J. Mater. Sci. Technol. ›› 2018, Vol. 34 ›› Issue (2): 355-364.DOI: 10.1016/j.jmst.2017.11.005
Special Issue: 材料计算 2018
• Orginal Article • Previous Articles Next Articles
Weiliang Chenab, Xueyong Dinga, Yuchao Fengb, Xiongjun Liuc, Kui Liub, Z.P. Luc, Dianzhong Lib, Yiyi Lib, C.T. Liud, Xing-Qiu Chenb()
Received:
2017-08-01
Revised:
2017-09-22
Accepted:
2017-10-25
Online:
2018-02-10
Published:
2018-02-10
Weiliang Chen, Xueyong Ding, Yuchao Feng, Xiongjun Liu, Kui Liu, Z.P. Lu, Dianzhong Li, Yiyi Li, C.T. Liu, Xing-Qiu Chen. Vacancy formation enthalpies of high-entropy FeCoCrNi alloy via first-principles calculations and possible implications to its superior radiation tolerance[J]. J. Mater. Sci. Technol., 2018, 34(2): 355-364.
i-th configuration | α | b | c | α | β | γ | V | △H |
---|---|---|---|---|---|---|---|---|
(?) | (?) | (?) | (°) | (°) | (°) | (?3/uc) | (meV/atom) | |
1 CrFeCoNi | 8.60 | 4.29 | 9.03 | 56.04 | 104.36 | 70.79 | 217.64 | 84.5 |
2 CrFeNiCo | 8.66 | 4.33 | 9.00 | 56.06 | 103.66 | 70.16 | 220.51 | 78.8 |
3 CrCoFeNi | 8.59 | 4.27 | 8.95 | 56.20 | 104.20 | 70.74 | 215.89 | 102.0 |
4 CrCoNiFe | 8.56 | 4.29 | 8.94 | 55.68 | 103.67 | 70.74 | 215.35 | 100.8 |
5 CrNiFeCo | 8.67 | 4.32 | 9.01 | 56.23 | 103.95 | 70.60 | 222.08 | 71.2 |
6 CrNiCoFe | 8.55 | 4.29 | 8.92 | 55.80 | 103.60 | 71.03 | 216.40 | 105.3 |
7 FeCrCoNi | 8.58 | 4.28 | 8.95 | 56.02 | 104.09 | 70.59 | 214.98 | 87.4 |
8 FeCrNiCo | 8.60 | 4.27 | 8.96 | 55.96 | 104.14 | 70.93 | 216.21 | 90.2 |
9 FeCoCrNi | 8.57 | 4.28 | 8.93 | 56.02 | 103.82 | 70.62 | 215.14 | 88.6 |
10 FeCoNiCr | 8.56 | 4.29 | 8.93 | 55.89 | 103.80 | 70.65 | 214.95 | 100.5 |
11 FeNiCrCo | 8.57 | 4.27 | 8.93 | 55.84 | 103.82 | 70.84 | 214.84 | 101.2 |
12 FeNiCoCr | 8.63 | 4.32 | 9.05 | 56.03 | 103.99 | 70.74 | 221.60 | 73.1 |
13 CoCrFeNi | 8.61 | 4.31 | 9.02 | 55.95 | 104.04 | 71.00 | 220.42 | 65.0 |
14 CoCrNiFe | 8.59 | 4.28 | 8.97 | 55.90 | 104.08 | 71.39 | 217.96 | 59.4 |
15 CoFeCrNi | 8.58 | 4.29 | 8.94 | 55.99 | 103.72 | 70.83 | 217.37 | 78.7 |
16 CoFeNiCr | 8.57 | 4.28 | 8.96 | 55.83 | 104.02 | 71.02 | 215.69 | 96.7 |
17 CoNiCrFe | 8.58 | 4.29 | 8.99 | 55.81 | 104.00 | 71.10 | 218.08 | 77.3 |
18 CoNiFeCr | 8.60 | 4.30 | 9.01 | 56.04 | 104.20 | 70.53 | 217.39 | 93.0 |
19 NiCrFeCo | 8.56 | 4.27 | 8.95 | 55.89 | 104.04 | 71.07 | 215.59 | 71.2 |
20 NiCrCoFe | 8.57 | 4.28 | 8.98 | 55.73 | 103.95 | 71.26 | 217.13 | 90.5 |
21 NiFeCrCo | 8.62 | 4.32 | 9.05 | 55.72 | 103.90 | 71.86 | 224.81 | 63.9 |
22 NiFeCoCr | 8.64 | 4.30 | 9.03 | 56.13 | 104.12 | 70.69 | 219.96 | 80.6 |
23 NiCoCrFe | 8.67 | 4.32 | 9.01 | 55.90 | 103.89 | 70.71 | 221.21 | 70.9 |
24 NiCoFeCr | 8.60 | 4.29 | 9.00 | 56.18 | 104.54 | 70.91 | 217.66 | 93.8 |
Table 1 DFT-obtained lattice parameters, equilibrium volumes, and enthalpies of formation for 24-ocupation configuration of the 20-atom-unit-cell ordered SQS structure.
