Precipitation in powder-metallurgy, nickel-base superalloys: review of modeling approach and formulation of engineering methods to determine input data

  • S. L. SemiatinEmail author
  • F. Zhang
  • R. Larsen
  • L. A. Chapman
  • D. U. Furrer


Methods for determining the various thermodynamic and kinetic parameters required for the modeling of γ′ precipitation in powder-metallurgy (PM), nickel-base superalloys are summarized. These parameters comprise the composition of the γ′ phase, the γ′ solvus temperature/equilibrium solvus approach curve, the free energy (∆G*) associated with the decomposition of the γ matrix to form γ′, the γ/γ′ interfacial energy σ, and an effective diffusivity for use in nucleation, growth, and coarsening calculations. Techniques to obtain the material data include phase extraction (for the average composition of γ′) and heat-treatment/quantitative metallography (for a two-parameter fit of the solvus approach curve). With regard to ∆G*, two methods, one based on the instantaneous composition of the γ and γ′ phases and the other on the enthalpy of transformation and the solvus temperature, are summarized. It is shown that the interfacial energy σ can be determined from the nucleation-onset temperature as indicated by on-cooling specific-heat measurements. Last, the use of a limited set of static-coarsening measurements to estimate the effective diffusivity is described. The application of the various protocols is illustrated for typical first-, second-, and third-generation PM superalloys, i.e., IN-100, René 88, and LSHR/ME3, respectively.


Precipitation Superalloys Gamma prime Nucleation Growth Coarsening Solvus approach curve Interface energy Free energy of transformation Diffusivity 



This work was conducted as part of the in-house research of the Metals Branch of the Air Force Research Laboratory’s Materials and Manufacturing Directorate. The support and encouragement of the Laboratory management is greatly appreciated. Technical discussions with T.P. Gabb and C.K. Sudbrack (NASA Glenn Research Center) are also gratefully acknowledged.


