Abstract
Abstract Two kinds of high-order periodic approximant phase of a decagonal quasi-crystal 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.
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