Temperature, Frequency, Doping Dependencies

Finally, before we may consider conduction models, some essential experimental observations and givens need to be reviewed which deal with the temperature, frequency and doping dependencies of conductivity. 

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A survey is given on electrical transport phenomena in polyacetylene. Data on the dependence of the conductivity on temperature frequency and doping concentration are reviewed and measurements of the magnetoresistance and of long-time aging effects under various storage conditions are presented. The experimental results are interpreted as superposition of intrachain, inter-chain and inter-fiber conduction mechanisms, and resemble some aspects of the hopping transport in disordered semiconductors. 

Figure 2.3. Catalysis (0), classical promotion ( ), electrochemical promotion ( , ) and electrochemical promotion of a classically promoted (sodium doped) ( , ) Rh catalyst deposited on YSZ during NO reduction by CO in presence of gaseous 02.14 The Figure shows the temperature dependence of the catalytic rates and turnover frequencies of C02 (a) and N2 (b) formation under open-circuit (o.c.) conditions and upon application (via a potentiostat) of catalyst potential values, UWr, of+1 and -IV. Reprinted with permission from Elsevier Science.

A notable exception may be Sr-doped ceria. As reported by Liu and Wu, LSCF electrodes on 10 mol % Sr-doped ceria exhibit a significant high-frequency impedance arc in air at 650—750 °C, which is comparable in frequency (but somewhat smaller) to that observed for identically processed and tested LSCF electrodes on 8 mol % YSZ. One explanation may be found in the thermodynamic data for the Sr— Ce—O system, which shows that the solubility of SrO in Ce02 is less than 10 mol % at these temperatures.Thus, precipitation of SrCeOs at the LSCF/ceria interface is favored, depending on the exact firing conditions and A/B ratio of the perovskite. Oddly, the authors did not consider this possibility. 

Finally, any doping leading to a finite conductivity cr will lead to a loss contribution according to tan5 = conduction mechanism like hopping conductivity may give rise to complicated temperature and frequency dependences, which cannot be discussed in detail here. 

Similar conclusions on the character of conductance in the polycrystalline diamond films were derived in [33], The resistive intercrystallite boundaries can involve nonlinear resistance in polycrystalline diamond films moderately doped with boron [34]. Later, more sophisticated analysis [35-37] of the frequency dependence of impedance of polycrystalline diamond films resulted in a conclusion that at higher temperatures, in addition to the aforementioned electric conductance caused by the motion of free holes in the valence band, a second component of conductance manifests itself. The second component is due to the hopping of charge carriers between local traps possibly associated with the intercrystallite boundaries. 

Mizoguchi et al.112 also have carried experiments of 1/Ti versus temperature as well as frequency dependence studies in FSOs-doped PA (10s S/cm). They have done the experiments at considerably low NMR frequencies and over a wide temperature range. Their T analysis with frequency shows quasi-ID... 

We now consider films doped to the AsQso phase. Raman spectra were obtained for K3C , (T, = 18 K) and Kb C (T, = 24 K) (Fig. 3). The striking feamre of these spectra is their simplicity. Only three modes are observed, the two A modes and the lowest frequency mode. Further, there is no dependence of the spectra on alkali dopant, indicating no A.-C60 mode is observed above 100 cm Spectra taken on a variety of K- and Rb-doped samples indicate that the Ag mode frequency in AjC o is 1445 2 cm . The FWHM of this mode is 9 cm , which is 6 cm less than the value for the pristine material. This reduction is likely due to the stationary orientation of the C<60 molecules on the time scale of the Raman scattering process, and is similar to the reduction observed in pristine as the molecules freeze at low temperatures (17). This result is consistent with recent NMR and x-ray difiraction results that indicate the molecules are jumping between symmetry-equivalent orientations in the K3C(,o material at room temperature (13). Finally, we point out that the lowest frequency Hg mode appears to remain, although it is significantly broadened. 

Abstract Contribution of the Jahn-Teller system to the elastic moduli and ultrasonic wave attenuation of the diluted crystals is discussed in the frames of phenomenological approach and on the basis of quantum-mechanical theory. Both, resonant and relaxation processes are considered. The procedure of distinguishing the nature of the anomalies (either resonant or relaxation) in the elastic moduli and attenuation of ultrasound as well as generalized method for reconstruction of the relaxation time temperature dependence are described in detail. Particular attention is paid to the physical parameters of the Jahn-Teller complex that could be determined using the ultrasonic technique, namely, the potential barrier, the type of the vibronic modes and their frequency, the tunnelling splitting, the deformation potential and the energy of inevitable strain. The experimental results obtained in some zinc-blende crystals doped with 3d ions are presented. 

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