Modeling atomic surfaces for the Al–Ni–Co basic decagonal phase

The atomic surfaces (ASs), supports of a probability density in perpendicular space, are a powerful instrument for describing quasicrystal structure. The attainable resolution of diffraction data does not allow a direct ASs determination hence they need to be modeled and refined. A simple set of geometric rules can be found for modeling ASs. The ASs shapes are constrained by interatomic distances, density and symmetry of the physical 3D structure. decagonal Al71Ni22Co7 is simultaneously the simplest (with only two 2D independent ASs) and the toughest proof for the technique, as the mentioned physical constraints are extremely difficult to be satisfied. It is hence necessary to allow for a probability smaller than one (i.e. partial atomic site occupancy) in part of the ASs. This adds further parameters to the model. Further, some physical constraints may be weakened, evidencing structural features such as pseudo symmetry elements, puckering of the periodic layers, chemical and geometric disorder.