Quasicrystals move to the macroscopic scale

The Alhambra Palace in Granada, Spain is famous for its lavish decorations typical of Nasrid art. For the visitor who enjoys art and science, this is an ideal site that shows most of the plan's 17 paving methods on a regular basis. However, in the twentieth^H In the twentieth century, mathematicians discovered that it was also possible to tile a plane without a periodic structure. In the 1970s, Roger Penrose popularized this idea with examples of tilings based on two patterns (such as “kite” and “darts” tilings). Simple mathematical curiosity? No: In 1982, chemist Dan Shechtman observed a substance with an ordered, but not periodic, structure. This was the birth of “quasicrystals”.

With this discovery and the observation of natural quasi-crystals, the classical concept of crystalline materials had to be rethought. From the usual point of view, crystals are arranged, with a periodic arrangement of atoms; These configurations seem to be the only ones possible. Quasicrystals and their non-periodic structures have opened the way to the development of new materials with many interesting properties. They are often hard, with low coefficients of friction and non-stick properties, and are used as coatings for kitchen utensils. Some are also very good thermal and electrical insulators. They are also interesting optical and acoustic crystals, offering the possibility of manipulating electromagnetic or sound waves.

However, the semi-crystalline structure seemed to be reserved for the smallest scales: atomic, nanometer, and micrometer. In fact, at these scales, thermal agitation is the main factor in the formation of these non-periodic materials. But this force becomes less effective as the size of the elements increases. However, it might be interesting to create macroscopic quasicrystals to exploit their properties at new levels.

Inspired by numerical simulations that shed light on the spontaneous formation of non-periodic macroscopic systems, Andrea Platti, Giuseppe Fofé and their colleagues from the University of Paris-Saclay explored this route using millimeter-diameter steel balls. These balls are placed on a vibrating metal plate. The trick then is to use two types of beads of slightly different sizes. The smaller balls move by sliding slightly underneath the larger balls. Using this device, researchers observed the spontaneous formation of macroscopic quasicrystals!

How did the researchers ensure that the beads did not form an extensive periodic network? To study an atomic crystal, it is bombarded with a beam of electrons that are deflected by a grating. We then obtain a set of light points on the downstream detector (which is the Fourier transform of the spatial structure of the crystal lattice). Analysis of the pattern of these points of light makes it possible to deduce the periodic structure of the crystal. A quasicrystal produces the same type of shape, but contains points that are impossible to exist in a periodic lattice. Andrea Platti and his colleagues recorded the position of all the beads and performed a Fourier transform of this data, finally obtaining the equivalent of a diffraction pattern, confirming the non-periodic nature of their system.

At first glance, plate motions play the same role as thermal agitation at the smallest scales. However, the team showed that the self-assembly mechanism here is very different and more complex. In fact, while quasicrystals form on the smallest scales in equilibrium systems, here the device constantly dissipates energy due to the friction of the balls. This loss is compensated by an external power supply through plate vibrations. Hence, this phenomenon exists at the intersection of granular physics and nonequilibrium statistical physics, an area that is still not well understood and where many open questions arise.

This system is of theoretical interest for the study of non-equilibrium systems, but may also inspire applications. For example, by operating at wavelengths different from those found in microscopic quasicrystals, this system can act as a switch, rectifier, or logic element for wave conduction.