Table of Contents Author Guidelines Submit a Manuscript
Advances in Materials Science and Engineering
Volume 2016, Article ID 7365906, 9 pages
http://dx.doi.org/10.1155/2016/7365906
Research Article

Temperature-Dependent Generalized Planar Fault Energy and Twinnability of Mg Microalloyed with Er, Ho, Dy, Tb, and Gd: First-Principles Study

1Department of Physics, Chongqing Three Gorges University, Chongqing 404100, China
2Institute for Structure and Function, Chongqing University, Chongqing 401331, China
3College of Materials Science and Engineering, Chongqing University, Chongqing 400044, China

Received 22 June 2016; Revised 30 September 2016; Accepted 11 October 2016

Academic Editor: Jinghuai Zhang

Copyright © 2016 Lili Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. K. U. Kainer, Magnesium-Alloys and Technologies, Wiley-VCH, Weinheim, Germany, 2003.
  2. A. H. Feng and Z. Y. Ma, “Microstructural evolution of cast Mg-Al-Zn during friction stir processing and subsequent aging,” Acta Materialia, vol. 57, no. 14, pp. 4248–4260, 2009. View at Publisher · View at Google Scholar · View at Scopus
  3. L. Wu, S. R. Agnew, D. W. Brown et al., “Internal stress relaxation and load redistribution during the twinning–detwinning-dominated cyclic deformation of a wrought magnesium alloy, ZK60A,” Acta Materialia, vol. 56, no. 14, pp. 3699–3707, 2008. View at Publisher · View at Google Scholar
  4. H. Van Swygenhoven, P. M. Derlet, and A. G. Frøseth, “Stacking fault energies and slip in nanocrystalline metals,” Nature Materials, vol. 3, no. 6, pp. 399–403, 2004. View at Publisher · View at Google Scholar · View at Scopus
  5. A. G. Frøseth, P. M. Derlet, and H. V. Swygenhoven, “Grown-in twin boundaries affecting deformation mechanisms in nc-metals,” Applied Physics Letters, vol. 85, no. 24, pp. 5863–5865, 2004. View at Publisher · View at Google Scholar · View at Scopus
  6. N. Bernstein and E. Tadmor, “Tight-binding calculations of stacking energies and twinnability in fcc metals,” Physical Review B, vol. 69, no. 9, Article ID 094116, 2004. View at Publisher · View at Google Scholar
  7. E. B. Tadmor and N. Bernstein, “A first-principles measure for the twinnability of FCC metals,” Journal of the Mechanics and Physics of Solids, vol. 52, no. 11, pp. 2507–2519, 2004. View at Publisher · View at Google Scholar · View at Scopus
  8. R. J. Asaro and S. Suresh, “Mechanistic models for the activation volume and rate sensitivity in metals with nanocrystalline grains and nano-scale twins,” Acta Materialia, vol. 53, no. 12, pp. 3369–3382, 2005. View at Publisher · View at Google Scholar · View at Scopus
  9. D. J. Siegel, “Generalized stacking fault energies, ductilities, and twinnabilities of Ni and selected Ni alloys,” Applied Physics Letters, vol. 87, no. 12, Article ID 121901, 2005. View at Publisher · View at Google Scholar
  10. S. Kibey, J. B. Liu, D. D. Johnson, and H. Sehitoglu, “Generalized planar fault energies and twinning in Cu–Al alloys,” Applied Physics Letters, vol. 89, no. 19, Article ID 191911, 2006. View at Publisher · View at Google Scholar
  11. S. Kibey, J. B. Liu, D. D. Johnson, and H. Sehitoglu, “Energy pathways and directionality in deformation twinning,” Applied Physics Letters, vol. 91, no. 18, Article ID 181916, 2007. View at Publisher · View at Google Scholar
  12. A. Datta, U. Ramamurty, S. Ranganathan, and U. V. Waghmare, “Crystal structures of a Mg–Zn–Y alloy: a first-principles study,” Computational Materials Science, vol. 37, no. 1-2, pp. 69–73, 2006. View at Publisher · View at Google Scholar · View at Scopus
