Use sound waves to create patterns that are never repeated

Mathematicians and engineers at the University of Utah have teamed up to show how ultrasound waves can organize carbon particles in water into a kind of pattern that never repeats. The results, according to them, can lead to materials called “quasi-crystals” with personal magnetic or electrical properties.

The research is published in Physical overview letters.

“Quasi-crystals are interesting to study because they have properties that crystals do not have,” says Fernando Guevara Vasquez, associate professor of mathematics. “It has been shown to be stiffer than similar periodic or disordered materials. They can also conduct electricity or scatter waves in different ways than crystals.”

Non-patterns

Suggest a chessboard. You can take a two-by-two square of two black tiles and two white (or red) tiles and copy and paste to get the whole checkerboard. Such “periodic” structures, with patterns that do repeated, occurs naturally in crystals. Take, for example, a grain of salt. At the atomic level, it is a lattice-like lattice of sodium and chloride atoms. You can copy and paste the grid of one part of the crystal and find a match in any other part.

But a quasi-periodic structure deceives. One example is the pattern called Penrose tiles. At first glance, the geometric diamond-shaped tiles appear in a regular pattern. But you can not copy and paste this pattern. This will not be repeated.

The discovery of quasi-periodic structures in some metal alloys by materials scientist Dan Schechtman won a 2011 Nobel Prize in Chemistry and began the study of quasi-crystals.

Since 2012, Guevara and Bart Raeymaekers, associate professor of mechanical engineering, have been collaborating on the design of materials with structures tailored to the microscale. They initially did not want to create quasi-periodic materials – their first theoretical experiments, led by China Mauck, were a doctoral student in mathematics, focusing on periodic materials and on what particle patterns it would be possible to use ultrasound waves. In each dimensional plane, they found that two pairs of parallel ultrasonic converters are sufficient to arrange particles in a periodic structure.

But what would happen if they still had a few inverters? To find out, Raeymaekers and graduate student Milo Prisbrey (now at Los Alamos National Laboratory) provided the experimental instruments, and mathematics professor Elena Cherkaev provided experience with the mathematical theory of quasi-crystals. Guevara and Mauck did theoretical calculations to predict the patterns that the ultrasound recorders would create.

Create the quasi-periodic patterns

Cherkaev says that quasi-periodic patterns can be viewed as using a cut-and-paste technique instead of a cut-and-paste approach.

If you are cutting-and-projecting to design quasi-periodic patterns on a line, start with a square grid in a plane. Then draw or cut a line so that it passes through only one grid knot. This can be done by drawing the line at an irrational angle by using an irrational number such as pi, an infinite series of numbers that are never repeated. Then you can project the nearest grid buttons on the line and be sure that the patterns of the distances between the points on the line are never repeated. They are quasi-periodic.

The approach is similar in a two-dimensional plane. “We start with a grid or a periodic function in a higher-dimensional space,” says Cherkaev. “We cut an airplane through this space and follow a similar procedure to limit the periodic function to an irrational 2-D cut.” When using ultrasound transducers, as in this study, the transducers generate periodic signals in that higher-dimensional space.

The researchers set up four pairs of ultrasound converters in an octagonal stop sign arrangement. “We knew this would be the simplest setup where we could demonstrate quasi-periodic particle arrangements,” says Guevara. “We also had limited control over the signals that had to be used to drive the ultrasound converters; we could actually only use the signal or its negative use.”

In this octagonal setup, the team placed small carbon nanoparticles suspended in water. Once the inverters turned on, the ultrasound waves guided the carbon particles into place and created a quasi-periodic pattern, similar to a penrose tile.

“After conducting the experiments, we compared the results with the theoretical predictions and got a very good agreement,” says Guevara.

Custom materials

The next step would be to produce a material with a quasi-periodic pattern setup. It would not be difficult, says Guevara, if the particles hung in a polymer instead of water that could be hardened or hardened once the particles were in position.

“With this method, we can create quasi-periodic materials that are 2-D or 3-D and that can have essentially any of the common quasi-periodic symmetries by choosing how we arrange the ultrasound converters and how we drive them,” says Guevara. .

It remains to be seen what the material can do, but an ultimate application could be to create materials that can manipulate electromagnetic waves such as those using 5G cellular technology today. Other well-known applications of quasi-periodic materials include non-stick coatings, due to their low coefficient of friction, and heat-insulating coatings, says Cherkaev.

Another example is the hardening of stainless steel by the introduction of small quasi-crystalline particles. The press release for the 2011 Nobel Prize in Chemistry states that quasi-crystals ‘can strengthen the material like armor’.

Thus, according to the researchers, we can hope for many new exciting applications of these new quasi-periodic structures created by the composition of ultrasound particles.