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In situ observation of solid-state amorphization in Nd2Fe14B alloy by electron irradiation
Materials Science and Engineering A 449–451 (2007) 1111–1114
In situ observation of solid-state amorphization in Nd2Fe14B alloy by electron irradiation Takeshi Nagase a , Akihiro Nino b , Yukichi Umakoshi a,∗ a
Division of Materials and Manufacturing Science, Graduate School of Engineering, Osaka University, 2-1 Yamada-oka, Suita, Osaka 565-0871, Japan b Department of Materials Science and Engineering, Graduate School of Engineering, Osaka University, 2-1 Yamada-oka, Suita, Osaka 565-0871, Japan Received 21 August 2005; received in revised form 5 December 2005; accepted 15 February 2006
Abstract In situ observation of solid-state amorphization in Nd2 Fe14 B compound was achieved by electron irradiation method. Under 2.0 MeV electron irradiation, crystalline contrast corresponding to Nd2 Fe14 B crystalline phase in a bright-field image disappeared suddenly when the total dose reached a critical value. The amorphous phase was rapidly formed under electron irradiation. Solid-state amorphization process at the critical total dose seems to be analogous to thermal melting process of crystal at the melting temperature. © 2006 Elsevier B.V. All rights reserved. Keywords: Solid-state amorphization; Electron irradiation; In situ observation; Intermetallic compound; Nd–Fe–B alloy
1. Introduction Amorphous alloys can be obtained not only by the liquid-toglass transition of liquid quenching (LQ) but also by the crystalto-glass transition of solid-state amorphization (SSA). The SSA means the formation of an amorphous phase during mechanical processes such as electron irradiation, ion irradiation, severe deformation, mechanical milling, hydrogen-absorption and inter-diffusion between multi-layers under the thermodynamical melting temperature (Tm ) [1,2]. Fig. 1 summarizes the results of electron irradiation induced SSA in intermetallic compounds reported up to date. The intermetallic compounds were classified into three groups based on the glass forming ability (GFA) in LQ by melt-spinning method and the phase stability of melt-spun amorphous alloys; (Group 1) an amorphous phase cannot be obtained by LQ, (Group 2) an amorphous phase is obtained by LQ and an amorphous-to-supercooled liquid transition is rarely observed by conventional DSC measurement, (Group 3) an amorphous phase is obtained by LQ and the amorphous-to-supercooled liquid transition can be confirmed by conventional DSC measurement. Amorphous alloys belonging
∗
Corresponding author. Tel.: +81 6 6879 7494; fax: +81 6 6879 7495. E-mail address: [email protected] (Y. Umakoshi).
0921-5093/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2006.02.250
to Group 3 are often called metallic glasses [3]. One can see that the GFA in electron irradiation induced SSA is much higher than that in LQ. The electron irradiation is a very effective process to obtain an amorphous phase for extremely high GFA. Many models have been proposed for SSA processes up to date; energizing model from the view point of thermodynamics [4–6], Born criterion [7], Egami–Waseda criterion [8], the vibration instability criterion [9] from the view point of the instability of crystalline phase. However, many experimental results which cannot be explained by the above models have been reported. Several crystalline materials exhibited the pressure and/or hydrostatic pressure induced SSA [10,11]. In Zr66.7 Cu33.3 metallic glass, the crystal-to-amorphous-to-crystal (C-A-C) transition during electron irradiation [12] and the cyclic transition between crystal and amorphous phases during mechanical milling [13] were reported. Okamoto et al. suggested that the generalized Lindemann melting criterion and SSA can be considered as a kinetically constrained melting behavior [14]. In such a situation, we realized the in situ observation of SSA during electron irradiation without interrupting SSA process in Nd2 Fe14 B alloy. This first achievement must offer a unique opportunity to understand the origin of SSA and confirm the validity of generalized Lindemann melting criterion comparing the analogy between thermal melting and SSA.
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Fig. 1. Evaluation of glass forming ability (GFA) in electron irradiation induced solid-state amorphization (SSA) process based on the experimental data reported up to date. The GFA in electron-irradiation-induced SSA is much higher than that of samples obtained by the liquid quenching (LQ) process.
