Abstract
The electrical conductivity of mesoscopic cubic cerium oxide crystals with space charge layers along their external boundaries has been calculated as a function of grain size. The equilibrium distribution of electronic and ionic charge carriers in this mixed conductor were obtained by numerical solution of the three-dimensional Poisson–Boltzmann equation in finite-difference approximation. At grain sizes comparable to the screening length λ, space charge layers overlap and penetrate the entire crystallite. Taking into account the inhomogeneous distribution of charge carriers, the partial electronic and ionic conductivities were calculated by numerical solution of the drift-diffusion equations in first-order expansion of the electrical potential under the non-equilibrium conditions imposed by an applied external voltage. Assuming a positive space charge potential, a characteristic grain-size-dependent increase of electronic and decrease of ionic conductivity was found. The obtained numerical results were combined with results from analytic solutions and compared with experimental data on the electrical conductivity of nanocrystalline cerium oxide.
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