Atom cluster arrangements in cubic approximant phases of icosahedral quasicrystals

Structural characteristics of six cubic approximant phases, alpha-(AlPdMnSi ), beta-(AlPdMnSi), gamma-(AlCuRuSi), (Al,Zn)(49)Mg-32, alpha-(AlMnSi) and Al12Mn, of icosahedral quasicrystals are discussed systematically in terms of atom cluster arrangements. The structures of those approximants can be c lassified into two groups: firstly, that characterized as a simple-cubic pa cking of atom clusters with icosahedral symmetry or a 'CsCl'-type packing o f two types of atom clusters, and, secondly, a body-centred packing of one type of atom cluster with icosahedral symmetry. The former, alpha-(AlPdMnSi ), beta-(AlPdMnSi) and gamma-(AlCuRuSi), is suggested to be approximant pha ses of F-type icosahedral phases, and the latter, (Al,Zn)(49)Mg-32, alpha-( AlMnSi) and Al12Mn, to be those of P-type icosahedral phases. Atomic arrang ements of the atom clusters with icosahedral symmetry in the approximant ph ases are characterized by the existence of a fundamental icosahedral cluste r and are classified into two groups by the manner of the packing of atoms on the fundamental icosahedral cluster: namely, the so-called octahedral (a lpha-(AlMnSi) and Al12Mn) and tetrahedral (alpha-(AlPdMnSi), beta-(AlPdMnSi ), gamma-(AlCuRuSi) and (Al,Zn)(49)Mg-32) packings.