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Application of the Peierls–Nabarro Model to Symmetric Tilt Low-Angle Grain Boundary with Full <a> Dislocation in Pure Magnesium

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Acta Metallurgica Sinica (English Letters) Aims and scope

Abstract

Three types of symmetric (11\(\bar{2}\)0) tilt low-angle grain boundaries (LAGBs) with array of basal, prismatic, and pyramidal edge full <a> dislocations in pure Mg have been studied by using the improved Peierls–Nabarro model in combination with the generalized stacking fault energy curve. The results show that with decreasing distance between the dislocations in all the three types of tilt LAGBs, the stress and strain fields are gradually suppressed. The reduction extent of the stress and strain fields decreases from the prismatic to basal to pyramidal dislocations. The variation of dislocation line energy (DLE) for all tilt LAGBs is divided into three stages: DLE changes slightly and linearly when the distance is larger than 300 Å, ~10%; DLE declines exponentially and quickly when the distance goes from 300 to 100 Å, ~70%; and finally, the descent speed lowers when the distance is smaller than 100 Å and the dislocation core energy is nearly half of the DLE. The grain boundary energy (GBE) decreases when the tilt angle of LAGB increases from 1° to 2° for all cases. The tilt LAGB consists of pyramidal dislocations always has the largest GBE, while that with array of prismatic dislocations has the smallest one in the whole range. The Peierls stress of dislocation in tilt LAGB is nearly unchanged, the same as that of single dislocation. This work is useful for further study of dissociated dislocation, solute segregation, precipitate nucleation in tilt LAGB and its interaction with single dislocations.