i-th configuration | α | b | c | α | β | γ | V | △H |
---|---|---|---|---|---|---|---|---|
(?) | (?) | (?) | (°) | (°) | (°) | (?3/uc) | (meV/atom) | |
1 CrFeCoNi | 8.60 | 4.29 | 9.03 | 56.04 | 104.36 | 70.79 | 217.64 | 84.5 |
2 CrFeNiCo | 8.66 | 4.33 | 9.00 | 56.06 | 103.66 | 70.16 | 220.51 | 78.8 |
3 CrCoFeNi | 8.59 | 4.27 | 8.95 | 56.20 | 104.20 | 70.74 | 215.89 | 102.0 |
4 CrCoNiFe | 8.56 | 4.29 | 8.94 | 55.68 | 103.67 | 70.74 | 215.35 | 100.8 |
5 CrNiFeCo | 8.67 | 4.32 | 9.01 | 56.23 | 103.95 | 70.60 | 222.08 | 71.2 |
6 CrNiCoFe | 8.55 | 4.29 | 8.92 | 55.80 | 103.60 | 71.03 | 216.40 | 105.3 |
7 FeCrCoNi | 8.58 | 4.28 | 8.95 | 56.02 | 104.09 | 70.59 | 214.98 | 87.4 |
8 FeCrNiCo | 8.60 | 4.27 | 8.96 | 55.96 | 104.14 | 70.93 | 216.21 | 90.2 |
9 FeCoCrNi | 8.57 | 4.28 | 8.93 | 56.02 | 103.82 | 70.62 | 215.14 | 88.6 |
10 FeCoNiCr | 8.56 | 4.29 | 8.93 | 55.89 | 103.80 | 70.65 | 214.95 | 100.5 |
11 FeNiCrCo | 8.57 | 4.27 | 8.93 | 55.84 | 103.82 | 70.84 | 214.84 | 101.2 |
12 FeNiCoCr | 8.63 | 4.32 | 9.05 | 56.03 | 103.99 | 70.74 | 221.60 | 73.1 |
13 CoCrFeNi | 8.61 | 4.31 | 9.02 | 55.95 | 104.04 | 71.00 | 220.42 | 65.0 |
14 CoCrNiFe | 8.59 | 4.28 | 8.97 | 55.90 | 104.08 | 71.39 | 217.96 | 59.4 |
15 CoFeCrNi | 8.58 | 4.29 | 8.94 | 55.99 | 103.72 | 70.83 | 217.37 | 78.7 |
16 CoFeNiCr | 8.57 | 4.28 | 8.96 | 55.83 | 104.02 | 71.02 | 215.69 | 96.7 |
17 CoNiCrFe | 8.58 | 4.29 | 8.99 | 55.81 | 104.00 | 71.10 | 218.08 | 77.3 |
18 CoNiFeCr | 8.60 | 4.30 | 9.01 | 56.04 | 104.20 | 70.53 | 217.39 | 93.0 |
19 NiCrFeCo | 8.56 | 4.27 | 8.95 | 55.89 | 104.04 | 71.07 | 215.59 | 71.2 |
20 NiCrCoFe | 8.57 | 4.28 | 8.98 | 55.73 | 103.95 | 71.26 | 217.13 | 90.5 |
21 NiFeCrCo | 8.62 | 4.32 | 9.05 | 55.72 | 103.90 | 71.86 | 224.81 | 63.9 |
22 NiFeCoCr | 8.64 | 4.30 | 9.03 | 56.13 | 104.12 | 70.69 | 219.96 | 80.6 |
23 NiCoCrFe | 8.67 | 4.32 | 9.01 | 55.90 | 103.89 | 70.71 | 221.21 | 70.9 |
24 NiCoFeCr | 8.60 | 4.29 | 9.00 | 56.18 | 104.54 | 70.91 | 217.66 | 93.8 |
Mixing enthalpy (meV/atom) | FeCo | FeCr | FeNi | CoCr | CoNi | CrNi | FeCoNiCr |
---|---|---|---|---|---|---|---|
ΔH [DFT] | -8 | -60 | -97 | 5 | -30 | -21 | -52.8 |
ΔH [Mie] | -10 | -20 | -20 | -72.5 | 0 | -103 | -56.5 |
ΔH [Exp] | -103 | 61 | -40 | 27 | 6 | 66 | 4.3 |
ΔH [This work; DFT values of the 24 configurations in average] | 84.4 | ||||||
ΔH (SQS [ | 76.7 | ||||||
ΔH (SRO [ | 15.8 |
Table 2 Mixing enthalpies of six equiatomic binary alloys derived through the first-principles high-throughput DFT calculations and by the empirical Miedema’s macroscopic models. The derived mixing enthalpy via Eq. (3) is also in comparison with our currently DFT calculations using the 24 configurations of the ordered SQS structure in average. The unit of the mixing enthalpy is meV/atom. Noted that the ΔH values obtained by Miedema’s macroscopic models and by experiments are taken from the Ref. [78,79] and the DFT values are from the Ref. [64] for all six binary compounds.
