[Springer Series in Materials Science] Crystallography of Quasicrystals Volume 126 || Structures...
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7 Structures with 1D Quasiperiodicity Basically, 1D quasicrystals can be equally well described in the framework of quasiperiodic structures and in the one of incommensurately modulated structures. However, in the cases where τ -scaling symmetry applies to the diffraction pattern, the QC-setting may be more appropriate. This is also true for 1D quasicrystals resulting from phase transformations of axial or icosahedral quasicrystals. Structural relationships between initial and final phases can be better described within the same approach. One class of 1D quasicrystals comprises vacancy-ordered phases, i.e. series of superstructures of the CsCl type, in systems such as Al-Pd, Al-Ni, Al-Cu- Ni. They are characterized by stackings of (111) layers, either fully occupied or containing vacancies, related to the Fibonacci sequence [1]. Stable 1D quasicrystals have been found in annealed samples with com- positions Al 75 Fe 10 Pd 15 [4] and Al 65 Cu 20 Fe 10 Mn 5 [5]. Some characteristic pa- rameters are listed in Table 7.1. The lattice parameter a is along a two-fold direction (A2P 1 ) and c the period along the ten-fold axis of the related decago- nal phase. Another class includes metastable 1D quasicrystals resulting as interme- diate states during the transformation from a decagonal phase to an ap- proximant. Examples are rapidly solidified Al 80 Ni 14 Si 6 , Al 65 Cu 20 Mn 15 and Al 65 Cu 20 Co 15 alloys [3] as well as slowly solidified Al 70 Co 15 Ni 15 . The phase transformation can be described by the application of linear phason strain, which also leads to a domain structure. 1 A2P marks directions along a twofold axis in case of icosahedral symmetry; for the decagonal phase this direction is characterized by a hexagonal appearance of six strong reflections in the diffraction pattern [2].
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Structures with 1D Quasiperiodicity
Basically, 1D quasicrystals can be equally well described in the frameworkof quasiperiodic structures and in the one of incommensurately modulatedstructures. However, in the cases where τ -scaling symmetry applies to thediffraction pattern, the QC-setting may be more appropriate. This is alsotrue for 1D quasicrystals resulting from phase transformations of axial oricosahedral quasicrystals. Structural relationships between initial and finalphases can be better described within the same approach.
One class of 1D quasicrystals comprises vacancy-ordered phases, i.e. seriesof superstructures of the CsCl type, in systems such as Al-Pd, Al-Ni, Al-Cu-Ni. They are characterized by stackings of (111) layers, either fully occupiedor containing vacancies, related to the Fibonacci sequence [1].
Stable 1D quasicrystals have been found in annealed samples with com-positions Al75Fe10Pd15 [4] and Al65Cu20Fe10Mn5 [5]. Some characteristic pa-rameters are listed in Table 7.1. The lattice parameter a is along a two-folddirection (A2P 1) and c the period along the ten-fold axis of the related decago-nal phase.
Another class includes metastable 1D quasicrystals resulting as interme-diate states during the transformation from a decagonal phase to an ap-proximant. Examples are rapidly solidified Al80Ni14Si6, Al65Cu20Mn15 andAl65Cu20Co15 alloys [3] as well as slowly solidified Al70Co15Ni15. The phasetransformation can be described by the application of linear phason strain,which also leads to a domain structure.
1 A2P marks directions along a twofold axis in case of icosahedral symmetry; forthe decagonal phase this direction is characterized by a hexagonal appearance ofsix strong reflections in the diffraction pattern [2].
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248 7 Structures with 1D Quasiperiodicity
Table 7.1. Lattice parameters of 1D quasicrystals, with a = m × 2.3 A and c =n × 2.0 A[6]
m a [A] n c [A] Composition References
3 6.9 8 16 Al80Ni14Si6 [3]5 11.5 6 12 Al65Cu20Mn15 [3]5 11.5 8 16 Al75Fe10Pd15 [4]8 18.4 6 12 Al65Cu20Fe10Mn5 [5, 6]8 18.4 8 16 Al75Fe10Pd15 [4]
13 29.9 2 4 Al65Cu20Co15 [3]13 29.9 6 12 Al65Cu20Fe10Mn5 [6]18 41.4 6 12 Al65Cu20Fe10Mn5 [6]
References
1. K. Chattopadhyay, S. Lele, N. Thangaraj, S. Ranganathan, Vacancy OrderedPhases and One-Dimensional Quasiperiodicity. Acta Metall. 35, 727–733 (1987)
2. K.K. Fung, C.Y. Yang, Y.Q. Zhou, J.G. Zhao, W.S. Zhan, B.G. Shen, Icosahe-drally Related Decagonal Quasi-Crystal in Rapidly Cooled Al-14-at.%-Fe Alloy.Phys. Rev. Lett. 56, 2060–2063 (1986)
3. L.X. He, X.Z. Li, Z. Zhang, K.H. Kuo, One-Dimensional Quasicrystal in RapidlySolidified Alloys. Phys. Rev. Lett. 61, 1116–1118 (1988)
4. A.P. Tsai, T. Masumoto, A. Yamamoto, Stable One-Dimensional Quasi-Crystalsin Al-Pd-Fe Alloys. Philos. Mag. Lett. 66, 203–208 (1992)
5. A.P. Tsai, A. Sato, A. Yamamoto, A. Inoue, T. Masumoto, Stable One-Dimensional Quasi Crystal in a Al-Cu-Fe-Mn System. Jap. J. Appl. Phys. Lett.31, L970–L973 (1992)
6. W.G. Yang, J.N. Gui, R.H. Wang, Some new stable one-dimensional quasicrystalsin an Al65Cu20Fe10Mn5 alloy. Philos. Mag. Lett. 74, 357–366 (1996)
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