Heikes equation

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. 

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 configurational entropy evaluated above omits all mention of electron spin. Because there are two spin directions, a spin degeneracy of 2, these must be included in the possible configurations. When this term is included, the Heikes equation becomes the Chaikin-Beni equation ... 

This equation is sometimes called the extended Heikes equation. 

The Seebeck coefficient can be altered significantly by both A-site and B-site substitutions. For example, A-site doping with Sr to form Laj Sr CoOj forces one Co " ion to transform to Co to maintain charge neutrality. The value of the Seebeck coefficient remains positive, as the Seebeck current is still due to hole migration, but the number of Co defects will increase in proportion to the amount of substituent. The number of defects is equal to the number of impurity Sr ions (ignoring the small concentration of Co in the parent compound), and so the fraction c in the Heikes equation is equal to x in Laj Sr CoOj and as a consequence the value of the Seebeck coefficient will fall (Figure 9.6). 

The value of c in the Heikes equation is equal to x in LaTi COj Oj, and as a consequence, the numerical value of the Seebeck coefficient will fall compared to the parent phase, and as electron transport is involved, the Seebeck coefficient is accordingly negative (Eigure 9.6). 

Optimisation of the Seebeck Coefficient by Doping Following the Heikes formula or the generalised Heikes formula, S should increase when the Co concentration decreases. Following the electroneutrality equation between the two different sublattices, the Co valency in the Cdl2 plane can be written as... 

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