Interpenetrating pseudo-icosahedral clusters model for quasicrystals and consequences: asymmetry of diffraction peaks and pseudo-inflation rules

Overview & Synopsis

The diffraction properties of an interpenetrating pseudo-icosahedral clusters (IPIC) model of icosahedral phase are studied. The structure factor is treated in perturbation over the icosahedral symmetry, the site multiplicities, the atomic scattering factors which takes into account the chemical disorder inside clusters, cluster deformations in real space, and distortions in reciprocal space. Its pseudo-G invariant character is studied assuming a strong integrability condition. A "virtual ideal i-quasicrystal" is associated uniquely with the real i-phase, as closest object obeying a 6D crystallography. The clusters and the quasilattice contributions to the peak positions and intensity properties are decoupled. The inflation rules coming from the quasilattice are superposed to the pseudo-inflation rules which arise from the ideal clusters. Peaks arising from clusters are non-symmetrical. Comparison with G-approximant crystals is made.