Since their discovery in 1984, several thousand papers have been published dealing with various aspects of quasicrystals. Despite this flurry of activity, questions concerning the development, structure, and physical properties of this new phase remain only partially answered. This article reviews investigations of the formation and stability of quasicrystals. A pedagogical approach is taken. A brief survey of atomic and structural models, defects, and metallurgical properties of selected systems is provided as necessary background. While most attention is focused on the icosahedral quasicrystalline phase, one section is devoted to another common quasicrystal, the decagonal phase. Aluminium based quasicrystals are most common and are reviewed here; the first review of titanium based quasicrystals is also provided.

Quasicrystals: structure and stability

Connecting the Chemical and Physical Viewpoints of What Determines Structure: From 1-D Chains to γ-Brasses Robert F. Berger, Peter L. Walters, Stephen Lee,* and Roald Hoffmann* Department of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853, United States Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States Department of Chemistry, University of Illinois, Urbana, Illinois 61801, United States

Connecting the Chemical and Physical Viewpoints of What Determines Structure: From 1-D Chains to γ-Brasses

The first observation of the Mossbauer effect with 86.5-keV γ rays from 155Gd nuclei was reported as early as 1962,1 only a few years after Mossbauer’s discovery of recoil-free emission and resonance absorption of γ rays by nuclei embedded in a solid.2 The further history of Gd Mossbauer spectroscopy is an illuminating example for the interplay of methodological developments on one side and of the evolving interest in rare-earth compounds, in their properties and their potential for technical applications on the other side.

Mössbauer Spectroscopy of New Materials Containing Gadolinium

In the present study we report on the formation mechanism of some binary Al-TM and ternary Al-Cu-TM (TM = transition metal) quasicrystals. We have found that the formation mechanism of quasicrystalline phases in the binary Al-TM system takes place at extremely high solidification rates, is linked to the location of the transition metal in the periodic table, depends upon the atomic radius ratio of the constituents, is composition sensitive, and as a result is strongly affected by the effective atomic radius ratio (aeff). Applying empirical criteria on the formation of ternary Al-Cu-TM quasicrystals we were able to calculate the composition range at which the formation tendency and stability of quasicrystalline phases is enhanced. The method presented can be viewed as an empirical criterion to find new and high quality quasicrystalline materials and to optimize the quasicrystalline material composition. Furthermore, it was observed that the stabilization mechanism of the quasicrystalline Al-Cu-(Fe, Co, Ru, Rh, Os, Ir) phases takes place when the atomic ratio (TM+Cu)/Al ranges from 0.46 to 0.69 and for aeff values between 4.10 and 7.30. At the same valence electron concentration, metastable icosahedral Al-Cu-(Cr, Mn) phases are formed at relatively smaller atomic ratios (TM+Cu)/Al and having higher aeff values in comparison to those of the stable D- and I-phases.

The significance of valence electron concentration on the formation mechanism of some ternary aluminum-based quasicrystals

The authors present here the determination of the distribution P(q) of the electric field gradient in Fe-doped Al-Si-Mn icosahedral and decagonal quasi-crystals and in the related crystalline phases, using in-field Mossbauer effect spectroscopy. The distribution P(q) for the quasi-crystalline compounds shows a bimodal, nearly symmetric form with P(0) approximately=0 and equal averages over positive and negative q=1/2eQVzz, -(q-) approximately=(q+) and equal standard deviations: sigma - approximately= sigma +. The results for the majority sign of the distribution P(q) will be compared to the results for the cubic, hexagonal and orthorhombic compounds. The results show that there are similarities in the local order between the icosahedral quasi-crystalline phase and the hexagonal phase. No evidence is found for a two-site model, which has recently been proposed by other authors.

https://iopscience.iop.org/article/10.1088/0953-8984/2/30/007/pdf

Crystalline and quasi-crystalline phases of the Al-Si-Mn system: a comparison of the 57Fe electric-field-gradient properties

In 1926 Hume Rothery discovered that for some simple alloys the electron to atom ratio e/a is a stability determining factor. We applied this energy band effect or Hume-Rothery rule to the quasicrystalline series Al80Mn20-xFex. The isomer shift of the Mossbauer spectra shows a maximum at x=9, where e/a=1.76. This strongly indicates a relatively low s-electron density, in agreement with the energy band effect.

Are quasicrystals hume-rothery alloys?

After some introductory remarks about quasicrystals, ME spectra of icosahedral AlMnFe-, AlCuFe- and TiNiFeSi-alloys are summarised. The results are interpreted in terms of the current understanding of the structure of quasicrystals. Further a ME-application to the stability criteria of quasicrystals is discussed. A dominant factor is the band splitting factor or the Hume-Rothery rule.

Quasicrystals

Mossbauer spectra of AlTFe-alloys with T=Cr or Mn, show a quadrupole splitting QS≈0.4 mm/s. This shows that the iron atom is not in an icosahedral site. In order to investigate the local symmetry further, we applied an external magnetic field Hext≈5T, so that the asymmetry parameter ν can be obtained. Using a one site approximation the results are: ν=0.7 for decagonal Al7(Mn0.7Fe0.3)2 and ν=0.8 for icosahedral Al6Cr0.7Fe0.3. This means that the iron atoms are in sites with a symmetry lower than axially symmetric. Most of the vertices in a Penrose lattice show such a symmetry.

Local symmetry in some quasicrystalline altfe alloys

Iron sites in quasicrystalline Al(TFe)-alloys have been investigated with Mossbauer spectroscopy. The quadrupole splitting of these materials is about 0.4 mm/s, showing that the iron atom is not in an icosahedral\((m\bar 3\bar 5)\) site. A measurement in an external magnetic field ofHext≈5 T yields the asymmetry parameter η=(Vxx−Vyy)/Vzz. The value of η enables one to decide between the applicability of some mathematical structure models of quasicrystals.

Local iron symmetry in quasicrystals

The isomer shift of binary iron alloys is related to the itineracy of the valence electrons. The problem of a volume correction in disordered alloys is discussed and further avoided by using data of intermetallic compounds. From a large selection of possible parameters a linear combination of the electronegativityφ* and the electron densitynws in the Wigner-Seitz cell seems to be a good choice for fitting the data. The problem that these parameters are of minor importance for the cohesion in transition metal alloys is discussed.

R. D. Werkman

Papers

Are quasicrystals hume-rothery alloys?

Quasicrystals

Local symmetry in some quasicrystalline altfe alloys

Local iron symmetry in quasicrystals

Isomer-shift in binary iron-alloys