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Effect of melting technique on the microstructure and mechanical properties of AZ91 commercial magnesium alloys
Materials Science and Engineering A 429 (2006) 320–323
Effect of melting technique on the microstructure and mechanical properties of AZ91 commercial magnesium alloys Peng Zhao a,∗ , Haoran Geng b , Qudong Wang a a
Light Alloy Net Forming National Engineering Research Center, Shanghai Jiaotong University, Shanghai 200030, PR China b College of Materials Science and Engineering, Jinan University, Jinan 250022, PR China Received 14 July 2005; received in revised form 5 May 2006; accepted 12 May 2006
Abstract The microstructure of AZ91 magnesium alloy refined by thermal rate treatment technique (TRT), and the -phase is more dispersive and uniform. Though the superheating microstructure is finer than microstructure with TRT technique, TRT technique can reduce the casting defects such as hot tears and shot run, more suits the practical requirement. The microstructure of AZ91 alloy keeps some characteristics of the high temperature melt after TRT. On the other hand, the microstructure of AZ91 magnesium alloy containing excess element Fe could not be refined and even be coarsened after thermal rate treatment, which brings on the decrease of mechanical properties as the results of interdendritic shrinkage microporosity and coarse -phases. These different effects of TRT on AZ91 magnesium alloys can be related to the presence of non-equilibrium condition in the mixed melt structure through mixing the high superheating temperature and low temperature melts in TRT technique. © 2006 Elsevier B.V. All rights reserved. Keywords: Magnesium alloys; Iron; Mechanical properties; Microstructure; Solidification
1. Introduction The so-called thermal rate treatment (TRT) technique which is used to improve the alloys properties includes two process: first heating the melt to a high enough temperature, setting a certain time, and then cooling the melt rapidly to pouring temperature. TRT as a physical method has unique advantages, so its application in nonferrous metals has been concerned all the while, such as in Al–Si and Zn–Al alloys. In these studies, TRT mainly modifies the precipitated phase [1–3]. The influence of different alloying elements on grain refining efficiency has been intensively investigated in the process of superheating process for magnesium alloys. These studies show that Al, Fe and Mn are essential elements for maximizing grain refinement, the degree of the refinement increase with the Al content and an excess Mn addition can negate the grain refinement effect [4]. However, chilling technique also has great influence on the alloys microstructure and few investigations have been done on the effect of TRT on precipitated phase. Therefore, this paper studied the effect of TRT technique on the AZ91 magne-
∗
Corresponding author. Tel.: +86 21 62932239; fax: +86 21 62932113. E-mail address: [email protected] (P. Zhao).
0921-5093/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2006.05.066
sium alloy with different Fe content, especially on the second phase. The AZ91 magnesium alloys was selected to investigated because it has higher Al content and proper contents of Mn and Fe, which can attain the maximize grain refinement by the superheating process than other commercial magnesium alloys [4]. 2. Experimental The AZ91 commercial magnesium alloys were melted in a steel crucible with a crucible electric resistance furnace. Iron was added as pure Fe alloy in order to study the effect of Fe on TRT efficiency. RJ-2 fluxes were put on the melt surface to prevent the oxidation and ignition of magnesium alloys. Cylindrical tensile specimens with a diameter of 12 mm were cast in a metal mould. Tensile tests were performed with a 60-tonnes universal material testing machine. The hardness test was carried out by Brinell hardness tester with the load 1000 kg, press head diameter 10 mm and loading time 30 s. Microstructure observations and examinations were performed with KH-2200 high-power video microscope and JXA-840 SEM and electron probe X-ray microanalyser. The procedure of TRT technique is, heating and melting most of the charge up to 870 ◦ C, setting a certain time; then cooling the melt rapidly to 720 ◦ C pouring temperature with the rest of
P. Zhao et al. / Materials Science and Engineering A 429 (2006) 320–323
321
Fig. 1. Sketch map showed three melting techniques: (1) melting, superheating; (2) setting; (3) chilling, stirring; (4) refining, setting; (5) pouring.
