Advertisement

Journal of Phase Equilibria and Diffusion

, Volume 39, Issue 5, pp 714–723 | Cite as

The Application of CALPHAD Calculations to Uranium-Based Metallic Nuclear Fuels

  • Y. Lu
  • Q. Q. Tang
  • C. P. Wang
  • Z. S. Li
  • Y. H. Guo
  • X. J. Liu
Article

Abstract

The thermodynamic calculation and optimization on the binary and ternary systems consisting of Mo, Pu, Th, Ti, U, V and Zr used in metallic nuclear fuel are systematically reviewed. By combining the optimized systems in literatures and present assessment of U-Mo-Zr ternary system, the thermodynamic databases of U-Mo-based and U-Zr-based nuclear fuels were established based on the Calculation of Phase Diagram (CALPHAD) method. The stable phase diagrams and dynamical phase diagrams under irradiation were reviewed based on the database. As the examples for the application of the two thermodynamic databases, the effect of alloying elements on the stability of bcc (γU) phase in different ternary and multicomponent alloys were discussed, which can provide essential theoretical guidance for the design Uranium-based metallic nuclear fuels.

Keywords

CALPHAD metallic nuclear fuels phase diagram uranium-based alloy 

Notes

Acknowledgments

The authors would like to thank the financial support for this research by National Key R&D Program of China (2017YFB0702401) and the Fundamental Research Funds for the Central Universities (20720170038).