2. Experimental procedure A master ingot of Fe77 Nd4.5 B18.5 alloy was prepared by arc melting in a purified Ar atmosphere. Rapidly quenched ribbon was produced from the ingot by a single roller melt-spinning method in an Ar atmosphere. Nd2 Fe14 B compound was obtained by thermal annealing of the melt-spun ribbon at 1340 K for 600 s. XRD pattern of the annealed specimen showed sharp diffraction peaks corresponding to ␣-Fe, Fe2 B and Nd2 Fe14 B compound. Thin foils for electron irradiation were prepared from the ribbon by ion milling at 298 K. Nd2 Fe14 B compound in the foils were electron irradiated by an ultra-high voltage electron microscope (UHVEM) H-3000 operating at an acceleration voltage of 2.0 MV. The irradiation was performed at 298 K. The applied dose rate was between 3.3 × 1024 and 1.1 × 1025 m−2 s−1 , with the maximum total dose density of 6.6 × 1026 m−2 . Changes in the bright-field (BF) images and selected area diffraction (SAD) patterns during electron irradiation were observed by UHVEM at 2.0 MV. For in situ TEM observation of SSA process without interrupting electron irradiation, television camera and digital video recorder system were used.
process. The SSA can be confirmed by annihilation of crystalline fringe contrast in Nd2 Fe14 B compound. Fig. 3 shows in situ observation result of change in BF images of Nd2 Fe14 B compound during 2.0 MeV electron irradiation at the dose rate of 3.3 × 1024 m−2 s−1 at 298 K. The BF images were obtained using television camera and digital video
3. Results Fig. 2 shows changes in BF images and SAD patterns of Nd2 Fe14 B compound during 2.0 MeV electron irradiation at the dose rate of 1.0 × 1025 m−2 s−1 at 298 K. Before electron irradiation (a), BF image shows no featureless contrast but dark and bright contrast. The grain size of Nd2 Fe14 B compound is about 1 m order and a nanocrystalline structure is not observed inside the grain. One can see that crystalline fringe contrast in the crystalline grain. After electron irradiation at the total dose of 6.6 × 1026 m−2 (b), typical featureless contrast corresponding to an amorphous phase appears. In SAD pattern, broad halo rings appear instead of sharp diffraction spots, Nd2 Fe14 B compound cannot maintain its original structure under 2.0 MeV electron irradiation. An amorphous phase forms through electron irradiation induced SSA, while this phase is rarely obtained by LQ
Fig. 2. Change in BF images and SAD patterns of Nd2 Fe14 B intermetallic compound during 2.0 MeV electron irradiation at the dose rate of 1.0 × 1025 m−2 s−1 at 298 K. (a) Before electron irradiation, (b) after electron irradiation at 60 s at the total dose of 6.6 × 1026 m−2 .
T. Nagase et al. / Materials Science and Engineering A 449–451 (2007) 1111–1114
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Fig. 3. In situ observation of change in BF images of Nd2 Fe14 B intermetallic compound during 2.0 MeV electron irradiation at the dose rate of 3.3 × 1024 m−2 s−1 at 298 K. The BF images were obtained by attached video-camera and change in the contrast of Nd2 Fe14 B alloy can be obtained without interrupting the electron irradiation. (a) Before electron irradiation, (b–o) BF images obtained in every 5 s during electron irradiation.