  13. S. Sandlöbes, M. Friák, S. Zaefferer et al., “The relation between ductility and stacking fault energies in Mg and Mg-Y alloys,” Acta Materialia, vol. 60, no. 6-7, pp. 3011–3021, 2012. View at Publisher · View at Google Scholar
  14. Z. Pei, L.-F. Zhu, M. Friák et al., “Ab initio and atomistic study of generalized stacking fault energies in Mg and Mg–Y alloys,” New Journal of Physics, vol. 15, no. 4, Article ID 043020, 2013. View at Publisher · View at Google Scholar
  15. T. W. Fan, L. T. Wei, B. Y. Tang et al., “Effect of temperature-induced solute distribution on stacking fault energy in Mg-X(X = Li, Cu, Zn, Al, Y and Zr) solid solution: a first-principles study,” Philosophical Magazine, vol. 94, no. 14, pp. 1578–1587, 2014. View at Google Scholar
  16. W. Li, S. Lu, Q. Hu, S. K. Kwon, B. Johansson, and L. Vitos, “Generalized stacking fault energies of alloys,” Journal of Physics: Condensed Matter, vol. 26, no. 26, Article ID 265005, 2014. View at Publisher · View at Google Scholar
  17. J. Han, X. M. Su, Z.-H. Jin, and Y. T. Zhu, “Basal-plane stacking-fault energies of Mg: a first-principles study of Li- and Al-alloying effects,” Scripta Materialia, vol. 64, no. 8, pp. 693–696, 2011. View at Publisher · View at Google Scholar · View at Scopus
  18. M. Muzyk, Z. Pakiela, and K. J. Kurzydlowski, “Generalized stacking fault energy in magnesium alloys: density functional theory calculations,” Scripta Materialia, vol. 66, no. 5, pp. 219–222, 2012. View at Publisher · View at Google Scholar · View at Scopus
  19. P. Kwasniak, M. Muzyk, H. Garbacz, and K. J. Kurzydlowski, “Influence of C, H, N, and O interstitial atoms on deformation mechanism in titanium—first principles calculations of generalized stacking fault energy,” Materials Letters, vol. 94, pp. 92–94, 2013. View at Publisher · View at Google Scholar · View at Scopus
  20. S. L. Shang, W. Y. Wang, Y. Wang et al., “Temperature-dependent ideal strength and stacking fault energy of fcc Ni: a first-principles study of shear deformation,” Journal of Physics: Condensed Matter, vol. 24, no. 15, Article ID 155402, 2012. View at Publisher · View at Google Scholar
  21. S. L. Shang, W. Y. Wang, B. C. Zhou et al., “Generalized stacking fault energy, ideal strength and twinnability of dilute Mg-based alloys: a first-principles study of shear deformation,” Acta Materialia, vol. 67, pp. 168–180, 2014. View at Publisher · View at Google Scholar
  22. S. Iikubo, K. Matsuda, and H. Ohtani, “Phase stability of long-period stacking structures in Mg-Y-Zn: a first-principles study,” Physical Review B, vol. 86, no. 5, Article ID 054105, 2012. View at Publisher · View at Google Scholar
  23. P. A. T. Olsson, “First principles investigation of the finite temperature dependence of the elastic constants of zirconium, magnesium and gold,” Computational Materials Science, vol. 99, pp. 361–372, 2015. View at Publisher · View at Google Scholar
  24. M. M. Avedesian and H. Baker, “Magnesium and magnesium alloys,” in ASM Speciality Handbook, ASM International, Metals Park, Ohio, USA, 1999. View at Google Scholar
  25. N. Birbilis, M. K. Cavanaugh, A. D. Sudholz, S. M. Zhu, M. A. Easton, and M. A. Gibson, “A combined neural network and mechanistic approach for the prediction of corrosion rate and yield strength of magnesium-rare earth alloys,” Corrosion Science, vol. 53, no. 1, pp. 168–176, 2011. View at Publisher · View at Google Scholar · View at Scopus
