-
Water-side oxidative corrosion of zirconium alloy is a key problem in the design of nuclear fuel rods cladding materials in pressurised water reactors (PWRs), and its corrosion resistance is one of the main factors limiting service life. At present, Zr-Sn-Nb system alloys are still the main development direction of advanced zirconium alloys. Sn and Nb can exhibit a variety of valence states in the oxide film of the cladding and significantly affect the stability of ZrO2. However, the influence mechanism of Sn and Nb on the fraction of t-ZrO2 and the t-m phase transition is unclear. In this work, the lattice properties, formation enthalpies, and oxygen vacancy formation energy of ZrO2 under the doping conditions of Sn and Nb with different valence states are calculated based on the first-principles, and the influence mechanism of Sn and Nb on the stability of ZrO2 is revealed at an atomic scale. The results show that there is a significant difference between the effects of Sn and Nb, as well as between low-valent and high-valent elements. Sn2+ and Nb3+ cause lattice swelling to be significantly distorted , Nb5+ causes lattice to shrink, which contributes to reducing the stresses within the film, and Sn4+ leads the lattice to slightly swell. The low-valent elements all make ZrO2 less stable and are unfavourable for the stability of t-ZrO2 relative to m-ZrO2. The high-valent Nb5+and Sn4+ promote the relative stability of t-ZrO2, thus inhibiting the t-m phase transition, with Nb5+ having a significant effect and Sn4+ having a weak effect. The relative stability of t-ZrO2 increases with pressure rising in a range of 0－3.5 GPa. Compared with high-valent elements, the low-valent elements are favourable for introduing oxygen vacancies into t-ZrO2, thus stabilising the interfacial t-ZrO2 and enhancing the corrosion resistance of the cladding. By investigating the electronic structure, it is found that the oxygen vacancy formation energy is positively correlated with the magnitude of charge transfer (or degree of electron localisation) between the alloying element ion and the oxygen vacancy. These results contribute to optimizing the composition and designing the structure for corrosion resistance of zirconium alloys.
-
Keywords:
- first-principles /
- Zr-Sn-Nb alloys /
- oxide films /
- phase stability
-
图 1 锆(亚)氧化物的原胞(绿色小球代表Zr原子, 红色小球代表O原子) (a) m-ZrO2; (b) t-ZrO2; (c) h-ZrO
Figure 1. Unit cells of Zr (sub)oxides (green balls represented Zr atoms and red balls represented O atoms): (a) m-ZrO2; (b) t-ZrO2; (c) h-ZrO.
图 2 纯ZrO2或25%, 6.25%浓度的Nb5+, Sn4+掺杂后ZrO2的$ {{\Delta }}E({\mathrm{O}}x, P) $随压力的变化
Figure 2. Dependence of $ {{\Delta }}E({\mathrm{O}}x, P) $ on pressure for pure ZrO2 or ZrO2 with 25% and 6.25% Nb5+ or Sn4+ doping.
图 3 三维差分电荷密度(e/Bohr3)([001]方向观察得到, 蓝色等值面值为–0.008 e/Bohr3, 黄色等值面值为0.008 e/Bohr3) (a) t-ZrO2中Nb3+与1NN氧空位; (b) t-ZrO2中Nb5+与1NN氧空位; (c) t-ZrO2中Sn2+与1NN氧空位; (d) t-ZrO2中Sn4+与1NN氧空位
Figure 3. Three-dimensional differential charge density (e/Bohr3), observed in the [001] direction: (a) Nb3+ with 1NN-Ovac in t-ZrO2; (b) Nb5+ with 1NN-Ovac in t-ZrO2; (c) Sn2+ with 1NN-Ovac in t-ZrO2; (d) Sn4+ with 1NN-Ovac in t-ZrO2. The value of the blue isosurface is -0.008 e/Bohr3, yellow isosurface is 0.008 e/Bohr3.
图 4 二维差分电荷密度(e/Bohr3), 取自$ {M}^{x+} $-Ovac对所在的(100)面 (a) Nb3+-Ovac; (b) Nb5+-Ovac; (c) Sn2+-Ovac; (d) Sn4+-Ovac
Figure 4. Two-dimensional differential charge density(e/Bohr3), taken from the (100) plane in which $ {M}^{x+} $-Ovac is located: (a) Nb3+-Ovac; (b) Nb5+-Ovac; (c) Sn2+-Ovac; (d) Sn4+-Ovac.
