A thermopower

Table 5.2 summarizes the values of the obtained so far except those shown in Figure 5.26. The sign represents that of the Hall coefficient. A positive Hall coefficient was reported by Komfeld and Sochava (1959). These measurements were recently verified by Nagels etal. (1970) who took special care to ascertain that the Hall coefficient was a genuine property of the amorphous phase and not caused by crystalline inclusions. This exception is remarkable because of the close chemical similarity of all the systems investigated. It wiU be remembered that this small gap material had a thermopower which was difficult to interpret. 

For cubic lattice symmetry the values Pij can be considered as scalars. It now remains to relate the coefficients to the experimentally measured quantities, such as electrical resistivity (p), thermal conductivity (A), thermopower (S), etc. This can be done by rewriting oqs. (2) and (3) in the following way ... 

A novel modification of the STM supplements images with those due to the thermopower signal across the tip-sample temperature gradient [49]. Images of guanine on graphite illustrate the potential of this technique. 

The interest of physicists in the conducting polymers, their properties and applications, has been focused on dry materials 93-94 Most of the discussions center on the conductivity of the polymers and the nature of the carriers. The current knowledge is not clear because the conducting polymers exhibit a number of metallic properties, i.e., temperature-independent behavior of a linear relation between thermopower and temperature, and a free carrier absorption typical of a metal. Nevertheless, the conductivity of these specimens is quite low (about 1 S cm"1), and increases when the temperature rises, as in semiconductors. However, polymers are not semiconductors because in inorganic semiconductors, the dopant substitutes for the host atomic sites. In conducting polymers, the dopants are not substitutional, they are part of a nonstoichiometric compound, the composition of which changes from zero up to 40-50% in... 

Nagels and Krikor143 studied the effect of y-irradiation on the electrical properties of fraws-polyacetylene. They reported a marked decrease of the conductivity and a slight increase of the thermopower after y-irradiation of 10 kGy (1 Mrad). Their study showed that no essential structural changes occur during irradiation. 

The Seebeck coefficient is frequently called the thermoelectric power or thermopower, and labeled Q or S. Neither of these alternatives is a good choice. The units of the Seebeck coefficient are not those of power. The symbol Q is most often used to signify heat transfer in materials. The designation S can easily be confused with the entropy of the mobile charge carriers, which is important because the Seebeck coefficient is equivalent to the entropy per mobile charge carrier (see Supplementary Material S3). 

The effect of fast neutron fluence on thermal conductivity and thermopower has been determined by Uher and Huang (70). For fluences to 3 x 1018 n/cm2 Tc decreases in Y-Ba-Cu-O to a temperature of 86 K, the thermal conductivity decreases and is without a peak above Tc and the thermopower starts from a negative value and approaches zero and becomes positive. As will be seen below the more usual value of thermopower is positive in the superconducting material but these authors note the variability dependent on sample preparation conditions. 

The thermopower or thermoelectric power is the electrostatic potential difference between the high and low temperature regions of a material with an impressed thermal gradient and zero electric current flow. The sign gives an indication of the sign of the charge carriers - positive for hole carriers. 

Figure 6.48 (a) Effect of doping on the electrical conductivity (solid line) and thermopower (broken line) of polyacetylene. (Following Etemad et al, 1982.) (b) solitons in trans-polyacetylene (i) neutral, (ii) positive and (iii) negative solitons. Arrow marks the boundary between the two symmetric configurations. A, acceptor D, donor. (Following Subramanyam Naik, 1985.)... 

We shall in this book use the concept of a degenerate gas of small—or at any rate heavy—polarons. Clearly we should not expect these to be formed unless the number of carriers is considerably less than the number of sites. We also remark, as mentioned earlier, that in all metals, at temperatures less than B phonons lead to a certain mass enhancement, of order less than 2. A treatment is given by Ashcroft and Mermin (1976, p. 520). This affects the thermopower some results for an amorphous alloy (Ca AlJ from Naugle (1984) are shown in Fig. 2.2. A theoretical treatment of the range between this situation and the polaron gas has not yet been given. 

Fig. 2J2 Thermopower 5 of metallic glasses Cax. Al, as a function of temperature. Since S is proportional to kBT/EF, these show an increase of p(=i 2k2/meff) above about...

In crystalline materials a characteristic of polaron motion is a difference between E the activation for conduction, and s, that for the thermopower written as S=(kB/e) (EsjkBT+ const). We expect that Ea=Ec—EF+WH and Es=Ec-Ef, where Ee is the extremity of the band in which the carriers move. 

Our model for the density of states is thus as in Fig. 4.7. The total density of states is mainly due to spin fluctuations, and has a maximum for n=1, where n is the number of electrons per atom. The curve for current carriers needs to be used for calculating thermopower and resistance the experimental evidence discussed in the following chapters suggests, however, that the Hall coefficient RH is given by the classical formula 1 jnec. 

This material, which has the corundum structure, is a semiconductor at low temperatures, the optical band gap being 0.2 eV (Lucovsky et al. 1979). We should probably consider it to be an intrinsic semiconductor, but the activation energy in the conductivity does not appear to be constant. The thermopower (Chandrasekhar et al. 1970) is about 900pVK 1 at 100K and 500pVK 1 at 200 K this would suggest an activation energy of about 0.06 eV, or less than half the band gap.f This makes it likely that one of the carriers is a small polaron the... 

Thermopower measurements due to Kwizera et al (1981) are shown in Fig 6.23. The equation for the thermopower in the metallic state, S=( n2fciT/e)dlnff/d , should not be valid above about 150K it can be seen that d In narrow band in the metallic state, possibly due to Brinkman-Rice enhancement or formation of spin polarons. 

Fig. 7.5 Thermopower of VOx and TiOx at room temperature as a function of x (Banus...

The disappearance of the sharp Verwey transition was discussed by Mott (1979), who suggested that at low temperatures the material is a Wigner glass , the electrons (Fe2 + ions) being frozen into random sites and the whole system stabilized by the fluorine. Discussion of the thermopower measurements show, according to Mott (1979), that a hopping mechanism is operative at low T. Ihle and Lorenz (1985), however, consider that the electrons in the wrong sites move by a small polaron band mechanism. 

In fluids, we have already postulated that quantum interference does not occur. Of course, in liquids no sharp metal-insulator transition can be expected, and therefore we define the transition as occurring when a = amln, the quantity given by equations (50 a, b) of Chapter 1. We therefore believe that it is legitimate to write for the thermopower... 

Turning now to fluid mercury and caesium, a fairly recent review is given by Freyland and Hensel (1985). Figure 10.9 shows the classic results of Hensel and Franck (1968) on the conductivity of mercury as a function of volume V the metal-insulator transition occurs when V/V0xl.3. Schonherr et al (1979) measured the conductivity a and thermopower S of mercury for conductivities between 200 and 5 2 1 cm 1 for mercury. Their results for a as a function of S are shown in Fig. 10.10(a). The slope is exactly as predicted, and a0 is in the range... 

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