Issues $\rightarrow$ Volume 25, Issue 1 (2024)

Precipitation of the Secondary Phase in Commercial Zirconium Alloys at Neutron Irradiation

KHARCHENKO D.O.$^{1}$, KHARCHENKO V.O.$^{1,2}$, SHCHOKOTOVA O.M.$^{1}$, KUPRIIENKO V.V.$^{1}$, LYSENKO O.B.$^{1}$, and KOKHAN S.V.$^{1}$

$^1$Institute of Applied Physics of the N.A.S. of Ukraine, 58 Petropavlivska Str., UA-40000 Sumy, Ukraine
$^2$Sumy State University, 2 Rymskogo-Korsakova Str., UA-40007 Sumy, Ukraine

Received 27.10.2023, final version 04.02.2024 Download PDF logo PDF

Abstract
The work deals with the study of secondary-phase precipitation in binary and ternary zirconium-based alloys with extra-small content of doping within the framework of the phase-field approach. Developed phase-field model is applied to study β-phase precipitation in the model system of commercial Zr–Nb–Sn and Zr–Nb alloys at thermal treatment. An analysis of local rearrangement of doping and equilibrium vacancies during precipitation is provided. Kinetics of precipitation, size and distribution of the precipitates, concentration of the species in precipitates and matrix are studied. Mechanical response including the plastic deformations in precipitated solid is discussed. As shown, the yield-strength change increases during precipitation. Yield and ultimate strength are studied at different shear rates for the annealed alloy. Formation and growth of slip planes and dislocation loop–precipitate interaction governed by elastic-moduli difference is analysed. As shown, the emergence of dislocation loops around precipitates follows the Orowan’s mechanism. Modelling the radiation-induced precipitation during neutron irradiation of zirconium alloys with low content of doping is performed within the framework of the developed phase-field model by taking into account ballistic mixing and the dynamics of point defects with their sinks. As shown, in a sample initially containing precipitates of the secondary phase, irradiation results in the dissolution of precipitates at small doses and reprecipitation with dose accumulation. Analysis of precipitation dynamics and statistical distributions of precipitates with local rearrangement of non-equilibrium vacancies around precipitates at neutron irradiation is provided. As shown, the competition between the ballistic mixing and the thermodynamic force plays a major role in kinetics of radiation-induced precipitation and precipitates’ dissolution. The estimation of mechanical properties of Zr–Nb alloy during irradiation under reactor conditions is provided.

Keywords: phase field, precipitation, neutron irradiation, defects, hardening.

DOI: https://doi.org/10.15407/ufm.25.01.027

Citation: D.O. Kharchenko, V.O. Kharchenko, O.M. Shchokotova, V.V. Kupriienko, O.B. Lysenko, and S.V. Kokhan, Modelling Precipitation of the Secondary Phase in Commercial Zirconium Alloys at Neutron Irradiation, Progress in Physics of Metals, 25, No. 1: 27–73 (2024)

References  
  1. Y. H. Jeong, K. O. Lee, and H. G. Kim, J. Nucl. Mater., 302, Iss. 1: 9 (2002). https://doi.org/10.1016/S0022-3115(02)00703-1
