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Damping properties in Mg–Zn–Y alloy with dispersion of quasicrystal phase particle
Materials Letters 65 (2011) 3251–3253
Contents lists available at ScienceDirect
Materials Letters j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / m a t l e t
Damping properties in Mg–Zn–Y alloy with dispersion of quasicrystal phase particle Hidetoshi Somekawa a,⁎, Hiroyuki Watanabe b, Toshiji Mukai a, c a b c
National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan Osaka Municipal Technical Research Institute, 1-6-50 Morinomiya Joto-ku 536-8553, Japan Kobe University, 1-1 Rokkoadai, Nada-ku 657-8501, Japan
a r t i c l e
i n f o
Article history: Received 27 April 2011 Accepted 1 July 2011 Available online 13 July 2011 Keyword: Magnesium alloy Quasicrystal Damping capacity Grain boundary sliding Dynamic modulus
a b s t r a c t The effect of the interface structure between the matrix and the particle on the damping capacity was investigated using Mg–Zn and Mg–Zn–Y alloys in this study. The damping capacity was not affected by the interface structure at room temperature. However, the onset of temperature, which was higher in the Mg–Zn–Y alloy than in the Mg–Zn alloy despite their similar grain sizes, increased the damping capacity through grain boundary relaxation by grain boundary sliding. Compared to the Mg–Zn alloy, the existence of the quasicrystal phase particles, which had the coherent interface with low interface energy, was likely to have suppressed and delayed the grain boundary sliding in the Mg–Zn alloy. © 2011 Elsevier B.V. All rights reserved.
1. Introduction The quasicrystalline phase possesses two- or five-fold symmetry and does not have translational symmetry, which is completely different from the conventional crystal phases [1]. In addition, this phase occurs in equilibrium with the metallic matrix, i.e., the formation of a coherent interface, and thus, this phase can be applied to the dispersed particle into the metallic matrix [2]. This strong matching interface between the matrix and the particle produces good mechanical properties in metallic materials: the quasicrystalline phase has a pinning effect on dislocation movements during the plastic deformation [3]; however, this phase does not become the origin of the fracture, e.g., high strength and ductility balances at room temperature [4]. The damping properties (internal friction) of materials at low frequencies provide useful information for evaluating the effect of the grain boundary and/or the interface on microscopic deformation, because the grain boundary and/or the interface behave in a viscous manner at high temperature. The viscous flow at the grain boundaries converts mechanical energy into thermal energy as a result of grain boundary relaxation or internal friction through grain boundary sliding. Pure magnesium is reported to have good damping properties [5]. In addition, magnesium systems are able to form the quasicrystal phase quite easily, and this phase can be dispersed by severe plastic deformation [6–9]. However, there are no reports on the damping properties of magnesium alloys with the dispersion of quasicrystal
⁎ Corresponding author. Tel.: + 81 29 859 2473; fax: + 81 29 859 2401. E-mail address: [email protected] (H. Somekawa). 0167-577X/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.matlet.2011.07.001
phase particles. Therefore, the damping properties of magnesium alloys with and without quasicrystal phase particles were investigated, and the effect of the interface structure on the damping capacity was specifically considered in this study. 2. Experimental procedure Mg–2.9 at.%Zn and Mg–2.6 at.%Zn–0.4 at.%Y alloys (hereafter denoted as, Mg–Zn and Mg–Zn–Y alloys) were produced by casting and were solution treated at a temperature of 603 K for 48 h and at 673 K for 24 h, respectively. Then, they were extruded with a reduction ratio of 18 at a temperature of 483 K. The previous initial microstructural observations by TEM showed that the Mg–Zn alloy had spherical shaped precipitate particles with incoherent interfaces [10], while the Mg–Zn–Y alloy contained quasicrystal phase particles with coherent interfaces [3,11]. The extruded alloys were annealed to remove the residual strains and to control the grain sizes. The average grain size, d, of both of the annealed alloys was ~15 μm. The damping capacity and dynamic Young's modulus for the annealed alloys were evaluated from room temperature to 573 K by employing the method of the resonant frequency in a cantilever holder. The resonant frequency in the experimental apparatus was 13–15 Hz at room temperature. All the specimens had a rectangular shape with a length of 60 mm, a width of 10 mm and a thickness of 1.5 mm. They were prepared by machining in the direction parallel to the extrusion direction. The damping constant was specified by the loss factor, η, of free vibration, which is related to the logarithmic decrement, Λ, of η = Λ/π, in this study. The loss factor was measured at strain amplitudes ranging from 5 × 10 − 5 to 5 × 10 − 4 at room temperature and at ~1 × 10 − 4 at elevated temperatures.
