X-ray structure determination of quasicrystals – limits and potentiality

State-of-the-art X-ray diffraction techniques allow quasicrystals to be characterised quantitatively. Based on two-dimensional scans of Bragg reflections with high spatial resolution twinned approximants or nanodomain structures can be reliably distinguished from quasiperiodic average structures. Linear phason strain as well as mosaicity can directly be detected in situ under non-ambient conditions. Accurate cell parameters can be obtained. The experimental limitations are discussed. Methods to determine the space group and the optimum n-dimensional unit cell are shown. The phases of the reduced structure amplitudes can be obtained by several techniques. Highly resolved electron density distributions are derived from a combination of Patterson deconvolution techniques with maximum entropy methods. Special emphasis is put on the achievable resolution of experimentally determined electron density distributions. Based on a subtle n-dimensional atomic surface modelling the structure can be described in an accurate way according to the standards in conventional crystallography. All relevant structural parameters are determined quantitatively by an n-dimensional structure refinement. Different structure models are distinguished by their likelihood. The reliability of a quantitative structure determination is examined.