  2. H. G. Kim, J. Y. Park, and Y. H. Jeong, J. Nucl. Mater., 347, Iss. 1–2: 140 (2005). https://doi.org/10.1016/j.jnucmat.2005.08.008
  3. P. Cirimello, G. Domizzi, and R. Haddad, J. Nucl. Mater., 350, Iss. 2: 135 (2006). https://doi.org/10.1016/j.jnucmat.2005.12.002
  4. C. P. Ramos, M. S. Granovsky, and C. Saragovi, Physica B, 389, Iss. 1: 67 (2007). https://doi.org/10.1016/j.physb.2006.07.026
  5. G. Choudhuri, Jagannath, M. K. Kumar, V. Kain, D. Srivastava, S. Basu, B. K. Shah, N. Saibaba, and G. K. Dey, J. Nucl. Mater., 441, Iss. 1–3: 178 (2013). https://doi.org/10.1016/j.jnucmat.2013.05.026
  6. M. Ito, K. Ko, H. Muta, M. Uno, and S. Yamanaka, J. Alloys Compd., 446: 451 (2007). https://doi.org/10.1016/j.jallcom.2007.01.084
  7. T. Toyama, Y. Matsukawa, K. Saito, Y. Satoh, H. Abe, Y. Shinohara, and Y. Nagai, Scr. Mater., 108: 156 (2015). https://doi.org/10.1016/j.scriptamat.2015.07.005
  8. V. N. Shishov, M. M. Peregud, A. V. Nikulina, Y. V. Pimenov, G. P. Kobylyansky, A. E. Novoselov, Z. E. Ostrovsky, and A. V. Obukhov, J. ASTM Int., 2, Iss. 8: JAI12431 (2005). https://doi.org/10.1520/JAI12431
  9. S. Doriot, D. Gilbon, J. L. Béchade, M. H. Mathon, L. Legras, and J. P. Mardon, J. ASTM Int., 2, Iss.7: JAI12332 (2005). https://doi.org/10.1520/JAI12332
  10. V. N. Shishov, A. V. Nikulina, V. A. Markelov, M. M. Peregud, A. V. Kozlov, S. A. Averin, S. A. Kolbenkow, and A. E. Novoselov, Zirconium in the Nuclear Industry: 11th Int. Symp. (Eds. E. R. Bradley and G. P. Sabol) (West Conshohocken, PA: ASTM STP: 1996), vol. 1295, p. 603. https://doi.org/10.1520/STP16192S
  11. C. D. Cann, C. B. So, R. C. Styles, and C. E. Coleman, J. Nucl. Mater., 205: 267 (1993). https://doi.org/10.1016/0022-3115(93)90089-H
  12. F. Onimus and J. L. Béchade, Comprehensive Nuclear Materials (Ed. R. J. M. Konings) (Oxford: Elsevier: 2012), vol. 4, p. 1. https://doi.org/10.1016/B978-0-08-056033-5.00064-1
  13. G. He, J. Liu, K. Li, J. Hu, A. H. Mir, S. Lozano-Perez, and C. Grovenor, J. Nucl. Mater., 526: 151738 (2019). https://doi.org/10.1016/j.jnucmat.2019.151738
  14. Q. Dong, Z. Yao, Q. Wang, H. Yu, M. A. Kirk, and M. R. Daymond, Metals, 7, Iss. 8: 287 (2017). https://doi.org/10.3390/met7080287
  15. T. Andersson and G. Vesterlund, Zirconium in the Nuclear Industry: 5th Int. Symp. (Philadelphia: ASTM STP: 1982), vol. 754, p. 75.
  16. T. Andersson and T. Thorvaldsson, Zirconium in the Nuclear Industry: 7th Int. Symp. (Eds. R. B. Adamson and L. F. P. Van Swam) (Philadelphia: ASTM STP: 1987), vol. 939, p. 321. https://doi.org/10.1520/STP28131S
  17. B. Cheng and R. B. Adamson, Zirconium in the Nuclear Industry: 7th Int. Symp. (Eds. R. B. Adamson and L. F. P. Van Swam) (Philadelphia: ASTM STP: 1987), vol. 939, p. 387. https://doi.org/10.1520/STP28134S
  18. R. M. Kruger, R. B. Adamson, and S. S. Brenner, J. Nucl. Mater., 189, Iss. 2: 193 (1992). https://doi.org/10.1016/0022-3115(92)90532-P
  19. T. Kubo and M. Uno, Zirconium in the Nuclear Industry: 9th Int. Symp. (Eds. C. M. Eucken and A. M. Garde) (Philadelphia: ASTM STP: 1991), vol. 1132, p. 476. https://doi.org/10.1520/STP25523S
