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BCC(体心立方)和FCC(面心立方)结构共存的高熵合金通常具有优异的综合力学性能, Al元素可以促进含Cu高熵合金由FCC向BCC结构转变. 本文基于Chan-Hilliard方程和Allen-Cahn方程, 建立AlxCuMnNiFe高熵合金三维相场模型, 模拟了AlxCuMnNiFe高熵合金(x = 0.4, 0.5, 0.6, 0.7)在823 K等温时效时纳米富Cu相的微观演化过程. 结果表明, AlxCuMnNiFe高熵合金时效时会产生两种复杂核壳结构: 富Cu核/B2s壳以及B2c核/FeMn壳, 通过讨论分析发现形成的B2c对纳米富Cu相的形成起到抑制作用, 这种抑制作用随着Al元素的增加而变大; 结合经验公式做出AlxCuMnNiFe高熵合金富Cu相的屈服强度随时效时间的变化曲线, 得到峰值屈服强度的时效时间和合金体系, 可以为时效工艺提供参考.High-entropy alloys with BCC and FCC coexisting structures usually have excellent comprehensive mechanical properties, and Al element can promote the transformation of Cu-containing high-entropy alloys from FCC structure to BCC structure to obtain the BCC and FCC coexisting structures. In order to illustrate the process of phase separation of high entropy alloys, a low-cost Al-TM transition group element high-entropy alloy is selected in this work. Based on the Chan-Hilliard equation and Allen-Cahn equation, a three-dimensional phase field model of AlxCuMnNiFe high-entropy alloy is established, and the microscopic evolution of the nano-Cu-rich phase of AlxCuMnNiFe high-entropy alloy (x = 0.4, 0.5, 0.6, 0.7) at 823 K isothermal aging is simulated. The results show that the AlxCuMnNiFe high-entropy alloy generates two complex core-shell structures upon aging: Cu-rich core/B2s shell and B2c core/FeMn shell, and it is found through discussion and analysis that the formed B2c plays an inhibitory role in the formation of the nano-Cu-rich phase, and that this inhibitory role becomes larger with the increase of Al element. Combining the empirical formula, the curve of yield strength of the Cu-rich phase varying with the aging time is obtained for the AlxCuMnNiFe high-entropy alloy, and the overall yield strength of the high-entropy alloy has a rising-and-then-falling trend with the change of time, and the aging time of the peak yield strength and the alloy system are obtained from the change of the curve, so that the best alloy system and aging time of the high-entropy alloy can provide a reference for aging process.
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Keywords:
- phase field method /
- high entropy alloy /
- Cu-rich phase /
- elastic energy
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图 1 时效温度为823 K时Al0.7Cu1.5Mn1Ni1Fe1.5高熵合金三维形貌演化图 (a)—(e) 分别表示元素Cu, Ni, Al, Mn, Fe元素以及序参量的形貌; (1)—(5)表示不同演化时间
Fig. 1. Evolution of three-dimensional morphology of Al0.7Cu1.5Mn1Ni1Fe1.5 high entropy alloys at aging temperature of 823 K: (a)–(e) The morphology of elements Cu, Ni, Al, Mn, Fe and order parameters, respectively; (1)–(5) indicates different evolution times.
图 2 时效温度为823 K时Al0.7Cu1.5Mn1Ni1Fe1.5高熵合金在时效过程中(a)总自由能与化学自由能(b)弹性能与界面能随时间的变化曲线
Fig. 2. Curves of (a) total free energy and chemical free energy (b) elastic energy and interfacial energy with time during aging of Al0.7Cu1.5Mn1Ni1Fe1.5 high entropy alloy at aging temperature of 823 K.
图 3 t * = 20000时Al0.7Cu1.5Mn1Ni1Fe1.5高熵合金形貌图 (a) Ni的三维空间分布, 球状的B2相和环状的B2壳; (b) 球状富Cu相及周围元素分布; (c) 球状B2相及周围元素分布; (d) 短棒状的富Cu相及元素分布; (e) 球状富Cu相成分曲线; (f) 球状B2相成分曲线; (g) 短棒状富Cu相成分曲线
Fig. 3. Morphology of Al0.7Cu1.5Mn1Ni1Fe1.5 high-entropy alloy at t * = 20000: (a) Three-dimensional spatial distribution of Ni, spherical B2 phase and annular B2 shell; (b) spherical Cu-rich phase and surrounding elemental distribution; (c) spherical B2 phase and surrounding elemental distribution; (d) short rod-like Cu-rich phase and elemental distribution; (e) spherical Cu-rich phase composition curve; (f) spherical B2 phase composition curve; (g) short rod-shaped Cu-rich phase composition curve.
