First-Principles Investigation of the Effect of Solutes on the Ideal Shear Resistance and Electronic Properties of Magnesium

  • P. Garg
  • I. Adlakha
  • K. N. SolankiEmail author
Conference paper
Part of the The Minerals, Metals & Materials Series book series (MMMS)


Solute addition is an effective way to enhance mechanical properties, especially in magnesium based alloys due to the limited number of slip systems available for deformation at the room temperature. Hence, the effects of various alloying elements on ideal shear resistance (ISR) across different slip systems of Mg were investigated using first-principles calculations. The addition of a Ce, Y, or Zr solute atom was found to decrease ISR, whereas the substitution of a Sn, Li, Al, or Zn atom increased the ISR of Mg. The most active slip system in Mg changed from the basal partial (0001)\( \left[ {10\bar{1}0} \right] \) to prismatic \( (10\bar{1}0)[11\bar{2}0] \) upon substitution of a Ce, Y, or Zr solute atom, whereas the addition of Sn, Li, Al, or Zn solute atom had negligible effect on the plastic anisotropy. Furthermore, the electronic density of states and valence charge transfer provides a quantum insight into the underlying factors influencing the observed softening/strengthening behavior. For instance, the electronic density of states calculation shows that the contribution from d states of Ce, Y, and Zr solute atoms decreases the electronic structure stability of their respective solid solution, thereby enhancing slip activities. Theoretical analyses were also performed, and a shearability parameter was introduced to understand the implications of the observed variation in ideal shear resistance on the macroscopic behavior of Mg alloys.


Magnesium Ideal shear resistance Electronic properties First principles 



The authors are grateful for the financial support for this work from the National Science Foundation, the Civil, Mechanical and Manufacturing Innovation (CMMI): Materials Engineering and Processing program via award number 1463656. We also appreciate Fulton High Performance Computing at Arizona State University for enabling us to conduct our simulations.


