VOLUME56, NUMBER 19 PHYSICAL REVIEW LETTERS 12 MAY 1986

Icosahedrally Related Decagonal Quasicrystal in Rapidly Cooled Al-14-at.%-Fe Alloy

K. K. Fung, (a) C. Y. Yang, Y. Q. Zhou, J. G. Zhao, W. S. Zhan, and B. G. Shen Institute of Physics, Chinese Academy of Sciences, Beijing, China

(Received 14 January 1986)

A decagonal quasicrystal with point group 10/mmm has been found in Al-14-at.°/o-Fe alloy. Zone-axis patterns of the decagonal phase appearing at the icosahedral positions are reminiscent of the appropriate icosahedral patterns. The symmetry and the angular separation of the zone axes can be obtained from the icosahedral phase by the addition of a mirror plane normal to a fivefold axis. This is supported by the observed diffuse streaking parallel to the tenfold axis. A similar de­cagonal phase in Al-20-at.°/o-Mn alloy reported by Bendersky can likewise be explained by the addi­tion of mirror planes intersecting a fivefold axis of the icosahedral phase.

PACS numbers: 61.55.Hg, 61.16.Di, 61.50.Em

The discovery of the icosahedral phase in rapidly cooled Al-14-at.°/o-Mn alloy by Shechtman et all has stimulated widespread interest in the icosahedral phase.2"4 In the study of Frank-Kasper phases, a simi­lar icosahedral phase has been observed in (Ti1_xVx)2Ni, x - 0 . 1 to 0.3, by Zhang, Ye, and Kuo.5

The icosahedral phase is characterized by the existence of fivefold axes which is incompatible with translation-

ai symmetry. The icosahedral phase can be explained in terms of a quasiperiodic Penrose lattice.6 Such quasiperiodic structures have been termed quasicrys-tals.7 Recently, we have found a decagonal quasicrys­tal in rapidly cooled Al-14-at.%-Fe alloy. This decago­nal phase is closely related to the icosahedral phase. Meanwhile, we have learned that a decagonal quasi-crystal in Al-20-at.%-Mn alloy with translational

FIG. 1. Selected-area electron diffraction patterns from Al-14-at.°/o-Fe alloy showing the decagonal quasicrystal symmetry.

2060 © 1986 The American Physical Society

VOLUME56, NUMBER 19 PHYSICAL REVIEW LETTERS 12 MAY 1986

FIG. 2. Diffraction patterns from (a) a fivefold axis of the decagonal phase.

periodicity along the tenfold axis has been reported by Bendersky.8 Although the relation between the Al-Mn decagonal and icosahedral phases is not known, a com­parison between the Al-Fe and Al-Mn decagonal phases shows that the diffraction patterns of the ten­fold axis and a zone axis normal to the tenfold axis are very similar. But the diffraction patterns of the other normal zone axis and the diffuse streakings are very different. This has prompted us to study the Al-20-at.%-Mn decagonal quasicrystal. It is found that this decagonal phase is also closely related to the icosahedral phase. The theoretical models9"11 pro­posed for the icosahedral phase should now be extend­ed to include the decagonal phase.

Thin ribbons of Al~14-at.%-Fe and Al-20-at.°/o-Mn alloys about 30 fitn thick were prepared by melt-spinning in the usual way. Specimens for transmission electron microscopy were prepared by ion milling. It is found that the Al~14-at.°/o-Fe specimens are rather in-homogeneous; amorphous, quasicrystal, and crystal phases are often found in the same specimen. The quasicrystal grains are quite small; those that we have studied range from about 50 to 200 nm. Figure 1 shows a set of selected-area electron diffraction pat­terns taken from two grains of Al-14-at.°/o-Fe arranged in a 36 stereographic sector. The Al~14-at.°/o-Fe ten­fold pattern is compared with a pattern from a fivefold axis of the icosahedral phase in Fig. 2. The two pat­terns are on the same scale. The diffraction spots in the icosahedral pattern have been labeled following the scheme of Bancel et al.2 Although the icosahedral pat­tern appears to be tenfold, it is actually fivefold sym­metric (Fig. 3). Lines along the mirror directions are designated P lines while lines orthogonal to the P lines are designated D lines. The patterns are so placed that

Al-Mn icosahedral phase and (b) the tenfold axis of the Al-Fe

the spots along the P lines of the icosahedral pattern are matched by equivalent spots in the decagonal pat­tern. The angle between adjacent P and D lines is 18°. Along the D lines, empty pentagonal rings of spots in the icosahedral pattern are replaced by centered dec­agonal rings of spots in the decagonal pattern. It is of interest to note that if the decagonal pattern is rotated by 18° relative to the icosahedral pattern and then re-scaled by a factor of 2cosl8° (or 2sin72°), the posi-

FIG. 3. Icosahedral stereographic projection along a five­fold axis. Dotted lines are added in the OPDP sector to show the decagonal symmetry of the Al-Fe quasicrystal in Fig. 1.