  20. G. Maussner, E. Steinberg, and E. Tenckhoff, Zirconium in the Nuclear Industry: 7th Int. Symp. (Eds. R. B. Adamson and L. F. P. Van Swam) (Philadelphia: ASTM STP: 1987), vol. 939, p. 307. https://doi.org/10.1520/STP28130S
  21. R. Krishnan and M. K. Asundi, Proc. Indian Acad. Sci. (Eng. Sci.), 4: 41 (1981). https://doi.org/10.1007/BF02843474
  22. S. C. Lumley, S. T. Murphy, P. A. Burr, R. W. Grimes, P. R. Chard-Tuckey, and M. R. Wenman, J. Nucl. Mater., 437, Iss. 1–3: 122 (2013). https://doi.org/10.1016/j.jnucmat.2013.01.335
  23. L. Wu, V. O. Kharchenko, D. O. Kharchenko, and R. Pan, Mater. Today Commun., 26: 101765 (2021). https://doi.org/10.1016/j.mtcomm.2020.101765
  24. Z. Yu, X. Xu, A. Mansoor, B. Du, K. Shi, K. Liu, S. Li, and W. Du, J. Mater. Sci. Technol., 88: 21 (2021). https://doi.org/10.1016/j.jmst.2021.01.070
  25. R. Liu, D. L. Yin, and J. T. Wang, Magnesium Technology 2012 (Eds. S. N. Mathaudhu, W. H. Sillekens, N. R. Neelameggham, and N. Hort) (Cham: Springer: 2012), p. 555. https://doi.org/10.1007/978-3-319-48203-3_98
  26. W. Cai, J. Zhang, Z. Y. Gao, and J. H. Sui, Appl. Phys. Lett., 92: 252502 (2008). https://doi.org/10.1063/1.2943661
  27. J. W. Cahn, Acta Metall., 9: 795 (1961). https://doi.org/10.1016/0001-6160(61)90182-1
  28. J. W. Cahn, Acta Metall., 10: 179 (1962). https://doi.org/10.1016/0001-6160(62)90114-1
  29. J. W. Cahn and J. E. Hilliard, Acta Metall., 19: 151 (1971). https://doi.org/10.1016/0001-6160(71)90127-1
  30. A. G. Khachaturyan, Theory of Structural Transformations in Solids (Courier Corporation: 2013).
  31. L. Q. Chen, Acta Metall. Mater., 42, Iss. 10: 3503 (1994). https://doi.org/10.1016/0956-7151(94)90482-0
  32. S. G. Kim, W. T. Kim, and T. Suzuki, Phys. Rev. E, 60: 7186 (1999). https://doi.org/10.1103/PhysRevE.60.7186
  33. L. Q. Chen, Annu. Rev. Mater. Res., 32: 113 (2002). https://doi.org/10.1146/annurev.matsci.32.112001.132041
  34. N. Moelans, B. Blanpain, and P. Wollants, CALPHAD, 32, Iss. 2: 268 (2008). https://doi.org/10.1016/j.calphad.2007.11.003
  35. K. Wu, S. Chen, F. Zhang, and Y. A. Chang, J. Phase Equilib. Diffus., 30: 571 (2009). https://doi.org/10.1007/s11669-009-9567-1
  36. I. Loginova, J. Odqvist, G. Amberg, and J. Agren, Acta Mater., 51, Iss. 5: 1327 (2003). https://doi.org/10.1016/S1359-6454(02)00527-X
  37. G. Choudhuri, S. Chakraborty, D. Srivastava, and G. K. Dey, Results in Physics, 3: 7 (2013). https://doi.org/10.1016/j.rinp.2012.12.003
  38. G. S. Was, Fundamentals of Radiation Materials Science (Berlin–Heidelberg: Springer-Verlag: 2007).
  39. K. Nuttall and D. Faulkner, J. Nucl. Mater., 67, Iss. 1–2: 131 (1977). https://doi.org/10.1016/0022-3115(77)90169-6
  40. R. M. Kruger and R. B. Adamson, J. Nucl. Mater., 205: 242 (1993). https://doi.org/10.1016/0022-3115(93)90086-E
  41. V. Perovic, A. Perovic, G. C. Weatherly, and G. R. Purdy, J. Nucl. Mater., 224, Iss. 1: 93 (1995). https://doi.org/10.1016/0022-3115(95)00044-5
  42. C. E. Coleman, R. W. Gilbert, G. J. C. Carpenter, and G. C. Weatherly, Proc. Phase Stability during Irradiation Symp. (Eds. J. R. Holland, L. K. Mansur, and D. I. Potter) (New York: The Metallurgical Society of AIME: 1981), p. 587.
