Structure determination of the hexagonal quasicrystal approximant μ′-(Al,Si) 4Cr by the strong reflections approach

Abstract

A number of different crystalline phases have been found in Al-rich Al–Cr–Si alloys by transmission electron microscopy (TEM). Among these, the new hexagonal phase μ′-(Al,Si) 4Cr ( a=2.01 and c=1.24 nm) often found coexisting with the hexagonal μ-(Al,Si) 4Cr ( a=1.998 and c=2.4673 nm, isostructural with μ-Al 4Mn) and also with the hexagonal λ-(Al,Si) 4Cr ( a=2.839 and c=1.239 nm, isostructural with λ-Al 4Mn). It is evident from their electron diffraction patterns that the structures of these three phases are related. The strong reflections in all three are distributed in a similar way. They all exhibit a pseudo-icosahedral symmetry. The structure factor amplitudes and phases for the strong reflections of the μ′ phase could therefore be adopted from those of the λ phase, according to the strong reflections approach. A structure model of the μ′ phase is thus deduced from the known λ-Al 4Mn. μ′ consists of chains of 3+3 or 4+2 interpenetrated icosahedra along the 〈1 0 0〉 directions. Similar to the λ phase, there are two flat layers (F) and four puckered layers (P) in each unit cell of μ′, stacked along the c -axis in a sequence of PFP(PFP)′ where the (PFP)′ block is related to the PFP block by a 6 3 screw.