METHODS FOR AB INITIO STRUCTURE SOLUTION OF DECAGONAL QUASICRYSTALS Torsten Haibach and Walter Steurer, Laboratorium für Kristallographie, ETH Zentrum, CH-8092 Zurich, Switzerland.

N-dimensional Patterson methods have been combined with the maximum entropy method for ab initio phase determination of decagonal structures [1].

To unravel the n-dimensional Patterson function the symmetry minimum function has been extended to the embedding dimensions. Given the n-dimensional space group this Patterson superposition method allows the positions of the hyperatoms to be located and a first crude structure model to be derived.

To retrieve the shape and chemical composition of the acceptance domain of each hyperatom, this procedure is combined with the maximum entropy method. This method is exclusively constrained by the positions of the hyperatoms in the n-dimensional unit cell and result of the symmetry minimum function in physical space. These constraints enforce quasiperiodicity and correct atomic distances can be easily implemented.

Applying the maximum entropy method in perpendicular space allows a detailed idealised decagonal structure model to be derived, as only solutions within the planes of the acceptance domains are possible. The physical space approach, however, provides the capability to determine more complex non-periodic structures as well as to introduce deviations from the ideal quasiperiodic structures.

The combined algorithm has been tested on decagonal Al₇₀Co₁₅Ni₁₅, where the existing structure model could be improved. The structure models of decagonal Al₇₁Fe₅Ni₂₄, Al_70.5Mn_16.5Pd₁₃ (using multiple anomalous dispersion data) and Al₈₀Os₁₀Pd₁₀ will be presented.

[1] Haibach, T, Steurer, W.: Five-dimensional Symmetry Minimum

Function and Maximum Entropy Method for ab initio Solution of

Decagonal Structures. Acta Crystallogr. A (1995) in press.