In summery, the local atomic pairing arrangement of the binary Zr-Ni, Zr-Ti, and pure Zr systems during room temperature severe deformation under high strain rates is simulated by MD method. The following conclusions can be reached from this part of study.
(1) For the Zr-Ni system, the local defect structures of the FCC Ni and HCP Zr, or the icosahedra clusters are seen to form first in the early stage of the amorphous transition, and the FCC 1421 or FCC/HCP 1422 close-packed pairs would decay rapidly at the same time.
(2) For the Zr-Ni system, the icosahedra defect local structures, or the 1541 pairs, will first evolve and then transform into the more stable icosahedra clusters, or the 1551 pairs. The three types of pairs, namely the 1551, 1431, and 1541 pairs occupy totally ~70% of the total pair population. The rest are the remaining FCC or HCP (1421 or 1422, accounting for ~15%) and the intermediate local structures (1441, 1661 or 1321, accounting for another ~15%).
(3) During the transient stage for the Zr-Ni system, the BCC-related cubic-typed 1321 pairs are formed up to 20%, which may be related to the intermetallic compounds that will form according to their equilibrium phase diagram. But this transient atomic pairs would disappear at the later stage. In addition, the FCC Ni seems to be more difficult to change into the amorphous phase than the HCP Zr, judging from the PRDF curves. And the FCC local pairing appears to change to the BCC-typed pairing before transforming into the fully amorphous state. The structure transition mechanism of the FCC seems to be more complex and more persistent than that for the HCP structure.
91
(5) With the same HCP crystal structure for both Zr and Ti, the transformation in the Zr-Ti system is basically simple. No apparent transient atomic packing is formed in the intermediate stage. The icosahedra-related atomic pairs occupy nearly 80% in the later stage.
(6) The current simulation results reveal that the short-range icosahedra structures always play an important role during the course of crystalline-to-amorphous transition, both during the solid state strain-induced ARB and rapid cooling processes.
(7) Finally, it is demonstrated by MD simulation that, under proper cooling and relative faster rolling speed, the crystalline pure Zr element should be able to transform into the amorphous phase. But there exists a critical strain rate for the phase transformation between crystalline and amorphous phase. Below this critical strain rate, the created defects in metallic matrix can be always rearranged and annihilated to maintain the stable-state for crystalline in long range order without vitrification.
In the part of MD study on the diffusion behaviors between incoherent interfaces of the Mg-Cu system, the structural transition of Mg-Cu multilayer annealing at three temperature conditions had been studied by employing EMT potential in the MD simulation. The results lead to following conclusions.
(1) As increasing temperature, there are more kinetic energy offer interfacial atoms to relax their local structures. However, the NVT ensemble applied the constraint on the lateral sides in the simulation box. That is similar to a high pressure condition which results Cu atoms congregate in the Mg matrix from network to clusters. On the other hand, the experiment results also show that there are not obvious amorphous structures in the similar condition, just
92
Mg2Cu compound forming in the Mg-Cu multilayer.
(2) A suitable ensemble, e.g. isothermal-isobaric (NPT) ensemble, is needed to take place of the current model to enhance the possibility of phase transition for forming the complex compound structures in Mg-Cu system. Diffusion behavior of atoms in lower temperature is strongly time-dependent and needs much longer time period. It could be better to investigate this propertie by MC method instead of MD in the future.
Through the molecular dynamics studies of the cyclic loading response of Zr50Cu50
metallic glasses, the following conclusions can be reached.
(1) Throughout the current cyclic deformation under the stress or strain control mode, there are no major atomic structure changes or stress-induced crystallization, as judged from the PRDF and HA index. This is thought to be a result of the limited simulated volume, within which the STZs are still in their early development. The mature shear bands are not yet fully developed even under the most severe strain control mode.
(2) The current simulated results demonstrate that the induced STZs, measuring 10-20 Å, are basically discrete and homogeneous. The temporary local STZs formed in one fatigue cycle frequently disappear in the subsequent unloading or reversed-stress loading cycles.
(3) Based on the deformation evolution as a function of cyclic loading, as evidenced by the simulated ABRA, potential energy, atomic density, and fatigue softening results, the current Zr-Cu amorphous alloy appears be deformed more readily in the initial fatigue stage, followed by gradual saturated behavior.
93
(4) It is found that structure relaxation, or dynamic recovery, has occurred in the current cyclic loading of the Zr-Cu metallic glass. When the fatigue stress or strain is low, still well within the elastic range, the dynamic recovery of RRCs will dominate the most atomic events.
When the fatigue stress or strain exceeds into the plastic regime, dynamic recovery of IRRCs becomes easier.
(5) Through the self-repairing and dynamic recovery capability of IRRCs, the current Zr-Cu metallic glass could reduce the local spatial defects in STZs induced by the previous cyclic deformation. Thus the overall metallic glassy structure under fatigue could resist the damage accumulation, exhibiting satisfactory fatigue resistance.
(6) The current simulation results suggest that the metallic glass in small size-scale can be quite fatigue resistant. The metallic bonds in the metallic glasses, once broken by local shear stress, can be self-repaired and re-bonded to neighboring atoms by the subsequent reverse shear stress. Such a dynamic recovery capability is particularly significant in fatigue loading.
