Journal of Materials Science & Technology  2019 , 35 (6): 1175-1183 https://doi.org/10.1016/j.jmst.2018.12.014

Composition and phase structure dependence of mechanical and magnetic properties for AlCoCuFeNix high entropy alloys

Cong Liua, Wenyi Penga, C.S. Jianga, Hongmin Guoa, Jun Taoa, Xiaohua Dengb, Zhaoxia Chena

a School of Materials Science and Engineering, Nanchang University, Nanchang, 330031, China
b Institute of Space Science and Technology, Nanchang University, Nanchang, 330031, China

Corresponding authors:   * Corresponding author.E-mail address: wypeng@ncu.edu.cn (W. Peng).

Received: 2018-08-6

Revised:  2018-10-13

Accepted:  2018-10-19

Online:  2019-06-20

Copyright:  2019 Editorial board of Journal of Materials Science & Technology Copyright reserved, Editorial board of Journal of Materials Science & Technology

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Abstract

In this study, the effects of composition and phase constitution on the mechanical properties and magnetic performance of AlCoCuFeNix (x = 0.5, 0.8, 1.0, 1.5, 2.0, 3.0 in molar ratio) high entropy alloys (HEAs) were investigated. The results show that Ni element could lead to the evolution from face centered cubic (FCC), body centered cubic (BCC) and ordered BCC coexisting phase structure to a single FCC phase. The change of phase constitution enhances the plasticity but reduces the hardness and strength. One of the interesting points is the excellent soft magnetic properties of AlCoCuFeNix HEAs. Soft magnetic performance is dependent on composition and phase transition. AlCoCuFeNi1.5 alloy, achieving a better balance of mechanical and magnetic properties, could be applied as structure materials and soft magnetic materials (SMMs). High Curie temperature (>900 K) and strong phase stability below 1350 K of AlCoCuFeNi0.5 alloy confirm its practicability in a high-temperature environment. Atomic size difference (δ) is utilized as the critical parameter to explain the lattice strain and phase transformation induced by Ni addition.

Keywords: High entropy alloy ; Phase transformation ; Mechanical property ; Soft magnetic performance ; Atomic size difference

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Cong Liu, Wenyi Peng, C.S. Jiang, Hongmin Guo, Jun Tao, Xiaohua Deng, Zhaoxia Chen. Composition and phase structure dependence of mechanical and magnetic properties for AlCoCuFeNix high entropy alloys[J]. Journal of Materials Science & Technology, 2019, 35(6): 1175-1183 https://doi.org/10.1016/j.jmst.2018.12.014

1. Introduction

High entropy alloys (HEAs) usually consist of more than five principal metallic elements with equal or near-equal atomic ratios [1]. Designed and regulated based on this new strategy, unexpectedly, HEAs prefer to solid into FCC, BCC or FCC + BCC duplex solid solutions, instead of intermetallic or complex solid solution. Four core effects, high-entropy effects, sluggish diffusion, severe lattice distortion and cocktail effects [2], make these HEAs exhibit special properties, such as high hardness and strength [3], [4], [5], good corrosion, wear and oxidation resistance [6], [7], [8], outstanding electrical and magnetic properties, excellent high-temperature performance [9]. Hence, HEAs expand the application of metallic materials.

Over the last couple of decades, many reports confirmed the significant composition dependence of HEAs. Alloying elements, eg. Al, Cu and Zr, display different effects on the phase constitution and properties of HEAs. Several elements and corresponding stabilized phases are summarized in Table 1.

Table 1   Alloying elements and corresponding stabilized phase in HEAs.

Stabilized PhaseElementsAlloysReference
FCCCuCoCrFeNiCuxA1-x[10]
CoFeCoxNiCuAl[11]
BCCAlAlxCoCrFeNi[12]
AlCoFeNi[13]
CrAlCoCuFeNiCr[5]
IntermetallicZrAlCoCrFeNiZrx[14]
TiAlCoCrFeNiTix[15]
SiCoFeNiSix[13]
NbAlCoCrFeNi[16]
(CoCrCuFeNi)100-xNbx[17]

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Because HEAs mainly compose of transitional elements, such as ferromagnetic elements Fe, Co, Ni, antiferromagnetic elements Cr, diamagnetic element Cu and paramagnetic element Ti [18], excellent electrical, magnetic and other functional properties can be carried out by HEAs. For example, FeCoNiMn0.25Al0.25 HEA possessed great saturation magnetization (Ms, 101 emu/g), low coercivity (HC, 268 A/m) [19]. The magnetic property of as-cast FeCoNi(CuAl)x HEAs changed with the microstructure transformation from FCC into BCC and FeCoNi(CuAl)0.8 approached the highest Ms [20]. AlxCoCrFeNi HEAs possess low carrier density (varying from 100 to 220 μΩ) and as-homogenized Al2.0CoCrFeNi exhibited a much smaller temperature coefficient of resistivity (82.5 ppm/K) [21]. It should be noticed that these samples also suggest the structure dependence of HEAs, which correlates highly with the alloying elements.

