Thermoelectric Material Tensor Derived from the Onsager-de Groot-Callen Model

The Onsager-de Groot-Callen model describes thermoelectricity in the framework of the thermodynamics of irreversible processes, which uses rather abstract kinetic matrix and generalized forces to describe the flux of the substance-like quantities electric charge and thermal energy (“heat”). A brief review of the derivation of the basic equations according to this model is given. Primarily, this model relies on the total differential of energy as in Gibb's thermodynamics, but it then removes entropy to capture the energy production rate as a measure of irreversibility. Depending on the fluxes of interest, “proper” generalized forces are identified. The use of Onsager's reciprocal relations helps to determine the coefficients of a kinetic matrix to link the generalized forces with the generalized potentials. The present article places entropy back into the as-obtained basic equations. The equations are then transformed such that the flux densities of electric charge and entropy appear with equal ranks. The respective conjugated intensive variables electrochemical potential and temperature then appear as the thermodynamic potentials. Moreover, the thermoelectric material is described by a material-specific tensor, which is composed only of the isothermal electric conductivity, the Seebeck coefficient and the entropy conductivity. The result is identical to that recently obtained by Fuchs using a direct entropic approach, which does not require Onsager's reciprocal relations as a prerequisite. The benefit of this approach is the appearance of a material-specific thermoelectric tensor rather than a so-called kinetic matrix, which not only provides a new quality to the discussion but also facilitates descriptions of the thermoelectric phenomenon and the underlying energy conversion process. The latter can easily be understood as the transfer of energy from thermal to electric phenomenon or vice versa when fluxes of entropy and electric charge, as well as the local thermodynamic potentials temperature and electrochemical potential, are known. © 2015 Walter de Gruyter GmbH. All rights reserved.