Icosahedral quasicrystals (i-phases) are exotic materials that occupy an intermediate position between periodic crystals and amorphous structures. Their unique properties, such as forbidden axes of high-order symmetry (for example, five-fold symmetry), order at large distances without translational periodicity, and unusual electronic structure, are of great interest from both fundamental and applied points of view. Studying the dynamic properties, in particular, the propagation of elementary excitations, allows us to better understand the nature of these materials and their relationship to the atomic structure.
In periodic crystals, the elementary excitations describing collective vibrations of atoms are phonons. In quasicrystals, in contrast to crystals, the dynamics of the atomic grid is characterized by the presence of two types of excitations: phonons associated with elastic deformations and phasons due to rearrangements in the quasiperiodic atomic structure. Phasons are specific to quasicrystals and describe transitions between different local configurations of atoms, while maintaining order over large distances. The interaction between phonons and phasons has a significant effect on the thermal, elastic, and diffusion properties of quasicrystals.
The i-Al62Cu25. 5Fe12. 5 quasicrystal is one of the most well-studied and stable icosahedral quasicrystals. It has a high quality of structure and is relatively easy to study experimentally. In this regard, it serves as a model object for studying the fundamental properties of quasicrystals, including their dynamics.
Various experimental methods are used to study the dynamic properties of quasicrystals, including inelastic neutron scattering (INS), inelastic X-ray scattering (IXS), and ultrasonic measurements. INS allows you to directly measure the dispersion curves of phonons and phasons, as well as determine their energies and lifetimes. IXS, due to its higher energy and momentum resolution, can be used to study dynamics at higher frequencies and wave vectors. Ultrasonic measurements provide information about elastic constants and the speed of sound, which makes it possible to estimate the contribution of phonons to elastic properties.
Numerous studies performed using various experimental methods have provided a detailed picture of the dynamic properties of the i-Al62Cu25.5Fe12. 5 quasicrystal. In particular, it was found that the phonon modes in this quasicrystal are similar to phonons in ordinary aluminum alloys, but differ in a higher degree of attenuation, which is due to the disordered atomic structure. Low-energy phase modes, which are absent in crystals and are a characteristic feature of quasicrystals, are found. These modes have a significant effect on thermal conductivity and other transport properties.
Phonon spectrum: Studies of inelastic neutron scattering have shown that the phonon spectrum of i-Al62Cu25. 5Fe12. 5 has a complex structure reflecting the quasiperiodicity of the atomic grid. A broadening of phonon lines is observed in comparison with ordinary crystals, which indicates the presence of anharmonic processes and phonon scattering at structural defects.
Phase modes: Experiments on inelastic X-ray scattering and theoretical calculations indicate the existence of low-energy phase modes in i-Al62Cu25, 5Fe12, 5. These modes are associated with rearrangements in the quasi-periodic structure and are characterized by a low propagation velocity.
Phonon-phason interaction: The interaction between phonons and phasons leads to renormalization of their energy spectra and the appearance of additional scattering channels. Experimental data indicate a strong relationship between phonons and phasons in i-Al62Cu25.5Fe12. 5,especially in the low-frequency region.
To interpret experimental data and gain a deeper understanding of the dynamic properties of quasicrystals, various theoretical methods are used, including molecular dynamics modeling (MD), finite element analysis (FEM), and analytical approaches based on the theory of elasticity of quasicrystals.
Molecular dynamics: MD modeling allows you to directly track the movement of atoms in a quasicrystal and calculate dynamic correlation functions, which are then used to determine the phonon and phase spectra. This method requires a lot of computational resources, but allows you to take into account anharmonic effects and complex structural defects.
Finite element method: FEM is used for modeling elastic deformations and calculating phonon modes in quasicrystals on large scales. This method is well suited for studying low-frequency oscillations, but it does not allow us to take into account the atomic structure in detail.
Theory of elasticity of quasicrystals: Analytical approaches based on the phenomenological theory of elasticity of quasicrystals allow us to obtain general relations between elastic constants and sound velocities. These approaches are useful for interpreting ultrasonic measurements and for establishing the relationship between macroscopic and microscopic properties of quasicrystals.
The dynamics of the atomic grid has a significant impact on a number of physical properties of quasicrystals, including thermal conductivity, elastic properties, electrical conductivity, and diffusion.
Thermal conductivity: The thermal conductivity of quasicrystals is usually significantly lower than that of their corresponding crystalline counterparts. This is due to the strong scattering of phonons on the disordered structure and on phasons. Low-energy phase modes make a significant contribution to heat transfer, especially at low temperatures.
Elastic properties: Quasicrystals have unusual elastic properties due to the presence of phasons. They exhibit abnormally high elasticity and a low Poisson’s ratio. The interaction between phonons and phasons leads to the dependence of elastic constants on temperature and frequency.
Electrical conductivity: The electrical conductivity of quasicrystals is characterized by a complex temperature dependence and can be sensitive to the presence of structural defects. Electron scattering by phonons and phasons plays an important role in the formation of electronic properties.
Diffusion: The diffusion of atoms in quasicrystals occurs by complex mechanisms involving transitions between different local configurations of atoms. Phasons can act as intermediaries in the diffusion process, facilitating the transition of atoms between different positions.
Studying the dynamics in the icosahedral quasicrystal i-Al62Cu25, 5Fe12, 5 has provided valuable information about phonons, phasons, and their interactions. Experimental and theoretical studies have confirmed the presence of low-energy phase modes, which have a significant effect on the thermal, elastic, and transport properties of quasicrystals.
Despite the progress made, many questions remain open. It is necessary to further study the dynamics of quasicrystals using more advanced experimental methods and more accurate theoretical models. In particular, an important area is the study of the influence of structural defects, impurities, and external influences (temperature, pressure) on the dynamic properties of quasicrystals.
Understanding the dynamics of the atomic grid of quasicrystals is essential for developing new materials with unique properties, such as thermoelectric materials, catalysts, and functional coatings. In the future, we can expect new technologies based on the use of quasicrystals, due to a deep understanding of their fundamental properties. The development of computational materials science using machine learning methods will make it possible to predict the dynamic properties of new quasicrystalline structures and speed up the process of searching for materials with specified characteristics. In particular, it is promising to develop algorithms that can efficiently find local energy minima in the complex energy landscape, which is characteristic of quasicrystals and amorphous alloys. This will make it possible to more accurately model the atomic structure and dynamics, as well as predict the stability of new quasicrystalline phases.
Author: R.A. Brand, J. Voss, Y. Calvayrac
The Institute: Department of Physics, Gerhard-Mercator-Universität Duisburg, D-47048 Duisburg, Germany, C.E.C.M./C.N.R.S., 15 rue G. Urbain, F-94407 Vitry cédex, France