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recorder system. Change in the contrast of Nd2 Fe14 B alloy can be observed without interrupting the electron irradiation. In the specimen before irradiation (a), the fringe contrast can be seen. Fig. 3(b–o) are BF images recorded for every 5 s during electron irradiation. No changes in crystalline contrast were observed in the irradiation period from 0 s (a) to 15 s (d). At the period from 20 s (e) to 35 s (h), a slight change in BF image occurred, but the fringe contrast still remained. In Fig. 3(i) for 40 s at the total dose of 1.3 × 1026 m−2 , the fringe contrast suddenly disappeared in the lower part of the irradiated grain as indicated by an arrow. At the further electron irradiation, featureless contrast moved gradually to the upper area in the irradiated grain as shown in Fig. 3(j–o). In Fig. 3(o) for 70 s at the total dose of 2.3 × 1026 m−2 , the irradiated grain shows featureless contrast corresponding to an amorphous phase. The annihilation of crystalline fringe contrast during electron irradiation seems to be analogous to that of thermal melting of crystalline phase reported by Sasaki and Saka [15]. This result indicates that the solid-state amorphization does not progress gradually under electron irradiation but occur suddenly at a critical concentration of atomic defects due to electron knock on effect. 4. Discussion In situ observation of SSA behavior of Nd2 Fe14 B compound implies that amorphous phase does not form gradually without a threshold value but form suddenly at a critical concentration of atomic defects. Such disordering phase transformation behavior seems to be analogous to that of thermal melting of metals at heating. Kiritani et al. discussed the local temperature rise of a specimen by electron beam [16]. The temperature rise in the present study was estimated to be about 10 K order from their model. Therefore, the present 2.0 MeV electron irradiation induced SSA in Nd2 Fe14 B compound is not attributed to the thermal melting. Okamoto et al. suggested that melting of crystalline phase is induced by two different ways: the thermodynamic melting by heating and the mechanical melting by disordering at the fixed temperature [14]. The present in situ observation result of SSA behavior under electron irradiation implies that SSA is a kind of melting behavior. 5. Conclusions In situ observation of change in BF images during 2.0 MeV electron irradiation induced solid-state amorphization without interrupting the irradiation was achieved in Nd2 Fe14 B compound at 298 K. The results were summarized and the following conclusions were reached: (i) Nd2 Fe14 B compound cannot maintain its original structure under 2.0 MV electron irradiation at 298 K. An amorphous
phase which was not realized by melt-spinning method was formed through electron irradiation induced SSA. (ii) Under electron irradiation, crystalline fringe contrast corresponding to Nd2 Fe14 B crystalline phase in a BF image disappeared suddenly when the total dose reached a critical value. SSA process at the critical dose seems to be analogous to thermal melting process of a crystal at the thermodynamical melting temperature. This result indicates that formation of an amorphous phase by SSA does not progress gradually under electron irradiation but occur suddenly at a critical concentration of atomic defects due to the electron knock on effect. Acknowledgements Electron irradiation tests were carried out using a facility in the Research Center for Ultrahigh Voltage Electron Microscopy, Osaka University. The authors are grateful to Prof. H. Mori and Dr. T. Sakata of the Research Center for operating the H3000 UHVEM. This work was supported by a Grant-in-Aid for Scientific Research on Priority Area A, “Materials Science of Metallic Glasses” from the Ministry of Education, Culture, Sports, Science and Technology of Japan. Part of this work was also supported by the same Ministry’s “Priority Assistance of the Formation of World-wide Renowned Centers of ResearchThe 21st Century COE Program (Project: Center of Excellence for Advanced Structural and Functional Materials Design)”. References [1] T. Masumoto, Materials Science of Amorphous Metals, Ohm Publication, Tokyo, 1982. [2] H. Mori, in: Y. Sakurai, Y. Hamakawa, T. Masumoto, K. Shirac, K. Suzuki (Eds.), Current Topics in Amorphous Materials: Physics and Technology, Elsevier Science Publishers, Amsterdam, 1997, pp. 120–126. [3] A. Inoue, Acta Mater. 48 (2000) 279–306. [4] R.B. Schwarz, W.L. Johnson, Phys. Rev. Lett. 51 (1983) 415–418. [5] R.B. Schwarz, C.C. Koch, Appl. Phys. Lett. 21 (1986) 146–148. [6] P.H. Shingu, Bull. JIM 27 (1988) 805–807. [7] M. Born, J. Chem. Phys. 7 (1939) 591–603. [8] T. Egami, Y. Waseda, J. Non-Cryst. Solids 64 (1984) 113–114. [9] F.A. Lindemann, Z. Phys. 11 (1910) 609–612. [10] O. Michima, L.D. Calvert, E. Whalley, Nature 310 (1984) 393–395. [11] S.M. Sharma, S.K. Sikka, Prog. Mater. Sci. 40 (1996) 1–77. [12] T. Nagase, Y. Umakoshi, Scripta Mater. 48 (2003) 1237–1242. [13] M. Sherif El-Eskandarany, A. Inoue, Metall. Mater. Trans. A 33 (2002) 2145–2153. [14] P.R. Okamoto, N.Q. Lam, L.E. Rein, in: H. Ehrenreich, F. Spaepen (Eds.), Solid State Physics, vol. 52, Academic Press, San Diego, 1999. [15] K. Sasaki, H. Saka, Mater. Res. Soc. Symp. Proc. 466 (1997) 185– 190. [16] M. Kiritani, K. Yoshida, H. Fujita, in: T. Imura, H. Hashimoto (Eds.), Proceedings of the Fifth International Conference on High Voltage Electron Microscopy, Japanese Society of Electron Microscopy, Tokyo, 1977, pp. 501–504.
