Fast grain boundary diffusion and surface exchange reactions at active surface sites of polycrystalline materials

Analytical solutions to the diffusion equations for fast grain boundary diffusion and surface exchange reactions at active surface sites are derived. The microstructure of the polycrystalline sample of finite thickness is modelled by parallel grain boundaries. The ratio between the surface exchange coefficient and the diffusion coefficient for the grain boundaries is assumed to be greater than or equal to that for the bulk. The analytical solutions allow the calculation of diffusion profiles for thin films. Special emphasis is laid on a detailed analysis of the time dependence of the total amount of diffusant exchanged between the constant diffusion source (e.g. gas phase) and the polycrystalline sample (e.g. oxide ceramics) which corresponds to relaxation curves obtained from, e.g., oxygen exchange measurements. The calculated relaxation curves refer to Harrison's type-A kinetics where homogeneous medium solutions are satisfactorily applicable, introducing effective kinetic parameters. Apart from expressions for the effective diffusion coefficient analogous relations for the effective surface exchange coefficient are proposed, depending on the microstructure of the polycrystalline material and the corresponding kinetic parameters of bulk and grain boundary regions, respectively.