Abstract
Results of investigations of the self-diffusion in gamma-uranium and metallic U-Mo alloys are presented. Calculations are performed using the method of atomistic modeling with the help of interatomic potentials based on the embedded-atom model and its modifications. Proposed potentials are verified by calculating thermodynamic and mechanical properties of uranium and U-Mo alloys. The formation energies of point defects and atomic diffusivities due to the diffusion of defects are calculated for gamma-uranium and alloy containing 9 wt % molybdenum. Self-diffusion coefficients of uranium and molybdenum are evaluated. Based on the data obtained, it has been concluded that the experimentally observed features of the self-diffusion in gamma-uranium can be explained by the prevalence of the interstitial mechanism.
Similar content being viewed by others
References
V. M. Chernov, V. A. Romanov, and A. O. Krutskikh, “Atomic mechanisms and energetics of thermally activated processes of helium redistribution in vanadium,” J. Nucl. Mater. 271-272, 274–279 (1999).
B. D. Wirth, “Materials science. How does radiation damage materials?“ Science 318(5852), 923–924 (2007).
Physical Material Science, Ed. by B. A. Kalin (Mos. Inzh.-Fiz. Inst., Moscow, 2008), Vol. 6, part 2 [in Russian].
S. Starikov, Z. Insepov, J. Rest, A. Y. Kuksin, G. Norman, V. Stegailov, and A. Yanilkin, “Radiation-induced damage and evolution of defects in Mo,” Phys. Rev. B: Condens. Matter Mater. Phys. 84, 104109 (2011).
V. V. Dremov, F. A. Sapozhnikov, G. V. Ionov, A. V. Karavaev, M. A. Vorobyova, and B. W. Chung, “MD simulations of phase stability of PuGa alloys: Effects of primary radiation defects and helium bubbles,” J. Nucl. Mater. 440, 278–282 (2013).
G. D. Samolyuk, S. I. Golubov, Y. N. Osetsky, and R. E. Stoller, “Self-interstitial configurations in hcp Zr: A first principles analysis,” Philos. Mag. Lett. 93, 93–100 (2013).
E. P. Pakhomov, “Defect structure and the phase diagram of uranium dioxide,” High Temper. 51, 215–223 (2013).
Y. Adda and A. Kirianenko, “Etude de l’autodiffusion de l’uranium en phase γ,” J. Nucl. Mater. 1, 120–126 (1959).
S. J. Rothman, L. T. Lloyd, and A. L. Harkness, “Self-diffusion in γ uranium,” Trans. Metall. Soc. AIME 218, 605–612 (1960).
Y. Adda and A. Kirianenko, “Etude de l’autodiffusion de l’uranium en phase α,” J. Nucl. Mater 6, 130–134 (1962).
G. B. Fedorov and E. A. Smirnov, Diffusion in the Materials for Nuclear Reactors (Atomizdat, Moscow, 1978) [In Russian].
E. A. Smirnov and K. E. Smirnov, “Diffusion processes in bcc phases of actinides,” Preprint No. MIFI-013092 (Moscow Eng.-Phys. Inst., 1992).
Y. Liu, D. Yu, Y. Du, G. Sheng, Z. Long, J. Wang, and L. Zhang, “Atomic mobilities, diffusivities and their kinetic implications for U-X (X = Ti, Nb and Mo) bcc alloys,” Calphad 37, 49–56 (2012).
V. Sinha, P. Hegde, G. Prasad, G. Dey, and H. Kamath, “Phase transformation of metastable cubic γ-phase in UMo alloys,” J. Alloys Compd. 506, 253–262 (2010).
V. Baranov, V. Nechaev, B. Produvalov, and D. Shornikov, “Interaction of uranium-molybdenum fuel with an aluminum matrix with deep burnup,” At. Energ. 108, 349–356 (2010).
A. V. Vatulin, A. V. Morozov, V. B. Suprun, Yu. I. Petrov, and Yu. I. Trifonov, “Radiation resistance of high-density uranium-molybdenum dispersion fuel for nuclear research reactors,” At. Energ. 100, 37–46 (2006).
W. Kohn, “Electronic structure of matter-Wave functions and density functionals,” Nobel lecture, 1999. http://www.nobelprize.org/nobel-prizes/chemistry/laureates/1998/kohn-lecture.pdf
W. Xiong, W. Xie, C. Shen, and D. Morgan, “Thermodynamic modeling of the U-Zr system-A revisit,” J. Nucl. Mater. 443, 331–341 (2013).