图 5 电子局域函数, 取自$ {M}^{x+} $-Ovac所在的(100)面 (a) Nb3+-Ovac; (b) Nb5+-Ovac; (c) Sn2+-Ovac; (d) Sn4+-Ovac
Figure 5. Electron localization function, taken from the (100) plane in which $ {M}^{x+} $-Ovac is located: (a) Nb3+-Ovac; (b) Nb5+-Ovac; (c) Sn2+-Ovac; (d) Sn4+-Ovac.
表 1 锆(亚)氧化物的晶格常数(a, b, c)、晶胞矢量夹角(α, β, γ)及形成焓(Hf)
Table 1. Lattice constants (a, b, c), unit cell vector angles (α, β, γ) and formation enthalpy (Hf) of Zr (sub)oxides.
Phase a/Å b/Å c/Å α/(°) β/(°) γ/(°) $ {H}_{{\mathrm{f}}} $/eV Ref. m-ZrO2 5.1901 5.2441 5.3760 90.00 99.63 90.00 –3.860 This work 5.1850 5.2780 5.2860 90.00 99.65 90.00 –3.778 DFT-GGA[41] 5.0791 5.1785 5.2340 90.00 99.49 90.00 — DFT-LDA[53] 5.0930 5.1760 5.2440 90.00 99.10 90.00 — DFT-LDA[54] 5.0790 5.2080 5.3110 90.00 99.23 90.00 — Exp.[55] 5.1473 5.2088 5.3166 90.00 99.21 90.00 — Exp.[53] t-ZrO2 3.6220 3.6220 5.2733 90.00 90.00 90.00 –3.823 This work 3.6370 3.6370 5.2820 90.00 90.00 90.00 –3.743 DFT-GGA[41] 3.5780 3.5780 5.1630 90.00 90.00 90.00 — DFT-LDA[40] 3.5948 3.5948 5.1824 90.00 90.00 90.00 — Exp.[56] 3.5916 3.5916 5.1790 90.00 90.00 90.00 — Exp.[57] 3.5961 3.5961 5.1770 90.00 90.00 90.00 — Exp.[58] h-ZrO 5.3110 5.3110 3.2005 90.00 90.00 120.00 –2.975 This work 5.2850 5.2850 3.1790 90.00 90.00 120.00 — DFT-GGA[59] 5.3100 5.3100 3.2000 90.00 90.00 120.00 — Exp.[22] 
DownLoad: CSV
表 2 12原子超胞的晶格常数(a, b, c)、基矢夹角(α, β, γ), ZrO2单元平均体积(V), $ {M}^{x+} $掺杂超胞体积的变化(ΔV)
Table 2. Lattice constants (a, b, c), basis vector angles (α, β, γ), average volume of ZrO2 unit (V) of the 12-atom supercell, and the volume change (ΔV) of supercell with $ {M}^{x+} $ doping.
Phase a/Å b/Å c/Å α/(°) β/(°) γ/(°) V/Å3 ΔV/Å3 ΔV/V0/% pure phases t 3.62 3.62 5.28 90.00 90.00 90.00 34.62 — — m 5.19 5.24 5.38 90.00 99.63 90.00 36.07 — — Nb5+ doping t 3.52 3.51 5.07 90.00 90.00 90.00 31.27 –3.34 –10.69 m 4.94 5.18 5.00 90.10 96.75 89.69 31.76 –4.31 –13.56 Nb4+ doping t 3.61 3.61 5.24 90.00 90.00 90.00 34.07 –0.55 –1.61 m 5.14 5.20 5.36 89.90 100.48 89.23 35.28 –0.79 –2.23 Nb3+ doping t 3.33 4.23 7.02 90.00 90.00 90.00 49.49 14.88 30.06 m 5.32 5.30 5.52 90.14 102.46 89.71 38.02 1.95 5.14 Sn4+ doping t 3.65 3.59 5.35 90.00 90.00 90.00 35.08 0.46 1.31 m 5.20 5.16 5.47 89.62 97.14 88.22 36.41 0.34 0.93 Sn2+ doping t 4.14 3.41 7.00 90.00 90.00 90.00 49.34 14.73 29.84 m 5.80 5.90 6.18 90.26 115.55 89.93 47.77 11.70 24.48
DownLoad: CSV
表 3 $ {E}_{{\mathrm{f}}}({\mathrm{O}}x, P) $, $ {{\Delta }}E({\mathrm{O}}x, P) $的计算值, 其中浓度$ C= $$ {M}^{x+}/({{\mathrm{Z}}{\mathrm{r}}}^{4+}+{M}^{x+}) $
Table 3. Values of $ {E}_{{\mathrm{f}}}({\mathrm{O}}x, P) $ and $ {{\Delta }}E({\mathrm{O}}x, P) $. $ {C}= $$ {M}^{x+}/({{\mathrm{Z}}{\mathrm{r}}}^{4+}+{M}^{x+}) $.