  43. Q. Dong, H. Yu, Z. Yao, F. Long, L. Balogh, and M. R. Daymond, J. Nucl. Mater., 481: 153 (2016). https://doi.org/10.1016/j.jnucmat.2016.09.017
  44. V. F. Urbanic and M. Griffiths, Zirconium in the Nuclear Industry: 12th Int. Symp. (Eds. G. P. Sabol and G. D. Moan) (Philadelphia: ASTM STP: 2000), vol. 1354, p. 641. https://doi.org/10.1520/STP14321S
  45. C. Song, CNL Nuclear Review, 5, Iss. 1: 17 (2016). https://doi.org/10.12943/cnr.2016.00010
  46. G. Monnet, Philos. Mag., 86, Iss. 36: 5927 (2006). https://doi.org/10.1080/14786430600860985
  47. J. Ribis, Comprehensive Nuclear Materials (2nd Ed.) (Eds. R. J. M. Konings and R. E. Stoller) (Oxford: Elsevier: 2020), vol. 1, p. 265. https://doi.org/10.1016/B978-0-12-803581-8.11647-9
  48. P. Bellon, Comprehensive Nuclear Materials (Ed. R. J. M. Konings) (Oxford: Elsevier: 2012), vol. 1, p. 411. https://doi.org/10.1016/B978-0-08-056033-5.00031-8
  49. D. O. Kharchenko, V. O. Kharchenko, I. O. Lysenko, and I. A. Shuda, Physica A, 486: 497 (2017). https://doi.org/10.1016/j.physa.2017.05.053
  50. D. O. Kharchenko, V. O. Kharchenko, Y. M. Ovcharenko, O. B. Lysenko, I. A. Shuda, L. Wu, and R. Pan, Condens. Matter. Phys., 21, No. 1: 13002 (2018). https://doi.org/10.5488/CMP.21.13002
  51. D. O. Kharchenko, V. O. Kharchenko, A. I. Bashtova, V. V. Kupriienko, and L. Wu, J. Appl. Phys., 129: 035104 (2021). https://doi.org/10.1063/5.0031917
  52. S. Rokkam, A. El-Azab, P. Millett, and D. Wolf, Modelling Simul. Mater. Sci. Eng., 17: 064002 (2009). https://doi.org/10.1088/0965-0393/17/6/064002
  53. D. O. Kharchenko and V. O. Kharchenko, Radiat. Eff. Defects Solids, 171, Iss. 11–12: 819 (2016). https://doi.org/10.1080/10420150.2016.1274753
  54. Y. Li, S. Hu, X. Sun, and M. Stan, npj Comput. Mater., 3: 16 (2017). https://doi.org/10.1038/s41524-017-0018-y
  55. M. R. Tonks, A. Cheniour, and L. Aagesen, Comput. Mater. Sci., 147: 353 (2018). https://doi.org/10.1016/j.commatsci.2018.02.007
  56. M. R. Tonks and L. K. Aagesen, Annu. Rev. Mater. Res., 49: 79 (2019). https://doi.org/10.1146/annurev-matsci-070218-010151
  57. D. O. Kharchenko, O. M. Shchokotova, V. O. Kharchenko, V. V. Kupriienko, S. V. Kokhan, X. Wu, and L. Wu, Radiat. Eff. Defects Solids, 175, Iss. 7–8: 602 (2020). https://doi.org/10.1080/10420150.2019.1684918
  58. A. Onuki, Phase Transition Dynamics (Cambridge : Cambridge University Press: 2002). https://doi.org/10.1017/CBO9780511534874
  59. A. Basak and V. I. Levitas, Acta Mater., 189: 255 (2020). https://doi.org/10.1016/j.actamat.2020.02.047
  60. A. Basak and V. I. Levitas, Comput. Meth. Appl. Mech. Eng., 343: 368 (2019). https://doi.org/10.1016/j.cma.2018.08.006
  61. N. Saunders and A. P. Miodownik, CALPHAD (Calculation of Phase Diagrams): A Comprehensive Guide, Pergamon Materials Series (Ed. R. W. Cahn) (Oxford: Pergamon: 1998), vol. 1.
