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The first principle method based on density functional theory and generalized gradient approximation is used to investigate the interaction of Ta and Re elements at Ni/Ni3Al interface and their influence on the interface strength. According to the calculations of the dissolution energy of these two alloying elements at 7 different positions, it can be concluded that in most of the stoichiometric ranges, Ta atoms preferentially occupy Ni sites in the γ phase, while Re atoms occupy preferentially Al sites in γ' phase. The doping positions do not change when these two atoms are co-alloyed. The calculation of Griffith fracture work of Ni/Ni3Al interface system shows that the doping of Ta atoms can improve the interface fracture strength of the phase boundary region between the γ/γ' coherent atomic layer and γ atomic layer. The interface is easier to fracture in the phase boundary area between γ/γ' coherent atomic layer and γ' atomic layer after Ta atoms have been doped. The doping of Re atoms can improve the interface fracture strength of the phase boundary region between γ/γ' coherent atomic layer and γ' atomic layer. The interface is easier to break in the phase boundary area between γ/γ' coherent atomic layer and γ atomic layer. The calculation results of the unstable stacking fault energy under the interface slip system
$ [110](001) $ before and after Ta and Re alloying show that the doping of these two types of atoms increases the value of the unstable stacking fault energy of the interface, and the slip system$ [110](001)$ becomes difficult to start, which enhances the ability of the interface to block the movement of dislocations, thus enhancing the creep strength of the nickel base superalloy. When doping Re atoms, the effect is greater, and the unstable stacking fault energy of the interface increases by 11.1%, which is better for improving the creep strength of the system. By studying the influence of alloying atoms on the path of vacancy migration and the energy barrier, it is concluded that the doping of Ta and Re atoms can increase the vacancy formation energy and the potential barrier of vacancy migration at the interface. The doping of Re atoms increases the migration energy barriers on both sides of the interface, and the doping of Ta atoms increases the migration energy barriers of γ phase. The increase of the migration barrier hinders the emission and absorption of vacancies, thereby improving the creep capability of the alloy.[1] 方昌德 2004 航空发动机 30 1
Fang C D 2004 Aeroengine 30 1
[2] Diranda L, Cormierb J, Jacquesa A, Jean-Philippe C, Schenka T, Ferrya O 2013 Mater. Charact. 77 32
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[4] Shang S L, Kim D E, Zacherl C L, Y Wang, Y Du, Z K Liu 2012 J. Appl. Phys 112 053515
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[5] Huang M, Zhu J 2016 Rare Metals 35 1
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[6] Chen K, Zhao L R, Tse J S 2004 Mater. Sci. Eng. A 365 80
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[7] Chen K, Zhao L R, Tse J S 2003 Acta Mater. 51 1079
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[8] Gong X F, Yang G X, Fu Y H, Xie Y Q, Zhuang J, Ning X J 2009 Comp. Mater. Sci. 47 320
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[9] 彭黎, 刘云国, 杜付明, 文大东, 黄利群, 彭平 2012 中国有色金属学报 22 3356