图 4 在时效温度为823 K时Al0.7Cu1.5Mn1Ni1Fe1.5高熵合金B2-NiAl演化图 (a)—(f) B2-NiAl相不同元素不随时间变化得三维演化图; (g)—(l)相对应时刻的成分曲线
Fig. 4. The evolution of Al0.6Cu1.5Mn1Ni1Fe1.5 high-entropy alloy B2-NiAl at an aging temperature of 823 K: (a)–(f) The three-dimensional evolution of different elements of B2-NiAl phase without changing with time; (g)–(l) the composition curves obtained at the corresponding time.
图 5 不同Al含量下AlxCuMnNiFe高熵合金 (a) 数量密度随时间变化; (b) 体积分数随时间变化; (c) 平均颗粒半径随时间变化
Fig. 5. Variation of (a) number density, (b) volume fraction and (c) average particle radius with time for AlxCuMnNiFe high-entropy alloys with different Al contents.
图 6 不同合金体系在随时间变化的三维模拟图 (a)—(d) 表示Al0.4, Al0.5, Al0.6, Al0.7四个体系. (1)—(5)分别表示开始形核时间以及四个体系到达峰值数量密度的时间
Fig. 6. Three-dimensional simulations of different alloy systems over time, (a)–(d) for Al0.4, Al0.5, Al0.6, and Al0.7, respectively; (1)–(5) for the start of nucleation and the time to peak number density for the four systems, respectively.
图 7 纳米富Cu相在时效过程中 (a) 共格强化、(b) 化学强化、(c) 模量强化、(d) Orowan强化和(e) 纳米富Cu相屈服强度随时效时间的变化
Fig. 7. (a) Co-grid strengthening, (b) chemical strengthening, (c) modulus strengthening, (d) Orowan strengthening and (e) variation of yield strength of nano-Cu-rich phase with aging time during aging.
表 1 合金元素成分的原子百分含量(单位: %)
Table 1. Atomic percent of alloying element composition (unit: %).
Alloy system Al Cu Mn Ni Fe Al0.4Cu1.5Mn1Ni1Fe1.5 7.4 27.8 18.5 18.5 27.8 Al0.5Cu1.5Mn1Ni1Fe1.5 9.2 27.2 18.2 18.2 27.2 Al0.6Cu1.5Mn1Ni1Fe1.5 10.8 26.8 17.8 17.8 26.8 Al0.7Cu1.5Mn1Ni1Fe1.5 12.28 26.36 17.5 17.5 26.36 
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表 2 合金元素的频率因子和扩散激活能[52]
Table 2. Frequency factor and activation energy of alloying elements.
Alloy elements Cu Mn Ni Al ${D}_{i}^{0, \varphi }/{({10}^{-5}~{\rm{m} } }^{2}{\cdot}{ {\rm{s} } }^{-1}$) ${\rm{\alpha } }({\rm{B} }{\rm{C} }{\rm{C} })$ 4.70 14.90 14.00 53.50 ${\rm{\gamma } }({\rm{F} }{\rm{C} }{\rm{C} })$ 4.30 1.78 1.08 2.20 ${Q}_{i}^{0, \varphi }/{({10}^{5}~{\rm{J} }{\cdot}{\rm{m} }{\rm{o} }{\rm{l} } }^{-1}$) ${\rm{\alpha } }({\rm{B} }{\rm{C} }{\rm{C} })$ 2.44 2.63 2.64 2.71 ${\rm{\gamma } } ({\rm{F} }{\rm{C} }{\rm{C} } )$ 2.80 2.64 2.73 2.67 $ {D}_{i}^{0, \varphi } $-frequency factor; $ {Q}_{i}^{0, \varphi } $-diffusion activation energy
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表 3 相场模型参数
Table 3. Phase field parameters.
