Quasicrystals are ordered materials which lack translational invariance. As for other incommensurate structures, the lack of periodicity leads to new long wavelength modes called phasons. At the microscopic level, this corresponds to the possibility for an atom to occupy two nearby positions having almost an equivalent local environment. Correlations between these microscopic rearrangements lead either to Bragg peak broadening or to diffuse scattering.

Both effects have been observed in the most perfect quasicrystals currently available, the icosahedral AlPdMn phase. The long wavelength phasons fluctuations give rise to a characteristic intensity distribution of the diffuse scattering around the Bragg reflections, which has been observed by neutron and X-ray diffraction. The observed distribution of the diffuse scattering can be reproduced using the elasticity theory of quasicrystals, and considering only two phason elastic constants. A temperature study of the diffuse scattering showed that it is related to pretransitional phasons fluctuations.

Unlike displacive modulated structures, but similarly to composite incommensurate structures, phason modes are not collective propagative modes in icosahedral quasicrystals, but are diffusive modes. A mode with a given wave-vector q, is expected to follow an exponentional time decay, with a q­2 dependence of the characteristic time decay. The time scale for such fluctuations has not yet been measured, but is supposed to be in the accessible range for coherent X-ray photon spectroscopy, i.e. of the order of minutes. Since the diffuse scattering is directly related to phason fluctuations, a measure of the time dependence of the speckle pattern in the diffuse scattering will give the time relaxation directly.

The coherent X-ray beam was produced by focussing optics located on beamline ID20. The incoming energy of the beam (7.6 keV) was selected by a double Si (111) crystal, with sagittal bending. A 10 µm diameter pinhole close to the sample provided a coherent beam. A Princeton Instrument Direct Illumination CCD chip was used as a 2-D photon counter using a droplet algorithm and was located 1.8 m away from the sample. With this setting, a ß = 40% coherence was achieved with a flux equal to 7.108 photon/sec at the sample position (200 mA beam current).

Figure 56 shows a speckle pattern recorded in 1 h at room temperature, at a distance q = 0.025 Å­1 away from a strong Bragg reflection. The slice through the 2-D intensity distribution, shows intensity fluctuations, much larger than the Poisson statistics, as expected for a speckle pattern. The sample was then slowly heated up to 550°C. At this temperature the first time dependence in the speckle pattern has been observed. Figure 57 shows the time correlation function retrieved from the measured data. As expected the phason fluctuations show an exponential time decay, with a time scale of the order of 400 s, for a phason wavelength equal to 250 Å. These results are very promising and open the route for a complete study (as a function of q and T) of the dynamics of phasons fluctuations in quasicrystals.

Authors
A. Létoublon (a) , F. Yakhou (b), F. Livet (a), F. Bley (a), M. de Boissieu (a), R. Caudron (c), C. Vettier (b).

(a) LTPCM UMR CNRS 5614, St Martin d'Heres (France)
(b) ESRF
(c) ONERA ­ LEM, Chatillon (France)