In situ observation of solid-state amorphization in Nd2Fe14B alloy by electron irradiation Takeshi Nagase a , Akihiro Nino b , Yukichi Umakoshi a,∗ a
Division of Materials and Manufacturing Science, Graduate School of Engineering, Osaka University, 2-1 Yamada-oka, Suita, Osaka 565-0871, Japan b Department of Materials Science and Engineering, Graduate School of Engineering, Osaka University, 2-1 Yamada-oka, Suita, Osaka 565-0871, Japan Received 21 August 2005; received in revised form 5 December 2005; accepted 15 February 2006
Abstract In situ observation of solid-state amorphization in Nd2 Fe14 B compound was achieved by electron irradiation method. Under 2.0 MeV electron irradiation, crystalline contrast corresponding to Nd2 Fe14 B crystalline phase in a bright-field image disappeared suddenly when the total dose reached a critical value. The amorphous phase was rapidly formed under electron irradiation. Solid-state amorphization process at the critical total dose seems to be analogous to thermal melting process of crystal at the melting temperature. © 2006 Elsevier B.V. All rights reserved. Keywords: Solid-state amorphization; Electron irradiation; In situ observation; Intermetallic compound; Nd–Fe–B alloy
1. Introduction Amorphous alloys can be obtained not only by the liquid-toglass transition of liquid quenching (LQ) but also by the crystalto-glass transition of solid-state amorphization (SSA). The SSA means the formation of an amorphous phase during mechanical processes such as electron irradiation, ion irradiation, severe deformation, mechanical milling, hydrogen-absorption and inter-diffusion between multi-layers under the thermodynamical melting temperature (Tm ) [1,2]. Fig. 1 summarizes the results of electron irradiation induced SSA in intermetallic compounds reported up to date. The intermetallic compounds were classified into three groups based on the glass forming ability (GFA) in LQ by melt-spinning method and the phase stability of melt-spun amorphous alloys; (Group 1) an amorphous phase cannot be obtained by LQ, (Group 2) an amorphous phase is obtained by LQ and an amorphous-to-supercooled liquid transition is rarely observed by conventional DSC measurement, (Group 3) an amorphous phase is obtained by LQ and the amorphous-to-supercooled liquid transition can be confirmed by conventional DSC measurement. Amorphous alloys belonging
∗
Corresponding author. Tel.: +81 6 6879 7494; fax: +81 6 6879 7495. E-mail address: [email protected] (Y. Umakoshi).
0921-5093/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2006.02.250
to Group 3 are often called metallic glasses [3]. One can see that the GFA in electron irradiation induced SSA is much higher than that in LQ. The electron irradiation is a very effective process to obtain an amorphous phase for extremely high GFA. Many models have been proposed for SSA processes up to date; energizing model from the view point of thermodynamics [4–6], Born criterion [7], Egami–Waseda criterion [8], the vibration instability criterion [9] from the view point of the instability of crystalline phase. However, many experimental results which cannot be explained by the above models have been reported. Several crystalline materials exhibited the pressure and/or hydrostatic pressure induced SSA [10,11]. In Zr66.7 Cu33.3 metallic glass, the crystal-to-amorphous-to-crystal (C-A-C) transition during electron irradiation [12] and the cyclic transition between crystal and amorphous phases during mechanical milling [13] were reported. Okamoto et al. suggested that the generalized Lindemann melting criterion and SSA can be considered as a kinetically constrained melting behavior [14]. In such a situation, we realized the in situ observation of SSA during electron irradiation without interrupting SSA process in Nd2 Fe14 B alloy. This first achievement must offer a unique opportunity to understand the origin of SSA and confirm the validity of generalized Lindemann melting criterion comparing the analogy between thermal melting and SSA.
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Fig. 1. Evaluation of glass forming ability (GFA) in electron irradiation induced solid-state amorphization (SSA) process based on the experimental data reported up to date. The GFA in electron-irradiation-induced SSA is much higher than that of samples obtained by the liquid quenching (LQ) process.