A. V. Evteev, A. V. Levchenko, I. V. Belova, and G. E. Murch, “Molecular dynamics simulation of surface segregation diffusion and reaction phenomena in equiatomic Ni-Al systems,” Phys. Met. Metallogr. 113, 1202–1243 (2012).
S. V. Starikov, “Atomic simulation of defect formation process in uranium dioxide upon fission-fragment flight,” Teplofiz. Vys. Temper. 53(1), (2015) (in press).
A. Yu. Kuksin, A. S. Rokhmanenkov, and V. V. Stegailov, “Atomic positions and diffusion paths of H and He in the α-Ti lattice,” Phys. Solid State 55, 367–372 (2013).
I. I. Novoselov, A. Yu. Kuksin, and A. V. Yanilkin, “Diffusion coefficients of vacancies and interstitials along tilt grain boundaries in molybdenum,” Phys. Solid State 56, 1025–1032 (2014).
D. E. Smirnova, S. V. Starikov, and V. V. Stegailov, “New interatomic potential for computation of mechanical and thermodynamic properties of uranium in a wide range of pressures and temperatures,” Phys. Met. Metallogr. 113, 107–116 (2012).
D. E. Smirnova, S. V. Starikov, and V. V. Stegailov, “Interatomic potential for uranium in a wide range of pressure and temperature,” J. Phys.: Cond. Mater. 24, 015702 (2012).
D. E. Smirnova, A. Yu. Kuksin, S. V. Starikov, V. V. Stegailov, Z. Insepov, and J. Rest, “A ternary EAM interatomic potential for U-Mo alloys with xenon,” Model. Simul. Mater. Sci. Eng. 21, 035011 (2013).
B. Beeler, C. Deo, M. Baskes, and M. Okunewski, “Atomistic properties of γ uranium,” J. Phys.: Condens. Matter. 24, 075401 (2012).
A. V. Yanilkin, Z. Insepov, G. E. Norman, J. Rest, and V. Stegailov, “Atomistic simulation of clustering and annihilation of point defects in molybdenum,” Defect Diffus. Forum 323-325, 95–100 (2012).
M. S. Veshchunov, A. V. Boldyrev, V. D. Ozrin, V. E. Shestak, and V. I. Tarasov, “A new mechanistic code SFPR for modeling of single fuel rod performance under various regimes of LWR operation,” Nucl. Eng. Design 241, 2822–2830 (2011).
M. Stan, “Multi-scale models and simulations of nuclear fuels,” Nucl. Eng. Technol. 41, 39–52 (2009).
M. Daw and M. Baskes, “Embedded-atom method: Derivation and application to impurities, surfaces, and other defects in metals,” Phys. Rev. B: Condens. Matter 29, 6443–6453 (1984).
D. Schopf, P. Brommer, B. Frigan, and H.-R. Trebin, “Embedded atom method potentials for Al-Pd-Mn phases,” Phys. Rev. B: Condens. Matter Mater. Phys. 85, 054201 (2012).
H. Park, M. R. Fellinger, T. J. Lenosky, W. W. Tipton, D. R. Trinkle, S. P. Rudin, C. Woodward, J. W. Wilkins, and R. G. Hennig, “Ab initio based empirical potential used to study the mechanical properties of molybdenum,” Phys. Rev. B: Condens. Matter Mater. Phys. 85, 214121 (2012).
D. K. Belashchenko, D. E. Smirnova, and O. I. Ostrovskii, “Molecular-dynamic simulation of the thermophysical properties of liquid uranium,” High Temperature 48, 363–375 (2010).
F. Ercolessi and J. B. Adams, “Interatomic potentials from first-principles calculations: The force-matching method,” Europhys. Lett. 26, 583–588 (1994).
G. Ivanovskis, G. E. Norman, and D. R. Usmanova, “Anomalous diffusivity in ionic liquids: A molecular dynamics study,” Dokl. Phys. 57, 427–430 (2012).
H. Mehrer, Diffusion in Solids, (Intellekt, Dolgoprudnyi, 2011) [in Russian].
S. Xiang, H. Huang, and L. Hsiung, “Quantum mechanical calculations of uranium phases and niobium defects in γ-uranium,” J. Nucl. Mater. 375, 113–119 (2008).
B. Beeler, B. Good, S. Rashkeev, C. Deo, M. Baskes, and M. Okuniewski, “First principles calculations for defects in U,” J. Phys.: Condens. Matter. 22, 505703 (2010).
H. Matter, J. Winter, and W. Triftshauser, “Investigation of vacancy formation and phase transformations in uranium by positron annihilation,” J. Nucl. Mater. 88, 273–278 (1980).