For applications of the metallic glasses in micro-electro-mechanical systems (MEMS), the current finding is encouraging.
94
Reference
1. K.L. Chapra, Thin Film Phenomena. 1969: McGraw-Hill.
2. P.S. Gramt, Progress in Materials Science, 1995, 39, 497.
3. B. Li, N. Nordstrom and E.J. Lavernia, Mater. Sci. Eng. A, 1997, 237, 207.
4. C.R.M. Afonso, C. Bolfarini, C.S. Kiminami, N.D. Bassim, M.J. Kaufman, M.F.
Amateau, T.J. Eden and J.M. Galbraith, Journal of Non-Crystalline Solids, 2001, 284, 134-138.
5. R. Liu, J. Li, K. Dong, C. Zheng and H. Liu, Mater. Sci. Eng. B, 2002, 94, 141.
6. C.C. Koch, O.B. Cavin, C.G. McKamey and J.O. Scarbrough, Applied Physics Letters, 1983, 43, 1017-1019.
7. J. Eckert, Mater. Sci. Eng. A, 1997, 226-228, 364.
8. N. Schultz, Mater. Sci. Eng., 1998, 97, 15.
9. F.Z. J. Lee, K. H. Chung, N. J. Kim, and E. J. Lavernia,, Metall. Mater. Trans. A, 2001, 32, 3109.
10. M. Sherif, E. Eskandarany and A. Inoue, Metall. Mater. Trans. A, 2002, 33, 135.
11. Z.P. Xing, S.B. Kang and H.W. Kim, Metallurgical and Materials Transactions a-Physical Metallurgy and Materials Science, 2002, 33, 1521-1530.
12. X.L. Yeh, K. Samwer and W.L. Johnson, Applied Physics Letters, 1983, 42, 242-244.
13. A. Sagel, H. Sieber, H.J. Fecht and J.H. Perepzko, Acta Materialia, 1998, 46, 4233.
14. N. Tsuji, Y. Saito, S.H. Lee and Y. Minamino, Advanced Engineering Materials, 2003, 5, 338.
15. Y. Saito, N. Tsuji, H. Utsunomiya, T. Sakai and R.G. Hong, Scripta Materialia, 1998, 39, 1221-1227.
16. R.B. Schwarz and W.L. Johnson, Physical Review Letters, 1983, 51, 415-418.
95
17. P. Haussler, F. Baumann, J. Krieg, G. Indlekofer, P. Oelhafen and H.J. Guntherodt, Physical Review Letters, 1983, 51, 714-717.
18. A.L. Greer, Science, 1995, 267, 1947-1953.
19. W.L. Johnson, Mrs Bulletin, 1999, 24, 42-56.
20. W.H. Wang, C. Dong and C.H. Shek, Materials Science & Engineering R-Reports, 2004, 44, 45-89.
21. J.P.K. Doye and D.J. Wales, Science, 1996, 271, 484-487.
22. F. Spaepen, Nature, 2000, 408, 781-782.
23. H.W. Sheng, W.K. Luo, F.M. Alamgir, J.M. Bai and E. Ma, Nature, 2006, 439, 419-425.
24. H. Tanaka, Journal of Non-Crystalline Solids, 2005, 351, 3396-3413.
25. Y.I. Golovin, V.I. Ivolgin, V.A. Khonik, K. Kitagawa and A.I. Tyurin, Scripta Materialia, 2001, 45, 947-952.
26. P. Murah and U. Ramamurty, Acta Materialia, 2005, 53, 1467-1478.
27. U. Ramamurty, S. Jana, Y. Kawamura and K. Chattopadhyay, Acta Materialia, 2005, 53, 705-717.
28. G.P. Zhang, W. Wang, B. Zhang, J. Tan and C.S. Liu, Scripta Materialia, 2005, 52, 1147-1151.
29. J.R. Morris, R.S. Aga, T. Egami and V.A. Levashov, International Journal of Modern Physics B, 2009, 23, 1229-1234.
30. K. Nordlund and R.S. Averback, Applied Physics Letters, 1997, 70, 3101-3103.
31. J.S. Robach, I.M. Robertson, H.J. Lee and B.D. Wirth, Acta Materialia, 2006, 54, 1679-1690.
32. H. Van Swygenhoven, P.M. Derlet and A.G. Froseth, Acta Materialia, 2006, 54, 1975-1983.
33. H. Van Swygenhoven, D. Farkas and A. Caro, Physical Review B, 2000, 62, 831-838.
96
34. D. Wolf, V. Yamakov, S.R. Phillpot, A. Mukherjee and H. Gleiter, Acta Materialia, 2005, 53, 1-40.
35. G.P. Zheng, Y.M. Wang and M. Li, Acta Materialia, 2005, 53, 3893-3901.
36. P.C. Millett, R.P. Selvam and A. Saxena, Acta Materialia, 2006, 54, 297-303.
37. P.J. Hsieh, Y.P. Hung and J.C. Huang, Scripta Materialia, 2003, 49, 173-178.
38. P.J. Hsieh, J.C. Huang, Y.P. Hung, S.I. Chou and J.S.C. Jang, Materials Chemistry and Physics, 2004, 88, 364-376.
39. P.J. Hsieh, Y.P. Hung, S.I. Chou and J.C. Huang, Materials Transactions, 2004, 45, 2686-2692.
40. S. Vautha and S.G. Mayr, Appl. Phys. Lett., 2005, 86, 061913.
41. X. He, S.H. Liang, J.H. Li and B.X. Liu, Physical Review B, 2007, 75, 10.
42. G.Y. Wang, P.K. Liaw, W.H. Peter, B. Yang, Y. Yokoyama, M.L. Benson, B.A. Green, M.J. Kirkham, S.A. White, T.A. Saleh, R.L. McDaniels, R.V. Steward, R.A. Buchanan, C.T. Liu and C.R. Brooks, Intermetallics, 2004, 12, 885-892.
