Chemical Diffusion Across Grain Boundaries: In-Situ Observation and Phenomenological Modeling

摘要

In this paper we report two recent achievements with respect to chemical diffusion across grain boundaries: (i) A model based on the concepts of electrostatic and chemical capacitances and electrochemical resistances is introduced. This model, which is derived from the Nernst-Planck-Poisson equations, turns out to be a very efficient tool yielding an adequate description of chemical diffusion across Schottky barriers. (ii) The model predictions were verified by a novel method which allows for in-situ monitoring of the diffusion front as it propagates across a single grain boundary in Fe- doped SrTiO3. The low symmetry boundary (near Sigma-13) shows a pronounced chemical resistance reflected by a distinct jump in the concentration profiles, while the highly symmetrical Simga-3 boundary is not of any measurable influence. The effects can be quantitatively explained by Schottky barriers acting on both electrons and ions. The diffusion profiles can be precisely modelled with the space charge potential as the only unknown parameter. The space charge potentials are found to be in good agreement with the values derived from electrical measurements.