Neutron and X-ray single-crystal study of the AlPdMn icosahedral phase

Abstract

Perfect single grains of the AlPdMn icosahedral phase have been used for structure determination by X-ray and neutron diffraction. Owing to the large difference between X-ray and neutron scattering factors, information is gained on the atomic positions of the three elements. A model is proposed as deduced from a six-dimensional (6D) Patterson analysis. Six different atomic hypersurfaces are located on node and body-centre sites of the 6D lattice. The superstructure that leads to a face-centred lattice is mainly due to a strong chemical ordering, all the palladium being on the even node and odd body centre of the 6D cube. The resulting 3D structure contains icosahedral clusters similar to the external shell of the Mackay icosahedron, with two kinds of chemical decoration. The structure may also be described via a quasi-periodic stacking of fivefold planes. Each set of planes is characterized by an average chemical composition and local order. This kind of description helps in the understanding of quasi-crystal growth, formation of dislocations and dynamic properties.

Structure determination of quasicrystals

“…As already observed for other icosahedral quasicrystals [31,32], the density is not at all uniform, but is concentrated and forms dense rows along particular directions. Densest planes correspond to the dense lines with the largest gaps in between them.…”

Comparison between experimental surface data and bulk structure models for quasicrystalline AlPdMn: Average atomic densities and chemical compositions

“…36 With time, it was modified and became known as the Katz-Gratias ͑KG͒ model. 11,12 Second, using x-ray and neutron diffraction, Boudard et al 13 constructed a bulk structural model for i-AlPdMn, and this is commonly referred to as the Boudard model. Although its structure was mainly based on the KG model, the Boudard model originally contained unreasonably short bond lengths between some pairs of atoms.…”

“…[4][5][6][7][8] Nonetheless, uncertainty remains about significant aspects of the surface structure. This is true in part because different models exist for the bulk structures of these quasicrystals: about seven different bulk models exist for i-AlPdMn, [9][10][11][12][13][14][15][16][17][18][19][20] although not all have been derived independently. Until now, each surface experiment has been compared to a single bulk structural model.…”

“…13,33 The solution to this conundrum was originally recognized by Boudard et al 13 and later exploited by Gierer et al, 22,23 who realized that the bulk structure can be classified into groups of self-similar planes and that one or more groups are probably favored over others as surface terminations. At present, there is a debate as to which group of planes is favored.…”

Copper adsorption on the fivefoldAl70Pd21Mn9quasicrystal surface

“…Consequently the definition of a crystal has been modified to incorporate quasicrystals. 1 Among the large family of quasicrystals, the icosahedral Al-Pd-Mn phase has been the most studied and a model explaining its bulk structure has been proposed by Boudard et al 2 in 1992 and later refined by Yamamoto. 3 The surface structure of this material has been identified and determined to be a termination of the bulk structure.…”