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Relation between calculated Lennard-Jones potential and thermal stability of Cu-based bulk metallic glasses
Physics Letters A 353 (2006) 497–499 www.elsevier.com/locate/pla
Relation between calculated Lennard-Jones potential and thermal stability of Cu-based bulk metallic glasses T. Lin, X.F. Bian ∗ , J. Jiang Key Laboratory of Structure and Heredity of Materials, Ministry of Education, Shandong University, South Campus, Jingshi road 73, Jinan 250061, China Received 4 August 2005; received in revised form 30 December 2005; accepted 6 January 2006 Available online 17 January 2006 Communicated by A.R. Bishop
Abstract Two metallic bulk glasses, Cu60 Zr30 Ti10 and Cu47 Ti33 Zr11 Ni8 Si1 , with a diameter of 3 mm were prepared by copper mold casting method. Dilatometric measurement was carried out on the two glassy alloys to obtain information about the average nearest-neighbour distance r0 and the effective depth of pair potential V0 . By assuming a Lennard-Jones potential, r0 and V0 were calculated to be 0.28 nm and 0.16 eV for Cu60 Zr30 Ti10 and 0.27 nm and 0.13 eV for Cu47 Ti33 Zr11 Ni8 Si1 , respectively. It was found that the glassy alloy Cu60 Zr30 Ti10 was more stable than Cu47 Ti33 Zr11 Ni8 Si1 against heating from both experiment and calculation. © 2006 Elsevier B.V. All rights reserved. PACS: 81.05.Kf; 68.60.Dv; 82.56.Na; 02.30.Em Keywords: Cu-based bulk metallic glass; Thermal stability; Structural relaxation; Lennard-Jones potential
1. Introduction Bulk metallic glasses (BMGs) have been drawing increasing attention in recent years due to their scientific and engineering significance [1,2]. As a member of the family of BMGs, great progress has been made in research of Cu-based BMGs. Comparing with other BMG systems, such as Zr-based and Pd-based BMGs, the product cost of Cu-based BMGs is much lower. In addition, they have high thermal stability against crystallization [3]. In last decade, a series of Cu-based bulk glassy alloys were developed, such as Cu–Ti–Zr–Ni [4], Cu–Zr–Ti [5], Cu–Zr–Al [6], Cu–Zr [7] and Cu–Zr–Al–Y [8]. Porscha and Nehauser measured the length and eigenfrequency change of a Cu64 Ti36 metallic glass ribbon simultaneously [9]. By assuming a Lennard-Jones type potential (LJ type potential) [10] B A V (r) = − m + n r r
where V (r) is pair potential of two atoms, r is inter-atomic distance, and A, B, m, and n are constants, they calculated the effective pair potentials over different atomic species and showed that the powers for the potential are 14 and 7, respectively. From a number of previous data, it seems that the addition of a small amount of another element to the basic ternary system increases the glass forming ability [11,12]. It has been reported that the critical diameters for Cu60 Zr30 Ti10 and Cu47 Ti33 Zr11 Ni8 Si1 are 4 mm and 7 mm, respectively. In this Letter, we measured the length change of these two glassy alloys due to structural relaxation at constant heating rate and calculated the nominal value of the interatomic average nearestneighbour distance r0 and the effective depth of pair potential V0 by assuming a 14-7 LJ type potential. Different thermal stability of these two alloys was discussed according to r0 and V0 . 2. Experimental procedure
(n > m),
* Corresponding author.