43. G.Y. Wang, P.K. Liaw, W.H. Peter, B. Yang, M. Freels, Y. Yokoyama, M.L. Benson, B.A. Green, T.A. Saleh, R.L. McDaniels, R.V. Steward, R.A. Buchanan, C.T. Liu and C.R. Brooks, Intermetallics, 2004, 12, 1219-1227.
44. W. Klement, R.H. Willens and P. Duwez, Nature, 1960, 187, 869-870.
45. H.S. Chen and D. Turnbull, Acta Metallurgica, 1969, 17, 1021-1031.
46. H.S. Chen, Acta Metallurgica, 1974, 22, 1505-1511.
47. D. Turnbull and J.C. Fisher, Journal of Chemical Physics, 1949, 17, 71-73.
48. Z.P. Lu and C.T. Liu, Acta Materialia, 2002, 50, 3501-3512.
49. L. Xia, S.S. Fang, Q. Wang, Y.D. Dong and C.T. Liu, Applied Physics Letters, 2006, 88, 3.
50. A.J. Drehman, A.L. Greer and D. Turnbull, Applied Physics Letters, 1982, 41, 716-717.
97
51. H.W. Kui, A.L. Greer and D. Turnbull, Applied Physics Letters, 1984, 45, 615-616.
52. W.L. Johnson, Progress in Materials Science, 1986, 30, 81-134.
53. A. Inoue, T. Zhang and T. Masumoto, Materials Transactions, JIM, 1989, 30, 965-972.
54. A. Inoue, Acta Materialia, 2000, 48, 279-306.
55. A. Inoue, A. Kato, T. Zhang, S.G. Kim and T. Masumoto, Materials Transactions, JIM, 1991, 32, 609-616.
56. T. Zhang, A. Inoue and T. Masumoto, Materials Transactions, JIM, 1991, 32, 1005-1010.
57. A. Inoue, T. Zhang, N. Nishiyama, K. Ohba and T. Masumoto, Materials Transactions, JIM, 1993, 34, 1234-1237.
58. A. Inoue, Materials Transactions, JIM, 1995, 36, 866-875.
59. A. Inoue, N. Nishiyama and H. Kimura, Materials Transactions, JIM, 1997, 38, 179-183.
60. A. Inoue, Materials Science and Engineering A, 2001, 304-306, 1-10.
61. M. Leonhardt, W. Loser and H.G. Lindenkreuz, Acta Materialia, 1999, 47, 2961-2968.
62. F.Q. Guo, S.J. Poon and G.J. Shiflet, Applied Physics Letters, 2004, 84, 37-39.
63. W.J. Meng, B. Fultz, E. Ma and W.L. Johnson, Applied Physics Letters, 1987, 51, 661-663.
64. W.J. Meng, C.W. Nieh and W.L. Johnson, Applied Physics Letters, 1987, 51, 1693-1695.
65. D. Wang, Y. Li, B.B. Sun, M.L. Sui, K. Lu and E. Ma, Applied Physics Letters, 2004, 84, 4029-4031.
66. D.H. Xu, B. Lohwongwatana, G. Duan, W.L. Johnson and C. Garland, Acta Materialia, 2004, 52, 2621-2624.
67. T. Hattori, H. Saitoh, H. Kaneko, Y. Okajima, K. Aoki and W. Utsumi, Physical Review Letters, 2006, 96, 4.
98
68. J.D. Bernal, Nature, 1959, 183, 141.
69. M.H. Cohen and D. Turnbull, Nature, 1964, 203, 964.
70. R. Wang, Nature, 1979, 278, 700-704.
71. A. Inoue, T. Negishi, H.M. Kimura, T. Zhang and A.R. Yavari, Materials Transactions Jim, 1998, 39, 318-321.
72. W.H. Wang, R.J. Wang, D.Q. Zhao, M.X. Pan and Y.S. Yao, Physical Review B, 2000, 62, 11292-11295.
73. W.H. Wang, Q. Wei, S. Friedrich, M.P. Macht, N. Wanderka and H. Wollenberger, Applied Physics Letters, 1997, 71, 1053-1055.
