After the epoch-making discovery of quasicrystals (QC), a question that immediately emerged was how would this new type of long-range order affect dynamical properties such as lattice vibrations? Mainly inelastic neutron scattering (INS) had been applied to study the phonon dynamics in QC, resulting in a neutron-weighted density of states (DOS) from which it has proved difficult to obtain the element-partial DOS. This renders a stringent comparison between model structures and measurements almost impossible. Such INS experiments for quasicrystals show smooth DOS functions while simulations indicate much more structure. In order to obtain such a partial DOS, we have applied nuclear inelastic scattering of synchrotron radiation in a QC enriched in 57Fe isotope [1]. The studies were made at the Nuclear Resonance Beamline ID18 where a high-resolution monochromator is available with 0.8 meV resolution. The product of nuclear absorption (atomic fluorescent radiation, delayed to synchrotron pulse) is counted as a function of the energy detuning with respect to the much sharper nuclear resonance. The sample studied was a powder of i-Al62Cu25.557Fe12.5, a well characterised stable quasicrystal.

Figure 65
Fig. 65: Energy spectrum of nuclear inelastic absorption of synchrotron radiation in i-Al 62Cu 25.5 57Fe 12.5 quasicrystal at room temperature and instrumental function of the energy spectrometer. Solid lines are to guide the eye. 

Figure 65 shows the instrumental function (single peak at zero energy), and the energy spectrum of nuclear inelastic absorption, which includes phonon creation and annihilation sidebands. The resulting iron-partial DOS (after correcting for multi-phonon contributions) is shown in Figure 66 compared with previous INS results [2]. The surprising result is the sharp single maximum in the iron-partial DOS contrary to the INS result. This is the first such measured sharp structure in a quasicrystal, and shows that differences must exist between the three atomic-partial DOS functions in i-AlCuFe. Furthermore, we have been able to use this synchrotron result to treat new INS studies of isotope-enriched samples [2], allowing us to deduce for the first time both the Al- and Cu-partial DOS as well (together with P.P. Parshin and M.G. Zemlyanov). All three partial-functions are very different in structure, showing the intricacy of the lattice dynamics in this quasicrystal. These functions are currently being compared to model structures of this archetypical quasicrystal (together with M. Mihalkovic). It is already clear that the vibrational structure depends sensitively on the lattice position as well as the atomic species, making such results invaluable in testing model structures.

Figure 66
Fig. 66: Iron-partial density of states in i-Al 62Cu 25.5 57Fe 12.5 quasicrystal in comparison to the neutron-weighted result from Ref. [2]. Solid lines are to guide the eye.

[1] R.A. Brand, A.-J. Dianoux, and Y. Calvayrac, Physical Review B 62 8849 (2000).
[2] T. Klein, G. Pares, J.B. Suck, G. Fourcaudot and F. Cyrot-Lackmann, J. Non-Cryst. Solids 153 & 154, 562 (1993).

Principal Publication and Authors
R.A. Brand (a), G. Coddens (b), A. Chumakov (c), and Y. Calvayrac (d), Physical Review B 59, R14145 (1999).
(a) Universität Duisburg (Germany)
(b) LLB, Gif-sur-Yvette (France)
(c) ESRF
(d) CECM/CNRS, Vitry (France)