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Peng L, Liu Y G, Du F M, Wen D D, Huang L Q, Peng P 2012 Chin. J. Nonferrous Met. 22 3356
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[10] 陈律, 彭平, 湛建平, 田泽安, 韩绍昌 2008 中国有色金属学报 18 890
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Chen L, Peng P, Zhan J P, Tian Z A, Han S C 2008 Chin. J. Nonferrous Met. 18 890
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[11] 彭平, 陈律, 周惦武, 田泽安, 韩绍昌, 金涛, 胡壮麒 2007 金属学报 43 137
Peng P, Chen L, Zhou D W, Tian Z A, Han S C, Jin T, Hu Z Q 2007 Acta Metall. Sin. 43 137
[12] Peng L, Peng P, Liu Y G, He S, Wei H, Jin T, Hu Z Q 2012 Comp. Mater. Sci. 63 292
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[13] Wen Y F, Sun J, Huang J 2012 Trans. Nonferrous Met. Soc. China 22 661
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[14] Zhu C, Yu T, Wang C, Wang D 2020 Comp. Mater. Sci. 175 109586
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Yu S, Wang C Y, Yu T 2007 Acta Phys. Sin. 56 3212
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[18] 黄彦彦, 周青华, 刘青, 蔡聪德 2018 稀有金属材料与工程 47 261
Huang Y Y, Zhou Q H, Liu Q, Cai C D 2018 Rare Metal Mat. Eng. 47 261
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[20] 孙跃军, 尚勇, 姜晓琳 2013 机械工程材料 37 6
Sun Y J, Shang Y, Jiang X L 2013 Mater. Mech. Eng. 37 6
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图 1 两种取向关系下Ni/Ni3Al相界面晶胞结构 (a) (002) γ//(001) γ'取向界面晶胞结构; (b) (002) γ'//(001) γ取向界面晶胞结构
Figure 1. Crystal cell structure of Ni/Ni3Al interface under two orientations: (a) (002) γ//(001) γ' oriented interface crystal cell structure; (b) (002) γ'//(001) γ oriented interface crystal cell structure
图 2 Ni/Ni3Al相界面中7个不同占位的界面模型
Figure 2. Interface models of seven different occupation sites in Ni/Ni3Al interface
图 3 Ni/Ni3Al相界面中8个与Re原子相对位置不同的Ta原子占位
Figure 3. Eight Ta atom occupation sites with different relative positions from Re atom in Ni/Ni3Al interface
图 4 纯Ni/Ni3Al相界面的两种取向关系下的断裂示意图 (a)从Region 1处断裂; (b)从Region 2处断裂
Figure 4. Two orientations and fracture diagram of pure Ni/Ni3Al interface: (a) Ni/Ni3Al interface breaks from Region 1; (b) Ni/Ni3Al interface breaks from Region 2
图 5 (a) [110](001)滑移系下的Ni/Ni3Al相界面晶胞以及(b)滑移矢量为50%时的滑移模型
Figure 5. (a) Ni/Ni3Al interface unit cell in [110](001) slip system and (b) slip model when the slip vector is 50%
图 6 纯Ni/Ni3Al相界面和各合金化界面在 [110](001)滑移系下
$ {\gamma _{{\text{GSF}}}} $ 随u变化的曲线Figure 6. Variation of
$ {\gamma _{{\text{GSF}}}} $ of pure Ni/Ni3Al interface and alloying interface with u in [110](001) slip system
图 7 纯界面以及合金化界面的空位迁移能垒 (a) 纯界面和Re合金化界面γ-cpNi到γ/γ'空位迁移能垒; (b) 纯界面和Re合金化界面γ-cpNi到γ-fcNi空位迁移能垒; (c) Ta合金化和Ta, Re共同合金化界面γ-fcNi到γ/γ'-Ni的空位迁移能垒; (d) 4种界面γ/γ'-Ni到γ'-Ni相的空位迁移能垒
Figure 7. Vacancy migration energy barriers at pure interface and alloying interface: (a) Vacancy migration barriers from γ-cpNi to γ/γ' at pure interface and Re alloying interface; (b) vacancy migration barriers from γ-cpNi to γ- fcNi at pure interface and Re alloying interface; (c) vacancy migration barrier from γ- fcNi to γ/γ'-Ni at Ta alloying interface and Ta, Re co-alloying interface; (d) vacancy migration barriers from γ/γ'-Ni to γ'-Ni at 4 interfaces
表 1 合金化Ni/Ni3Al-Ta界面和Ni/Ni3Al-Re界面的溶解能计算结果
Table 1. Calculation results of interface dissolution energy of the Ni/Ni3Al-Ta and Ni/Ni3Al-Re interface systems
位置序号 掺杂原
子占位Ni/Ni3Al-Ta
溶解能
/(meV·atom–1)Ni/Ni3Al-Re
溶解能