  1. 1.
    Donachie MJ (ed) (1984) Superalloys: source book. ASM International, Materials ParkGoogle Scholar
  2. 2.
    Forbes Jones RM, Jackman LA (1999) The structural evolution of superalloy ingots during hot working. JOM 51(1):27–31CrossRefGoogle Scholar
  3. 3.
    Muzyka DR (1979) Physical metallurgy and effects of process variables on the microstructure of wrought superalloys. In: Abrams H, Maniar GN, Nail DA, Solomon HD (eds) MiCon 78: optimization of processing, properties, and service performance through microstructural control, ASTM STP 672. American Society for Testing and Materials, Philadelphia, pp 526–546CrossRefGoogle Scholar
  4. 4.
    Doherty RD (1996) Diffusive phase transformations in the solid state. In: Cahn RW, Haasen P (eds) Physical Metallurgy, North-Holland Publishers, Amsterdam, ch. 15.CrossRefGoogle Scholar
  5. 5.
    Martin JW, Doherty RD, Cantor B (1997) Stability of microstructure in metallic systems. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  6. 6.
    Turnbull D (1956) Phase changes. In: Seitz F, Turnbull D (eds) Solid-state physics, vol 3. Academic Press, New York, pp 226–306Google Scholar
  7. 7.
    Kelly A, Nicholson RB (1963) Precipitation hardening. Prog Mat Sci 10:151–391CrossRefGoogle Scholar
  8. 8.
    Russell KC (1970) Nucleation in solids. In: Phase transformations. ASM, Metals Park, OH, pp 219–268Google Scholar
  9. 9.
    Christian JW (1975) The theory of transformations in metals and alloys, 2nd edn. Pergamon Press, OxfordGoogle Scholar
  10. 10.
    Russell KC (1980) Nucleation in solids: the induction and steady-state effects. Adv Colloid Interface Sci 13:205–318CrossRefGoogle Scholar
  11. 11.
    Haasen P, Gerold V, Wagner R, Ashby MF (1984) Decomposition of alloys: the early stages. Pergamon Press, OxfordGoogle Scholar
  12. 12.
    Aaronson HI, LeGoues FK (1992) An assessment of studies on homogeneous diffusional nucleation kinetics in binary metallic alloys. Metall Trans A 23:1915–1945CrossRefGoogle Scholar
  13. 13.
    Carslaw HS, Jaeger JC (1959) Conduction of heat in solids. Oxford University Press, LondonGoogle Scholar
  14. 14.
    Aaron HB, Fainstein D, Kotler GR (1970) Diffusion-limited phase transformations: a comparison and critical evaluation of the mathematical approximations. J Appl Phys 41:4404–4410CrossRefGoogle Scholar
  15. 15.
    Lifshitz IM, Slyozov VV (1961) The kinetics of precipitation from supersaturated solid solutions. J Phys Chem Solids 19:35–51CrossRefGoogle Scholar
  16. 16.
    Wagner C (1961) Theorie der alterung von niederschlägen durch umlösen (Ostwald‐reifung). Zeit Elektrochem 65:581–591Google Scholar
  17. 17.
    Ardell AJ (1972) The effect of volume fraction on particle coarsening: theoretical considerations. Acta Metall 20:61–71CrossRefGoogle Scholar
  18. 18.
    Brailsford AD, Wynblatt P (1979) The dependence of Ostwald ripening kinetics on particle volume fraction. Acta Metall 27:489–497CrossRefGoogle Scholar
  19. 19.
    Voorhees PW, Glicksman ME (1984) Solution to the multi-particle diffusion problem with applications to Ostwald ripening—I. Theory. Acta Metall 32:2001–2011CrossRefGoogle Scholar
  20. 20.
    Voorhees PW, Glicksman ME (1984) Solution to the multi-particle diffusion problem with applications to Ostwald ripening—II. Computer simulations. Acta Metall 32:2013–2030CrossRefGoogle Scholar
  21. 21.
    Calderon HA, Voorhees PW, Murray JL, Kostorz G (1994) Ostwald ripening in concentrated alloys. Acta Metall Mater 42:991–1000CrossRefGoogle Scholar
  22. 22.
    Umantsev A, Olson GB (1993) Ostwald ripening in multicomponent alloys. Scripta Metall Mater 29:1135–1140CrossRefGoogle Scholar
  23. 23.
    Morral JE, Purdy GR (1994) Particle coarsening in binary and multicomponent alloys. Scripta Metall Mater 30:905–908CrossRefGoogle Scholar
  24. 24.
    Kuehmann CJ, Voorhees PW (1996) Ostwald ripening in ternary alloys. Metall Mater Trans A 27:937–943CrossRefGoogle Scholar
  25. 25.
    Wendt H, Haasen P (1983) Nucleation and growth of γ′ precipitates in Ni-14 at.%Al. Acta Metall 31:1649–1659CrossRefGoogle Scholar
  26. 26.
    Xiao SQ, Haasen P (1991) HREM investigation of homogeneous decomposition in a Ni-12 at.%Al alloy. Acta Metall Mater 39:651–659CrossRefGoogle Scholar
  27. 27.