the charge. The sketch map showing TRT, conventional melting (CM) and cast directly at 870 ◦ C technique procedure is giving in Fig. 1. 3. Results and discussion 3.1. Effect of excess Fe The mechanical properties of AZ91 alloys added by different Fe content by different technique are shown in Fig. 2. Excess Fe has little influence on the ultimate tensile strengthen of AZ91 alloys with CM technique despite higher Fe addition decreasing strengthens slightly. However, the addition of Fe has great influence on the modification efficiency by the TRT technique. The successful mechanical properties improvement of AZ91 alloys can be obtained by simple TRT, which show well modification efficiency. However, the additions of Fe not only have not the modification efficiency of AZ91 alloys but also can decrease that by TRT technique, which can be seen from that the elongations are almost zero and the strengthens are decreased greatly by TRT technique. Figs. 3 and 4 show the microstructure of alloys containing excess different Fe elements by the TRT technique. The microstructures of AZ91 magnesium alloys have been greatly changed with the addition of Fe by thermal rate treatment technique, especially the second phase. However, the addition
Fig. 2. Effect of Fe content on mechanical property of AZ91 magnesium alloys by different techniques.
quantities of Fe elements have little influence on the change of microstructure. The small rod-shaped or nodular particles gathered to massive particles, but the second phases are still scattered. Such second phases are obviously detrimental to the mechanical properties, especially to elongation. 3.2. Effect of chilling technique Fig. 5 shows the microstructures of AZ91 magnesium alloys by different techniques. Alloys cast directly at 870 ◦ C melt temperature and with TRT technique have finer grain in comparison with that with CM technique, especially in Fig. 5(b), the grain of the alloy cast directly at 870 ◦ C is the finest. Moreover, the -phase in Fig. 5(b) and (c) is more dispersive and uniform than that in Fig. 5(a). The superheating process resulted in the grain refinement of AZ91 magnesium alloys (Fig. 5(b)). Chilling technique can keep the melt microstructure formed at high temperature though the addition of coarse grain charge can result in some deterioration of the structure. The difference of the structure of the alloys treated with TRT and CM indicated that TRT technique could keep or partly keep the characteristic of the high temperature melts. On the other hand, TRT technique can improve the tensile strength and elongation of AZ91 magnesium alloys (Table 1). Although the tensile strength and elongation
Fig. 3. SEI of alloy 2 with different techniques: (a) CM technique and (b) TRT technique.
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Fig. 4. SEI of alloy 3 with different techniques: (a) CM technique and (b) TRT technique.
Fig. 5. SEM photos of AZ91 magnesium alloys treated with different techniques: (a) CM, (b) cast directly at 870 ◦ C and (c) TRT.
Table 1 Mechanical property of AZ91 magnesium alloys by different techniques Melting technique
UTS (MPa)
EI (%)
Hardness (HB)
CM Cast directly at 870 ◦ C TRT
148 195 190
2.8 4.0 3.8
55 58 60
with cast at 870 ◦ C melt temperature is higher than that with TRT technique, TRT technique can reduce the casting defects such as hot tears and shot run, more suits the practical requirement and let melt possess a reduced disposition to burn. So TRT technique can be practically applied. However, it must be clearly that the grain refinement is not caused with chilling process but superheating process.
Al alloys, the addition of iron produces grain refinement without superheating, Fe- and Al-rich intermetallic particles are possibly nucleants for magnesium grains [7]. And in high-purity Fe-bearing Mg–9% Al alloy, Fe–Al–C–O compound was also found that may be one reason to grain refinement after superheating [8]. So the Al–Fe–Mn or Al–C composite may be the crystal nucleus. However, addition of Fe has no microstructure refinement after TRT process in this study, which show that the grain refinement mechanism of superheating cannot be simply explained by some nucleus. Moreover, fine superheating microstructure need to be kept by chilling technique as discussed above. This can be seen from
4. Mechanism The influencing factors of thermal rate treatment are chilling technique, superheating temperature, holding time and alloy composition. For superheating process, the grain refine mechanism has not been fully understood. Several theories have been proposed. These include the Fe precipitation, the formation of oxides or Al4 C3 and the temperature–solubility nucleation theory [4-6]. In this paper, the analysis by EPMA finds the composition of foreign substances in magnesium alloys (as shown in Fig. 6) includes Al, Fe, Mn, O, Si and C after TRT process. O elements enter into this phase because of surface oxidation in polishing process [5]. As in high purity Mg–3% Al and Mg–9%
Fig. 6. Microstructure of foreign substances.
