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Co-Al-W基高温合金的团簇成分式

马启慧 张宇 王清 董红刚 董闯

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Co-Al-W基高温合金的团簇成分式

马启慧, 张宇, 王清, 董红刚, 董闯

Cluster formulas of Co-Al-W-base superalloys

Ma Qi-Hui, Zhang Yu, Wang Qing, Dong Hong-Gang, Dong Chuang
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  • Co-Al-W基高温合金具有类似于Ni基高温合金的$\gamma + \gamma′$相组织结构. 根据面心立方固溶体的团簇加连接原子结构模型, Ni基高温合金的成分式即最稳定的化学近程序结构单元可以描述为第一近邻配位多面体团簇加上次近邻的三个连接原子. 本文应用类似方法, 首次给出了Co-Al-W基高温合金的团簇成分式. 利用原子半径和团簇共振模型, 可计算出Co-Al-W三元合金的团簇成分通式, 为[Al-Co12](Co,Al,W)3, 即以Al为中心原子、Co为壳层原子的[Al-Co12]团簇加上三个连接原子. 对于多元合金, 需要先将元素进行分类: 溶剂元素—类Co元素$\overline {{\rm{Co}}} $ (Co, Cr, Fe, Re, Ni, Ir, Ru)和溶质元素—类Al元素$\overline {{\rm{Al}}} $ (Al, W, Mo, Ta, Ti, Nb, V等); 进而根据合金元素的配分行为, 将类Co元素分为${\overline {{\rm{Co}}} ^\gamma }$ (Cr, Fe, Re)和${\overline {{\rm{Co}}} ^{\gamma′}}$ (Ni, Ir, Ru); 根据混合焓, 将类Al元素分为Al, $\overline {\rm{W}} $ (W, Mo)和$\overline {{\rm{Ta}}} $ (Ta, Ti, Nb, V等). 由此, 任何多元Co-Al-W基高温合金均可简化为$\overline {{\rm{Co}}} \text{-} \overline {{\rm{Al}}} $伪二元体系或者$\overline {{\rm{Co}}} \text{-} {\rm{Al}} \text{-}\left( {\overline {\rm{W}}, \overline {{\rm{Ta}}} } \right)$伪三元体系, 其团簇加连接原子成分式为$\left[ {\overline {{\rm{Al}}} \text{-} {{\overline {{\rm{Co}}} }_{12}}} \right]$$\left( {{{\overline {{\rm{Co}}} }_{1.0}}{{\overline {{\rm{Al}}} }_{2.0}}} \right)$ (或$\left[ {{\rm{Al}} \text{-} {{\overline {{\rm{Co}}} }_{12}}} \right]{\overline {{\rm{Co}}} _{1.0}}{\rm{A}}{{\rm{l}}_{0.5}}{\left( {\overline {\rm{W}},\overline {{\rm{Ta}}} } \right)_{1.5}}$ = ${\overline {{\rm{Co}}} _{81.250}}{\rm{A}}{{\rm{l}}_{9.375}}{\left( {\overline {\rm{W}},\overline {{\rm{Ta}}} } \right)_{9.375}}$ at.%). 其中, ${\gamma }$${\gamma′}$相的团簇成分式分别为$\left[ {\overline {{\rm{Al}}} \text{-} {{\overline {{\rm{Co}}} }_{12}}} \right]\!\left( {{{\overline {{\rm{Co}}} }_{1.5}}{{\overline {{\rm{Al}}} }_{1.5}}} \right)$ (或$\left[ {{\rm{Al}} \text{-} {{\overline {{\rm{Co}}} }_{12}}} \right]{\overline {{\rm{Co}}} _{1.5}}{\rm{A}}{{\rm{l}}_{0.5}}{\left( {\overline {\rm{W}},\overline {{\rm{Ta}}} } \right)_{1.0}}$ = ${\overline {{\rm{Co}}} _{84.375}}{\rm{A}}{{\rm{l}}_{9.375}}$${\left( {\overline {\rm{W}},\overline {{\rm{Ta}}} } \right)_{6.250}}$ at.%)和$\left[ {\overline {{\rm{Al}}} \text{-} {{\overline {{\rm{Co}}} }_{12}}} \right]\left( {{{\overline {{\rm{Co}}} }_{0.5}}{{\overline {{\rm{Al}}} }_{2.5}}} \right)$ (或$\left[ {{\rm{Al}} \text{-} {{\overline {{\rm{Co}}} }_{12}}} \right]{\overline {{\rm{Co}}} _{0.5}}{\rm{A}}{{\rm{l}}_{0.5}}{\left( {\overline {\rm{W}},\overline {{\rm{Ta}}} } \right)_{2.0}}$ = $ {\overline {{\rm{Co}}} _{78.125}}{\rm{A}}{{\rm{l}}_{9.375}}{\left( {\overline {\rm{W}},\overline {{\rm{Ta}}} } \right)_{12.500}}$ at.%). 例如, Co82Al9W9合金的团簇成分式为[Al-Co12]Co1.1Al0.4W1.4 (~[Al-Co12]Co1.0Al0.5W1.5), 其中${\gamma }$相的团簇成分式为[Al-Co12]Co1.6Al0.4W1.0 (~[Al-Co12]Co1.5Al0.5W1.0), ${\gamma′}$相的团簇成分式为[Al-Co12]Co0.3Al0.5W2.2 (~[Al-Co12]Co0.5Al0.5W2.0).
    Having a $\gamma /\gamma′ $ microstructure similar to Ni-base superalloys and also including various alloying elements such as Al and W, new Co-base superalloy, namely Co-Al-W-base alloy, has been widely studied as a kind of potential alternative of Ni-base superalloy, which is the most important high-temperature structural material in industrial applications. Besides, Co-Al-W-base alloy has also excellent mechanical properties, for example, creep properties comparable to those of the first-generation Ni-base single crystal superalloys. In our previous work, the ideal composition formula of Ni-base superalloy has been obtained by applying the cluster-plus-glue-atom structure model of faced centered cubic solid solution, which shows that the most stable chemical short-range-order unit is composed of a nearest-neighbor cluster and three next-neighbor glue atoms. In this paper, the ideal cluster formula of Co-Al-W-base superalloy is addressed by using the same approach. Based on cluster-plus-glue-atom model theory, according to lattice constants and atom radii, calculations are carried out. The results show that the atom radius of Al is