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Phase-Field Simulation of the Separation Kinetics of a Nanoscale Phase in a Fe-Cr Alloy

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Abstract

The separation of a Cr-enriched nanometer-scale α′ phase can induce the embrittlement of Fe-Cr alloys at high temperature, and the separation kinetics of the α′ phase determines its spatial morphology. The quantitative kinetics of the α′ phase formed by spinodal decomposition was studied in a Fe-42 at.% Cr alloy by phase-field simulation at various aging temperatures; the temporal morphology, average particle radius, volume fraction, particle number density, and particle size distribution of α′ phase were investigated. The results indicate that the coarsening rate of the α′ phase increases with increasing aging temperature, and the particle number density shows a large slope in the coarsening stage at higher aging temperature. The particle size distribution also demonstrates faster growth and coarsening rates of the α′ phase at higher aging temperature. The mutual effects of supercooling and diffusion during phase decomposition result in a highest decomposition rate at 725 K than that of 700 and 750 K in the Fe-42 at.% Cr alloy. The simulation results of the kinetics of the Cr-enriched α′ phase provide a basic understanding of the thermal aging and morphology evolution of Fe-Cr alloys.

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References

  1. R.L. Klueh and A.T. Nelson, Ferritic/Martensitic Steels for Next-Generation Reactors, J. Nucl. Mater., 2007, 371, p 37–52

    Article  Google Scholar 

  2. S. Novy, P. Pareige, and C. Pareige, Atomic Scale Analysis and Phase Separation Understanding in a Thermally Aged Fe-20 at.% Cr Alloy, J. Nucl. Mater., 2009, 384, p 96–102

    Article  Google Scholar 

  3. K.H. Park, J.C. Lasalle, L.H. Schwartz, and M. Kato, Mechanical Properties of Spinodally Decomposed Fe-30 wt%Cr Alloys: Yield Strength and Aging Embrittlement, Acta Metall., 1986, 34, p 1853–1865

    Article  Google Scholar 

  4. T. Aoki, Y. Saito, and Y. Suwa, Kinetics of Phase Separation in Iron-Based Ternary Alloys. I. Theoretical Analysis of Phase Separation Behavior in Iron-Based Ternary Alloys, Intermetallics, 2003, 11, p 1273–1277

    Article  Google Scholar 

  5. R.M. Fisher, E.J. Dulis, and K.G. Carroll, Identification of the Precipitate Accompanying 885 F Embrittlement in Chromium Steels, Trans. AIME., 1953, 197, p 690–695

    Google Scholar 

  6. W. Xiong, P. Hedström, M. Selleby, J. Odqvist, M. Thuvander, and Q. Chen, An Improved Thermodynamic Modeling of the Fe-Cr System Down to Zero Kelvin Coupled with Key Experiments, Calphad, 2011, 35, p 355–366

    Article  Google Scholar 

  7. J.K. Sahu, U. Krupp, R.N. Ghosh, and H.J. Christ, Effect of 475 °C Embrittlement on the Mechanical Properties of Duplex Stainless Steel, Mater. Sci. Eng. A, 2009, 508, p 1–14

    Article  Google Scholar 

  8. D. Chandra and L.H. Schwartz, Mössbauer Effect Study of the 475 °C Decomposition of Fe-Cr, Metall. Trans. A, 1971, 2, p 511–519

    Article  Google Scholar 

  9. V.M. Lopez-Hirata, O. Soriano-Vargas, H.J. Rosales-Dorantes, and M.L. Saucedo-Muñoz, Phase Decomposition in an Fe-40 at.% Cr Alloy After Isothermal Aging and its Effect on Hardening, Mater. Charact., 2011, 62, p 789–792

    Article  Google Scholar 

  10. M.K. Miller, J.M. Hyde, M.G. Hetherington, A. Cerezo, G.D.W. Smith, and C.M. Elliott, Spinodal Decomposition in Fe-Cr Alloys: Experimental Study at the Atomic Level and Comparison with Computer Models—I. Introduction and Methodology, Acta Metall. Mater., 1995, 43, p 3385–3401

    Article  Google Scholar 

  11. J.M. Hyde, M.K. Miller, M.G. Hetherington, A. Cerezo, G.D.W. Smith, and C.M. Elliott, Spinodal Decomposition in Fe-Cr Alloys: Experimental Study at the Atomic Level and Comparison with Computer Models—II. Development of Domain Size and Composition Amplitude, Acta Metall. Mater., 1995, 43, p 3403–3413