K. R. Lund, K. G. Lynn, M. H. Weber, and M. A. Okuniewski, “Vacancy formation enthalpy in polycrystalline depleted uranium,” J. Phys.: Conf. Ser. 443, 01202 (2013).
A. Yu. Kuksin and D. E. Smirnova, “Calculation of diffusion coefficients of defects and ions in UO2,” Phys. Solid State 56, 1214–1223 (2014).
M. I. Mendelev and B. S. Bokstein, “Molecular dynamics study of selfdiffusion in Zr,” Philos. Mag. 90, 637–654 (2010).
Y. Adda and A. Kirianenko, “Abaissement des coeffients d’autodiffusion de l’uranium en phase γ par des additions de molybdene, de zirconium ou de niobium,” J. Nucl. Mater. 6, 135–136 (1962).
K. Huang, D. D. Keiser, Jr., and Y. Sohn, “Interdiffusion, intrinsic diffusion, atomic mobility, and vacancy wind effect in γ (bcc) uranium-molybdenum alloy,” Metall. Mater. Trans. A 44, 738–746 (2013).
Y. Mishin, M. Mehl, and D. Papaconstantopoulos, “Phase stability in the Fe-Ni system: Investigation by first-principles calculations and atomistic simulations,” Acta Mater. 53, 4029–4041 (2005).
G. Kresse, “Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set,” Phys. Rev. B: Condens. Matter 54, 11169–11186 (1996).
J. P. Perdew, J. A. Chevary, S. H. Vosko, K. A. Jakson, M. R. Pederson, D. J. Singh, and C. Fiolhais, “Atoms, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlation,” Phys. Rev. B: Condens. Matter 46, 6671–6687 (1992).
A. Dwight, “The uranium-molybdenum equilibrium diagram below 900°C,” J. Nucl. Mater. 2, 81–87 (1960).
D. Burkes, R. Prabhakaran, and J.-F. Jue, “Mechanical properties of DU-xMo alloys with x = 7 to 12 weight percent,” Metall. Mater. Trans. A 40, 1069–1079 (2009).
R. McGeary, Development and Properties of Uranium-Based Alloys Resistant to Corrosion in High-Temperature Water, SAEC Report WAPD-127-part 1, 1955.
J. Bridge, C. Schwartz, and D. Vaughan, “X-ray diffraction determination of the coefficient of expansion of alpha-uranium,” Trans. AIME 206, 160–166 (1956).
V. Sinha, G. Prasad, P. Hegde, G. Dey, and H. Kamath, “Effect of molybdenum addition on metastability of cubic γ-uranium,” J. Alloys Compd. 491, 753–760 (2010).
D. E. Burkes, C. A. Papesch, A. P. Maddison, T. Hartmann, and F. J. Rice, “Thermo-physical properties of DU-10 wt % Mo alloys,” J. Nucl. Mater. 403, 160–166 (2010).
I. Tkach, N.-T. H. Kim-Ngan, S. Maskov, M. Dzevenko, L. Havela, A. Warren, C. Stitt, and T. Scott, “Characterization of cubic-phase uranium molybdenum alloys synthesized by ultrafast cooling,” J. Alloys Compd. 534, 101–109 (2012).
T. Kutty, S. Dash, J. Banerjee, S. Kaity, A. Kumar, and C. Basak, “Thermophysical properties of U2Mo intermetallic,” J. Nucl. Mater. 420, 193–197 (2012).
J. Akella, G. S. Smith, R. Grover, Y. Wu, and S. Martin, “Static EOS of uranium to 100 GPa pressure,” High. Pres. Res. 2, 295–302 (1990).
C.-S. Yoo, H. Cynn, and P. Soderlind, “Phase diagram of uranium at high pressures and temperatures,” Phys. Rev. B: Condens. Matter Mater. Phys. 57, 10359–10362 (1998).
A. Landa, P. Soderlind, and P. Turchi, “Density-functional study of U-Mo and U-Zr alloys,” J. Nucl. Mater. 414, 132–137 (2011).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © D.E. Smirnova, A.Yu. Kuksin, S.V. Starikov, V.V. Stegailov, 2015, published in Fizika Metallov i Metallovedenie, 2015, Vol. 116, No. 5, pp. 473–483.
Rights and permissions
About this article
Cite this article
Smirnova, D.E., Kuksin, A.Y., Starikov, S.V. et al. Atomistic modeling of the self-diffusion in γ-U and γ-U-Mo. Phys. Metals Metallogr. 116, 445–455 (2015). https://doi.org/10.1134/S0031918X1503014X
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0031918X1503014X