equal to Covalent radius (0.126 nm) and for $\gamma′ $ phase the atom radius of W changes obviously (0.1316 nm). After analyzing atomic radii, the chemical formula for Co-Al-W ternary alloy is calculated to be [Al-Co12](Co,Al,W)3, which signifies an Al centered atom and twelve Co nearest-neighbored cluster atoms plus three glue atoms, which is in good consistence with that for Ni-base single crystal superalloy. For multi-element alloy, the alloying elements are classified, according to the heat of mixing between the alloying elements and Co as well as partition behavior of alloying elements, as solvent elements-Co-like elements $\overline {{\rm{Co}}} $ (Co, Ni, Ir, Ru, Cr, Fe, and Re) and solute elements-Al-like elements $\overline {{\rm{Al}}} $ (Al, W, Mo, Ta, Ti, Nb, V, etc.). The solvent elements can be divided into two kinds according to partition behaves: ${\overline {{\rm{Co}}} ^{\gamma }}$ (Cr, Fe, and Re) and ${\overline {{\rm{Co}}} ^{\gamma′}}$ (Ni, Ir, and Ru). The latter is further grouped into Al, ${\overline {\rm{W}} }$ (W and Mo, which have weaker heat of mixing than Al-Co ) and ${\overline {{\rm{Ta}}} }$ (Ta, Ti, Nb, V, etc., which have stronger heat of mixing than Al-Co). Then all chemically complex Co-Al-W-base superalloys are simplified into $\overline {{\rm{Co}}} \text{-} \overline {{\rm{Al}}} $ pseudo-binary or $\overline {{\rm{Co}}} \text{-} {\rm{Al}} \text{-} \left( {\overline {\rm{W}},\overline {{\rm{Ta}}} } \right)$ pseudo-ternary system. Within the framework of the cluster-plus-glue-atom formulism and by analyzing the compositions of alloy, it is shown that the Co-Al-W-base superalloy satisfies the ideal formula $\left[ {\overline {{\rm{Al}}} \text{-} {{\overline {{\rm{Co}}} }_{12}}} \right]\left( {{{\overline {{\rm{Co}}} }_{1.0}}{{\overline {{\rm{Al}}} }_{2.0}}} \right)$ (or $\left[ {{\rm{Al}} \text{-} {{\overline {{\rm{Co}}} }_{12}}} \right]{\overline {{\rm{Co}}} _{1.0}}{\rm{A}}{{\rm{l}}_{0.5}}{\left( {\overline {\rm{W}},\overline {{\rm{Ta}}} } \right)_{1.5}}$ = ${\overline {{\rm{Co}}} _{81.250}}{\rm{A}}{{\rm{l}}_{9.375}}{\left( {\overline {\rm{W}},\overline {{\rm{Ta}}} } \right)_{9.375}}$ at.%). In the same way, those of $\gamma $ and $\gamma′ $ phases are respectively $\left[ {\overline {{\rm{Al}}} \text{-} {{\overline {{\rm{Co}}} }_{12}}} \right]\left( {{{\overline {{\rm{Co}}} }_{1.5}}{{\overline {{\rm{Al}}} }_{1.5}}} \right)$ (or $\left[ {{\rm{Al}} \text{-} {{\overline {{\rm{Co}}} }_{12}}} \right]{\overline {{\rm{Co}}} _{1.5}}{\rm{A}}{{\rm{l}}_{0.5}}{\left( {\overline {\rm{W}},\overline {{\rm{Ta}}} } \right)_{1.0}}$ = ${\overline {{\rm{Co}}} _{84.375}}{\rm{A}}{{\rm{l}}_{9.375}}{\left( {\overline {\rm{W}},\overline {{\rm{Ta}}} } \right)_{6.250}}$ at.%) and $\left[ {\overline {{\rm{Al}}} \text{-} {{\overline {{\rm{Co}}} }_{12}}} \right]\left( {{{\overline {{\rm{Co}}} }_{0.5}}{{\overline {{\rm{Al}}} }_{2.5}}} \right)$ (or $\left[ {{\rm{Al}} \text{-} {{\overline {{\rm{Co}}} }_{12}}} \right]{\overline {{\rm{Co}}} _{0.5}}{\rm{A}}{{\rm{l}}_{0.5}}{\left( {\overline {\rm{W}},\overline {{\rm{Ta}}} } \right)_{2.0}}$ = ${\overline {{\rm{Co}}} _{78.125}}{\rm{A}}{{\rm{l}}_{9.375}}{\left( {\overline {\rm{W}},\overline {{\rm{Ta}}} } \right)_{12.500}}$ at.%). For example, alloy Co82Al9W9 and its $\gamma $ and $\gamma′ $ phases are formulated respectively as [Al-Co12]Co1.1Al0.4W1.4 (~ [Al-Co12]Co1.0Al0.5W1.5), [Al-Co12]Co1.6Al0.4W1.0 (~ [Al-Co12]Co1.5Al0.5W1.0), and [Al-Co12]Co0.3Al0.5W2.2 (~[Al-Co12]Co0.5Al0.5W2.0).
      通信作者: 董闯, dong@dlut.edu.cn
    • 基金项目: 国家自然科学基金航空重大研究计划培育项目(批准号: 91860108)和国家自然科学基金(批准号: 11674045)资助的课题.
      Corresponding author: Dong Chuang, dong@dlut.edu.cn
    • Funds: Project supported by the Aviation Major Research Program Cultivation Project of the National Natural Science Foundation of China (Grant No. 91860108) and the National Natural Science Foundation of China (Grant No. 11674045).
    [1]

    Sims C T, Hagel W C 1972 The Superalloys (New York: John Wiley & Sons) p1

    [2]

    Sato J, Omori T, Oikawa K, Ohnuma I, Kainuma R, Ishida K 2006 Science 312 90Google Scholar

