Grain-boundary atomic structure in nanocrystalline palladium from x-ray atomic distribution functions

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Abstract
We discuss the scattering theory of nanocrystalline solids, based on an evaluation of the intragrain and intergrain parts of the atomic distribution function. The results are applied to experimental x-ray scattering data obtained on a set of nanocrystalline Pd samples, prepared by inert-gas condensation, with different consolidation, aging, and annealing parameters. The experimental results show that the number of atomic neighbors in the crystal lattice coordination shells of nanocrystalline Pd is substantially lower than the one in the coarse-grained polycrystal lattice. The findings suggest that as a function of their age and thermal treatment, the samples have two different atomic structures. In samples aged for several months at room temperature, and in annealed samples, practically all atoms are located on crystal lattice sites, and the reduction in nearest-neighbor coordination number is an effect of the finite size of the crystallites. In fine-grained samples examined within 10 days of preparation, about 10% of the atoms are located on nonlattice sites with little or no atomic short-range order. This corresponds to about two atomic monolayers of atoms on nonlattice sites at the grain boundaries in as-prepared samples, as compared to 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 Pd is not measurably widened compared to the one of coarse-grained reference samples, indicating that disorder in the crystal lattice, as probed by the x-ray Debye-Waller parameter, involves displacements correlated over several lattice parameters, rather than short-range, uncorrelated atomic displacements.