Mx+ Phases C/% 25 6.25 3.125 E(Ox, 0)
/(eV·atom–1)Pure t –3.82 m –3.86 Sn4+ t –3.47 –3.74 –3.78 m –3.51 –3.77 –3.82 Sn2+ t –2.72 –3.54 –3.68 m –2.83 –3.59 –3.72 Nb5+ t –4.38 –3.96 –3.89 m –4.39 –3.98 –3.92 Nb4+ t –3.44 –3.75 –3.79 m –3.49 –3.79 –3.82 Nb3+ t –2.72 –3.54 –3.68 m –2.68 –3.60 –3.73 $ \Delta $E($ {\mathrm{O}}x $, 0)
/(meV·atom–1)Pure –36.92 Sn4+ –38.14 –33.90 –35.47 Sn2+ –115.96 –49.31 –42.26 Nb5+ –7.99 –20.81 –29.65 Nb4+ –51.89 –38.89 –38.11 Nb3+ 38.71 –60.04 –48.30
DownLoad: CSV
表 4 t-ZrO2中氧空位形成能. $ {\mathrm{O}}x $表示纯ZrO2或3.125%浓度$ {M}^{x+} $掺杂的ZrO2; $ {M}^{x+} $包括Nb3+, Nb4+, Nb5+, Sn2+, Sn4+; $ {E}_{{\mathrm{f}}}^{{1{\mathrm{N}}{\mathrm{N}}-{\mathrm{O}}}_{{\mathrm{v}}{\mathrm{a}}{\mathrm{c}}}} $, $ {E}_{{\mathrm{f}}}^{{2{\mathrm{N}}{\mathrm{N}}-{\mathrm{O}}}_{{\mathrm{v}}{\mathrm{a}}{\mathrm{c}}}} $分别表示$ {M}^{x+} $的1NN, 2NN氧空位形成能
Table 4. Oxygen vacancy formation energy in t-ZrO2. $ {\mathrm{O}}x $ represent pure ZrO2 or ZrO2 with 3.125% $ {M}^{x+} $ doping, and $ {M}^{x+}= $ Nb3+, Nb4+, Nb5+, Sn2+, Sn4+. $ {E}_{{\mathrm{f}}}^{{1{\mathrm{N}}{\mathrm{N}}-{\mathrm{O}}}_{{\mathrm{v}}{\mathrm{a}}{\mathrm{c}}}} $ and $ {E}_{{\mathrm{f}}}^{{2{\mathrm{N}}{\mathrm{N}}-{\mathrm{O}}}_{{\mathrm{v}}{\mathrm{a}}{\mathrm{c}}}} $ represent the 1NN and 2NN oxygen vacancy formation energies of $ {M}^{x+} $, respectively.
$ Ox $ Pure Nb5+ Nb4+ Nb3+ Sn4+ Sn2+ $ {E}_{{\mathrm{f}}}^{{1{\mathrm{N}}{\mathrm{N}}-{\mathrm{O}}}_{{\mathrm{v}}{\mathrm{a}}{\mathrm{c}}}} $/eV 6.353 5.771 5.691 5.252 4.474 3.905 $ {E}_{{\mathrm{f}}}^{{2{\mathrm{N}}{\mathrm{N}}-{\mathrm{O}}}_{{\mathrm{v}}{\mathrm{a}}{\mathrm{c}}}} $/eV 5.938 5.919 5.362 5.257 5.029
DownLoad: CSV
-
[1] Yuan R, Xie Y P, Li T, Xu C H, Yao M Y, Xu J X, Guo H B, Zhou B X 2021 Acta Mater. 209 116804
Google Scholar
[2] Kim T, Couet A, Kim S, Lee Y, Yoo S C, Kim J H 2020 Corros. Sci. 173 108745
Google Scholar
[3] Liu S M, Beyerlein I J, Han W Z 2020 Nat. Commun. 11 5766
Google Scholar
[4] Wei K J, Chen L, Qu Y, Zhang Y F, Jin X Y, Xue W B, Zhang J L 2018 Corros. Sci. 143 129
Google Scholar
[5] Zhou B F, Feng K Q 2018 RSC Adv. 8 26251
Google Scholar
[6] Bell B D C, Murphy S T, Burr P A, Comstock R J, Partezana J M, Grimes R W, Wenman M R 2016 Corros. Sci. 105 36
Google Scholar
[7] Nikulina A V 2004 Met. Sci. Heat Treat. 46 458
Google Scholar
[8] Ruiz-Hervias J, Simbruner K, Cristobal-Beneyto M, Perez-Gallego D, Zencker U 2021 J. Nucl. Mater. 544 152668
Google Scholar
[9] Zhang F L, Chai L J, Qi L, Wang Y Y, Wu L, Pan H C, Teng C Q, Murty K L 2023 J. Nucl. Mater. 577 154284
Google Scholar
[10] Qin W, Nam C, Li H L, Szpunar J A 2007 Acta Mater. 55 1695
Google Scholar
[11] Liao J J, Yang Z B, Qiu S Y, Peng Q, Li Z C, Zhang J S 2019 J. Nucl. Mater. 524 101
