References
- R.C. Reed, The Superalloys : Fundamentals and Applications, Cambridge university press, New York, 2006.
- F. Valenza, M.L. Muolo, and A. Passerone, Wetting and interactions of Ni- and Co-based superalloys with different ceramic materials, J. Mater. Sci. 45 (2010), pp. 2071–2079. doi: 10.1007/s10853-009-3801-4
- C.M.F. Rae and R.C. Reed, The precipitation of topologically close-packed phases in rhenium-containing superalloys, Acta. Mater. 49 (2001), pp. 4113–4125. doi: 10.1016/S1359-6454(01)00265-8
- X.P. Tan, J.L. Liu, T. Jin, Z.Q. Hu, H.U. Hong, B.G. Choi, I.S. Kim, and C.Y. Jo, Intergrowth of P phase with µ phase in a Ru-containing single-crystal Ni-based superalloy, Philos. Mag. Lett. 92 (2012), pp. 556–562. doi: 10.1080/09500839.2012.700409
- I. Lopez-Galilea, J. Koßmann, A. Kostka, R. Drautz, L.M. Roncery, T. Hammerschmidt, S. Huth, and W. Theisen, The thermal stability of topologically close-packed phases in the single-crystal Ni-base superalloy ERBO/1, J. Mater. Sci. 51 (2016), pp. 2653–2664. doi: 10.1007/s10853-015-9579-7
- A. Heckl, S. Neumeier, S. Cenanovic, M. Göken, and R.F. Singer, Reasons for the enhanced phase stability of Ru-containing nickel-based superalloys, Acta. Mater. 59 (2011), pp. 6563–6573. doi: 10.1016/j.actamat.2011.07.002
- B. Seiser, R. Drautz, and D.G. Pettifor, TCP phase predictions in Ni-based superalloys: structure maps revisited, Acta. Mater. 59 (2011), pp. 749–763. doi: 10.1016/j.actamat.2010.10.013
- C.H. Radhakrishna, and K.P. Rao, The formation and control of Laves phase in superalloy 718 welds, J. Mater. Sci. 32 (1997), pp. 1977–1984. doi: 10.1023/A:1018541915113
- H.Q. Ye, D.N. Wang, and K.H. Kuo, Domain structures of tetrahedrally close-packed phases with juxtaposed pentagonal antiprisms II. domain boundary structures of the CI4 Laves phase, Philos. Mag. a-Phys. Cond. Matter Struct. Defects Mech. Prop. 51 (1985), pp. 839–848.
- H. Okaniwa, D. Shindo, M. Yoshida, and T. Takasugi, Determination of site occupancy of additives X (X = V, Mo, W and Ti) in the Nb–Cr–X Laves phase by ALCHEMI, Acta. Mater. 47 (1999), pp. 1987–1992. doi: 10.1016/S1359-6454(99)00065-8
- A.V. Keitz, and G. Sauthoff, Laves phases for high temperatures—part II: stability and mechanical properties, Intermetallics 10 (2002), pp. 497–510. doi: 10.1016/S0966-9795(02)00025-0
- C.T. Liu, J.H. Zhu, M.P. Brady, C.G. Mckamey, and L.M. Pike, Physical metallurgy and mechanical properties of transition-metal Laves phase alloys, Intermetallics 8 (2000), pp. 1119–1129. doi: 10.1016/S0966-9795(00)00109-6
- Q. Yao, J. Sun, D. Lin, S. Liu, and B. Jiang, First-principles studies of defects, mechanical properties and electronic structure of Cr-based Laves phases, Intermetallics 15 (2007), pp. 694–699. doi: 10.1016/j.intermet.2006.10.022
- Q. Yao, J. Sun, Y. Zhang, and B. Jiang, First-principles studies of ternary site occupancy in the C15 NbCr2 laves phase, Acta. Mater. 54 (2006), pp. 3585–3591. doi: 10.1016/j.actamat.2006.03.039
