Powder diffraction line profiles from the size and shape of nanocrystallites

A numerical procedure to carry out the integral on the powder diffraction sphere in reciprocal space and obtain accurate powder diffraction peak profiles for small crystallites is presented. In doing so, the literature surrounding the effect of crystallite size and shape on the powder peak profile is briefly reviewed. Powder patterns simulated by this technique are compared with those calculated by the tangent plane approximation and Debye function for spherical, cubic and cylindrical crystallites having sizes of only a few nanometres. The tangent plane approximation is found to produce inaccurate peak profiles and peak positions in simulated patterns of the cubic and cylindrical nanocrystallites. This performance is in contrast to that of the proposed powder integration technique, which results in powder patterns that are in good agreement with those from the Debye function, for all crystallite sizes and shapes considered here.