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Phase stability, elastic, and thermodynamic properties of the L12 (Co,Ni)3(Al,Mo,Nb) phase from first-principles calculations

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Abstract

Phase stability, elastic, and thermodynamic properties of (Co,Ni)3(Al,Mo,Nb) with the L12 structure have been investigated by first-principles calculations. Calculated phonon density of states show that (Co,Ni)3(Al,Mo,Nb) is dynamically stable, and calculated elastic constants indicate that (Co,Ni)3(Al,Mo,Nb) possesses intrinsic ductility. Young’s and shear moduli of the simulated polycrystalline (Co,Ni)3(Al,Mo,Nb) phase are calculated using the Voigt–Reuss–Hill approach and are found to be smaller than those of Co3(Al,W). Calculated electronic density of states depicts covalent-like bonding existing in (Co,Ni)3(Al,Mo,Nb). Temperature-dependent thermodynamic properties of (Co,Ni)3(Al,Mo,Nb) can be described satisfactorily using the Debye–Grüneisen approach, including heat capacity, entropy, enthalpy, and linear thermal expansion coefficient. Predicted heat capacity, entropy, and linear thermal expansion coefficient of (Co,Ni)3(Al,Mo,Nb) show significant change as a function of temperature. Furthermore the obtained data can be used in the modeling of thermodynamic and mechanical properties of Co-based alloys to enable the design of high temperature alloys.

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References

  1. C.T. Sims, N.S. Stoloff, and W.C. Hagel: Superalloys II (Wiley, New York, 1987).

    Google Scholar 

  2. Z.L. Peng, S. Miura, and Y. Mishima: High-temperature creep behavior in Ni3(Al, Ta) single crystals with different orientations. Mater. Trans., JIM 38(7), 653 (1997).

    Article  CAS  Google Scholar 

  3. J. Sato, T. Omori, K. Oikawa, I. Ohnuma, R. Kainuma, and K. Ishida: Cobalt-base high-temperature alloys. Science 312(5770), 90 (2006).

    Article  CAS  Google Scholar 

  4. A. Suzuki and T.M. Pollock: High-temperature strength and deformation of γ/γ′ two-phase Co–Al–W-base alloys. Acta Mater. 56(6), 1288 (2008).

    Article  CAS  Google Scholar 

  5. H. Chinen, T. Omori, K. Oikawa, I. Ohnuma, R. Kainuma, and K. Ishida: Phase equilibria and ternary intermetallic compound with L12 structure in Co–W–Ga system. J. Phase Equilib. Diffus. 30(6), 587 (2009).

    Article  CAS  Google Scholar 

  6. H. Chinen, J. Sato, T. Omori, K. Oikawa, I. Ohnuma, R. Kainuma, and K. Ishida: New ternary compound Co3(Ge, W) with L12 structure. Scr. Mater. 56(2), 141 (2007).

    Article  CAS  Google Scholar 

  7. S.K. Makineni, B. Nithin, and K. Chattopadhyay: Synthesis of a new tungsten-free γ-γ′ cobalt-based superalloy by tuning alloying additions. Acta Mater. 85, 85 (2015).

    Article  CAS  Google Scholar 

  8. C.F. Yu, H.C. Cheng, and W.H. Chen: Structural, mechanical and thermodynamic properties of AuIn2 crystal under pressure: A first-principles density functional theory calculation. J. Alloys Compd. 619, 576 (2015).

    Article  CAS  Google Scholar 

  9. G. Yi, X. Zhang, J. Qin, J. Ning, S. Zhang, M. Ma, and R. Liu: Mechanical, electronic and thermal properties of Cu5Zr and Cu5Hf by first-principles calculations. J. Alloys Compd. 640, 455 (2015).

    Article  CAS  Google Scholar 

  10. B. Huang, Y.H. Duan, Y. Sun, M.J. Peng, and S. Chen: Electronic structures, mechanical and thermodynamic properties of cubic alkaline-earth hexaborides from first principles calculations. J. Alloys Compd. 635, 213 (2015).

