We introduce numerical methods and algorithms to estimate the main parameters of fractal-like particle aggregates from their optical structure factor (i.e. light scattering diagrams). The first algorithm is based on a direct and simple method, but its applicability is limited to aggregates with large size parameter and intermediate fractal dimension. The second algorithm requires to build calibration curves based on accurate particle agglomeration and particle light scattering models. It allows analyzing the optical structure factor of much smaller aggregates, regardless of their fractal dimension and the size of the single particles. Therefore, this algorithm as well as the introduction of a criterial curve to detect the different scattering regimes, are thought to be powerful tools to perform reliable and reproducible analysis.

One of the challenges of modern crystallography of complex systems (complex metallic alloys, proteins, aperiodic crystals and quasicrystals) is to properly describe the disorder in these systems and discuss correctly the refinement results in terms of the structural disorder. In this paper we briefly discuss a new approach to phasons and phonons in quasicrystals and focus on the new theory of phonons in these materials. A newly derived correction factor for phonons in the form of the Bessel function is the approximated way of describing optic modes in the phonon spectra of quasicrystals. It is applied to a real decagonal quasicrystal in the Al-Cu-Rh system with 56/38 atoms per thick/thin structural unit, based on 2092 unique reflections selected from the collected diffraction data, significantly improving the refinement results. The final R-factor value is 7.24%, which is over 0.5% better result comparing to originally reported. We believe our work will open a broader discussion on the disorder in quasicrystals (and other aperiodic systems) and motivate to develop new approaches to treat the diffraction data influenced by different types of disorder in the new way.