74. A. Inoue, Bulk Amorphous Alloys. 1998: Trans Tech Publications.
75. J.D. Honeycutt and H.C. Andersen, Journal of Physical Chemistry, 1987, 91, 4950-4963.
76. H. Jonsson and H.C. Andersen, Physical Review Letters, 1988, 60, 2295-2298.
77. J.H. He and E. Ma, Physical Review B, 2001, 64, 12.
78. J.H. He, H.W. Sheng, P.J. Schilling, C.L. Chien and E. Ma, Physical Review Letters, 2001, 86, 2826-2829.
79. W.K. Luo, H.W. Sheng, F.M. Alamgir, J.M. Bai, J.H. He and E. Ma, Physical Review Letters, 2004, 92, 4.
80. C.F. Li, J. Saida, M. Matsushita and A. Inoue, Applied Physics Letters, 2000, 77, 528-530.
81. H. Reichert, O. Klein, H. Dosch, M. Denk, V. Honkimaki, T. Lippmann and G. Reiter, Nature, 2000, 408, 839-841.
82. D.R.N.a.F. Spaepen, Solid State Physics, 1989, 42, 1.
83. J. Saida, M. Matsushita and A. Inoue, Applied Physics Letters, 2001, 79, 412-414.
84. W.H. Wang, E. Wu, R.J. Wang, S.J. Kennedy and A.J. Studer, Physical Review B, 2002, 66, 5.
99
85. T. Waniuk, J. Schroers and W.L. Johnson, Physical Review B, 2003, 67, 9.
86. J.M. Cowley, Ultramicroscopy, 2002, 90, 197-206.
87. N. Mattern, U. Kuhn, H. Hermann, H. Ehrenberg, J. Neuefeind and J. Eckert, Acta Materialia, 2002, 50, 305-314.
88. T.C. Hufnagel, Nature Materials, 2004, 3, 666-667.
89. A. Hirata, Y. Hirotsu, E. Matsubara, T. Ohkubo and K. Hono, Physical Review B, 2006, 74, 6.
90. D.B. Miracle, Nature Materials, 2004, 3, 697-702.
91. G.L. Chen, X.J. Liu, X.D. Hui, H.Y. Hou, K.F. Yao, C.T. Liu and J. Wadsworth, Applied Physics Letters, 2006, 88, 3.
92. C. Fan, P.K. Liaw, V. Haas, J.J. Wall, H. Choo, A. Inoue and C.T. Liu, Physical Review B, 2006, 74, 6.
93. C. Fan, P.K. Liaw, T.W. Wilson, H. Choo, Y.F. Gao, C.T. Liu, T. Proffen and J.W.
Richardson, Applied Physics Letters, 2006, 89, 3.
94. C. Fan, P.K. Liaw, T.W. Wilson, W. Dmowski, H. Choo, C.T. Liu, J.W. Richardson and T. Proffen, Applied Physics Letters, 2006, 89, 3.
95. A. Takeuchi and A. Inoue, Materials Science and Engineering a-Structural Materials Properties Microstructure and Processing, 2004, 375, 1140-1144.
96. K.M. Flores and R.H. Dauskardt, Acta Materialia, 2001, 49, 2527-2537.
97. K.M. Flores and R.H. Dauskardt, Journal of Materials Research, 1999, 14, 638-643.
98. A. Inoue and A. Takeuchi, Materials Transactions, 2002, 43, 1892-1906.
99. W.L. Johnson, Jom-Journal of the Minerals Metals & Materials Society, 2002, 54, 40-43.
100. C.C. Hays, C.P. Kim and W.L. Johnson, Physical Review Letters, 2000, 84, 2901-2904.
101. J. Schroers and W.L. Johnson, Physical Review Letters, 2004, 93, 4.
100
102. M.H. Cohen and D. Turnbull, Journal of Chemical Physics, 1959, 31, 1164-1169.
103. F. Spaepen, Acta Metallurgica, 1977, 25, 407-415.
104. A.S. Argon, Acta Metallurgica, 1979, 27, 47-58.
105. P.L. Michael Miller, Bulk Metallic Glasses: An Overview. Hardcover ed. 2007:
Springer
106. A. Vandenbeukel and J. Sietsma, Acta Metallurgica Et Materialia, 1990, 38, 383-389.
107. B. Yang, M.L. Morrison, P.K. Liaw, R.A. Buchanan, G.Y. Wang, C.T. Liu and M.
Denda, Applied Physics Letters, 2005, 86, 141904.
108. F. Albano and M.L. Falk, Journal of Chemical Physics, 2005, 122, 8.
109. Q.K. Li and M. Li, Applied Physics Letters, 2006, 88, 3.
110. Q.K. Li and M. Li, Physical Review B, 2007, 75, 5.
111. M.W. Chen, Annual Review of Materials Research, 2008, 38, 445-469.
112. C.A. Schuh, T.C. Hufnagel and U. Ramamurty, Acta Materialia, 2007, 55, 4067-4109.
113. C.A. Schuh and A.C. Lund, Nature Materials, 2003, 2, 449-452.
114. P.G. Debenedetti and F.H. Stillinger, Nature, 2001, 410, 259-267.
115. W.L. Johnson and K. Samwer, Physical Review Letters, 2005, 95, 4.
116. M. Zink, K. Samwer, W.L. Johnson and S.G. Mayr, Physical Review B, 2006, 73, 3.
117. M.L. Falk and J.S. Langer, Physical Review E, 1998, 57, 7192-7205.
118. M.L. Manning, J.S. Langer and J.M. Carlson, Physical Review E, 2007, 76, 16.
119. Y.F. Shi, M.B. Katz, H. Li and M.L. Falk, Physical Review Letters, 2007, 98, 4.
120. J.S. Langer, Physical Review E, 2008, 77, 021502.
121. M.L. Manning, E.G. Daub, J.S. Langer and J.M. Carlson, Physical Review E, 2009, 79, 17.
122. E. Pekarskaya, C.P. Kim and W.L. Johnson, Journal of Materials Research, 2001, 16, 2513-2518.
123. J. Li, F. Spaepen and T.C. Hufnagel, Philosophical Magazine A, 2002, 82, 2623-2630.
101
124. T.C. Hufnagel, T. Jiao, Y. Li, L.Q. Xing and K.T. Ramesh, Journal of Materials Research, 2002, 17, 1441-1445.
125. Q.K. Li and M. Li, Applied Physics Letters, 2005, 87, 031910 126. Q.K. Li and M. Li, Intermetallics, 2006, 14, 1005-1010.
