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Whipple’s solution of the problem of grain boundary diffusion and Le Claire’s relation, which is often used to determine grain boundary diffusion coefficients, are examined for a broad range of ratios of grain boundary to bulk diffusivities Δ and diffusion times t. Different reasons leading to errors in determining the grain boundary diffusivity (DGB) when using Le Claire’s relation are discussed. It is shown that nonlinearities of the diffusion profiles in ln Cav-y6/5 plots and deviations from “Le Claire’s constant” (-0.78) are the major error sources (Cav=averaged concentration, y=coordinate in diffusion direction). An improved relation (replacing Le Claire’s constant) is suggested for analyzing diffusion profiles particularly suited for small diffusion lengths (short times) as often required in diffusion experiments on nanocrystalline materials. [ABSTRACT FROM AUTHOR]

Abstract: The results of DFT supercell calculations of oxygen behavior upon the UN (001) and (110) surfaces as well as at the tilt grain boundary are presented. Oxygen adsorption, migration, incorporation into the surface N vacancies on (001) and (110) surfaces have been modeled using 2D slabs of different thicknesses and supercell sizes. The temperature dependences of the N vacancy formation energies and oxygen incorporation energies are calculated. We demonstrate that O atoms easily penetrate into UN surfaces and grain boundaries containing N vacancies, due to negative incorporation energies and a small energy barrier. The Gibbs free energies of N vacancy formation and O atom incorporation therein at the two densely-packed surfaces and tilt grain boundaries are compared. It has been also shown that the adsorbed oxygen atoms are highly mobile which, combined with easy incorporation into surface N vacancies, explains efficient (but unwanted) oxidation of UN surfaces. The atomistic mechanism of UN oxidation via possible formation of oxynitrides is discussed. [Copyright &y& Elsevier]

Abstract: Diffusion in polycrystalline materials is investigated by means of numerical finite element simulations for constant source conditions. The grain boundaries are assumed to provide fast diffusion paths. Main emphasis is put on situations that typically occur for nanocrystals, viz. on situations in which (i) the diffusion length is significant compared with grain size, (ii) the influence of boundaries that are parallel to the surface become important in addition to the perpendicular ones. Furthermore, we treat the influence of blocking space charge layers sandwiching the core pathways and thus channeling grain boundary diffusion. [Copyright &y& Elsevier]