Grain boundary diffusion: non-random topology and effective medium approximation

Driven by the success of grain boundary (GB) engineering, it is desirable to establish a relationship between the properties of polycrystalline materials and their GB network structures. Here we particularly explore GB diffusion using a two-dimensional GB network model to establish a connection between the effective diffusivity of GB networks and the network topology for random and two crystallographically consistent networks. For all the networks, the effective diffusivity against GB characters exhibits two distinct behaviours, that is, composite and percolation, based on the diffusivity contrast of individual GB properties. Generalised effective medium (GEM) equation, which combines the effective medium theory and the percolation theory, can be applied to predict the behaviour of crystallographically consistent networks when incorporating the shift of the effective diffusivity percolation threshold. The shift of the percolation threshold resulting from local constraints can be connected to the population of triple junctions. Notably, the population of J₂ plays a key role in determining the shift by changing the connectivity of high-diffusivity boundaries.