Use of the Debye-Waller approximation in diffraction-pattern calculation

A new method of diffraction-pattern calculation is proposed and tested on quasicrystals. With use of an appropriately defined reference lattice, a structure factor can be well approximated by a rapidly convergent series expansion of a variable u that describes nearest distances between atomic positions and points of the reference lattice. Only the first few terms are significant for difffraction-pattern calculation. The possibility of using the Debye-Waller approximation is discussed. In this case an appropriate shift of the reference structure is required. Calculations based on the Debye-Waller formula in real and phason spaces give similar results.