Cluster formulas of Co-Al-W-base superalloys

Ma Qi-Hui; Zhang Yu; Wang Qing; Dong Hong-Gang; Dong Chuang

doi:10.7498/aps.68.20181030

Abstract

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]Co_1.1Al_0.4W_1.4 (～ [Al-Co₁₂]Co_1.0Al_0.5W_1.5), [Al-Co₁₂]Co_1.6Al_0.4W_1.0 (～ [Al-Co₁₂]Co_1.5Al_0.5W_1.0), and [Al-Co₁₂]Co_0.3Al_0.5W_2.2 (～[Al-Co₁₂]Co_0.5Al_0.5W_2.0).

Keywords:

Authors and contacts

Key Laboratory of Materials Modification by Laser, Ion and Electron Beams Ministry of Education, Dalian University of Technology, Dalian 116024, China

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).

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Cited By

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

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

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

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

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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 $和$\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

Figure 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 ${\overline {{\rm{Co}}} _{81.250}}{\rm{A}}{{\rm{l}}_{9.375}}{\left( {\overline {\rm{W}} ,\overline {{\rm{Ta}}} } \right)_{9.375}}$

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

Figure 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

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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 $
Co₈₂Al₉W₉	Co_81.7Al_9.3W₉	0.3580	0.3579	0.0001
Co₈₃Al₉W₈	Co_81.9Al_10.0W_8.1	0.3576	0.3575	0.0001
Co₈₀Al₉W₁₁	Co_80.7Al_9.2W_10.2	0.3586	0.3588	0.0002
Co₇₄Al₉W₉Cr₈	Co_73.9Al_8.0W_6.8Cr_11.2	0.3578	0.3575	0.0003
Co₆₄Al₉W₉Ni₁₈	Co_69.1Al_6.8W_7.0Ni_16.9	0.3577	0.3562	0.0015
Co₆₅Al₉W₉Ni₉Cr₈	Co_66.7Al_7.8W_6.7Ni_8.3Cr_10.7	0.3581	0.3584	0.0003
Co₅₆Al₉W₉Ni₁₈Cr₈	Co_59.2Al_6.0W_7.4Ni_15.6Cr_11.8	0.3583	0.3581	0.0002
Co_72.5Ni₁₀Al₁₀W_7.5	Co_76.2Al_8.7W_5.4Ni_9.7	0.3578	0.3562	0.0016

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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/nm	W原子半径/nm
Co₈₂Al₉W₉	Co_77.49Al_10.03W_12.48	0.3594	0.1317
Co₈₃Al₉W₈	Co_76.6Al_9.4W₁₄	0.3589	0.1306
Co₈₀Al₉W₁₁	Co_75.1Al_9.1W_15.8	0.3595	0.1311
Co₇₄Al₉W₉Cr₈	Co_73.9Al_9.4W_10.4Cr_6.3	0.3587	0.1314
Co₆₄Al₉W₉Ni₁₈	Co_58.9Al_10.8W_11.0Ni_19.3	0.3590	0.1317
Co₆₅Al₉W₉Ni₉Cr₈	Co_64.2Al_10.1W_9.9Ni_9.4Cr_6.4	0.3587	0.1317
Co₅₆Al₉W₉Ni₁₈Cr₈	Co_54.5Al_10.5W_9.7Ni_19.7Cr_5.6	0.3587	0.1319
Co_72.5Ni₁₀Al₁₀W_7.5	Co_68.8Al_10.8W_9.9Ni_10.5	0.3593	0.1324

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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	–4	0.48—0.60
	Fe	–1
	Re	2
${\overline {{\rm{Co}}} ^{\gamma′ }}$	Ni	–2	1.08—1.27
	Ru	–1
	Ir	–3
Al	Al	–19	0.93—1.60
${\overline {\rm{W}} }$	W	–1	1.03—6.21
${\overline {\rm{W}} }$	Mo	–5	1.03—6.21
${\overline {{\rm{Ta}}} }$	V	–14	1.57—8.67
	Ta	–24
	Nb	–25
	Ti	–28
	Sc	–30
	Hf	–35