P. Zhao et al. / Materials Science and Engineering A 429 (2006) 320–323 Table 2 Chemical compositions of phases at grain boundary by different techniques as determined by EDS (wt.%) Alloy
CM TRT Cast directly at 870 ◦ C
Highly supersaturated ␣-Mg
Eutectic -phase
Mg
Al
Mg
Al
Zn
91.27 87.32 86.99
8.73 12.68 13.01
63.7 62.74 70.95
32.46 33.30 26.26
3.84 3.96 2.79
323
while with the increase of temperature, these solid-like clusters were solute in the melt, so the melt changed to disorder and homogeneity state. In the process of TRT technique, the mixture of high temperature melt having disorder and homogeneity state with low temperature melt having order state, which heated low temperature melt quickly and chilled high temperature, show a non-equilibrium state with large fluctuations in temperature and energy. The non-equilibrium state depends on several factors. These factors would have influence on the information of nucleus because of changing melt microstructure and phase composition, such as Fe in this paper. So only appropriate factors, like composition and melt temperature, would get successful TRT efficiency. 5. Conclusion
Fig. 7. Interdendritic shrinkage microporosity existing in AZ91 magnesium alloys added by excess Fe after TRT technique.
the various composition of phases located at grain boundary by different technique (Table 2). These phases include eutectic phase and highly supersaturated ␣-Mg. The eutectic -phase is surrounded by the highly supersaturated ␣-Mg [9], as shown in Fig. 5. The phase compositions have both changed after superheating process. However, the intermetallica phase composition of TRT alloy is about the same as that of CM alloy and the superheated ␣-Mg composition of TRT alloy is about the same as that of directly cast alloy, which show superheating and low temperature melt both remain characteristics in TRT microstructure. The change of phase composition must have some relation with the variety of alloy microstructure by different techniques. A lot of shrinkage microporosities appear in the microstructure of AZ91 magnesium alloys for the addition of Fe, especially after TRT technique (Fig. 7). Aggravation of Interdendritic shrinkage microporosities indicated that there exists nonequilibrium state of wide temperature range in the process of TRT technique. These can be explained by cluster physics and nonequilibrium theory [10]. Melt contain some solid-like clusters with short-range order if the melt temperature is relatively low,
(1) The addition of Fe to AZ91 magnesium alloys has no refining efficiency after TRT technique. Moreover, interdendritic shrinkage microporosity and coarse Mg17 Al12 phases appear in the TRT microstructure, which decreases the mechanical properties of magnesium alloys. (2) TRT technique can refine the microstructure of AZ91 magnesium alloys, and the Mg17 Al12 phase is more dispersive and uniform. Chilling technique could partly keep the microstructure and compositions of phase located at grain boundary of high temperature superheating melt. (3) These observations made in this study can be related to the presence of non-equilibrium condition in the mixed melt structure through mixing the high superheating and low temperature melts. References [1] X.F. Bian, W.M. Wang, Mater. Lett. 44 (2000) 54–58. [2] H.R. Geng, X.F. Tian, H.W. Cui, C.D. Li, P. Zhao, Mater. Sci. Eng. A 316 (2001) 109–114. [3] T. Ohmi, K. Matsuura, M. Kudoh, Y. Itoh, J. Jpn. Inst. Light. Met. 48 (1998) 42–47. [4] Y.C. Lee, A.K. Dahle, D.H. St. John, Metall. Mater. Trans. A 31 (2000) 2895–2906. [5] T. Motegi, E. Yano, Y. Tamura, E. Sato, Mater. Sci. Forum. 350 (2000) 191–198. [6] P. Cao, M. Qian, D. St. John, in: N.R. Neelameggham, H.I. Kaplan, B.R. Powell (Eds.), Magnesium Technology, TMS (The Minerals, Metals & Materials Society), Warrendale, PA, 2005, pp. 297–302. [7] P. Cao, M. Qian, D.H. St. John, Scripta Mater. 51 (2004) 125–129. [8] Y. Tamura, T. Motegi, N. Kono, E. Sato, Mater. Sci. Forum 350 (2000) 199–204. [9] S. Spigarelli, M. Regev, E. Evangelista, A. Rosen, Mater. Sci. Technol. 17 (2001) 627–638. [10] G.H. Wang, Chin. Prog. Phys. 14 (1994) 121–172 (in Chinese).
