Fascinating quasicrystals

Walter Steurer

Walter Steurer studied chemistry and received his PhD at the University of Vienna. In 1980, he moved to the University of Munich, Germany, where he concluded his habilitation thesis in 1987. From 1992 until 1993, he was professor of crystallography at the University of Hanover, Germany. After declining calls to the Universities of Hamburg and Munich, Germany, he has been professor of crystallography at the ETH and University of Zurich since 1993. At present, his research interests comprise structural studies of quasicrystals and their phase transformations, the modeling of order/disorder phenomena, and higher-dimensional crystallography.

Nobody believed Dan Shechtman when he presented his discovery, made on April 12th, 1982, to his colleagues. “A long-range ordered material with icosahedral diffraction symmetry? Impossible!” – this was the reflex of those knowing the laws of crystallography: three-dimensional (3D) lattice periodicity is incompatible with icosahedral point group symmetry. Consequently, not only the eminent chemist and double Nobel-laureate Linus Pauling tried to explain Shechtman's findings with multiple orientational twinning of cubic compounds with giant unit cells. It needed a paradigm change for asking the obvious question: “Is there any kind of long-range order that could be compatible with icosahedral diffraction symmetry?” The answer is amazingly simple: “Yes. Lattice symmetry is a prerequisite of sharp Bragg reflections, indeed, but the dimensionality of the lattice is not restricted to three.” Since icosahedral point symmetry leaves already a 6D lattice invariant, the structure of an icosahedral quasicrystal can be described as a 3D cut of a 6D hypercrystal structure. According to the properties of the Fourier transform, the diffraction pattern of the quasicrystal then corresponds to a projection of the 6D diffraction pattern onto the 3D physical space. The mathematical studies on the problems of diffraction from general non-periodic structures are discussed in the contribution of M. Baake and U. Grimm (DOI: 10.1039/C2CS35120J).

Today thermodynamically stable quasicrystals are known not only in many intermetallic systems but also in self-assembled colloidal systems, ter-block star-copolymers and even packings of hard tetrahedra, for instance. While in the case of metallic quasicrystals the diffraction symmetries are decagonal or icosahedral, in the latter case they are almost exclusively dodecahedral. Unfortunately, the invited reviews for this kind of quasiperiodic systems as well as for the structure and properties of surfaces of quasicrystals could not be prepared within the given timeframe for this themed issue. I just want to point out that the surfaces of metallic quasicrystals are bulk-terminated and do not reconstruct. Furthermore, the surfaces show flat terraces and, from their general appearance, are comparable to surfaces of periodic intermetallics. A large variety of elements have been deposited in different concentrations on the surfaces and the resulting ordering in the epitaxial layers studied. For more information see one of the recent reviews.

Without electron microscopy and electron diffraction, quasicrystals would not have been discovered. The identification of phases in the process of the study of phase diagrams has usually been done employing powder X-ray diffraction. This method has the crucial disadvantage that it does not provide any direct symmetry information. Indeed, we know today that phases already synthesized in the thirties of the last century were quasiperiodic but not identified as that. A tutorial review on the study of quasicrystals by electron microscopy has been provided by E. Abe (DOI: 10.1039/C2CS35303B).

The diffraction patterns even of perfect quasicrystals contain diffuse parts beside the Bragg reflections. They consist of thermal and phason diffuse scattering, TDS and PDS, respectively, originating from phonon and phason modes. The signature of phason modes in quasicrystals are correlated atomic jumps in double-well potentials. In contrast, phonon modes lead to correlated continuous atomic displacements. A detailed discussion of experimental observation of phason modes and the theoretical background of the hydrodynamic theory, needed for their interpretation, are presented by M. de Boissieu (DOI: 10.1039/C2CS35212E).

Phenomenologically, the formation and growth of intermetallic phases is well understood. This is different when it comes to atomistic modelling of the processes from nucleation to the growth of macroscopic crystals of complex intermetallics. How does the thousandth atom find its site in a giant unit cell with thousands of atoms? Which role does lattice periodicity play on this scale? And what is the growth mechanism for quasiperiodic structures? These questions are discussed in the review by W. Steurer (DOI: 10.1039/C2CS35063G).

Quite early after the discovery of quasicrystals, a particular valence electron concentration was identified to be necessary for their stability. This was also the rationale underlying the search for new quasicrystals. Its success proved the validity of this hypothesis, but does not exclude the existence of quasicrystals stabilized by other mechanisms, which would not have been found applying this search strategy. The theory of the electronic stabilization of quasicrystals and the non-trivial determination of proper values of the electron concentration in quasicrystals is reviewed by U. Mizutani et. al. (DOI: 10.1039/C2CS35161G).

Materials with strange structures could show strange physical properties – this assumption was the driving force for many physicists jumping into QC research immediately after learning about the discovery. Was this assumption justified? This question is addressed in the review by J. Dolinšek (DOI: 10.1039/C2CS35036J). Since quasiperiodicity is a long-range-order property, its influence should be largest for the electronic structure and transport properties. The results of experimental and theoretical studies on the electrical and thermal conductivity are discussed and the true intrinsic properties of quasicrystalline phases characterized.

Also the mechanical properties were expected to significantly differ from those of periodic intermetallic phases. On one hand this is caused by the high symmetry, on the other hand by the quasiperiodic long-range order. In the case of the highest-symmetric periodic phases, i.e. the cubic ones, the number of independent coefficients of the elasticity tensor equals three. In the case of icosahedral quasicrystals, there is no difference from isotropic amorphous materials, which show only two coefficients. Since plastic deformation of periodic structures is governed by the movement of dislocations, which is simplest in small-unit cell periodic structures, we can expect quite a different behaviour for quasicrystals. This topic is discussed in detail in the contribution by M. Feuerbacher (DOI: 10.1039/C2CS35150A).

Are there any applications of quasicrystals or cluster-based intermetallics of similar complexity, in general? J.-M. Dubois (DOI: 10.1039/C2CS35110B) addresses this question with a focus on adhesion and friction, but also considering other potential fields of applications such as catalysis.

Footnote

† Part of a themed issue on Quasicrystals in honour of the 2011 Nobel Prize in Chemistry winner, Professor Dan Shechtman.

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