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References

  1. T.M. Pollock, Science 328, 986 (2010)

    Article  Google Scholar 

  2. X.H. Chen, L.Z. Liu, J. Liu, F.S. Pan, Acta Metall. Sin. (Engl. Lett.) 28, 492 (2015)

  3. C. Potzies, K.U. Kainer, Adv. Eng. Mater. 6, 281 (2004)

    Article  Google Scholar 

  4. R. Gehrmann, M.M. Frommert, G. Gottstein, Mater. Sci. Eng., A 395, 338 (2005)

    Article  Google Scholar 

  5. C.H. Cáceres, A. Blake, Phys. Stat. Sol. (A) 194, 147 (2002)

  6. V.M. Segal, Mater. Sci. Eng., A 271, 322 (1999)

    Article  Google Scholar 

  7. Y. Wang, M. Chen, F. Zhou, E. Ma, Nature 419, 912 (2002)

    Article  Google Scholar 

  8. Y.T. Zhu, X. Liao, Nat. Mater. 3, 351 (2004)

    Article  Google Scholar 

  9. L. Wang, E. Mostaed, X. Cao, G. Huang, A. Fabrizi, F. Bonollo, C. Chi, M. Vedani, Mater. Des. 89, 1 (2016)

    Google Scholar 

  10. J. Zhang, Z. Kang, L. Zhou, Mater. Sci. Eng., A 647, 184 (2015)

    Article  Google Scholar 

  11. Y. Yuan, A. Ma, X. Gou, J. Jiang, F. Lu, D. Song, Y. Zhu, Mater. Sci. Eng., A 630, 45 (2015)

    Article  Google Scholar 

  12. H.G. Svoboda, F. Vago, Proc. Mater. Sci. 9, 590 (2015)

    Article  Google Scholar 

  13. E. Mostaed, A. Fabrizi, D. Dellasega, F. Bonollo, M. Vedani, J. Alloys Compd. 638, 267 (2015)

    Article  Google Scholar 

  14. P. Minárik, R. Král, J. Pešička, F. Chmelík, J. Mater. Res. Technol. 4, 75 (2015)

    Article  Google Scholar 

  15. M. Gzyl, A. Rosochowski, S. Boczkal, L. Olejnik, Mater. Sci. Eng., A 638, 20 (2015)

    Article  Google Scholar 

  16. J. Zhang, C. Xin, K. Nie, W. Cheng, H. Wang, C. Xu, Mater. Sci. Eng., A 611, 108 (2014)

    Article  Google Scholar 

  17. P.J. Hsieh, Y.P. Hung, J.C. Huang, Scripta Mater. 49, 173 (2003)

    Article  Google Scholar 

  18. G. Garces, M.A. Muñoz-Morris, D.G. Morris, P. Perez, P. Adeva, Mater. Sci. Eng., A 614, 96 (2014)

    Article  Google Scholar 

  19. R. Jahadi, M. Sedighi, H. Jahed, Mater. Sci. Eng., A 593, 178 (2014)

    Article  Google Scholar 

  20. X. Sauvage, F. Wetscher, P. Pareige, Acta Mater. 53, 2127 (2005)

    Article  Google Scholar 

  21. F. Li, W. Shi, N. Bian, H.B. Wu, Acta Metall. Sin. (Engl. Lett.) 28, 649 (2015)

  22. L. Dupuy, J.J. Blandin, Acta Mater. 50, 3253 (2002)

    Article  Google Scholar 

  23. Z. Horita, T. Fujinami, M. Nemoto, T.G. Langdon, J. Mater. Process. Technol. 117, 288 (2001)

    Article  Google Scholar 

  24. A. Hassani, M. Zabihi, Mater. Des. 39, 140 (2012)

    Article  Google Scholar 

  25. R.Z. Valiev, E.V. Kozlov, Y.F. Ivanov, J. Lian, A.A. Nazarov, B. Baudelet, Acta Metal. Mater. 42, 2467 (1994)

    Article  Google Scholar 

  26. Y.M. Wang, E. Ma, Acta Mater. 52, 1699 (2004)

    Article  Google Scholar 

  27. K.V. Ivanov, E.V. Naydenkin, Mater. Sci. Eng., A 608, 123 (2014)

    Article  Google Scholar 

  28. W.J. Kim, S.I. Hong, Y.S. Kim, S.H. Min, H.T. Jeong, J.D. Lee, Acta Mater. 51, 3293 (2003)

    Article  Google Scholar 

  29. M. Mabuchi, H. Iwasaki, K. Yanase, K. Higashi, Scripta Mater. 36, 681 (1997)

    Article  Google Scholar 

  30. T.C. Chang, J.Y. Wang, C.L. Chu, S. Lee, Mater. Lett. 60, 3272 (2006)

    Article  Google Scholar 

  31. A. Yamashita, Z. Horita, T.G. Langdon, Mater. Sci. Eng., A 300, 142 (2001)

    Article  Google Scholar 

  32. R.Z. Valiev, I.V. Alexandrov, Y.T. Zhu, T.C. Lowe, J. Mater. Res. 17, 5 (2002)

    Article  Google Scholar 

  33. R. Valiev, Nat. Mater. 3, 511 (2004)

    Article  Google Scholar 

  34. Y.H. Zhao, J.F. Bingert, Y.T. Zhu, X.Z. Liao, R.Z. Valiev, Z. Horita, T.G. Langdon, Y.Z. Zhou, E.J. Lavernia, Appl. Phys. Lett. 92, 081903 (2008)

    Article  Google Scholar 

  35. S. Biswas, S. Singh Dhinwal, S. Suwas, Acta Mater. 58, 3247 (2010)

    Article  Google Scholar 

  36. R.Z. Valiev, R.K. Islamgaliev, I.V. Alexandrov, Prog. Mater Sci. 45, 103 (2000)

    Article  Google Scholar 

  37. O.S. Sitdikov, R.O. Kaybyshev, I.M. Safarov, I.A. Mazurina, Phys. Met. Metallogr. 92, 270 (2001)

    Google Scholar 

  38. P. Molnár, A. Jäger, P. Lejček, J. Mater. Sci. 47, 3265 (2012)

    Article  Google Scholar 

  39. A.P. Sutton, R.W. Balluffi, Interfaces in Crystalline Materials (Oxford University Press, New York, 1995)

    Google Scholar 

  40. M. Peach, J.S. Koehler, Phys. Rev. 80, 436 (1950)

    Article  Google Scholar 

  41. J.P. Hirth, J. Lothe, Theory of Dislocations, 2nd edn. (Wiley, New York, 1982)

    Google Scholar 

  42. I.A. Ovid’ko, A.G. Sheinerman, R.Z. Valiev, Scripta Mater. 76, 45 (2014)

  43. J.D. Eshelby, W.T. Read, W. Shockley, Acta Metall. 1, 251 (1953)

    Article  Google Scholar 

  44. J.E. Lennard-Jones, Proc. Phys. Soc. 43, 461 (1931)

    Article  Google Scholar 

  45. D.Y. Sun, M.I. Mendelev, C.A. Becker, K. Kudin, T. Haxhimali, M. Asta, J.J. Hoyt, A. Karma, D.J. Srolovitz, Phys. Rev. B 73, 024116 (2006)