    [3]

    Suzuki A, Pollock T M 2008 Acta Mater. 56 1288Google Scholar

    [4]

    Bauer A, Neumeiera S, Pyczakb F, Singer R F, Göken M 2012 Mater. Sci. Eng. 550 333Google Scholar

    [5]

    Klein L, Shen Y, Killian M S, Virtanen S 2011 Corros. Sci. 53 2713Google Scholar

    [6]

    Ooshima M, Tanaka K, Okamoto N L, Kishida K, Inui H 2010 J. Alloys Compd. 508 71Google Scholar

    [7]

    Chen M, Wang C Y 2009 Scr. Mater. 60 659Google Scholar

    [8]

    Bauer A, Neumeier S, Pyczakc F, Göken M 2010 Scr. Mater. 63 1197Google Scholar

    [9]

    Kobayashi S, Tsukamoto Y, Takasugi T 2012 Intermetallics 31 94Google Scholar

    [10]

    Meher S, Yan H Y, Nag S, Dye D, Banerjee R 2012 Scr. Mater. 67 850Google Scholar

    [11]

    Morinaga M, Yukawa N, Ezaki H, Adachi H 1984 Superalloys (Warrendale, PA: The Metallurgical Society of AIME) p523

    [12]

    张继山, 崔华, 胡壮麟, 村田纯教, 森永正彦, 汤川夏夫 1993 金属学报 29 289Google Scholar

    Zhang J S, Cui H, Hu Z L, Murata Y, Morinaga M, Yukawa N 1993 Acta Metall. Sin. 29 289Google Scholar

    [13]

    Dong C, Wang Q, Qiang J B, Wang Y M, Jiang N, Han G, Li Y H, Wu J, Xia J H 2007 J. Phys. D: Appl. Phys. 40 R273Google Scholar

    [14]

    Han G, Qiang J B, Li F W, Yuan L, Quan S G, Wang Q, Wang Y M, Dong C, Häussler P 2011 Acta Mater. 59 5917Google Scholar

    [15]

    Luo L J, Chen H, Wang Y M, Qiang J B, Wang Q, Dong C, Häussler P 2014 Philos. Mag. 94 2520Google Scholar

    [16]

    张宇, 王清, 董红刚, 董闯, 张洪宇, 孙晓峰 2017 金属学报 54 591Google Scholar

    Zhang Y, Wang Q, Dong H G, Dong C, Zhang H Y, Sun X F 2017 Acta Metall. Sin. 54 591Google Scholar

    [17]

    Bragg W L, Williams E J 1934 Proc. R. Soc. London, Ser. A 151 699

    [18]

    Williams E 1935 Proc. R. Soc. London, Ser. A 152 231Google Scholar

    [19]

    Bethe H 1935 Proc. R. Soc. London, Ser. A 150 552Google Scholar

    [20]

    Cowly J 1950 Phys. Rev. 77 669Google Scholar

    [21]

    Cowly J 1960 Phys. Rev. 120 1648Google Scholar

    [22]

    Cowly J 1965 Phys. Rev. 138 A1384Google Scholar

    [23]

    Chen H, Wang Q, Wang Y M, Qiang J B, Dong C 2010 Philos. Mag. 90 3935Google Scholar

    [24]

    Chen H, Wang Q, Wang Y M, Wang Y, Dong C 2011 Isr. J. Chem. 51 1226Google Scholar

    [25]

    Wang Y, Wang Q, Zhao J, Dong C 2010 Scr. Mater. 63 178Google Scholar

    [26]

    Yuan L, Pang C, Wang Y M, Wang Q, Qiang J B, Dong C 2010 Intermetallics 18 1800Google Scholar

    [27]

    Li F W, Qiang J B, Wang Q, Wang Y M, Dong X L, Dong C, Zhu S J 2012 Intermetallics 30 86Google Scholar

    [28]

    Wang Z R, Dong D D, Qiang J B, Wang Q, Wang Y M, Dong C 2013 Sci. China: Phys. Mech. Astron. 56 1419Google Scholar

    [29]

    Wang Q, Zhu C L, Li Y H, Wu J, Dong C, Qiang J B, Zhang W, Inoue A 2007 Mater. Sci. Forum 561−565 1275Google Scholar

    [30]

    谷俊杰 2011 硕士学位论文 (大连: 大连理工大学)

    Gu J J 2011 M. S. Thesis (Dalian: Dalian University of Technology) (in Chinese)

    [31]

    Wang Q, Li Q, Li X N, Zhang R Q, Gao X X, Dong C, Liaw P K 2015 Metall. Mater. Trans. A 46 3924Google Scholar

    [32]

    王清, 查钱锋, 刘恩雪, 董闯, 王学军, 谭朝鑫, 龚春俊 2012 金属学报 48 1201Google Scholar

    Wang Q, Zha Q F, Liu E X, Dong C, Wang X J, Tan C X, Gong C J 2012 Acta Metall. Sin. 48 1201Google Scholar

    [33]

    马仁涛, 郝传璞, 王清, 任明法, 王英敏, 董闯 2010 金属学报 46 1034Google Scholar

    Ma R T, Hao C P, Wang Q, Ren M F, Wang Y M, Dong C 2010 Acta Metall. Sin. 46 1034Google Scholar

    [34]

    董丹丹 2017 博士学位论文 (大连: 大连理工大学)

    Dong D D 2017 Ph. D. Dissertation (Dalian: Dalian University of Technology) (in Chinese)

    [35]

    董闯, 董丹丹, 王清 2018 金属学报 54 293Google Scholar

    Dong C, Dong D D, Wang Q 2018 Acta Metall. Sin. 54 293Google Scholar

    [36]

    Hong H L, Wang Q, Dong C 2015 Sci. China: Mater. 58 355Google Scholar

    [37]

    Hong H L, Wang Q, Dong C, Liaw P K 2014 Sci. Rep. 4 7065Google Scholar

    [38]