Google Scholar
[12] Motta A T, Couet A, Comstock R J 2015 Annu. Rev. Mater. Res. 45 311
Google Scholar
[13] Hillner E, Franklin D G, Smee J D 2000 J. Nucl. Mater. 278 334
Google Scholar
[14] Couet A, Motta A T, Ambard A 2015 Corros. Sci. 100 73
Google Scholar
[15] Yilmazbayhan A, Motta A T, Comstock R J, Sabol G P, Lai B, Cai Z 2004 J. Nucl. Mater. 324 6
Google Scholar
[16] Massih A R, Vesterlund G 1992 Nucl. Eng. Des. 137 57
Google Scholar
[17] Motta A T 2011 JOM 63 59
[18] Bouineau V, Bénier G, Pêcheur D, Thomazet J, Ambard A, Blat M 2010 Nucl. Technol. 170 444
Google Scholar
[19] Takagi I, Une K, Miyamura S, Kobayashi T 2011 J. Nucl. Mater. 419 339
Google Scholar
[20] Couet A, Borrel L, Liu J L, Hu J, Grovenor C 2019 Corros. Sci. 159 108134
Google Scholar
[21] Hu J, Garner A, Frankel P, Li M, Kirk M A, Lozano-Perez S, Preuss M, Grovenor C 2019 Acta Mater. 173 313
Google Scholar
[22] Liu J L, Yu H B, Karamched P, Hu J, He G Z, Goran D, Hughes G M, Wilkinson A J, Lozano-Perez S, Grovenor C R M 2019 Acta Mater. 179 328
Google Scholar
[23] Kurpaska L, Favergeon J, Lahoche L, Moulin G, Marssi M El, Roelandt J M 2013 Oxid. Met. 79 261
Google Scholar
[24] Xun G, Qingdong L, Wenqing L, Meiyi Y, Bangxin Z 2008 Rare Met. Mater. Eng. 37 1415
Google Scholar
[25] Beie H, Mitwalsky A, Garzarolli F, Ruhmann H, Sell H 1994 Zirconium in the Nuclear Industry: Tenth International Symposium (West Conshohocken, PA: ASTM International) pp615–643
[26] Barberis P 1995 J. Nucl. Mater. 226 34
Google Scholar
[27] Polatidis E, Frankel P, Wei J, Klaus M, Comstock R J, Ambard A, Lyon S, Cottis R A, Preuss M 2013 J. Nucl. Mater. 432 102
Google Scholar
[28] Bouvier P, Godlewski J, Lucazeau G 2002 J. Nucl. Mater. 300 118
Google Scholar
[29] Preuss M, Frankel P, Polatidis E, Wei J, Smith J W, Wang C, Cottis R A, Lyon S B, Lozano-Perez S, Hudson D, Ni N, Grovenor C R M, Smith G D W, Sykes J, Cerezo A, Storer S, Fitzpatrick M E 2011 16th International Symposium on Zirconium in the Nuclear Industry Chengdu, China, May 9–13, 2010
[30] Wei J, Frankel P, Polatidis E, Blat M, Ambard A, Comstock R J, Hallstadius L, Hudson D, Smith G D W, Grovenor C R M, Klaus M, Cottis R A, Lyon S, Preuss M 2013 Acta Mater. 61 4200
Google Scholar
[31] Garner A, Hu J, Harte A, Frankel P, Grovenor C, Lozano-Perez S, Preuss M 2015 Acta Mater. 99 259
Google Scholar
[32] Jeong Y H, Lee K O, Kim H G 2002 J. Nucl. Mater. 302 9
Google Scholar
[33] Jeong Y H, Kim H G, Kim T H 2003 J. Nucl. Mater. 317 1
Google Scholar
[34] Sakamoto K, Une K, Aomi M, Otsuka T, Hashizume K 2015 J. Nucl. Sci. Technol. 52 1259
Google Scholar
[35] Liao J J, Xu F, Peng Q, Yang Z B, Li Z C, Qiu S Y 2020 J. Nucl. Mater. 528 151846
