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Zr既是反应堆中核燃料组件的包壳材料，也是核燃料UO2的一种裂变产物，不可避免地会掺杂到UO2中，对其性质等产生一定的影响.本文通过第一性原理密度泛函理论计算，研究了Zr掺杂所引起的Xe在UO2中溶解能力的变化.首先应用引入Hubbard U修正的广义梯度近似密度泛函计算了U，O间隙和空位缺陷的形成能，结果与文献值符合，验证了计算方法的可靠性.在此基础上对Zr掺杂后空位缺陷的形成能及Xe吸附到空位缺陷所需的结合能的变化情况进行了研究.结果表明，Zr的掺杂会增加空位缺陷的形成能，减小大部分Xe吸附的结合能，且空位缺陷形成能的变化量普遍更大，从而在整体上增加了Xe在UO2中的溶解能.说明在UO2中，Zr掺杂主要是通过增加缺陷的形成难度而减弱了Xe在其中的溶解能力.As a major fuel of the light-water reactors, UO2 has excellent properties such as high melting point, good radiation resistance, corrosion resistance, compatibility with cladding materials, and strong ability to tolerate fission gas. The Zr atoms are inevitably introduced into UO2 lattice during the operation of a nuclear reactor, which can affect the solubility of Xe in the UO2. In this paper, we calculate the formation energy of vacancy defect and the binding energy of Xe in vacancy of Zr doped UO2. The calculations presented here are based on density functional first-principle and projector augmented-wave method. A plane-wave basis set with a cutoff energy of 400 eV is used. The generalized gradient approximation refined by Perdew, Burke and Ernxerhof is employed for determining the exchange and correlation energy. Hubbard U term is used for considering the f-electron localization. Brillouin zone is set to be within 555 k point mesh generated by the Monkhorst-Pack scheme. The self-consistent convergence of total energy is 110-4 eV/atom. The calculations are performed in a 222 supercell. In order to verify the calculating process, the formation energies of U and O point defects are compared with those in the literature. Then the influence of Zr doping in the UO2 on the solubility of Xe in the UO2 is studied. The results show that the ability to form the vacancy defects is different in the U-rich and O-rich environment of UO2. The vacancy defects in UO2 are more likely to form in O-rich UO2. The Zr doping will lead to the increasing of the formation energies of defects in both cases. The Zr doping will also change the binding energy of Xe in void. For all the systems studied, only the binding energy of Xe adsorbed to the void consisting of four point defects increases, while the rest decrease. The solution energy, equaling the sum of the binding energy of Xe and the vacancy formation energy, will increase after doping Zr, because the decrement in binding energy is generally less than the increment in vacancy formation energy. In summary, the presence of Zr will weaken the solubility of Xe in UO2, which is mainly due to the hindering of vacancy defects from forming. This result has a certain value in studying the dissolution of fission product Xe after a small amount of Zr has entered into the UO2 fuel in nuclear reactor.
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Keywords:
- UO2 /
- Zr /
- Xe /
- solubility
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[14] Yu J G, Devanathan R, Weber W J 2009 J. Phys.:Condens. Matter 21 435401
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[16] Kresse G, Joubert D 1999 Phys. Rev. B 59 1758
[17] Kresse G, Furthmller J 1996 Phys. Rev. B 54 11169
[18] Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865
[19] Dudarev S L, Botton G A, Savrasov S Y, Humphreys C J, Sutton A P 1998 Phys. Rev. B 57 1505
[20] Vathonne E, Wiktor J, Freyss M, Jomard G, Bertolus M 2014 J. Phys.:Condens. Matter 26 325501
[21] Dorado B, Amadon B, Freyss M, Bertolus M 2009 Phys. Rev. B 79 235125
[22] Dorado B, Jomard G, Freyss M, Bertolus M 2010 Phys. Rev. B 82 035114
[23] Sinnott S B, Uberuaga B P 2014 Am. Ceram. Soc. Bull. 93 28
[24] Ngayamhappy R, Krack M, Pautz A 2015 J. Phys.:Condens. Matter 27 455401
[25] Hong M, Phillpot S R, Lee C W, Nerikar P, Uberuaga B P, Stanek C R, Sinnott S B 2012 Phys. Rev. B 85 144110
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[1] Wang H, Yin C G, Liu J H 2013 J. Alloys Compd. 579 305
[2] Song J H, Park I K, Shin Y S, Kim J H, Hong S W, Min B T, Kim H D 2003 Nucl. Eng. Des. 222 1
[3] Lei Y L, Huang H W, Yu C, Yang J, Liu Y J 2014 J. Mater. Sci. Eng. 32 126 (in Chinese) [雷艳丽, 黄华伟, 喻冲, 杨静, 刘艳军 2014 材料科学与工程学报 32 126]
[4] Matzke H, Turos A, Linker G 1994 Nucl. Instrum. Methods Phys. Res. Sect. B 91 294
[5] Brutzel L V, Rarivomanantsoa M 2006 J. Nucl. Mater. 358 209
[6] Martin G, Garcia P, Brutzel L V, Dorado B, Maillard S 2011 Nucl. Instrum. Methods Phys. Res. Sect. B 269 1727
[7] Xing Z H, Ying S H 2000 Nucl. Power Eng. 21 560 (in Chinese) [邢忠虎, 应诗浩 2000 核动力工程 21 560]
[8] Yun Y, Kim H, Kim H, Park K 2008 J. Nucl. Mater. 378 40
[9] Andersson D A, Uberuaga B P, Nerikar P V, Unal C, Stanek C R 2011 Phys. Rev. B 84 2989
[10] Andersson A D, Perriot R T, Pastore G, Tonks M R, Cooper M W, Liu X Y, Goyal A, Uberuaga B P, Stanek C R https://www.osti.gov/scitech/biblio/1291258/[2017-8-9]
[11] Kulkarni N K, Krishnan K, Kasar U M, Rakshit S K, Sali S K, Aggarwal S K 2009 J. Nucl. Mater. 384 81
[12] Yang C, Zhang X 2004 Mater. Sci. Eng. A 372 287
[13] Lan J H, Wang L, Li S, Yuan L Y, Feng Y X, Sun W, Zhao Y L, Chai Z F, Shi W Q 2013 J. Appl. Phys. 113 183514
[14] Yu J G, Devanathan R, Weber W J 2009 J. Phys.:Condens. Matter 21 435401
[15] Grimes R W, Catlow C R A 1991 Philos. Trans. Phys. Sci. Eng. 335 609
[16] Kresse G, Joubert D 1999 Phys. Rev. B 59 1758
[17] Kresse G, Furthmller J 1996 Phys. Rev. B 54 11169
[18] Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865
[19] Dudarev S L, Botton G A, Savrasov S Y, Humphreys C J, Sutton A P 1998 Phys. Rev. B 57 1505
[20] Vathonne E, Wiktor J, Freyss M, Jomard G, Bertolus M 2014 J. Phys.:Condens. Matter 26 325501
[21] Dorado B, Amadon B, Freyss M, Bertolus M 2009 Phys. Rev. B 79 235125
[22] Dorado B, Jomard G, Freyss M, Bertolus M 2010 Phys. Rev. B 82 035114
[23] Sinnott S B, Uberuaga B P 2014 Am. Ceram. Soc. Bull. 93 28
[24] Ngayamhappy R, Krack M, Pautz A 2015 J. Phys.:Condens. Matter 27 455401
[25] Hong M, Phillpot S R, Lee C W, Nerikar P, Uberuaga B P, Stanek C R, Sinnott S B 2012 Phys. Rev. B 85 144110
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