A General Formalism to Model the Diffraction Pattern of Layered and Faulted Materials

A general formalism is proposed to describe the diffraction pattern of structures containing any quantity and type of defects in the layer stacking sequence. Starting from a modular description of the material, a general form of the diffraction problem is derived, from which the powder diffraction pattern can be obtained by suitable integration in reciprocal space. Under the tangent plane approximation, for a 3D periodic lattice the formula reduces to the Whole Powder Pattern Modelling. Under the tangent cylinder approximation, it can be transformed in any of the available equations employed for the description of faulted structures possessing any degree of entropy. Instrument- and specimen-related line profile broadening, including arbitrary domain shape and size distributions, can be easily considered. By extending the DIFFaX+ and PM2K ideas, the new algorithm can be employed to refine both structural and microstructural parameters (including the faulting pattern) from X-ray, electron and neutron diffraction data.