Phononic and phasonic Debye-Waller factors for 1D quasicrystals

The main purpose of crystallography is to solve and refine crystal structures based on measured diffraction data. One of important corrections crucial in the refinement process is the Debye-Waller factor correction for phonons in physical, and phasons in perpendicular space. In our paper we show the limitations of the standard approaches to the Debye-Waller correction in case of quasicrystals and propose new approach based on the statistical method. For the model 1D quasicrystal we show that in case of phonons there is no significant objection against classical (exponential) Debye-Waller factor, however using different forms can slightly improve the results of a refinement. In case of phasons the classical formula gives no rise to the efficiency of the refinement and completely new approach is required. We propose a redefinition of the Debye-Waller factor in terms of the statistical approach and show its effectiveness