    Article  CAS  Google Scholar 

  11. Y.T. Hu and H. Gong: First principles study of thermodynamic and mechanical properties of Pd50Cu50. J. Alloys Compd. 639, 635 (2015).

    Article  CAS  Google Scholar 

  12. Z.K. Liu: First-principles calculations and CALPHAD modeling of thermodynamics. J. Phase Equilib. Diffus. 30(5), 517 (2009).

    Article  CAS  Google Scholar 

  13. S.R. Joshi, K.V. Vamsi, and S. Karthikeyan: First principles study of structural stability and site preference in Co3(W,X). MATEC Web of Conferences 14, 18001 (2014).

    Article  Google Scholar 

  14. W.W. Xu, J.J. Han, Z.W. Wang, C.P. Wang, Y.H. Wen, X.J. Liu, and Z.Z. Zhu: Thermodynamic, structural and elastic properties of Co3X (X = Ti, Ta, W, V, Al) compounds from first-principles calculations. Intermetallics 32, 303 (2013).

    Article  CAS  Google Scholar 

  15. Q. Yao, Y.H. Zhu, and Y. Wang: Structural stability and elastic properties of L12 Co3(Ga,W) precipitate from first-principle calculations. Phys. B 406(8), 1542 (2011).

    Article  CAS  Google Scholar 

  16. Q. Yao, Y. Wang, and Y.H. Zhu: Elastic properties and electronic structures of L12 Co3(Ge,W). Phys. B 405(12), 2753 (2010).

    Article  CAS  Google Scholar 

  17. M. Chen and C.Y. Wang: First-principles investigation of the site preference and alloying effect of Mo, Ta and platinum group metals in γ′-Co3(Al, W). Scr. Mater. 60(8), 659 (2009).

    Article  CAS  Google Scholar 

  18. C. Jiang: First-principles study of Co3(Al,W) alloys using special quasi-random structures. Scr. Mater. 59(10), 1075 (2008).

    Article  CAS  Google Scholar 

  19. K. Tanaka, T. Ohashi, K. Kishida, and H. Inui: Single-crystal elastic constants of Co3(Al,W) with the L12 structure. Appl. Phys. Lett. 91(18), 181097 (2007).

    Article  CAS  Google Scholar 

  20. Q. Yao, H. Xing, and J. Sun: Structural stability and elastic property of the L12 ordered Co3(Al,W) precipitate. Appl. Phys. Lett. 89(16), 161906 (2006).

    Article  CAS  Google Scholar 

  21. S. Makineni, A. Samanta, T. Rojhirunsakool, T. Alam, B. Nithin, A. Singh, R. Banerjee, and K. Chattopadhyay: A new class of high strength high temperature cobalt based γ–γ′ Co–Mo–Al alloys stabilized with Ta addition. Acta Mater. 97, 29 (2015).

    Article  CAS  Google Scholar 

  22. A. Zunger, S. Wei, L.G. Ferreira, and J.E. Bernard: Special quasirandom structures. Phys. Rev. Lett. 65(3), 353 (1990).

    Article  CAS  Google Scholar 

  23. R.K. Rhein, P.C. Dodge, M.H. Chen, M.S. Titus, T.M. Pollock, and V.D.V. Anton: Role of vibrational and configurational excitations in stabilizing the L12 structure in Co-rich Co–Al–W alloys. Phys. Rev. B: Condens. Matter Mater. Phys. 92(17), 174117 (2015).

    Article  CAS  Google Scholar 

  24. J. Koßmann, T. Hammerschmidt, S. Maisel, S. Müller, and R. Drautz: Solubility and ordering of Ti, Ta, Mo and W on the Al sublattice in L12-Co3Al. Intermetallics 64, 44 (2015).

