The methodology and the software for the analysis of the atomic density modulation underneath the surface of a nanocrystal

S. Gierlotka, K. Skrobas, S. Stelmakh, W. Palosz, B. Palosz
Institute of High Pressure Physics PAS, PL

Keywords: nanocrystals, real space analysis, modeling

Summary:

Internal structure of nanocrystals can be extracted from Pair Distribution Function, which is obtained by Fourier transform of the diffraction data. Such a transform, G(r), contains complete information on inter-atomic distances present in the investigated material. To describe differences between specific inter-atomic distances in a nanocrystal and a reference single crystal we introduced the function δ(r)=Δri/ri,0, where Δri is the deviation of a given (volume averaged) inter-atomic distance derived from the experimental G(r) from the corresponding ri,0 distance in the related perfect crystal lattice. NanoPDF software is designed to (i) build atomic models with spherical symmetry, (ii) featuring spherical density modulation waves between the surface and the grain center, (iii) calculate theoretical diffraction patterns and G(r) functions of the models built,(iv) derive differences between average inter-atomic distances in the reference perfect lattice and a model of the nanocrystal with density waves calculated from its Pair Distribution Histograms and, (v) determine experimental δ(r) functions by fitting G(r) calculated for the models to experimental G(r) values. The match of specific atomic structure to the examined material is made by comparing experimental δ(r) plot to those calculated for different models with density waves.