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H. Somekawa et al. / Materials Letters 65 (2011) 3251–3253
3. Result and discussion The variation in the loss factor as a function of strain amplitude at room temperature is shown in Fig. 1. The data of pure magnesium with different purities are also included in this figure [12,13]. The loss factors of both of the present alloys are found to be of similar values and tendencies; the loss factors are almost constant at low strain amplitudes, but increase at high strain amplitudes. In general, the loss factor can be divided into two regions with low and high strain amplitudes. The loss factor, ηL, is independent of the strain amplitude at low strains. Granato and Lücke reported that the loss factor, ηL, depends on the dislocation density, ρ, and the length of weakly pinned segments, L, according to ηL ∝ ρL 4 [14,15]. Fig. 1 shows that the loss factor of pure magnesium is larger than that of the present alloys at low strains and increases with higher purities. The lower loss factors in the present alloys result from the additional solute atoms such as Zn and Y. Since these solute atoms cause weak pinning of dislocations, the spacing of L in the present alloys is shorter than that of pure magnesium. In the second region, the loss factor, ηH, increases rapidly with increasing strain amplitude. Although the strain amplitude, which has an influence on the loss factor (i.e., dependent loss factor on strain amplitude), is in the range of ~10 − 5 for pure magnesium, higher values of ~4 × 10 − 4 is obtained for the present alloys. Lambri et al. reported that the strain amplitude, which changes from an independent loss factor to a dependent loss factor, is sensitive to the dislocation density [16]. However, this microstructural factor, i.e., the dislocation density, is not likely to have an effect on the critical strain, since the present alloys were annealed before the damping tests and were observed to form fully recrystallized grain structures with high-angle grain boundaries. Diqing et al. mentioned that the transitional strain amplitude becomes larger with the addition of solute atoms [17]. Thus, the large transitional strain amplitude in the present alloys is due to the existence of Zn and Y atoms. In addition, the comparable transitional strain amplitude in the present alloys results from the similarity in the total concentration of additional elements, i.e., ~ 3 at.%. This result indicates that the damping properties at room temperature are influenced not by the difference in the interface structures, i.e., coherent or incoherent interfaces, but by the amount of solute atoms. The variation in the loss factor as a function of temperature is shown in Fig. 2. The loss factor of the present alloys does not depend on temperature in the low temperature region, while the loss factor shows a sudden increase in the high temperature region. The increase in the loss factor with temperature results from the viscous manner through grain boundary sliding at the grain boundaries and/or the interfaces [18,19]. This mechanism has been reported in magnesium
Fig. 1. The variation in the loss factor as a function of strain amplitude at room temperature. This figure includes the data of pure magnesium with purity of 99.9% [13] and 99.99% [12].
Fig. 2. The variations in the loss factor as a function of temperature in Mg–Zn and Mg–Zn–Y alloys.
