- Email: [email protected]
Formation of icosahedral quasicrystals in (Ag,Au)-based ternary systems
Journal of Non-Crystalline Solids 353 (2007) 3412–3416 www.elsevier.com/locate/jnoncrysol
Formation of icosahedral quasicrystals in (Ag,Au)-based ternary systems R. Tamura a
a,b,*
, A. Katahoka a, K. Nishimoto a, S. Takeuchi
a
Department of Materials Science and Technology, Tokyo University of Science, Noda, Chiba 278-8510, Japan b CREST, Japan Science and Technology Corporation, Japan Available online 30 July 2007
Abstract We investigated the phase constitution of rapidly solidified (Ag,Au)-based ternary alloys at various compositions of (M,X)85.7RE14.3 (M = Ag, Au, X = Al,Ga,In, RE = Er,Lu). It is found that an icosahedral phase is formed at an average electrons per atom ratio close to 2.0 as well as at the composition ratio of (M,X)6RE, suggesting that these factors have crucial roles in the stability of the icosahedral phases. It is also found that the trend of the icosahedral phase formation in the Au-based alloys is quite different from that in the Ag-based alloys. Ó 2007 Published by Elsevier B.V. PACS: 61.43.Dq; 61.44.Br; 61.10.Nz; 61.14. x Keywords: Amorphous metals; Metallic glasses; Quasicrystals; X-ray diffraction; Electron diffraction
1. Introduction Recently, much attention has been paid to the structural relationship between icosahedral quasicrystals and bulk metallic glasses since an icosahedral phase is often formed as a primary precipitation phase in a number of bulk metallic glasses with high glass forming ability, suggesting that their local atomic configurations are closely related to each other. The aim of the present work is to synthesize thermodynamically stable icosahedral quasicrystals that are mainly based on the group I elements of the periodic table, such as copper, silver and gold. In this paper, we report on the formation of icosahedral quasicrystals in rapidly solidified (Ag,Au)-based ternary alloys and discuss their formation condition in terms of the average valence electrons per atom (e/a) as well as of the relative sizes of the constituent elements. *
Corresponding author. Address: Department of Materials Science and Technology, Tokyo University of Science, Noda, Chiba 278-8510, Japan. Tel.: +81 4 7124 1501; fax: +81 4 7122 1499. E-mail address: [email protected] (R. Tamura). 0022-3093/$ - see front matter Ó 2007 Published by Elsevier B.V. doi:10.1016/j.jnoncrysol.2007.06.021
Prior to the present work, we investigated the phase constitution of alloys prepared at compositions (M,X)85.7RE14.3 (M = Ag,Au, X = Al,Ga,In, RE = rare earth metals). The reason we have chosen these compositions is because a number of 1/1-cubic approximant phases such as those of Cd6Y-type [1], which are closely related to the recently discovered Cd5.7Yb and Cd5.7Ca binary quasicrystals [2,3], are stabilized at the particular concentration of M85.7RE14.3, i.e., M6RE. In this respect, we systematically prepared rapidly quenched alloys by slightly varying the concentration ratio of M to X in (M,X)85.7RE14.3 and have found that a quasicrystalline phase is formed as a primary phase in the rapidly solidified state around the alloy composition of M48.6X37.1RE14.3, which has an e/a ratio close to 2, i.e., 2.03. For this reason, this composition has been chosen for further investigations on the formation of the icosahedral phase. 2. Experimental procedures (Ag,Au)-based (Ag,Au)48.6(Ga,Al,In)37.1RE14.3 ternary alloys were prepared by melting the constituent elements
211111 221001
Figs. 1 and 2 present X-ray diffraction patterns of rapidly quenched Ag48.6X37.1Lu14.3 (X = Al,Ga,In) and Ag48.6X37.1Er14.3 (X = Al,Ga,In) alloys, respectively. It is found that a mostly single icosahedral phase is obtained for the Ag48.6Al37.1Lu14.3, Ag48.6In37.1Lu14.3, Ag48.6Al37.1Er14.3 and Ag48.6In37.1Er14.3 alloys, as are indexed using the projection method from six dimensional space. Figs. 3– 6 present electron diffraction patterns of these alloys along (a) twofold, (b) threefold and (c) fivefold axes, respectively, verifying the formation of an icosahedral phase in all these alloys. We have found that an icosahedral phase is not formed in the rapidly quenched state for the Ga-bearing Ag48.6Ga37.1Lu14.3 and Ag48.6Ga37.1Er14.3 alloys although gallium has the same valence electrons, i.e., 3 electrons, as aluminum and indium. From Figs. 3–6 it is seen that the fivefold pattern of the Ag48.6In37.1Er14.3 alloys exhibits many sharp Bragg spots with little deviation from the ideal positions of the icosahedral symmetry, implying that the icosahedral phase possesses high structural perfection among the alloys studied in the present work. These icosahedral phases, however, are found to be metastable since they transform into equilibrium crystalline phases upon annealing, mostly into 1/1-
Intensity(arb.units)
332002
X=Al
211111 221001
X=Ga
X=In
60
40
332002
X=In
20
60
40
80
2θ (degree) Fig. 2. X-ray diffraction patterns of rapidly quenched Ag48.6X37.1Er14.3 (X = Al,Ga,In) alloys. The indexed peaks are from the icosahedral phase.