    洪海莲, 董闯, 王清, 张宇, 耿遥祥 2016 物理学报 65 036101Google Scholar

    Hong H L, Dong C, Wang Q, Zhang Y, Geng Y X 2016 Acta Phys. Sin. 65 036101Google Scholar

    [39]

    Pearson W B 1973 J. Appl. Cryst. 6 306Google Scholar

    [40]

    Pyczak F, Bauer A, Göken M, Lorenz U, Neumeier S, Oehring M, Paul J, Schell N, Schreyer A, Stark A, Symanzik F 2015 J. Alloys Compd. 632 110Google Scholar

    [41]

    Povstugar I, Zenk C H, Li R, Choi P P, Neumeier S, Dolotko O, Hoelzel M, Göken M, Raabe D 2016 Mater. Sci. Technol. 32 220Google Scholar

    [42]

    Shinagawa K, Omori T, Sato J, Oikawa K, Ohnuma I, Kainuma R, Ishida K 2008 Mater. Trans. 49 1474Google Scholar

    [43]

    Wang Y J, Wang C Y 2009 Appl. Phys. Lett. 94 261909Google Scholar

    [44]

    Bocchini P J, Lass E A, Moon K W, Williams M E, Campbell C E, Kattner U R, Dunand D C, Seidman D N 2013 Scr. Mater. 68 563Google Scholar

    [45]

    Povstugar I, Choi P P, Neumeier S, Bauer A, Zenk C H, Göken M, Raabe D 2014 Acta Mater. 78 78Google Scholar

    [46]

    Meher S, Banerjee R 2014 Intermetallics 49 138Google Scholar

    [47]

    Lass E A, Williams M E, Campbell C E, Moon K W, Kattner U R 2014 J. Phase Equilib. Diffus. 35 711Google Scholar

    [48]

    Zhong F, Li S S, Sha J B 2015 Mater. Sci. Eng. A 637 175Google Scholar

    [49]

    Sauza D J, Bocchini P J, Dunand D C, Seidman D N 2016 Acta Mater. 117 135Google Scholar

    [50]

    Zhou H J, Xue F, Chang H, Feng Q 2018 J. Mater. Sci. Technol. 34 799Google Scholar

    [51]

    Takeuchi A, Inoue A 2005 Mater. Trans. 46 2817Google Scholar

    [52]

    Shinagawa K, Omori T, Oikawa K, Kainuma R, Ishida K 2009 Scr. Mater. 61 612Google Scholar

    [53]

    Chen M, Wang C Y. 2010 Phys. Lett. A 374 3238Google Scholar

    [54]

    Ping D H, Cui C Y, Gu Y F, Harada H 2007 Ultramicroscopy 107 791Google Scholar

    [55]

    Makineni S K, Nithin B, Chattopadhyay K 2015 Scr.Mater. 98 36Google Scholar

    [56]

    Makineni S K, Samanta A, Rojhirunsakool T, Alam T, Nithin B, Singh A K, Banerjee R, Chattopadhyay K 2015 Acta Mater. 97 29Google Scholar

    [57]

    Pollock T M, Dibbern J, Tsunekane M, Suzuki 2010 JOM 62 58Google Scholar

    [58]

    Yan H Y, Vorontsov V A, Dye D 2014 Intermetallics 48 44Google Scholar

    [59]

    Xue F, Zhou H J, Ding X F, Wang M L, Feng Q 2013 Mater. Lett. 112 215Google Scholar

    [60]

    Xue F, Zhou H J, Feng Q 2014 JOM 66 2486Google Scholar

    [61]

    Titus M S, Suzuki A, Pollock T M 2012 High Temperature Creep of New L12 Containing Cobalt‐Base Superalloys (New York: John Wiley Sons. Inc.) p823

    [62]

    Shi L, Yu J J, Cui C Y, Sun X F 2015 Mater. Lett. 149 58Google Scholar

  • 图 1  Co-Al基的面心立方固溶体及AuCu3有序结构中的立方八面体[Al-Co12]团簇

    Fig. 1.  Cuboctahedron [Al-Co12] cluster in Co-Al-base faced centered cubic solid solution and in AuCu3-type ordered structure

    图 2  合金数量随Co含量的变化, 虚线表示平均成分式$\left[ {\overline {{\rm{Al}}} \text{-} {{\overline {{\rm{Co}}} }_{12}}} \right]{\overline {{\rm{Co}}} _{1.0}}{\overline {{\rm{Al}}} _{2.0}}$

    Fig. 2.  Statistical distribution of alloy compositions as a function of at.% Co. The dashed vertical line represents the ideal composition formula $\left[ {\overline {{\rm{Al}}} \text{-} {{\overline {{\rm{Co}}} }_{12}}} \right]{\overline {{\rm{Co}}} _{1.0}}{\overline {{\rm{Al}}} _{2.0}}$

    图 3  $\overline {{\rm{Co}}} \text{-} {\rm{Al}} \text{-} \left( {\overline {\rm{W}},\overline {{\rm{Ta}}} } \right)$伪三元成分分布 (a) 合金成分; (b) $\gamma $$\gamma′ $两相成分; 图中虚线为 Co-Al-W三元相图中富Co端1173 K等温截面相图[2], 中心成分点${\overline {{\rm{Co}}} _{81.250}}{\rm{A}}{{\rm{l}}_{9.375}}$${\left( {\overline {\rm{W}} ,\overline {{\rm{Ta}}} } \right)_{9.375}}$用蓝色空心三角形标出

    Fig. 3.  $\overline {{\rm{Co}}} \text{-} {\rm{Al}} \text{-} \left( {\overline {\rm{W}} ,\overline {{\rm{Ta}}} } \right)$ pseudo-ternary composition diagram: (a) Alloy compositions; (b) $\gamma $ and $\gamma′ $ two phases compositions, where the dashed lines represent the isothermal section of the Co-Al-W ternary system in the Co-rich portion at 1173 K[2], and the blue hollow triangle points to the center composition ${\overline {{\rm{Co}}} _{81.250}}{\rm{A}}{{\rm{l}}_{9.375}}{\left( {\overline {\rm{W}} ,\overline {{\rm{Ta}}} } \right)_{9.375}}$

