Percolative composite model for prediction of the properties of nanocrystalline materials

A physical percolating composite model is presented for description of the changes in the transport-type properties with grain size in nanocrystalline materials. The model is based on hierarchial percolation through the different microstructural components such as grain boundaries, triple lines, and quadruple nodes at grain sizes when their respective percolation thresholds are reached. The model yields critical grain sizes at which the properties may change significantly. These grain sizes depend on the grain boundary thickness. Master curves were calculated for the elastic modulus and compared to the experimental data from the literature. Better fit was found with the experimental data in comparison to Hill's approximation model. The critical grain size at grain boundary percolation threshold is suggested as a criterion for definition of materials to exhibit nanocrystalline properties.