Faceting in bond-oriented glasses and quasicrystals

We show that long-range positional order in the sense that the density Fourier transform is a set of {δ} functions is not essential for the phenomenon of facet formation. Facets can occur in certain classes of perfect bond-oriented systems which lack the conventional long-range positional order, allowing the appearance of widths in the diffraction peaks. The predicted facets in some of these systems are consistent with the recently observed triacontahedral grain shapes in Al₆{LiCu}₃$ and dodecahedral grain shapes in Al-Mn-Si, as well as the strong spatial disorder as indicated by the x-ray diffraction measurements.