    Article  CAS  Google Scholar 

  25. A. Van de Walle, P. Tiwary, M. De Jong, D. Olmsted, M. Asta, A. Dick, D. Shin, Y. Wang, L.Q. Chen, and Z.K. Liu: Efficient stochastic generation of special quasirandom structures. Calphad 42, 13 (2013).

    Article  CAS  Google Scholar 

  26. A. van de Walle: Multicomponent multisublattice alloys, nonconfigurational entropy and other additions to the Alloy Theoretic Automated Toolkit. Calphad 33(2), 266 (2009).

    Article  CAS  Google Scholar 

  27. G. Kresse and D. Joubert: From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B: Condens. Matter Mater. Phys. 59(3), 1758 (1999).

    Article  CAS  Google Scholar 

  28. G. Kresse and J. Furthmüller: Software VASP, vienna. Phys. Rev. B: Condens. Matter Mater. Phys. 54(11), 169 (1996).

    Google Scholar 

  29. J.P. Perdew, K. Burke, and M. Ernzerhof: Generalized gradient approximation made simple. Phys. Rev. Lett. 77(18), 3865 (1996).

    Article  CAS  Google Scholar 

  30. P.E. Blöchl, O. Jepsen, and O.K. Andersen: Improved tetrahedron method for Brillouin-zone integrations. Phys. Rev. B: Condens. Matter Mater. Phys. 49(23), 16223 (1994).

    Article  Google Scholar 

  31. Y. Wang, J. Wang, W. Wang, Z. Mei, S.L. Shang, L. Chen, and Z.K. Liu: A mixed-space approach to first-principles calculations of phonon frequencies for polar materials. J. Phys.: Condens. Matter 22(20), 202201 (2010).

    CAS  Google Scholar 

  32. S.L. Shang, Y. Wang, and Z.K. Liu: First-principles elastic constants of α-and θ-Al2O3. Appl. Phys. Lett. 90(10), 101909 (2007).

    Article  CAS  Google Scholar 

  33. Y. Wang, J. Wang, H. Zhang, V. Manga, S.L. Shang, L. Chen, and Z.K. Liu: A first-principles approach to finite temperature elastic constants. J. Phys.: Condens. Matter 22(22), 225404 (2010).

    CAS  Google Scholar 

  34. S.L. Shang, D. Kim, C. Zacherl, Y. Wang, Y. Du, and Z. Liu: Effects of alloying elements and temperature on the elastic properties of dilute Ni-base superalloys from first-principles calculations. J. Appl. Phys. 112(5), 053515 (2012).

    Article  CAS  Google Scholar 

  35. O.L. Anderson: A simplified method for calculating the Debye temperature from elastic constants. J. Phys. Chem. Solids. 24(7), 909 (1963).

    Article  CAS  Google Scholar 

  36. M.Y. Gutkin, T. Ishizaki, S. Kuramoto, and I.A. Ovid’ko: Nanodisturbances in deformed gum metal. Acta Mater. 54(9), 2489 (2006).

    Article  CAS  Google Scholar 

  37. S.L. Shang, Y. Wang, D. Kim, and Z-K. Liu: First-principles thermodynamics from phonon and Debye model: Application to Ni and Ni3Al. Comput. Mater. Sci. 47(4), 1040 (2010).

    Article  CAS  Google Scholar 

  38. V. Moruzzi, J. Janak, and K. Schwarz: Calculated thermal properties of metals. Phys. Rev. B: Condens. Matter Mater. Phys. 37(2), 790 (1988).

    Article  CAS  Google Scholar 

  39. W.W. Xu, J.J. Han, Y. Wang, C.P. Wang, X.J. Liu, and Z.K. Liu: First-principles investigation of electronic, mechanical and thermodynamic properties of L12 ordered Co3(M,W) (M = Al, Ge, Ga) phases. Acta Mater. 61(14), 5437 (2013).

    Article  CAS  Google Scholar 

  40. Q. Liu, J. Coakley, D.N. Seidman, and D.C. Dunand: Precipitate evolution and creep behavior of a W-free Co-based superalloy. Metall. Mater. Trans. A 47(12), 6090 (2016).

