Skip to main content
SpringerLink
Log in

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

  • Published:
Journal of Phase Equilibria and Diffusion Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  1. R. Rhodes, Carbon Emissions: More Nuclear Power can Speed CO2 Cuts, Nature, 2017, 548(7667), p 281

    Article  ADS  Google Scholar 

  2. A.J. Koning and D. Rochman, Towards Sustainable Nuclear Energy: Putting Nuclear Physics to Work, Ann. Nucl. Energy, 2008, 35(11), p 2024-2030

    Article  Google Scholar 

  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 578-584

    Article  ADS  Google Scholar 

  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 115-120

    Article  Google Scholar 

  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 1285-1286

    Article  Google Scholar 

  6. N. Saunders, M. Fahrmann, and C.J. Small, The application of CALPHAD calculations to Ni-based superalloys, Superalloys, 2000, p 803-811

  7. J.C. Zhao and M.F. Henry, CALPHAD-Is It Ready for Superalloy Design?, Adv. Eng. Mater., 2010, 4(7), p 501-508

    Article  Google Scholar 

  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 2443-2459

    Article  Google Scholar 

  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 8-18

    Article  ADS  Google Scholar 

  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 282-293

    Article  ADS  Google Scholar 

  11. M. Hasebe, Thermodynamic Database and Materials Design for Ceramics, Ceram. Jpn., 2002, 37, p 502-508

    Google Scholar 

  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 4206

    Google Scholar 

  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 1429-1435

    Google Scholar 

  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 41-68

    Article  ADS  Google Scholar 

  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 178-226

    Article  ADS  Google Scholar 

  16. G.B. Olson and C.J. Kuehmann, Materials Genomics: From CALPHAD to Flight, Scr. Mater., 2014, 70(1), p 25-30

    Article  Google Scholar 

  17. L. Kaufman and J. Agren, CALPHAD, First and Second Generation-Birth of the Materials Genome, Scr. Mater., 2014, 70(10), p 3-6

    Article  Google Scholar 

  18. J. Ågren, The Materials Genome and CALPHAD, Sci. Bull., 2014, 59(15), p 1635-1640

    Article  Google Scholar 

  19. T.C. Duong and R. Arroyave, Multiscale Modeling of Discontinuous Precipitation in U-Nb, Springer, Berlin, 2015, p 481-490

    Google Scholar 

  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 1060-1065

    Article  Google Scholar 

  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 101-106

    Article  Google Scholar 

  22. Z.K. Liu, First-Principles Calculations and CALPHAD Modeling of Thermodynamics, J. Phase Equilib., 2009, 30(5), p 517

    Article  Google Scholar 

  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 79-86

    Article  ADS  Google Scholar 

  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 214-219

    Article  ADS  Google Scholar 

  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 66-71

    Article  ADS  Google Scholar 

  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 122-131

    Article  Google Scholar 

  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 105-110

    Article  ADS  Google Scholar 

  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 99-104

    Article  ADS  Google Scholar 

  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 126-131

    Article  Google Scholar 

  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 216-222

    Article  ADS  Google Scholar 

  31. M. Kurata, Thermodynamic Assessment of the Pu-U, Pu-Zr, and Pu-U-Zr Systems, Calphad, 1999, 23(3–4), p 305-337

    Article  ADS  Google Scholar 

  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 636-640

    Article  Google Scholar 

  33. J. Wang, Thermodynamic Assessments in the U-Based System, Master’s thesis, Xiamen University, China, 2007

  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 425-441

    Article  ADS  Google Scholar 

  35. H.A.J. Oonk, Phase theory: The thermodynamics of heterogeneous equilibria, Elsevier, Amsterdam, 1981

    Google Scholar 

  36. J.H. Hildebrand, Solubility. XII. Regular Solutions1, J. Am. Chem. Soc., 1929, 51(1), p 66-80

    Article  Google Scholar 

  37. M. Hillert and L.I. Staffansson, The Regular Solution Model for Stoichiometric Phases and Ionic Melts, Acta Chem. Scand., 1970, 24(10), p 3618-3626

