On December 18, 2025, a regular session of the interfaculty scientific seminar “Modern Problems of Physics and Materials Science,” led by the Head of the ECT Department, Professor A.S. Opanasyuk, took place in a remote format. The seminar featured a report by Dr. Sc. Serhiy Malykhin, Head of the Department of Physics of Metals and Semiconductors at the National Technical University “Kharkiv Polytechnic Institute” (NTU “KhPI”), titled “Quasicrystals: Discovery, Structural Features, and Scientific Results of Ukrainian Scientists.” In his presentation, the speaker familiarized the audience with research conducted in Ukraine over the past few years and at the department he heads in Kharkiv.
Since ancient times, fifth-order symmetry has been associated with magic and mysticism. One can recall the stars on the flags of many countries or the famous painting “Vitruvian Man” (originally known as “The Proportions of the Human Body according to Vitruvius”) by the great Renaissance artist Leonardo da Vinci. It is known that fifth-order symmetries are frequently found in nature within living systems; however, it was long believed that they did not occur in inanimate nature. Indeed, such symmetry is impossible in ideal crystals due to the translational symmetry of crystal lattices; atoms can only form 1st, 2nd, 3rd, 4th, and 6th-order axes, as a fivefold rotation (by 72°) does not allow atoms to precisely repeat their positions when filling space without breaking the lattice periodicity.
However, reality, as always, proved to be more multifaceted than theory. Structures with fivefold symmetry, named quasicrystals, were first observed by Dan Shechtman in electron diffraction experiments on a rapidly cooled Al6Mn alloy conducted on April 8, 1982. For this discovery, he was awarded the Nobel Prize in Chemistry in 2011. The first quasicrystalline alloy he discovered was named “Shechtmanite.”
Shechtman’s paper was accepted for publication twice and was eventually published in a condensed form, co-authored by prominent specialists I. Blech, D. Gratias, and J. Cahn. The resulting diffraction pattern contained sharp (Bragg) peaks typical of crystals but exhibited an overall icosahedral point symmetry—specifically, a fifth-order symmetry axis, which is impossible in a three-dimensional lattice. Initially, the diffraction experiment allowed for an explanation involving multiple crystal twins grown into grains with icosahedral symmetry. However, subsequent, more refined experiments proved that the symmetry of quasicrystals is present at all scales down to the atomic level, confirming that these unusual substances are indeed a new form of matter organization.
It later became clear that physicists had encountered quasicrystals long before their official discovery, particularly while studying Debye-Scherrer powder diffraction patterns from intermetallic grains in aluminum alloys in the 1940s. At that time, icosahedral quasicrystals were mistakenly identified as cubic crystals with a large lattice constant. Predictions regarding the existence of icosahedral structures in quasicrystals were made in 1981 by Kleinert and Mackey. Currently, hundreds of types of quasicrystals are known, exhibiting icosahedral point symmetry, as well as decagonal, octagonal, and dodecagonal symmetries.
Serhiy Malykhin discussed the synthesis of such quasicrystals and the study of their properties in Ukraine.є
The seminar was conducted using a new methodology and was organized by the SumDU Center for Personnel Potential Development. This made it possible to reach a wider audience of lecturers and students through notifications in the participants’ personal accounts. From now on, participation in the seminar grants hours that can be credited toward professional development under the cumulative system.