and its alloys [13,19–22]. The onset temperatures that cause an increase in the loss factor are ~400 K and ~460 K for the Mg–Zn and Mg–Zn–Y alloys, respectively. This indicates that the grain boundary sliding occurs less frequently in the Mg–Zn–Y alloy than in the Mg–Zn alloy at the temperature regions of 400–450 K. The loss factor generally increases with grain refinement due to the enhancement of grain boundary sliding [20,23]. However, the present alloys have similar grain sizes of 15 μm; therefore, this factor, i.e., grain size, can be left out of consideration. The loss factors are also influenced by the grain boundary segregation of solute atoms and the existence of particles at the grain boundary [22]. The presence of the solute atoms at the grain boundary is ineffective in this study because of the formation of many particles. On the other hand, the interface between the matrix and the quasicrystal phase particle has low interface energy due to the strong interface matching [24]. The unique interface boundaries with low energy tend to suppress the grain boundary sliding, and thus, the Mg–Zn–Y alloy shows a delay in the increase of the loss factor for temperatures up to around 460 K. The variation in the dynamic Young's modulus as a function of temperature is shown in Fig. 3. The dynamic Young's modulus for both alloys is found to decrease linearly with increasing temperature in the low temperature range. The temperature dependence of elastic constants (dE/dT) is calculated to be −0.021 and − 0.020 GPa K − 1 for the Mg–Zn and Mg–Zn–Y alloys, respectively. The linearity as well as the dE/dT values of −0.024 GPa K − 1 [20,25] infers that the Young's moduli of the present alloys are unrelaxed in the low temperature range. This figure shows that the dynamic Young's modulus for the present alloys deviates from linearity above the temperature of ~450 K for the Mg–Zn alloy and ~ 510 K for the Mg–Zn–Y alloy, respectively.
Fig. 3. The variation in the dynamic Young's modulus as a function of temperature in Mg–Zn and Mg–Zn–Y alloys.
H. Somekawa et al. / Materials Letters 65 (2011) 3251–3253
This tendency is not observed in the single crystalline (absent from the grain boundary) and the coarse-grained materials [19,26,27]. The drop in the dynamic modulus is due to the grain boundary relaxation. Mg–Zn–Y alloy is found to have about 60 K higher temperature for the drop in the modulus compared to that in the Mg–Zn alloy, which is similar to the result of damping capacity. Bae et al. reported that the yield and ultimate tensile stresses in the Mg–Zn–Y alloy with d = 14 μm decreases immediately above temperature of 473 K [28]. This result indicates that the grain boundary sliding occurs in this temperature range, which agrees with the present result. Thus, the quasicrystal phase, which has a coherent interface, has a role of suppressing the occurrence of grain boundary sliding. 4. Summary The damping properties in Mg–Zn and Mg–Zn–Y alloys at room temperature were lower than that in pure magnesium due to the existence of solute atoms. The effect of the interface structure between the matrix and the particle on the damping properties was ineffective in the present observed strain regions. The loss factor increased gradually and the dynamic modulus decreased linearly with temperature in both alloys; however, the change occurred more abruptly above a certain temperature probably due to the grain boundary sliding. The transition temperatures in the Mg–Zn–Y alloy were around 60 K higher than that in the Mg–Zn alloy. This was resulted that the interface between the matrix and the quasicrystal phase, which had low interface energy, suppressed the occurrence of grain boundary sliding. Acknowledgment One of the authors (HS) is grateful to Ms. M. Isaki (National Institute for Materials Science) for the sample preparation. This work
3253
was partly supported by the JSPS Grant-in-Aid No. 21760564 and No. 21360347.