127. N.P. Bailey, J. Schiotz and K.W. Jacobsen, Physical Review B, 2006, 73, 12.
128. F. Shimizu, S. Ogata and J. Li, Acta Materialia, 2006, 54, 4293-4298.
129. F. Shimizu, S. Ogata and J. Li, Materials Transactions, 2007, 48, 2923-2927.
130. S. Ogata, F. Shimizu, J. Li, M. Wakeda and Y. Shibutani, Intermetallics, 2006, 14, 1033-1037.
131. J.J. Lewandowski and A.L. Greer, Nature Materials, 2006, 5, 15-18.
132. F. Spaepen, Nature Materials, 2006, 5, 7-8.
133. B. Yang, C.T. Liu, T.G. Nieh, M.L. Morrison, P.K. Liaw and R.A. Buchanan, Journal of Materials Research, 2006, 21, 915-922.
134. M.L. Morrison, R.A. Buchanan, P.K. Liaw, B.A. Green, G.Y. Wang, C. Liu and J.A.
Horton, Materials Science and Engineering a-Structural Materials Properties Microstructure and Processing, 2007, 467, 190-197.
135. M.L. Morrison, R.A. Buchanan, P.K. Liaw, B.A. Green, G.Y. Wang, C.T. Liu and J.A.
Horton, Materials Science and Engineering a-Structural Materials Properties Microstructure and Processing, 2007, 467, 198-206.
136. C.J. Gilbert, V. Schroeder and R.O. Ritchie, Metallurgical and Materials Transactions a-Physical Metallurgy and Materials Science, 1999, 30, 1739-1753.
137. C.J. Gilbert, J.M. Lippmann and R.O. Ritchie, Scripta Materialia, 1998, 38, 537-542.
138. K.K. Cameron and R.H. Dauskardt, Scripta Materialia, 2006, 54, 349-353.
139. M.E. Launey, R. Busch and J.J. Kruzic, Acta Materialia, 2008, 56, 500-510.
140. D.F.a.B. Smit, Understanding Molecular Simulation from Algorithms to Applications.
2nd edition ed. 2002: Academic Press.
102
141. F.F. Chen, H.F. Zhang, F.X. Qin and Z.Q. Hu, Journal of Chemical Physics, 2004, 120, 1826-1831.
142. M.P. Allen and D.J. Tildesly, Computer Simulation of Liquids. 1987: Clarendon.
143. W.J. Minkowycz and E.M. Sparrow, Numerical Heat Transfer Part a-Applications, 2002, 42, 1.
144. W.J. Minkowycz and E.M. Sparrow, Numerical Heat Transfer Part B-Fundamentals, 1998, 33, 3-3.
145. M.S. Daw and M.I. Baskes, Physical Review B, 1984, 29, 6443-6453.
146. L.V. Woodcock, Chemical Physics Letters, 1971, 10, 257-&.
147. S. Nose, Progress of Theoretical Physics Supplement, 1991, 1-46.
148. H.C. Andersen, Journal of Chemical Physics, 1980, 72, 2384-2393.
149. S. Nose, Journal of Chemical Physics, 1984, 81, 511-519.
150. S. Nose, Molecular Physics, 1984, 52, 255-268.
151. W.G. Hoover, Physical Review A, 1986, 34, 2499-2500.
152. M. Parrinello and A. Rahman, Physical Review Letters, 1980, 45, 1196-1199.
153. M.P. Allen, 2004.
154. F. Cleri and V. Rosato, Physical Review B, 1993, 48, 22-33.
155. H.K. F. Shimizu, H. Kaburaki, J. Li and S. Yip. in Proceedings of the Fourth International Conference SNA2000. 2000.
156. G. Duan, D.H. Xu, Q. Zhang, G.Y. Zhang, T. Cagin, W.L. Johnson and W.A. Goddard, Physical Review B, 2005, 71, 9.
157. V. Yamakov, D. Wolf, S.R. Phillpot, A.K. Mukherjee and H. Gleiter, Nature Materials, 2002, 1, 45-48.
158. J. Liu, J.Z. Zhao and Z.Q. Hu, Materials Science and Engineering a-Structural Materials Properties Microstructure and Processing, 2007, 452, 103-109.