  1. 1.
    H. Friedrich, S. Schumann, Research for a “new age of magnesium” in the automotive industry, J. Mater. Process. Technol. 117 (2001) 276–281. Scholar
  2. 2.
    A.A. Luo, Recent magnesium alloy development for automotive powertrain applications, in: Mater. Sci. Forum, Trans Tech Publ, 2003: pp. 57–66.CrossRefGoogle Scholar
  3. 3.
    M.E. Kassner, T.A. Hayes, Creep cavitation in metals, Int. J. Plast. 19 (2003) 1715–1748. Scholar
  4. 4.
    S.N. Mathaudhu, E.A. Nyberg, Magnesium Alloys in Us Military Applications: Past, Current and Future Solutions, Pacific Northwest National Laboratory (PNNL), Richland, WA (US), 2010. (accessed November 11, 2015).
  5. 5.
    T.M. Pollock, Weight loss with magnesium alloys, Science. 328 (2010) 986–987.CrossRefGoogle Scholar
  6. 6.
    P. Garg, I. Adlakha, K.N. Solanki, Effect of solutes on ideal shear resistance and electronic properties of magnesium: A first-principles study, Acta Mater. 153 (2018) 327–335. Scholar
  7. 7.
    S. Farzadfar, E. Martin, M. Sanjari, E. Essadiqi, S. Yue, Texture weakening and static recrystallization in rolled Mg–2.9 Y and Mg–2.9 Zn solid solution alloys, J. Mater. Sci. 47 (2012) 5488–5500.CrossRefGoogle Scholar
  8. 8.
    C. Kale, M. Rajagopalan, S. Turnage, B. Hornbuckle, K. Darling, S.N. Mathaudhu, K.N. Solanki, On the roles of stress-triaxiality and strain-rate on the deformation behavior of AZ31 magnesium alloys, Mater. Res. Lett. 6 (2018) 152–158. Scholar
  9. 9.
    P. Garg, M.A. Bhatia, S.N. Mathaudhu, K.N. Solanki, Solute Effect on Strength and Formability of Mg: A First-Principle Study, in: K.N. Solanki, D. Orlov, A. Singh, N.R. Neelameggham (Eds.), Magnesium Technology 2017, Springer International Publishing, Cham, 2017: pp. 483–489. Scholar
  10. 10.
    C. Kale, M. Rajagopalan, S. Turnage, B. Hornbuckle, K. Darling, S.N. Mathaudhu, K.N. Solanki, Dynamic Behavior of an AZ31 Alloy Under Varying Strain Rates and Stress Triaxialities, in: K.N. Solanki, D. Orlov, A. Singh, N.R. Neelameggham (Eds.), Magnesium Technology 2017, Springer International Publishing, 2017: pp. 247–251.Google Scholar
  11. 11.
    N. Stanford, M.R. Barnett, The origin of “rare earth” texture development in extruded Mg-based alloys and its effect on tensile ductility, Mater. Sci. Eng. A. 496 (2008) 399–408. Scholar
  12. 12.
    M.A. Bhatia, S.N. Mathaudhu, K.N. Solanki, Atomic-scale investigation of creep behavior in nanocrystalline Mg and Mg–Y alloys, Acta Mater. 99 (2015) 382–391. Scholar
  13. 13.
    S. Sandlöbes, M. Friák, S. Zaefferer, A. Dick, S. Yi, D. Letzig, Z. Pei, L.-F. Zhu, J. Neugebauer, D. Raabe, The relation between ductility and stacking fault energies in Mg and Mg–Y alloys, Acta Mater. 60 (2012) 3011–3021. Scholar
  14. 14.
    K.-H. Kim, J.B. Jeon, N.J. Kim, B.-J. Lee, Role of yttrium in activation of <c + a> slip in magnesium: An atomistic approach, Scr. Mater. 108 (2015) 104–108. Scholar
  15. 15.
    N. Stanford, D. Atwell, A. Beer, C. Davies, M.R. Barnett, Effect of microalloying with rare-earth elements on the texture of extruded magnesium-based alloys, Scr. Mater. 59 (2008) 772–775. Scholar
  16. 16.
    J.A. Del Valle, M.T. Pérez-Prado, O.A. Ruano, Deformation mechanisms responsible for the high ductility in a Mg AZ31 alloy analyzed by electron backscattered diffraction, Metall. Mater. Trans. A. 36 (2005) 1427–1438.Google Scholar
  17. 17.
    L. Zhou, K. Su, Y. Wang, Q. Zeng, Y. Li, First-principles study of the properties of Li, Al and Cd doped Mg alloys, J. Alloys Compd. 596 (2014) 63–68. Scholar
  18. 18.
    J. Han, X.M. Su, Z.-H. Jin, Y.T. Zhu, Basal-plane stacking-fault energies of Mg: A first-principles study of Li-and Al-alloying effects, Scr. Mater. 64 (2011) 693–696.CrossRefGoogle Scholar
  19. 19.
    A. Akhtar, E. Teghtsoonian, Solid solution strengthening of magnesium single crystals—ii the effect of solute on the ease of prismatic slip, Acta Metall. 17 (1969) 1351–1356. Scholar
  20. 20.
    A.H. Blake, C.H. Cáceres, Solid-solution hardening and softening in Mg–Zn alloys, Mater. Sci. Eng. A. 483–484 (2008) 161–163. Scholar
  21. 21.
