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Quasicrystals – Materials That Should Not Exist

Quasicrystals - materials that shouldn't exist

“A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die and a new generation grows up that is familiar with it.”Max Planck

Dan Shechtman’s lab at the National Institute for Standards (NIST) in Gaithersburg, Maryland, was small and dominated by an almost 3 meters-high tower of a Transmission Electron Microscope (TEM), a device capable of seeing the tiniest parts of matter.

Shechtman has just completed his usual morning lab routine by inspecting the microscope, adjusting the electrical lenses, and skimming through the list of samples scheduled for the analysis. He wrote the date on the top of his lab book page – April 8, ’82, and loaded the sample in the microscope. It was an alloy produced by melt-spinning consisting of 86% of aluminum and 14% of manganese.

The beam of accelerated electrons pierced through the thin specimen and several illuminated green dots appeared on the phosphor screen forming the diffraction pattern.

A diffraction pattern Shechtman observed on the morning April 8, ’82.
A diffraction pattern Shechtman observed on the morning April 8, ’82.

There was something strange about this sample. “There could be no such thing,” he mumbled to himself. After inspecting a few different spots on the specimen, he observed the same anomaly. Finally, he wrote a note in his lab book next to the sample label: “10 fold ???” 

Shechtman’s lab book with a note “10 fold???” next to the sample label.
Shechtman’s lab book with a note “10 fold???” next to the sample label.

Why was Shechtman so perplexed by this particular diffraction pattern? The definition of a crystal at the time was: “A substance in which the constituent atoms, molecules, or ions are packed in a regularly ordered, periodical, three-dimensional pattern”.

Any crystalline material, due to its regular structure, acts as a grating through which the electrons can be diffracted. This process compels the electrons to concentrate in discrete spots on the detector.

Thus, formed diffraction pattern enables a skilled material scientist to visualise the crystal structure of the analysed material. Simply put, the dots that are further from the center correspond to smaller distances between crystal planes and vice versa.

SEM images of the aluminum/quasicrystal and 2124 aluminum alloy/quasicrystal. (a) 2124/AlCuFe. (b) 2124/AlPdMn. (c) Al/AlCuFe. (d) Al/AlPdMn. [9]

Furthermore, the symmetry of crystal structure can be identified from the number of dots belonging to the same feature (i.e. having the same distance from the center). For example, six dots would indicate a hexagonal (six-fold) symmetry typical for metals. Such crystal would resemble a honeycomb where hexagons are periodically and densely packed (Figure 1-left).

However, what Shechtman observed was a perfect diffraction pattern exhibiting 10-fold symmetry, which could stem from a decagon- or pentagon-like arrangement of atoms. As it is impossible to pack pentagons densely in a periodical pattern (Figure 1-right), such crystal structure was at the time believed to be absurd.

Figure 1. Left) Dense periodic packing of hexagons; Right) Dense packing of pentagons always leaves some space unfilled.

Knowing that his observation contradicts the fundamental laws of crystallography, Shechtman has spent the rest of the day unsuccessfully trying to find a reasonable explanation. Nevertheless, he decided to show the results to the group leader, famous material scientist John W. Cahn. He was at first skeptical but eventually encouraged Shechtman to further pursue the investigation of the strange material.

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Two years later and after a few rejections from renowned scientific journals, they published a paper in Metallurgical Transactions A. [2] Soon after, Shechtman and his work met with a rebuff from the crystallographic community. One senior colleague even accused him of being a disgrace and asked him to leave the group.

Over time, as other scientists started reproducing his results the opposition dwindled. The term ‘quasiperiodic crystals’ or ‘quasicrystals’ was coined to account for their exotic trait of regularity without three-dimensional periodicity. In 1991, French scientists conducted a neutron diffraction study on Al-Cu-Fe quasicrystal of 2 millimeters and obtained a discrete diffraction pattern corresponding to five-fold symmetry.[3]

Dan Shechtman, 1983. (Credit: Technion – Israel Institute of Technology)

This was a strong proof that five-fold symmetry was not an oddity found only on the nanoscale, but a real feature of certain aluminium alloys. To account for the new group of materials, The International Union of Crystallography decided in 1991 to change the old definition of crystal to “A material having an essentially distinct diffraction pattern “.

Still, some scientists persisted in opposition. Such was the double Nobel Prize winner Linus Pauling who was, until his death in 1994, strongly against the idea of quasicrystals, frequently stating: “There are no quasicrystals, only quasi-scientists.”

The similarity between the structure of Islamic decorative patterns and quasicrystals. Quasiperiodic patterns found in several Moroccan historical buildings constructed in the 14th century.

How is it then possible to reconcile five- and ten-fold symmetry with dense packing? The crucial part of this puzzle came from the work of Roger Penrose, an English mathematical physicist famous for his work on black holes. In his paper published in 1974, “The role of aesthetics in pure and applied mathematical research” [4], he demonstrated how an aperiodic pattern with five-fold symmetry can emerge from the particular arrangement of two simple building blocks.

