Application of the apparent lattice parameter to determination of the core-shell structure of nanocrystals

In this review work we discuss applicability of Bragg scattering to examination of nanocrystals. We approximate the structure of nanograins by a commonly accepted core-shell model. We show that, for principal reasons, the Bragg equation is not applicable directly to nanocrystals. We use the Bragg relation through application of the apparent lattice parameter (alp) concept which we use to evaluate quantitatively the core-shell model. We also introduce a new parameter of the structure, Equivalent Cubic Lattice Parameter (EClp), which quantifies deviation of the real (trigonal) lattice from its parent fcc structure due to the lattice deformation (e.g. by the stacking faults). We show examples of an analysis of experimental X-ray and neutron diffraction data based on the alp methodology and on the theoretical patterns calculated for various core-shell models.