Arrangement of atomic clusters in a 2/1 cubic approximant in the Al-Zn-Mg alloy system |
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Authors: | Kenji Hiraga Kazumasa Sugiyama Yasushi Ishii |
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Institution: | 1. Institut für Experimentalphysik, Universit?t Kiel , D-24098, Kiel, Germany;2. Fachnchtung Kristallographie, Universit?t des Saarlandes , D-66041, Saarbrücken, Germany |
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Abstract: | An arrangement of the so-called Bergman clusters of atoms in a 2/1 cubic crystalline approximant phase, which is closely related to Frank-Kasper-type icosahedral quasicrystals, in an Al-Zn-Mg alloy system is discussed in detail. The 2/1 cubic structure has eight Bergman clusters in its unit cell and the positions of the clusters can be understood as twelvefold sites in the 2/1 cubic approximant of the three-dimensional Penrose lattice. The atomic clusters are located at vertices of two types of rhombohedron, which are formed by six rhombic planes with an edge length of 3 1/2 a 2 /( 2 + 1) 1/2 and a shorter diagonal of 2 a 2 /( 2 + 1) 1/2 ( is the golden ratio and a is a quasilattice constant), which correspond to half a body diagonal and an edge length respectively of the 1/1 cubic approximant unit cell. The present results provide an important key for understanding the arrangements of atomic clusters in icosahedral quasicrystals. |
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