159. Y.T. Zhu and X.Z. Liao, Applied Physics Letters, 2005, 86, 3.
103
160. J.D. Honeycutt and H.C. Andersen, Chemical Physics Letters, 1984, 108, 535-538.
161. K.W. Jacobsen, J.K. Norskov and M.J. Puska, Physical Review B, 1987, 35, 7423-7442.
162. K.W. Jacobsen, P. Stoltze and J.K. Norskov, Surface Science, 1996, 366, 394-402.
163. J. Schiotz and K.W. Jacobsen, Science, 2003, 301, 1357-1359.
164. N.P. Bailey, J. Schiotz and K.W. Jacobsen, Physical Review B, 2004, 69, 11.
165. A. Paduraru, A. Kenoufi, N.P. Bailey and J. Schiotz, Advanced Engineering Materials, 2007, 9, 505-508.
166. M.E. Tuckerman and G.J. Martyna, Journal of Physical Chemistry B, 2000, 104, 159-178.
167. M.E. Tuckerman, D.A. Yarne, S.O. Samuelson, A.L. Hughes and G.J. Martyna, Computer Physics Communications, 2000, 128, 333-376.
168. C.J. Mundy, S. Balasubramanian, K. Bagchi, M.E. Tuckerman, G.J. Martyna and M.L.
Klein, Nonequilibrium molecular dynamics, in Reviews in Computational Chemistry, Vol 14. 2000, Wiley-Vch, Inc: New York. p. 291-397.
169. Y.H. Lai, C.J. Lee, Y.T. Cheng, H.S. Chou, H.M. Chen, X.H. Du, C.I. Chang, J.C.
Huang, S.R. Jian, J.S.C. Jang and T.G. Nieh, Scripta Materialia, 2008, 58, 890-893.
170. C.J. Lee, J.C. Huang and T.G. Nieh, Applied Physics Letters, 2007, 91, 3.
171. G.P. Potirniche, M.F. Horstemeyer, G.J. Wagner and P.M. Gullett, International Journal of Plasticity, 2006, 22, 257-278.
172. G.P. Potirniche, M.F. Horstemeyer, P.M. Gullett and B. Jelinek, Proceedings of the Royal Society a-Mathematical Physical and Engineering Sciences, 2006, 462, 3707-3731.
173. L. Tayebi, C.E. Lekka and G.A. Evangelakis. Poisson ratio under compressive and tensile strain; effect on the mechanical response of the Cu46Zr54 metallic glass. 2008:
Wiley-V C H Verlag Gmbh.
104
174. Z.W. Shan, J. Li, Y.Q. Cheng, A.M. Minor, S.A.S. Asif, O.L. Warren and E. Ma, Physical Review B, 2008, 77, 6.
175. P.J. Hsieh, Y.C. Lo, J.C. Huang and S.P. Ju, Intermetallics, 2006, 14, 924-930.
176. A.C. Lund and C.A. Schuh, Journal of Applied Physics, 2004, 95, 4815-4822.
177. C.A. Schuh, A.C. Lund and T.G. Nieh, Acta Materialia, 2004, 52, 5879-5891.
178. L.J. Peng, J.R. Morris and Y.C. Lo, Physical Review B, 2008, 78, 4.
179. Y.F. Shi and M.L. Falk, Physical Review B, 2006, 73, 10.
180. P. Nash, Phase Diagrams of Binary Alloys, ed. M. Park. 1991, Ohio, USA: ASM International.
181. T.B. Massalski, Binary Alloy Phase Diagrams. second edition ed. 1990, Ohio, USA:
ASM International, Materials Park,.
182. M.S. Ong, Y. Li, D.J. Blackwood and S.C. Ng. The influence of heat treatment on the corrosion behaviour of amorphous melt-spun binary Mg-18 at.% Ni and Mg-21 at.%
Cu alloy. 2001: Elsevier Science Sa.
183. O.P. Pandey, S.N. Ojha and T.R. Anantharaman, Journal of Materials Science Letters, 1992, 11, 1260-1262.
184. Y.C. Lo, J.C. Huang, C.L. Chen, S.P. Ju, H.S. Chou, X.H. Du, M.C. Liu and C.N. Kuo, Journal of Computational and Theoretical Nanoscience, 2008, 5, 1717-1721.
185. J.J. Kim, Y. Choi, S. Suresh and A.S. Argon, Science, 2002, 295, 654-657.
186. C.L. Na Wang, Zhenmin Du, Fuming Wang, and Weijing Zhanga, Computer Coupling of Phase Diagrams and Thermochemistry, 2006, 30, 461.
187. V.A. Khonik, A.T. Kosilov, V.A. Mikhailov and V.V. Sviridov, Acta Materialia, 1998, 46, 3399-3408.
188. V.I. Belyavsky, K. Csach, V.A. Khonik, V.A. Mikhailov and V. Ocelik, Journal of Non-Crystalline Solids, 1998, 241, 105-112.
189. G. Kumar, H.X. Tang and J. Schroers, Nature, 2009, 457, 868-872.
105
190. A. Takeuchi and A. Inoue. Size dependence of soft to hard magnetic transition in (Nd, Pr)-Fe-Al bulk amorphous alloys. 2004: Elsevier Science Sa.
191. K. Wang, T. Fujita, Y.Q. Zeng, N. Nishiyama, A. Inoue and M.W. Chen, Acta Materialia, 2008, 56, 2834-2842.
106
Ts
Table2-1 Bulk metallic glasses and their developed years [20].
