A square quasicrystal

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Aug 24, 2018
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Quasicrystals (QCs) are complex. A short definition of a QC could be: an aperiodic material which exhibits long-range order with no translational symmetry, whilst displaying ‘unusual’ orders of rotational symmetry. Unusual means for example, 5-fold pentagonal or 10-fold decagonal. Examples of systems with quasicrystalline order include some intermetallic alloys, and mathematical constructs such as the Penrose tiling.

Despite the interest in n ≥ 5-fold rotationally symmetric quasicrystals, the level of complexity associated with their structures often makes it difficult to correlate physical properties to specific structural features. Therefore, it follows that a quasiperiodic system with a straightforward structure would be quite valuable as a stepping stone to understanding more complex arrangements.

One simple aperiodic structure is the 1-dimensional Fibonacci chain, which is composed of two segments: S and L. Starting with L, and applying substitution rules where L is replaced by LS, and S is replaced by L, we find: L, LS, LSL, LSLLS, LSLLSLSL… etc.

Using the Fibonacci chain, Ron Lifshitz (Tel Aviv University) constructed what is most likely the simplest 2-dimensional QC. By superimposing sets of orthogonal Fibonacci chains, he created what is known as a Fibonacci square grid. Unfortunately, the drawback is that the Fibonacci square grid has not been observed in any `natural’ quasicrystalline system. As Ron himself noted: “to the best of my knowledge, no alloys or real quasicrystals exist with the structure of the square … Fibonacci tiling”.

In our paper, we report the first observation of a physical system exhibiting a Fibonacci square grid structure. Our group has focused on inducing quasicrystalline order in adsorbates on QCs, typically either organic molecules or metals. To compare with our previous observations of fullerenes on 5-fold and 10-fold quasicrystal surfaces, we deposited C60 on the 2-fold surface of an Al-Pd-Mn quasicrystal. We chose C60 as an adsorbate as it can be modelled as a large, electron accepting atom.

Fullerenes decorate a Mn Fibonacci square grid on the 2-fold surface of an AlPdMn model. The 5-fold Mn atoms are decorated with a Penrose tiling.

Prior to our work, only two articles had reported investigations of the clean 2-fold Al-Pd-Mn surface using our primary techniques (Scanning Tunnelling Microscopy and Low Electron Energy Diffraction). One of these papers was from our own group; both are over 10 years old. The relative paucity of research on this surface made it attractive for further investigation.

As detailed in our paper, we observed the formation of a C60 Fibonacci square grid. This was due to bonding of C60 molecules to minority manganese atom sites at the surface. These manganese sites in turn were found to be distributed  in a square grid..

We are hopeful that the physical realisation of this simple QC structure leads to further work on this system, with potential for probing of physical properties to compare with predictions of theory. Of particular interest could be the production of quasiperiodic molecular magnetic arrays, photonic materials, or novel electronic devices.

Go to the profile of Sam Coates

Sam Coates

PhD Student, University of Liverpool

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