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Stacking fault energy of face-centered-cubic high entropy alloys S.F. Liua, Y. Wua, H.T. Wangb,∗∗, J.Y. Hea, J.B. Liuc, C.X. Chenc, X.J. Liua, H. Wanga, Z.P. Lua,∗ a b c
State Key Laboratory for Advance Metals and Materials, University of Science and Technology Beijing, Beijing 10083, China Institute of Applied Mechanics, Zhejiang University, Hangzhou 310027, China School of Materials Science and Engineering, Zhejiang University, Hangzhou 310027, China
A R T I C L E I N F O
A B S T R A C T
Keywords: Stacking fault energy High-entropy alloys Twining Mechanical properties
The stacking fault energy (SFE) values of several typical face-centered-cubic (fcc) high-entropy alloys (HEAs) were experimentally measured by weak-beam dark-ﬁeld transmission electron microscopy. It was found that the SFE of the Fe-Co-Ni-Cr-Mn HEA system strongly depends on the SFE of the individual constituents. Speciﬁcally, the SFE of this HEA system is closely associated with the Ni concentration in the alloys. Additionally, the lower SFE tends to promote formation of more deformation twins with a smaller thickness under loading, leading to better mechanical properties, especially at low temperatures.
1. Introduction Recently, high-entropy alloys (HEAs) consisting of multiple principle elements in equal or near equal atomic ratio have attracted extensive attention because of their interesting structural and mechanical properties [1–5]. Surprisingly, these multi-principal-element alloys tend to form simple crystalline structures, instead of multiple phases or intermetallic compounds. For example, FeCoNiCrMn is a single phase alloy with a face-centered cubic (fcc) lattice. It was reported  that FeCoNiCrMn has excellent fracture toughness even at cryogenic temperature of 77 K, and mechanical twins were found to be responsible for the outstanding low-temperature properties. As such, more and more scientiﬁc activities were recently focused on systematic and in-depth research on the stacking fault energy (SFE) of HEAs, particularly fcc HEAs, and aimed to further optimize their mechanical performance and reveal the related deformation mechanisms [7–12]. Theoretical SFE calculations of FeCoNiCrMn have been conducted by several diﬀerent research groups; S. Huang et al.  reported that the SFE of FeCoNiCrMn is 21 mJ m−2 via ab initio calculations, whilst A.J. Zaddach et al.  determined the SFE for a series of Fe-Co-Ni-CrMn alloys with diﬀerent number of constituents (i.e., Ni, FeNi, FeNiCr, FeCoNiCr and FeCoNiCrMn) using both X-ray diﬀraction measurements and ﬁrst-principles calculations. It was found that the SFE decreases with the increase in the number of components, i.e. conﬁgurational entropy. The SFE of quinary FeCoNiCrMn and quaternary FeCoNiCr lies in-between 20 and 25 mJ m−2, and that of ternary FeNiCr is increased up to 60 mJ m−2. However, experimental validation of these calculations in HEAs has rarely been reported, although it is not only
important for validating the computation results, but also imperative for properly understanding mechanical behavior of HEAs with large conﬁguration entropy, especially the low-temperature deformation mechanisms. In order to uncover experimentally eﬀects of elemental constituents on the SFE and the relationship between the SFE and mechanical properties in HEAs, NiCoCr, FeCoNiCr, FeCoNiCrMn, (FeCoNiCr)94Mn6, (FeCoNiCr)86Mn14 and Fe20Co15Ni25Cr20Mn20 were selected. The approach using the weak-beam dark-ﬁeld (WBDF) imaging technique proposed previously  was employed to analyze the partial dislocation pairs and determine the SFE in this work. 2. Experimental details The selected alloys were produced by arc-melting the pure elements (purity > 99.98%) in a Ti-gettered high-purity Ar atmosphere. Each ingot was ﬂipped and re-melted at least four times to ensure chemical homogeneity. The melted alloys were then cast into a copper mold with a dimension of 10 mm × 10 mm × 60 mm. The drop-cast alloys were subsequently homogenized at 1473 K for 10 h in Ar atmosphere, followed by water quenching. Then the ingots were cold-rolled to 65% thickness reduction and annealed at 800 °C for 1 h. The dog boneshaped tensile specimens with a gauge length of 20 mm, a width of 5 mm and a thickness of 1.3 mm were cut from the sheet in the direction parallel to the rolling direction by electric discharging machining and polished to the 2000-grit SiC paper. Shear modulus and Poisson's ratio of the as-cast alloys were measured by resonant ultrasound spectroscopy while lattice parameters of
Corresponding author. Corresponding author. E-mail address: [email protected]
http://dx.doi.org/10.1016/j.intermet.2017.10.004 Received 3 August 2017; Received in revised form 6 October 2017; Accepted 8 October 2017 0966-9795/ © 2017 Elsevier Ltd. All rights reserved.
