Seebeck coefficients

Type J thermocouples (Table 11.58) are one of the most common types of industrial thermocouples because of the relatively high Seebeck coefficient and low cost. They are recommended for use in the temperature range from 0 to 760°C (but never above 760°C due to an abrupt magnetic transformation that can cause decalibration even when returned to lower temperatures). Use is permitted in vacuum and in oxidizing, reducing, or inert atmospheres, with the exception of sulfurous atmospheres above 500°C. For extended use above 500°C, heavy-gauge wires are recommended. They are not recommended for subzero temperatures. These thermocouples are subject to poor conformance characteristics because of impurities in the iron. 

Called the Seebeck coefficient. It is given here at the high-temperature end of the range many thermocouples are nonlinear. 

The primary thermoelectric phenomena considered in practical devices are the reversible Seebeck, Peltier, and, to a lesser extent, Thomson effects, and the irreversible Eourier conduction and Joule heating. The Seebeck effect causes a voltage to appear between the ends of a conductor in a temperature gradient. The Seebeck coefficient, L, is given by... 

Because the third law of thermodynamics requires S = 0 at absolute zero, the following equation is derived, which enables the determination of the absolute value of the Seebeck coefficient for a material without the added complication of a second conductor ... 

Voltage measurement have been made at very low temperatures using a superconductor as one leg of a thermocouple. Eor a superconductor, S is zero, so the output of the couple is entirely from the active leg. The Thomson heat is then measured at higher temperatures to extend the absolute values of the Seebeck coefficients (7,8). The Thomson heat is generally an order of magnitude less than the Peltier heat and is often neglected in device design calculations. 

When the two ends of a material containing mobile charge carriers, holes or electrons, are held at different temperatures, a voltage is produced, a phenomenon called the Seebeck effect (Fig. 1.11). The Seebeck coefficient of a material, a, is defined as the ratio of the electric potential produced when no current flows to the temperature... 

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). 

Figure 1.12 Seebeck coefficient of the oxide LaNil Coi- c03 as a function of the composition, x. [Data adapted from R. Robert, L. Becker, M. Trottmann, A. Reller, and A. Weidenkraft, J. Solid State Chem., 179, 3893-3899, (2006).]...

The number of mobile holes is equal to the number of impurity Ni2+ ions, and so the fraction c in the Heikes equation is equal to x in LaNi,Coi -,(+. In accord with the theory, the Seebeck coefficient, a, is positive and greatest at low values of x and decreases as x increase (Fig. 1.12). Substituting a value of c = 0.02 into the equation yields a value of a = +335 pV K-1, in good agreement with the experimental value of 360 pV K-1 (Robert el al., 2006). Note that the above example also shows that an experimentally determined value of the Seebeck coefficient can be used to estimate the concentration of impurity defects in a doped oxide. 

The Seebeck coefficient for pure LaCo03 is +600 xVK-1. (a) What are the mobile charge carriers (b) Suppose these occur because the crystal contains a trace of an impurity, Co4+, calculate the defect concentration and the formula of the material (data from Robert et al., 2006). 

Estimate the Seebeck coefficient for the reduced oxide TKV94, assuming that the defects are Ti3+ ions and the parent phase is Ti02. 

Nickel oxide, NiO, is doped with lithium oxide, Li20, to form Li Ni, xO with the sodium chloride structure, (a) Derive the form of the Heikes equation for the variation of Seebeck coefficient, a, with the degree of doping, x. The following table gives values of a versus log[(l-x)/x] for this material, (b) Are the current carriers holes or electrons (c) Estimate the value of the constant term k/e. 

Because the value of the Seebeck coefficient a depends upon the number of defects present, it should vary systematically with the composition. A common form of the... 

Figure 7.4 Theoretical variation of the Seebeck coefficient as a function of composition for a hopping semiconducting oxide MOx, where x can take values of between 1.0 and 2.0.

The same analysis can be applied to compounds with a more complex formula. For example, the oxide LaCoCL, which adopts the cubic perovskite structure, usually shows a large positive Seebeck coefficient, of the order of +700 jjlV K-1, when prepared in air (Hebert et al., 2007). This indicates that there are holes present in the material. The La ions have a fixed valence, La3+, hence the presence of holes must be associated with the transition-metal ion present. Previous discussion suggests that LaCo03 has become slightly oxidized to LaCoCL+j, and contains a population of Co4+ ions (Co3+ + h or Coc0)- Each added oxygen ion will generate two holes, equivalent to two Co4+ ... 

The Seebeck coefficient of a slightly nonstoichiometric La3 B3 0 ( perovskite structure oxide is negative. The defects present are ... 

The Seebeck coefficient of the layered structure Bi2Sr2Co06+s is —33 p,V K-1 at 250 K. The defects are confined to the Co02 planes in the structure, (a) Is the conductivity by way of holes or electrons (b) What are the ionic states of the Co ions in the phase (c) What is the ionic formula of the compound, (d) What is the value of 8 [Note the structure is very similar to that of Bi2Sr2CuC>6, Section 8.6. Data adapted from Y. Nagao and I. Terasaki, Phys. Rev., B76, 144203-1-144203-4 (2007).]... 

LaCo03 can be donor doped with Ce02 to give a mixed conductor, (a) Write defect equations for the reaction. A sample of nominal composition Lao.99Ce0.oiCo03 has a Seebeck coefficient of approximately — 300 pVK-1. 

Note that the above model is for a simple system in which there is only one defect and one type of mobile charge carrier. In semiconductors both holes and electrons contribute to the conductivity. In materials where this analysis applies, both holes and electrons contribute to the value of the Seebeck coefficient. If there are equal numbers of mobile electrons and holes, the value of the Seebeck coefficient will be zero (or close to it). Derivation of formulas for the Seebeck coefficient for band theory semiconductors such as Si and Ge, or metals, takes us beyond the scope of this book. 

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