References [1] Shechtman D, Blech I, Gratias D, Cahn JW. Phys Rev Letts 1984;53:1951. [2] Tsai AP, Niikura A, Inoue A, Masumoto T, Nishida Y, Tsuda K, et al. Philo Mag Lett 1994;70:169. [3] Somekawa H, Singh A, Mukai T. Scripta Mater 2007;56:1091. [4] Somekawa H, Singh A, Mukai T. Mater Trans 2007;48:1422. [5] Sugimoto K, Niiya K, Okamoto T, Kishitake K. Mater Trans JIM 1977;18:277. [6] Luo Z, Zhang S, Tang Y, Zhao D. Scripta Mater 1993;28:1513. [7] Bae DH, Kim SH, Kim DH, Kim WT. Acta Mater 2002;50:2343. [8] Singh A, Nakamura M, Watanabe M, Kato A, Tsai AP. Scripta Mater 2003;49:417. [9] Zhang Y, Zeng X, Liu L, Lu C, Zhou H, Li Q, et al. Mater Sci Eng 2004;A373:320. [10] Somekawa H, Singh A, Mukai T. Scripta Mater 2009;60:411. [11] Singh A, Watanabe M, Kato A, Tsai AP. Mater Sci Eng 2004;A385:382. [12] Wan D, Wang J, Lin L, Feng Z, Yang G. Physica B 2008;403:2438. [13] Hu XS, Wu K, Zheng MY, Gan WM, Wang XJ. Mater Sci Eng 2007;A452-453:374. [14] Granato A, Lücke K. J Appl Phys 1956;27:593. [15] Granato A, Lücke K. J Appl Phys 1956;27:789. [16] Lambri OA, Riehemann W, Lucioni EJ, Bolmaro RE. Mater Sci Eng 2006;A442:476. [17] Diqing W, Jincheng W, Gencang Y. Mater Sci Eng 2009;A517:114. [18] Zener C. Phys Rev 1941;60:906. [19] Kê T-S. Phys Rev 1947;71:533. [20] Watanabe H, Mukai T, Sugioka M, Ishikawa K. Scripta Mater 2004;51:291. [21] Chuvil'deev VN, Nieh TG, Gryaznov YM, Sysoev AN, Kopylov VI. Scripta Mater 2004;50:861. [22] Starr CD, Vicars EC, Goldberg A, Dorn JE. Trans ASM 1953;45:275. [23] Dudarev EF, Pochivalova GP, Kolobov YR, Naydenkin EV, Kashin OA. Mater Sci Eng 2009;A503:58. [24] Lee JY, Kim DH, Kim HK, Kim DH. Mater Letts 2005;59:3801. [25] Frost HJ, Ashby MF. Deformation mechanism map. Oxford: Pergamon Press; 1982. p. 43. [26] Kê T-S. Phys Rev 1947;72:41. [27] Watanabe H, Mukai T, Ishikawa K. Mater Letts 2005;59:1511. [28] Bae DH, Kim SH, Kim WT, Kim DH. Mater Trans 2001;42:2144.
Contents lists available at ScienceDirect
Materials Letters j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / m a t l e t
Damping properties in Mg–Zn–Y alloy with dispersion of quasicrystal phase particle Hidetoshi Somekawa a,⁎, Hiroyuki Watanabe b, Toshiji Mukai a, c a b c
National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan Osaka Municipal Technical Research Institute, 1-6-50 Morinomiya Joto-ku 536-8553, Japan Kobe University, 1-1 Rokkoadai, Nada-ku 657-8501, Japan
a r t i c l e
i n f o
Article history: Received 27 April 2011 Accepted 1 July 2011 Available online 13 July 2011 Keyword: Magnesium alloy Quasicrystal Damping capacity Grain boundary sliding Dynamic modulus
a b s t r a c t The effect of the interface structure between the matrix and the particle on the damping capacity was investigated using Mg–Zn and Mg–Zn–Y alloys in this study. The damping capacity was not affected by the interface structure at room temperature. However, the onset of temperature, which was higher in the Mg–Zn–Y alloy than in the Mg–Zn alloy despite their similar grain sizes, increased the damping capacity through grain boundary relaxation by grain boundary sliding. Compared to the Mg–Zn alloy, the existence of the quasicrystal phase particles, which had the coherent interface with low interface energy, was likely to have suppressed and delayed the grain boundary sliding in the Mg–Zn alloy. © 2011 Elsevier B.V. All rights reserved.