cubic approximant phases, which are crystalline analog to the icosahedral phases. 3.2. Ternary Au48.6(Al,Ga,In)37.1RE14.3 alloys Figs. 7 and 8 present X-ray diffraction patterns of rapidly quenched Au48.6X37.1Lu14.3 (X = Al,Ga,In) and Au48.6X37.1Er14.3 (X = Al,Ga,In) alloys, respectively, and Fig. 9 shows electron diffraction patterns of the rapidly quenched Au48.6Ga37.1Lu14.3 alloy along (a) twofold, (b) threefold and (c) fivefold axes, clearly showing the formation of an icosahedral phase. In contrast to the case of the Ag-based alloys, an icosahedral phase does not occur in the Au–X–Lu (X = Al, In) and Au–X–Er (X = Al, In) systems but is found to form in the Au48.6Ga37.1Lu14.3 alloy although we expect similar results for Au48.6X37.1RE14.3 (X = Al,Ga,In) alloys since the atomic radius of gold (0.1442 nm) is nearly the same as that of silver (0.1444 nm). Moreover, it is seen that an icosahedral phase is not formed in the rapidly quenched Au48.6Ga37.1Er14.3 alloy, which is in contrast to the case of the Au48.6Ga37.1Lu14.3 alloy. 4. Discussion
332002
20
X=Ga
332002
3.1. Ternary Ag48.6(Al,Ga,In)37.1RE14.3 alloys
X=Al
211111 221001
3. Results
Intensity(arb.units)
in an arc furnace under argon atmosphere. The alloys were then rapidly quenched by the single-roll melt-spinning technique. The obtained phases were studied by powder X-ray diffraction experiments using Cu Ka radiation and the formation of quasicrystalline phases was examined and confirmed by electron diffraction experiments.
3413
211111 221001
R. Tamura et al. / Journal of Non-Crystalline Solids 353 (2007) 3412–3416
80
2θ (degree) Fig. 1. X-ray diffraction patterns of rapidly quenched Ag48.6X37.1Lu14.3 (X = Al,Ga,In) alloys. The indexed peaks are from the icosahedral phase.
The absence of an icosahedral phase in the Ag–Ga–RE alloys can be understood by considering that the atomic radius of gallium (0.1221 nm) is substantially smaller than those of aluminum (0.1431 nm) and indium (0.1626 nm), which is also evidenced by the peak shift of the 1/1-cubic phases towards higher 2h angles in the Ag48.6Ga37.1Lu14.3 and Ag48.6Ga37.1Er14.3 alloys compared with those of the icosahedral phases in Ag48.6Al37.1Lu14.3, Ag48.6In37.1Lu14.3, Ag48.6Al37.1Er14.3 and Ag48.6In37.1Er14.3 alloys. Thus, poor matching of the atomic sizes among the constituent elements may be responsible for the absence of the icosahedral
3414
R. Tamura et al. / Journal of Non-Crystalline Solids 353 (2007) 3412–3416
Fig. 3. Electron diffraction patterns of the rapidly quenched Ag48.6Al37.1Lu14.3 alloy along (a) twofold, (b) threefold and (c) fivefold axes.