    Article  Google Scholar 

  12. J.M. Hyde, M.K. Miller, M.G. Hetherington, A. Cerezo, G.D.W. Smith, and C.M. Elliott, Spinodal Decomposition in Fe-Cr alloys: Experimental Study at the Atomic Level and Comparison with Computer Models—III. Development of Morphology, Acta Metall. Mater., 1995, 43, p 3415–3426

    Article  Google Scholar 

  13. O. Senninger, E. Martínez, F. Soisson, M. Nastar, and Y. Bréchet, Atomistic Simulations of the Decomposition Kinetics in Fe-Cr Alloys: Influence of Magnetism, Acta Mater., 2014, 59, p 97–106

    Article  Google Scholar 

  14. T. Kuwajimaa, Y. Saitoa, and Y. Suwaa, Kinetics of Phase Separation in Iron-Based Ternary Alloys. II. Numerical Simulation of Phase Separation in Fe-Cr-X (X=Mo, Cu) Ternary Alloys, Intermetallics, 2003, 11, p 1279–1285

    Article  Google Scholar 

  15. B.Q. Zhu and M. Militzer, Phase-Field Modeling for Intercritical Annealing of a Dual-Phase Steel, Metall. Mater. Trans. A, 2015, 46, p 1073–1084

    Article  Google Scholar 

  16. I. Steinbach and O. Shchyglo, Phase-Field Modelling of Microstructure Evolution in Solids: Perspectives and Challenges, Curr. Opin. Solid State Mater. Sci., 2011, 15, p 87–92

    Article  Google Scholar 

  17. N. Moelans, B. Blanpain, and P. Wollants, An Introduction to Phase-Field Modeling of Microstructure Evolution, Calphad, 2008, 32, p 268–294

    Article  Google Scholar 

  18. Y. Zhong and T. Zhu, Phase-Field Modeling of Martensitic Microstructure in NiTi Shape Memory Alloys, Acta Mater., 2014, 75, p 337–347

    Article  Google Scholar 

  19. Y.S. Li, S.X. Li, and T.Y. Zhang, Effect of Dislocations on Spinodal Decomposition in Fe-Cr Alloys, J. Nucl. Mater., 2009, 395, p 120–130

    Article  Google Scholar 

  20. J.W. Cahn, On Spinodal Decomposition, Acta Metal., 1961, 9, p 795–801

    Article  Google Scholar 

  21. R.R. Mohanty, J.E. Guyer, and Y.H. Sohn, Diffusion Under Temperature Gradient: A Phase-Field Model Study, J. Appl. Phys., 2009, 106, p 034912

    Article  Google Scholar 

  22. J.O. Andersson and J. Ågren, Models for Numerical Treatment of Multicomponent Diffusion in Simple Phases, J. Appl. Phys., 1992, 72, p 1350–1355

    Article  Google Scholar 

  23. G.E. Dieter, Mechanical Metallurgy, McGraw-Hill, London, 1988

    Google Scholar 

  24. J.W. Cahn, Phase Separation by Spinodal Decomposition in Isotropic Systems, J. Chem. Phys., 1965, 42, p 93–99

    Article  Google Scholar 

  25. J.O. Andersson and B. Sundman, Thermodynamic Properties of the Cr-Fe System, Calphad, 1987, 11, p 83–92

    Article  Google Scholar 

  26. A.T. Dinsdale, SGTE Data for Pure Elements, Calphad, 1991, 15, p 317–425

    Article  Google Scholar 

  27. J.W. Cahn and J.E. Hilliard, Free Energy of a Nonuniform System. I. Interfacial Free Energy, J. Chem. Phys., 1958, 28, p 258–267

    Article  Google Scholar 

  28. A.G. Khachaturyan, Theory of Structural Transformations in Solids, Wiley, New York, 1983

    Google Scholar 

  29. S.Y. Hu and L.Q. Chen, A Phase-Field Model for Evolving Microstructures with Strong Elastic Inhomogeneity, Acta Mater., 2001, 49, p 1879–1890

    Article  Google Scholar 

  30. Y.S. Li, Y.Z. Yu, X.L. Cheng, and G. Chen, Phase Field Simulation of Precipitates Morphology with Dislocations Under Applied Stress, Mater. Sci. Eng. A, 2011, 528, p 8628–8634

