Abstract
A continuum model for yttria-stabilized zirconia (YSZ) in the framework of non-equilibrium thermodynamics is developed. Particular attention is given to (i) modeling of the YSZ-metal-gas triple phase boundary, (ii) incorporation of the lattice structure and immobile oxide ions within the free energy model and (iii) surface reactions. A finite volume discretization method based on modified Scharfetter-Gummel fluxes is derived in order to perform numerical simulations. The model is used to study the impact of yttria and immobile oxide ions on the structure of the charged boundary layer and the double layer capacitance. Cyclic voltammograms of an air-half cell are simulated to study the effect of parameter variations on surface reactions, adsorption and anion diffusion.
Highlights
Detailed continuum models of high temperature solid oxide electrochemical cells (SOEC)1 describe the underlying chemistry with spatially distinguished phases of the triple phase boundary [1,2,3,4]
The overpotential correlates with the excess concentration of oxide ions available for the electrontransfer reaction in steady-state scenarios, it cannot capture the dynamics of the double layer
The thermodynamic state of the bulk yttria-stabilized zirconia (YSZ) is described by three quantities: filling ratio y, electrostatic potential φ and pressure p
Summary
Detailed continuum models of high temperature solid oxide electrochemical cells (SOEC) describe the underlying chemistry with spatially distinguished phases (oxide ion conductor, electric conductor, gas) of the triple phase boundary [1,2,3,4]. The free energy model of the bulk YSZ, capturing the crystalline structure, immobile oxide ions and elastic deformation, is developed in the “Bulk YSZ” section. The free energy density ρψ of YSZ is assumed to be a function of temperature T , partial mass densities ρα and the electric field E. The mass balance equations imply constant number densities for the immobile species, i.e., ∂t nα = 0 for α = Zr, Y, Oi, and the barycentric velocity is given by ρυ = ρOmυOm which can be expressed in terms of the diffusion flux of the mobile oxide ions as (ρZr + ρY + ρOi)υ = JOm. The assumptions of incompressibility and vanishing lattice velocity may be viewed alternatively as a description of the charge transport in the reference frame of the cation lattice which does not undergo any deformation
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