First-principles study on effects of alloying elements Sn and Nb on phase stability of corrosion oxide films of zirconium alloys

Chen Tun; Cui Jie-Chao; Li Min; Chen Wen; Sun Zhi-Peng; Fu Bao-Qin; Hou Qing

doi:10.7498/aps.73.20240602

Abstract

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:

Authors and contacts

1.
Key Laboratory for Radiation Physics and Technology, Ministry of Education, Institute of Nuclear Science and Technology, Sichuan University, Chengdu 610064, China
2.
Science and Technology on Reactor System Design Technology Laboratory, Nuclear Power Institute of China, Chengdu 610200, China

Corresponding author: Fu Bao-Qin, bqfu@scu.edu.cn ; Hou Qing, qhou@scu.edu.cn

Funds: Project supported by the Science and Technology Program of Sichuan Province, China (Grant No. 2023NSFSC0044) and the Fundamental Research Funds for the Central Universities, China.

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References

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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.

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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.

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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-O_vac in t-ZrO₂; (b) Nb⁵⁺ with 1NN-O_vac in t-ZrO₂; (c) Sn²⁺ with 1NN-O_vac in t-ZrO₂; (d) Sn⁴⁺ with 1NN-O_vac in t-ZrO₂. The value of the blue isosurface is –0.008 e/Bohr³, yellow isosurface is 0.008 e/Bohr³.

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图 4 二维差分电荷密度(e/Bohr³), 取自$ {M}^{x+} $-O_vac对所在的(100)面　(a) Nb³⁺-O_vac; (b) Nb⁵⁺-O_vac; (c) Sn²⁺-O_vac; (d) Sn⁴⁺-O_vac

Figure 4. Two-dimensional differential charge density (e/Bohr³), taken from the (100) plane in which $ {M}^{x+} $-O_vac is located: (a) Nb³⁺-O_vac; (b) Nb⁵⁺-O_vac; (c) Sn²⁺-O_vac; (d) Sn⁴⁺-O_vac.

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图 5 电子局域函数, 取自$ {M}^{x+} $-O_vac所在的(100)面　(a) Nb³⁺-O_vac; (b) Nb⁵⁺-O_vac; (c) Sn²⁺-O_vac; (d) Sn⁴⁺-O_vac

Figure 5. Electron localization function, taken from the (100) plane in which $ {M}^{x+} $-O_vac is located: (a) Nb³⁺-O_vac; (b) Nb⁵⁺-O_vac; (c) Sn²⁺-O_vac; (d) Sn⁴⁺-O_vac.

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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(H_f)

Table 1. Lattice constants (a, b, c), unit cell vector angles (α, β, γ ) and formation enthalpy (H_f) 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^[40]
	5.0791	5.1785	5.2340	90.00	99.49	90.00	—	DFT-LDA^[50]
	5.0930	5.1760	5.2440	90.00	99.10	90.00	—	DFT-LDA^[51]
	5.0790	5.2080	5.3110	90.00	99.23	90.00	—	Exp.^[52]
	5.1473	5.2088	5.3166	90.00	99.21	90.00	—	Exp.^[50]
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^[40]
	3.5780	3.5780	5.1630	90.00	90.00	90.00	—	DFT-LDA^[39]
	3.5948	3.5948	5.1824	90.00	90.00	90.00	—	Exp.^[53]
	3.5916	3.5916	5.1790	90.00	90.00	90.00	—	Exp.^[54]
	3.5961	3.5961	5.1770	90.00	90.00	90.00	—	Exp.^[55]
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^[56]
	5.3100	5.3100	3.2000	90.00	90.00	120.00	—	Exp.^[22]

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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+} $掺杂超胞体积的变化($\Delta V $)

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 ($ \Delta V$) 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	—	—
pure phases	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
Nb⁵⁺ doping	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
Nb⁴⁺ doping	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
Nb³⁺ doping	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
Sn⁴⁺ doping	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
Sn²⁺ doping	m	5.80	5.90	6.18	90.26	115.55	89.93	47.77	11.70	24.48

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表 3 $ {E}_{{\mathrm{f}}}({\mathrm{O}}x, P) $, $ {{\Delta }}E({\mathrm{O}}x, P) $的计算值, 其中浓度$ C= $ $ {n}_{M}/({n}_{{\mathrm{Z}}{\mathrm{r}}}+{n}_{M}) $

Table 3. Values of $ {E}_{{\mathrm{f}}}({\mathrm{O}}x, P) $ and $ {{\Delta }}E({\mathrm{O}}x, P) $. $ C= $$ {n}_{M}/({n}_{{\mathrm{Z}}{\mathrm{r}}}+{n}_{M}) $.

	M^x+	Phases	C/%
	M^x+	Phases	25	6.25	3.125
E(Ox, 0) /(eV·atom^–1)	Pure	t	–3.82
	Pure	m	–3.86
	Sn⁴⁺	t	–3.47	–3.74	–3.78
	Sn⁴⁺	m	–3.51	–3.77	–3.82
	Sn²⁺	t	–2.72	–3.54	–3.68
	Sn²⁺	m	–2.83	–3.59	–3.72
	Nb⁵⁺	t	–4.38	–3.96	–3.89
	Nb⁵⁺	m	–4.39	–3.98	–3.92
	Nb⁴⁺	t	–3.44	–3.75	–3.79
	Nb⁴⁺	m	–3.49	–3.79	–3.82
	Nb³⁺	t	–2.72	–3.54	–3.68
	Nb³⁺	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

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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}}{\text{-}}{\mathrm{O}}}_{{\mathrm{v}}{\mathrm{a}}{\mathrm{c}}}} $, $ {E}_{{\mathrm{f}}}^{{2{\mathrm{N}}{\mathrm{N}}{\text{-}}{\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}}{\text{-}}{\mathrm{O}}}_{{\mathrm{v}}{\mathrm{a}}{\mathrm{c}}}} $ and $ {E}_{{\mathrm{f}}}^{{2{\mathrm{N}}{\mathrm{N}}{\text{-}}{\mathrm{O}}}_{{\mathrm{v}}{\mathrm{a}}{\mathrm{c}}}} $ represent the 1NN and 2NN oxygen vacancy formation energies of $ {M}^{x+} $, respectively.

	$ {\mathrm{O}}x $
	Pure	Nb⁵⁺	Nb⁴⁺	Nb³⁺	Sn⁴⁺	Sn²⁺
$ {E}_{{\mathrm{f}}}^{{1{\mathrm{N}}{\mathrm{N}}{\text{-}}{\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}}{\text{-}}{\mathrm{O}}}_{{\mathrm{v}}{\mathrm{a}}{\mathrm{c}}}} $/eV	6.353	5.938	5.919	5.362	5.257	5.029

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[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 Google Scholar
[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
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