    Sudbrack CK, Yoon KE, Noebe RD, Seidman DN (2006) Temporal evolution of the nanostructure and phase compositions in a model Ni-Al-Cr alloy. Acta Mater 54:3199–3210CrossRefGoogle Scholar
  28. 28.
    Sudbrack CK, Noebe RD, Seidman DN (2007) Compositional pathways and capillarity effects during isothermal precipitation in a nondilute Ni-Al-Cr alloy. Acta Mater 55:119–130CrossRefGoogle Scholar
  29. 29.
    Rougier L, Jacot A, Gandin CA, Napoli PD, Thery PY, Ponsen D, Jaquet V (2013) Numerical simulation of precipitation in multicomponent Ni-Base alloys. Acta Mater 61:6396–6405CrossRefGoogle Scholar
  30. 30.
    Wlodek ST, Kelly M, Alden DA (1996) The structure of René 88DT. In: Kissinger RD, Deye DJ, Anton DL, Cetel AD, Nathal MV, Pollock TM, Woodford DA (eds) Superalloys 1996. TMS, Warrendale, pp 129–136Google Scholar
  31. 31.
    Furrer DU (1999) Microstructure and mechanical property development in alloy U720LI. DEng Thesis, University of Ulm, UlmGoogle Scholar
  32. 32.
    Furrer DU, Fecht HJ (1999) γ′ formation in superalloy U720LI. Scripta Mater 40:1215–1220CrossRefGoogle Scholar
  33. 33.
    Gabb TP, Backman DG, Wei DY, Mourer DP, Furrer DU, Garg A, Ellis DL (2000) γ′ formation in a nickel-base disk superalloy. In: Pollock TM, Kissinger RD, Bowman RR, Green KA, McLean M, Olson S, Schirra JJ (eds) Superalloys 2000. TMS, Warrendale, pp 405–414CrossRefGoogle Scholar
  34. 34.
    Jou HJ, Voorhees PW, Olson GB (2004) Computer simulations for the prediction of microstructure/property variation in aeroturbine disks. In: Green KA, Pollock TM, Harada H, Howson TE, Reed RC, Schirra JJ, Walston S (eds) Superalloys 2004. TMS, Warrendale, pp 877–886CrossRefGoogle Scholar
  35. 35.
    Olson GB, Jou HJ, Jung J, Sebastian JT, Misra A, Locci I, Hull D (2008) Precipitation model validation in 3rd generation aeroturbine disc alloys. In: Reed RC, Green KA, Caron P, Gabb TP, Fahrmann MG, Huron ES, Woodard SA (eds) Superalloys 2008. TMS, Warrendale, pp 923–932Google Scholar
  36. 36.
    Wu K, Zhang F, Chen S, Cao W, Chang YA (2008) A modeling tool for the precipitation simulations of superalloys during heat treatments. In: Reed RC, Green KA, Caron P, Gabb TP, Fahrmann MG, Huron ES, Woodard SA (eds) Superalloys 2008. TMS, Warrendale, pp 933–939Google Scholar
  37. 37.
    Wen Y, Simmons JP, Shen C, Woodward C, Wang Y (2003) Phase-field modeling of bimodal particle size distributions during continuous cooling. Acta Mater 51:1123–1132CrossRefGoogle Scholar
  38. 38.
    Wang JC, Osawa M, Yokokawa T, Harada H, Enomoto M (2007) Modeling the microstructural evolution of Ni-base superalloys by phase field method combined with CALPHAD and CVM. Comp Mater Sci 39:871–879CrossRefGoogle Scholar
  39. 39.
    Simmons JP, Wen Y, Shen C, Wang Y (2004) Microstructural development involving nucleation and growth phenomena simulated with the phase field method. Mater Sci Eng A365:136–143CrossRefGoogle Scholar
  40. 40.
    Wen Y, Lill JV, Chen SL, Simmons JP (2010) A ternary phase-field model incorporating commercial CALPHAD software and its application to precipitation in superalloys. Acta Mater 58:875–885CrossRefGoogle Scholar
  41. 41.
    Kitashima T, Harada H (2009) A new phase-field method for simulating γ′ precipitation in multicomponent nickel-base superalloys. Acta Mater 57:2020–2028CrossRefGoogle Scholar
  42. 42.
    Kampmann L, Kahlweit M (1970) On the theory of precipitation II. Berichte der Bunsen-Gesellschaft Physikalische Chemie 94:456–462Google Scholar
  43. 43.
    Perez M (2005) Gibbs-Thomson effects in phase transformations. Scripta Mater 52:709–712CrossRefGoogle Scholar
  44. 44.
    Grong O, Shercliff HR (2002) Microstructural modelling in metals processing. Prog Mat Sci 47:163–282CrossRefGoogle Scholar
  45. 45.
    Cao W, Chen S-L, Zhang F, Wu K, Yang Y, Chang YA, Schmid-Fetzer R, Oates WA (2009) PANDAT software with PanEngine, PanOptimizer and PanPrecipitation for multi-component phase diagram calculation and materials property simulation. Calphad 33:328–342CrossRefGoogle Scholar
  46. 46.
    Dyson BF (2001) Predicting creep behavior in commercial precipitation-strengthened alloys. In: Proceedings Euromat 2001, Remini, Italy. (CD ROM).Google Scholar
  47. 47.
