Transport and Thermodynamic Analyses of Steady-State Currents in Solids

Abstract

The usual derivation of the well-known Gibbs-Duhem relation (or its electrochemical analog) from equilibrium thermodynamics is based on certain assumptions which are only approximately met for nonhomogeneous systems; the postulate of local equilibrium generally employed in nonequilibrium thermodynamics is commonly utilized to extend the results to the nonequilibrium domain. The application of the electrochemical Gibbs-Duhem relation to the particular case of several charged diffusing species in a solid is utilized herein to obtain an expression for the local electric field which is then compared with an expression for the field deduced by an ordinary phenomenological transport analysis. The two approaches yield consistent results only in the limit of thermodynamic equilibrium. Implications of the analyses are pointed out for the special problem of the growth of oxides and similar tarnish films on metals.