E-mail address: [email protected] (X.F. Bian). 0375-9601/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.physleta.2006.01.012
(1) The alloy ingots of nominal compositions Cu60 Zr30 Ti10 and Cu47 Ti33 Zr11 Ni8 Si1 were prepared by arc melting mixtures of pure Cu(99.9%), Zr(99.7%), Ti(99.9%), Ni(99.9%), Si(99.9%) in a Ti-gettered argon atmosphere. Bulk glassy alloys in a cylin-
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T. Lin et al. / Physics Letters A 353 (2006) 497–499
drical rod form with a diameter of 3 mm were produced by the copper mould casting method. X-ray diffraction (XRD, D/maxrB) experiments were performed to identify the formation of the amorphous phase in the as-cast samples using a Cu-Kα source. Thermal stability associated with glass transition and supercooled liquid region was examined by differential scanning calorimeter (Netzsch DSC 404C) with a heating rate of 20 K/min. A Netzsch DIL 402C was utilized for dilatometric measurement at constant heating rate. The length of samples is about 22 mm. 3. Results and discussion Fig. 1 shows the X-ray diffraction patterns taken from the cross sections of 3 mm thick cast rods of Cu60 Zr30 Ti10 and Cu47 Ti33 Zr11 Ni8 Si1 alloys. Each of the pattern exhibits a broad diffraction maximum characteristic of amorphous structure. The DSC curves with a heating rate of 20 K/min of the cast Cu–Zr–Ti and Cu–Ti–Zr–Ni–Si glassy alloys are shown in Fig. 2. The glass transition temperature (Tg ) and crystallization temperature (Tx ) are marked with arrows. The Tg and Tx are 448 ◦ C and 475 ◦ C for the Cu60 Zr30 Ti10 alloy, and 415 ◦ C and 466 ◦ C for Cu47 Ti33 Zr11 Ni8 Si1 alloy, respectively. The supercooled liquid region Tg (= Tx − Tg ) is 27 ◦ C and 51 ◦ C for the two alloys. The melting behavior of these two alloys is also shown in Fig. 2. It can be seen that the Cu60 Zr30 Ti10 alloy
Fig. 1. X-ray diffraction patterns of cast Cu60 Zr30 Ti10 and Cu47 Ti33 Zr11 Ni8 Si1 alloy rods with a diameter of 3 mm.
Fig. 2. DSC curves of Cu47 Ti33 Zr11 Ni8 Si1 (a) and Cu60 Zr30 Ti10 (b) glassy alloys.
has higher solidus (Tm ) and liquidus (Tl ) temperature than the Cu47 Ti33 Zr11 Ni8 Si1 alloy. Fig. 3 shows the total length change of the as-cast Cu47 Ti33 Zr11 Ni8 Si1 alloy rod versus temperature with a heating rate of 5 K/min. The transition into the supercooled liquid state is indicated by the increase of the thermal expansion coefficient, which is in agreement with observations in other bulk glasses [13,14]. Tg is defined as ‘onset temperature’ by crossing the neighbouring slopes of the dL/L0 effect. At about 448 ◦ C, the sample contracted drastically, and then follows two stages of crystallization corresponding to the first two stages of the DSC curve (Fig. 2(a)). The difference of the temperatures is connected with different heating rates. Dilatometer measurement of a sample annealed at 750 ◦ C for one hour was carried out at the same heating rate for comparison. Because the sample underwent full structural relaxation and crystallization during annealing, the figure exhibits basically a straight line. The difference between the two curves before glass transition can be taken as the total structural relaxation effect. Fig. 4 shows the temperature dependence of α for Cu47 Ti33 Zr11 Ni8 Si1 in the amorphous and crystallized states. The two curves intersects at about 240 ◦ C. It is assumed as the structural relaxation temperature (Tr ). The structural relaxation in an amorphous alloy
Fig. 3. Dilatometry curves of Cu47 Ti33 Zr11 Ni8 Si1 in the amorphous and crystallized states.
Fig. 4. Temperature dependence of the thermal expansion coefficient α for Cu47 Ti33 Zr11 Ni8 Si1 in the amorphous (a) and crystallized (b) states. A segment of the diagram is magnified (inset).
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positional order in the liquid phase. Thus the liquid phase is stabilized with respect to the competing crystalline phase. This is in accordance with the lower melting temperature of Cu47 Ti33 Zr11 Ni8 Si1 than Cu60 Zr30 Ti10 alloy (Fig. 2). The decrease in r0 may be attributed to the addition of the element Si. The depth of the pair potential V0 represents the binding energy and stability of solids. Alloy Cu60 Zr30 Ti10 has a higher V0 , is more stable in the solid state, and has higher glass transition temperature (Tg ) and structural relaxation temperature (Tr ). Although the results of r0 and V0 are only mean values here, they provide information on the binding energy and stability of the alloys and have a clear physical significance [20]. Fig. 5. Dilatometry curves of Cu60 Zr30 Ti10 glassy alloy at different heating rates.
