The superstructure in decagonal Al-Ni-Co has a unit cell in 5D space 5 times larger than that of the normal structure. A 3D model of this structure proposed recently [K. Hiraga, W. Sun, and A. Yamamoto, Mater. Trans. JIM 35, 657 (1994)] has a 20 {} cluster on each vertex of the Penrose pattern with an edge length of 20 {}. This Letter shows a corresponding 5D model. There are 20 occupation domains in a unit cell, two of which are independent under the symmetry of P10₅/mcm(10⁷1mm). This 5D model shows diffraction patterns similar to those of the superstructure. The phase transition from the normal phase to the superstructure occurs by a phason jump.
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Yamamoto et al. (1997) studied this question.
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