Parameter type Parameter Value Unit Cahn-Hilliard model[55] $ {\kappa }_{c} $ $ 5.0\times {10}^{-15} $ ${\rm{J} \cdot}{ {\rm{m} } }^{2}{\cdot{\rm{m} }{\rm{o} }{\rm{l} } }^{-1}$ $ {\kappa }_{\eta } $ $ 1.0\times {10}^{-15} $ $ {\rm{J}}{\cdot{\rm{m}}}^{2}{\cdot{\rm{m}}{\rm{o}}{\rm{l}}}^{-1} $ $ Y $ $ 2.14\times {10}^{11} $ $ {\rm{P}}{\rm{a}} $ $ {V}_{{\rm{m}}} $ $ 7.09\times {10}^{-6} $ ${ {\rm{m} } }^{3}{\cdot {\rm{m} }{\rm{o} }{\rm{l} } }^{-1}$ $ W $ $ 5.0\times {10}^{3} $ ${\rm J} {\cdot} {\rm mol}^{-1}$ $ T $ 823 K Elasticity constant[56] $ {C}_{11}^{{\rm{m}}} $ 228 GPa $ {C}_{12}^{{\rm{m}}} $ 132 GPa $ {C}_{44}^{{\rm{m}}} $ 116.5 GPa $ {C}_{11}^{{\rm{p}}} $ 169 GPa $ {C}_{12}^{{\rm{p}}} $ 122 GPa $ {C}_{44}^{{\rm{p}}} $ 75.3 GPa Lattice misfit coefficient[55] $ {\varepsilon }_{{\rm{C}}{\rm{u}}}^{0} $ $ 3.29\times {10}^{-2} $ $ {\varepsilon }_{{\rm{M}}{\rm{n}}}^{0} $ $ 5.22\times {10}^{-4} $ $ {\varepsilon }_{{\rm{N}}{\rm{i}}}^{0} $ $ 4.75\times {10}^{-4} $ $ {\varepsilon }_{{\rm{A}}{\rm{l}}}^{0} $ $ 1.64\times {10}^{-4} $ Simulation parameters $ {\rm{d}}x $ 1 nm $ {\rm{d}}y $ 1 nm $ {\rm{d}}z $ 1 nm $ \Delta t $ 0.01 $ {\kappa }_{c}, {\kappa }_{\eta } $-gradient energy coefficient; $ Y $-average stiffness; $ {V}_{{\rm{m}}} $-molar volume; $ W $-structural transformation barriers; $ {C}_{11}^{{\rm{m}}}, {C}_{12}^{{\rm{m}}}, {C}_{44}^{{\rm{m}}} $-elastic constant of the matrix phase; $ {C}_{11}^{{\rm{p}}}, {C}_{12}^{{\rm{p}}}, {C}_{44}^{{\rm{p}}} $-elastic constant of the precipitated phase; $ {\varepsilon }_{i}^{0}(i={\rm{C}}{\rm{u}}, {\rm{M}}{\rm{n}}, {\rm{N}}{\rm{i}}, {\rm{A}}{\rm{l}}) $- lattice misfit coefficients of Cu, Mn, Ni, Al; $ {\rm{d}}x, {\rm{d}}y, {\rm{d}}z $ unit length of simulated meshes; $ \Delta t $-unit time step
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表 4 AlxCuMnNiFe中各元素的
$ {\Delta H}_{{\rm{m}}{\rm{i}}{\rm{x}}} $ [59](单位: kJ/mol)Table 4.
$ {\Delta H}_{{\rm{m}}{\rm{i}}{\rm{x}}} $ between elements in AlxCuMnNiFe alloy (unit: kJ/mol)Alloy elements Al Cu Mn Ni Fe Al — –1 –19 –22 –11 Cu –1 — 4 4 13 Mn –19 4 — –8 0 Ni –22 4 –8 — –2 Fe –11 13 0 –2 —
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表 5 不同合金体系强化的基本数据
Table 5. Basic data on strengthening of different alloy systems.
Alloy system t * $ {N}_{v} $/($ \times {10}^{23}{{\rm{m}}}^{-3}) $ f/% r/nm Strengthening/MPa Al0.4Cu1.5Mn1Ni1Fe1.5 4500 3.9291 0.0116 1.9148 1166 Al0.5Cu1.5Mn1Ni1Fe1.5 4500 4.0817 0.0123 1.9286 1188 Al0.6Cu1.5Mn1Ni1Fe1.5 5000 3.3951 0.0103 1.9343 1038 Al0.7Cu1.5Mn1Ni1Fe1.5 7500 4.04 0.031 2.63 775 When r$\; \leqslant \;$2 nm, it is a dislocation slicing mechanism, and when r > 2 nm, it is a dislocation bypassing mechanism.