References

  1. 1.
    R. Rhodes, Carbon Emissions: More Nuclear Power can Speed CO2 Cuts, Nature, 2017, 548(7667), p 281ADSCrossRefGoogle Scholar
  2. 2.
    A.J. Koning and D. Rochman, Towards Sustainable Nuclear Energy: Putting Nuclear Physics to Work, Ann. Nucl. Energy, 2008, 35(11), p 2024-2030CrossRefGoogle Scholar
  3. 3.
    M. Salvatores, Fuel Cycle Strategies for the Sustainable Development of Nuclear Energy: The Role of Accelerator Driven Systems, Nucl. Instrum. Methods A., 2006, 562(2), p 578-584ADSCrossRefGoogle Scholar
  4. 4.
    V.P. Sinha, P.V. Hegde, G.J. Prasad, G.P. Mishra, and S. Pal, Development of High Density Uranium Compounds and Alloys as Dispersion Fuel for Research and Test Reactors, Trans. Indian Inst. Metals, 2008, 61(2–3), p 115-120CrossRefGoogle Scholar
  5. 5.
    J.O. Kellerth and A.J. Szumski, A Feasibility Study of LEU Enrichment Uranium Fuels for MNSR Conversion Using MCNP, Ann. Nucl. Energy, 2009, 36(8), p 1285-1286CrossRefGoogle Scholar
  6. 6.
    N. Saunders, M. Fahrmann, and C.J. Small, The application of CALPHAD calculations to Ni-based superalloys, Superalloys, 2000, p 803-811Google Scholar
  7. 7.
    J.C. Zhao and M.F. Henry, CALPHAD-Is It Ready for Superalloy Design?, Adv. Eng. Mater., 2010, 4(7), p 501-508CrossRefGoogle Scholar
  8. 8.
    E.A. Lass, Application of Computational Thermodynamics to the Design of a Co-Ni-Based γ′-Strengthened Superalloy, Metall. Mater. Trans. A, 2017, 48, p 2443-2459CrossRefGoogle Scholar
  9. 9.
    A. Danon and C. Servant, Contribution to a Thermodynamic Database and Phase Equilibria Calculations for Low Activation Ta-Containing Steels, J. Nucl. Mater., 2003, 321(1), p 8-18ADSCrossRefGoogle Scholar
  10. 10.
    Y. Yang and J.T. Busby, Thermodynamic Modeling and Kinetics Simulation of Precipitate Phases in AISI, 316 Stainless Steels, J. Nucl. Mater., 2014, 448(1–3), p 282-293ADSCrossRefGoogle Scholar
  11. 11.
    M. Hasebe, Thermodynamic Database and Materials Design for Ceramics, Ceram. Jpn., 2002, 37, p 502-508Google Scholar
  12. 12.
    P.E.A. Turchi, V. Drchal, J. Kudrnovský, C. Colinet, L. Kaufman, and Z.K. Liu, Application of Ab Initio and CALPHAD Thermodynamics to Mo-Ta-W Alloys, Phys. Rev. B, 2004, 71(9), p 4206Google Scholar
  13. 13.
    E.T. Tanaka and E.T. Iida, Application of A Thermodynamic Database to the Calculation of Surface Tension for Iron-Base Liquid Alloys, Steel Res. Int., 1994, 65(1), p 1429-1435Google Scholar
  14. 14.
    R.O. Sack and M.S. Ghiorso, Importance of Considerations of Mixing Properties in Establishing an Internally Consistent Thermodynamic Database: Thermochemistry of Minerals in the System Mg2SiO4-Fe2SiO4-SiO2, Contrib. Minerol. Petrol., 1989, 102(1), p 41-68ADSCrossRefGoogle Scholar
  15. 15.
    T.B. Lindemer, T.M. Besmann, and C.E. Johnson, Thermodynamic review and calculations—alkali-metal oxide systems with nuclear fuels, fission products, and structural materials, J. Nucl. Mater., 1981, 100(1), p 178-226ADSCrossRefGoogle Scholar
  16. 16.
    G.B. Olson and C.J. Kuehmann, Materials Genomics: From CALPHAD to Flight, Scr. Mater., 2014, 70(1), p 25-30CrossRefGoogle Scholar
  17. 17.
    L. Kaufman and J. Agren, CALPHAD, First and Second Generation-Birth of the Materials Genome, Scr. Mater., 2014, 70(10), p 3-6CrossRefGoogle Scholar
  18. 18.
    J. Ågren, The Materials Genome and CALPHAD, Sci. Bull., 2014, 59(15), p 1635-1640CrossRefGoogle Scholar
  19. 19.
    T.C. Duong and R. Arroyave, Multiscale Modeling of Discontinuous Precipitation in U-Nb, Springer, Berlin, 2015, p 481-490Google Scholar
  20. 20.
    W. Xiong, K.A. Grönhagen, J. Ågren, M. Selleby, J. Odqvist, and Q. Chen, Investigation of Spinodal Decomposition in Fe-Cr Alloys: CALPHAD Modeling and Phase Field Simulation, Solid State Phenom., 2011, 172–174, p 1060-1065CrossRefGoogle Scholar
  21. 21.
    I. Steinbach, B. Böttger, J. Eiken, N. Warnken, and S.G. Fries, CALPHAD and Phase-Field Modeling: A Successful Liaison, J. Phase Equilib., 2007, 28(1), p 101-106CrossRefGoogle Scholar
  22. 22.
    Z.K. Liu, First-Principles Calculations and CALPHAD Modeling of Thermodynamics, J. Phase Equilib., 2009, 30(5), p 517CrossRefGoogle Scholar
  23. 23.
