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 nanoc rystalline materials. The model is based on hierarchial percolation th rough the different microstructural components such as grain boundarie s, triple lines, and quadruple nodes at grain sizes when their respect ive percolation thresholds are reached. The model yields critical grai n sizes at which the properties may change significantly. These grain sizes depend on the grain boundary thickness. Master curves were calcu lated for the elastic modulus and compared to the experimental data fr om the literature. Better fit was found with the experimental data in comparison to Hill's approximation model. The critical grain size at g rain boundary percolation threshold is suggested as a criterion for de finition of materials to exhibit nanocrystalline properties.