A detailed study of the atomic structure is necessary for a full understanding of the structure and properties of icosahedral quasicrystals. This paper presents a study of the modulated icosahedral phase of Al-Fe-Cu using single-crystal X-ray diffraction. The use of a single-crystal sample allowed us to obtain highly accurate data on the diffraction pattern and determine the parameters of the structure modulation.
The experimental data were obtained on a diffractometer equipped with a two-dimensional detector. Analysis of diffraction reflections revealed the presence of additional peaks surrounding the main Bragg reflections, which indicates the modulated nature of the structure. The reflections were indexed in six-dimensional space, which allowed us to take into account the icosahedral symmetry of the quasicrystal.
The obtained results indicate that the modulation of the structure in Al-Fe-Cu is associated with periodic deviations of atomic positions from the ideal icosahedral lattice. These deviations can be caused by the presence of compositional disorder or internal stresses in the structure. Further analysis of the data will allow us to construct a model of the modulated structure and determine the amplitudes and directions of atomic displacements.
Single crystal X-ray diffraction is a powerful tool for studying the atomic structure of quasicrystals. The results can be used to improve our understanding of the physical and chemical properties of these unique materials.
For quantitative description of the modulated structure, formalism of higher dimensions was applied. Six-dimensional description allows to represent three-dimensional quasicrystal as a section of periodic structure in six-dimensional space. Modulation is manifested in the form of deviations of atomic surfaces from the ideal form, which leads to the appearance of additional diffraction reflections.
A procedure for refining the structural parameters was carried out, including determination of atomic coordinates, population factors and atomic displacement parameters. Accounting for anharmonic vibrations of atoms allowed us to improve the convergence of the model with experimental data. Analysis of the electron density showed the presence of pronounced peaks corresponding to the positions of Al, Fe and Cu atoms.
The obtained model of the modulated structure allows us to explain the observed diffraction pattern and gives an idea of the atomic structure of the icosahedral phase of Al-Fe-Cu. The preferred positions for atoms of various elements, as well as the nature of their displacements from the ideal icosahedral lattice, are revealed.
The presented study contributes to the understanding of the nature of modulated structures in quasicrystals and opens up new possibilities for studying their properties. Further studies aimed at studying the dynamics of atoms and the effect of temperature on the modulation of the structure will provide a more complete picture of these unique materials.
Author: N. Menguya, M. deBoissieu, P. Guyot, M. Audier, E. Elkaim, J. P. Lauriat
Institute: Laboratory of Thermodynamics and Physical Chemistry of Metals, UA CNRS 29, ENSEEG BP 75, 38402 Saint-Martin-d’Hères, France, LURE/CNRS/CEA/MEN, Bat. 209D, 91405 Orsay, France