INDEXING OF DECAGONAL QUASI-CRYSTALS .1. THE T-8-PHASE

Indexing of a decagonal quasicrystal using the scheme utilizing five p lanar vectors and one perpendicular to them is examined in detail. A m ethod for determining the indices of zone axes that a reciprocal vecto r would make in a decagonal phase of any periodicity has been proposed . By this method, the location of the zone axes made by any reciprocal vector can be predicted. The orthogonality condition has been simplif ied for the zone axes containing twofold vectors. The locations of zon e axes have also been determined by an alternative method, utilizing s pherical trigonometric calculations, which confirm the zone-axis locat ions given by the indices. The effect of one-dimensional periodicity o n the indices and the accuracy of the zone-axis determination is discu ssed. Rules for the formation of zone axes between several reciprocal vectors and the prediction of all the reciprocal vectors in a zone are evolved.