    Article  Google Scholar 

  46. X.Y. Liu, J.B. Adams, F. Ercolessi, J.A. Moriarty, Model. Simul. Mater. Sci. Eng. 4, 293 (1996)

    Article  Google Scholar 

  47. V. Vitek, M. Igarashi, Philos. Mag. A 63, 1059 (1991)

    Article  Google Scholar 

  48. J.A. Yasi, T. Nogaret, D.R. Trinkle, Y. Qi, L.G. Hector Jr., W.A. Curtin, Model. Simul. Mater. Sci. Eng. 17, 055012 (2009)

    Article  Google Scholar 

  49. Y. Tang, J.A. El-Awady, Acta Mater. 71, 319 (2014)

    Article  Google Scholar 

  50. T.W. Fan, L.G. Luo, L. Ma, B.Y. Tang, L.M. Peng, W.J. Ding, Mater. Sci. Eng., A 582, 299 (2013)

    Article  Google Scholar 

  51. B. Joós, Q. Ren, M.S. Duesbery, Phys. Rev. B 50, 5890 (1994)

    Article  Google Scholar 

  52. J. Hartford, B. von Sydow, G. Wahnström, B.I. Lundqvist, Phys. Rev. B 58, 2487 (1998)

    Article  Google Scholar 

  53. G. Schoeck, Acta Mater. 49, 1179 (2001)

    Article  Google Scholar 

  54. P. Carrez, D. Ferré, P. Cordier, Nature 446, 68 (2007)

    Article  Google Scholar 

  55. T.W. Fan, Q. Zhang, L. Ma, P.Y. Tang, B.Y. Tang, L.M. Peng, W.J. Ding, Eur. J. Mech. A-Solids 45, 1 (2014)

    Article  Google Scholar 

  56. S. Kibey, J.B. Liu, D.D. Johnson, H. Sehitoglu, Acta Mater. 55, 6843 (2007)

    Article  Google Scholar 

  57. S. Kibey, J.B. Liu, M.J. Curtis, D.D. Johnson, H. Sehitoglu, Acta Mater. 54, 2991 (2006)

    Article  Google Scholar 

  58. G. Lu, N. Kioussis, V.V. Bulatov, E. Kaxiras, Phil. Mag. Lett. 80, 675 (2000)

    Article  Google Scholar 

  59. G. Schoeck, Philos. Mag. A 69, 1085 (1994)

    Article  Google Scholar 

  60. G. Schoeck, M. Krystian, Philos. Mag. 85, 949 (2005)

    Article  Google Scholar 

  61. G.P.M. Leyson, W.A. Curtin, Philos. Mag. 93, 2428 (2013)

    Article  Google Scholar 

  62. V. Vitek, Philos. Mag. 18, 773 (1968)

    Article  Google Scholar 

  63. S. Dai, Y. Xiang, D.J. Srolovitz, Acta Mater. 61, 1327 (2013)

    Article  Google Scholar 

  64. S. Dai, Y. Xiang, D.J. Srolovitz, Acta Mater. 69, 162 (2014)

    Article  Google Scholar 

  65. W.W. Hu, Z.Q. Yang, H.Q. Ye, Scripta Mater. 117, 77 (2016)

    Article  Google Scholar 

  66. G. Kresse, J. Hafner, Phys. Rev. B 47, 558 (1993)

    Article  Google Scholar 

  67. G. Kresse, J. Furthmüller, Comp. Mater. Sci. 6, 15 (1996)

    Article  Google Scholar 

  68. G. Kresse, J. Furthmüller, Phys. Rev. B 54, 11169 (1996)

    Article  Google Scholar 

  69. P.E. Blöchl, Phys. Rev. B 50, 17953 (1994)

    Article  Google Scholar 

  70. J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996)

    Article  Google Scholar 

  71. H.J. Monkhorst, J.D. Pack, Phys. Rev. B 13, 5188 (1976)

    Article  Google Scholar 

  72. J.A. Yan, C.Y. Wang, S.Y. Wang, Phys. Rev. B 70, 174105 (2004)

    Article  Google Scholar 

  73. B. Joós, M. Duesbery, Phys. Rev. Lett. 78, 266 (1997)

    Article  Google Scholar 

  74. V.V. Bulatov, E. Kaxiras, Phys. Rev. Lett. 78, 4221 (1997)

    Article  Google Scholar 

  75. Z. Pei, L.F. Zhu, M. Friák, S. Sandlöbes, J.V. Pezold, H.W. Sheng, C.P. Race, S. Zaefferer, B. Svendsen, D. Raabe, J. Neugebauer, N. J. Phys. 15, 043020 (2013)

