Beside crystalline and amorphous solids, quasicrystals are a new type of space filling form of matter. These compounds exhibit a specific long-range order together with an orientational order associated with symmetry properties, which are forbidden in periodic crystals. Among quasicrystals the icosahedral AlPdMn is considered as a model system.

A striking feature of quasicrystals is that in spite of the fact that they are non-periodic in 3-D space, their structure can still be characterised by a minimal set of parameters in a six-dimensional superspace. This periodic 6-D structure can be projected on 3-D space to obtain an idealised quasicrystalline structure. Starting from these models, one obtains not only long-range order but also evidences for a high local order with respect to distances and orientations. In particular, this description implies a finite set of local atomic structures around the Mn atoms.

Hard X-ray holography using an inside reference point is a method capable of imaging the local environment of selected atoms in 3-D without resorting to any a priori model [1]. In the last few years the technique has been developed to a level, which makes its application practical. The real space resolution has reached the diffraction limit (see ESRF highlights 1999) and the imaging of light atoms has also been demonstrated [2].

Figure 92
Fig. 92: Hologram of a quasicrystal recorded in inverse mode at 16 keV, using Mn as detector atom. 

Based on these recent advances of X-ray holography we applied the technique to quasicrystals on beamline ID22. We imaged holographically the surroundings of the Mn atoms in an Al70.4Pd21Mn8.6 quasicrystal. The hologram is shown in Figure 92 and the real space reconstruction in Figure 93. The interpretation of this picture is not as trivial as the interpretation of the results in the case of "normal" crystals. The expected weight of an atomic site is proportional to (f/r)2, where f stands for the average scattering factor of the site considered and r is its distance to the central atom. Usually the sites giving the highest intensity are the nearest ones. From considerations on the chemistry and the material density, the brightest spots imaged in Figure 93 cannot be the first atomic neighbours. In order to understand this picture, we turn to models of the atomic decoration of this quasicrystal. It turns out that the nearest shells around the Mn have low occupancy so that they can hardly be seen, while the highest occupancy arises from a combination of the fifth coordination shell of Pd, the third of Al and the first of Mn (yellow lines in Figure 93).

Figure 93
Fig. 93: Holographic reconstruction, the lines connect the atomic sites with highest occupancy.

An extended analysis by comparing the experimental data at different energies and at different sites (Pd) with the average occupation values will further ascertain the validity of the different models. This will contribute significantly to the understanding of the quasicrystals. Ultimately the mapping of average 3-D atomic decorations in various types of these fascinating materials becomes reality.

[1] G. Faigel and M. Tegze, Reports on Progress in Physics 62, 355 (1999).
[2] M. Tegze, G. Faigel, S. Marchesini, M. Belakhovsky and O. Ulrich, Nature, 407, 38 (2000).

Principal Publication and Authors
S. Marchesini (a, b), F. Schmithüsen (c), M. Tegze (d), G. Faigel (d), Y. Calvayrac (e), M. Belakhovsky (b), J. Chevrier (f), and A. S. Simionovici (c), Phys. Rev. Lett., 85, 4723, (2000).
(a) LBNL, Berkeley, California (USA); formerly at (b)
(b) CEA Grenoble (France)
(c) ESRF
(d) Research Institute for Solid State Physics and Optics, Budapest (Hungary)
(e) CECM CNRS, Vitry (France)
(f) LEPES CNRS, Grenoble (France)