Fig. 4. Electron diffraction patterns of the rapidly quenched Ag48.6In37.1Lu14.3 alloy along (a) twofold, (b) threefold and (c) fivefold axes.
Fig. 5. Electron diffraction patterns of the rapidly quenched Ag48.6Al37.1Er14.3 alloy along (a) twofold, (b) threefold and (c) fivefold axes.
Fig. 6. Electron diffraction patterns of the rapidly quenched Ag48.6In37.1Er14.3 alloy along (a) twofold, (b) threefold and (c) fivefold axes.
R. Tamura et al. / Journal of Non-Crystalline Solids 353 (2007) 3412–3416
3415
X=Al
Intensity(arb.units)
Intensity(arb.units)
211111 221001
X=Al
332002
X=Ga
X=Ga
X=In
20
40
60
X=In
80
20
2θ (degree) Fig. 7. X-ray diffraction patterns of rapidly quenched Au48.6X37.1Lu14.3 (X = Al,Ga,In) alloys. The indexed peaks are from the icosahedral phase.
40
60
80
2θ (degree) Fig. 8. X-ray diffraction patterns of rapidly quenched Au48.6X37.1Er14.3 (X = Al,Ga,In) alloys.
Fig. 9. Electron diffraction patterns of the rapidly quenched Au48.6Ga37.1Lu14.3 alloy along (a) twofold, (b) threefold and (c) fivefold axes.
phase in the rapidly solidified state for the Ag48.6Ga37.1Lu14.3 and Ag48.6Ga37.1Er14.3 alloys . Recently, Dong et al. [4] have argued that two factors have important roles in the stability of the quasicrystalline phase in the Al–(Cu,Pd,Ni) systems; one is the e/a ratio and the other is the close packing requirement for the 1stshell of the icosahedral cluster (the cluster composition). The second requirement assumes that the icosahedral cluster is most stabilized when the topological close packing requirement is satisfied. In the present case, the 1st-shell is a dodecahedron made of Ag and In(Al) atoms and, in this respect, the atomic radius of gallium may be too small to stabilize the dodecahedral cluster, resulting in the absence of the icosahedral phase in the Ag–Ga–RE systems. On the other hand, the reason for the absence of an icosahedral phase in the Au-Ga-Er alloy is not clear at the moment since an icosahedral phase is formed in both Ag–X–Lu and Ag–X–Er alloys for the same elements, X, in the case of Ag-based alloys and gold (0.1442 nm) has almost the same atomic radius as silver (0.1444 nm). The reason of such discrepancies between the Ag- and Au-
based alloys might be attributed to different electronic configurations between silver and gold. Finally, we note that the e/a ratio is the same, nearly 2.0, for all the icosahedral phases presented in this paper, which suggests that the e/a ratio plays an important role in the formation of the quasicrystals, hence, of their stability. 5. Conclusion We have observed formation of an icosahedral phase in rapidly solidified Ag48.6Al37.1Lu14.3, Ag48.6In37.1Lu14.3, Ag48.6Al37.1Er14.3, Ag48.6In37.1Er14.3 and Au48.6Ga37.1Lu14.3 alloys by both X-ray and electron diffraction experiments. The formation of the icosahedral phases at these compositions suggests that the ratio of (M,X) (M = Ag, Au, X = Al, Ga, In) to RE and the average valence electrons per atom (e/a) have very crucial roles in the formation, hence the stability, of the icosahedral phases: The ratio of (M,X)6RE and the e/a ratio of 2.0 are favored for the formation of the icosahedral phase in the ternary (Ag,Au)-(Ga,Al,In)-RE alloys. Furthermore, the trend of
3416
R. Tamura et al. / Journal of Non-Crystalline Solids 353 (2007) 3412–3416
the icosahedral phase formation in the Au-based alloys is found to be quite different from that in the Ag-based alloys. References [1] A.C. Larson, D. Cromer, Acta Cryst. B 27 (1971) 1875. [2] A.P. Tsai, J.Q. Guo, E. Abe, H. Takakura, T.J. Sato, Nature (London) 408 (2000) 537.
[3] J.Q. Guo, E. Abe, A.P. Tsai, Phys. Rev. B 62 (2000) R14605. [4] C. Dong, J.B. Qiang, Y.M. Wang, N. Jiang, J. Wu, P. Thiel, Philos. Mag. 86 (2006) 263.
