Impact of microstructure on grain-boundary diffusion in polycrystals

The impact of a complex microstructure on polycrystalline diffusion is investigated using both numerical and analytical methods. In particular, the diffusion equation is numerically integrated using the finite-difference method to obtain the concentration profile for a diffusant in a simplified microstructural representation. The methodology is first validated for an idealized model of diffusion in a prototypical, single grain-boundary system and then applied to a Voronoi model of a microstructure resulting from homogeneous nucleation and growth. The diffusive behavior is quantified by obtaining uptake curves as a function of time for different ratios of grain boundary to lattice diffusivities. Such curves can be used to estimate an unknown grain-boundary diffusivity, given certain microstructural assumptions. Finally, approximate analytical equations describing a diffusant uptake in polycrystalline microstructural models are developed and found to agree well with the numerical results. (c) 2005 American Institute of Physics.