  26. L. Gao, R. S. Chen, and E. H. Han, “Effects of rare-earth elements Gd and Y on the solid solution strengthening of Mg alloys,” Journal of Alloys and Compounds, vol. 481, no. 1-2, pp. 379–384, 2009. View at Publisher · View at Google Scholar
  27. S. Sandlöbes, S. Zaefferer, I. Schestakow, S. Yi, and R. Gonzalez-Martinez, “On the role of non-basal deformation mechanisms for the ductility of Mg and Mg-Y alloys,” Acta Materialia, vol. 59, no. 2, pp. 429–439, 2011. View at Publisher · View at Google Scholar · View at Scopus
  28. K. Hantzsche, J. Bohlen, J. Wendt, K. U. Kainer, S. B. Yi, and D. Letzig, “Effect of rare earth additions on microstructure and texture development of magnesium alloy sheets,” Scripta Materialia, vol. 63, no. 7, pp. 725–730, 2010. View at Publisher · View at Google Scholar · View at Scopus
  29. T. L. Chia, M. A. Easton, S. M. Zhu, M. A. Gibson, N. Birbilis, and J. F. Nie, “The effect of alloy composition on the microstructure and tensile properties of binary Mg-rare earth alloys,” Intermetallics, vol. 17, no. 7, pp. 481–490, 2009. View at Publisher · View at Google Scholar · View at Scopus
  30. Q. Zhang, T.-W. Fan, L. Fu, B.-Y. Tang, L.-M. Peng, and W.-J. Ding, “Ab-initio study of the effect of rare-earth elements on the stacking faults of Mg solid solutions,” Intermetallics, vol. 29, pp. 21–26, 2012. View at Publisher · View at Google Scholar
  31. J. Zhang, Y. C. Dou, G. B. Liu, and Z. X. Guo, “First-principles study of stacking fault energies in Mg-based binary alloys,” Computational Materials Science, vol. 79, pp. 564–569, 2013. View at Publisher · View at Google Scholar · View at Scopus
  32. R. Pynn and G. L. Squires, “Measurements of the normal-mode frequencies of magnesium,” Proceedings of the Royal Society of London. Series A, vol. 326, no. 1566, p. 347, 1972. View at Publisher · View at Google Scholar
  33. G. Kresse and J. Hafner, “Ab initio molecular dynamics for open-shell transition metals,” Physical Review B, vol. 48, no. 17, p. 13115, 1993. View at Publisher · View at Google Scholar
  34. G. Kresse and J. Furthmller, “Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set,” Computational Materials Science, vol. 6, no. 1, pp. 15–50, 1996. View at Publisher · View at Google Scholar
  35. G. Kresse and J. Furthmüller, “Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set,” Physical Review B, vol. 54, no. 16, pp. 11169–11186, 1996. View at Publisher · View at Google Scholar
  36. P. E. Blöchl, “Projector augmented-wave method,” Physical Review B, vol. 50, no. 24, pp. 17953–17979, 1994. View at Google Scholar
  37. G. Kresse and D. Joubert, “From ultrasoft pseudopotentials to the projector augmented-wave method,” Physical Review B, vol. 59, no. 3, pp. 1758–1775, 1999. View at Publisher · View at Google Scholar · View at Scopus
  38. J. P. Perdew, K. Burke, and M. Ernzerhof, “Generalized gradient approximation made simple,” Physical Review Letters, vol. 77, no. 18, pp. 3865–3868, 1996. View at Publisher · View at Google Scholar · View at Scopus
  39. J. P. Perdew, K. Burke, and M. Ernzerhof, “Generalized gradient approximation made simple [Phys. Rev. Lett. 77, 3865 (1996)],” Physical Review Letters, vol. 78, no. 7, p. 1396, 1996. View at Publisher · View at Google Scholar
  40. H. J. Monkhorst and J. D. Pack, “Special points for Brillouin-zone integrations,” Physical Review. B. Solid State, vol. 13, no. 12, pp. 5188–5192, 1976. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  41. N. W. Ashcroft and N. D. Mermin, Solid State Physics, Holt, Rinehart and Winston, New York, NY, USA, 1976.