Effect of melting technique on the microstructure and mechanical properties of AZ91 commercial magnesium alloys Peng Zhao a,∗ , Haoran Geng b , Qudong Wang a a
Light Alloy Net Forming National Engineering Research Center, Shanghai Jiaotong University, Shanghai 200030, PR China b College of Materials Science and Engineering, Jinan University, Jinan 250022, PR China Received 14 July 2005; received in revised form 5 May 2006; accepted 12 May 2006
Abstract The microstructure of AZ91 magnesium alloy refined by thermal rate treatment technique (TRT), and the -phase is more dispersive and uniform. Though the superheating microstructure is finer than microstructure with TRT technique, TRT technique can reduce the casting defects such as hot tears and shot run, more suits the practical requirement. The microstructure of AZ91 alloy keeps some characteristics of the high temperature melt after TRT. On the other hand, the microstructure of AZ91 magnesium alloy containing excess element Fe could not be refined and even be coarsened after thermal rate treatment, which brings on the decrease of mechanical properties as the results of interdendritic shrinkage microporosity and coarse -phases. These different effects of TRT on AZ91 magnesium alloys can be related to the presence of non-equilibrium condition in the mixed melt structure through mixing the high superheating temperature and low temperature melts in TRT technique. © 2006 Elsevier B.V. All rights reserved. Keywords: Magnesium alloys; Iron; Mechanical properties; Microstructure; Solidification
1. Introduction The so-called thermal rate treatment (TRT) technique which is used to improve the alloys properties includes two process: first heating the melt to a high enough temperature, setting a certain time, and then cooling the melt rapidly to pouring temperature. TRT as a physical method has unique advantages, so its application in nonferrous metals has been concerned all the while, such as in Al–Si and Zn–Al alloys. In these studies, TRT mainly modifies the precipitated phase [1–3]. The influence of different alloying elements on grain refining efficiency has been intensively investigated in the process of superheating process for magnesium alloys. These studies show that Al, Fe and Mn are essential elements for maximizing grain refinement, the degree of the refinement increase with the Al content and an excess Mn addition can negate the grain refinement effect [4]. However, chilling technique also has great influence on the alloys microstructure and few investigations have been done on the effect of TRT on precipitated phase. Therefore, this paper studied the effect of TRT technique on the AZ91 magne-
∗
Corresponding author. Tel.: +86 21 62932239; fax: +86 21 62932113. E-mail address: [email protected] (P. Zhao).
0921-5093/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2006.05.066
sium alloy with different Fe content, especially on the second phase. The AZ91 magnesium alloys was selected to investigated because it has higher Al content and proper contents of Mn and Fe, which can attain the maximize grain refinement by the superheating process than other commercial magnesium alloys [4]. 2. Experimental The AZ91 commercial magnesium alloys were melted in a steel crucible with a crucible electric resistance furnace. Iron was added as pure Fe alloy in order to study the effect of Fe on TRT efficiency. RJ-2 fluxes were put on the melt surface to prevent the oxidation and ignition of magnesium alloys. Cylindrical tensile specimens with a diameter of 12 mm were cast in a metal mould. Tensile tests were performed with a 60-tonnes universal material testing machine. The hardness test was carried out by Brinell hardness tester with the load 1000 kg, press head diameter 10 mm and loading time 30 s. Microstructure observations and examinations were performed with KH-2200 high-power video microscope and JXA-840 SEM and electron probe X-ray microanalyser. The procedure of TRT technique is, heating and melting most of the charge up to 870 ◦ C, setting a certain time; then cooling the melt rapidly to 720 ◦ C pouring temperature with the rest of
P. Zhao et al. / Materials Science and Engineering A 429 (2006) 320–323
321
Fig. 1. Sketch map showed three melting techniques: (1) melting, superheating; (2) setting; (3) chilling, stirring; (4) refining, setting; (5) pouring.