That pattern was later named Penrose tiling (Figure 2a). In contrast to an ordinary tilling (Figure 2b) and despite being arranged in an orderly manner (structure regularity), not a single motif of this pattern is repeated along any direction (lack of periodicity). Notice that tiles can also be arranged densely but without any regularity of structure (Figure 2c).

Figure 3. Three different ways of dense area coverage corresponding to three kinds of material structure: quasicrystals, ordinary crystals, and glasses.
Figure 2. Three different ways of dense area coverage corresponding to three kinds of material structure: quasicrystals, ordinary crystals, and glasses.

These three ways of arranging tiles can be regarded as 2D interpretations of material structure. Accordingly, irregular tiling in Figure 2c corresponds to glasses, periodic and regular tiling in Figure 2b to classic conception of a crystal, whereas the regular but aperiodic structure shown in Figure 2a resembles the structure of a quasicrystal.

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Quasicrystals today are roughly divided into two categories: two-dimensional and rarer three-dimensional. Two-dimensional quasicrystals are periodic along one axis, whereas the three-dimensional ones are aperiodic in every direction.

In the latter case, a three-dimensional equivalent of Penrose tiling emerges from dense packing of dodecahedra (Figure 3-left). Similar to ordinary crystals, three-dimensional quasicrystals on macroscopic scale favour shapes that resemble their microscopic structure (Figure 3-right).

Figure 3. Left) Artistic representation of dense packing of dodecahedra in space (source: Pinterest, Regolo Bizzi). Right) A Ho–Mg–Zn quasicrystal in the shape of a dodecahedron [5].

It often happens in science that discoveries are preceded by natural appearance and practical applications. Once the new concept is introduced, its numerous manifestations seem to be everywhere.

For example, quasicrystal-like decagonal patterns can be found in Islamic art from the 15th century in the Darb-e-Imam shrine in Ishafan, Iran (Figure 4) [6], while a natural quasicrystal was found in Khatyrka meteorite in 2009.[7]

Figure 5. The decagonal pattern on a spandrel from the Darb-e-Imam shrine
Figure 4. The decagonal pattern on a spandrel from the Darb-e-Imam shrine.

Quasicrystals are hard and brittle materials and their use is currently limited to only a few niche applications. Low-friction Al-Cu-Fe-Cr quasicrystals are used as a coating for frying pans, while the addition of small quasicrystal particles can be used for the hardening of steel.

Nevertheless, quasicrystal research is ongoing and new fascinating properties (e.g. superconductivity [8]) are being continuously discovered.

Dan Shechtman, a scientist who despite all the opposition and common wisdom dared to stand for the idea of quasicrystals was in 2011 awarded with Nobel Prize for Chemistry. When asked to advise aspiring scientists, he said, “Look for something that seems impossible, look for something that cannot be”.

"Materials are essential not just for technical progress, but for the advancement of human civilization. Knowledge about materials should, therefore, be easily accessible to everybody, experts and non-experts alike."
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[1] D. Gratias and M. Quiquandon, “Discovery of quasicrystals: The early days,” Comptes Rendus Phys., vol. 20, no. 7–8, pp. 803–816, 2019.
[2] D. Shechtman and I. A. Blech, “The microstructure of rapidly solidified Al6Mn,” Metall. Trans. A, vol. 16, no. 6, pp. 1005–1012, Jun. 1985.
[3] M. Cornier-Quiquandon et al., “Neutron-diffraction study of icosahedral Al-Cu-Fe single quasicrystals,” Phys. Rev. B, vol. 44, no. 5, pp. 2071–2084, Aug. 1991.
[4] R. Penrose, “The role of aesthetics in pure and applied mathematical research,” Bull. Inst. Math. Appl., vol. 10, pp. 266–271, 1974.
[5] I. R. Fisher et al., “Magnetic and transport properties of single-grain R-Mg-Zn icosahedral quasicrystals,” Phys. Rev. B, vol. 59, no. 1, pp. 308–321, Jan. 1999.
[6] P. J. Lu and P. J. Steinhardt, “Decagonal and Quasi-Crystalline Tilings in Medieval Islamic Architecture,” Science (80-. )., vol. 315, no. 5815, pp. 1106–1110, Feb. 2007.
[7] L. Bindi et al., “Evidence for the extraterrestrial origin of a natural quasicrystal,” Proc. Natl. Acad. Sci. U. S. A., vol. 109, no. 5, pp. 1396–1401, 2012.
[8] K. Kamiya et al., “Discovery of superconductivity in quasicrystal,” Nat. Commun., vol. 9, no. 1, p. 154, Dec. 2018.
[9] Wolf, Witor & Aliaga, Luis César & Travessa, Dilermando & Afonso, Conrado & Bolfarini, C. & Kiminami, Claudio & Botta, Walter. (2016). Enhancement of Mechanical Properties of Aluminum and 2124 Aluminum Alloy by the Addition of Quasicrystalline Phases. Materials Research. 19. 74-79. 10.1590/1980-5373-MR-2016-0088.

*This article is the work of the guest author shown above. The guest author is solely responsible for the accuracy and the legality of their content. The content of the article and the views expressed therein are solely those of this author and do not reflect the views of Matmatch or of any present or past employers, academic institutions, professional societies, or organizations the author is currently or was previously affiliated with.

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