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相场法研究AlxCuMnNiFe高熵合金富Cu相析出机理

王凯乐 杨文奎 史新成 侯华 赵宇宏

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相场法研究AlxCuMnNiFe高熵合金富Cu相析出机理

王凯乐, 杨文奎, 史新成, 侯华, 赵宇宏

Phase-field-method-studied mechanism of Cu-rich phase precipitation in AlxCuMnNiFe high-entropy alloy

Wang Kai-Le, Yang Wen-Kui, Shi Xin-Cheng, Hou Hua, Zhao Yu-Hong
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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.
      通信作者: 赵宇宏, zhaoyuhong@nuc.edu.cn
    • 基金项目: 国家自然科学基金(批准号: 52074246, 22008224, 52275390, 52205429, 52201146)、国防基础科研项目(批准号: JCKY2020408B002, WDZC2022-12)、山西省重点研发项目(批准号: 202102050201011, 202202050201014)和山西省研究生创新项目(批准号: 2021Y592)资助的课题.
      Corresponding author: Zhao Yu-Hong, zhaoyuhong@nuc.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 52074246, 22008224, 52275390, 52205429, 52201146), the National Defense Basic Scientific Research Program of China (Grant Nos. JCKY2020408B002, WDZC2022-12), the Key Research and Development Program of Shanxi Province (Grant Nos. 202102050201011, 202202050201014), and the Shanxi Graduate Innovation Project, China (Grant No. 2021Y592)
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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 systemAlCuMnNiFe
    Al0.4Cu1.5Mn1Ni1Fe1.57.427.818.518.527.8
    Al0.5Cu1.5Mn1Ni1Fe1.59.227.218.218.227.2
    Al0.6Cu1.5Mn1Ni1Fe1.510.826.817.817.826.8
    Al0.7Cu1.5Mn1Ni1Fe1.512.2826.3617.517.526.36
    下载: 导出CSV

    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 elementsCuMnNiAl
    ${D}_{i}^{0, \varphi }/{({10}^{-5}~{\rm{m} } }^{2}{\cdot}{ {\rm{s} } }^{-1}$)${\rm{\alpha } }({\rm{B} }{\rm{C} }{\rm{C} })$4.7014.9014.0053.50
    ${\rm{\gamma } }({\rm{F} }{\rm{C} }{\rm{C} })$4.301.781.082.20
    ${Q}_{i}^{0, \varphi }/{({10}^{5}~{\rm{J} }{\cdot}{\rm{m} }{\rm{o} }{\rm{l} } }^{-1}$)${\rm{\alpha } }({\rm{B} }{\rm{C} }{\rm{C} })$2.442.632.642.71
    ${\rm{\gamma } } ({\rm{F} }{\rm{C} }{\rm{C} } )$2.802.642.732.67
    $ {D}_{i}^{0, \varphi } $-frequency factor; $ {Q}_{i}^{0, \varphi } $-diffusion activation energy
    下载: 导出CSV

    表 3  相场模型参数

    Table 3.  Phase field parameters.

    Parameter typeParameterValueUnit
    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 $823K
    Elasticity constant[56]$ {C}_{11}^{{\rm{m}}} $228GPa
    $ {C}_{12}^{{\rm{m}}} $132GPa
    $ {C}_{44}^{{\rm{m}}} $116.5GPa
    $ {C}_{11}^{{\rm{p}}} $169GPa
    $ {C}_{12}^{{\rm{p}}} $122GPa
    $ {C}_{44}^{{\rm{p}}} $75.3GPa
    Lattice misfit coefficient[55]$ {\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 $1nm
    $ {\rm{d}}y $1nm
    $ {\rm{d}}z $1nm
    $ \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
    下载: 导出CSV

    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 elementsAlCuMnNiFe
    Al–1–19–22–11
    Cu–14413
    Mn–194–80
    Ni–224–8–2
    Fe–11130–2
    下载: 导出CSV

    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 systemt *$ {N}_{v} $/($ \times {10}^{23}{{\rm{m}}}^{-3}) $f/% r/nmStrengthening/MPa
    Al0.4Cu1.5Mn1Ni1Fe1.545003.92910.01161.91481166
    Al0.5Cu1.5Mn1Ni1Fe1.545004.08170.01231.92861188
    Al0.6Cu1.5Mn1Ni1Fe1.550003.39510.01031.93431038
    Al0.7Cu1.5Mn1Ni1Fe1.575004.040.0312.63775
    When r$\; \leqslant \;$2 nm, it is a dislocation slicing mechanism, and when r > 2 nm, it is a dislocation bypassing mechanism.
    下载: 导出CSV
  • [1]

    Cantor B, Chang I T H, Knight P, Vincent A 2004 Mater. Sci. Eng., A 375 213

    [2]

    Zhang Y 2019 High-Entropy Materials (Singapore: Springer Nature Singapore Pte Ltd) p215

    [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 299Google Scholar

    [4]

    Zhou Y J, Zhang Y, Wang Y L, Chen G L 2007 Appl. Phys. Lett. 90 253

    [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 1237Google Scholar

    [7]

    Chen X, Hu J X, Liu Y, Xiang F 2021 Met. Mater. Int. 27 2230Google Scholar

    [8]

    Pradeep K G, Wanderka N, Choi P, Banhart J, Murty B S, Raabe D 2013 Acta Mater. 61 4696Google Scholar

    [9]

    Jones N G, Frezza A, Stone H J 2014 Mater. Sci. Eng., A 615 214Google Scholar

    [10]

    Dąbrowa J, Cieślak G, Stygar M, Mroczka K, Berebt K, Kulik T, Danielewski M 2017 Intermetallics 84 52Google Scholar

    [11]

    Wu P H, Liu N, Yang W, Zhu Z X, Liu Y P, Wang X J 2015 Mater. Sci. Eng. , A 642 142Google Scholar

    [12]

    Xian X, Lin L, Zhong Z, Zhang C, Chen C, Song K J, Cheng J G, Wu Y C 2018 Mater. Sci. Eng., A 713 134Google Scholar

    [13]

    Borkar T, Gwalani B, Choudhuri D, Alam T, Mantri A S, Gibson M A 2016 Intermetallics 71 31Google 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 170Google Scholar

    [15]

    Shim S H, Pouraliakbar H, Hong S I 2022 Scr. Mater. 210 114473Google Scholar

    [16]

    Lahiri A 2022 J. Indian Inst. Sci. 102 39Google Scholar

    [17]

    Chen L Q 2002 Annu. Rev. Mater. Res. 32 113Google Scholar

    [18]

    Chen L Q, Zhao Y H 2021 Prog. Mater. Sci. 124 100868

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出版历程
  • 收稿日期:  2022-12-26
  • 修回日期:  2023-01-30
  • 上网日期:  2023-02-09
  • 刊出日期:  2023-04-05

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