TY - JOUR

T1 - Arrangement of atomic clusters in a 2/1 cubic approximant in the Al-Zn-Mg alloy system

AU - Hiraga, Kenji

AU - Sugiyama, Kazumasa

AU - Ishii, Yasushi

PY - 2002/6/1

Y1 - 2002/6/1

N2 - 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 31/2aτ2/(τ2 + 1)1/2 and a shorter diagonal of 2aτ2/(τ2 + 1)1/2 (τ 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.

AB - 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 31/2aτ2/(τ2 + 1)1/2 and a shorter diagonal of 2aτ2/(τ2 + 1)1/2 (τ 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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U2 - 10.1080/09500830210135571

DO - 10.1080/09500830210135571

M3 - Article

AN - SCOPUS:0036605854

VL - 82

SP - 341

EP - 347

JO - Philosophical Magazine Letters

JF - Philosophical Magazine Letters

SN - 0950-0839

IS - 6

ER -