Electron microscopy of quasi-crystals in rapidly solidified Al-14% Mn alloys

Abstract

Recently Shechtman et al. (1) have reported a new phase in rapidly solidified Al-14at% Mn alloys. The diffraction patterns from this phase correspond to an icosahedral point group symmetry which is inconsistent with lattice translation, The observation is consistent with a long range icosahedral orientational order (termed quasi-crystal) modelled by using Penrose lattice (2,3). A second model proposed by 5achdev and Nelson (4) postulates a superposition of density waves with an icosahedral symmetry. These investigators considered stars composed of 12 vertices, 30 edges or 20 faces of a regular lcosahedron with the basis vectors comprising the stars being incommensurate in nature, Using Landau theory, they developed the hierarchy of spots in reciprocal space for vertex, edge and face models. These models are the counter part of simple cubic, f.c.c, and b.c.c, phases in normal crystals derived from an octahedron" These three types of quasi-crystals cannot be distinguished in three and five fold symmetry positions. However, the two fold symmetry shows a marked difference and hence a particular model can be identified. Additionally as pointed out by Levine and Steinhardt (3), the concept of quasi crystals can also be extended to irregular polyhedra