consists of long range topological relaxation and short range chemical relaxation [15]. The relative length change is directly related to the annihilation of the “free volume” and therefore corresponds mainly to a long range topological relaxation and with the diffusion of different atoms [16]. Below Tr , the thermal expansion coefficient of the amorphous state is a little bigger than that of the crystallized state, and begins to decrease when the temperature is higher than Tr . So, Tr indicates the long range topological relaxation. Fig. 5 shows the dilatometry curves of Cu60 Zr30 Ti10 glassy alloy at heating rates of 2, 5 and 10 K/min. By increasing the heating rate, it can be seen that Tg and Tr move to high temperature, indicating their kinetic characteristic rather than phase transition [17]. The Tg and Tr are 435 ◦ C and 255 ◦ C, respectively, for the Cu60 Zr30 Ti10 glassy alloy at a heating rate of 5 K/min, higher than that of Cu47 Ti33 Zr11 Ni8 Si1 (411 ◦ C and 240 ◦ C, respectively) at the same heating rate. According to classical solid theory, the average nearestneighbour distance r0 and the effective depth of pair potential V0 can be calculated by the following equations [9]: (m + n + 3)k 1/3 r0 = (2) , 12Eα Er03 (3) , mn where k is the Boltzmann constant, E is the Young’s modules and α is the average thermal expansion coefficient. The measured value of α (T < 100 ◦ C) is 1.09 × 10−5 K−1 and 1.36 × 10−5 K−1 , respectively, for Cu60 Zr30 Ti10 and Cu47 Ti33 Zr11 Ni8 Si1 glassy alloys. The Young’s modules were reported to be 114 GPa [18] and 100 GPa [19] at room temperature for the two BMGs. By assuming a 14-7 LJ type potential (n = 14, m = 7), r0 and V0 are calculated as 0.28 nm and 0.16 eV for Cu60 Zr30 Ti10 and 0.27 nm and 0.13 eV for Cu47 Ti33 Zr11 Ni8 Si1 , respectively. A smaller r0 means a higher atomic packing density, and it favors forming short range comV0 =
4. Conclusions A decrease of thermal expansion indicating the long range topological relaxation before glass transition is observed in Cu60 Zr30 Ti10 glassy alloy. The average nearest-neighbour distance r0 and the effective depth of pair potential V0 are calculated to be 0.28 nm and 0.16 eV for Cu60 Zr30 Ti10 and 0.27 nm and 0.13 eV for Cu47 Ti33 Zr11 Ni8 Si1 , respectively. Both r0 and V0 favor that alloy Cu60 Zr30 Ti10 is more stable during heating. Acknowledgements This work is supported by the National Natural Science Foundation of China (Project No. 50471052) and Specialized Research Fund for the Doctoral Program of Higher Education (Project No. 20050422024). References [1] W.L. Johnson, J. Metals 54 (2002) 40. [2] A. Inoue, Acta Mater. 48 (2000) 279. [3] Z.X. Wang, D.Q. Zhao, W.H. Wang, J. Phys.: Condens. Matter 15 (2003) 5923. [4] X.H. Lin, W.L. Johnson, J. Appl. Phys. 78 (1995) 6514. [5] A. Inoue, W. Zhang, T. Zhang, Acta Mater. 49 (2001) 2645. [6] A. Inoue, W. Zhang, Mater. Trans. 43 (2002) 2921. [7] D.H. Xu, et al., Acta Mater. 52 (2004) 2621. [8] D.H. Xu, G. Duan, W.L. Johnson, Phys. Rev. Lett. 92 (2004) 245504. [9] B. Porscha, H. Neuhauser, Phys. Status Solidi B 186 (1994) 119. [10] J.E. Lennard-Jones, Physica 4 (1937) 941. [11] A. Inoue, Mater. Sci. Eng. A 226–228 (1997) 357. [12] A. Inoue, Acta Mater. 48 (2000) 279. [13] I.-R. Lu, G.P. Görler, H.-J. Fecht, R. Willnecker, J. Non-Cryst. Solids 274 (2000) 294. [14] N. Mattern, U. Kühn, H. Hermann, S. Roth, H. Vinzelberg, J. Eckert, Mater. Sci. Eng. A 375–377 (2004) 351. [15] A. van den Beukel, Key Eng. Mat. 3 (1993) 81. [16] B. Porscha, H. Neuhauser, Scr. Metall. Mater. 32 (1995) 931. [17] H.R. Sinning, Acta Metall. 39 (1991) 851. [18] A. Inoue, W. Zhang, T. Zhang, K. Kurosaka, J. Non-Cryst. Solids 304 (2002) 200. [19] M. Calin, J. Eckert, L. Schultz, Scr. Mater. 48 (2003) 653. [20] C.H. Shek, G.M. Lin, Mater. Lett. 57 (2003) 1229.