Google Scholar
[36] Froideval A, Degueldre C, Segre C U, Pouchon M A, Grolimund D 2008 Corros. Sci. 50 1313
Google Scholar
[37] Hulme H, Baxter F, Babu R P, Denecke M A, Gass M, Steuwer A, Norén K, Carlson S, Preuss M 2016 Corros. Sci. 105 202
Google Scholar
[38] Sakamoto K, Une K, Aomi M, Otsuka T, Hashizume K 2015 J. Nucl. Sci. Technol. 52 1259
Google Scholar
[39] Wu J W, Xie Y P, Yao M Y, Guan S H, Zhao Y, Pan R J, Wu L, Liu Z P 2023 Phys. Chem. Chem. Phys. 25 8934
Google Scholar
[40] Zhao X S, Shang S L, Liu Z K, Shen J Y 2011 J. Nucl. Mater. 415 13
Google Scholar
[41] 赵毅, 王栋, 徐晨皓, 吴江桅, 王洋, 谢耀平 2021 上海金属 43 112
Google Scholar
Zhao Y, Wang D, Xu C H, Wu J W, Wang Y, Xie Y P 2021 Shanghai Met. 43 112
Google Scholar
[42] Kresse G, Hafner J 1993 Phys. Rev. B 47 558
Google Scholar
[43] Kresse G, Furthmüller J 1996 Comput. Mater. Sci. 6 15
Google Scholar
[44] Kresse G, Furthmüller J 1996 Phys. Rev. B 54 11169
Google Scholar
[45] Blöchl P E 1994 Phys. Rev. B 50 17953
Google Scholar
[46] Perdew J P, Burke K, Ernzerhof M 1997 Phys. Rev. Lett. 78 1396
[47] Monkhorst H J, Pack J D 1976 Phys. Rev. B 13 5188
Google Scholar
[48] Methfessel M, Paxton A T 1989 Phys. Rev. B 40 3616
Google Scholar
[49] Barbour O, Crocombette J P, Schuler T, Tupin M 2020 J. Nucl. Mater. 539 152333
Google Scholar
[50] Zhang P, Lu Y, He C H, Zhang P 2011 J. Nucl. Mater. 418 143
Google Scholar
[51] Fisher E S, Renken C J 1964 Phys. Rev. 135 A482
Google Scholar
[52] Anada H, Takeda K 1996 Zirconium in the Nuclear Industry: Eleventh International Symposium (West Conshohocken, PA: ASTM International) pp35–54
[53] Fukui H, Fujimoto M, Akahama Y, Sano-Furukawa A, Hattori T 2019 Acta Crystallogr. Sect. B Struct. Sci. Cryst. Eng. Mater. 75 742
Google Scholar
[54] Delaforce P M, Yeomans J A, Filkin N C, Wright G J, Thomson R C 2007 J. Am. Ceram. Soc. 90 918
Google Scholar
[55] Torres F J, Amigó J M, Alarcón J 2003 J. Solid State Chem. 173 40
Google Scholar
[56] Lutterotti L, Scardi P 1990 J. Appl. Crystallogr. 23 246
Google Scholar
[57] Bouvier P, Djurado E, Lucazeau G, Le Bihan T 2000 Phys. Rev. B 62 8731
Google Scholar
[58] Bondars B, Heidemane G, Grabis J, Laschke K, Boysen H, Schneider J, Frey F 1995 J. Mater. Sci. 30 1621
Google Scholar
[59] Puchala B, der Ven A 2013 Phys. Rev. B 88 94108
Google Scholar
[60] Wang C, Zinkevich M, Aldinger F 2004 Calphad 28 281
Google Scholar
[61] Chevalier P Y, Fischer E, Cheynet B 2004 Calphad 28 15
Google Scholar
[62] Schubert H, Frey F 2005 J. Eur. Ceram. Soc. 25 1597
Google Scholar
[63] Becke A D, Edgecombe K E 1990 J. Chem. Phys. 92 5397
Google Scholar
DownLoad:
Metrics
- Abstract views: 269
- PDF Downloads: 29
- Cited By: 0
