What is the theoretical density of a nanocrystalline material?

We prepared nanocrystalline Ni by a severe deformation method – high-energy ball milling – and collected neutron diffraction patterns during the annealing of nanocrystalline Ni. Analyzing the neutron diffraction patterns provides the lattice parameter, dislocation density and grain size of nanocrystalline Ni. We found that a low-temperature (T < 260 °C) anneal annihilates the statistically stored dislocations whereas a high-temperature (T > 260 °C) anneal grows the nanograins. For T < 260 °C, where nanocrystalline Ni has a constant grain size, the excess volume is proportional to the density of statistically stored dislocations. For T > 260 °C, where the statistically stored dislocations are completely annealed out, the excess volume is inversely proportional to the grain size. However, 80% of the excess volume in our severely deformed nanocrystalline Ni is due to the statistically stored dislocations. We finally used our experimental data to derive the grain size dependence of the theoretical density of a nanocrystalline material free from excess dislocations. The derived theoretical density agrees well with the experimentally measured density of nanocrystalline metallic materials that are relatively free from deformation-induced defects.