the charge. The sketch map showing TRT, conventional melting (CM) and cast directly at 870 ◦ C technique procedure is giving in Fig. 1. 3. Results and discussion 3.1. Effect of excess Fe The mechanical properties of AZ91 alloys added by different Fe content by different technique are shown in Fig. 2. Excess Fe has little influence on the ultimate tensile strengthen of AZ91 alloys with CM technique despite higher Fe addition decreasing strengthens slightly. However, the addition of Fe has great influence on the modification efficiency by the TRT technique. The successful mechanical properties improvement of AZ91 alloys can be obtained by simple TRT, which show well modification efficiency. However, the additions of Fe not only have not the modification efficiency of AZ91 alloys but also can decrease that by TRT technique, which can be seen from that the elongations are almost zero and the strengthens are decreased greatly by TRT technique. Figs. 3 and 4 show the microstructure of alloys containing excess different Fe elements by the TRT technique. The microstructures of AZ91 magnesium alloys have been greatly changed with the addition of Fe by thermal rate treatment technique, especially the second phase. However, the addition
Fig. 2. Effect of Fe content on mechanical property of AZ91 magnesium alloys by different techniques.
quantities of Fe elements have little influence on the change of microstructure. The small rod-shaped or nodular particles gathered to massive particles, but the second phases are still scattered. Such second phases are obviously detrimental to the mechanical properties, especially to elongation. 3.2. Effect of chilling technique Fig. 5 shows the microstructures of AZ91 magnesium alloys by different techniques. Alloys cast directly at 870 ◦ C melt temperature and with TRT technique have finer grain in comparison with that with CM technique, especially in Fig. 5(b), the grain of the alloy cast directly at 870 ◦ C is the finest. Moreover, the -phase in Fig. 5(b) and (c) is more dispersive and uniform than that in Fig. 5(a). The superheating process resulted in the grain refinement of AZ91 magnesium alloys (Fig. 5(b)). Chilling technique can keep the melt microstructure formed at high temperature though the addition of coarse grain charge can result in some deterioration of the structure. The difference of the structure of the alloys treated with TRT and CM indicated that TRT technique could keep or partly keep the characteristic of the high temperature melts. On the other hand, TRT technique can improve the tensile strength and elongation of AZ91 magnesium alloys (Table 1). Although the tensile strength and elongation
Fig. 3. SEI of alloy 2 with different techniques: (a) CM technique and (b) TRT technique.
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P. Zhao et al. / Materials Science and Engineering A 429 (2006) 320–323
Fig. 4. SEI of alloy 3 with different techniques: (a) CM technique and (b) TRT technique.
Fig. 5. SEM photos of AZ91 magnesium alloys treated with different techniques: (a) CM, (b) cast directly at 870 ◦ C and (c) TRT.
Table 1 Mechanical property of AZ91 magnesium alloys by different techniques Melting technique
UTS (MPa)
EI (%)
Hardness (HB)
CM Cast directly at 870 ◦ C TRT
148 195 190
2.8 4.0 3.8
55 58 60
with cast at 870 ◦ C melt temperature is higher than that with TRT technique, TRT technique can reduce the casting defects such as hot tears and shot run, more suits the practical requirement and let melt possess a reduced disposition to burn. So TRT technique can be practically applied. However, it must be clearly that the grain refinement is not caused with chilling process but superheating process.
Al alloys, the addition of iron produces grain refinement without superheating, Fe- and Al-rich intermetallic particles are possibly nucleants for magnesium grains [7]. And in high-purity Fe-bearing Mg–9% Al alloy, Fe–Al–C–O compound was also found that may be one reason to grain refinement after superheating [8]. So the Al–Fe–Mn or Al–C composite may be the crystal nucleus. However, addition of Fe has no microstructure refinement after TRT process in this study, which show that the grain refinement mechanism of superheating cannot be simply explained by some nucleus. Moreover, fine superheating microstructure need to be kept by chilling technique as discussed above. This can be seen from
4. Mechanism The influencing factors of thermal rate treatment are chilling technique, superheating temperature, holding time and alloy composition. For superheating process, the grain refine mechanism has not been fully understood. Several theories have been proposed. These include the Fe precipitation, the formation of oxides or Al4 C3 and the temperature–solubility nucleation theory [4-6]. In this paper, the analysis by EPMA finds the composition of foreign substances in magnesium alloys (as shown in Fig. 6) includes Al, Fe, Mn, O, Si and C after TRT process. O elements enter into this phase because of surface oxidation in polishing process [5]. As in high purity Mg–3% Al and Mg–9%
Fig. 6. Microstructure of foreign substances.