  62. A. T. Dinsdale, Calphad, 15, Iss. 4: 317 (1991). https://doi.org/10.1016/0364-5916(91)90030-N
  63. Y. Li, S. Hu, C. H. Henager, H. Deng, F. Gao, X. Sun, and M. A. Khaleel, J. Nucl. Mater., 427, Iss. 1–3: 259 (2012). https://doi.org/10.1016/j.jnucmat.2012.05.004
  64. P. C. Millett, S. Rokkam, A. El-Azab, M. Tonks, and D. Wolf, Modelling Simul. Mater. Sci. Eng., 17: 064003 (2009). https://dx.doi.org/10.1088/0965-0393/17/6/064003
  65. Y. H. Wang, D. C. Zhang, Z. P. Pi, J. G. Lin, and C. Wen, J. Appl. Phys., 126: 085102 (2019). https://doi.org/10.1063/1.5096820
  66. S. B. Biner, Programming Phase-Field Modeling (Cham: Springer: 2017). https://doi.org/10.1007/978-3-319-41196-5
  67. S. I. Golubov, A. V. Barashev, and R. E. Stoller, Comprehensive Nuclear Materials (Ed. R. J. M. Konings) (Oxford: Elsevier: 2012), vol. 1, p. 357. https://doi.org/10.1016/B978-0-08-056033-5.00029-X
  68. A. V. Barashev, S. I. Golubov, and R. E. Stoller, J. Nucl. Mater., 461: 85 (2015). https://doi.org/10.1016/j.jnucmat.2015.02.001
  69. A. Patra, C. N. Tomé, and S. I. Golubov, Philos. Mag., 97, Iss. 23: 2018 (2017). https://doi.org/10.1080/14786435.2017.1324648
  70. R. A. Enrique and P. Bellon, Phys. Rev. Lett., 84: 2885 (2000). https://doi.org/10.1103/PhysRevLett.84.2885
  71. R. A. Enrique and P. Bellon, Phys. Rev. B, 63: 134111 (2001). https://doi.org/10.1103/PhysRevB.63.134111
  72. R. A. Enrique, K. Nordlund, R. S. Averback, and P. Bellon, J. Appl. Phys., 93: 2917 (2003). https://doi.org/10.1063/1.1540743
  73. R. A. Enrique and P. Bellon, Phys. Rev. B, 70: 224106 (2004). https://doi.org/10.1103/PhysRevB.70.224106
  74. G. Demange, L. Luneville, V. Pontikis, and D. Simeone, J. Appl. Phys., 121: 125108 (2017). https://doi.org/10.1063/1.4978964
  75. V. O. Kharchenko, T. Xin, L. Wu, D. O. Kharchenko, V. V. Kupriienko, and I. O. Shuda, Modelling Simul. Mater. Sci. Eng., 30: 075006 (2022). https://doi.org/10.1088/1361-651X/ac8fad
  76. V. O. Kharchenko, X. Kong, T. Xin, L. Wu, O. M. Shchokotova, D. O. Kharchenko, and S. V. Kokhan, Phys. Scr., 98, No. 3: 035714 (2023). https://doi.org/10.1088/1402-4896/acbcf9
  77. V. Kharchenko, D. Kharchenko, V. Kupriienko, S. Kokhan, T. Xin, and L. Wu, Proc. 2022 IEEE 12th Int. Conf. Nanomaterials: App. & Prop. (NAP) (Sep. 11–16, 2022, Krakow, Poland) (IEEE: 2022), p. 1. https://doi.org/10.1109/NAP55339.2022.9934767
  78. P. C. Hohenberg and B. I. Halperin, Rev. Mod. Phys., 49: 435 (1977). https://doi.org/10.1103/RevModPhys.49.435
  79. J. D. Gunton, M. S. Miguel, and P. Sahni, Phase Transitions and Critical Phenomena (Eds. C. Domb and J. L. Lebowitz) (New York: Academic Press: 1983), vol. 8, p. 267.