    Article  Google Scholar 

  31. E.A. Brandes and G.B. Brook, Smithells Metals Reference Book, 8th ed., ASM International, Butterworth, 2004

    Google Scholar 

  32. D.J. Dever, Temperature Dependence of the Elastic Constants in α-iron Single Crystals: Relationship to Spin Order and Diffusion Anomalies, J. Appl. Phys., 1972, 43, p 3293–3301

    Article  Google Scholar 

  33. K.W. Katahara, M. Nimalendran, M.H. Manghnani, and E.S. Fisher, Elastic Moduli of Paramagnetic Chromium and Ti-V-Cr alloys, J. Phys. F, 1979, 9, p 2167–2176

    Article  Google Scholar 

  34. L.Q. Chen and J. Shen, Applications of Semi-implicit Fourier-Spectral Method to Phase Field Equations, Comput. Phys. Commun., 1998, 108, p 147–158

    Article  Google Scholar 

  35. T. Ujihara and K. Osamura, Kinetic Analysis of Spinodal Decomposition Process in Fe-Cr Alloys by Small Angle Neutron Scattering, Acta Mater., 2000, 48, p 1629–1637

    Article  Google Scholar 

  36. I.M. Lifshitz and V.V. Slyosov, The Kinetics of Precipitation from Supersaturated Solid Solutions, J. Phys. Chem. Solids, 1961, 19, p 35–50

    Article  Google Scholar 

  37. H.A. Calderon, P.W. Voorhees, J.L. Murray, and G. Kostorz, Ostwald Ripening in Concentrated Alloys, Acta Metall. Mater., 1994, 42, p 991–1000

    Article  Google Scholar 

  38. A. Baldan, Review Progress in Ostwald Ripening Theories and Their Applications to Nickel-Base Superalloys-Part I: Ostwald Ripening Theories, J. Mater. Sci., 2002, 37, p 2171–2202

    Article  Google Scholar 

  39. O. Soriano-Vargas, E.O. Avila-Davila, V.M. Lopez-Hirata, N. Cayetano-Castro, and J.L. Gonzalez-Velazquez, Effect of Spinodal Decomposition on the Mechanical Behavior of Fe-Cr Alloys, Mater. Sci. Eng. A, 2010, 527, p 2910–2914

    Article  Google Scholar 

  40. G. Kostorz, Phase Transformations in Materials, Wiley-VCH, New York, 2001

    Book  Google Scholar 

  41. S.S. Brenner, M.K. Miller, and W.A. Soffa, Spinodal Decomposition of Iron-32 at.% Chromium at 470 °C, Scr. Metall., 1982, 16, p 831–836

    Article  Google Scholar 

  42. P. Hedström, S. Baghsheikhi, P. Liu, and J. Odqvist, A Phase-Field and Electron Microscopy Study of Phase Separation in Fe-Cr Alloys, Mater. Sci. Eng. A, 2012, 534, p 552–556

    Article  Google Scholar 

  43. A.V. Danilychev and V.A. Apkarian, Temperature Induced Mobility and Recombination of Atomic Oxygen in Crystalline Kr and Xe. I. Experiment, J. Chem. Phys., 1993, 99, p 8617–8627

    Article  Google Scholar 

Download references

Acknowledgment

The authors acknowledge the financial support by the National Natural Science Foundation of China (No. 51571122), the Fundamental Research Funds for the Central Universities (No. 30920130121012), and the Graduate Innovation Project of Jiangsu Province (No. SJLX_0157).

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Authors and Affiliations

  1. School of Materials Science and Engineering, Nanjing University of Science and Technology, Nanjing, People’s Republic of China

    Wei Liu, Yongsheng Li, Xingchao Wu, Zhiyuan Hou & Kai Hu

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  1. Wei Liu
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  2. Yongsheng Li
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Correspondence to Yongsheng Li.

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Liu, W., Li, Y., Wu, X. et al. Phase-Field Simulation of the Separation Kinetics of a Nanoscale Phase in a Fe-Cr Alloy. J. of Materi Eng and Perform 25, 1924–1930 (2016). https://doi.org/10.1007/s11665-016-2022-7

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  • DOI: https://doi.org/10.1007/s11665-016-2022-7

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