Diffraction profiles from small crystallites

The diffraction profile for a small crystallite has been obtained as the orientational average of the diffraction intensity given by Ino & Minami [Acta Cryst. (1979), A35, 163-170]. The formula obtained is a type of Debye interference function modified by a function {cal V}(r) (the self-convolution of a crystal shape function) and is expressed as a sum over all the atomic distance vectors in the crystal structure. Since the set of the vectors has Laue symmetry (the order of the group: L), the summation can be simplified to a sum over a reduced range corresponding to 1/L of the original range, while the {cal V}(r) is changed to { v}(r) = ΣLp = 1= {cal V}(Rpr)/(LVt) (Vt: volume of the crystal; R1, . . . , RL: element of Laue symmetry group). Once the { v} function is determined, the profile for a complicated crystal of any size and any crystal system can be systematically and efficiently calculated.