    J. Wang, X.J. Liu, and C.P. Wang, Thermodynamic Modeling of the Al-U and Co-U Systems, J. Nucl. Mater., 2008, 374(1), p 79-86ADSCrossRefGoogle Scholar
  24. 24.
    C.P. Wang, G.C. Wang, Y. Lu, D. Wang, and X.J. Liu, Thermodynamic Assessments of the Au-Th and As-U Systems, J. Nucl. Mater., 2013, 440, p 214-219ADSCrossRefGoogle Scholar
  25. 25.
    C.P. Wang, W.J. Yu, Z.S. Li, X.J. Liu, A.T. Tang, and F.S. Pan, Thermodynamic Assessments of the Bi-U and Bi-Mn Systems, J. Nucl. Mater., 2011, 412, p 66-71ADSCrossRefGoogle Scholar
  26. 26.
    S. Chatain, C. Guéneau, D. Labroche, O. Dugne, and J. Rogez, Thermodynamic Assessment of the Fe-U Binary System, J. Phase Equilib., 2003, 24(2), p 122-131CrossRefGoogle Scholar
  27. 27.
    J. Wang, X.J. Liu, and C.P. Wang, Thermodynamic Calculation of Phase Equilibria of the U-Ga and U-W Systems, J. Nucl. Mater., 2008, 380, p 105-110ADSCrossRefGoogle Scholar
  28. 28.
    X.J. Liu, Z.S. Li, J. Wang, and C.P. Wang, Thermodynamic Modeling of the U-Mn and U-Nb Systems, J. Nucl. Mater., 2008, 380, p 99-104ADSCrossRefGoogle Scholar
  29. 29.
    C.P. Wang, Y. He, H.L. Zhang, and X.J. Liu, Thermodynamic Assessments of the U-Ni and Th-Ni Systems, J. Alloys. Compd., 2009, 487, p 126-131CrossRefGoogle Scholar
  30. 30.
    J. Wang, L.L. Jin, C.C. Chen, W.F. Rao, C.P. Wang, and X.J. Liu, Critical Evaluation and Thermodynamic Optimization of the U-Pb and U-Sb Binary Systems, J. Nucl. Mater., 2016, 480, p 216-222ADSCrossRefGoogle Scholar
  31. 31.
    M. Kurata, Thermodynamic Assessment of the Pu-U, Pu-Zr, and Pu-U-Zr Systems, Calphad, 1999, 23(3–4), p 305-337ADSCrossRefGoogle Scholar
  32. 32.
    M. Kurata, T. Ogata, K. Nakamura, and T. Ogawa, Thermodynamic assessment of the Fe-U, U-Zr and Fe-U-Zr systems, J. Alloys. Compd., 1998, 271–273(10), p 636-640CrossRefGoogle Scholar
  33. 33.
    J. Wang, Thermodynamic Assessments in the U-Based System, Master’s thesis, Xiamen University, China, 2007Google Scholar
  34. 34.
    A. Perron, P.E.A. Turchi, and A. Landa, The Pu-U-Am System: An Ab Initio, Informed CALPHAD Thermodynamic Study, J. Nucl. Mater., 2015, 458(1), p 425-441ADSCrossRefGoogle Scholar
  35. 35.
    H.A.J. Oonk, Phase theory: The thermodynamics of heterogeneous equilibria, Elsevier, Amsterdam, 1981Google Scholar
  36. 36.
    J.H. Hildebrand, Solubility. XII. Regular Solutions1, J. Am. Chem. Soc., 1929, 51(1), p 66-80CrossRefGoogle Scholar
  37. 37.
    M. Hillert and L.I. Staffansson, The Regular Solution Model for Stoichiometric Phases and Ionic Melts, Acta Chem. Scand., 1970, 24(10), p 3618-3626CrossRefGoogle Scholar
  38. 38.
    H.K. Hardy, A “Sub-Regular” Solution Model Applied to the Immiscibility Curve in Liquid Lead-Zinc Alloys, Acta Metall., 1953, 1(5), p 611-612CrossRefGoogle Scholar
  39. 39.
    B.O. Sundmanand, The Sublattice Mode, MRS. Publishing, Cambridge, 1982, p 19Google Scholar
  40. 40.
    J.W. Cahn and J.E. Hilliard, Free Energy of Nanuniform System. I. Interfacial Free Energy, J. Chem. Phys., 1958, 8(2), p 258-267ADSCrossRefGoogle Scholar
  41. 41.
    W. Li, Introduction to Nuclear Materials, Chemical Industry Press, Beijing, 2007Google Scholar
  42. 42.
    G.S. Was, Fundamentals of Radiation Materials Science, Vol 10(10), Springer, Berlin, 2007, p 52Google Scholar
  43. 43.
    G. Martin, Phase Stability Under Irradiation: Ballistic Effects, Prog. Mater Sci., 1984, 28(3), p 229-434Google Scholar
  44. 44.
    X.J. Liu, Y.L. Zhao, Y. Lu, W.W. Xu, J.P. Jia, and C.P. Wang, Steady-State Dynamical Phase Diagram Calculation of U-Nb Binary System Under Irradiation: Ballistic Effect, J. Nucl. Mater., 2014, 451(1–3), p 366-371ADSCrossRefGoogle Scholar
  45. 45.
    J.M. Roussel and P. Bellon, Self-Diffusion and Solute Diffusion in Alloys Under Irradiation: Influence of Ballistic Jumps, Phys. Rev. B, 2002, 65(14), p 144107ADSCrossRefGoogle Scholar
  46. 46.
    G.S. Was, Phase Stability Under Irradiation, Prog. Mater Sci., 1984, 28(3), p 229-434Google Scholar
  47. 47.
    N. Ravishankar, T.A. Abinandanan, and K. Chattopadhyay, Application of Effective Potential Formalism to Mechanical Alloying in Ag-Cu and Cu-Fe Systems, Mater. Sci. Eng., 2001, 304, p 413-417CrossRefGoogle Scholar
  48. 48.
