Icosahedral alloy

F. Denoyer, X-Ray Diffraction Study of Slowly Solidified Icosahedral Alloys. Ini. Hargittai, ed., Quasicrystals, Networks, and Molecules of Fivefold Symmetry, VCH, New York, 1990, pp. 69-82. 

Fig. 8. Electron micrograph showing crystallization of icosahedral phase from glassy Pd—U—Si alloy.

I conclude that the evidence in support of the proposal that the so-called icosahedral and decahedral quasicrystals are icosatwins and decatwins of cubic crystals is now convincingly strong. I point out that there is no reason to expect these alloys to have unusual physical properties. 

Lithium has been alloyed with gaUium and small amounts of valence-electron poorer elements Cu, Ag, Zn and Cd. like the early p-block elements (especially group 13), these elements are icosogen, a term which was coined by King for elements that can form icosahedron-based clusters [24]. In these combinations, the valence electron concentrations are reduced to such a degree that low-coordinated Ga atoms are no longer present, and icosahedral clustering prevails [25]. Periodic 3-D networks are formed from an icosahedron kernel and the icosahedral symmetry is extended within the boundary of a few shells. 

Fig. 29. Icosahedral phase in electrodeposited Mn-Al alloys (a) bright field image (b) electron diffraction pattern showing 5-fold symmetry. Reproduced from Grushko et al. [126] by permission of Elsevier.

In a famous paper by Shechtman et al. (1984) electron diffraction patterns were shown of rapidly quenched and solidified aluminium-manganese alloys. Sharp diffraction peaks, suggesting long-range translational order, were observed with the presence however of five-fold symmetry (that is of a non-crystallographic symmetry see 3.6.1.1). By different orientation of the specimen five-fold axes (in 6 directions), three-fold axes (in 10 directions) and two-fold axes (in 15 directions) were identified with the subsequent observation of the existence also of an inver-sion centre the assignment of this phase to the icosahedral point group, m36, was defined. 

Icosahedral Al-Mg-Zn type with a quasi-lattice constant of about 520 pm and a concentration of free electrons of about 2.1 electrons per atom. Examples are represented by Li3CuAl6 (ar = 504 pm, super-space-group Pm35), Li3AuA16, Pd13Mg44Al43, CuMg4Al6, Mg32Zn52Ga16, Y-Mg-Zn andY-Zr-Mg-Zn alloys, etc. 

Among many fascinating properties, quasicrystals with high structural quality, such as the icosahedral AlCuFe and AlPdMn alloys, have unconventional conduction properties when compared with standard intermetallic alloys. Their conductivities can be as low as 450-200 (Qcm) [7]. Furthermore the conductivity increases with disorder and with temperature, a behaviour just at the opposite of that of standard metal. In a sense the most striking property is the so-called inverse Mathiessen rule [8] according to which the increases of conductivity due to different sources of disorder seems to be additive. This is just the opposite that happens with normal metals where the increases of resistivity due to several sources of scattering are additive. Finally the Drude peak which is a signature of a normal metal is also absent in the optical conductivity of these quasicrystals. 

Since the discovery of Shechtman et al. (1984) that the rapidly quenched Al-14% Mn alloy is quasicrystalline with icosahedral symmetry, there has been intense activity to explore such alloys to find out whether there would be a conceptual revolution in crystallography. Pauling (1985) proposed that the icosahedral symmetry results from multiple twinning of cubic crystals, but many features of these unique alloys, especially their electron diffraction patterns, cannot be understood on the basis of twinning alone. 

At present, a number of quasi-crystalline alloys with icosahedral, decagonal, and octagonal symmetry are synthesized by different methods. The quasicrystalline form of the solids turned out to be widespread in a great extent. The absence of the translation symmetry and the presence of numerous interstitial sites of the different types in the structure of icosahedral quasicrystals makes some of them interesting objects for hydride chemistry. We cannot wait for any sensational discoveries here, as the general laws of M-H interaction do not depend on matrix structure. However, encouraging results were obtained for icosahedral Ti45Zr38Nii7... 

Independent of Mackay s predictions and Shechtman s experiments, there was another line of research by Steinhardt and Levine, leading to a model encompassing all the features of shechtmanite (the original quasiperiodic alloy was eventually named so) and other materials that are symmetric and icosahedral, but nonperiodic [143], It was a perfect timing that as soon as they built up their model and produced its simulated diffraction pattern, they could see its proof from a real experiment. 

L. Pauling, Evidence from x-ray and neutron powder diffraction patterns that the so-called icosahedral and decagonal quasicrystals of MNA16 and other alloys are twinned cubic crystals. Proc. Natl. Acad. Sd. (USA) 84, 3951-3953 (1987). 

L. Pauling, Interpretation of so-called icosahedral and decagonal quasicrystals of alloys showing apparent icosahedral symmetry elements as twins of an 820-atom cubic crystal. Computers Math. Applic. 17, 337-339 (1989). 

P. Bak, Phenomenological theory of icosahedral incommensurate ( quasiperiodic ) order in Mn-Al alloys. Phys. Rev. Lett. 54, 1517-1519 (1985). 

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