Formation of icosahedral quasicrystals in (Ag,Au)-based ternary systems R. Tamura a
a,b,*
, A. Katahoka a, K. Nishimoto a, S. Takeuchi
a
Department of Materials Science and Technology, Tokyo University of Science, Noda, Chiba 278-8510, Japan b CREST, Japan Science and Technology Corporation, Japan Available online 30 July 2007
Abstract We investigated the phase constitution of rapidly solidified (Ag,Au)-based ternary alloys at various compositions of (M,X)85.7RE14.3 (M = Ag, Au, X = Al,Ga,In, RE = Er,Lu). It is found that an icosahedral phase is formed at an average electrons per atom ratio close to 2.0 as well as at the composition ratio of (M,X)6RE, suggesting that these factors have crucial roles in the stability of the icosahedral phases. It is also found that the trend of the icosahedral phase formation in the Au-based alloys is quite different from that in the Ag-based alloys. Ó 2007 Published by Elsevier B.V. PACS: 61.43.Dq; 61.44.Br; 61.10.Nz; 61.14. x Keywords: Amorphous metals; Metallic glasses; Quasicrystals; X-ray diffraction; Electron diffraction
1. Introduction Recently, much attention has been paid to the structural relationship between icosahedral quasicrystals and bulk metallic glasses since an icosahedral phase is often formed as a primary precipitation phase in a number of bulk metallic glasses with high glass forming ability, suggesting that their local atomic configurations are closely related to each other. The aim of the present work is to synthesize thermodynamically stable icosahedral quasicrystals that are mainly based on the group I elements of the periodic table, such as copper, silver and gold. In this paper, we report on the formation of icosahedral quasicrystals in rapidly solidified (Ag,Au)-based ternary alloys and discuss their formation condition in terms of the average valence electrons per atom (e/a) as well as of the relative sizes of the constituent elements. *
Corresponding author. Address: Department of Materials Science and Technology, Tokyo University of Science, Noda, Chiba 278-8510, Japan. Tel.: +81 4 7124 1501; fax: +81 4 7122 1499. E-mail address: [email protected] (R. Tamura). 0022-3093/$ - see front matter Ó 2007 Published by Elsevier B.V. doi:10.1016/j.jnoncrysol.2007.06.021
Prior to the present work, we investigated the phase constitution of alloys prepared at compositions (M,X)85.7RE14.3 (M = Ag,Au, X = Al,Ga,In, RE = rare earth metals). The reason we have chosen these compositions is because a number of 1/1-cubic approximant phases such as those of Cd6Y-type [1], which are closely related to the recently discovered Cd5.7Yb and Cd5.7Ca binary quasicrystals [2,3], are stabilized at the particular concentration of M85.7RE14.3, i.e., M6RE. In this respect, we systematically prepared rapidly quenched alloys by slightly varying the concentration ratio of M to X in (M,X)85.7RE14.3 and have found that a quasicrystalline phase is formed as a primary phase in the rapidly solidified state around the alloy composition of M48.6X37.1RE14.3, which has an e/a ratio close to 2, i.e., 2.03. For this reason, this composition has been chosen for further investigations on the formation of the icosahedral phase. 2. Experimental procedures (Ag,Au)-based (Ag,Au)48.6(Ga,Al,In)37.1RE14.3 ternary alloys were prepared by melting the constituent elements
211111 221001
Figs. 1 and 2 present X-ray diffraction patterns of rapidly quenched Ag48.6X37.1Lu14.3 (X = Al,Ga,In) and Ag48.6X37.1Er14.3 (X = Al,Ga,In) alloys, respectively. It is found that a mostly single icosahedral phase is obtained for the Ag48.6Al37.1Lu14.3, Ag48.6In37.1Lu14.3, Ag48.6Al37.1Er14.3 and Ag48.6In37.1Er14.3 alloys, as are indexed using the projection method from six dimensional space. Figs. 3– 6 present electron diffraction patterns of these alloys along (a) twofold, (b) threefold and (c) fivefold axes, respectively, verifying the formation of an icosahedral phase in all these alloys. We have found that an icosahedral phase is not formed in the rapidly quenched state for the Ga-bearing Ag48.6Ga37.1Lu14.3 and Ag48.6Ga37.1Er14.3 alloys although gallium has the same valence electrons, i.e., 3 electrons, as aluminum and indium. From Figs. 3–6 it is seen that the fivefold pattern of the Ag48.6In37.1Er14.3 alloys exhibits many sharp Bragg spots with little deviation from the ideal positions of the icosahedral symmetry, implying that the icosahedral phase possesses high structural perfection among the alloys studied in the present work. These icosahedral phases, however, are found to be metastable since they transform into equilibrium crystalline phases upon annealing, mostly into 1/1-
Intensity(arb.units)
332002
X=Al
211111 221001
X=Ga
X=In
60
40
332002
X=In
20
60
40
80
2θ (degree) Fig. 2. X-ray diffraction patterns of rapidly quenched Ag48.6X37.1Er14.3 (X = Al,Ga,In) alloys. The indexed peaks are from the icosahedral phase.
