Structural disorder in the decagonalAl–Co–Ni. I. Patterson analysis of diffuse x-ray scattering data

Abstract

The three-dimensional (3D) difference Patterson (autocorrelation) function of a disordered quasicrystal (Edagawa phase) has been analyzed. 3D diffuse x-ray diffraction data were collected in situ at 300, 1070, and $1120\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. A method, the punch-and-fill technique, has been developed for separating diffuse scattering and Bragg reflections. Its potential and limits are discussed in detail. The different Patterson maps are interpreted in terms of intercluster correlations as a function of temperature. Both at high and low temperatures, the clusters decorate the vertices of the same quasiperiodic covering. At low temperatures, for the disordered part of the structure, short-range intercluster correlations are present, whereas at higher temperatures, medium-range intercluster correlations are formed. This indicates disorder mainly inside clusters at low temperatures, whereas at higher temperatures disorder takes place inside larger superclusters. Qualitatively, the Patterson maps may be interpreted by intercluster correlations mainly inside pentagonal superclusters below $1120\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, and inside the larger decagonal superclusters at $1120\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. The results of our diffraction study are published in two parts. Part I focuses on the 3D Patterson analysis based on experimental data, Part II reports modeling of structural disorder in decagonal $\mathrm{Al}--\mathrm{Co}--\mathrm{Ni}$.