Hall coefficient, positive

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... 

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)). 

If one looks along the strip in the direction of the current, with the magnetic lield directed downward, then, with si rips of antimony, cohall, zinc, or iron, the electric potential drop is toward the right and the effect is said to he positive. With gold, silver, platinum, nickel, bismuth, copper, and aluminum, it is toward the left, and Ihe effect is called negative. The transverse electric potential gradient per anil magnetic lield intensity per unit current density is called the Hall coefficient" for the metal in question Thus, the Hall coeflicienL is delined us... 

Inasmuch as the electrical resistivity peak appeared in the cooling half of the resistivity curve from incomplete cycle was not matched by any such change in the Hall coefficient measurement, the afore mentioned circumstances apply. Consequently, the band structure of TiNi can be regarded as either a simple single band or one positive band dominating over the others in the temperature being considered. This conclusion did have the support of the transport data obtained independently by other investigator [38]. 

With this understanding, it is clear that in a given conduction 0 covalent transformation, a decrease or increase in the number of conduction electrons is an essential feature that should be observable in the transport properties. Assuming that the band structure of TiNi consists of a single positive band, a decrease in the number of conduction (free) electrons in the course of Ms —> As is equivalent to an increase in the number of hole carriers as seen in (c). Consequently, the positive Hall coefficient should decrease and is so observed in (b). Because holes contribute to Pauli paramagnetic susceptibility in precisely the same manner [42] as electrons, the paramagnetic susceptibility, %, is expected to rise and is so observed in (d). An increase in the hole carrier, Nh, would result in an increase in the conductivity (lowering in the resistivity) as... 

Considering the fact that (1) the Hall coefficients were obtained from bulk material and that (2) the Hall mobility was assumed to be the same for different bands, the rough agreements as shown in Fig. 11 is rather impressive. Obviously we do not know how to treat the metals showing a positive Hall coefficient without a detailed knowledge of the band structure involved. Therefore, the metals with positive Hall coefficients are not included in the statistical tabulation. 

A further correlation between tellurium and sulfur should be mentioned. In the solid state tellurium changes from negative to positive Hall coefficient at 503°K (41) at atmospheric pressure and at 519°K at 2 kb (47). At several pressures to 13 kb a resistance discontinuity in tellurium has been observed in solid media apparatus (48) also at 503°K. In sulfur the approximate temperature and slope of the boundary above... 

In order to understand the electronic transport of a solid, it is necessary to know its charge carrier densities and mobilities. For most solids, the Hall coefficient (Rh) is used to determine the concentration and sign of the majority charge carriers. Once known, the mobility is determined from the conductivity values, a. The MAX phases, however, are unlike most other metallic conductors in that their Hall and Seebeck coefficients are quite small - in some cases vanishingly small - and a weak function of temperature [52, 84—87]. Furthermore, the magnetoresistance (MR) (Aq/q = q(B) — q(B = 0)/q(B = 0)]), where B, the applied magnetic field intensity, is positive, parabolic, and nonsaturating. Said otherwise, the MAX phases are compensated conductors, and a two-band conduction model is needed to understand their electronic transport. In the low-field, B, limit of the two-band model, the... 

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. 

Fig. 7.59. E-k relationship for an isotropic liquid. At the Fermi energy d /dk is positive so that Hall coefficient is negative even though the band is more than half full.

The Fermi surface topology in refractory carbides has also been studied in detail. The Fermi surface in TiC was first calculated by the linear combination of atomic orbitals (LCAO) method (Em and Switendick, 1965) and then by the KKR method (Schadler, Weinberger, Klima and Neckel, 1984). It was shown that the largest sheets of the Fermi surface are hole-like in character. This contradicts the results of Hall coefficient measurements for TiC (Bittner and Goretzki, 1960 Dubrovskaya, Borukhovich and Nazarova, 1971), which clearly show the electronic character of conductivity. This contradiction was explained by calculations of the effective mass of carriers in TiC and TiN (Zhukov et al 1988a). Despite the hole character of the Fermi surface, effective masses of carriers in TiC along the main directions in the Brillouin zone appear to be positive in most cases, i.e., the electric conductivity of TiC is of electronic character. 

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