107
Table2-2 Summary of yield and ultimate tensile strengths, fatigue-endurance limits at 107 cycles, and fatigue ratios based on the stress amplitudes of Zr-based BMGs and various crystalline alloys from the current study and literature reports. Test configuration refers to the fatigue-test geometry and R is the stress ratio of σmin to σmax [134, 135].
Table 3-1 Parameters for Lennard-Jones potential for inert molecules [143].
108
Table 4-1 Parameters used in the tight-binding potential.
109
Table 4-2 Effective medium potential parameters [162, 164].
E0 (eV) S0 (Å) V0 (eV) η2 (Å) k (Å-1) λ (Å-1) n0 (Å-3) Cu -3.51 1.412964 2.476 3.12170 5.17763 3.60166 0.06140 Ag -2.96 1.592892 2.132 3.12170 5.27211 3.57521 0.03691 Au -3.80 1.5876 2.321 3.16327 5.42895 4.12320 0.04743 Ni -4.44 1.37592 3.673 3.15382 5.20975 3.68103 0.06950 Pd -3.90 1.518804 2.773 3.43537 5.87113 4.07218 0.04642 Pt -5.85 1.53468 4.067 3.42404 5.94293 4.14210 0.05411 Mg -1.487 1.766399 2.22987 2.541137 4.435425 3.292725 0.035544
110
Figures
Fig. 2-1. (a) The fivefold symmetry and an icosahedral arrangement are shown with the brighter spheres (b) A face-centered-cubic arrangement. The same pair will become the hcp arrangement if the top close-packed plane is shifted to take the same type of position as the bottom plane [77].
(a) (b)
111
Fig. 2-2. (a) HREM image taken from an annealed specimen (773 K), together with nanobeam electron-diffraction patterns in (b), (c), and (d). Simulated HREM image is also shown in the inset of (a). (e) HREM image of minor regions in the specimen annealed up to 773 K [89].
112
Fig. 2-3. The portions of a single cluster unit cell for the dense cluster packing model. (a) A two-dimensional representation of a dense cluster-packing structure in a (100) plane of clusters illustrating the features of interpenetrating clusters and efficient atomic packing around each solute. (b) A portion of a cluster unit cell of model in [12109] system representing a Zr-(Al,Ti)-(Cu,Ni)-Be alloy. The α sites are occupied by blue spheres, the β sites are occupied by purple spheres and the γ sites are occupied by orange spheres. Pink Zr solvent spheres form relaxed icosahedra around each α solute [90].
(a) (b)
113
Fig. 2-4. The coordination number distribution of the solute atoms in several representative metallic glasses obtained from ab initio calculations [23].
114
Fig. 2-5. The packing of the solute-centred quasi-equivalent clusters, showing their medium range order. (a) The cluster common-neighbour analysis showing that the local clusters in the metallic glasses exhibit icosahedral type ordering. The typical cluster connections, exhibiting the fivefold symmetry, are detailed for Ni81B19, Ni80P20 and Zr84Pt16 in (b), (c) and (d), respectively [23].
115
Fig. 2-6. (a) The structure of the as-cast bulk metallic glasses after reverse Monte Carlo refinement, (b) clusters of imperfect icosahedral and cubic forms extracted from [94].
(a)
(b)
116
Fig. 2-7. Relationship between tensile strength, Young’s modulus, and Vickers hardness for bulk glassy alloys. The data of crystalline metallic alloys are also shown for comparison [54, 190].
117
Fig. 2-8. (a) Failure surface from a tensile sample which exhibited cup and cone morphology.
The droplets are indicative of localized melting reprinted from [96]. (b) Typical vein pattern on the fracture surface of a ductile Pd30Ni50P20 bulk metallic glass subjected to compression testing [191].
(a) (b)
118
Fig. 2-9. (a) SEM backscattered electron image of in situ composite microstructure. (Inset:
X-ray diffraction pattern for Zr-Ti-Nb in situ composite). (b) Compressive stress strain curve for cylindrical in situ composite specimen [100].
(a)
(b)
119
Fig. 2-10. (a) Stress-strain curve of amorphous monolithic Pt-Cu-Ni-P. The curve was determined under quasistatic compression of a bar shaped sample. The material undergoes about 20% plastic deformation before failure. (b) Optical micrograph of the Pt-Cu-Ni-P BMG which was bent over a mandrel of radius 6.35 mm, which corresponds to a strain of about 14% [101].
(a)
(b)
120
Fig. 2-11. SEM micrograph showing shear bands near a notch in a bend-test specimen coated with tin[131].
Fig. 2-12. Illustration of free-volume for an atom to move into a open space [105].
Open space
121
Fig. 2-13. A two dimensional schematic of a shear transformation zone deformation in the amorphous metal. (a) A two-dimensional schematic of a shear transformation zone in an amorphous metal. A shear displacement occurs to accommodate an applied shear stress τ, with the darker upper atoms moving with respect to the lower atoms. (b) The applied shear stress τ necessary to maintain a given atomic shear displacement, normalized by the maximum value of τ at σn = 0, τ0 [111].
122
Fig. 2-14. Plot of effective temperature χ as a function of time for (a) an STZ solution for δχ0
= 0.01 that localizes and (b) an STZ solution for δχ0 = 0.001 that does not localize. Dashed vertical lines correspond to calculated values for the time the material first reaches the yield stress, τy, and the time the material reaches its maximum stress τmax [118].