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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]Co_0.5Al_0.6W_1.6Ta_0.3	${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.5}{\rm{A}}{{\rm{l}}_{0.6}}{\overline {\rm{W}} _{1.6}}{\overline {{\rm{Ta}}} _{0.3}}$
Co₇₈Al₉W₁₀Mo₃	[Al-Co₁₂]Co_0.5Al_0.4W_1.6Mo_0.5	${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.5}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{2.1}}$
Co₇₉Al₉W₁₀Ti₂	[Al-Co₁₂]Co_0.6Al_0.4W_1.6Ti_0.3	${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.6}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.6}}{\overline {{\rm{Ta}}} _{0.3}}$
Co₇₉Al₉W₁₀V₂	[Al-Co₁₂]Co_0.6Al_0.4W_1.6V_0.3	${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.6}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.6}}{\overline {{\rm{Ta}}} _{0.3}}$
Co₇₉Al₉W₁₀Si₂	[Al-Co₁₂]Co_0.6Al_0.4W_1.6Si_0.3	${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.6}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.6}}{\overline {{\rm{Ta}}} _{0.3}}$
Co₇₉Al₉W₈Ta₂Nb₂	[Al-Co₁₂]Co_0.6Al_0.4W_1.3Ta_0.3Nb_0.3	${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.6}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.3}}{\overline {{\rm{Ta}}} _{0.6}}$
Co₇₉Al₉W₈Ta₂V₂	[Al-Co₁₂]Co_0.6Al_0.4W_1.3Ta_0.3V_0.3	${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.6}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.3}}{\overline {{\rm{Ta}}} _{0.6}}$
Co₇₉Al₈W₉Ta₂Ti₂	[Al-Co₁₂]Co_0.6Al_0.3W_1.4Ta_0.3Ti_0.3	${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.6}{\rm{A}}{{\rm{l}}_{0.3}}{\overline {\rm{W}} _{1.4}}{\overline {{\rm{Ta}}} _{0.6}}$
Co_79.5Al_9.7W_10.8	[Al-Co₁₂]Co_0.7Al_0.6W_1.7	${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.7}{\rm{A}}{{\rm{l}}_{0.6}}{\overline {\rm{W}} _{1.7}}$
Co_79.9Al_9.4W_10.7	[Al-Co₁₂]Co_0.8Al_0.5W_1.7	${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.8}{\rm{A}}{{\rm{l}}_{0.5}}{\overline {\rm{W}} _{1.7}}$
Co₈₀Al₉W₁₁	[Al-Co₁₂]Co_0.8Al_0.4W_1.8	${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.8}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.8}}$
Co₈₀Al₉W₉Ti₂	[Al-Co₁₂]Co_0.8Al_0.4W_1.4Ti_0.3	${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.8}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.4}}{\overline {{\rm{Ta}}} _{0.3}}$
Co₈₀Al₉W₉V₂B_0.04	[Al-Co₁₂]Co_0.8Al_0.4W_1.4V_0.3	${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.8}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.4}}{\overline {{\rm{Ta}}} _{0.3}}$
Co₈₀Al₉W₉Ta₂	[Al-Co₁₂]Co_0.8Al_0.4W_1.4Ta_0.3	${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.8}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.4}}{\overline {{\rm{Ta}}} _{0.3}}$
Co_80.3Al_9.3W_10.4	[Al-Co₁₂]Co_0.8Al_0.5W_1.7	${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.8}{\rm{A}}{{\rm{l}}_{0.5}}{\overline {\rm{W}} _{1.7}}$
Co_80.5Al₉W₁₀Si_0.5	[Al-Co₁₂]Co_0.9Al_0.4W_1.6Si_0.1	${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.9}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.6}}{\overline {{\rm{Ta}}} _{0.1}}$
Co₈₁Al₉W₉Mo₁B_0.04	[Al-Co₁₂]Co_1.0Al_0.4W_1.4Mo_0.2	${\overline {{\rm{Co}}} ^{\gamma′ }}_{1.0}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.6}}$
Co₈₁Al₉W₈Ta₂	[Al-Co₁₂]Co_1.0Al_0.4W_1.3Ta_0.3	${\overline {{\rm{Co}}} ^{\gamma′ }}_{1.0}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.3}}{\overline {{\rm{Ta}}} _{0.3}}$
Co_81.3Al_9.2W_9.5	[Al-Co₁₂]Co_1.0Al_0.5W_1.5	${\overline {{\rm{Co}}} ^{\gamma′ }}_{1.0}{\rm{A}}{{\rm{l}}_{0.5}}{\overline {\rm{W}} _{1.5}}$
Co_81.5Al₉W₉Nb_0.5	[Al-Co₁₂]Co_1.0Al_0.4W_1.4Nb_0.1	${\overline {{\rm{Co}}} ^{\gamma′ }}_{1.0}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.4}}{\overline {{\rm{Ta}}} _{0.1}}$
Co_81.5Al₉W_5.5Ta₂Mo₂	[Al-Co₁₂]Co_1.0Al_0.4W_0.9Ta_0.3Mo_0.3	${\overline {{\rm{Co}}} ^{\gamma′ }}_{1.0}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.2}}{\overline {{\rm{Ta}}} _{0.3}}$
Co₈₂Al₉W₉	[Al-Co₁₂]Co_1.1Al_0.4W_1.4	${\overline {{\rm{Co}}} ^{\gamma′ }}_{1.1}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.4}}$
Co₇₂Al₉W₉Ni₁₀	[Al-Co_11.7Ni_0.3]Ni_1.1Al_0.4W_1.4	${\overline {{\rm{Co}}} ^{\gamma′ }}_{1.1}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.4}}$
Co₈₂Al₉W_7.5Mo_1.5	[Al-Co₁₂]Co_1.1Al_0.4W_1.4	${\overline {{\rm{Co}}} ^{\gamma′ }}_{1.1}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.4}}$
Co₈₀Al₉W₉Cr₂B_0.04	[Al-Co₁₂]Co_0.8Cr_0.3Al_0.4W_1.4	${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.8}{\overline {{\rm{Co}}} ^\gamma }_{0.3}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.6}}$
Co₇₈Al₉W₉Cr₄	[Al-Co₁₂]Co_0.6Cr_0.6Al_0.4W_1.4	${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.6}{\overline {{\rm{Co}}} ^\gamma }_{0.6}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.4}}$
Co₇₃Al₉W₉Ni₉	[Al-Co_11.7Ni_0.3]Ni_1.1Al_0.4W_1.4	${\overline {{\rm{Co}}} ^{\gamma′ }}_{1.1}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.4}}$
Co₆₄Al₉W₉Ni₁₈	[Al-Co_10.2Ni_1.8]Ni_1.1Al_0.4W_1.4	${\overline {{\rm{Co}}} ^{\gamma′ }}_{1.1}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.4}}$
Co_81.8Al_9.2W₉	[Al-Co₁₂]Co_1.1Al_0.5W_1.4	${\overline {{\rm{Co}}} ^{\gamma′ }}_{1.1}{\rm{A}}{{\rm{l}}_{0.5}}{\overline {\rm{W}} _{1.4}}$
Co_72.5Al₁₀W_7.5Ni₁₀	[Al-Co_11.6Ni_0.4]Ni_1.2Al_0.4W_1.4	${\overline {{\rm{Co}}} ^{\gamma′ }}_{1.2}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.4}}$
Co_81.5Al₉W_5.5Ta₂Ir₂	[Al-Co₂]Co_1.0Al_0.4W_0.9Ta_0.3Ir_0.3	${\overline {{\rm{Co}}} ^{\gamma′ }}_{1.3}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{0.9}}{\overline {{\rm{Ta}}} _{0.3}}$
Co₇₉Al₉W₈Ta₂Cr₂	[Al-Co₁₂]Co_0.6Cr_0.3Al_0.4W_1.3Ta_0.3	${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.6}{\overline {{\rm{Co}}} ^\gamma }_{0.3}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.3}}{\overline {{\rm{Ta}}} _{0.3}}$

