MS27-P02 Statistical method of structural description of complex systemsThe statistical method is a commonly approved and confirmed by many results approach to structural and diffractional studies of crystals. It is particularly successful in terms of complex systems, like modulated crystals or quasicrystals. In our presentation we will show the fundamentals of the method, including the basic concept behind – called the average unit cell concept , and discuss its application to modulated crystals and quasicrystals [2,3].
The average unit cell is the probability distribution function P(u) of atomic positions calculated against some periodic reference lattices. A Fourier transform of P(u) gives the diffraction pattern. Structural modeling within the statistical approach involves a modeling of the P(u) distribution, which is an object in physical space, and enables including all kinds of structural disorder in a derivation of the structure factor. We will show how this methodology applies for the harmonically modulated crystal (with harmonic modulation and incommensurate scattering vector), including its correspondence to a quasicrystal, and selected decagonal quasicrystals.
The method has no limit in applying it also to such complex systems, like proteins of macromolecules, where the structural disorder appears to play a crucial role, and attempts to use crystallographic methods known for periodic crystals are rather doubtful. We will shortly introduce a possible benefits from applying the statistical method to complex organic systems.References:
 Strzałka, R., Bugański, J., Wolny, J. (2016), Crystals, 6, 104.
 Wolny, J., Bugański, I., Strzałka, R. (2015), Philos. Mag., 96, 1344-1359.
 Wolny, J., Bugański, I., Strzałka, R. (2018), Cryst. Rev., 25, 22-64.Keywords: structure modeling, statistical method, complex systems