Thermoelectric power

Thermoelectric power is an important property essential for determining the sign of the charge carriers, in amorphous materials. When 

Since Oe = eN E) E)kT, and also since N E) and p( ) can be assumed as constant in the extended states, the above expression can be integrated so that. 

The absolute thermoelectric power a = 8 fiV/K and a= 10 iV/K for room temperature was measured on two CeSe single crystals and the conduction was p-type, Hulliger et al. [5, p. 92]. 

The remarkable linearity of S T) and the negligible non linear contribution to thermoelectric power in high quality metallic (CH), indicate that the lattice contribution to thermoelectric power due to phonons is less significant. The S T) is quite linear even in the case of samples on the insulating side of the M-I transition [18]. 

Interpolated Results of Measurements of the Specific Electrical Resistivity, R (4.2 to 1300 K), Thermal Conductivity (80.3 to 376.4 K), and the Absolute Thermoelectric Power, SjhN (80-3 to 376.4 K) of High-Density Zone-Melted ThN [21]. (Extrapolated values are given in parentheses.) 

The Seebeck coefficient S of ThN was first stated to be a few V/K at room temperature [15]. Values relative to Cu from 4 to 375 K measured by the differential technique have been reported graphically by Auskern, Aronson [16]. From an extrapolation of the thermoelectric power data with the slope -0.81 x10 (V/K) to 0 K they estimate the Fermi energy level from the equation S 2n V JZe-HE as Ep = 6 eV and the electron effective mass as 0.7 mg, where mg is the electron rest mass. 

Weaver [21] has reported results of measurements of the thermoelectric power, PThN,constaman obtained with arc-cast and zone-melted ThN in the temperature range 86 to 402 K. The data 

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Because almost all alpha radiation is stopped within the solid source and its container, giving up its energy, polonium has attracted attention for uses as a lightweight heat source for thermoelectric power in space satellites. 

The basic ideas of thermoelectricity have been known for nearly two centuries, but until well after the Second World War the primary use was for temperature measurement (qv) using metallic wires. Then, upon improvements in semiconductor technology, thermoelectric power generation and refrigeration came under serious consideration. 

Taking all of the above into account, it can be shown that the efficiency, Tj, of a thermoelectric power generator, neglecting Thomson heat, is given by... 

Thermoelectric devices represent niche markets, but as economic and environmental conditions continue to change, they appear poised to advance into more common use. Thermoelectric power generators are in use in many areas, including sateUites, deep-space probes, remote-area weather stations, undersea navigational devices, military and remote-area communications, and cathodic protection. 

Thermocouples are unsurpassed for making temperature-difference measurements. The thermoelectric power of thermocouple materials makes them adequate for use at hquid-air temperatures and above. At 20 K and below, the thermoelectric power drops to a few lV/K, and their use in this range is as much art as science. 

Electrical resistivity measurements have also been performed on individual SWCNT and on bundles of SWCNT. In the latter case thermoelectric power measurements have been carried out very recently (cf. Sec. 5.3.2). 

The general expression for the diffusion thermoelectric power for a given group of charge carriers is given by the Mott formula ... 

Fig. 6. Temperature dependence of the thermoelectric power of three SWCNT samples [11].

The interpretation of thermoelectric power data in most materials is a delicate job and this is particularly true for the case of carbons and graphites. In the case of SWCNTs the data are not consistent with those calculated from the known band structure which leads to much smaller values than observed. Hone et al. [11] suggest from their data that they may indicate that the predicted electron-hole symmetry of metallic CNTs is broken when they are assembled into bundles (ropes). 

Two thermocouples, Em at x = 0 and Ex at a distance x, permit the monitoring of the atomic hydrogen concentration change along the side-tube. The atoms recombining on the thermocouple tip covered by the active catalyst evolve the heat of reaction and thus the thermoelectric power becomes a relative measure of the concentration of atoms in the gas phase. Finally, one obtains for the direct use in an experimental work the following equation... 

The charge transport and optical properties of the [Si(Pc)0]-(tos)y)n materials as y=0 -+ 0.67 are reminiscent of the [Si(Pc)0]-(BF4)y)n system, but with some noteworthy differences. Again there is an insulator-to-metal transition in the thermoelectric power near y 0.15-0.20. Beyond this doping stoichiometry, the tosylates also show a continuous evolution through a metallic phase with decreasing band-filling. However, the transition seems somewhat smoother than in the BF4 system for y)>0.40, possibly a consequence of a more disordered tosylate crystal structure. Both [Si(Pc)0]-(tos)y)n optical reflectance spectra and four-probe conductivities are also consistent with a transition to a metal at y 0.15-0.20. Repeated electrochemical cycling leads to considerably more decomposition than in the tetrafluoroborate system. 

Si(Pc)0] (S04)o.09)n> i-s limited by the oxidative stability of the sulfate anion. Thermoelectric power, optical reflectivity, magnetic susceptibility, and four-probe electrical conductivity measurements evidence behavior typical of an [Si(PcP+)0]n compound where p 0.20. That is, there is no evidence that the more concentrated counterion charge has induced significant localization of the band structure. 

Calvet and Persoz (29) have discussed at length the question of the sensitivity of the Calvet calorimeter in terms of the number of thermocouples used, the cross section and the length of the wires, and the thermoelectric power of the couples. On the basis of this analysis, the micro-calorimetric elements are designed to operate near maximum sensitivity. The present-day version of a Tian-Calvet microcalorimetric element, which has been presented in Fig. 2, contains approximately 500 chromel-to-constantan thermocouples. The microcalorimeter, now commercially available, in which two of these elements are placed (Fig. 3) may be used from room temperature up to 200°C. 

Calvet and Guillaud (S3) noted in 1965 that in order to increase the sensitivity of a heat-flow microcalorimeter, thermoelectric elements with a high factor of merit must be used. (The factor of merit / is defined by the relation / = e2/pc, where e is the thermoelectric power of the element, p its electrical resistivity, and c its thermal conductivity.) They remarked that the factor of merit of thermoelements constructed with semiconductors (doped bismuth tellurides usually) is approximately 19 times greater than the factor of merit of chromel-to-constantan thermocouples. They described a Calvet-type microcalorimeter in which 195 semiconducting thermoelements were used instead of the usual thermoelectric pile. 

The proportionality constant g includes such parameters as the number of thermoelectric couples in the pile, their thermoelectric power, and the gain of the amplification device. It is supposed, moreover, that the response of the recording line is considerably faster than the thermal lag in the calorimeter. The Tian equation may also be written therefore ... 

The use of the thermoelectric power of metallic junctions presents the following advantages ... 

Unfortunately, the thermoelectric power vanishes when temperature tends to zero pairs as the classic Cu/constantan thermocouples show very low sensitivity below 10 K (see Fig. 9.2). 

Obviously, the small thermoelectric powers produced by metal pairs at low temperatures cannot be measured using a reference temperature of 0°C, where the thermoelectric power is high a 4.2 K bath is a typical reference. 

Fig. 9.3. Thermoelectric power of Pd doped with Fe (in ppm) as a function of temperature. The value for the pure sample has been multiplied by 10 for sake of clarity [64].

The main drawback in this type of thermometry is the presence of spurious thermoelectric powers due to chemical inhomogeneity, stress in conductors, contact effects in switches if present, etc. 

As we said, the sensitivity of a metallic thermometer drastically falls below about 10 K as it was the case of the thermoelectric power it is possible to increase the sensitivity by introducing some magnetic impurities. The most commonly used magnetic alloy is the commercial Rh-0.5% Fe (see Fig. 9.5). 

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