cubic approximant phases, which are crystalline analog to the icosahedral phases. 3.2. Ternary Au48.6(Al,Ga,In)37.1RE14.3 alloys Figs. 7 and 8 present X-ray diffraction patterns of rapidly quenched Au48.6X37.1Lu14.3 (X = Al,Ga,In) and Au48.6X37.1Er14.3 (X = Al,Ga,In) alloys, respectively, and Fig. 9 shows electron diffraction patterns of the rapidly quenched Au48.6Ga37.1Lu14.3 alloy along (a) twofold, (b) threefold and (c) fivefold axes, clearly showing the formation of an icosahedral phase. In contrast to the case of the Ag-based alloys, an icosahedral phase does not occur in the Au–X–Lu (X = Al, In) and Au–X–Er (X = Al, In) systems but is found to form in the Au48.6Ga37.1Lu14.3 alloy although we expect similar results for Au48.6X37.1RE14.3 (X = Al,Ga,In) alloys since the atomic radius of gold (0.1442 nm) is nearly the same as that of silver (0.1444 nm). Moreover, it is seen that an icosahedral phase is not formed in the rapidly quenched Au48.6Ga37.1Er14.3 alloy, which is in contrast to the case of the Au48.6Ga37.1Lu14.3 alloy. 4. Discussion
332002
20
X=Ga
332002
3.1. Ternary Ag48.6(Al,Ga,In)37.1RE14.3 alloys
X=Al
211111 221001
3. Results
Intensity(arb.units)
in an arc furnace under argon atmosphere. The alloys were then rapidly quenched by the single-roll melt-spinning technique. The obtained phases were studied by powder X-ray diffraction experiments using Cu Ka radiation and the formation of quasicrystalline phases was examined and confirmed by electron diffraction experiments.
3413
211111 221001
R. Tamura et al. / Journal of Non-Crystalline Solids 353 (2007) 3412–3416
80
2θ (degree) Fig. 1. X-ray diffraction patterns of rapidly quenched Ag48.6X37.1Lu14.3 (X = Al,Ga,In) alloys. The indexed peaks are from the icosahedral phase.
The absence of an icosahedral phase in the Ag–Ga–RE alloys can be understood by considering that the atomic radius of gallium (0.1221 nm) is substantially smaller than those of aluminum (0.1431 nm) and indium (0.1626 nm), which is also evidenced by the peak shift of the 1/1-cubic phases towards higher 2h angles in the Ag48.6Ga37.1Lu14.3 and Ag48.6Ga37.1Er14.3 alloys compared with those of the icosahedral phases in Ag48.6Al37.1Lu14.3, Ag48.6In37.1Lu14.3, Ag48.6Al37.1Er14.3 and Ag48.6In37.1Er14.3 alloys. Thus, poor matching of the atomic sizes among the constituent elements may be responsible for the absence of the icosahedral
3414
R. Tamura et al. / Journal of Non-Crystalline Solids 353 (2007) 3412–3416
Fig. 3. Electron diffraction patterns of the rapidly quenched Ag48.6Al37.1Lu14.3 alloy along (a) twofold, (b) threefold and (c) fivefold axes.
Fig. 4. Electron diffraction patterns of the rapidly quenched Ag48.6In37.1Lu14.3 alloy along (a) twofold, (b) threefold and (c) fivefold axes.