    图 4  合金数量随类Co元素总量$\overline {{\rm{Co}}} $的变化 (a) $\gamma $$\gamma′ $相成分; (b) 合金成分; 竖虚线表示各自理想成分

    Fig. 4.  Evolution of numbers of alloys with $\overline {{\rm{Co}}} $ content: (a) $\gamma′ $ and $\gamma $ phases; (b) alloys. Vertical dashed lines represent the ideal compositions

    表 1  实测的$\gamma $相成分和晶格常数[40-42], 以及按照(7)式计算的晶格常数

    Table 1.  Measured compositions and lattice constants of $\gamma $ phase in Co-Al-W-base superalloys[40-42], in comparison with the calculated lattice constants

    合金成分/at.%$\gamma $相成分/at.%晶格常数实验值/nm晶格常数计算值/nm绝对误差$\varDelta $
    Co82Al9W9Co81.7Al9.3W90.35800.35790.0001
    Co83Al9W8Co81.9Al10.0W8.10.35760.35750.0001
    Co80Al9W11Co80.7Al9.2W10.20.35860.35880.0002
    Co74Al9W9Cr8Co73.9Al8.0W6.8Cr11.20.35780.35750.0003
    Co64Al9W9Ni18Co69.1Al6.8W7.0Ni16.90.35770.35620.0015
    Co65Al9W9Ni9Cr8Co66.7Al7.8W6.7Ni8.3Cr10.70.35810.35840.0003
    Co56Al9W9Ni18Cr8Co59.2Al6.0W7.4Ni15.6Cr11.80.35830.35810.0002
    Co72.5Ni10Al10W7.5Co76.2Al8.7W5.4Ni9.70.35780.35620.0016
    下载: 导出CSV

    表 2  实测$\gamma′ $相成分和晶格常数[40-42]以及根据(9)式计算的W原子半径

    Table 2.  Atomic radii of W fitted from measured compositions and lattice constants $\gamma′$ phases in different alloys[40-42]

    合金成分/at.%$\gamma′ $相成分/at.%晶格常数实验值/nmW原子半径/nm
    Co82Al9W9Co77.49Al10.03W12.480.35940.1317
    Co83Al9W8Co76.6Al9.4W140.35890.1306
    Co80Al9W11Co75.1Al9.1W15.80.35950.1311
    Co74Al9W9Cr8Co73.9Al9.4W10.4Cr6.30.35870.1314
    Co64Al9W9Ni18Co58.9Al10.8W11.0Ni19.30.35900.1317
    Co65Al9W9Ni9Cr8Co64.2Al10.1W9.9Ni9.4Cr6.40.35870.1317
    Co56Al9W9Ni18Cr8Co54.5Al10.5W9.7Ni19.7Cr5.60.35870.1319
    Co72.5Ni10Al10W7.5Co68.8Al10.8W9.9Ni10.50.35930.1324
    下载: 导出CSV

    表 3  合金化组元与基体组元Co之间的混合焓$\Delta H$ (单位: kJ/mol)及在$\gamma / \gamma′ $两相中的配分系数(${K_x} = {C_x}^{\gamma′}/{C_x}^\gamma $)[9,10,40-42,44-52]

    Table 3.  Heats of mixing $\Delta H$ (unit: kJ/mol) between alloying elements and matrix element Co and their partition coefficients (${K_x} = {C_x}^{\gamma′ }/$${C_x}^\gamma $) for $\gamma$ and $\gamma′$[9,10,40-42,44-52]

    元素
    分类
    合金化
    元素
    混合焓
    $\Delta H$/kJ·mol
    元素配分
    系数K
    ${\overline {{\rm{Co}}} ^{\gamma }}$Cr–40.48—0.60
    Fe–1
    Re2
    ${\overline {{\rm{Co}}} ^{\gamma′ }}$Ni–21.08—1.27
    Ru–1
    Ir–3
    AlAl–190.93—1.60
    ${\overline {\rm{W}} }$W–11.03—6.21
    Mo–5
    ${\overline {{\rm{Ta}}} }$V–141.57—8.67
    Ta–24
    Nb–25
    Ti–28
    Sc–30
    Hf–35
    下载: 导出CSV

    表 4  Co-Al-W基多元合金的团簇成分式, 所列成分源自文献[2-4, 6, 8, 10, 39, 40-42, 44, 45, 48, 51, 57-62]

    Table 4.  Compositions formulas of Co-Al-W-base multi-element superalloys. The alloy compositions are taken from references [2-4, 6, 8, 10, 39, 40-42, 44, 45, 48, 51, 57-62]