Please cite this article as: Liu, S.F., Intermetallics (2017), http://dx.doi.org/10.1016/j.intermet.2017.10.004
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the alloys were determined by X-ray diﬀraction. The SFE measurements were conducted using a JEM-2100 TEM operated at 200 kV. The specimens were ﬁrst strained under tension at a rate of 1 × 10−3 s−1 to the yield point. Disks of 3-mm diameter were then taken from the central part of these pre-tensioned specimens, mechanically polished to 50 μm thickness through SiC paper and then electron-polished by twinjet technique using a mixed solution of HClO4:C2H6O = 1:9. Dark ﬁeld images of Shockley partial dislocations were observed by the method of WBDF with a beam direction near the  zone on the (111) defect habit plane using < -220 > -type g-vectors. At least four diﬀerent dislocations were characterized for each alloy to measure the Shockley partial dislocation separations. In additional, tensile tests of all the alloys were conducted at the same strain rate of 1 × 10−3 s−1 at room temperature and liquid nitrogen temperature.
Gbp2 2 − v 2vcos 2θ ⎞ · ·⎛1 − 8πγ 1 − v ⎝ 2−v ⎠
where G is the shear modulus, bp is the 1/6a0 < 112 > partial dislocation Burgers vector (a 0 is the lattice parameter determined by X-ray diﬀraction) and v is the Poisson's ratio. Shear modulus and Poisson's ratio of the alloys were measured by resonant ultrasound spectroscopy. The measured data of FeCoNiCrMn, FeCoNiCr and NiCoCr are similar to those reported in literature . Table 1 lists the shear modulus, Poisson's ratio, lattice parameter and SFE of all the investigated alloys. The experimentally obtained SFE of FeCoNiCrMn and NiCoCr is 26.5 ± 4.5 and 18 ± 4 mJ m−2, respectively, which is similar to that reported by George et al. [17,18] (i.e., 30 ± 5 mJ m−2 and 22 ± 4 mJ m−2, respectively) using the same WBDF method, verifying the reliability of our measurements. As can be seen from Table 1, the SFE value of the (FeCoNiCr)94Mn6 and (FeCoNiCr)86Mn14 alloys is similar to that of FeCoNiCrMn and FeCoNiCr. It seems that addition of Mn has inappreciable inﬂuence on the SFE of the Fe-Co-Ni-Cr-Mn alloy system. Nevertheless, it was conﬁrmed that the SFE of Fe-Mn-(Al-Si) steel increases with the increase of Mn , indicating that even the same element has diﬀerent impact on the SFE in diﬀerent alloy systems, which may be related to diﬀerent electronic, volumetric and magnetic eﬀects . For the particular quinary Fe-Co-Ni-Cr-Mn alloy system, however, we found that Ni plays a dominant role in the SFE, as shown in Fig. 2. The higher the Ni content, the larger the SFE, which could be related to the large SFE of Ni (γNi = 125 mJ m−2 ). Replacing the constituents having low SFE (e.g., Co, γCo = 27 mJ m−2 ) with those having high SFE tends to increase the SFE of the resultant alloy. For example, substitution of 5% Co with Ni in FeCoNiCrMn (i.e., the Fe20Co15Ni25Cr20Mn20 HEA) increases the SFE from 26.5 ± 4.5 to 38 ± 6 mJ m−2. Based on these observations, it is clear that the SFE value of individual elements in the
3. Results and discussion The SFE of alloys can be measured by observing the sizes of extended dislocation nodes or width of partial dislocations using TEM. However, it was reported that the sizes of dislocation nodes are very sensitive to heat treatment, but the width between partial dislocations is not . Fig. 1a–c show typical WBDF images of dissociated dislocations of three representative NiCoCr, FeCoNiCr and Fe20Co15Ni25Cr20Mn20 HEAs on their (111) habit planes, respectively. As can be seen, the partial dislocation core separation of NiCoCr is much wider than that of FeCoNiCr and Fe20Co15Ni25Cr20Mn20. The separation distance (d) and the angle (θ) between the dislocation and the Burgers vector of full dislocation of these three alloys are measured and plotted in Fig. 1d. Theoretical partial dislocation curves are ﬁtted to the experimental data to determine the SFE based on the following equation :
Fig. 1. The WBDF images of dissociated dislocations of NiCoCr (a), FeCoNiCr (b) and Fe20Co15Ni25Cr20Mn20 (c), and (d) Dissociation width of partial dislocations as a function of the angle between the dislocation line and the total Burgers vector.
