F-type icosahedral phase and a related cubic phase in the Al-Rh-Cu system
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I.
INTRODUCTION
AS for cubic crystalline phases, icosahedral phases also have three possible lattices, which can be most conveniently described as projections in three dimensions of the six-dimensional simple (P), body-centered (I), and face-centered (F) cubic Bravais lattice.[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 t 3 (t 5 (1 1 =5)/2) for the P-type icosahedral phase and of t 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. For examples, the i-Al73Mn21Si6[5] and i-Ga20Mg36Zn42[6] are P-type icosahedral quasicrystals and the i-Al-Cu-Fe[3,4,7] and i-Al70.5Mn8.5Pd21[8] are F-type icosahedral quasicrystals. The existence of crystalline phases structurally related to the icosahedral phases was noticed in the beginning of the study of quasicrystals. These crystalline phases are referred to as (crystalline) approximants, and they are valuable and indispensable for understanding atomic arrangements in quasicrystals. The structure of cubic a-Al73Mn16Si11[9] contains the 54-atom Mackay cluster, which is the structural motif in the i-Al-Mn-type icosahedral phase (space group Pm35); the structure of the R-Al5CuLi3[10] contains the 137atom Bergman cluster, which is the structural motif in the i-Al-Li-Cu-type icosahedral phase (space group Pm35). Recently, the structures of a-Al67Mn14Pd11Si8[11] and b-Al[12] phases were determined by X-ray 70Pd23Mn6Si1 single-crystal analysis. They are considered to be the (1/1) X.Z. LI, Guest Scientist, is with the Centre for Materials Science, Faculty of Mathematics and Natural Sciences, University of Oslo, N-0371 Oslo, Norway. K.-T. PARK, Postdoctoral Student, K. SUGIYAMA, Associate Professor, and K. HIRAGA, Professor, are with the Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan. Manuscript submitted November 10, 1997. METALLURGICAL AND MATERIALS TRANSACTIONS A
and (2/1) approximants of the i-Al-Pd-Mn F-type icosahedral phase (space group Fm35). Structural models of the i-Al-Mn-Pd F-type icosahedral phase were then proposed based on the structures of the two crystalline phases.[13,14] The coexistence of decagonal and crystalline phases in a conventional solidified Al65Rh20Cu15 alloy was briefly reported in early 1989 based on the results of powder X-ray diffraction experiments.[15] For the purpose of identifying the quasicrystals and related crystalline phases in the AlRh-Cu system, a transmission electron microscopy (TEM) study was carried out in our laboratory. Decagonal quasicrystalline and a
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