What periodicities can be found in diffraction patterns of quasicrystals?. Issue 2 (19th February 2014) - Wolny, Janusz; Kozakowski, Bartlomiej; Kuczera, Pawel; Pytlik, Lucjan; Strzalka, Radoslaw
<x xml:space="preserve">Abstract</x> The structure of quasicrystals is aperiodic. Their diffraction patterns, however, can be considered periodic. They are composed solely of series of peaks which exhibit a fully periodic arrangement in reciprocal space. Furthermore, the peak intensities in each series define the so‐called `envelope function'. A Fourier transform of the envelope function gives an average unit cell, whose definition is based on the statistical distribution of atomic coordinates in physical space. If such a distribution is lifted to higher‐dimensional space, it becomes the so‐called atomic surface – the most fundamental feature of higher‐dimensional analysis.