2. Experimental procedure A master ingot of Fe77 Nd4.5 B18.5 alloy was prepared by arc melting in a purified Ar atmosphere. Rapidly quenched ribbon was produced from the ingot by a single roller melt-spinning method in an Ar atmosphere. Nd2 Fe14 B compound was obtained by thermal annealing of the melt-spun ribbon at 1340 K for 600 s. XRD pattern of the annealed specimen showed sharp diffraction peaks corresponding to ␣-Fe, Fe2 B and Nd2 Fe14 B compound. Thin foils for electron irradiation were prepared from the ribbon by ion milling at 298 K. Nd2 Fe14 B compound in the foils were electron irradiated by an ultra-high voltage electron microscope (UHVEM) H-3000 operating at an acceleration voltage of 2.0 MV. The irradiation was performed at 298 K. The applied dose rate was between 3.3 × 1024 and 1.1 × 1025 m−2 s−1 , with the maximum total dose density of 6.6 × 1026 m−2 . Changes in the bright-field (BF) images and selected area diffraction (SAD) patterns during electron irradiation were observed by UHVEM at 2.0 MV. For in situ TEM observation of SSA process without interrupting electron irradiation, television camera and digital video recorder system were used.
process. The SSA can be confirmed by annihilation of crystalline fringe contrast in Nd2 Fe14 B compound. Fig. 3 shows in situ observation result of change in BF images of Nd2 Fe14 B compound during 2.0 MeV electron irradiation at the dose rate of 3.3 × 1024 m−2 s−1 at 298 K. The BF images were obtained using television camera and digital video
3. Results Fig. 2 shows changes in BF images and SAD patterns of Nd2 Fe14 B compound during 2.0 MeV electron irradiation at the dose rate of 1.0 × 1025 m−2 s−1 at 298 K. Before electron irradiation (a), BF image shows no featureless contrast but dark and bright contrast. The grain size of Nd2 Fe14 B compound is about 1 m order and a nanocrystalline structure is not observed inside the grain. One can see that crystalline fringe contrast in the crystalline grain. After electron irradiation at the total dose of 6.6 × 1026 m−2 (b), typical featureless contrast corresponding to an amorphous phase appears. In SAD pattern, broad halo rings appear instead of sharp diffraction spots, Nd2 Fe14 B compound cannot maintain its original structure under 2.0 MeV electron irradiation. An amorphous phase forms through electron irradiation induced SSA, while this phase is rarely obtained by LQ
Fig. 2. Change in BF images and SAD patterns of Nd2 Fe14 B intermetallic compound during 2.0 MeV electron irradiation at the dose rate of 1.0 × 1025 m−2 s−1 at 298 K. (a) Before electron irradiation, (b) after electron irradiation at 60 s at the total dose of 6.6 × 1026 m−2 .
T. Nagase et al. / Materials Science and Engineering A 449–451 (2007) 1111–1114
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Fig. 3. In situ observation of change in BF images of Nd2 Fe14 B intermetallic compound during 2.0 MeV electron irradiation at the dose rate of 3.3 × 1024 m−2 s−1 at 298 K. The BF images were obtained by attached video-camera and change in the contrast of Nd2 Fe14 B alloy can be obtained without interrupting the electron irradiation. (a) Before electron irradiation, (b–o) BF images obtained in every 5 s during electron irradiation.
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recorder system. Change in the contrast of Nd2 Fe14 B alloy can be observed without interrupting the electron irradiation. In the specimen before irradiation (a), the fringe contrast can be seen. Fig. 3(b–o) are BF images recorded for every 5 s during electron irradiation. No changes in crystalline contrast were observed in the irradiation period from 0 s (a) to 15 s (d). At the period from 20 s (e) to 35 s (h), a slight change in BF image occurred, but the fringe contrast still remained. In Fig. 3(i) for 40 s at the total dose of 1.3 × 1026 m−2 , the fringe contrast suddenly disappeared in the lower part of the irradiated grain as indicated by an arrow. At the further electron irradiation, featureless contrast moved gradually to the upper area in the irradiated grain as shown in Fig. 3(j–o). In Fig. 3(o) for 70 s at the total dose of 2.3 × 1026 m−2 , the irradiated grain shows featureless contrast corresponding to an amorphous phase. The annihilation of crystalline fringe contrast during electron irradiation seems to be analogous to that of thermal melting of crystalline phase reported by Sasaki and Saka [15]. This result indicates that the solid-state amorphization does not progress gradually under electron irradiation but occur suddenly at a critical concentration of atomic defects due to electron knock on effect. 