Thermoelectric Properties The Seebeck Coefficient as an Example

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 

5The 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). 

This equation is formally equivalent to the Heikes equation  

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. 

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