123
Fig. 2-15. The local shear strain distribution at different mean sample strains, (a) 4.10%, (b) 12.28%, (c) 20.44%, and (d) 40.81%. The color scheme reflects the change in the rotation angle of the nearest atomic bonds. Only a small section containing the shear band and its immediate vicinity is shown in the sample containing 288000 atoms arranged in a 49.73×4.07×97.60 nm3 rectangular box [110].
Fig. 2-16. The Voronoi volume distributions for (a) Cu and (b) Zr atoms at different mean sample shear strains (%). The lower dotted lines are the Voronoi volumes of the undeformed samples at 300 K and the upper dotted lines are the volumes of the undercooled liquid at Tg. The changes due to the finite size at the sample boundaries can be seen [110].
124
Fig. 2-17. Aged-rejuvenation-glue-liquid (ARGL) model of shear band in BMGs. The shading represents temperature [128].
Fig. 2-18. GSF γ(δ) of a glass as a function of a sharp displacement discontinuity δ. The solid curve illustrates the behavior without any recovery process. The dashed curve shows that, as time increases, recovery occurs and the energy traps get deeper [128].
125
Fig. 2-19. Comparison between glass-transition temperature and calculated shear-band temperature at fracture strength for different bulk metallic glasses [133].
126
Fig. 2-20. A proposed fatigue-crack-initiation mechanism: (a) formation of shear band, (b) formation of shear-off step, and (c) microcrack initiation [42, 43].
Fig. 2-21. The fatigue fracture surface of the Zr50Al10Cu40 specimen was tested at σmax = 1. 2 GPa in vacuum. The whole fatigue fracture surface consisted of four main regions[42, 43]:
the fatigue-crack-initiation, crackpropagation, final-fast-fracture, and apparent-melting fareas.
127
Fig. 2-22. Schematic illustrating how overall alteration of the fatigue and fracture properties in BMGs can be obtained by concurrently controlling [139]: (a) residual stresses to improve both the fatigue threshold, KTH, and the fracture toughness, KIC, and (b) the free volume to improve the fatigue limit but degrade the fracture toughness, KIC.
128
Fig. 3-1. Form of the Lennard-Jones (12-6) potential which describes the interaction of two inert gas atoms [143].
129
Fig. 3-2. The energy of the atom i is determined by the local electron density at the position of i atom and the ρi describes the contribution to the electronic density at the site of the atom i from all atoms j.
130
Fig. 3-3. Periodic boundary conditions. As a particle moves out of the simulation box, an image particle moves in to replace it. In calculating particle interactions within the cutoff range, both real and image neighbors are included [153].
131
Fig. 3-4. The Verlet list on its construction, later, and too late. The potential cutoff range within rc (solid circle), and the list range within rv (dashed circle), are indicated. The list must be reconstructed before particles originally outside the list range (black) have passed the potential cutoff sphere[153].
Fig. 3-5. The cell structure. The potential cutoff range is indicated. In searching for neighbours of an atom, it is only necessary to examine the atom's own cell, and its nearest-neighbour cells (shaded) [153].
L
132
Fig. 3-6. Flow chart of molecular dynamics simulation.
133
Fig. 4-1. A schematic representation of the simulated strain-and-stack process: (a) two of crystalline elemental bilayer structures (b) are elongated to twice its original length and half its original thickness and (c) subsequently halved along the solid line and stacked atop itself.
The inset (d) shows a typical atomic structure at their interfaces [176].
(a)
(b)
(c) (d)
134
Fig. 4-2. Two decomposition methods for parallel MD: (a) is particle decomposition method, and (b) is spatial decomposition method; each forty particles are allotted to 4 processors [155].
135
Fig. 4-3. The schematic drawing of the related HA pairs [159].
Fig. 4-4. Different type of clusters formed in crystals and glasses [158].
136
Fig. 4-5. The scheme of the initial Mg-Cu simulation model. The blue particles represent Mg atoms and red particles represent Cu atoms.
137
Fig. 4-6 (a) Density map V, position P(x) and velocity P(V) distribution functions obtained from Nosé-Hoover dynamics of a harmonic oscillator (dotted line). The solid line is the exact result. (b) Those three properties of a harmonic oscillator obtained from the Nosé-Hoover chain dynamics (dotted line). The solid line is the exact result [166, 167].
138
0 20000 40000 60000
Time step (fs) -4
-2 0 2 4
Applied stress
σ zz
(GPa) (a)
0 100000 200000 300000 400000
Time step (fs)
-4 -2 0 2 4
Induce Stress σzz (GPa) (b)
Fig. 4-7. Fatigue-loading conditions during MD simulations of Zr-Cu metallic glass: (a) the stress-control mode for a tension fatigue experiment at σmax = 2 GPa, and (b) the strain-control mode for a tension-compression fatigue experiment at εmax = 10% (showing the induced stress amplitude).
Fig. 4-8. Illustration of simulation model in cyclic loading fatigue.
139
(a) (b)
(c) (d)
Fig. 5-1. The 2-D sliced plots parallel to the xz plane of the Zr-Ni metallic layers for (a) Ni layer and (b) Zr layer, rrespectively. (c) Schematic illustration of the transformation mechanism via interdiffusion, and (d) the interface between Ni grain (blue particles) and Zr grain (red particles).