Application of powder diffraction methods to the analysis of short- and long-range atomic order in nanocrystalline diamond and SiC: the concept of the apparent lattice parameter (alp)

Two methods of analysis of powder diffraction patterns of diamond and SiC nanocrystals of different grain size are presented: (1) examination of changes of the lattice parameters ("apparent lattice parameter", alp) with the diffraction vector Q, which refers to Bragg scattering, and (2), examination of inter-atomic distances based on the analysis of the atomic Pair Distribution Function, PDF. Application of these methods based on theoretical diffraction patterns computed for models of nanocrystals having either a perfect, uniform crystal lattice or a core-shell structure constituting a two-phase system was studied. The models are defined by the lattice parameter of the grain core, thickness of the surface shell and the magnitude and the strain field distribution in the shell. X-ray and neutron diffraction data of nanocrystalline SiC and diamond powders of grain diameters from 4 nm up to micrometer range were analyzed. The effects of the internal pressure and strain at the grain surface on the structure, based on the experimentally determined dependence of the alp values on the Q-vector, and changes of the inter-atomic distances with the grain size determined experimentally by the atomic Pair Distribution Function (PDF) analysis are discussed. The experimental results lend strong support to the concept of a two-phase, core and the surface shell structure of nanocrystalline diamond and SiC.