Quasicrystal structure in Al─Cu─Fe annealed alloy

Icosahedral clusters, icosaheral order and stability of quasicrystals—a view of metallurgy∗

“…Figure 2 shows twofold patterns of the primitive (P-type) and face-centered (F-type) iQcs indexed along the fivefold direction. Along this fivefold direction, the distance between the reflections shows an inflation by τ 3 for the Ptype iQc and by τ for the F-type iQc [20,21]. The indexing of these reflections is shown in table 1.…”

F-type icosahedral phase and a related cubic phase in the Al-Rh-Cu system

“…Thus, the structure of F-type icosahedral phases is supposed to be a superlattice of the P-type icosahedral lattice with two kinds of icosahedral clusters at even and odd vertices. For examples, the i-Al 73 Mn 21 Si 6 [5] and i-Ga 20 Mg 36 Zn 42 [6] are P-type icosahedral quasicrystals and the i-Al-Cu-Fe [3,4,7] and i-Al 70.5 Mn 8.5 Pd 21 [8] are F-type icosahedral quasicrystals.…”

“…[1] The F-type icosahedral phases (space group Fm35) can be readily distinguished from the P-type icosahedral phases (space group Pm35) by their diffraction patterns. The positions of the diffraction spots along odd-parity (threefold and fivefold) directions form a sequence increasing by a power of 3 ( ϭ (1 ϩ )/2) for the P-type icosahedral phase and of ͌5 for the F-type icosahedral phase. [2,3,4] The F-type icosahedral phases are explained as face centering of the sixdimensional hypercubic unit cell due to chemical ordering of the atoms.…”

“…The positions of the diffraction spots along odd-parity (threefold and fivefold) directions form a sequence increasing by a power of 3 ( ϭ (1 ϩ )/2) for the P-type icosahedral phase and of ͌5 for the F-type icosahedral phase. [2,3,4] The F-type icosahedral phases are explained as face centering of the sixdimensional hypercubic unit cell due to chemical ordering of the atoms. Thus, the structure of F-type icosahedral phases is supposed to be a superlattice of the P-type icosahedral lattice with two kinds of icosahedral clusters at even and odd vertices.…”

Millimetre-size single quasicrystals in Al—Cu—Fe alloy

“…This icosahedral phase has a new type of structure (Ishimasa, Fukano and Tsuchimori 1988) belonging to the F-type icosahedral phase (Ebalard and Spaepen 1989) which has been theoretically studied by Cahn, Shechtman and Gratias (1986), and by Levitov and Rhyner (1988). The second feature is that this icosahedral phase has a higher degree of structural perfection than have other icosahedral phases (Hiraga, Zhang, Hirabayashi, Inoue and Masumoto 1988).…”