Structural Analysis of the Decagonal Quasicrystal Al70Ni15Co15 Using Symmetry-Adapted Functions

Overview & Synopsis

The decagonal quasicrystalline structure of Al70Ni15Co15 is analyzed within the superspace formalism. Symmetry-adapted functions have been used for the parametrization of the limits of the atomic surfaces that represent the atoms in superspace. As diffraction data, 253 independent reflections from [Steurer W., Haibach T., Zhang B., Kek S. and Lück R. Acta Cryst. B49 (1993) 661.] have been considered. Starting from a circular approximation for the atomic surfaces, their boundaries were refined with the program QUASI. A fit comparable to that reported in the above reference was attained with 15% fewer adjustable parameters. The main difference is the non-inclusion of Debye-Waller-type factors in internal space. The boundaries of the resulting atomic surfaces are rather wavy or circular in contrast with the polygonal forms of the previous model. It could be verified that these polygons evolve in a free refinement towards the obtained wavy forms. The effect on the diffraction intensities of Debye-Waller factors along internal space is rather equivalent to that of wavy boundaries for the atomic surfaces. An open question is, then, whether the polygonal forms considered in previous models are physically significant or model-forced. The resulting differences in physical space between the two models are subtle, the main features being essentially identical; however, both of them present a significant proportion of non-physical atomic distances that concern fully occupied atomic positions. Previous quantitative diffraction analyses of other quasicrystalline structures have also shown this tendency to introduce a significant number of unphysical interatomic distances; its cause remains unclear, but could be related with the recently conjectured existence of non-dense atomic surfaces in real quasicrystals.