Nanocrystalline materials show exceptional mechanical properties relative to their coarse-grained varieties. Because the volume fraction of grain boundaries in nanocrystalline materials can be as large as 30%, the mechanical properties of nanocrystalline materials are significantly influenced by this amorphous grain boundary phase. For example, the elastic modulus has been shown to decrease by 30% for nanocrystalline metals and more than 50% for nanocrystalline ionic materials. This is because the amorphous grain boundary regions are less dense than the crystalline grains, and thus have a larger volume per atom, \Omega. Assuming the interatomic potential, U(\Omega), is the same within the grain boundaries as in the bulk grains, the elastic modulus, E \propto \partial^2 U/\partial \Omega^2, will be smaller in the grain boundary regions than in the bulk grains. Thus, via the
rule of mixtures, a nanocrystalline material will have a lower elastic modulus than its bulk crystalline form.
Nanocrystalline metals The exceptional yield strength of nanocrystalline metals is due to
grain boundary strengthening, as grain boundaries are extremely effective at blocking the motion of dislocations. Yielding occurs when the stress due to dislocation pileup at a grain boundary becomes sufficient to activate slip of dislocations in the adjacent grain. This critical stress increases as the grain size decreases, and these physics are empirically captured by the Hall-Petch relationship, :\sigma_y = \sigma_0 + Kd^{-1/2}, where \sigma_y is the yield stress, \sigma_0 is a material-specific constant that accounts for the effects of all other strengthening mechanisms, K is a material-specific constant that describes the magnitude of the metal's response to grain size strengthening, and d is the average grain size. Additionally, because nanocrystalline grains are too small to contain a significant number of dislocations, nanocrystalline metals undergo negligible amounts of
strain-hardening,
Nanocrystalline ceramics While the mechanical behavior of ceramics is often dominated by flaws, i.e. porosity, instead of grain size, grain-size strengthening is also observed in high-density ceramic specimens. Additionally, nanocrystalline ceramics have been shown to sinter more rapidly than bulk ceramics, leading to higher densities and improved mechanical properties, although extended exposure to the high pressures and elevated temperatures required to sinter the part to full density can result in coarsening of the nanostructure. The large volume fraction of grain boundaries associated with nanocrystalline materials causes interesting behavior in ceramic systems, such as
superplasticity in otherwise brittle ceramics. The large volume fraction of grain boundaries allows for a significant diffusional flow of atoms via
Coble creep, analogous to the grain boundary sliding deformation mechanism in nanocrystalline metals. Because the diffusional creep rate scales as d^{-3} and linearly with the grain boundary diffusivity, refining the grain size from 10 μm to 10 nm can increase the diffusional creep rate by approximately 11 orders of magnitude. This superplasticity could prove invaluable for the processing of ceramic components, as the material may be converted back into a conventional, coarse-grained material via additional thermal treatment after forming. == Processing ==