Contents

The mathematical theory of the powder diffraction intensity function is presented in the form accessible to the theoretical crystallography audience. The theory elucidates how a-priori estimates and values of certain averages, or moments of the intensity function bear witness to the fractal dimension and symmetry structure of the material under investigation. While peak analysis is today’s key method of processing the diffraction data, this paper stresses the importance of the moments of the intensity function. The moments are easy to compute and are robust to noise and errors. On the other hand, they represent a unique signature of a particular underlying symmetry type and generally tend to increase with the extent of the order in the material’s crystal structure. Supposedly, the moments reach a maximum in the case of the cubic lattice, and this is closely related to the Erdös distanc