P. Zhao et al. / Materials Science and Engineering A 429 (2006) 320–323 Table 2 Chemical compositions of phases at grain boundary by different techniques as determined by EDS (wt.%) Alloy
CM TRT Cast directly at 870 ◦ C
Highly supersaturated ␣-Mg
Eutectic -phase
Mg
Al
Mg
Al
Zn
91.27 87.32 86.99
8.73 12.68 13.01
63.7 62.74 70.95
32.46 33.30 26.26
3.84 3.96 2.79
323
while with the increase of temperature, these solid-like clusters were solute in the melt, so the melt changed to disorder and homogeneity state. In the process of TRT technique, the mixture of high temperature melt having disorder and homogeneity state with low temperature melt having order state, which heated low temperature melt quickly and chilled high temperature, show a non-equilibrium state with large fluctuations in temperature and energy. The non-equilibrium state depends on several factors. These factors would have influence on the information of nucleus because of changing melt microstructure and phase composition, such as Fe in this paper. So only appropriate factors, like composition and melt temperature, would get successful TRT efficiency. 5. Conclusion
Fig. 7. Interdendritic shrinkage microporosity existing in AZ91 magnesium alloys added by excess Fe after TRT technique.
the various composition of phases located at grain boundary by different technique (Table 2). These phases include eutectic phase and highly supersaturated ␣-Mg. The eutectic -phase is surrounded by the highly supersaturated ␣-Mg [9], as shown in Fig. 5. The phase compositions have both changed after superheating process. However, the intermetallica phase composition of TRT alloy is about the same as that of CM alloy and the superheated ␣-Mg composition of TRT alloy is about the same as that of directly cast alloy, which show superheating and low temperature melt both remain characteristics in TRT microstructure. The change of phase composition must have some relation with the variety of alloy microstructure by different techniques. A lot of shrinkage microporosities appear in the microstructure of AZ91 magnesium alloys for the addition of Fe, especially after TRT technique (Fig. 7). Aggravation of Interdendritic shrinkage microporosities indicated that there exists nonequilibrium state of wide temperature range in the process of TRT technique. These can be explained by cluster physics and nonequilibrium theory [10]. Melt contain some solid-like clusters with short-range order if the melt temperature is relatively low,
(1) The addition of Fe to AZ91 magnesium alloys has no refining efficiency after TRT technique. Moreover, interdendritic shrinkage microporosity and coarse Mg17 Al12 phases appear in the TRT microstructure, which decreases the mechanical properties of magnesium alloys. (2) TRT technique can refine the microstructure of AZ91 magnesium alloys, and the Mg17 Al12 phase is more dispersive and uniform. Chilling technique could partly keep the microstructure and compositions of phase located at grain boundary of high temperature superheating melt. (3) These observations made in this study can be related to the presence of non-equilibrium condition in the mixed melt structure through mixing the high superheating and low temperature melts. References [1] X.F. Bian, W.M. Wang, Mater. Lett. 44 (2000) 54–58. [2] H.R. Geng, X.F. Tian, H.W. Cui, C.D. Li, P. Zhao, Mater. Sci. Eng. A 316 (2001) 109–114. [3] T. Ohmi, K. Matsuura, M. Kudoh, Y. Itoh, J. Jpn. Inst. Light. Met. 48 (1998) 42–47. [4] Y.C. Lee, A.K. Dahle, D.H. St. John, Metall. Mater. Trans. A 31 (2000) 2895–2906. [5] T. Motegi, E. Yano, Y. Tamura, E. Sato, Mater. Sci. Forum. 350 (2000) 191–198. [6] P. Cao, M. Qian, D. St. John, in: N.R. Neelameggham, H.I. Kaplan, B.R. Powell (Eds.), Magnesium Technology, TMS (The Minerals, Metals & Materials Society), Warrendale, PA, 2005, pp. 297–302. [7] P. Cao, M. Qian, D.H. St. John, Scripta Mater. 51 (2004) 125–129. [8] Y. Tamura, T. Motegi, N. Kono, E. Sato, Mater. Sci. Forum 350 (2000) 199–204. [9] S. Spigarelli, M. Regev, E. Evangelista, A. Rosen, Mater. Sci. Technol. 17 (2001) 627–638. [10] G.H. Wang, Chin. Prog. Phys. 14 (1994) 121–172 (in Chinese).