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表 5 部分Co-Al-W基高温合金中$\gamma $和$\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]Co_1.6Al_0.4W_1.0	[Al-Co₁₂]Co_0.3Al_0.5W_2.2
Co₇₈Al₉W₉Cr₄	[Al-Co₁₂]Co_0.9Al_0.3W_0.9Cr_0.9	[Al-Co₁₂]Co_0.2Al_0.5W_1.8Cr_0.5
Co₇₃Al₉W₉Ni₁₈	[Al-Co_11.1Ni_0.9]Al_0.1W_1.1Ni_1.8	[Al-Co_9.4Ni_2.6]Al_0.7W_1.8Ni_0.5
Co_79.5Al_9.7W_10.8	[Al-Co₁₂]Co_1.7Al_0.4W_0..9	[Al-Co₁₂]Co_0.4Al_0.6W_2.0
Co₈₀Al₉W₉Ti₂	[Al-Co₁₂]Co_1.6Al_0.4W_0.8Ti_0.2	[Al-Co₁₂]Co_0.2Al_0.4W_1.9Ti_0.4
Co₈₀Al₉W₉Ta₂	[Al-Co₁₂]Co_1.8Al_0.4W_0.7Ta_0.1	[Al-Co₁₂]Co_0.2Al_0.4W_1.9Ta_0.5
Co₇₉Al₈W₉Ta₂Ti₂	[Al-Co₁₂]Co_2.0Al_0.3W_0.5Ta_0.04Ti_0.1	[Al-Co₁₂]Co_0.1Al_0.4W_1.9Ta_0.3Ti_0.3
Co₇₈Al₁₀W₁₀Ta₂	[Al-Co₁₂]Co_1.6Al_0.7W_0.7Ta_0.1	[Al-Co₁₂]Al_0.7W_1.9Ta_0.4
Co₇₈Al₉W₁₀Mo₃	[Al-Co₁₂]Co_1.7Al_0.1W_0.8Mo_0.4	[Al-Co₁₂]Co_0.2Al_0.6W_1.7Mo_0.5

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