  42. Y. Qi and R. K. Mishra, “Ab initio study of the effect of solute atoms on the stacking fault energy in aluminum,” Physical Review B, vol. 75, no. 22, Article ID 224105, 2007. View at Publisher · View at Google Scholar
  43. P. E. Blöchl, O. Jepsen, and O. K. Andersen, “Improved tetrahedron method for Brillouin-zone integrations,” Physical Review B, vol. 49, pp. 16223–16233, 1994. View at Google Scholar
  44. G. Kresse, M. Marsman, and J. Furthmüller, “VASP the guide,” http://www.vasp.at/
  45. A. Togo, L. Chaput, I. Tanaka, and G. Hug, “First-principles phonon calculations of thermal expansion in Ti3SiC2, Ti3AlC2, and Ti3GeC2,” Physical Review B, vol. 81, no. 17, Article ID 174301, 6 pages, 2010. View at Publisher · View at Google Scholar
  46. A. Togo, F. Oba, and I. Tanaka, “First-principles calculations of the ferroelastic transition between rutile-type and CaCl2-type SiO2 at high pressures,” Physical Review B, vol. 78, no. 13, Article ID 134106, 2008. View at Publisher · View at Google Scholar
  47. A. Togo, Phonopy, http://phonopy.sourceforge.net/i
  48. P. Vinet, J. H. Rose, J. Ferrante, and J. R. Smith, “Universal features of the equation of state of solids,” Journal of Physics: Condensed Matter, vol. 1, no. 11, pp. 1941–1963, 1989. View at Publisher · View at Google Scholar · View at Scopus
  49. J. R. Rice, “Dislocation nucleation from a crack tip: an analysis based on the Peierls concept,” Journal of the Mechanics and Physics of Solids, vol. 40, no. 2, pp. 239–271, 1992. View at Publisher · View at Google Scholar
  50. N. Chetty and M. Weinert, “Stacking faults in magnesium,” Physical Review B, vol. 56, no. 17, pp. 10844–10851, 1997. View at Publisher · View at Google Scholar · View at Scopus
  51. L. Wen, P. Chen, Z.-F. Tong, B.-Y. Tang, L.-M. Peng, and W.-J. Ding, “A systematic investigation of stacking faults in magnesium via first-principles calculation,” The European Physical Journal B, vol. 72, no. 3, article 397, 2009. View at Publisher · View at Google Scholar
  52. Q. Zhang, L. Fu, and T. W. Fan, “Abinitio study of the effect of solute atoms Zn and Y on stacking faults in Mg solid solution,” Physica B: Condensed Matter, vol. 416, pp. 39–44, 2013. View at Publisher · View at Google Scholar
  53. A. Datta, U. V. Waghmare, and U. Ramamurty, “Structure and stacking faults in layered Mg–Zn–Y alloys: a first-principles study,” Acta Materialia, vol. 56, no. 11, pp. 2531–2539, 2008. View at Publisher · View at Google Scholar · View at Scopus
  54. J. A. Yasi, T. Nogaret, D. R. Trinkle, Y. Qi, L. G. Hector Jr., and W. A. Curtin, “Basal and prism dislocation cores in magnesium: comparison of first-principles and embedded-atom-potential methods predictions,” Modelling and Simulation in Materials Science and Engineering, vol. 17, no. 5, Article ID 055012, 2009. View at Publisher · View at Google Scholar
  55. T. W. Fan, B. Y. Tang, L. M. Peng, and W. Ding, “First-principles study of long-period stacking ordered-like multi-stacking fault structures in pure magnesium,” Scripta Materialia, vol. 64, no. 10, pp. 942–945, 2011. View at Google Scholar
  56. Y. Wang, L.-Q. Chen, Z.-K. Liu, and S. N. Mathaudhu, “First-principles calculations of twin-boundary and stacking-fault energies in magnesium,” Scripta Materialia, vol. 62, no. 9, pp. 646–649, 2010. View at Publisher · View at Google Scholar · View at Scopus
  57. A. E. Smith, “Surface, interface and stacking fault energies of magnesium from first principles calculations,” Surface Science, vol. 601, no. 24, pp. 5762–5765, 2007. View at Publisher · View at Google Scholar
  58. A. Couret and D. Caillard, “An in situ study of prismatic glide in magnesium-II. Microscopic activation parameters,” Acta Metallurgica, vol. 33, no. 8, pp. 1455–1462, 1985. View at Publisher · View at Google Scholar · View at Scopus
  59. R. L. Fleischer, “High-temperature, high-strength materials—an overview,” JOM, vol. 37, no. 12, pp. 16–20, 1985. View at Publisher · View at Google Scholar
  60. R. L. Fleischer, “Stacking fault energies of HCP metals,” Scripta Metallurgica, vol. 20, no. 2, pp. 223–224, 1986. View at Publisher · View at Google Scholar · View at Scopus
  61. Y. T. Zhu, X. Z. Liao, and X. L. Wu, “Deformation twinning in nanocrystalline materials,” Progress in Materials Science, vol. 57, no. 1, pp. 1–62, 2012. View at Publisher · View at Google Scholar