Analysis of short and long range atomic order in nanocrystalline diamonds with application of powder diffractometry

Fundamental limitations, with respect to nanocrystalline materials, of the traditional elaboration of powder diffraction data like the Rietveld method are discussed. A tentative method of the analysis of powder diffraction patterns of nanocrystals based on the examination of the variation of lattice parameters calculated from individual Bragg lines (named the "apparent lattice parameter", alp) is introduced. We examine the application of our methodology using theoretical diffraction patterns computed for models of nanocrystals with a perfect crystal lattice and for grains with a two-phase, core-shell structure. We use the method for the analysis of X-ray and neutron experimental diffraction data of nanocrystalline diamond powders of 4, 6 and 12 nm in diameter. The effects of an internal pressure and strain at the grain surface are discussed. The results are based on the dependence of the alp values on the diffraction vector Q and on the PDF analysis. It is shown, that the experimental results lend a strong support to the concept of a two-phase structure of nanocrystalline diamond.