Fig. 5. Electron diffraction patterns of the rapidly quenched Ag48.6Al37.1Er14.3 alloy along (a) twofold, (b) threefold and (c) fivefold axes.
Fig. 6. Electron diffraction patterns of the rapidly quenched Ag48.6In37.1Er14.3 alloy along (a) twofold, (b) threefold and (c) fivefold axes.
R. Tamura et al. / Journal of Non-Crystalline Solids 353 (2007) 3412–3416
3415
X=Al
Intensity(arb.units)
Intensity(arb.units)
211111 221001
X=Al
332002
X=Ga
X=Ga
X=In
20
40
60
X=In
80
20
2θ (degree) Fig. 7. X-ray diffraction patterns of rapidly quenched Au48.6X37.1Lu14.3 (X = Al,Ga,In) alloys. The indexed peaks are from the icosahedral phase.
40
60
80
2θ (degree) Fig. 8. X-ray diffraction patterns of rapidly quenched Au48.6X37.1Er14.3 (X = Al,Ga,In) alloys.
Fig. 9. Electron diffraction patterns of the rapidly quenched Au48.6Ga37.1Lu14.3 alloy along (a) twofold, (b) threefold and (c) fivefold axes.
phase in the rapidly solidified state for the Ag48.6Ga37.1Lu14.3 and Ag48.6Ga37.1Er14.3 alloys . Recently, Dong et al. [4] have argued that two factors have important roles in the stability of the quasicrystalline phase in the Al–(Cu,Pd,Ni) systems; one is the e/a ratio and the other is the close packing requirement for the 1stshell of the icosahedral cluster (the cluster composition). The second requirement assumes that the icosahedral cluster is most stabilized when the topological close packing requirement is satisfied. In the present case, the 1st-shell is a dodecahedron made of Ag and In(Al) atoms and, in this respect, the atomic radius of gallium may be too small to stabilize the dodecahedral cluster, resulting in the absence of the icosahedral phase in the Ag–Ga–RE systems. On the other hand, the reason for the absence of an icosahedral phase in the Au-Ga-Er alloy is not clear at the moment since an icosahedral phase is formed in both Ag–X–Lu and Ag–X–Er alloys for the same elements, X, in the case of Ag-based alloys and gold (0.1442 nm) has almost the same atomic radius as silver (0.1444 nm). The reason of such discrepancies between the Ag- and Au-
based alloys might be attributed to different electronic configurations between silver and gold. Finally, we note that the e/a ratio is the same, nearly 2.0, for all the icosahedral phases presented in this paper, which suggests that the e/a ratio plays an important role in the formation of the quasicrystals, hence, of their stability. 5. Conclusion We have observed formation of an icosahedral phase in rapidly solidified Ag48.6Al37.1Lu14.3, Ag48.6In37.1Lu14.3, Ag48.6Al37.1Er14.3, Ag48.6In37.1Er14.3 and Au48.6Ga37.1Lu14.3 alloys by both X-ray and electron diffraction experiments. The formation of the icosahedral phases at these compositions suggests that the ratio of (M,X) (M = Ag, Au, X = Al, Ga, In) to RE and the average valence electrons per atom (e/a) have very crucial roles in the formation, hence the stability, of the icosahedral phases: The ratio of (M,X)6RE and the e/a ratio of 2.0 are favored for the formation of the icosahedral phase in the ternary (Ag,Au)-(Ga,Al,In)-RE alloys. Furthermore, the trend of
3416
R. Tamura et al. / Journal of Non-Crystalline Solids 353 (2007) 3412–3416
the icosahedral phase formation in the Au-based alloys is found to be quite different from that in the Ag-based alloys. References [1] A.C. Larson, D. Cromer, Acta Cryst. B 27 (1971) 1875. [2] A.P. Tsai, J.Q. Guo, E. Abe, H. Takakura, T.J. Sato, Nature (London) 408 (2000) 537.
[3] J.Q. Guo, E. Abe, A.P. Tsai, Phys. Rev. B 62 (2000) R14605. [4] C. Dong, J.B. Qiang, Y.M. Wang, N. Jiang, J. Wu, P. Thiel, Philos. Mag. 86 (2006) 263.