- J.M. Joubert, J.C. Crivello, M. Andasmas, and P. Joubert, Phase stability in the ternary Re–W–Zr system, Acta. Mater. 70 (2014), pp. 56–65. doi: 10.1016/j.actamat.2014.02.010
- J.C. Crivello and J.M. Joubert, First principles calculations of the σ and χ phases in the Mo-Re and W-Re systems, J. Phys. Condens. Mat. 22 (2010), p. 035402. doi: 10.1088/0953-8984/22/3/035402
- M. Palumbo, S.G. Fries, T. Hammerschmidt, T. Abe, J.C. Crivello, A.A.H. Breidi, J.M. Joubert, and R. Drautz, First-principles-based phase diagrams and thermodynamic properties of TCP phases in Re–X systems (X = Ta, V, W), Comput. Mater. Sci. 81 (2014), pp. 433–445. doi: 10.1016/j.commatsci.2013.08.051
- R. Mathieu, N. Dupin, J.C. Crivello, K. Yaqoob, A. Breidi, J.M. Fiorani, N. David, and J.M. Joubert, CALPHAD description of the Mo–Re system focused on the sigma phase modeling, Calphad 43 (2013), pp. 18–31. doi: 10.1016/j.calphad.2013.08.002
- K. Yaqoob, J.C. Crivello, and J.M. Joubert, Comparison of the site occupancies determined by combined rietveld refinement and density functional theory calculations: example of the ternary Mo-Ni-Re σ phase, Inorg. Chem. 51 (2012), pp. 3071–3078. doi: 10.1021/ic202479y
- C. Freysoldt, B. Grabowski, T. Hickel, J. Neugebauer, G. Kresse, A. Janotti, and C.G. Van de Walle, First-principles calculations for point defects in solids, Rev. Mod. Phys. 86 (2014), pp. 253–305. doi: 10.1103/RevModPhys.86.253
- C.G.V.D. Walle and J. Neugebauer, First-principles calculations for defects and impurities: applications to III-nitrides, J. Appl. Phys. 95 (2004), pp. 3851–3879. doi: 10.1063/1.1682673
- M.D. Segall, P.J.D. Lindan, M.J. Probert, C.J. Pickard, P.J. Hasnip, S.J. Clark, and M.C. Payne, First-principles simulation: ideas, illustrations and the CASTEPcode, J. Phys. Condens. Matter. 14 (2002), pp. 2717–2744. doi: 10.1088/0953-8984/14/11/301
- W. Kohn, and L.J. Sham, Self-Consistent equations including exchange and correlation effects, Phys. Rev. 140 (1965), pp. A1133–A1138. doi: 10.1103/PhysRev.140.A1133
- J.P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77 (1996), pp. 3865–3868. doi: 10.1103/PhysRevLett.77.3865
- D. Vanderbilt, Soft self-consistent pseudopotentials in a generalized eigenvalue formalism, Phys. Rev B 41 (1990), pp. 7892–7895. doi: 10.1103/PhysRevB.41.7892
- P. Villars, L.D. Calvert, Pearson's Handbook of Crystallographic Data for Intermetallic Phases, ASM, Cleveland, OH, 1985.
- J. Pavlů, J. Vřešt'ál, and M. Šob, Re-modeling of Laves phases in the Cr–Nb and Cr–Ta systems using first-principles results, Calphad 33 (2009), pp. 179–186. doi: 10.1016/j.calphad.2008.04.006
- F.B. Cuff, N.J. Grant, and C.F. Floe, Titanium-Chromium phase diagram, J. Metals 4 (1952), pp. 848–853.
- X.Q. Chen, W. Wolf, R. Podloucky, and P. Rogl, Ab initio study of ground-state properties of the Laves phase compounds TiCr2 , ZrCr2 , and HfCr2, Phys. Rev. B 71 (2005), p. 268.