  80. Y. Wang, L. Q. Chen, and A. G. Khachaturyan, Computer Simulation in Materials Science Nano/Meso/Macroscopic Space & Time Scales (Eds. H. O. Kirchner, K. P. Kubin, and V. Pontikis) (Dordrecht, the Netherlands: Kluwer Academic Publishers: 1996), p. 325.
  81. Y. Wang and L. Q. Chen, Methods in Materials Research (Ed. E. N. Kaufmann) (New York: Wiley: 2000), p. 2a.3.1.
  82. K. Wu, J. E. Morral, and Y. Wang, Acta Mater., 49, Iss. 17: 3401 (2001). https://doi.org/10.1016/S1359-6454(01)00257-9
  83. C. Huang, M. O. de La Cruz, and B. W. Swift, Macromolecules, 28: 7996 (1995). https://doi.org/10.1021/ma00128a005
  84. A. A. Turkin and A. S. Bakai, J. Nucl. Mater., 358, Iss. 1: 10 (2006). https://doi.org/10.1016/j.jnucmat.2006.05.054
  85. R. R. Mohanty, J. E. Guyer, and Y. H. Sohn, J. Appl. Phys., 106: 034912 (2009). https://doi.org/10.1063/1.3190607
  86. M. J. Norgett, M. T. Robinson, and I. M. Torrens, Nucl. Eng. Des., 33, Iss. 1: 50 (1975). https://doi.org/10.1016/0029-5493(75)90035-7
  87. J. H. Ke, E. R. Reese, E. A. Marquis, G. R. Odette, and D. Morgan, Acta Mater., 164: 586 (2019). https://doi.org/10.1016/j.actamat.2018.10.063
  88. F. Kh. Mirzoev, V. Ya. Panchenko, and L. A. Shelepin, Phys.-Usp., 39: 1 (1996). https://doi.org/10.1070/pu1996v039n01abeh000125
  89. D. O. Kharchenko, V. O. Kharchenko, A. I. Bashtova, and I. O. Lysenko, Physica A, 463: 152 (2016). https://doi.org/10.1016/j.physa.2016.07.019
  90. G. J. C. Carpenter, R. H. Zee, and A. Rogerson, J. Nucl. Mater., 159: 86 (1988). https://doi.org/10.1016/0022-3115(88)90087-6
  91. A. Jostsons, P. M. Kelly, R. G. Blake, and K. Farrell, Effects of Radiation on Structural Materials (Eds. J. A. Sprague and D. Kramer) (ASTM STP: 1979), p. 46. https://doi.org/10.1520/STP38157S
  92. S. R. MacEwen and G. J. C. Carpenter, J. Nucl. Mater., 90, Iss. 1–3: 108 (1980). https://doi.org/10.1016/0022-3115(80)90249-4
  93. L. Q. Chen and J. Shen, Comput. Phys. Commun., 108, Iss. 2–3: 147 (1998). https://doi.org/10.1016/S0010-4655(97)00115-X
  94. J. I. Ramos and C. Canuto, Applied Mathematical Modelling (New York: Springer-Verlag: 1988).
  95. T. Korhonen, M. J. Puska, and R. M. Nieminen, Phys. Rev. B, 51, Iss. 15: 9526 (1995). https://doi.org/10.1103/PhysRevB.51.9526
  96. F. Legrain and S. Manzhos, AIP Adv., 6, Iss. 4: 045116 (2016). https://doi.org/10.1063/1.4948434
  97. W. G. Wolfer, Comprehensive Nuclear Materials (Ed. R. J. M. Konings) (Oxford: Elsevier: 2012), vol. 1, p. 1. https://doi.org/10.1016/B978-0-08-056033-5.00001-X
  98. E. S. Fisher and C. J. Renken, Phys. Rev., 135: A482 (1964). https://doi.org/10.1103/PhysRev.135.A482
  99. Y. J. Hao, L. Zhang, X. R. Chen, Y. H. Li, and H. L. He, J. Phys.: Condens. Matter., 20: 235230 (2008). https://doi.org/10.1088/0953-8984/20/23/235230
  100. G. Simmons and H. Wang, Single Crystal Elastic Constants and Calculated Aggregate Properties: A Handbook (Cambridge: MIT Press: 1971).