    Article  CAS  Google Scholar 

  41. J.H. Xu, T. Oguchi, and A. Freeman: Solid-solution strengthening: Substitution of V in Ni3Al and structural stability of Ni3 (Al, V). Phys. Rev. B: Condens. Matter Mater. Phys. 36(8), 4186 (1987).

    Article  CAS  Google Scholar 

  42. Y.S. Touloukian, R.K. Kirby, R.E. Taylor, and P.D. Desai: Thermophysical properties of matter—The TPRC data series: Thermal Expansion Metallic Elements and Alloys (Plenum, New York, 1975).

    Google Scholar 

  43. B. Ihsan: Thermochemical data of pure substances. (VCH, New York, 1995).

    Google Scholar 

  44. Y.J. Wang and C.Y. Wang: A comparison of the ideal strength between L12 Co3(Al,W) and Ni3Al under tension and shear from first-principles calculations. Appl. Phys. Lett. 94(26), 261909 (2009).

    Article  CAS  Google Scholar 

  45. F. Kayser and C. Stassis: The elastic constants of Ni3Al at 0 and 23.5 °C. Phys. Status Solidi A 64(1), 335 (1981).

    Article  CAS  Google Scholar 

  46. M. Born and K. Huang: Dynamical Theory of Crystal Lattices (Clarendon Press, Oxford, 1954).

    Google Scholar 

  47. S.F. Pugh: Relations between the elastic moduli and the plastic properties of polycrystalline pure metals. Philos. Mag. 45, 823 (1954).

    Article  CAS  Google Scholar 

  48. D. Pettifor: Theoretical predictions of structure and related properties of intermetallics. Mater. Sci. Technol. 8(4), 345 (1992).

    Article  CAS  Google Scholar 

  49. S. Prikhodko, H. Yang, A. Ardell, J. Carnes, and D. Isaak: Temperature and composition dependence of the elastic constants of Ni3Al. Metall. Mater. Trans. A 30(9), 2403 (1999).

    Article  Google Scholar 

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ACKNOWLEDGMENTS

This work is funded by the National Natural Science Foundation of China through grant No. 51201074. Q. Yao acknowledges the support from Jiangsu Government Scholarship for Overseas Studies. The efforts at the Pennsylvania State University were partially supported by the National Science Foundation under grants DMR-1006557 and CMMI-1333999. First-principles calculations were carried out on the LION clusters at the Pennsylvania State University supported by the Materials Simulation Center and the Institute for CyberScience. Calculations were also carried out on the CyberStar cluster funded by the NSF through Grant No. OCI-0821527.

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Authors and Affiliations

  1. National Supervising & Testing Center for Engineering Composite Materials’ Quality, Jiangsu Provincial Supervising & Testing Research Institute for Products’ Quality, Nanjing, 210007, People’s Republic of China

    Qiang Yao, Qiong Wang & Tong Lu

  2. Department of Materials Science and Engineering, The Pennsylvania State University, University Park, Pennsylvania, 16802, USA

    Qiang Yao, Shun-Li Shang, Kang Wang, Yi Wang & Zi-Kui Liu

  3. State Key Laboratory of Solidification Processing, Northwestern Polytechnical University, Shaanxi, 710072, People’s Republic of China

    Kang Wang & Feng Liu

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  1. Qiang Yao
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Correspondence to Qiang Yao.

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Supplementary material: Phase stability, elastic and thermodynamic properties of L12 (Co,Ni)3(Al,Mo,Nb) phase from first-principles calculations (approximately 1.12 MB)

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Yao, Q., Shang, SL., Wang, K. et al. Phase stability, elastic, and thermodynamic properties of the L12 (Co,Ni)3(Al,Mo,Nb) phase from first-principles calculations. Journal of Materials Research 32, 2100–2108 (2017). https://doi.org/10.1557/jmr.2017.8

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