Scattering theory for nanocrystalline solids was considered on the basis of an evaluation of the intra-grain and inter-grain parts of the atomic distribution function. The results were applied to experimental X-ray scattering data from nanocrystalline samples which had been prepared by inert-gas condensation using various consolidation, aging and annealing conditions. The results showed that the number of atomic neighbors in the crystal lattice coordination shells of the nanocrystalline material was much lower than that in a coarse-grained polycrystalline lattice. This suggested that the samples had 2 different atomic structures, depending upon their aging and thermal treatments. In the case of samples which had been aged for several months at room temperature, and in annealed samples, almost all of the atoms were located in crystal lattice sites and the reduction in nearest-neighbor coordination number was an effect of the finite size of the crystallites. In the case of fine-grained samples which were examined within 10 days of preparation, some 10% of the atoms were located in non-lattice sites, with little or no atomic short-range order. This corresponded to the presence of about 2 atomic monolayers of atoms in non-lattice sites at the grain boundaries of as-prepared samples, as compared with about one-quarter of a monolayer in aged or annealed samples. The distribution of nearest-neighbor interatomic spacings for atoms on crystal lattice sites in nanocrystalline material did not appear to be wider when compared with that in coarse-grained samples. It was concluded that the disorder of the crystal lattice, as reflected by the X-ray Debye-Waller factor, involved displacements which were correlated over several lattice parameters; rather than short-range uncorrelated atomic displacements.

J.Löffler, J.Weissmüller: Physical Review B, 1995, 52[10], 7076-93