INDEXING OF DECAGONAL QUASI-CRYSTALS .2. A COMPARISON OF ZONE-AXIS PATTERN MAPS OF DECAGONAL PHASES OF DIFFERENT PERIODICITIES

The reciprocal space of the different decagonal phases T-2, T-4, T-6 a nd T-8, corresponding to periodicities of about 0.4, 0.8, 1.2 and 1.6 nm respectively are studied. Five prominent reciprocal vectors have be en identified for the T-2- and T-4- phases, and six prominent reciproc al vectors for T-6 and T-8. Important zone axes have been identified b y drawing traces of these vectors on a stereogram. Six integer indices of the zone axes have been determined for these zone axes. The angula r separation of the zone axes have been calculated from these indices. The c/a ratio has been chosen to be 4.236, close to tau(3), for the T -2-phase and the corresponding multiples for the other phases. The ang ular 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 s paces 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.