Atom cluster arrangements in cubic approximant phases of icosahedral quasicrystals

Abstract

Structural characteristics of six cubic approximant phases, α-(AlPdMnSi), β-(AlPdMnSi), γ-(AlCuRuSi), (Al,Zn)₄₉Mg₃₂, α-(AlMnSi) and Al₁₂Mn, of icosahedral quasicrystals are discussed systematically in terms of atom cluster arrangements. The structures of those approximants can be classified into two groups: firstly, that characterized as a simple-cubic packing of atom clusters with icosahedral symmetry or a “CsCl”-type packing of two types of atom clusters, and, secondly, a body-centred packing of one type of atom cluster with icosahedral symmetry. The former, α-(AlPdMnSi), β-(AlPdMnSi) and γ-(AlCuRuSi), is suggested to be approximant phases of F-type icosahedral phases, and the latter, (Al,Zn)₄₉Mg₃₂, α-(AlMnSi) and Al₁₂Mn, to be those of P-type icosahedral phases. Atomic arrangements of the atom clusters with icosahedral symmetry in the approximant phases are characterized by the existence of a fundamental icosahedral cluster and are classified into two groups by the manner of the packing of atoms on the fundamental icosahedral cluster: namely, the so-called octahedral (α-(AlMnSi) and AlpMn) and tetrahedral (α-(AlPdMnSi), β-(AlPdMnSi), γ-(AlCuRuSi) and (Al,Zn)₄₉Mg₃₂) packings.