1. Introduction The quasicrystalline phase possesses two- or five-fold symmetry and does not have translational symmetry, which is completely different from the conventional crystal phases [1]. In addition, this phase occurs in equilibrium with the metallic matrix, i.e., the formation of a coherent interface, and thus, this phase can be applied to the dispersed particle into the metallic matrix [2]. This strong matching interface between the matrix and the particle produces good mechanical properties in metallic materials: the quasicrystalline phase has a pinning effect on dislocation movements during the plastic deformation [3]; however, this phase does not become the origin of the fracture, e.g., high strength and ductility balances at room temperature [4]. The damping properties (internal friction) of materials at low frequencies provide useful information for evaluating the effect of the grain boundary and/or the interface on microscopic deformation, because the grain boundary and/or the interface behave in a viscous manner at high temperature. The viscous flow at the grain boundaries converts mechanical energy into thermal energy as a result of grain boundary relaxation or internal friction through grain boundary sliding. Pure magnesium is reported to have good damping properties [5]. In addition, magnesium systems are able to form the quasicrystal phase quite easily, and this phase can be dispersed by severe plastic deformation [6–9]. However, there are no reports on the damping properties of magnesium alloys with the dispersion of quasicrystal
⁎ Corresponding author. Tel.: + 81 29 859 2473; fax: + 81 29 859 2401. E-mail address: [email protected] (H. Somekawa). 0167-577X/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.matlet.2011.07.001
phase particles. Therefore, the damping properties of magnesium alloys with and without quasicrystal phase particles were investigated, and the effect of the interface structure on the damping capacity was specifically considered in this study. 2. Experimental procedure Mg–2.9 at.%Zn and Mg–2.6 at.%Zn–0.4 at.%Y alloys (hereafter denoted as, Mg–Zn and Mg–Zn–Y alloys) were produced by casting and were solution treated at a temperature of 603 K for 48 h and at 673 K for 24 h, respectively. Then, they were extruded with a reduction ratio of 18 at a temperature of 483 K. The previous initial microstructural observations by TEM showed that the Mg–Zn alloy had spherical shaped precipitate particles with incoherent interfaces [10], while the Mg–Zn–Y alloy contained quasicrystal phase particles with coherent interfaces [3,11]. The extruded alloys were annealed to remove the residual strains and to control the grain sizes. The average grain size, d, of both of the annealed alloys was ~15 μm. The damping capacity and dynamic Young's modulus for the annealed alloys were evaluated from room temperature to 573 K by employing the method of the resonant frequency in a cantilever holder. The resonant frequency in the experimental apparatus was 13–15 Hz at room temperature. All the specimens had a rectangular shape with a length of 60 mm, a width of 10 mm and a thickness of 1.5 mm. They were prepared by machining in the direction parallel to the extrusion direction. The damping constant was specified by the loss factor, η, of free vibration, which is related to the logarithmic decrement, Λ, of η = Λ/π, in this study. The loss factor was measured at strain amplitudes ranging from 5 × 10 − 5 to 5 × 10 − 4 at room temperature and at ~1 × 10 − 4 at elevated temperatures.
3252
H. Somekawa et al. / Materials Letters 65 (2011) 3251–3253
3. Result and discussion The variation in the loss factor as a function of strain amplitude at room temperature is shown in Fig. 1. The data of pure magnesium with different purities are also included in this figure [12,13]. The loss factors of both of the present alloys are found to be of similar values and tendencies; the loss factors are almost constant at low strain amplitudes, but increase at high strain amplitudes. In general, the loss factor can be divided into two regions with low and high strain amplitudes. The loss factor, ηL, is independent of the strain amplitude at low strains. Granato and Lücke reported that the loss factor, ηL, depends on the dislocation density, ρ, and the length of weakly pinned segments, L, according to ηL ∝ ρL 4 [14,15]. Fig. 1 shows that the loss factor of pure magnesium is larger than that of the present alloys at low strains and