    P.Y. Chevalier, E. Fischer, and B. Cheynet, Progress in the Thermodynamic Modelling of the O-U-Zr Ternary System, Cheminform, 2004, 28(1), p 15-40Google Scholar
  49. 49.
    Z.S. Li, X.J. Liu, and C.P. Wang, Thermodynamic Modeling of the Th-U, Th-Zr and Th-U-Zr Systems, J. Alloy. Compds., 2009, 476(1), p 193-198Google Scholar
  50. 50.
    C.P. Wang, Y.F. Li, X.J. Liu, and K. Ishida, Thermodynamic Assessments of the Cu-Th and Mo-Th Systems, J. Alloy. Compds., 2008, 458(1), p 208-213CrossRefGoogle Scholar
  51. 51.
    C.P. Wang and Z.S. Li, Thermodynamic Database and the Phase Diagrams of the (U, Th, Pu)-X Binary Systems, J. Phase Equilib., 2009, 30(5), p 535CrossRefGoogle Scholar
  52. 52.
    A. Landa and P.E.A. Turchi, Thermodynamic Database, Lower Length Scale (MS-12LL060209) Part I: Thermodynamic Assessment of the Ternary Alloy System Mo-Pu-U (M3MS-12LL0602091), Lawrence Livermore National Laboratory, Livermore, 2012Google Scholar
  53. 53.
    R.J. Pérez and S. Bo, Thermodynamic Assessment of the Mo-Zr Binary Phase Diagram, Calphad, 2003, 27(3), p 253-262CrossRefGoogle Scholar
  54. 54.
    O. Beneš, D. Manara, and R.J.M. Konings, Thermodynamic Assessment of the Th-U-Pu System, J. Nucl. Mater., 2014, 449(1–3), p 15-22ADSCrossRefGoogle Scholar
  55. 55.
    A. Berche, N. Dupin, C. Guéneau, C. Rado, B. Sundman, and J.C. Dumas, Calphad Thermodynamic Description of Some Binary Systems Involving U, J. Nucl. Mater., 2011, 411(1), p 131-143ADSCrossRefGoogle Scholar
  56. 56.
    A. Kostov and D. Živković, Thermodynamic Analysis of Alloys Ti-Al, Ti-V, Al-V and Ti-Al-V, J. Alloy. Compds, 2008, 460(1), p 164-171CrossRefGoogle Scholar
  57. 57.
    Y.L. Gao, C.P. Guo, and C.G. Li, Thermodynamic optimization of the Ti-Zr and Ru-Ti-Zr systems, National Phase Diagram Conference and International Symposium on Phase Diagrams and Materials Design, Shengyang, China, 2010Google Scholar
  58. 58.
    X.S. Zhao, G.H. Yuan, M.Y. Yao, Q. Yue, and J.Y. Shen, First-Principles Calculations and Thermodynamic Modeling of the V-Zr System, Calphad, 2012, 36(2), p 163-168ADSCrossRefGoogle Scholar
  59. 59.
    R. Boucher, Etude sur les alliages uranium-plutonium-molybdene, J. Nucl. Mater., 1962, 6(1), p 84-95ADSCrossRefGoogle Scholar
  60. 60.
    O.S. Ivanov, G.N. Bagrov, Isothermal Cross Sections at 600 °C, 575 °C, and 500 °C, Polythermal Sections, and the Phase Diagram of the Triple System Uranium-Molybdenum-Zirconium, Struct. Alloys Certain Syst. Cont. Uranium Thorium, 1963, p 154-176Google Scholar
  61. 61.
    B. Blumenthal, J.E. Sanecki, and D.E. Busch, Thorium-Uranium-Plutonium Alloys As Potential Fast Power-Reactor Fuels. Part I. Thorium-Uranium-Plutonium Phase Diagram, U.S. Atomic Energy Commission, Washington, 1968CrossRefGoogle Scholar
  62. 62.
    D.R. O’Boyle and A.E. Dwight, Plutonium 1970 and Other Actinides, Proceedings of 4th International Conference on Pu and Other Actinides, Santa Fe, New Mexico, 1970, 2, pp. 720–732Google Scholar
  63. 63.
    M. Kurata, Thermodynamic Database on U-Pu-Zr-Np-Am-Fe Alloy System I-Re-Evaluation of U-Pu-Zr Alloy System, IOP Conf. Ser. Mater. Sci. Eng., 2010, 9, p 012022CrossRefGoogle Scholar
  64. 64.
    T.A. Badaeva and G.K. Alekseenko, Structure of Alloys of Certain Systems Containing Uranium and Thorium, Translatied from Stroenie Splavov Nekotorykh Sistem Uranom I Toriem, 1963, p 321-357Google Scholar
  65. 65.
    B.W. Howlett, The Alloy System Uranium-Titanium-Zirconium, J. Nucl. Mater., 1959, 1(3), p 289-299ADSCrossRefGoogle Scholar
  66. 66.
    Y. Zeng, P. Zhou, Y. Du, W. Mo, B. Bai, X. Wang, and J. Zhao, A Thermodynamic Description of the U-Ti-Zr System, Calphad, 2018, 60, p 90-97CrossRefGoogle Scholar
  67. 67.
    C.P. Wang, L.Y. Lig, Y. Lu, Y.H. Guo, and X.J. Liu, University, Phase Diagram Calculation of Zr-Nb Binary Alloy Under Irradiation, J. Xiamen Univ., 2018, 2, p 194-200Google Scholar

Copyright information

© ASM International 2018

Authors and Affiliations

  1. 1.College of Materials and Fujian Provincial Key Laboratory of Materials GenomeXiamen UniversityXiamenPeople’s Republic of China
  2. 2.Department of Materials Science and EngineeringHarbin Institute of TechnologyShenzhenPeople’s Republic of China

Personalised recommendations