A new approach to the determination of the true atomic structure of nanocrystals is presented. It is based on the analysis of the Pair Distribution Function. A model of a nanocrystal with a modulation of the atomic density that has a form of a wave going from the center of a nanocrystal towards it's surface is examined. A dedicated software package NanoPDF  which serves for modeling and PDF data analysis is presented.
There has been a common agreement that the surface of the nanocrystals is different, in terms of the atomic arrangement, from the bulk, what follows from basic physical laws referring to crystal symmetry, surface energy etc. A diffraction pattern essentially contains all the information on the atomic arrangements in an investigated sample. There exist sophisticated methods to investigate fine details of atomic arrangements in quasi-infinite crystals, and there exist methods to determine structure of materials without any long-range order. True nanocrystals fall in between the two categories: their size matters when one plans the experiment and analyses the data and their atomic structure is only periodic-like.
In the past we have predicted and showed experimentally that in diffraction patterns of nanocrystals the position of every Bragg peak points to a slightly different lattice parameter. Examination of this behavior led us to elaboration of a core-shell model of various nano-materials . However, when analyzing only average lattice parameter calculated from Bragg reflections one rejects some important information contained in a diffraction pattern. The method that uses all available data is the Total Scattering Analysis. Reconstruction of the direct space is performed through calculation of the Atomic Pair Distribution Function (PDF) by Fourier transformation of the diffraction data. Such a transform, usually denoted G(r), contains complete information on inter-atomic distances present in the investigated material. In case of a macroscopic crystal peak positions in G(r) are uniquely defined by the sample's lattice parameter. In case of a nanocrystal which lacks ideal periodicity of the crystal lattice the peaks positions in the G(r) function are displaced with respect to the positions they would have for a perfectly periodic lattice .
To evaluate deviation of the true structure of nanocrystals from a parent crystal lattice the experimental curve is scanned by fitting inside limited sections of G(r) for given r-intervals. We have derived experimental function δ(r) describing deviations of individual inter-atomic distances from those of a perfect crystal lattice. In order to propose an atomistic model for a given nanocrystalline sample we examined theoretical models of a nanocrystal which are composed of a core surrounded by several shells where inter-atomic distances change from shell to shell in a quasi periodic manner. While the analysis of the experimental data can be automated, the step of finding the best matching model is a sort of a trial-and-error procedure. Both the analysis of the experimental G(r) and the calculation of the models is handled by the dedicated NanoPDF software .
With use of the above procedure models of nanocrystalline diamond, SiC and CdSe were proposed.
This work was supported by NCN through grant No. 2011/03/B/ST5/03256 and 2011/01/B/ST3/02292.
 K. Skrobas et al.,NanoPDF Software Package; http://www.unipress.waw.pl/soft/crystallography/nano.pdf.
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