Stability and formation of Al-Cu-(Li,Mg) icosahedral phases

The structure of quasicrystals

The aim of the present article is to give a review of the state-of-the-art on quasicrystal structure analysis. After a short discussion of the term “crystal” in chapter 1, the geometrical generation of quasilattices is touched in chapter 2. In the following the higher-dimensional description of 1d, 2d and 3d quasi-crystals is demonstrated in detail as well as the derivation of structure factor equations and symmetry relationships in the higher-dimensional space. Chapter 4 shows the experimental techniques and structure determination methods for the study of quasicrystals. The experimental results of structural studies performed with different tech-niques are critically reviewed in chapter 5. Some of the results of the literature research are that five years after the detection of the first quasicrystal not a single quantitative (in terms of a regular structure determination) analysis of its structure has been carried out, and that the famous Mackay-icosahedra do not play the important role as the basic structural building elements as one supposed before.

A Study of the Phase Mg2Cu6Ga5, Isotypic with Mg2Zn11. A Route to an Icosahedral Quasicrystal Approximant

The new title compound was synthesized by high-temperature means and its X-ray structure refined in the cubic space group Pm3macro, Z = 3, a = 8.278(1) A. The structure exhibits a 3-D framework made from a Ga(14) and Mg network within which large and small cavities are occupied by centered GaCu(12) icosahedral and Cu(6) octahedral clusters, respectively. The clusters are well bonded within the network. Electronic structure calculations show that a pseudogap exists just above the Fermi energy, and nearly all pairwise covalent interactions remain bonding over a range of energy above that point. Analysis suggests that the compound is hypoelectronic with a four-electron deficiency per unit cell, and such a derivative with Sc substituting for Mg is an appropriate quasicrystal approximant (Im3macro). Such characteristics seem to be key factors in the formation of icosahedral quasicrystals.