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tions of the spots in the two patterns become identical. In Fig. 2, the spot at the center of the marked decagon in the Al-Fe pattern will become the spot / in the icosahedral pattern.

When we tilt about a P line, patterns at angles of about 32°, 37°, and 63° from the tenfold axis are ob­tained as shown in Fig. 1. Equivalent patterns are ob­tained by tilting about an adjacent P line. This means that the axial symmetry of the quasicrystal is indeed tenfold (10mm). Figure 3 shows an icosahedral stereographic projection along a fivefold axis. A sector with dotted lines in Fig. 3 shows the 10mm symmetry. This sector corresponds to Fig. 1. Note that Figs. 1 and 3 are related by a relative rotation of 90°, or equivalents 18°. The patterns at 32°, 37°, and 63° are "degenerate" twofold, threefold, and fivefold patterns of the icosahedral quasicrystal. Another grain in a de­generate fivefold orientation is tilted about the P axis so that at about 26° on one side, the degenerate three­fold pattern is obtained, while at about 26° on the op­posite side, a pattern with apparent translation perio­dicity is obtained as shown in Fig. 1. This pattern which is 90° from the tenfold axis is therefore a P zone-axis pattern. The apparent periodicity is along the tenfold axis. When we tilt about the tenfold axis, an equivalent P pattern (P in Fig. 3) is obtained at 36°. Midway between these two P patterns is a D pattern

with satellites and diffuse streaking along the tenfold axis. The D and P patterns have been designated B and C in Al-20-at.°/o-Mn by Bendersky. Similar de­generate zone-axis patterns have been obtained from the Al-Mn decagonal phase. It should be pointed out that the P and D patterns have their counterparts in the icosahedral phase. The D pattern corresponds to a twofold pattern (Fig. 3). The P pattern corresponds to a pattern midway between two twofold axes on a line joining a fivefold axis and a threefold axis. Figure 3 shows that the P axis is 26.57° from a nearby fivefold axis, 10.8° from the threefold axis, and 18° from two twofold axes. This is the subsidiary twofold pattern mentioned by Bancel et al. The P axis is therefore 90° from the central fivefold axis since the fivefold axes are 63.43° apart. Figure 4 compares the P and D pat­terns of the icosahedral and decagonal phases. The patterns are arranged so that the tenfold axis is hor­izontal. With neglect of the weak spots, the icosahedral P pattern in Fig. 4 appears to have perio­dicity along the fivefold axis. In the Al-Fe P pattern, the pseudoperiodicity is doubled. In the Al-Mn P pat­tern, the periodicity is tripled with diffuse streaking at the \ positions. The diffuse streaking turns into spots in the corresponding D pattern. The periodicity which is 6 times the icosahedral pseudoperiodicity is 1.24 nm along the tenfold axis. This large period makes it easy

FIG. 4. Pand D patterns (upper and lower rows) from (a) icosahedral Al-Mn phase, (b) decagonal Al-Fe phase, and (c) de­cagonal Al-Mn phase. The icosahedral D pattern is a twofold pattern. Note how this pattern is related to the P pattern and the decagonal D patterns. Note also that the diffuse streaking in Al-Fe and Al-Mn decagonal phases is along and perpendicular to the tenfold axis.

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to be detected by convergent-beam electron diffraction along the tenfold axis. The icosahedral D pattern is a twofold pattern rotated from its symmetric position. Figure 4 shows how it is related to the icosahedral P pattern and the decagonal D patterns. It can be seen that the incommensurate spacings in the decagonal phases normal to the tenfold axis are the same as those of the tilted icosahedral two pattern. In Al-Fe, the periodicity in the D pattern is not evident. Further tilt­ing confirms the presence of a mirror plane normal to the tenfold axis. Therefore, the point group of the de­cagonal phases is 10/mmm. However, the presence of mirror planes in Al-Fe has not been confirmed by convergent-beam electron diffraction. This may be due to the presence of defects in the decagonal phase as suggested by the diffuse streaking in the diffraction patterns. The streaking in Al-Fe and Al-Mn quasicrys-tals is parallel and perpendicular to the tenfold axis which is clearly shown in the D patterns in Fig. 4. We interpret the streaking in Al-Fe as due to the stacking of planar slabs along the tenfold axis while in Al-Mn it is due to the packing of rods parallel to the tenfold axis, as suggested by Bendersky.