- J.M. Filho, A.W. Carbonari, W.P. Jr, J.I. Moura, and R.N. Saxena, X-ray and time differential perturbed angular correlation measurements in ZrCr2 and ZrCr2H3 Laves phase compounds, J. Alloys & Compd. 224 (1995), pp. 60–65. doi: 10.1016/0925-8388(95)01513-2
- J. Belošević-Čavor, V. Koteski, J. Radaković, and B. Cekić, Ab initio study of hyperfine interaction parameters in C14 Hf and Zr Laves-phase compounds, Phys. Rev. B 79 (2009), p. 293. doi: 10.1103/PhysRevB.79.172407
- Y.-J. Li, Q.-M. Hu, D.-S. Xu, and R. Yang, Strengthening of γ-TiAl-Nb by short-range ordering of point defects, Intermetallics 19 (2011), pp. 793–796. doi: 10.1016/j.intermet.2010.11.020
- Y. Chen, J.X. Shang, and Y. Zhang, Bonding characteristics and site occupancies of alloying elements in different Nb5Si3 phases from first principles, Phys. Rev. B 76 (2007), p. 76.
- L. Shao, T.T. Shi, J. Zheng, H.C. Wang, X.Z. Pan, and B.Y. Tang, First-principles study of point defects in C14 MgZn2 Laves phase, J. Alloys & Compd. 654 (2016), pp. 475–481. doi: 10.1016/j.jallcom.2015.09.142
- F. Chu, D.J. Thoma, P.G. Kotula, S. Gerstl, T.E. Mitchell, I.M. Anderson, and J. Bentley, Phase stability and defect structure of the C15 laves phase Nb(Cr,V)2, Acta. Mater. 46 (1998), pp. 1759–1769. doi: 10.1016/S1359-6454(97)00291-7
- T. Hong, T.J. Watsonyang, A.J. Freeman, T. Oguchi, and J. Xu, Crystal structure, phase stability, and electronic structure of Ti-Al intermetallics: TiAl3, Phys. Rev. B 41 (1990), pp. 12462–12467. doi: 10.1103/PhysRevB.41.12462
- W.C. Hu, Y. Liu, D.J. Li, X.Q. Zeng, and C.S. Xu, First-principles study of structural and electronic properties of C14-type Laves phase Al2Zr and Al2Hf, Comput. Mater. Sci. 83 (2014), pp. 27–34. doi: 10.1016/j.commatsci.2013.10.029
- A.R. Merlino, C.R. Luna, A. Juan, and M.E. Pronsato, A DFT study of hydrogen storage in Zr(Cr0.5 Ni 0.5) 2 Laves phase, Int. J. Hydrogen Energy 41 (2016), pp. 2700–2710. doi: 10.1016/j.ijhydene.2015.10.077
- L.G. Hector, J.F. Herbst, and T.W. Capehart, Electronic structure calculations for LaNi5 and LaNi5H7: energetics and elastic properties, J. Alloys & Compd. 353 (2003), pp. 74–85. doi: 10.1016/S0925-8388(02)01324-5
- M. Topsakal, E. Aktürk, and S. Ciraci, First-principles study of two-and one-dimensional honeycomb structures of boron nitride, Phys. Rev. B 79 (2009), p. 115442. doi: 10.1103/PhysRevB.79.115442
- P.L. Mao, Y.U. Bo, Z. Liu, F. Wang, and J.U. Yang, Mechanical properties and electronic structures of MgCu2, Mg2Ca and MgZn2 Laves phases by first principles calculations, T. Nonferr. Metal. Soc. China 24 (2014), pp. 2920–2929. doi: 10.1016/S1003-6326(14)63427-0
- C.F. Guerra, J.W. Handgraaf, E.J. Baerends, and F.M. Bickelhaupt, Voronoi deformation density (VDD) charges: assessment of the Mulliken, Bader, Hirshfeld, Weinhold, and VDD methods for charge analysis, J. Comput. Chem. 25 (2004), pp. 189–210. doi: 10.1002/jcc.10351
- F. Stein, M. Palm, and G. Sauthoff, Structure and stability of Laves phases. part I. critical assessment of factors controlling Laves phase stability, Intermetallics 12 (2004), pp. 713–720. doi: 10.1016/j.intermet.2004.02.010