    Article  Google Scholar 

  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 611-612

    Article  Google Scholar 

  39. B.O. Sundmanand, The Sublattice Mode, MRS. Publishing, Cambridge, 1982, p 19

    Google Scholar 

  40. J.W. Cahn and J.E. Hilliard, Free Energy of Nanuniform System. I. Interfacial Free Energy, J. Chem. Phys., 1958, 8(2), p 258-267

    Article  ADS  Google Scholar 

  41. W. Li, Introduction to Nuclear Materials, Chemical Industry Press, Beijing, 2007

    Google Scholar 

  42. G.S. Was, Fundamentals of Radiation Materials Science, Vol 10(10), Springer, Berlin, 2007, p 52

    Google Scholar 

  43. G. Martin, Phase Stability Under Irradiation: Ballistic Effects, Prog. Mater Sci., 1984, 28(3), p 229-434

    Google Scholar 

  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 366-371

    Article  ADS  Google Scholar 

  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 144107

    Article  ADS  Google Scholar 

  46. G.S. Was, Phase Stability Under Irradiation, Prog. Mater Sci., 1984, 28(3), p 229-434

    Google Scholar 

  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 413-417

    Article  Google Scholar 

  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 15-40

    Google Scholar 

  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 193-198

    Google Scholar 

  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 208-213

    Article  Google Scholar 

  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 535

    Article  Google Scholar 

  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, 2012

    Google Scholar 

  53. R.J. Pérez and S. Bo, Thermodynamic Assessment of the Mo-Zr Binary Phase Diagram, Calphad, 2003, 27(3), p 253-262

    Article  Google Scholar 

  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 15-22

    Article  ADS  Google Scholar 

  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 131-143

    Article  ADS  Google Scholar 

  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 164-171

    Article  Google Scholar 

  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, 2010

  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 163-168

    Article  ADS  Google Scholar 

  59. R. Boucher, Etude sur les alliages uranium-plutonium-molybdene, J. Nucl. Mater., 1962, 6(1), p 84-95

    Article  ADS  Google Scholar 

  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 154-176

  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, 1968

    Book  Google Scholar 

  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. 720–732

  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 012022

    Article  Google Scholar 

  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 321-357

  65. B.W. Howlett, The Alloy System Uranium-Titanium-Zirconium, J. Nucl. Mater., 1959, 1(3), p 289-299

    Article  ADS  Google Scholar 

  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 90-97

    Article  Google Scholar 

  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 194-200

    Google Scholar 

Download references

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).

Author information

Authors and Affiliations

  1. College of Materials and Fujian Provincial Key Laboratory of Materials Genome, Xiamen University, Xiamen, People’s Republic of China

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

  2. Department of Materials Science and Engineering, Harbin Institute of Technology, Shenzhen, People’s Republic of China

    X. J. Liu

Authors
  1. Y. Lu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Q. Q. Tang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. C. P. Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Z. S. Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Y. H. Guo
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. X. J. Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to C. P. Wang or X. J. Liu.

Additional information

This invited article is part of a special issue of the Journal of Phase Equilibria and Diffusion in honor of Prof. Zhanpeng Jin’s 80th birthday. The special issue was organized by Prof. Ji-Cheng (JC) Zhao, The Ohio State University; Dr. Qing Chen, Thermo-Calc Software AB; and Prof. Yong Du, Central South University.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lu, Y., Tang, Q.Q., Wang, C.P. et al. The Application of CALPHAD Calculations to Uranium-Based Metallic Nuclear Fuels. J. Phase Equilib. Diffus. 39, 714–723 (2018). https://doi.org/10.1007/s11669-018-0677-5

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11669-018-0677-5

Keywords

Search

Navigation