    I. Adlakha, M.A. Bhatia, M.A. Tschopp, K.N. Solanki, Atomic scale investigation of grain boundary structure role on intergranular deformation in aluminium, Philos. Mag. 94 (2014) 3445–3466. Scholar
  22. 22.
    J.A. Yasi, T. Nogaret, D.R. Trinkle, Y. Qi, L.G. Hector Jr, W.A. Curtin, Basal and prism dislocation cores in magnesium: comparison of first-principles and embedded-atom-potential methods predictions, Model. Simul. Mater. Sci. Eng. 17 (2009) 055012.CrossRefGoogle Scholar
  23. 23.
    S. Ogata, J. Li, S. Yip, Ideal pure shear strength of aluminum and copper, Science. 298 (2002) 807–811.CrossRefGoogle Scholar
  24. 24.
    S.L. Shang, W.Y. Wang, B.C. Zhou, Y. Wang, K.A. Darling, L.J. Kecskes, S.N. Mathaudhu, Z.K. Liu, Generalized stacking fault energy, ideal strength and twinnability of dilute Mg-based alloys: A first-principles study of shear deformation, Acta Mater. 67 (2014) 168–180. Scholar
  25. 25.
    Y.-J. Wang, C.-Y. Wang, Influence of the alloying element Re on the ideal tensile and shear strength of γ′-Ni3Al, Scr. Mater. 61 (2009) 197–200. Scholar
  26. 26.
    S. Ogata, J. Li, N. Hirosaki, Y. Shibutani, S. Yip, Ideal shear strain of metals and ceramics, Phys. Rev. B. 70 (2004).
  27. 27.
    G. Kresse, J. Hafner, Norm-conserving and ultrasoft pseudopotentials for first-row and transition elements, J. Phys. Condens. Matter. 6 (1994) 8245.Google Scholar
  28. 28.
    P.E. Blöchl, O. Jepsen, O.K. Andersen, Improved tetrahedron method for Brillouin-zone integrations, Phys. Rev. B. 49 (1994) 16223.CrossRefGoogle Scholar
  29. 29.
    P.E. Blöchl, Projector augmented-wave method, Phys. Rev. B. 50 (1994) 17953.CrossRefGoogle Scholar
  30. 30.
    Z. Pei, L.-F. Zhu, M. Friák, S. Sandlöbes, J. von Pezold, H.W. Sheng, C.P. Race, S. Zaefferer, B. Svendsen, D. Raabe, J. Neugebauer, Ab initio and atomistic study of generalized stacking fault energies in Mg and Mg–Y alloys, New J. Phys. 15 (2013) 043020. Scholar
  31. 31.
    L.J. Slutsky, C.W. Garland, Elastic constants of magnesium from 4.2 K to 300 K, Phys. Rev. 107 (1957) 972.CrossRefGoogle Scholar
  32. 32.
    J.A. Yasi, L.G. Hector, D.R. Trinkle, First-principles data for solid-solution strengthening of magnesium: From geometry and chemistry to properties, Acta Mater. 58 (2010) 5704–5713. Scholar
  33. 33.
    Z. Pei, D. Ma, M. Friák, B. Svendsen, D. Raabe, J. Neugebauer, From generalized stacking fault energies to dislocation properties: Five-energy-point approach and solid solution effects in magnesium, Phys. Rev. B. 92 (2015) 064107.Google Scholar
  34. 34.
    L. Fu, Q. Zhang, B.Y. Tang, First-Principles Study on the Ideal Strengths of Typical Hcp Metals, in: Adv. Mater. Res., Trans Tech Publ, 2012: pp. 2523–2529. (accessed November 11, 2015).CrossRefGoogle Scholar
  35. 35.
    P. Garg, S. Balachandran, I. Adlakha, P.J. Lee, T. Bieler, K. Solanki, Revealing the role of nitrogen on hydride nucleation and stability in pure niobium using first principles calculations, Supercond. Sci. Technol. (2018). Scholar
  36. 36.
    P. Garg, I. Adlakha, S. Balachandran, T. Bieler, P. Lee, K. Solanki, Role of Nitrogen on Hydride Nucleation in Pure Niobium by First Principles Calculations, in: JACOW, Geneva, Switzerland, 2018: pp. 741–745.Google Scholar
  37. 37.
    J. Frenkel, Zur theorie der elastizitätsgrenze und der festigkeit kristallinischer körper, Z. Für Phys. 37 (1926) 572–609.Google Scholar
  38. 38.
    P.B. Legrand, Relations entre la structure électronique et la facilité de glissement dans les métaux hexagonaux compacts, Philos. Mag. B. 49 (1984) 171–184.CrossRefGoogle Scholar
  39. 39.
    A. Moitra, S.-G. Kim, M.F. Horstemeyer, Solute effect on basal and prismatic slip systems of Mg, J. Phys. Condens. Matter. 26 (2014) 445004. Scholar
  40. 40.
    M. Muzyk, Z. Pakiela, K.J. Kurzydlowski, Generalized stacking fault energy in magnesium alloys: density functional theory calculations, Scr. Mater. 66 (2012) 219–222.CrossRefGoogle Scholar

Copyright information

© The Minerals, Metals & Materials Society 2019

Authors and Affiliations

  1. 1.School for Engineering of Matter, Transport, and EnergyArizona State UniversityTempeUSA
  2. 2.Department of Applied MechanicsIndian Institute of Technology-MadrasChennaiIndia

Personalised recommendations