Relation between calculated Lennard-Jones potential and thermal stability of Cu-based bulk metallic glasses T. Lin, X.F. Bian ∗ , J. Jiang Key Laboratory of Structure and Heredity of Materials, Ministry of Education, Shandong University, South Campus, Jingshi road 73, Jinan 250061, China Received 4 August 2005; received in revised form 30 December 2005; accepted 6 January 2006 Available online 17 January 2006 Communicated by A.R. Bishop
Abstract Two metallic bulk glasses, Cu60 Zr30 Ti10 and Cu47 Ti33 Zr11 Ni8 Si1 , with a diameter of 3 mm were prepared by copper mold casting method. Dilatometric measurement was carried out on the two glassy alloys to obtain information about the average nearest-neighbour distance r0 and the effective depth of pair potential V0 . By assuming a Lennard-Jones potential, r0 and V0 were calculated to be 0.28 nm and 0.16 eV for Cu60 Zr30 Ti10 and 0.27 nm and 0.13 eV for Cu47 Ti33 Zr11 Ni8 Si1 , respectively. It was found that the glassy alloy Cu60 Zr30 Ti10 was more stable than Cu47 Ti33 Zr11 Ni8 Si1 against heating from both experiment and calculation. © 2006 Elsevier B.V. All rights reserved. PACS: 81.05.Kf; 68.60.Dv; 82.56.Na; 02.30.Em Keywords: Cu-based bulk metallic glass; Thermal stability; Structural relaxation; Lennard-Jones potential
1. Introduction Bulk metallic glasses (BMGs) have been drawing increasing attention in recent years due to their scientific and engineering significance [1,2]. As a member of the family of BMGs, great progress has been made in research of Cu-based BMGs. Comparing with other BMG systems, such as Zr-based and Pd-based BMGs, the product cost of Cu-based BMGs is much lower. In addition, they have high thermal stability against crystallization [3]. In last decade, a series of Cu-based bulk glassy alloys were developed, such as Cu–Ti–Zr–Ni [4], Cu–Zr–Ti [5], Cu–Zr–Al [6], Cu–Zr [7] and Cu–Zr–Al–Y [8]. Porscha and Nehauser measured the length and eigenfrequency change of a Cu64 Ti36 metallic glass ribbon simultaneously [9]. By assuming a Lennard-Jones type potential (LJ type potential) [10] B A V (r) = − m + n r r
where V (r) is pair potential of two atoms, r is inter-atomic distance, and A, B, m, and n are constants, they calculated the effective pair potentials over different atomic species and showed that the powers for the potential are 14 and 7, respectively. From a number of previous data, it seems that the addition of a small amount of another element to the basic ternary system increases the glass forming ability [11,12]. It has been reported that the critical diameters for Cu60 Zr30 Ti10 and Cu47 Ti33 Zr11 Ni8 Si1 are 4 mm and 7 mm, respectively. In this Letter, we measured the length change of these two glassy alloys due to structural relaxation at constant heating rate and calculated the nominal value of the interatomic average nearestneighbour distance r0 and the effective depth of pair potential V0 by assuming a 14-7 LJ type potential. Different thermal stability of these two alloys was discussed according to r0 and V0 . 2. Experimental procedure
(n > m),
* Corresponding author.