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Table 1 Shear modulus (G), Poisson's ratio (v), lattice parameter (a0) and stacking fault energy (r) of the alloys investigated in this work. Alloy
G (GPa) (this work)
G (GPa) (ref )
v (this work)
v (ref )
NiCoCr FeCoNiCr FeCoNiCrMn (FeCoNiCr)94Mn6 (FeCoNiCr)86Mn14 Fe20Co15Ni25Cr20Mn20
88 85 82 81 82 77
87 84 80 – – –
0.30 0.29 0.28 0.30 0.31 0.32
0.30 0.28 0.26 – – –
3.529 3.565 3.576 3.567 3.571 3.578
± ± ± ± ± ±
2 2 2 2 2 2
0.01 0.01 0.01 0.01 0.01 0.01
± ± ± ± ± ±
0.018 0.014 0.014 0.012 0.019 0.016
18 ± 4 27 ± 4 26.5 ± 4.5 28 ± 4 29 ± 4 38 ± 6
mechanical twinning. Such mechanical twins eﬀectively increase the dislocation storage capacity and provide steady source of work hardening, improving strength and ductility by postponing the onset of plastic instability by necking. Tensile tests of all the investigated alloys at the liquid nitrogen temperature were also conducted, and the corresponding results are shown in Fig. 3b. The strength and ductility of all these alloys are increased, as compared with those at room temperature. It has been reported that as the temperature decreases, the SFE of FeCoNiCrMn is also decreased and reaches about 3.4 mJ m−2 at 0 K . Therefore, the reduced SFE may be responsible for the improvement of mechanical properties of these alloys at the low temperature. NiCoCr shows the best
system is critical for that of the resultant alloy; either increasing the constituents having low SFE or reducing those with high SFE tends to lead to the HEA which deforms via twining-dominant process. However, further studies are needed to verify whether such observation also holds in the other HEA systems. The room-temperature engineering stress-strain curves of six alloys studied in this work are shown in Fig. 3a, and as presented, NiCoCr which has the lowest SFE shows the best combination of strength and ductility at room temperature. The excellent room-temperature mechanical properties of NiCoCr were ascribed to the mechanical twinning induced by deformation . The twinning stress (σT) can be computed by the following equation :
γ 1/2 σT = K ⎛ ⎞ ⎝ Gb ⎠
± ± ± ± ± ±
γ (mJ·m−2) (this work)
where K is a constant and b is Burgers vector. From Eqs. (1) and (2), it is known that the twinning stress (σT) is proportional to the inverse of the square root of the separation distance between the Shockley partials (d). Therefore, it is reasonable to speculate that in the NiCoCr alloy, which has much wider partial dislocations separations, twinning can occur more easily, as compared with that in the FeCoNiCrMn HEA. Indeed, it was reported that in NiCoCr, nanotwinning can occur over a wide strain range, allowing the necking instability to be postponed more eﬀectively in NiCoCr and eventually giving rise to superior mechanical properties at room temperature . On the other hand, for materials with relatively high SFE, the partial dislocations are easy to associate because of relatively narrow separations. However, dissociation into partial dislocations is more favorable and the partial dislocations separation is larger in materials with low SFE, making it diﬃcult for dissociated dislocations to associate and thus impeding the cross-slip and climb of dislocations. As a result, the main plastic deformation mechanism is more easily to change from dislocation glide to
Fig. 2. SFE as a function of the Ni content of ﬁve quinary HEAs. Black symbols represent the alloys investigated in this work while red ones are the data from Ref. .
Fig. 3. Engineering stress-strain curves for the HEAs tested at diﬀerent temperatures. (a) room temperature and (b) 77 K.
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Fig. 4. Deformation twins analysis after pretensioned about 12% in liquid nitrogen of NiCoCr (ﬁgures on the left) and Fe20Co15Ni25Cr20Mn20 (ﬁgures on the right). (a, b) Bright ﬁeld TEM images of deformation twins, (c, d) dark ﬁeld TEM images with SAD patterns showing diﬀraction spots from the twin and matrix, and (e, f) twin thickness distribution.
formation of thicker twins. Usually, nucleation and thickening of twins are closely related to cross-slip [25,26], and in materials with low SFE, twin growth would be impeded as a result of low ability of cross-slip of the dislocations. Consequently, the twin growth is more diﬃcult for materials with low SFE. Moreover, a suﬃcient stress concentration is needed to overcome the resistance of dislocations when twins nucleate (i.e. the twinning stress), and such stress promotes the twins to propagate to large sizes .
mechanical properties at the liquid nitrogen temperature, indicating that it still has the lowest SFE with the decreasing temperature. The pretensioned specimens of NiCoCr and Fe20Co15Ni25Cr20Mn20 were characterized by TEM and the corresponding results are shown in Fig. 4. Deformation twins are observed in these samples, indicating that even in Fe20Co15Ni25Cr20Mn20 with a relatively high SFE, mechanical twinning was also induced at the liquid nitrogen temperature. From Fig. 4, it is clear that the deformation twins in NiCoCr are more concentrated and thinner than those in Fe20Co15Ni25Cr20Mn20. Statistical measurements from numerous deformation twins edge-on as demonstrated in Fig. 4e and f, revealing that in NiCoCr, the average twin thickness is about 8 nm, narrower than that of Fe20Co15Ni25Cr20Mn20 with an average twin thickness value of about 14 nm. As discussed earlier, the twinning stress of Fe20Co15Ni25Cr20Mn20 is likely higher than that of NiCoCr with wider partial dislocation separations, which results in
4. Conclusion The SFE of six typical fcc HEAs, i.e., NiCoCr, FeCoNiCr, FeCoNiCrMn, (FeCoNiCr)94Mn6, (FeCoNiCr)86Mn14 and Fe20Co15Ni25Cr20Mn20 were experimentally measured. It was found that in the particular Fe-Co-Ni-Cr-Mn system, elemental constituents 4
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