of a scattering reaction occurring in a two-state curve-crossing system, where the initial and final state of the scattered particle may be characterized by the momenta p, and pf, respectively. We wish to calculate the probability Pi 2 that... 

A further important property of a MQC description is the ability to correctly describe the time evolution of the electronic coefficients. A proper description of the electronic phase coherence is expected to be particularly important in the case of multiple curve-crossings that are frequently encountered in bound-state relaxation dynamics [163]. Within the limits of the classical-path approximation, the MPT method naturally accounts for the coherent time evolution of the electronic coefficients (see Fig. 5). This conclusion is also supported by the numerical results for the transient oscillations of the electronic population, which were reproduced quite well by the MFT method. Similarly, it has been shown that the MFT method in general does a good job in reproducing coherent nuclear motion on coupled potential-energy surfaces. 

As has been discussed in Section 111, the initial phase-space distribution pyj, for the nuclear DoF xj and pj may be chosen from the action-angle (18) or the Wigner (17) distribution of the initial state of the nuclear DoF. To specify the electronic phase-space distribution pgj, let us assume that the system is initially in the electronic state v i ). According to Eq. (80b), the electronic state vl/ ) is mapped onto Ne harmonic oscillators, whereby the nth oscillator is in its first excited state while the remaining Nei — 1 oscillators are in their ground state. The initial density operator is thus given by... 

The charge-transport equation includes the electrochemical kinetics for both anode and cathode catalyst layers. If we assume an infinitely large electric conductivity of the electronic phase, the electrode becomes an equipotential line, such that... 

If the electric conductivity of electrode matrixes and plates is limited, an additional equation governing charge transport in the electronic phase would have to be solved. This issue is separately addressed in section 3.4. 

To calculate the electron-transport effect through GDL and flow plate, the charge conservation equation for the electronic phase must be solved additionally, namely... 

The important processes occurring in a catalyst layer include interfacial ORR at the electrochemically active sites, proton transport in the electrolyte phase, electron conduction in the electronic phase (i.e., Pt/C), and oxygen diffusion through the gas phase, liquid water, and electrolyte phase. 

Figure 3. Phenomenological roles of the electronically conducting (electronic) phase (a), gas phase (/ ), and ionically conducting (ionic) phase [y] in accomplishing oxygen reduction.

Figure 4. Some mechanisms thought to govern oxygen reduction in SOFC cathodes. Phases a, and y refer to the eiectronic phase, gas phase, and ionic phase, respectiveiy (a) Incorporation of oxygen into the buik of the electronic phase (if mixed conducting) (b) adsorption and/or partial reduction of oxygen on the surface of the electronic phase (c) bulk or (d) surface transport of or respectively, to the oJy interface, (e) Electrochemical charge transfer of or (f) combinations of and e , respectively, across the aJy interface, and (g) rates of one or more of these mechanisms wherein the electrolyte itself is active for generation and transport of electroactive oxygen species.

We have recently introduced the Wigner intracule (2), a two-electron phase-space distribution. The Wigner intracule, W ( , v), is related to the probability of finding two electrons separated by a distance u and moving with relative momentum v. This reduced function provides a means to interpret the complexity of the wavefunction without removing all of the explicit multi-body information contained therein, as is the case in the one-electron density. 

Ishiguro T, Ito H, Yamauchi Y, Ohmichi E, Kubota M, Yamochi H, Saito G, Kartsovnik MV, Tanatar MA, Sushko YV, Logvenov GY (1997) Electronic phase diagrams and Fermi surfaces of k-(ET)2X, the high T organic superconductors. Synth Met 85 1471-1478... 

Tajima N, Sugawara N, Tamura M, Nishio Y, Kajita K (2006) Electronic phases in an organic conductor a-(BEDT-TTF)2l3 ultra narrow gap semiconductor, superconductor, metal, and charge-ordered insulator. J Phys Soc Jpn 75 051010/1-10... 

Discuss the origin of the Hume-Rothery electron phases within the framework of Jones original rigid-band analysis. How does second-order perturbation theory help quantify Mott and Jones earlier supposition on the importance of the free electron sphere touching a Brillouin zone boundary ... 

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