Patterson analysis of aperiodic crystals

Aspects of the Patterson-function (PF) analysis of the structure of aperiodic crystals are studied experimentally on icosahedral Al-Mn-Si and by computer simulation. In the icosahedral Al-Mn-Si system, a PF analysis using only the experimentally distinguishable peaks and neglecting the remaining background changes the two Mn-Mn distances of 4.6 and 5.0 A to a single 4.8 A distance. Computer simulations on one-dimensional (1D) and 2D models of aperiodic structures show that neglect of background in the PF analysis distorts disordered structures toward the quasicrystalline model, indicating that care should be exercised in drawing conclusions from the analysis of diffraction data.