Phase-field-method-studied mechanism of Cu-rich phase precipitation in Al<sub><i>x</i></sub>CuMnNiFe high-entropy alloy

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Abstract

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 Al _xCuMnNiFe high-entropy alloy is established, and the microscopic evolution of the nano-Cu-rich phase of Al _xCuMnNiFe high-entropy alloy ( x= 0.4, 0.5, 0.6, 0.7) at 823 K isothermal aging is simulated. The results show that the Al _xCuMnNiFe high-entropy alloy generates two complex core-shell structures upon aging: Cu-rich core/B2 _sshell and B2 _ccore/FeMn shell, and it is found through discussion and analysis that the formed B2 _cplays 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 Al _xCuMnNiFe 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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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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Alloy system	Al	Cu	Mn	Ni	Fe
Al_0.4Cu_1.5Mn₁Ni₁Fe_1.5	7.4	27.8	18.5	18.5	27.8
Al_0.5Cu_1.5Mn₁Ni₁Fe_1.5	9.2	27.2	18.2	18.2	27.2
Al_0.6Cu_1.5Mn₁Ni₁Fe_1.5	10.8	26.8	17.8	17.8	26.8
Al_0.7Cu_1.5Mn₁Ni₁Fe_1.5	12.28	26.36	17.5	17.5	26.36

DownLoad: CSV

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

DownLoad: CSV

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

DownLoad: CSV

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	—

DownLoad: CSV

Alloy system	t^*	$ {N}_{v} $/($ \times {10}^{23}{{\rm{m}}}^{-3}) $	f/%	r/nm	Strengthening/MPa
Al_0.4Cu_1.5Mn₁Ni₁Fe_1.5	4500	3.9291	0.0116	1.9148	1166
Al_0.5Cu_1.5Mn₁Ni₁Fe_1.5	4500	4.0817	0.0123	1.9286	1188
Al_0.6Cu_1.5Mn₁Ni₁Fe_1.5	5000	3.3951	0.0103	1.9343	1038
Al_0.7Cu_1.5Mn₁Ni₁Fe_1.5	7500	4.04	0.031	2.63	775
Whenr$\; \leqslant \;$2 nm, it is a dislocation slicing mechanism, and whenr> 2 nm, it is a dislocation bypassing mechanism.

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Vol. 72, Issue 7 - 2023-04-05

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