Application of the Apparent Lattice Parameter to determination of the Core-Shell Structure of Nanocrystals Bogdan PALOSZ 1 , Svetlana STELMAKH 1, 2 , Ewa GRZANKA 1 , Stanislaw GIERLOTKA 1 , Witold PALOSZ 3 1 Institute of High Pressure Physics UNIPRESS, Polish Academy of Sciences, 01 142 Warszawa, ul. Sokolowska 29/37 2 Physics and Astronomy Department, TCU, Fort Worth, TX 76129 3 Brimrose Corporation, Baltimore, MD 21236, USA Running title: Structure of nano-crystals as the key to understanding the unique properties of nano-materials. Abstract One of the key problems in "nanoscience" is designing the right experiments to measure specific size-dependent physical properties, which is necessary to understand the origin of differences in the properties between nano- and larger crystals. Nanocrystal is a unique "piece of material" with its individual atomic structure and properties which are closely related to its characteristic dimensions. Nanoscience comes into picture when properties of the material can no longer be described using conventional tools, in particular using relationships derived for ordinary materials. In other words, we deal with nanoscience when the property is clearly related to the small characteristic dimension(s) of the object. This statement is valid for any nano-property of a material and concerns also application of diffraction methods. Evaluation of powder diffractograms is usually done using standard numerical procedures like the Rietveld program which is used for refinement of structural parameters and provides satisfactory results for conventional-size materials [1, 2]. However, all those methods have an inherent limitation which follows from the fact that they are based on the assumption that the sample structure can be satisfactorily approximated by an infinite crystal lattice and represented by a unit cell. A nano-crystal cannot be regarded as a single crystal due to, (i), its limited dimensions, and (ii), a large fraction of atoms being associated with the grain surface which has different environment than the interior atoms. Because the assumption of a uniform crystal structure of nano-materials is not justified, application of routine procedures of collection and elaboration of diffraction data has to be verified/revised since it may lead to misinterpretation of the experiments and to incorrect conclusions about the atomic structure of the samples. There is a variety of specific problems that might address diffraction structural studies on nanocrystals, for instance: (i), what is the nanocrystal basic crystallographic structure (in its interior? average for the entire volume?), (ii), what are the differences between similar crystal phases present in nano- and micro- polycrystalline samples (do those differences really