Both the symmetry and the angular separation of the zone axes of the decagonal phases can be obtained from the icosahedral phase by the addition of a mirror plane to a fivefold axis. The addition of a mirror plane normal to a fivefold axis of the icosahedral phase gives the Al-Fe decagonal phase. The addition of a set of mirror planes intersecting a fivefold axis and perpen­dicular to the existing mirror planes gives the Al-Mn decagonal phase. The addition of a mirror plane at dif­ferent sites will give rise to stacking of planar slabs in the former case and packing of rods in the latter case. This explanation is supported by the diffuse streaking observed in the respective decagonal phases.

A high-resolution electron-microscopy image of the Al-Fe quasicrystal in the tenfold orientation gives a Penrose pattern similar to that of the icosahedral phase. This means that the quasicrystal Al-Fe alloy is

a single phase, and not an aggregate of twins. Howev­er, it is of interest to report here that tenfold twins have actually been observed in the Al-Fe specimen. The twins have been identified to be Al13Fe4.12 It is not clear if the twins and the decagonal phase are relat­ed. The fact that the decagonal phases are so closely related to the icosahedral phase merits more attention. The study of the decagonal phases will shed light on the transition of the icosahedral phase to the crystal­line phase.

One of the authors (K.K.F.) has benefitted from discussions with Z. Zhang of the Institute of Metal Research, Chinese Academy of Sciences, Shenyang, China. The orthogonal relation of the fivefold axis and the P axis was brought to our attention by Z. Zhang.

(a)Also at Beijing Laboratory of Electron Microscopy, Chinese Academy of Sciences, Beijing, China.

1D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, Phys. Rev. Lett. 53, 1951 (1984).

2P. A. Bancel, P. A. Heiney, P. W. Stephens, A. I. Gold­man, and P. M. Horn, Phys. Rev. Lett. 54, 2422 (1985).

3L. A. Bursill and J. L. Peng, Nature (London) 316, 50 (1985).

4K. Hiraga, M. Hirabayashi, A. Inoue, and T. Masumoto, Sci. Rep. Res. Inst., Tohoku Univ., Ser. A 32, 309 (1985), and J. Phys. Soc. Jpn. 54, 4077 (1985).

5Z. Zhang, H. Q. Ye, and K. H. Kuo, Philos. Mag. 52, L41 (1985).

6R. Penrose, Math. Intelligencer 2, 32 (1979). 7D. Levine and P. J. Steindhardt, Phys. Rev. Lett. 53,

2477 (1984). 8L. Bendersky, Phys. Rev. Lett. 55, 1461 (1985). 9P. Bak, Phys. Rev. Lett. 54, 1517 (1985).

10V. Elser, to be published. UM. Duneau and A. Katz, Phys. Rev. Lett. 54, 2688

(1985). 12P. J. Black, Acta Crystallogr. 8, 43, 175 (1955).

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FIG. 1. Selected-area electron diffraction patterns from Al-14-at.%-Fe alloy showing the decagonal quasicrystal symmetry.

; • # . • • • »^« • . . .

• • • • • • • • • • •

. . . • _ • - • •

• • * • • • • • - • • « ^ » •

FIG. 2. Diffraction patterns from (a) a fivefold axis of the Al-Mn icosahedral phase and (b) the tenfold axis of the Al-Fe decagonal phase.

• • • • • •

• • • # • • • • < • • • • • . . . . . . . • • • • • • •

. . . • • • • • • • • . . • • • •

. « . . . » * • « . * * 4 * • • • •

U iUil i i i

(c)

FIG. 4. Pand D patterns (upper and lower rows) from (a) icosahedral Al-Mn phase, (b) decagonal Al-Fe phase, and (c) de­cagonal Al-Mn phase. The icosahedral D pattern is a twofold pattern. Note how this pattern is related to the P pattern and the decagonal D patterns. Note also that the diffuse streaking in Al-Fe and Al-Mn decagonal phases is along and perpendicular to the tenfold axis.