increases with higher purities. The lower loss factors in the present alloys result from the additional solute atoms such as Zn and Y. Since these solute atoms cause weak pinning of dislocations, the spacing of L in the present alloys is shorter than that of pure magnesium. In the second region, the loss factor, ηH, increases rapidly with increasing strain amplitude. Although the strain amplitude, which has an influence on the loss factor (i.e., dependent loss factor on strain amplitude), is in the range of ~10 − 5 for pure magnesium, higher values of ~4 × 10 − 4 is obtained for the present alloys. Lambri et al. reported that the strain amplitude, which changes from an independent loss factor to a dependent loss factor, is sensitive to the dislocation density [16]. However, this microstructural factor, i.e., the dislocation density, is not likely to have an effect on the critical strain, since the present alloys were annealed before the damping tests and were observed to form fully recrystallized grain structures with high-angle grain boundaries. Diqing et al. mentioned that the transitional strain amplitude becomes larger with the addition of solute atoms [17]. Thus, the large transitional strain amplitude in the present alloys is due to the existence of Zn and Y atoms. In addition, the comparable transitional strain amplitude in the present alloys results from the similarity in the total concentration of additional elements, i.e., ~ 3 at.%. This result indicates that the damping properties at room temperature are influenced not by the difference in the interface structures, i.e., coherent or incoherent interfaces, but by the amount of solute atoms. The variation in the loss factor as a function of temperature is shown in Fig. 2. The loss factor of the present alloys does not depend on temperature in the low temperature region, while the loss factor shows a sudden increase in the high temperature region. The increase in the loss factor with temperature results from the viscous manner through grain boundary sliding at the grain boundaries and/or the interfaces [18,19]. This mechanism has been reported in magnesium
Fig. 1. The variation in the loss factor as a function of strain amplitude at room temperature. This figure includes the data of pure magnesium with purity of 99.9% [13] and 99.99% [12].
Fig. 2. The variations in the loss factor as a function of temperature in Mg–Zn and Mg–Zn–Y alloys.
and its alloys [13,19–22]. The onset temperatures that cause an increase in the loss factor are ~400 K and ~460 K for the Mg–Zn and Mg–Zn–Y alloys, respectively. This indicates that the grain boundary sliding occurs less frequently in the Mg–Zn–Y alloy than in the Mg–Zn alloy at the temperature regions of 400–450 K. The loss factor generally increases with grain refinement due to the enhancement of grain boundary sliding [20,23]. However, the present alloys have similar grain sizes of 15 μm; therefore, this factor, i.e., grain size, can be left out of consideration. The loss factors are also influenced by the grain boundary segregation of solute atoms and the existence of particles at the grain boundary [22]. The presence of the solute atoms at the grain boundary is ineffective in this study because of the formation of many particles. On the other hand, the interface between the matrix and the quasicrystal phase particle has low interface energy due to the strong interface matching [24]. The unique interface boundaries with low energy tend to suppress the grain boundary sliding, and thus, the Mg–Zn–Y alloy shows a delay in the increase of the loss factor for temperatures up to around 460 K. The variation in the dynamic Young's modulus as a function of temperature is shown in Fig. 3. The dynamic Young's modulus for both alloys is found to decrease linearly with increasing temperature in the low temperature range. The temperature dependence of elastic constants (dE/dT) is calculated to be −0.021 and − 0.020 GPa K − 1 for the Mg–Zn and Mg–Zn–Y alloys, respectively. The linearity as well as the dE/dT values of −0.024 GPa K − 1 [20,25] infers that the Young's moduli of the present alloys are unrelaxed in the low temperature range. This figure shows that the dynamic Young's modulus for the present alloys deviates from linearity above the temperature of ~450 K for the Mg–Zn alloy and ~ 510 K for the Mg–Zn–Y alloy, respectively.
Fig. 3. The variation in the dynamic Young's modulus as a function of temperature in Mg–Zn and Mg–Zn–Y alloys.
