An evaluation was made of the macroscopic diffusivity of grain boundary networks with randomly distributed or crystallographically correlated grain boundary character. In high-contrast networks, where the local diffusivity varied by more than 4 orders of magnitude between grain boundaries of different character, the macroscopic diffusivity was governed by the development of a percolating path of high-diffusivity boundaries. In low-contrast systems, the effective network diffusivity was less sensitive to topology and could be described by composite averaging schemes. High- and low-contrast regimes were delineated quantitatively, and a generalized effective medium approximation was considered that quantitatively linked the network structure to effective macroscopic transport properties at all levels of contrast. It was also shown how effective medium theory could be adapted so as to capture crystallographic correlations among boundary types, and expanded to include a broader range of boundary types.

Diffusion on Grain Boundary Networks - Percolation Theory and Effective Medium Approximations. Y.Chen, C.A.Schuh: Acta Materialia, 2006, 54[18], 4709-20