4. Discussion In situ observation of SSA behavior of Nd2 Fe14 B compound implies that amorphous phase does not form gradually without a threshold value but form suddenly at a critical concentration of atomic defects. Such disordering phase transformation behavior seems to be analogous to that of thermal melting of metals at heating. Kiritani et al. discussed the local temperature rise of a specimen by electron beam [16]. The temperature rise in the present study was estimated to be about 10 K order from their model. Therefore, the present 2.0 MeV electron irradiation induced SSA in Nd2 Fe14 B compound is not attributed to the thermal melting. Okamoto et al. suggested that melting of crystalline phase is induced by two different ways: the thermodynamic melting by heating and the mechanical melting by disordering at the fixed temperature [14]. The present in situ observation result of SSA behavior under electron irradiation implies that SSA is a kind of melting behavior. 5. Conclusions In situ observation of change in BF images during 2.0 MeV electron irradiation induced solid-state amorphization without interrupting the irradiation was achieved in Nd2 Fe14 B compound at 298 K. The results were summarized and the following conclusions were reached: (i) Nd2 Fe14 B compound cannot maintain its original structure under 2.0 MV electron irradiation at 298 K. An amorphous
phase which was not realized by melt-spinning method was formed through electron irradiation induced SSA. (ii) Under electron irradiation, crystalline fringe contrast corresponding to Nd2 Fe14 B crystalline phase in a BF image disappeared suddenly when the total dose reached a critical value. SSA process at the critical dose seems to be analogous to thermal melting process of a crystal at the thermodynamical melting temperature. This result indicates that formation of an amorphous phase by SSA does not progress gradually under electron irradiation but occur suddenly at a critical concentration of atomic defects due to the electron knock on effect. Acknowledgements Electron irradiation tests were carried out using a facility in the Research Center for Ultrahigh Voltage Electron Microscopy, Osaka University. The authors are grateful to Prof. H. Mori and Dr. T. Sakata of the Research Center for operating the H3000 UHVEM. This work was supported by a Grant-in-Aid for Scientific Research on Priority Area A, “Materials Science of Metallic Glasses” from the Ministry of Education, Culture, Sports, Science and Technology of Japan. Part of this work was also supported by the same Ministry’s “Priority Assistance of the Formation of World-wide Renowned Centers of ResearchThe 21st Century COE Program (Project: Center of Excellence for Advanced Structural and Functional Materials Design)”. References [1] T. Masumoto, Materials Science of Amorphous Metals, Ohm Publication, Tokyo, 1982. [2] H. Mori, in: Y. Sakurai, Y. Hamakawa, T. Masumoto, K. Shirac, K. Suzuki (Eds.), Current Topics in Amorphous Materials: Physics and Technology, Elsevier Science Publishers, Amsterdam, 1997, pp. 120–126. [3] A. Inoue, Acta Mater. 48 (2000) 279–306. [4] R.B. Schwarz, W.L. Johnson, Phys. Rev. Lett. 51 (1983) 415–418. [5] R.B. Schwarz, C.C. Koch, Appl. Phys. Lett. 21 (1986) 146–148. [6] P.H. Shingu, Bull. JIM 27 (1988) 805–807. [7] M. Born, J. Chem. Phys. 7 (1939) 591–603. [8] T. Egami, Y. Waseda, J. Non-Cryst. Solids 64 (1984) 113–114. [9] F.A. Lindemann, Z. Phys. 11 (1910) 609–612. [10] O. Michima, L.D. Calvert, E. Whalley, Nature 310 (1984) 393–395. [11] S.M. Sharma, S.K. Sikka, Prog. Mater. Sci. 40 (1996) 1–77. [12] T. Nagase, Y. Umakoshi, Scripta Mater. 48 (2003) 1237–1242. [13] M. Sherif El-Eskandarany, A. Inoue, Metall. Mater. Trans. A 33 (2002) 2145–2153. [14] P.R. Okamoto, N.Q. Lam, L.E. Rein, in: H. Ehrenreich, F. Spaepen (Eds.), Solid State Physics, vol. 52, Academic Press, San Diego, 1999. [15] K. Sasaki, H. Saka, Mater. Res. Soc. Symp. Proc. 466 (1997) 185– 190. [16] M. Kiritani, K. Yoshida, H. Fujita, in: T. Imura, H. Hashimoto (Eds.), Proceedings of the Fifth International Conference on High Voltage Electron Microscopy, Japanese Society of Electron Microscopy, Tokyo, 1977, pp. 501–504.