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A whole pattern iterative refinement method for powder X-ray diffraction spectra of two-phase coherent alloys

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Abstract

An iterative refining method using FullProf software (Rietveld refinement) as a multi-input–output black-box with cyclic feedback is proposed in order to accurately measure the lattice misfit in two-phase coherent alloys. The method uses two X-ray diffraction spectra taken on the same powder sample. In addition, it requires the volumetric fraction of the phases and the size of the crystallite in the precipitated phase as derived from the measurements made by the transmission electron microscopy–energy dispersive spectroscopy technique. The measurement of the lattice misfit in a Fe2AlV-strengthened ferritic Fe76Al12V12 alloy is shown as an application of the method.

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References

  1. Reed RC (2006) The superalloys fundamentals and applications. Cambridge University Press, Cambridge

    Book  Google Scholar 

  2. Mughrabi H (2009) Microstructural aspects of high temperature deformation of monocrystalline nickel base superalloys: some open problems. Mater Sci Technol 25:191–204

    Article  Google Scholar 

  3. Hao SM, Takayama T, Ishida K, Nishizawa T (1984) Miscibility gap in Fe–Ni–Al and Fe–Ni–Al–Co systems. Metall Trans A 15:1819–1828

    Article  Google Scholar 

  4. Mendiratta MG, Ehlers SK, Lipsitt HA (1987) DO3-B2-alpha phase relations in Fe–Al–Ti alloys. Metall Trans A 18:509–518

    Article  Google Scholar 

  5. Maebashi T, Kozakai T, Doi M (2004) Phase equilibria in iron-rich Fe–Al–V ternary alloy system. Z Met 95:1005–1010

    Article  Google Scholar 

  6. Bhadeshia HKDH (2001) Design of ferritic creep-resistant steels. ISIJ Int 41:626–640

    Article  Google Scholar 

  7. Stallybrass C, Sauthoff G (2004) Ferritic Fe–Al–Ni–Cr alloys with coherent precipitates for high-temperature applications. Mater Sci Eng A 387–389:985–990

    Article  Google Scholar 

  8. Vo NQ, Liebscher CH, Rawlings MJS, Asta M, Dunand DC (2014) Creep properties and microstructure of a precipitation-strengthened ferritic Fe–Al–Ni–Cr alloy. Acta Mater 71:89–99

    Article  Google Scholar 

  9. Krein R, Palm M, Heilmaier M (2009) Characterization of microstructures, mechanical properties, and oxidation behavior of coherent A2 + L21 Fe–Al–Ti. J Mater Res 24:3412–3421

    Article  Google Scholar 

  10. Ferreirós PA, Alonso PR, Gargano PH, Bozzano PB, Troiani HE, Baruj A, Rubiolo GH (2014) Characterization of microstructures and age hardening of Fe1−2x AlxVx alloys. Intermetallics 50:65–78

    Article  Google Scholar 

  11. Senčekova L, Palm M, Pešička J, Veselý J (2016) Microstructures, mechanical properties and oxidation behaviour of single-phase Fe3Al(D03) and two-phase α-Fe, Al(A2) + Fe3Al(D03) Fe–Al–V alloys. Intermetallics 73:58–66

    Article  Google Scholar 

  12. Calderon HA, Fine ME, Weertman JR (1988) Coarsening and morphology of β′ particles in Fe–Ni–Al–Mo ferritic alloys. Metall Trans A 19:1135–1146

    Article  Google Scholar 

  13. Svoboda J, Lukáš P (1998) Model of creep in <001> -oriented superalloy single crystals. Acta Mater 46:3421–3431

    Article  Google Scholar 

  14. Onaka S, Kobayashi N, Fujii T, Kato M (2003) Energy analysis with a superspherical shape approximation on the spherical to cubical shape transitions of coherent precipitates in cubic materials. Mater Sci Eng A 347:42–49

    Article  Google Scholar 

  15. Maebashi T, Doi M (2004) Coarsening behaviours of coherent γ′ and γ precipitates in elastically constrained Ni–Al–Ti alloys. Mater Sci Eng A 373:72–79

    Article  Google Scholar 

  16. Heckl A, Neumeier S, Göken M, Singer RF (2011) The effect of Re and Ru on γ/γ′ microstructure, γ-solid solution strengthening and creep strength in nickel-base superalloys. Mater Sci Eng A 528:3435–3444

    Article  Google Scholar 

  17. Mughrabi H (2014) The importance of sign and magnitude of γ/γ′ lattice misfit in superalloys-with special reference to the new γ′-hardened cobalt-base superalloys. Acta Mater 81:21–29

    Article  Google Scholar 

  18. Long H, Wei H, Liu Y, Mao S, Zhang J, Xiang S, Chen Y, Gui W, Li Q, Zhang Z, Han X (2016) Effect of lattice misfit on the evolution of the dislocation structure in Ni-based single crystal superalloys during thermal exposure. Acta Mater 120:95–107

    Article  Google Scholar 

  19. Pyczak F, Neumeier S, Göken M (2009) Influence of lattice misfit on the internal stress and strain states before and after creep investigated in nickel-base superalloys containing rhenium and ruthenium. Mater Sci Eng A 510–511:295–300

    Article  Google Scholar 

  20. Collins DM, Yan L, Marquis EA, Connor LD, Ciardiello JJ, Evans AD, Stone HJ (2013) Lattice misfit during ageing of a polycrystalline nickel-base superalloy. Acta Mater 61:7791–7804

