Structure/Microstructure Analysis of Faulted and Modular Materials from Powder Diffraction Data: Beyond the Deterministic Approach

Lattice parameters, asymmetric unit, symmetry elements and modulation vectors are usually employed for the description of a crystalline material. However, not always such information is sufficient to reconstruct the X-ray powder diffraction pattern (XRPD) of a real specimen, even if instrument and specimen-related broadening effects are properly taken into account. Odd profile shapes, deeply anisotropic broadening, extra features can in fact be present e.g. as the result of local breaking of the 3D periodicity of the lattice. The modular approach should be invoked in this case to move from a deterministic (regular) to a probabilistic (quasiregular or irregular) description of thematerial. When single crystals are available, diffuse scattering and the Reverse Monte-Carlo approach are the ideal tools to analyse the extra intensity appearing in between Bragg peaks. It will be here shown how faulted structures and modular systems built with 2D symmetric modules can be analysed from XRPD data.