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[1] Cantor B, Chang I T H, Knight P, Vincent A 2004 Mater. Sci. Eng., A 375 213
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[3] Yeh J W, Chen S K, Lin S J, Gan J Y, Chin T S, Shun T T, Tsau C H, Chang S Y. 2004 Adv. Eng. Mater. 6 299
Google Scholar
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[5] Niu S Z, Kou H C, Wang J, Li J S 2021 Rare Met. 40 2508
[6] Sha M H, Zhang L, Zhang J W, Li N, Li T Z, Wang N 2017 Rare Met. Mater. Eng. 46 1237
Google Scholar
[7] Chen X, Hu J X, Liu Y, Xiang F 2021 Met. Mater. Int. 27 2230
Google Scholar
[8] Pradeep K G, Wanderka N, Choi P, Banhart J, Murty B S, Raabe D 2013 Acta Mater. 61 4696
Google Scholar
[9] Jones N G, Frezza A, Stone H J 2014 Mater. Sci. Eng., A 615 214
Google Scholar
[10] Dąbrowa J, Cieślak G, Stygar M, Mroczka K, Berebt K, Kulik T, Danielewski M 2017 Intermetallics 84 52
Google Scholar
[11] Wu P H, Liu N, Yang W, Zhu Z X, Liu Y P, Wang X J 2015 Mater. Sci. Eng. , A 642 142
Google Scholar
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Google Scholar
[13] Borkar T, Gwalani B, Choudhuri D, Alam T, Mantri A S, Gibson M A 2016 Intermetallics 71 31
Google Scholar
[14] Gwalani B, Choudhuri D, Soni V, Ren Y, Styles M, Hwang J Y, Nam S J, Ryu H, Hong S H, Banerjee R 2017 Acta Mater. 129 170
Google Scholar
[15] Shim S H, Pouraliakbar H, Hong S I 2022 Scr. Mater. 210 114473
Google Scholar
[16] Lahiri A 2022 J. Indian Inst. Sci. 102 39
Google Scholar
[17] Chen L Q 2002 Annu. Rev. Mater. Res. 32 113
Google Scholar
[18] Chen L Q, Zhao Y H 2021 Prog. Mater. Sci. 124 100868
[19] Xin T Z, Zhao Y H, Mahjoub R, Jiang J X, Yadav A, Nomoto K, Niu R M, Tang S, Ji F, Quadir Z, Miskovic D, Daniels J, Xu W Q, Liao X Z, Chen L Q, Hagihara K, Li X Y, Ringer S, Ferry M 2021 Sci. Adv. 7 eabf3039
Google Scholar
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Google Scholar
[21] Tian X L, Zhao Y H, Gu T, Guo Y L, Xu F Q, Hou H 2022 Mater. Sci. Eng., A 849 143485
Google Scholar
[22] Zhao Y H, Zhang B, Hou H, Chen W P, Wang M 2019 J. Mater. Sci. Technol. 35 1044
Google Scholar
[23] Zhang J B, Wang H F, Kuang W W, Zhang Y C, Li S, Zhao Y H, Herlach D M 2018 Acta Mater. 148 86
Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
[29] Kadirvel K, Kloenne Z, Jensen J K, Fraser H, Wang Y 2021 Appl. Phys. Lett. 119 171905
Google Scholar
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Google Scholar
[31] Li J L, Li Z, Wang Q, Dong C, Liaw P K 2020 Acta Mater. 197 10
Google Scholar
[32] Coutinho Y A, Kunwar A, Moelans N 2022 J. Mater. Sci. 57 10600
Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
[37] 栾亨伟, 赵威, 姚可夫 2020 材料热处理学报 41 1
Luan H W, Zhao W, Yao K F 2020 Trans. Mater. Heat Treat. 41 1
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Google Scholar
[39] 郝家苗 2020 硕士学位论文 (大连: 大连理工大学)
Hao J M 2020 M. S. Thesis (Dalian: Dalian University of Technology) (in chinese)
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