  101. S. N. Vaboya and G. C. Kennedy, J. Phys. Chem. Solids, 31, Iss. 10: 2329 (1970). https://doi.org/10.1016/0022-3697(70)90247-7
  102. P. F. Weck, E. Kim, V. Tikare, and J. A. Mitchell, Dalton Trans., 44: 18769 (2015). https://doi.org/10.1039/C5DT03403E
  103. A. C. P. Jain, P. A. Burr, and D. R. Trinkle, Phys. Rev. Materials, 3: 033402 (2019). https://doi.org/10.1103/PhysRevMaterials.3.033402
  104. F. Christien and A. Barbu, J. Nucl. Mater., 346, Iss. 2–3: 272 (2005). https://doi.org/10.1016/j.jnucmat.2005.06.024
  105. J. García-Ojalvo and J. M. Sancho, Noise in Spatially Extended Systems (New York: Springer: 1999). https://doi.org/10.1007/978-1-4612-1536-3
  106. B. Holmedal, Philos. Mag. Lett., 95, Iss. 12: 594 (2015). https://doi.org/10.1080/09500839.2015.1125029
  107. J. D. Robson, J. Nucl. Mater., 377, Iss. 3: 415 (2008). https://doi.org/10.1016/j.jnucmat.2008.03.016
  108. I. M. Lifshitz and V. V. Slyozov, J. Phys. Chem. Solids, 19, Iss. 1–2: 35 (1961). https://doi.org/10.1016/0022-3697(61)90054-3
  109. C. Wagner, Z. Elektrochem, 65, Iss. 7–8: 581 (1961). https://doi.org/10.1002/bbpc.19610650704
  110. W. D. Callister, Jr. and D. G. Rethwisch, Fundamentals of Materials Science and Engineering: An Integrated Approach (Wiley: 2012).
  111. D. J. Bacon, U. F. Kocks, and R. O. Scattergood, Philos. Mag., 28, Iss. 6: 1241 (1973). https://doi.org/10.1080/14786437308227997
  112. A. Lehtinen, L. Laurson, F. Granberg, K. Nordlund, and M. J. Alava, Sci. Rep., 8: 6914 (2018). https://doi.org/10.1038/s41598-018-25285-z
  113. B. Kombaiah and K. L. Murty, Metall. Mater. Trans. A, 46: 4646 (2015). https://doi.org/10.1007/s11661-015-3060-8
  114. A. Onuki, Phys. Rev. E, 68: 061502 (2003). https://doi.org/10.1103/PhysRevE.68.061502
  115. A. Minami and A. Onuki, Phys. Rev. B, 70: 184114 (2004). https://doi.org/10.1103/PhysRevB.70.184114
  116. A. Minami and A. Onuki, Phys. Rev. B, 72: 100101 (2005). https://doi.org/10.1103/PhysRevB.72.100101
  117. A. Onuki, A. Furukawa, and A. Minami, Pramana – J. Phys., 64: 661 (2005). https://doi.org/10.1007/BF02704575
  118. A. Minami and A. Onuki, Acta Mater., 55, Iss. 7: 2375 (2007). https://doi.org/10.1016/j.actamat.2006.11.030
  119. S. Y. Hu and L. Q. Chen, Acta Mater., 49, Iss. 11: 1879 (2001). https://doi.org/10.1016/S1359-6454(01)00118-5
  120. V. A. Serbenta, N. V. Skripnyak, V. A. Skripnyak, and E. G. Skripnyak, AIP Conf. Proc., 1909: 020190 (2017). https://doi.org/10.1063/1.5013871
  121. M. F. Horstemeyer, M. I. Baskes, and S. J. Plimpton, Acta Mater., 49, Iss. 20: 4363 (2001). https://doi.org/10.1016/S1359-6454(01)00149-5
  122. Z. L. Liu, X. C. You, and Z. Zhuang, Int. J. Solids Struct., 45, Iss. 13: 3674 (2008). https://doi.org/10.1016/j.ijsolstr.2007.08.032
  123. Y. Guo, Z. Zhuang, X. Y. Li, and Z. Chen, Int. J. Solids Struct., 44, Iss. 3–4: 1180 (2007). https://doi.org/10.1016/j.ijsolstr.2006.06.008
  124. W. Zhou, X. Ren, Y. Yang, Z. Tong, and L. Chen, Int. J. Adv. Manuf. Technol., 108: 1073 (2020). https://doi.org/10.1007/s00170-019-04822-8