    合金成分/at.%团簇成分式-[团簇](连接原子)3连接原子
    Co78Al10W10Ta2[Al-Co12]Co0.5Al0.6W1.6Ta0.3${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.5}{\rm{A}}{{\rm{l}}_{0.6}}{\overline {\rm{W}} _{1.6}}{\overline {{\rm{Ta}}} _{0.3}}$
    Co78Al9W10Mo3[Al-Co12]Co0.5Al0.4W1.6Mo0.5${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.5}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{2.1}}$
    Co79Al9W10Ti2[Al-Co12]Co0.6Al0.4W1.6Ti0.3${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.6}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.6}}{\overline {{\rm{Ta}}} _{0.3}}$
    Co79Al9W10V2[Al-Co12]Co0.6Al0.4W1.6V0.3${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.6}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.6}}{\overline {{\rm{Ta}}} _{0.3}}$
    Co79Al9W10Si2[Al-Co12]Co0.6Al0.4W1.6Si0.3${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.6}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.6}}{\overline {{\rm{Ta}}} _{0.3}}$
    Co79Al9W8Ta2Nb2[Al-Co12]Co0.6Al0.4W1.3Ta0.3Nb0.3${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.6}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.3}}{\overline {{\rm{Ta}}} _{0.6}}$
    Co79Al9W8Ta2V2[Al-Co12]Co0.6Al0.4W1.3Ta0.3V0.3${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.6}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.3}}{\overline {{\rm{Ta}}} _{0.6}}$
    Co79Al8W9Ta2Ti2[Al-Co12]Co0.6Al0.3W1.4Ta0.3Ti0.3${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.6}{\rm{A}}{{\rm{l}}_{0.3}}{\overline {\rm{W}} _{1.4}}{\overline {{\rm{Ta}}} _{0.6}}$
    Co79.5Al9.7W10.8[Al-Co12]Co0.7Al0.6W1.7${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.7}{\rm{A}}{{\rm{l}}_{0.6}}{\overline {\rm{W}} _{1.7}}$
    Co79.9Al9.4W10.7[Al-Co12]Co0.8Al0.5W1.7${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.8}{\rm{A}}{{\rm{l}}_{0.5}}{\overline {\rm{W}} _{1.7}}$
    Co80Al9W11[Al-Co12]Co0.8Al0.4W1.8${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.8}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.8}}$
    Co80Al9W9Ti2[Al-Co12]Co0.8Al0.4W1.4Ti0.3${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.8}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.4}}{\overline {{\rm{Ta}}} _{0.3}}$
    Co80Al9W9V2B0.04[Al-Co12]Co0.8Al0.4W1.4V0.3${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.8}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.4}}{\overline {{\rm{Ta}}} _{0.3}}$
    Co80Al9W9Ta2[Al-Co12]Co0.8Al0.4W1.4Ta0.3${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.8}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.4}}{\overline {{\rm{Ta}}} _{0.3}}$
    Co80.3Al9.3W10.4[Al-Co12]Co0.8Al0.5W1.7${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.8}{\rm{A}}{{\rm{l}}_{0.5}}{\overline {\rm{W}} _{1.7}}$
    Co80.5Al9W10Si0.5[Al-Co12]Co0.9Al0.4W1.6Si0.1${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.9}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.6}}{\overline {{\rm{Ta}}} _{0.1}}$
    Co81Al9W9Mo1B0.04[Al-Co12]Co1.0Al0.4W1.4Mo0.2${\overline {{\rm{Co}}} ^{\gamma′ }}_{1.0}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.6}}$
    Co81Al9W8Ta2[Al-Co12]Co1.0Al0.4W1.3Ta0.3${\overline {{\rm{Co}}} ^{\gamma′ }}_{1.0}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.3}}{\overline {{\rm{Ta}}} _{0.3}}$
    Co81.3Al9.2W9.5[Al-Co12]Co1.0Al0.5W1.5${\overline {{\rm{Co}}} ^{\gamma′ }}_{1.0}{\rm{A}}{{\rm{l}}_{0.5}}{\overline {\rm{W}} _{1.5}}$
    Co81.5Al9W9Nb0.5[Al-Co12]Co1.0Al0.4W1.4Nb0.1${\overline {{\rm{Co}}} ^{\gamma′ }}_{1.0}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.4}}{\overline {{\rm{Ta}}} _{0.1}}$
    Co81.5Al9W5.5Ta2Mo2[Al-Co12]Co1.0Al0.4W0.9Ta0.3Mo0.3${\overline {{\rm{Co}}} ^{\gamma′ }}_{1.0}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.2}}{\overline {{\rm{Ta}}} _{0.3}}$
    Co82Al9W9[Al-Co12]Co1.1Al0.4W1.4${\overline {{\rm{Co}}} ^{\gamma′ }}_{1.1}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.4}}$
    Co72Al9W9Ni10[Al-Co11.7Ni0.3]Ni1.1Al0.4W1.4${\overline {{\rm{Co}}} ^{\gamma′ }}_{1.1}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.4}}$
    Co82Al9W7.5Mo1.5[Al-Co12]Co1.1Al0.4W1.4${\overline {{\rm{Co}}} ^{\gamma′ }}_{1.1}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.4}}$
    Co80Al9W9Cr2B0.04[Al-Co12]Co0.8Cr0.3Al0.4W1.4${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.8}{\overline {{\rm{Co}}} ^\gamma }_{0.3}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.6}}$
    Co78Al9W9Cr4[Al-Co12]Co0.6Cr0.6Al0.4W1.4${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.6}{\overline {{\rm{Co}}} ^\gamma }_{0.6}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.4}}$
    Co73Al9W9Ni9[Al-Co11.7Ni0.3]Ni1.1Al0.4W1.4${\overline {{\rm{Co}}} ^{\gamma′ }}_{1.1}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.4}}$
    Co64Al9W9Ni18[Al-Co10.2Ni1.8]Ni1.1Al0.4W1.4${\overline {{\rm{Co}}} ^{\gamma′ }}_{1.1}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.4}}$
    Co81.8Al9.2W9[Al-Co12]Co1.1Al0.5W1.4${\overline {{\rm{Co}}} ^{\gamma′ }}_{1.1}{\rm{A}}{{\rm{l}}_{0.5}}{\overline {\rm{W}} _{1.4}}$
    Co72.5Al10W7.5Ni10[Al-Co11.6Ni0.4]Ni1.2Al0.4W1.4${\overline {{\rm{Co}}} ^{\gamma′ }}_{1.2}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.4}}$
    Co81.5Al9W5.5Ta2Ir2[Al-Co2]Co1.0Al0.4W0.9Ta0.3Ir0.3${\overline {{\rm{Co}}} ^{\gamma′ }}_{1.3}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{0.9}}{\overline {{\rm{Ta}}} _{0.3}}$
    Co79Al9W8Ta2Cr2[Al-Co12]Co0.6Cr0.3Al0.4W1.3Ta0.3${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.6}{\overline {{\rm{Co}}} ^\gamma }_{0.3}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.3}}{\overline {{\rm{Ta}}} _{0.3}}$
    下载: 导出CSV

    表 5  部分Co-Al-W基高温合金中$\gamma $$\gamma′ $两相团簇式[40,42,44,45]

    Table 5.  Composition formulas of $\gamma $ and $\gamma′ $ phases in some Co-Al-W-base superalloys[40,42,44,45]

