The study of the phonon density of states (DOS) in quasicrystals (QCs) is key to understanding their thermal and transport properties. The icosahedral QC Al62Cu25.5Fe12.5 is an archetypal material exhibiting ideal long-range order but lacking the translational symmetry characteristic of conventional crystals. This leads to unique features in the vibrational spectrum, significantly different from periodic structures.
Experimental determination of the FPS in Al62Cu25.5Fe12.5 is associated with a number of difficulties caused by the need to obtain sufficiently large and perfect samples, as well as the high level of neutron absorption by iron. Nevertheless, modern methods of inelastic neutron scattering allow obtaining fairly accurate information on vibrational modes in a wide energy range.
To study the vibrational density of states (VDS) in the i-AlCuFe quasicrystal, namely in i-Al57Cu25.5Fe12.5 samples with different isotopic compositions, the methods of inelastic nuclear resonance absorption (INRA) of X-rays and time-of-flight inelastic neutron scattering (TOF) were used. INRA allows one to measure the partial VDS of iron, while TIF gives a neutron-weighted “generalized” VDS.
The obtained data revealed an unexpected feature: the partial CPS of iron is characterized by a single pronounced peak. Neutron-weighted generalized CPS for different copper (natural Cu and 65Cu) and iron (natural Fe and 57Fe) isotopes shows that the partial CPS of copper also has a significant enhancement, but at a significantly lower energy.
These results are discussed in the context of the icosahedral Kac-Gratias quasicrystalline model and heat capacity data that indicate a discrepancy between the speed of sound, heat capacity, and the low-energy limit of the CPS.
Theoretical calculations of the FPS in the Al62Cu25.5Fe12.5 QC are usually based on molecular dynamics methods and first-principles calculations. For adequate modeling, it is necessary to take into account the complex atomic structure, including the presence of icosahedral clusters and the features of their interaction. Comparison of theoretical and experimental data allows us to verify the models and obtain a deeper understanding of the nature of vibrational excitations in the QC.
Analysis of the obtained FPS shows the presence of features not observed in conventional crystals, such as a fractal structure and an excess of low-frequency modes. These features are associated with the absence of translational symmetry and the presence of localized vibrational modes. The study of the FPS in the Al62Cu25.5Fe12.5 QC contributes to the development of fundamental knowledge about the lattice dynamics in disordered systems and opens up new possibilities for creating materials with unique thermal properties.
Author: R. A Brand, G Coddens, A. Chumakov, A.-J Dianoux, Y Calvayrac
Institute: Department of Physics, Gerhard Mercator University Duisburg, D-47048 Duisburg, Germany, Leon Brillouin Laboratory, CEA/CNRS, F-91191 Gif-sur-Yvette, France, European Synchrotron Radiation Facility, BP 220, F-38043 Grenoble, France, Institut Laue-Langevin, BP 156, F-38043 Grenoble, France, CECM/CNRS, 15 rue G. Urbain, F-94407 Vitry sur Seine Cedex, France