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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 ZrO ₂. However, the influence mechanism of Sn and Nb on the fraction of t-ZrO ₂and the t- mphase transition is unclear. In this work, the lattice properties, formation enthalpies, and oxygen vacancy formation energy of ZrO ₂under 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 ZrO ₂is 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. Sn ²⁺and Nb ³⁺cause lattice swelling to be significantly distorted , Nb ⁵⁺causes lattice to shrink, which contributes to reducing the stresses within the film, and Sn ⁴⁺leads the lattice to slightly swell. The low-valent elements all make ZrO ₂less stable and are unfavourable for the stability of t-ZrO ₂relative to m-ZrO ₂. The high-valent Nb ⁵⁺and Sn ⁴⁺promote the relative stability of t-ZrO ₂, thus inhibiting the t- mphase transition, with Nb ⁵⁺having a significant effect and Sn ⁴⁺having a weak effect. The relative stability of t-ZrO ₂increases 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-ZrO ₂, thus stabilising the interfacial t-ZrO ₂and 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.

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Authors and contacts

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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DownLoad: Full-Size Img PowerPoint

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]

DownLoad: CSV

	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

DownLoad: CSV

	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

DownLoad: CSV

	$ {\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

DownLoad: CSV

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Vol. 73, Issue 15 - 2024-08-05

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