Indexing of decagonal quasicrystals II. A comparison of zone-axis pattern maps of decagonal phases of different periodicities

Abstract

The reciprocal space of the different decagonal phases T₂, T₄, T₆ and T₈, corresponding to periodicities of about 0·4, 0·8, 1·2 and 1·6nm respectively are studied. Five prominent reciprocal vectors have been identified for the T₂- and T₄- phases, and six prominent reciprocal vectors for T₆ and T₈. Important zone axes have been identified by drawing traces of these vectors on a stereogram. Six integer indices of the zone axes have been determined for these zone axes. The angular separation of the zone axes have been calculated from these indices. The c/a ratio has been chosen to be 4·236, close to τ³, for the T₂-phase and the corresponding multiples for the other phases. The angular relationships between zone axes were also calculated by spherical trigonometry using the same reciprocal vectors and the c/a ratio. The angular values obtained from the indices, spherical trigonometry and experiments show good correspondence. A comparison of the reciprocal spaces of the decagonal phases of different periodicities has been made and the possible causes of the multiple periodicity discussed on the basis of the results.