    Payton EJ (2009) Characterization and modeling of grain coarsening in powder-metallurgical nickel-base superalloys. PhD Dissertation, the Ohio State University, Columbus, OH USA.Google Scholar
  48. 48.
    Gabb TP, Garg A, Ellis, DL (2004) Microstructural evaluations of baseline HSR/EPM disk alloys. Report NASA/TM-2004-213123, NASA Glenn Research Center, Cleveland, OH USA.Google Scholar
  49. 49.
    Mao J, Chang K-M, Furrer D (2000) Quench cracking characterization of superalloys using fracture mechanics approach. In: Pollock TM, Kissinger RD, Bowman RR, Green KA, McLean M, Olson S, Schirra JJ (eds) Superalloys 2000. TMS, Warrendale, PA, pp 109–116CrossRefGoogle Scholar
  50. 50.
    Semiatin SL, Kim S-L, Zhang F, Tiley JS (2015) An investigation of high-temperature precipitation in powder-metallurgy, gamma/gamma prime nickel-base superalloys. Metall Mater Trans A 46:1715–1730CrossRefGoogle Scholar
  51. 51.
    Larsen R, Goerz T (2015) Thermophysical properties of three nickel alloys (Report TPRL 5287). Thermophysical Properties Research Laboratory, West Lafayette, INGoogle Scholar
  52. 52.
    Larsen R (2015) Specific heat of three nickel alloys (Report TPRL 5329, Rev A). Thermophysical Properties Research Laboratory, West Lafayette, INGoogle Scholar
  53. 53.
    Larsen R (2015) Specific heat of one nickel alloy (Report TPRL 5370). Thermophysical Properties Research Laboratory, West Lafayette, INGoogle Scholar
  54. 54.
    Gabb TP, Gayda J, Telesman J, Kantzos PT (2005) Thermal and mechanical property characterization of the advanced disk alloy LSHR. Report NASA/TM-2005-213645, NASA Glenn Research Center, Cleveland, OH USA.Google Scholar
  55. 55.
    Robson JD, Jones MJ, Prangnell PB (2003) Extension of the N-model to predict competing homogeneous and heterogeneous precipitation in Al-Sc alloys. Acta Mater vol 51:1453–1468CrossRefGoogle Scholar
  56. 56.
    Booth-Morrison C, Weninger J, Sudbrack CK, Mao Z, Noebe RD, Seidman DN (2008) Effects of solute concentrations on kinetic pathways in Ni-Al-Cr alloys. Acta Mater 56:3422–3438CrossRefGoogle Scholar
  57. 57.
    Nesbitt JW, Heckel RW (1987) Interdiffusion in Ni-Rich, Ni-Cr-Al alloys at 1100 and 1200 °C: part I. Diffusion paths and microstructures. Metall Trans A 18:2061–2073CrossRefGoogle Scholar
  58. 58.
    Dayananda MA (1989) Multicomponent diffusion studies in selected high-temperature alloy systems. Mater Sci Eng A121:351–359CrossRefGoogle Scholar
  59. 59.
    Semiatin SL, Shank JM, Saurber WM, Pilchak AL, Ballard DL, Zhang F, Gleeson B (2104) Alloying-element loss during high-temperature processing of a nickel-base superalloy. Metall Mater Trans A 45:962–979CrossRefGoogle Scholar
  60. 60.
    Campbell CE, Zhao JC, Henry MF (2004) Comparison of experimental and simulated multicomponent Ni-Base superalloy diffusion couples. J Phase Equil Diff 25:6–15CrossRefGoogle Scholar
  61. 61.
    Karunaratne MSA, Cox DC, Carter P, Reed RC (2000) Modelling of the microsegregation in CMSX-4 superalloy and its homogenization during heat treatment. In: Pollock TM, Kissinger RD, Bowman RR, Green KA, McLean M, Olson S, Schirra JJ (eds) Superalloys 2000. TMS, Warrendale, PA, pp 263–272CrossRefGoogle Scholar
  62. 62.
    Payton EJ, Picard R, Saurber A, Semiatin SL (2015) Unpublished research. Air Force Research Laboratory, Wright-Patterson Air Force base, OH USA.Google Scholar
  63. 63.
    Gabb TP, Garg A, Gayda J, Johnson D, Kang E, Locci I, MacKay RA, Rogers R, Sudbrack CK, Semiatin SL (2015) Comparison of γ-γ′ coarsening response of three powder metal disk alloys. Report NASA/TM-2016, NASA Glenn Research Center, Cleveland, OH USA, in press.Google Scholar
  64. 64.
    Ardell AJ, Ozolins V (2005) Trans-interface diffusion-controlled coarsening. Nat Mater 4:309–316CrossRefGoogle Scholar

Copyright information

© Semiatin et al. 2016

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  • S. L. Semiatin
    • 1
    Email author
  • F. Zhang
    • 2
  • R. Larsen
    • 3
  • L. A. Chapman
    • 4
  • D. U. Furrer
    • 5
  1. 1.Air Force Research Laboratory, Materials and Manufacturing DirectorateAFRL/RXCMWright-Patterson Air Force BaseUSA
  2. 2.CompuTherm, LLCMadisonUSA
  3. 3.Thermophysical Properties Research Laboratory, Inc.West LafayetteUSA
  4. 4.National Physical LaboratoryTeddingtonUK
  5. 5.Pratt & WhitneyEast HartfordUSA

Personalised recommendations