    Article  Google Scholar 

  21. Collins DM, D’Souza N, Panwisawas C (2017) In-situ neutron diffraction during stress relaxation of a single crystal nickel-base superalloy. Scr Mater 131:103–107

    Article  Google Scholar 

  22. Brunetti G, Settefrati A, Hazotte A, Denis S, Fundenberger J-J, Tidu A, Bouzy E (2012) Determination of γ-γ′ lattice misfit in a single-crystal nickel-based superalloy using convergent beam electron diffraction aided by finite element calculations. Micron 43:396–406

    Article  Google Scholar 

  23. Mukherji D, Gilles R, Barbier B, Del Genovese D, Hasse B, Strunz P, Wroblewski T, Fuess H, Rösler J (2003) Lattice misfit measurement in Inconel 706 containing coherent γ′ and γ″ precipitates. Scr Mater 48:333–339

    Article  Google Scholar 

  24. Sugui T, Minggang W, Huichen Y, Xingfu Y, Tang L, Benjiang Q (2010) Influence of element Re on lattice misfits and stress rupture properties of single crystal nickel-based superalloys. Mater Sci Eng A 527:4458–4465

    Article  Google Scholar 

  25. Zenk CH, Neumeier S, Stone HJ, Göken M (2014) Mechanical properties and lattice misfit of γ/γ′ strengthened Co-base superalloys in the Co–W–Al–Ti quaternary system. Intermetallics 55:28–39

    Article  Google Scholar 

  26. Madsen C, Scarlett NVY (2008) Quantitative Phase Analysis. In: Dinnebier RE, Billinge SJL (eds) Powder diffraction theory and practice. The Royal Society of Chemistry, Cambridge, pp 298–329

    Chapter  Google Scholar 

  27. Rietveld HM (1967) Line profiles of neutron powder-diffraction peaks for structure refinement. Acta Cryst A 22:151–152

    Article  Google Scholar 

  28. Rietveld HM (1969) A profile refinement method for nuclear and magnetic structures. J Appl Cryst 2:65–71

    Article  Google Scholar 

  29. Rodriguez-Carbajal J (1993) Recent advances in magnetic structure determination by neutron powder diffraction. Phys B 192:55–69

    Article  Google Scholar 

  30. Young RA, Sakthivel A, Moss TS, Co Paiva-Santos (1995) DBWS-9411—an upgrade of the DBWS*.* programs for Rietveld refinement with PC and mainframe computers. J Appl Cryst 28:366–367

    Article  Google Scholar 

  31. Larson AC, Von Dreele RB (2004) General structure analysis system (GSAS), Los Alamos National Laboratory Report LAUR 86-748, University of California

  32. Hammond C (2009) The basic of crystallography and diffraction, 3rd edn. Oxford University Press, IUCr

    Google Scholar 

  33. Rodríguez-Carvajal J (2001) An introduction to the program FullProf 2000. Laboratoire Léon Brillouin, France

    Google Scholar 

  34. Zhan W-P, Zhang H-R, Li Q, Zhu Y-H, Feng Z-J, Gao H-H, Shen W-F, Wu P, Ding G-T, Cao M (2015) Automated method for varying the order in which parameters are refined in powder diffraction. Comput Mater Sci 107:210–215

    Article  Google Scholar 

  35. Ferreirós PA, Alonso PR, Rubiolo GH (2017) Coarsening process and precipitation hardening in Fe2AlV-strengthened ferritic Fe76Al12V12 alloy. Mater Sci Eng, A 684:394–405

    Article  Google Scholar 

  36. Thompson P, Cox DE (1987) Hastings JB Rietveld refinement of Debye–Scherrer synchrotron X-ray data from Al2O3. J Appl Cryst 20:79–83

    Article  Google Scholar 

  37. Finger LW (1998) PROFVAL: functions to calculate powder-pattern peak profiles with axial divergence asymmetry. J Appl Cryst 31:111

    Article  Google Scholar 

  38. Palm M, Inden G, Thomas N (1995) The Fe–AI–Ti System. J Phase Equilib 16:209–222

    Article  Google Scholar 

  39. Vasundhara M, Srinivas V, Rao VV (2008) Evidence for cluster glass behavior in Fe2VAl Heusler alloys. Phys Rev B 78(064401):1–10

    Google Scholar 

  40. Reed RC, Rae CMF (2014) Physical metallurgy of the nickel-based superalloys. In: Laughlin DE, Hono K (eds) Physical metallurgy, vol 3, 5th edn. Elsevier, Amsterdam, pp 2215–2290

    Chapter  Google Scholar 

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Acknowledgements

The authors wish to thank Dr. Daniel Vega for the services provided by the Difracción de Rayos X Laboratory, Física de la Materia Condensada Department, Gerencia de Investigaciones y Aplicaciones, GAIyANN-CAC-CNEA. PAF was supported by a Comisión Nacional de Energía Atómica (CNEA) professional fellowship.

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Correspondence to P. A. Ferreirós.

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Ferreirós, P.A., Rubiolo, G.H. A whole pattern iterative refinement method for powder X-ray diffraction spectra of two-phase coherent alloys. J Mater Sci 53, 2802–2811 (2018). https://doi.org/10.1007/s10853-017-1682-5

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  • DOI: https://doi.org/10.1007/s10853-017-1682-5

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