Hall voltage

Due to the symmetrical construction the resulting magnetic field between the two coils is zero in y-direction, if a conductive structure is symmetrically situated in the area a (see fig. 3) in the near of the probe. A resulting field is detectable by the Hall-effect device, if there are unsym-metrics in the structure in area a. The value of the Hall voltage is proportional to the detected magnetic field. 

Several additional conclusions concerning the nature of the chemisorbed layer can be drawn from the Hall effect measurements (33, 34) The chemisorbed species, together with the surface metal atoms, represent complexes analogical to the ordinary chemical compounds and, consequently, one might expect that the metal atoms involved in these complexes will contribute to lesser extent or not at all to the bulk properties of the metal. Then we should speak about the demetallized surface layer (41). When the Hall voltage was measured as a function of the evaporated film thickness... 

This same equation is, of course, also used to rationalise the general electronic behaviour of metals, semiconductors and insulators. The quantitative application of Eqn (2.1) is handicapped for ionic conductors by the great difficulty in obtaining independent estimates of c,- and u,-. Hall effect measurements can be used with electronic conductors to provide a means of separating c, and u,- but the Hall voltages associated with ionic conduction are at the nanovolt level and are generally too small to measure with any confidence. Furthermore, the validity of Hall measurements on hopping conductors is in doubt. 

Morrison (31) has compared measurements of the Hall effect and of the resistance. The Hall voltage is inversely proportional to the average concentration of carriers in the material (24), and so, for zinc oxide, will be inversely proportional to the concentration of carriers in the large grains (Fig. 2) of the material. Figure 3 shows an example in which the resistance and the inverse of the Hall voltage measured on a sintered sample of zinc oxide are plotted as functions of the time. This illustrates that the number of carriers in the bulk of the sample may remain relatively constant, while the conductance varies widely, all at constant temperature. 

Morrison (31), using sintered zinc oxide, applied a different technique to study the conductivity effects in the range between room temperature and 500°C. He studied the variation in conductance as a function of time with the temperature held constant. Figure 3 shows one such conductivity-time experiment. The sample used was a slab of zinc oxide cut from a pill which had been compressed and sintered in air for eighteen hours at 1000°C. The sample was immersed in oil (the oil does not penetrate into the pores of the sample) at the start of the run. The sample container was immersed in boiling water, the temperature reaching 100 C in the order of one-half of a minute. The conductance was recorded as a function of time while the sample was held at 100°C. The results are shown in Fig. 3. The inverse of the Hall voltage is also plotted as a function of time. An interpretation of the Hall measurement is discussed in Section III. 

From Fig. 3 it is evident, upon comparison with the Hall voltage, that the reversible time dependence of the conductance is also associated with... 

Ettingshausen temperature gradient can produce a thermoelectric voltage, which adds to the Hall voltage. 

The supporting evidence for this kind of band model, in which W03 has been called an eleotronless metal which is populated by electron donors M, comes from various kinds of measurements, some of which are given below. These include resistivity vs. temperature, Hall voltage, thermoelectric power, and magnetic susceptibility measurements. 

A peak position is given by a time value (or a Hall voltage value in a magnetic analyser or a voltage value in a quadrupole), which must be converted into a mass value. This supposes a preliminary calibration with known products (PFK, (Csl) , etc.). The masses furnished by the calibrating product are stored in the computer. A relationship of the type m = ax + b is calibrated with two known peaks and is checked or corrected with known peaks located in other mass areas. 

Figure 15 (a) Temperature dependence of the Hall voltage in the relaxed state of (TMTSF)2C104 at T = 0.35 K. The outset of a FISDW phase is visible at 4 T. (From W. Kang, private communication.) (b) Thermopower data of (TMTSF)2C104. (After Ref. 67b.)... 

Figure 44 Quantized Hall voltage of (TMTSF)2PF6 and phase diagram. The integers indicate the number of filled Landau levels in each subphase. (After Ref. 127.)...

Figure 45 Quantized Hall voltage in (TMTSF)2C104 (two samples) (after Ref. 130) and phase diagram (from Ref. 132). A new phase line has been discovered around 1 K and 30 T (after R. C. Yu et al, Phys. Rev. Lett, 65 2458 (1990)). The phase that extends from 8 to 27 T is presumably N = 1 [130].

The final transport measurement to be considered is the Hall effect. This is the most intriguing transport property, but has been so difiicult to imderstand that it has not contributed much towards the elucidation of the conduction mechanisms. The reason is that the Hall effect is anomalous and has the opposite sign from that which is normally expected. Thus holes give a negative Hall voltage and... 

Hall voltage was measured by a four-point probe method for the samples shaped like a cross, using dc current and dc magnetic field. 

In one method, the sensor is calibrated after installation. The offset is subtracted and the amplification is adjusted to the altered sensitivity. In addition, the temperature drift of the sensor and the drift of the permanent magnet used in the specific application can be programmed into the ASIC [35]. In a second method, the offset is actively compensated for by chopping [36]. Here, the applied current and the taps of the Hall voltage are continuously commutated. An advanced version of this technique is the spinning-current method, in which 8 or even 12 different current directions are used [37, 38]. The current direction is spun... 

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