Mixing enthalpy (meV/atom) | FeCo | FeCr | FeNi | CoCr | CoNi | CrNi | FeCoNiCr |
---|---|---|---|---|---|---|---|
ΔH [DFT] | -8 | -60 | -97 | 5 | -30 | -21 | -52.8 |
ΔH [Mie] | -10 | -20 | -20 | -72.5 | 0 | -103 | -56.5 |
ΔH [Exp] | -103 | 61 | -40 | 27 | 6 | 66 | 4.3 |
ΔH [This work; DFT values of the 24 configurations in average] | 84.4 | ||||||
ΔH (SQS [ | 76.7 | ||||||
ΔH (SRO [ | 15.8 |
Fig. 2. Vacancy formation enthalpies (in eV) for each type of atoms in FeCrCoNi HEAs. Note that for each type of atom we have 120 different calculations by all possible local configurations. These data are compiled in an ascending order. In comparison, we also list the vacancy formation enthalpy of each type X atom in its solid and ordered fcc and bcc structures.
HXVac (Calc.) | Distribution of HSQSi (Calc. in%) | Fcc (Calc.) | Fcc (Expt.) | ||||
---|---|---|---|---|---|---|---|
eV | <1.0 | 1.0-1.5 | 1.5-2.0 | >2.0 | eV | eV | |
Fe | 1.58 | 12.5 | 28.3 | 39.1 | 20.0 | 1.89 (this work), 1.86 [ | |
Cr | 1.61 | 9.1 | 35.8 | 35.8 | 20.8 | 1.62 (this work), 1.58 [ | |
Co | 1.70 | 3.3 | 36.7 | 36.7 | 23.3 | 1.85 this work), 1.83 [ | |
Ni | 1.89 | 2.5 | 49.1 | 49.1 | 34.2 | 1.41 (this work), 1.46 [ | 1.79 [ |
Table 3 Vacancy formation enthalpies (averaged HXVac and HSQSi in eV) at 0 K of the FeCrCoNi HEA in comparison to those of the ordered fcc-type Fe, Cr, Co and Ni metals.
HXVac (Calc.) | Distribution of HSQSi (Calc. in%) | Fcc (Calc.) | Fcc (Expt.) | ||||
---|---|---|---|---|---|---|---|
eV | <1.0 | 1.0-1.5 | 1.5-2.0 | >2.0 | eV | eV | |
Fe | 1.58 | 12.5 | 28.3 | 39.1 | 20.0 | 1.89 (this work), 1.86 [ | |
Cr | 1.61 | 9.1 | 35.8 | 35.8 | 20.8 | 1.62 (this work), 1.58 [ | |
Co | 1.70 | 3.3 | 36.7 | 36.7 | 23.3 | 1.85 this work), 1.83 [ | |
Ni | 1.89 | 2.5 | 49.1 | 49.1 | 34.2 | 1.41 (this work), 1.46 [ | 1.79 [ |
Fig. 4. Influence of the vacancy on the local magnetic moments in the FeCrCoNi HEA. In panel (a) the Fe-, Cr-, Co- and Ni-magnetic moments with the presence of a Fe single vacancy; Panel (b), the Fe-, Cr-, Co- and Ni-magnetic moments with the presence of a Cr single vacancy; Panel (c) the Fe-, Cr-, Co- and Ni-magnetic moments with the presence of a Co single vacancy; Panel (d) the Fe-, Cr-, Co- and Ni-magnetic moments with the presence of a Ni single vacancy. Note that all magnetic moments (hollow squares) with the presence of the vacancy are compared with the magnetic moment (solid circles) without any vacancies.
Fig. 5. 3D visualization of the nearest neighboring distances and their local moments of Fe-Cr (a), Fe-Co (b), Fe-Fe (c) and Fe-Ni (d) for the FeCrCoNi HEA without any vacancies; Panels (e, f, g, and h) are the 3D visualized nearest neighboring distances related with their local moments of Fe-Cr (e), Fe-Co (f), Fe-Fe (g) and Fe-Ni (h) for the FeCrCoNi HEA with a Fe single vacancy. The red plane denotes the averaged nearest neighboring distance.
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