H. Somekawa et al. / Materials Letters 65 (2011) 3251–3253
This tendency is not observed in the single crystalline (absent from the grain boundary) and the coarse-grained materials [19,26,27]. The drop in the dynamic modulus is due to the grain boundary relaxation. Mg–Zn–Y alloy is found to have about 60 K higher temperature for the drop in the modulus compared to that in the Mg–Zn alloy, which is similar to the result of damping capacity. Bae et al. reported that the yield and ultimate tensile stresses in the Mg–Zn–Y alloy with d = 14 μm decreases immediately above temperature of 473 K [28]. This result indicates that the grain boundary sliding occurs in this temperature range, which agrees with the present result. Thus, the quasicrystal phase, which has a coherent interface, has a role of suppressing the occurrence of grain boundary sliding. 4. Summary The damping properties in Mg–Zn and Mg–Zn–Y alloys at room temperature were lower than that in pure magnesium due to the existence of solute atoms. The effect of the interface structure between the matrix and the particle on the damping properties was ineffective in the present observed strain regions. The loss factor increased gradually and the dynamic modulus decreased linearly with temperature in both alloys; however, the change occurred more abruptly above a certain temperature probably due to the grain boundary sliding. The transition temperatures in the Mg–Zn–Y alloy were around 60 K higher than that in the Mg–Zn alloy. This was resulted that the interface between the matrix and the quasicrystal phase, which had low interface energy, suppressed the occurrence of grain boundary sliding. Acknowledgment One of the authors (HS) is grateful to Ms. M. Isaki (National Institute for Materials Science) for the sample preparation. This work
3253
was partly supported by the JSPS Grant-in-Aid No. 21760564 and No. 21360347.
References [1] Shechtman D, Blech I, Gratias D, Cahn JW. Phys Rev Letts 1984;53:1951. [2] Tsai AP, Niikura A, Inoue A, Masumoto T, Nishida Y, Tsuda K, et al. Philo Mag Lett 1994;70:169. [3] Somekawa H, Singh A, Mukai T. Scripta Mater 2007;56:1091. [4] Somekawa H, Singh A, Mukai T. Mater Trans 2007;48:1422. [5] Sugimoto K, Niiya K, Okamoto T, Kishitake K. Mater Trans JIM 1977;18:277. [6] Luo Z, Zhang S, Tang Y, Zhao D. Scripta Mater 1993;28:1513. [7] Bae DH, Kim SH, Kim DH, Kim WT. Acta Mater 2002;50:2343. [8] Singh A, Nakamura M, Watanabe M, Kato A, Tsai AP. Scripta Mater 2003;49:417. [9] Zhang Y, Zeng X, Liu L, Lu C, Zhou H, Li Q, et al. Mater Sci Eng 2004;A373:320. [10] Somekawa H, Singh A, Mukai T. Scripta Mater 2009;60:411. [11] Singh A, Watanabe M, Kato A, Tsai AP. Mater Sci Eng 2004;A385:382. [12] Wan D, Wang J, Lin L, Feng Z, Yang G. Physica B 2008;403:2438. [13] Hu XS, Wu K, Zheng MY, Gan WM, Wang XJ. Mater Sci Eng 2007;A452-453:374. [14] Granato A, Lücke K. J Appl Phys 1956;27:593. [15] Granato A, Lücke K. J Appl Phys 1956;27:789. [16] Lambri OA, Riehemann W, Lucioni EJ, Bolmaro RE. Mater Sci Eng 2006;A442:476. [17] Diqing W, Jincheng W, Gencang Y. Mater Sci Eng 2009;A517:114. [18] Zener C. Phys Rev 1941;60:906. [19] Kê T-S. Phys Rev 1947;71:533. [20] Watanabe H, Mukai T, Sugioka M, Ishikawa K. Scripta Mater 2004;51:291. [21] Chuvil'deev VN, Nieh TG, Gryaznov YM, Sysoev AN, Kopylov VI. Scripta Mater 2004;50:861. [22] Starr CD, Vicars EC, Goldberg A, Dorn JE. Trans ASM 1953;45:275. [23] Dudarev EF, Pochivalova GP, Kolobov YR, Naydenkin EV, Kashin OA. Mater Sci Eng 2009;A503:58. [24] Lee JY, Kim DH, Kim HK, Kim DH. Mater Letts 2005;59:3801. [25] Frost HJ, Ashby MF. Deformation mechanism map. Oxford: Pergamon Press; 1982. p. 43. [26] Kê T-S. Phys Rev 1947;72:41. [27] Watanabe H, Mukai T, Ishikawa K. Mater Letts 2005;59:1511. [28] Bae DH, Kim SH, Kim WT, Kim DH. Mater Trans 2001;42:2144.