    合金成分/at.%$\gamma $相团簇成分式$\gamma′ $相团簇成分式
    Co82Al9W9[Al-Co12]Co1.6Al0.4W1.0[Al-Co12]Co0.3Al0.5W2.2
    Co78Al9W9Cr4[Al-Co12]Co0.9Al0.3W0.9Cr0.9[Al-Co12]Co0.2Al0.5W1.8Cr0.5
    Co73Al9W9Ni18[Al-Co11.1Ni0.9]Al0.1W1.1Ni1.8[Al-Co9.4Ni2.6]Al0.7W1.8Ni0.5
    Co79.5Al9.7W10.8[Al-Co12]Co1.7Al0.4W0..9[Al-Co12]Co0.4Al0.6W2.0
    Co80Al9W9Ti2[Al-Co12]Co1.6Al0.4W0.8Ti0.2[Al-Co12]Co0.2Al0.4W1.9Ti0.4
    Co80Al9W9Ta2[Al-Co12]Co1.8Al0.4W0.7Ta0.1[Al-Co12]Co0.2Al0.4W1.9Ta0.5
    Co79Al8W9Ta2Ti2[Al-Co12]Co2.0Al0.3W0.5Ta0.04Ti0.1[Al-Co12]Co0.1Al0.4W1.9Ta0.3Ti0.3
    Co78Al10W10Ta2[Al-Co12]Co1.6Al0.7W0.7Ta0.1[Al-Co12]Al0.7W1.9Ta0.4
    Co78Al9W10Mo3[Al-Co12]Co1.7Al0.1W0.8Mo0.4[Al-Co12]Co0.2Al0.6W1.7Mo0.5
    下载: 导出CSV
  • [1]

    Sims C T, Hagel W C 1972 The Superalloys (New York: John Wiley & Sons) p1

    [2]

    Sato J, Omori T, Oikawa K, Ohnuma I, Kainuma R, Ishida K 2006 Science 312 90Google Scholar

    [3]

    Suzuki A, Pollock T M 2008 Acta Mater. 56 1288Google Scholar

    [4]

    Bauer A, Neumeiera S, Pyczakb F, Singer R F, Göken M 2012 Mater. Sci. Eng. 550 333Google Scholar

    [5]

    Klein L, Shen Y, Killian M S, Virtanen S 2011 Corros. Sci. 53 2713Google Scholar

    [6]

    Ooshima M, Tanaka K, Okamoto N L, Kishida K, Inui H 2010 J. Alloys Compd. 508 71Google Scholar

    [7]

    Chen M, Wang C Y 2009 Scr. Mater. 60 659Google Scholar

    [8]

    Bauer A, Neumeier S, Pyczakc F, Göken M 2010 Scr. Mater. 63 1197Google Scholar

    [9]

    Kobayashi S, Tsukamoto Y, Takasugi T 2012 Intermetallics 31 94Google Scholar

    [10]

    Meher S, Yan H Y, Nag S, Dye D, Banerjee R 2012 Scr. Mater. 67 850Google Scholar

    [11]

    Morinaga M, Yukawa N, Ezaki H, Adachi H 1984 Superalloys (Warrendale, PA: The Metallurgical Society of AIME) p523

    [12]

    张继山, 崔华, 胡壮麟, 村田纯教, 森永正彦, 汤川夏夫 1993 金属学报 29 289Google Scholar

    Zhang J S, Cui H, Hu Z L, Murata Y, Morinaga M, Yukawa N 1993 Acta Metall. Sin. 29 289Google Scholar

    [13]

    Dong C, Wang Q, Qiang J B, Wang Y M, Jiang N, Han G, Li Y H, Wu J, Xia J H 2007 J. Phys. D: Appl. Phys. 40 R273Google Scholar

    [14]

    Han G, Qiang J B, Li F W, Yuan L, Quan S G, Wang Q, Wang Y M, Dong C, Häussler P 2011 Acta Mater. 59 5917Google Scholar

    [15]

    Luo L J, Chen H, Wang Y M, Qiang J B, Wang Q, Dong C, Häussler P 2014 Philos. Mag. 94 2520Google Scholar

    [16]

    张宇, 王清, 董红刚, 董闯, 张洪宇, 孙晓峰 2017 金属学报 54 591Google Scholar

    Zhang Y, Wang Q, Dong H G, Dong C, Zhang H Y, Sun X F 2017 Acta Metall. Sin. 54 591Google Scholar

    [17]

    Bragg W L, Williams E J 1934 Proc. R. Soc. London, Ser. A 151 699

    [18]

    Williams E 1935 Proc. R. Soc. London, Ser. A 152 231Google Scholar

    [19]

    Bethe H 1935 Proc. R. Soc. London, Ser. A 150 552Google Scholar

    [20]

    Cowly J 1950 Phys. Rev. 77 669Google Scholar

    [21]

    Cowly J 1960 Phys. Rev. 120 1648Google Scholar

    [22]

    Cowly J 1965 Phys. Rev. 138 A1384Google Scholar

    [23]

    Chen H, Wang Q, Wang Y M, Qiang J B, Dong C 2010 Philos. Mag. 90 3935Google Scholar

    [24]

    Chen H, Wang Q, Wang Y M, Wang Y, Dong C 2011 Isr. J. Chem. 51 1226Google Scholar

    [25]

    Wang Y, Wang Q, Zhao J, Dong C 2010 Scr. Mater. 63 178Google Scholar

    [26]

    Yuan L, Pang C, Wang Y M, Wang Q, Qiang J B, Dong C 2010 Intermetallics 18 1800Google Scholar

    [27]

    Li F W, Qiang J B, Wang Q, Wang Y M, Dong X L, Dong C, Zhu S J 2012 Intermetallics 30 86Google Scholar

    [28]

    Wang Z R, Dong D D, Qiang J B, Wang Q, Wang Y M, Dong C 2013 Sci. China: Phys. Mech. Astron. 56 1419Google Scholar

    [29]

    Wang Q, Zhu C L, Li Y H, Wu J, Dong C, Qiang J B, Zhang W, Inoue A 2007 Mater. Sci. Forum 561−565 1275Google Scholar

    [30]

    谷俊杰 2011 硕士学位论文 (大连: 大连理工大学)

