Seebeck coefficient materials

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 ... 

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). 

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). 

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. 

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+ ... 

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. 

The thermoelectric effect is due to the gradient in electrochemical potential caused by a temperature gradient in a conducting material. The Seebeck coefficient a is the constant of proportionality between the voltage and the temperature gradient which causes it when there is no current flow, and is defined as (A F/A7) as AT- 0 where A Fis the thermo-emf caused by the temperature gradient AT it is related to the entropy transported per charge carrier (a = — S /e). The Peltier coefficient n is the proportionality constant between the heat flux transported by electrons and the current density a and n are related as a = Tr/T. 

The Seebeck coefficients Qa and <2b are material constants of conductors A and B, respectively. They depend primarily on two parameters their work function (see Appendix C) and their thermal conductivity. There are many combinations of electronic conductors producing V of few mV °C 1. It is interesting to note that direct modulation of one or both Seebeck coefficients by chemical interaction with an electron acceptor or electron donor gas is possible. It has been demonstrated as a sensing principle for detection of gaseous NO2 with an ti Oj/Au thermocouple junction (Liess and Steffes, 2000). 

The minus sign of the Seebeck coefficient indicates an n-type semiconductor as shown in Figure 18.6. The absolute values increase except for the specimen (M = Cu, X = 0.1), where the metallic Cu is supposed to exist in the crystal. The Seebeck coefficient in the specimen of Cu (0.01 mol%) increased against temperature although the electrical resistivity did not change much, implying a good characteristic for the TE material. 

This expression shows that the imposition of a temperature difference dT in the absence of any current produces a difference d i in electrochemical potential i.e., d ife) = —z/a, dT. This effect is known as the thermoelectric effect, and the ratio d i/e)/dT, or A(f,/e)/Ar = —ZiCii is known as the Seebeck coefficient (1823), or thermoelectric power.Experimentally, the difference of electrochemical potential may be measured by a voltmeter under open circuit conditions, and dT, measured by means of thermocouples a, is thereby experimentally determined. As defined here for p-type (n-type) material the measured Seebeck coefficient is a positive (negative) quantity. For, and both increase in the direction of increasing hole or electron concentration, which is in a direction opposite to the increase in temperature. Comparison with (6.9.2) shows that Ui = ZiSgfe. Then Eq. (6.9.6) becomes... 

Efficient thermoelectric devices require the use of high figure of merit thermoelectric materials. The thermoelectric figure of merit, ZT, can be expressed as oQ-oTIk, where a is the Seebeck coefficient, o the electrical conductivity, T, the temperature, and k, the thermal conductivity. Among the various thermoelectric materials, bismuth telluride (Bi2Te3) has been the main focus of research because of its superior ZT near room temperature [58]. 

In this paper, thermoelectric figure of merit for n-type sintered materials of SiGe and PbTe has theoretically been estimated considering effects of grain boundaries on carrier mobility and Seebeck coefficient based on a model. 

The maximum figure of merit is achieved by way of material optimization. It is well known that in semiconductors Seebeck coefficient a, conductivity a and heatconductivity k are the functions of current carrier concentration n, p which in their turn are the functions of impurity concentrations Ne, Np... 

The materials combination of SiGe and PbTe was selected as a model system for the verification of the percolation concept. The measurements were carried out on the thermal conductivity, electrical resistivity and Seebeck coefficient, which are involved in the figure of merit, of non-graded composites, as well as of the monolithic SiGe and PbTe. 

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