E-mail address: [email protected] (X.F. Bian). 0375-9601/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.physleta.2006.01.012
(1) The alloy ingots of nominal compositions Cu60 Zr30 Ti10 and Cu47 Ti33 Zr11 Ni8 Si1 were prepared by arc melting mixtures of pure Cu(99.9%), Zr(99.7%), Ti(99.9%), Ni(99.9%), Si(99.9%) in a Ti-gettered argon atmosphere. Bulk glassy alloys in a cylin-
498
T. Lin et al. / Physics Letters A 353 (2006) 497–499
drical rod form with a diameter of 3 mm were produced by the copper mould casting method. X-ray diffraction (XRD, D/maxrB) experiments were performed to identify the formation of the amorphous phase in the as-cast samples using a Cu-Kα source. Thermal stability associated with glass transition and supercooled liquid region was examined by differential scanning calorimeter (Netzsch DSC 404C) with a heating rate of 20 K/min. A Netzsch DIL 402C was utilized for dilatometric measurement at constant heating rate. The length of samples is about 22 mm. 3. Results and discussion Fig. 1 shows the X-ray diffraction patterns taken from the cross sections of 3 mm thick cast rods of Cu60 Zr30 Ti10 and Cu47 Ti33 Zr11 Ni8 Si1 alloys. Each of the pattern exhibits a broad diffraction maximum characteristic of amorphous structure. The DSC curves with a heating rate of 20 K/min of the cast Cu–Zr–Ti and Cu–Ti–Zr–Ni–Si glassy alloys are shown in Fig. 2. The glass transition temperature (Tg ) and crystallization temperature (Tx ) are marked with arrows. The Tg and Tx are 448 ◦ C and 475 ◦ C for the Cu60 Zr30 Ti10 alloy, and 415 ◦ C and 466 ◦ C for Cu47 Ti33 Zr11 Ni8 Si1 alloy, respectively. The supercooled liquid region Tg (= Tx − Tg ) is 27 ◦ C and 51 ◦ C for the two alloys. The melting behavior of these two alloys is also shown in Fig. 2. It can be seen that the Cu60 Zr30 Ti10 alloy
Fig. 1. X-ray diffraction patterns of cast Cu60 Zr30 Ti10 and Cu47 Ti33 Zr11 Ni8 Si1 alloy rods with a diameter of 3 mm.
Fig. 2. DSC curves of Cu47 Ti33 Zr11 Ni8 Si1 (a) and Cu60 Zr30 Ti10 (b) glassy alloys.
has higher solidus (Tm ) and liquidus (Tl ) temperature than the Cu47 Ti33 Zr11 Ni8 Si1 alloy. Fig. 3 shows the total length change of the as-cast Cu47 Ti33 Zr11 Ni8 Si1 alloy rod versus temperature with a heating rate of 5 K/min. The transition into the supercooled liquid state is indicated by the increase of the thermal expansion coefficient, which is in agreement with observations in other bulk glasses [13,14]. Tg is defined as ‘onset temperature’ by crossing the neighbouring slopes of the dL/L0 effect. At about 448 ◦ C, the sample contracted drastically, and then follows two stages of crystallization corresponding to the first two stages of the DSC curve (Fig. 2(a)). The difference of the temperatures is connected with different heating rates. Dilatometer measurement of a sample annealed at 750 ◦ C for one hour was carried out at the same heating rate for comparison. Because the sample underwent full structural relaxation and crystallization during annealing, the figure exhibits basically a straight line. The difference between the two curves before glass transition can be taken as the total structural relaxation effect. Fig. 4 shows the temperature dependence of α for Cu47 Ti33 Zr11 Ni8 Si1 in the amorphous and crystallized states. The two curves intersects at about 240 ◦ C. It is assumed as the structural relaxation temperature (Tr ). The structural relaxation in an amorphous alloy
Fig. 3. Dilatometry curves of Cu47 Ti33 Zr11 Ni8 Si1 in the amorphous and crystallized states.
Fig. 4. Temperature dependence of the thermal expansion coefficient α for Cu47 Ti33 Zr11 Ni8 Si1 in the amorphous (a) and crystallized (b) states. A segment of the diagram is magnified (inset).
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positional order in the liquid phase. Thus the liquid phase is stabilized with respect to the competing crystalline phase. This is in accordance with the lower melting temperature of Cu47 Ti33 Zr11 Ni8 Si1 than Cu60 Zr30 Ti10 alloy (Fig. 2). The decrease in r0 may be attributed to the addition of the element Si. The depth of the pair potential V0 represents the binding energy and stability of solids. Alloy Cu60 Zr30 Ti10 has a higher V0 , is more stable in the solid state, and has higher glass transition temperature (Tg ) and structural relaxation temperature (Tr ). Although the results of r0 and V0 are only mean values here, they provide information on the binding energy and stability of the alloys and have a clear physical significance [20]. Fig. 5. Dilatometry curves of Cu60 Zr30 Ti10 glassy alloy at different heating rates.