/(meV·atom–1)1 γ'-Ni –52.25 –66.52 2 γ'-Al –56.53 –66.65 3 γ/γ'-Ni –66.92 –54.03 4 γ-fcNi –74.27 –47.82 5 γ-cpNi –76.44 –46.00 6 γ-fcNi –76.53 — 7 γ-cpNi –76.55 — 
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表 2 Re原子和Ta原子共同合金化后界面溶解能计算结果
Table 2. Calculation results of interface dissolution energy after co-alloying of Re atom and Ta atom
Ta原子
所在位置序号 相对距离/Å 溶解能/(meV·atom–1) γ/γ'-Ni 1 2.48 55.89 2 4.30 53.68 γ-Ni 3 4.30 47.17 4 3.53 45.47 5 4.98 46.94 γ'-Ni 6 2.48 67.89 7 2.48 67.64 8 4.30 66.15
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表 3 两种取向关系下Ni/Ni3Al相界面合金化前后的格里菲斯断裂功
Table 3. Griffith work before and after Ni/Ni3Al interface alloying under two orientations
界面体系 格里菲斯断裂功/(J·m–2) Region 1 Region 2 Ni/Ni3Al 4.145 4.403 Ni/Ni3Al-Ta 4.099 4.571 Ni/Ni3Al-Re 4.574 4.323 Ni/Ni3Al-Re-Ta 4.557 4.518
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表 4 纯界面和合金化界面不同Ni空位位置的空位形成能
Table 4. Vacancy formation energy of different Ni positions at pure interface and alloying interface
界面体系 Ni空位位置 γ'-Ni γ/γ'-Ni γ-fcNi γ-cpNi Ni/Ni3Al 1.288 1.376 1.360 1.321 Ni/Ni3Al-Ta 1.322 1.342 1.355 1.467 Ni/Ni3Al-Re 1.375 1.475 1.407 1.233 Ni/Ni3Al-Ta-Re 1.489 1.563 1.460 1.511
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[1] 方昌德 2004 航空发动机 30 1
Fang C D 2004 Aeroengine 30 1
[2] Diranda L, Cormierb J, Jacquesa A, Jean-Philippe C, Schenka T, Ferrya O 2013 Mater. Charact. 77 32
Google Scholar
[3] Yamabe-Mitarai Y, Ro Y, Harada H, T Maruko 1998 Metall. Mater. Trans. A 29 537
Google Scholar
[4] Shang S L, Kim D E, Zacherl C L, Y Wang, Y Du, Z K Liu 2012 J. Appl. Phys 112 053515
Google Scholar
[5] Huang M, Zhu J 2016 Rare Metals 35 1
Google Scholar
[6] Chen K, Zhao L R, Tse J S 2004 Mater. Sci. Eng. A 365 80
Google Scholar
[7] Chen K, Zhao L R, Tse J S 2003 Acta Mater. 51 1079
Google Scholar
[8] Gong X F, Yang G X, Fu Y H, Xie Y Q, Zhuang J, Ning X J 2009 Comp. Mater. Sci. 47 320
Google Scholar
[9] 彭黎, 刘云国, 杜付明, 文大东, 黄利群, 彭平 2012 中国有色金属学报 22 3356
Google Scholar
Peng L, Liu Y G, Du F M, Wen D D, Huang L Q, Peng P 2012 Chin. J. Nonferrous Met. 22 3356
Google Scholar
[10] 陈律, 彭平, 湛建平, 田泽安, 韩绍昌 2008 中国有色金属学报 18 890
Google Scholar
Chen L, Peng P, Zhan J P, Tian Z A, Han S C 2008 Chin. J. Nonferrous Met. 18 890
Google Scholar
[11] 彭平, 陈律, 周惦武, 田泽安, 韩绍昌, 金涛, 胡壮麒 2007 金属学报 43 137
Peng P, Chen L, Zhou D W, Tian Z A, Han S C, Jin T, Hu Z Q 2007 Acta Metall. Sin. 43 137
[12] Peng L, Peng P, Liu Y G, He S, Wei H, Jin T, Hu Z Q 2012 Comp. Mater. Sci. 63 292
Google Scholar
[13] Wen Y F, Sun J, Huang J 2012 Trans. Nonferrous Met. Soc. China 22 661
Google Scholar
[14] Zhu C, Yu T, Wang C, Wang D 2020 Comp. Mater. Sci. 175 109586
Google Scholar
[15] Zhao W, Sun Z, Gong S 2017 Acta Mater. 135 25
Google Scholar
[16] Sun M, Wang C Y 2016 Chin. Phys. B 25 067104
Google Scholar
[17] 于松, 王崇愚, 于涛 2007 56 3212
Google Scholar
Yu S, Wang C Y, Yu T 2007 Acta Phys. Sin. 56 3212
Google Scholar
[18] 黄彦彦, 周青华, 刘青, 蔡聪德 2018 稀有金属材料与工程 47 261
Huang Y Y, Zhou Q H, Liu Q, Cai C D 2018 Rare Metal Mat. Eng. 47 261
[19] Tian S, Wu J, Shu D, Su Y, Yu H, Qian B 2014 Mater. Sci. Eng. A 616 260
Google Scholar
[20] 孙跃军, 尚勇, 姜晓琳 2013 机械工程材料 37 6
Sun Y J, Shang Y, Jiang X L 2013 Mater. Mech. Eng. 37 6
[21] Tian S, Yu X, Yang J, Zhao N, Xu Y, Hu Z 2004 Mater. Sci. Eng. A 379 141
Google Scholar
[22] Wang C, Wang C Y 2008 Surf. Sci. 602 2604
Google Scholar
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