  125. E. Schmid and W. Boas, Plasticity of Crystals (F. A. Hughes & Co.: 1950).
  126. L. M. Brown and W. M. Stobbs, Philos. Mag., 23, Iss. 185: 1185 (1971). https://doi.org/10.1080/14786437108217405
  127. J. D. Atkinson, L. M. Brown, and W. M. Stobbs, Philos. Mag., 30, Iss. 6: 1247 (1974). https://doi.org/10.1080/14786437408207280
  128. H. G. Kim, Y. H. Jeong, and T. H. Kim, J. Nucl. Mater., 326, Iss. 2–3: 125 (2004). https://doi.org/10.1016/j.jnucmat.2004.01.015
  129. A. Harte, M. Griffiths, and M. Preuss, J. Nucl. Mater., 505: 227 (2018). https://doi.org/10.1016/j.jnucmat.2018.03.030
  130. J. A. Marqusee and J. Ross, J. Chem. Phys., 80: 536 (1984). https://doi.org/10.1063/1.446427
  131. K. C. Russell, KTG/BNES Conf. Irradiation Behaviour of Fuel Cladding and Core Component Materials (Karlsruhe: 1974).
  132. R. A. Holt, A. R. Causey, N. Christodoulou, M. Griffiths, E. T. C. Ho, and C. H. Woo, Zirconium in the Nuclear Industry: 11th Int. Symp. (Eds. E. R. Bradley and G. P. Sabol) (West Conshohocken, PA: ASTM STP: 1996), vol. 1295, p. 623. https://doi.org/10.1520/STP16193S
  133. H. L. Yang, Y. Matsukawa, S. Kano, Z. G. Duan, K. Murakami, and H. Abe, J. Nucl. Mater., 481: 117 (2016). https://doi.org/10.1016/j.jnucmat.2016.09.016
  134. L. Chai, B. Luan, D. Xiao, M. Zhang, K. L. Murty, and Q. Liu, Mater. Des., 85: 296 (2015). https://doi.org/10.1016/j.matdes.2015.06.088
  135. R. C. Rau and J. Moteff, Radiat. Eff., 8, Iss. 1–2: 99 (1971). https://doi.org/10.1080/00337577108231014
  136. S. Kotrechko, V. Dubinko, N. Stetsenko, D. Terentyev, X. He, and M. Sorokin, J. Nucl. Mater., 464: 6 (2015). https://doi.org/10.1016/j.jnucmat.2015.04.014
  137. Y. Matsukawa, H. L. Yang, K. Saito, Y. Murakami, T. Maruyama, T. Iwai, K. Murakami, Y. Shinohara, T. Kido, T. Toyama, Z. Zhao, Y. F. Li, S. Kano, Y. Satoh, Y. Nagai, and H. Abe, Acta Mater., 102: 323 (2016). https://doi.org/10.1016/j.actamat.2015.09.038
  138. G. R. Odette and D. Frey, J. Nucl. Mater., 85–86: 817 (1979). https://doi.org/10.1016/0022-3115(79)90360-X
  139. L. Wu, V. O. Kharchenko, X. Kong, and D. O. Kharchenko, J. Nucl. Mater., 554: 153079 (2021). https://doi.org/10.1016/j.jnucmat.2021.153079

Creative Commons License
This work is licensed under a Creative Commons Attribution-NoDerivatives 4.0 International License
© G. V. Kurdyumov Institute for Metal Physics of the N.A.S. of Ukraine,