In this work, three questions are investigated. The first one is the variation of microstructure, mechanical properties and magnetic performance, thermal stability for as-cast AlCoCuFeNix HEAs with the adjustable molar ratio of Ni element. The second question to be studied is the composition and phase structure dependence of mechanical and magnetic properties. Thirdly, parameter approach is utilized to analyze the key factor which induces the phase transformation with the addition of Ni atoms. Compressive stress-strain curves, hardness, hysteresis loops, thermomagnetic measurements and DSC curves were used to estimate corresponding properties of AlCoCuFeNix high entropy alloys.

2. Experimental

Alloy ingots with nominal compositions of AlCoCuFeNix (x = 0.5, 0.8, 1.0, 1.5, 2.0 and 3.0, in molar ratio) HEAs were prepared by arc-melting pure alloy elements with a purity better than 99.9 wt.% in a titanium-gettered high purity argon atmosphere. To assure chemical homogeneity, each alloy ingot was reversed and remelted at least four times. Six alloy ingots were denoted by Ni0.5, Ni0.8, Ni1.0, Ni1.5, Ni2.0 and Ni3.0, respectively.

The phase constitutions of these as-cast samples were characterized by X-ray diffraction (XRD, PANalytical Empyrean X-ray diffractometer) using Cu Kα radiation. Microstructure and crystalline structure were observed by scanning electron microscopy (SEM, FEI Quanta 200 F and JEOL JSM 6701 F) and high resolution transmission electron microscopy (HRTEM, JEM 2100 F). To detect the component distribution of HEAs, SEM was equipped with an energy dispersive spectrometer (EDS). Hardness of specimens was examined using an HXS-1000 Vickers microhardness tester under a load of 200 g for 15 s. At least seven random points were conducted for each sample to obtain average values. The thermal behaviours were characterized in purified argon atmosphere using a differential scanning calorimeter (DSC, Netzsch STA 449 F5 Jupiter®) at a heating rate of 10 K/min. Compression test was performed on a MTS electron universal testing machine at room temperature, with a strain rate of 1 × 10-4 s-1, where the samples were cut into 3 mm × 3 mm × 6 mm. The magnetic properties, including hysteresis loops (M-H curves) and thermomagnetic (M-T) curve, were measured by Physical Property Measurement System (PPMS) equipped with Vibrating Sample Magnetometer (VSM). M-H curves were detected at an internal magnetic field up to 2 T at room temperature. M-T curve was obtained in a variable temperature range at a heating speed of 10 K/min.

3. Results

3.1. Crystal structures of AlCoCuFeNix HEAs

Fig. 1 shows the XRD patterns of the as-cast (x = 0.5, 0.8, 1.0, 1.5, 2.0, 3.0) alloys. Ni0.5, Ni0.8, Ni1.0, Ni1.5, Ni2.0 alloys are mainly composed of three phases: FCC, BCC and ordered BCC (B2) [5,12]. Slight Bragg peaks of B2 can be observed at around 30° and indexed to Al-rich intermetallic for Ni0.5, Ni0.8, Ni1.0, Ni1.5 and Ni2.0 alloys. When Nickel content is less than x = 0.8, the main solid solution is BCC phase. When Nickel content is larger than x = 1.0, FCC phase becomes the dominant phase. As x rising to 3.0, this alloy becomes a single FCC solid solution, whereas BCC and B2 phases almost disappear. The intensity ratios of the strongest peaks of FCC and BCC phases (I(110)B/ I(111)F), listed in Table 2, give us an explicit view of the change of relative phase volume fraction. The value of I(110)B/ I(111)F decreases sharply from 3.16 at x = 0.5 to 0.49 at x = 1.5 and finally to 0 at x = 2.0 and 3.0, indicating that Ni element can obviously promote the formation of FCC phase in AlCoCuFeNix high entropy alloys. The Bragg peak intensity of B2 phase also increases when Ni content is increasing. It should be noted that Ni element shifts the (111) peak of FCC and the (110) peak of BCC into higher angles. The movements of the strongest peaks mean the lattice constants of FCC phase and BCC phase are decreasing, which can be ascribed to the smaller atomic size of Ni element. The lattice constants are 0.3641 nm and 0.2885 nm for FCC and BCC respectively in the Ni0.5 alloy, and FCC phases also have a larger lattice constant than BCC phases in Ni0.8, Ni1.0, Ni1.5 alloys. It is clear that the addition of Ni has reduction impact on the lattice constant of FCC and BCC phases.

