Sharp Diffraction Maxima from an Icosahedral Glass

Abstract

We consider densely packed assemblies of icosahedra, such that icosahedral bond-orientational order is enforced throughout the sample. The peaks in the calculated diffraction patterns may be put in a one-to-one correspondence with the electron and x-ray diffraction patterns from icosahedral Al-Mn alloys, allowing the determination of the packing-unit size. We show that these maxima are not Bragg diffraction peaks, but have an intrinsic width, and may be understood as resulting from the interference between two or more characteristic lengths, as originally discussed by Hendricks and Teller.