    Gu J J 2011 M. S. Thesis (Dalian: Dalian University of Technology) (in Chinese)

    [31]

    Wang Q, Li Q, Li X N, Zhang R Q, Gao X X, Dong C, Liaw P K 2015 Metall. Mater. Trans. A 46 3924Google Scholar

    [32]

    王清, 查钱锋, 刘恩雪, 董闯, 王学军, 谭朝鑫, 龚春俊 2012 金属学报 48 1201Google Scholar

    Wang Q, Zha Q F, Liu E X, Dong C, Wang X J, Tan C X, Gong C J 2012 Acta Metall. Sin. 48 1201Google Scholar

    [33]

    马仁涛, 郝传璞, 王清, 任明法, 王英敏, 董闯 2010 金属学报 46 1034Google Scholar

    Ma R T, Hao C P, Wang Q, Ren M F, Wang Y M, Dong C 2010 Acta Metall. Sin. 46 1034Google Scholar

    [34]

    董丹丹 2017 博士学位论文 (大连: 大连理工大学)

    Dong D D 2017 Ph. D. Dissertation (Dalian: Dalian University of Technology) (in Chinese)

    [35]

    董闯, 董丹丹, 王清 2018 金属学报 54 293Google Scholar

    Dong C, Dong D D, Wang Q 2018 Acta Metall. Sin. 54 293Google Scholar

    [36]

    Hong H L, Wang Q, Dong C 2015 Sci. China: Mater. 58 355Google Scholar

    [37]

    Hong H L, Wang Q, Dong C, Liaw P K 2014 Sci. Rep. 4 7065Google Scholar

    [38]

    洪海莲, 董闯, 王清, 张宇, 耿遥祥 2016 物理学报 65 036101Google Scholar

    Hong H L, Dong C, Wang Q, Zhang Y, Geng Y X 2016 Acta Phys. Sin. 65 036101Google Scholar

    [39]

    Pearson W B 1973 J. Appl. Cryst. 6 306Google Scholar

    [40]

    Pyczak F, Bauer A, Göken M, Lorenz U, Neumeier S, Oehring M, Paul J, Schell N, Schreyer A, Stark A, Symanzik F 2015 J. Alloys Compd. 632 110Google Scholar

    [41]

    Povstugar I, Zenk C H, Li R, Choi P P, Neumeier S, Dolotko O, Hoelzel M, Göken M, Raabe D 2016 Mater. Sci. Technol. 32 220Google Scholar

    [42]

    Shinagawa K, Omori T, Sato J, Oikawa K, Ohnuma I, Kainuma R, Ishida K 2008 Mater. Trans. 49 1474Google Scholar

    [43]

    Wang Y J, Wang C Y 2009 Appl. Phys. Lett. 94 261909Google Scholar

    [44]

    Bocchini P J, Lass E A, Moon K W, Williams M E, Campbell C E, Kattner U R, Dunand D C, Seidman D N 2013 Scr. Mater. 68 563Google Scholar

    [45]

    Povstugar I, Choi P P, Neumeier S, Bauer A, Zenk C H, Göken M, Raabe D 2014 Acta Mater. 78 78Google Scholar

    [46]

    Meher S, Banerjee R 2014 Intermetallics 49 138Google Scholar

    [47]

    Lass E A, Williams M E, Campbell C E, Moon K W, Kattner U R 2014 J. Phase Equilib. Diffus. 35 711Google Scholar

    [48]

    Zhong F, Li S S, Sha J B 2015 Mater. Sci. Eng. A 637 175Google Scholar

    [49]

    Sauza D J, Bocchini P J, Dunand D C, Seidman D N 2016 Acta Mater. 117 135Google Scholar

    [50]

    Zhou H J, Xue F, Chang H, Feng Q 2018 J. Mater. Sci. Technol. 34 799Google Scholar

    [51]

    Takeuchi A, Inoue A 2005 Mater. Trans. 46 2817Google Scholar

    [52]

    Shinagawa K, Omori T, Oikawa K, Kainuma R, Ishida K 2009 Scr. Mater. 61 612Google Scholar

    [53]

    Chen M, Wang C Y. 2010 Phys. Lett. A 374 3238Google Scholar

    [54]

    Ping D H, Cui C Y, Gu Y F, Harada H 2007 Ultramicroscopy 107 791Google Scholar

    [55]

    Makineni S K, Nithin B, Chattopadhyay K 2015 Scr.Mater. 98 36Google Scholar

    [56]

    Makineni S K, Samanta A, Rojhirunsakool T, Alam T, Nithin B, Singh A K, Banerjee R, Chattopadhyay K 2015 Acta Mater. 97 29Google Scholar

    [57]

    Pollock T M, Dibbern J, Tsunekane M, Suzuki 2010 JOM 62 58Google Scholar

    [58]

    Yan H Y, Vorontsov V A, Dye D 2014 Intermetallics 48 44Google Scholar

    [59]

    Xue F, Zhou H J, Ding X F, Wang M L, Feng Q 2013 Mater. Lett. 112 215Google Scholar

    [60]

    Xue F, Zhou H J, Feng Q 2014 JOM 66 2486Google Scholar

    [61]

    Titus M S, Suzuki A, Pollock T M 2012 High Temperature Creep of New L12 Containing Cobalt‐Base Superalloys (New York: John Wiley Sons. Inc.) p823

    [62]

    Shi L, Yu J J, Cui C Y, Sun X F 2015 Mater. Lett. 149 58Google Scholar

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    [19] 赵有祥, 刘志毅, 王守证, 郭树权. 高压高温处理对A15Nb3(Al,Ge)结构成分及其超导性能的影响. 物理学报, 1983, 32(1): 108-117. doi: 10.7498/aps.32.108
    [20] 高树濬, 钱知强. 均匀合金自扩散的准化学模型. 物理学报, 1965, 21(3): 622-629. doi: 10.7498/aps.21.622
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出版历程
  • 收稿日期:  2018-05-28
  • 修回日期:  2019-01-15
  • 上网日期:  2019-03-12
  • 刊出日期:  2019-03-20

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