Looking beyond limitations of diffraction methods of structural analysis of nanocrystalline materials |
Ewa Grzanka , Svitlana Stelmakh , Stanisław Gierlotka , Bogdan F. Palosz |
Polish Academy of Sciences, Institute of High Pressure Physics (UNIPRESS), Sokolowska 29/37, Warszawa 01-142, Poland |
Abstract |
There is variety of models of a nanocrystal offered in the literature, starting from the assumption that nano-crystal is basically a small single crystal. Usually, however, it is assumed that nanocrystals have a core-shell structure, where interatomic distances at the surface are different than those in the bulk. One might also consider complex models assuming a modulation of the lattice density, what is equivalent to changes of interatomic distances within the particle volume. Such a structure might look like a sequence of tensile followed by compressive strains between the surface and the grain interior. The question is, which model best describes the results of the diffraction data analysis. There are two basic methods of analysis of powder diffraction: reciprocal space analysis, which refers to characteristic Bragg scattering, and real space analysis called atomic Pair Distribution Function analysis (PDF). Both techniques give information on the atomic structure which is, however, a volumetric average of the sample. None of those techniques is capable of providing a complete, unique description of a nano-crystal, but each has a unique capabilities with respect to information about the structure. An analysis made in "reciprocal space", which refers to a unit cell and is based on examination of characteristic Bragg-type scattering, is sensitive directly to the long range-atomic order. If needed, structural refinement, e.g. with application of the Rietveld refinement software, is being done. In this case the diffuse scattering is ignored. Analysis made in "real space", which provides information on the length and abundance of interatomic distances between pairs of atoms, is based on examination of the total scattering (this includes both characteristic Bragg reflections and diffuse scattering underneath the Bragg peaks) and thus, in principle, provides information on every single atom present in the sample. The problem is that there are no simple (straightforward) methods which would allow to link specific interatomic distances to different structural components of the sample. In our case, it is impossible to find out in which part of the sample volume, the core or the surface, given interatomic distances occur. Neither real- nor reciprocal space analysis alone is well suited for nano-crystallography. The best approach encompasses a combination of both techniques, with extraction of consistent information derived from both methods. That may be a very effective searching tool for a unique model of nanocrystals. In this work we discuss various models of nanograins and compare the effects that specific structures have on Bragg scattering and on interatomic distances (determined with PDF analysis). |