Hall coefficient

Hall effect is another important transport phenomenon and has been extensively studied in amorphous semiconductors. The Hall effect studies also assumed importance because of an anomaly observed between the sign of the charge carriers indicated by Hall coefficient and S in amorphous semiconductors. The Hall coefficient Rh is given by. 

In the above expression, a is the inter-site distance, N(Ec) is the DOS at the mobility edge, J is the overlap integral (which determines E), z is the coordination number and z is the average number of closed three site paths around a given site. The above formulation suggest that the Hall mobility is temperature independent. Assuming that z z, a 3 A and J = BUz 1 eV, pw is about lO cm V s which may be compared with electron mobilities from conductivity studies of about 10 cm V s. xh for hopping electrons in localized states turns out to be even smaller. 

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The Group 4—6 carbides are thermodynamically very stable, exhibiting high heats of formation, great hardness, elevated melting points, and resistance to hydrolysis by weak acids. At the same time, these compounds have values of electrical conductivity. Hall coefficients, magnetic susceptibiUty, and heat capacity in the range of metals (7). 

On lowering the temperature through Ty, a bandgap Eg = 0.1 eV appears in the FeB-ai(l) conduction band of Fig. 3 at Ep. The Hall coefficient increases as Rh exp(Ty/T), indicating that the charge-carrier density increases exponentially with T" , as in a normal semiconductor, and the Hall mobility increases from about 0.1 to 0.4 cm /Vs on lowering the temperature from Ty = 120 K to 77 K ... 

The Hall effect, an electric field perpendicular to both the impressed current flow and to the applied magnetic field, gives information about the mobility of the charge carriers as well as their sign. The Hall coefficient RH - Ey/JxHe is proportional to the reciprocal of the carrier density. The Hall coefficient is negative for electron charge carriers. 

Early results of Hall coefficient measurements were presented in a review article by Tanaka (78). For the La-Ba-Cu-O material as a function of the increasing fraction of barium the Hall coefficient is positive, decreasing, and nearly temperature independent above Tc. These results are shown in Figure 20. For Y-Ba-Cu-O RH increases... 

Figure 20 Temperature dependence of the Hall coefficient for (La,Ba)2Cu04. Ref. 78.

Figure 21 Temperature dependence of the reciprocal of the Hall coefficient for two samples of Y-Ba-Cu-O. Ref. 79.

Figure 22 Temperature dependence of the Hall coefficient RH in single crystal Nd-Ce-Cu-O with Tc = 20 K. The field of 15 Tesla is applied normal to the Cu02 planes. Ref. 82.

Hall effect. The Hall coefficient R, of a solid with a single type of charge... 

The NFE behaviour has been observed experimentally in studies of the Fermi surface, the surface of constant energy, F, in space which separates filled states from empty states at the absolute zero of temperature. It is found that the Fermi surface of aluminium is indeed very close to that of a spherical free-electron Fermi surface that has been folded back into the Brillouin zone in a manner not too dissimilar to that discussed earlier for the simple cubic lattice. Moreover, just as illustrated in Fig. 5.7 for the latter case, aluminium is found to have a large second-zone pocket of holes but smaller third- and fourth-zone pockets of electrons. This accounts very beautifully for the fact that aluminium has a positive Hall coefficient rather than the negative value expected for a gas of negatively charged free carriers (see, for example, Kittel (1986)). 

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. 

Fig. 10.18 Hall coefficient R for metal-ammonia solutions, plotted as a function of concentration in the form RFE/R0bs- From Cohen and Thompson (1968).

The Hall coefficient is normal in the metallic region, but drops off as we approach the metal-non-metal transition (Fig. 10.18). It is found to be temperature-independent. 

Xd is the electronic contribution to the paramagnetism, obtainable either from the ESR signal or by direct measurements with subtraction of the diamagnetic term RH is the Hall coefficient, the formula being due to Friedman (1971). K is the Knight shift, g is found to drop from 1 to about 0.3 in this range and a is then about 50 2 1 cm x. This then should mark the metal-insulator transition. A plot of g deduced from the various data is shown in Fig. 10.20. This we consider further evidence for the absence of quantum interference in liquids (Section 2). 

Apart from the drop in the susceptibility as we approach the transition, the increase in the Hall-coefficient ratio (Fig. 10.18) is further evidence for the model as we have seen, evidence from doped semiconductors shows that RH does not deviate from the free-electron form when EF lies in the pseudogap for current carriers in a highly correlated gas (unless antiferromagnetic order sets in). Also, the susceptibility increases with temperature this may be because the molecular dimers dissociate. 

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