HIGH-ORDER PERIODIC APPROXIMANTS OF A DECAGONAL QUASI-CRYSTAL IN AL70NI15CO15

Two kinds of high-order periodic approximant phase of a decagonal quasicrystal have been found to form in a slowly cooled Al70Ni15Co15 alloy. For both of them, the two-dimensional decagonal symmetry, 10 mm, breaks down to one of its subgroups, 2 mm, in the quasi-periodic plane of the decagonal phase. One of them has periodicity along two mutually perpendicular twofold axes in the quasi-periodic plane of the decagonal phase with periods, 3.8 nm and 5.2 nm. The other is periodic along one of the twofold axes with a period of 6.2 nm, and it apparently maintains quasi-periodicity along the other twofold axis within the experimental resolution. Structural relations of the two phases to the decagonal phase are discussed in the framework of the projection scheme from a five-dimensional hyperspace.