consists of long range topological relaxation and short range chemical relaxation [15]. The relative length change is directly related to the annihilation of the “free volume” and therefore corresponds mainly to a long range topological relaxation and with the diffusion of different atoms [16]. Below Tr , the thermal expansion coefficient of the amorphous state is a little bigger than that of the crystallized state, and begins to decrease when the temperature is higher than Tr . So, Tr indicates the long range topological relaxation. Fig. 5 shows the dilatometry curves of Cu60 Zr30 Ti10 glassy alloy at heating rates of 2, 5 and 10 K/min. By increasing the heating rate, it can be seen that Tg and Tr move to high temperature, indicating their kinetic characteristic rather than phase transition [17]. The Tg and Tr are 435 ◦ C and 255 ◦ C, respectively, for the Cu60 Zr30 Ti10 glassy alloy at a heating rate of 5 K/min, higher than that of Cu47 Ti33 Zr11 Ni8 Si1 (411 ◦ C and 240 ◦ C, respectively) at the same heating rate. According to classical solid theory, the average nearestneighbour distance r0 and the effective depth of pair potential V0 can be calculated by the following equations [9]: (m + n + 3)k 1/3 r0 = (2) , 12Eα Er03 (3) , mn where k is the Boltzmann constant, E is the Young’s modules and α is the average thermal expansion coefficient. The measured value of α (T < 100 ◦ C) is 1.09 × 10−5 K−1 and 1.36 × 10−5 K−1 , respectively, for Cu60 Zr30 Ti10 and Cu47 Ti33 Zr11 Ni8 Si1 glassy alloys. The Young’s modules were reported to be 114 GPa [18] and 100 GPa [19] at room temperature for the two BMGs. By assuming a 14-7 LJ type potential (n = 14, m = 7), r0 and V0 are calculated as 0.28 nm and 0.16 eV for Cu60 Zr30 Ti10 and 0.27 nm and 0.13 eV for Cu47 Ti33 Zr11 Ni8 Si1 , respectively. A smaller r0 means a higher atomic packing density, and it favors forming short range comV0 =
4. Conclusions A decrease of thermal expansion indicating the long range topological relaxation before glass transition is observed in Cu60 Zr30 Ti10 glassy alloy. The average nearest-neighbour distance r0 and the effective depth of pair potential V0 are calculated to be 0.28 nm and 0.16 eV for Cu60 Zr30 Ti10 and 0.27 nm and 0.13 eV for Cu47 Ti33 Zr11 Ni8 Si1 , respectively. Both r0 and V0 favor that alloy Cu60 Zr30 Ti10 is more stable during heating. Acknowledgements This work is supported by the National Natural Science Foundation of China (Project No. 50471052) and Specialized Research Fund for the Doctoral Program of Higher Education (Project No. 20050422024). References [1] W.L. Johnson, J. Metals 54 (2002) 40. [2] A. Inoue, Acta Mater. 48 (2000) 279. [3] Z.X. Wang, D.Q. Zhao, W.H. Wang, J. Phys.: Condens. Matter 15 (2003) 5923. [4] X.H. Lin, W.L. Johnson, J. Appl. Phys. 78 (1995) 6514. [5] A. Inoue, W. Zhang, T. Zhang, Acta Mater. 49 (2001) 2645. [6] A. Inoue, W. Zhang, Mater. Trans. 43 (2002) 2921. [7] D.H. Xu, et al., Acta Mater. 52 (2004) 2621. [8] D.H. Xu, G. Duan, W.L. Johnson, Phys. Rev. Lett. 92 (2004) 245504. [9] B. Porscha, H. Neuhauser, Phys. Status Solidi B 186 (1994) 119. [10] J.E. Lennard-Jones, Physica 4 (1937) 941. [11] A. Inoue, Mater. Sci. Eng. A 226–228 (1997) 357. [12] A. Inoue, Acta Mater. 48 (2000) 279. [13] I.-R. Lu, G.P. Görler, H.-J. Fecht, R. Willnecker, J. Non-Cryst. Solids 274 (2000) 294. [14] N. Mattern, U. Kühn, H. Hermann, S. Roth, H. Vinzelberg, J. Eckert, Mater. Sci. Eng. A 375–377 (2004) 351. [15] A. van den Beukel, Key Eng. Mat. 3 (1993) 81. [16] B. Porscha, H. Neuhauser, Scr. Metall. Mater. 32 (1995) 931. [17] H.R. Sinning, Acta Metall. 39 (1991) 851. [18] A. Inoue, W. Zhang, T. Zhang, K. Kurosaka, J. Non-Cryst. Solids 304 (2002) 200. [19] M. Calin, J. Eckert, L. Schultz, Scr. Mater. 48 (2003) 653. [20] C.H. Shek, G.M. Lin, Mater. Lett. 57 (2003) 1229.