    Article  Google Scholar 

  76. M. Muzyk, Z. Pakiela, K.J. Kurzydlowski, Scripta Mater. 66, 219 (2012)

    Article  Google Scholar 

  77. I. Shin, E.A. Carter, Model. Simul. Mater. Sci. Eng. 20, 015006 (2012)

    Article  Google Scholar 

  78. T. Nogaret, W.A. Curtin, J.A. Yasi, L.G. Hector Jr., D.R. Trinkle, Acta Mater. 58, 4332 (2010)

    Article  Google Scholar 

  79. X. Wu, R. Wang, S. Wang, Appl. Surf. Sci. 256, 3409 (2010)

    Article  Google Scholar 

  80. Q. Zu, Y.F. Guo, X.Z. Tang, Acta Metall. Sin. (Engl. Lett.) 28, 876 (2015)

  81. J. Han, X.M. Su, Z.H. Jin, Y.T. Zhu, Scripta Mater. 64, 693 (2011)

    Article  Google Scholar 

  82. T. Uesugi, M. Kohyama, M. Kohzu, K. Higashi, Mater. Sci. Forum 419–422, 225 (2003)

    Article  Google Scholar 

  83. J.C.M. Li, Acta Metall. 8, 296 (1960)

    Article  Google Scholar 

  84. J.C.M. Li, Acta Metall. 8, 563 (1960)

    Article  Google Scholar 

  85. J.A. Yasi, L.G. Hector Jr., D.R. Trinkle, Acta Mater. 58, 5704 (2010)

    Article  Google Scholar 

  86. Z.R. Liu, D.Y. Li, Acta Mater. 89, 225 (2015)

    Article  Google Scholar 

  87. S.H. Wang, C.H. Liu, J.H. Chen, X.L. Li, D.H. Zhu, G.H. Tao, Mater. Sci. Eng., A 585, 233 (2013)

    Article  Google Scholar 

  88. J.A. Yasi, L.G. Hector Jr., D.R. Trinkle, Acta Mater. 60, 2350 (2012)

    Article  Google Scholar 

  89. J.A. Yasi, L.G. Hector Jr., D.R. Trinkle, Acta Mater. 59, 5652 (2011)

    Article  Google Scholar 

  90. W.T. Read, W. Shockley, Phys. Rev. 78, 275 (1950)

    Article  Google Scholar 

  91. J.P. Hirth, Metall. Trans. 3, 3047 (1972)

    Article  Google Scholar 

  92. T.J. Rupert, D.S. Gianola, Y. Gan, K.J. Hemker, Science 326, 1686 (2009)

    Article  Google Scholar 

  93. A.T. Lim, Mechanical and Aerospace Engineering (Princeton University, Candidacy, 2012)

    Google Scholar 

  94. T. Vreeland Jr., Acta Metall. 7, 240 (1959)

    Article  Google Scholar 

  95. A. Akhtar, E. Teghtsoonian, Acta Metall. 17, 1339 (1969)

    Article  Google Scholar 

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Acknowledgments

This work is supported by the National Natural Science Foundation of China (Nos. 11427806, 51471067, 51371081, 51171063, 51501059 and 51501060), the National Basic Research (973) Program of China (No. 2009CB623704), the Chinese Postdoctoral Science Foundation (No. 2015M582324), and the Hunan Provincial Natural Science Foundation (No. 14JJ4052) and the Science and Technology Project for Good Postdoctoral Education of China (No. 2015RS4020) .

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Authors and Affiliations

  1. Center for High-Resolution Electron Microscopy, College of Materials Science and Engineering, Hunan University, Changsha, 410082, China

    Tou-Wen Fan, Xiu-Bo Yang, Jiang-Hua Chen, Ling-Hong Liu, Ding-Wan Yuan, Yong Zhang & Cui-Lan Wu

  2. Department of Applied Physics, School of Physics and Electronics, Hunan University, Changsha, 410082, China

    Xiu-Bo Yang

  3. Hunan Province Key Laboratory for Spray Deposition Technology and Application, Hunan University, Changsha, 410082, China

    Jiang-Hua Chen

  4. College of Science, Central South University of Forestry and Technology, Changsha, 410004, China

    Ling-Hong Liu

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  1. Tou-Wen Fan
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Fan, TW., Yang, XB., Chen, JH. et al. Application of the Peierls–Nabarro Model to Symmetric Tilt Low-Angle Grain Boundary with Full <a> Dislocation in Pure Magnesium. Acta Metall. Sin. (Engl. Lett.) 29, 1053–1063 (2016). https://doi.org/10.1007/s40195-016-0480-4

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