Fig. 1.   XRD patterns of the as-cast AlCoCuFeNix (x = 0.5, 0.8, 1.0, 1.5, 2.0, 3.0) alloys.

Table 2   Intensity ratio of the strongest peaks for FCC and BCC phases (I(110)B/I(111)F) and the lattice constants of FCC and BCC phases in the as-cast AlCoCuFeNix high-entropy alloys.

AlloyI(110)B/I(111)FLattice constants (nm)
FCCBCC
Ni0.53.160.36410.2885
Ni0.82.910.36300.2882
Ni1.00.940.36240.2878
Ni1.50.650.36120.2874
Ni2.0-0.3596-
Ni3.0-0.3599-

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3.2. Microstructures of AlCoCuFeNix HEAs

The back scattering SEM images presented in Fig. 2 illustrate the microstructure evolution of these as-cast AlCoCuFeNix high-entropy alloy. For all the six alloys, their structures are typical as-cast dendritic (DR) and interdendritic (ID). Affected by Ni element, the dendrite morphologies change from smooth oval shape (Fig. 2(a)) into mess bamboo-leaf shape (Fig. 2(b) and (c)), then, into bulk fishbone shape (Fig. 2(d)). A mass of fine FCC phase is dispersed in the Ni0.8 and Ni1.0 alloys and encircled by BCC phase. With Ni content increasing, the volume fraction of dark BCC phase decreases and the volume fraction of light FCC phase increases. As for Ni2.0 alloy (Fig. 2(e)), the morphology of FCC is transformed into the continuous dendritic, a small amount of irregular BCC phase distributes discontinuously. When x value reaches 3.0 (Fig. 2(f)), only the FCC structure remains, the grain boundary in FCC phase is too narrow. Coarsening of FCC phase indicates the substitution of FCC phase for BCC phase, according well with the result of XRD patterns above.

Fig. 2.   Back scattering SEM images of AlCoCuFeNix high entropy alloys: (a) x = 0.5, (b) x = 0.8, (c) x = 1.0, (d) x = 1.5, (e) x = 2.0, (f) x = 3.0.

Notably, with low Nickel contents (x = 0.5, 0.8, 1.0), the dendrites show an intricate two-phase netlike structure. For example, the inset of Fig. 2(a) is the enlargement of region A. Black needle-shaped plates distributed across and periodically in the span of several microns. An EDS line scan in Fig. 3 confirms the fluctuation tendency of Al, Co, Fe, Ni elements in the BCC phase. Black needle-shaped plates are enriched in Fe, Co while the lighter region is rich in Al element. According to the XRD patterns, the light matrix BCC phase is the Al-rich B2 phase and the black needle-shaped plates are the disordered BCC phase. For x = 0.8, the matrix becomes Al-Ni-rich B2 phase. This netlike structure is probably caused by spinodal decomposition. Similar structures also can be found at high aluminum content as-homogenized AlxCoCrFeNi HEAs [12] and as -cast AlxCoCrCuFeNi HEAs [22].

Fig. 3.   EDS line scan of AlCoCuFeNi0.5 high entropy alloys.

Elemental segregation ratio (SR), which are defined as the ratio of elemental concentration in BCC phase to FCC phase, are detected by EDS and summarized in Fig. 4. Due to the narrow grain boundary in Ni3.0 alloy, the atomic concentration of the grain boundary cannot be measured. But, the molar ratios of the atomic concentration of Al, Co, Cu, Fe to Ni in FCC grain are close to 1:3, which is in agreement to the nominal composition, as shown in Table 3. Apparently, for Ni0.5 alloy, FCC phase is rich in Cu element while BCC phase is a Cu-deficient structure. That is, BCC phase has higher contents of Al, Co, Fe, Ni elements. Table 4 displays the mixing enthalpies (ΔHmix) among five elements. Positive mixing enthalpies of Cu-X (X=Al, Co, Fe) atom pairs result in the presence of miscibility gap, leading to the segregation of Cu element. This phenomenon has been reported by Zhuan [23,24] and Tsai [25]. However, due to great chemical compatibility between Ni and other elements, further addition of Ni effectively mitigates repulsion of Cu atoms and sharply declines the SR values of ferromagnetic elements Fe, Co and Ni. When Ni molar ratio is larger than 1.5, BCC phase becomes Al-rich solid solution, FCC becomes Fe-Co-rich solid solution, Ni and Cu are homogeneously distributed in BCC and FCC phases. Negative mixing enthalpy means the large atomic bonding force. Formation of Al-Ni-rich B2 phase is related to the ΔHmix between Al and Ni which is the most negative one in Table 4.

Fig. 4.   Elemental segregation ratio in the BCC and FCC regions in AlCoCuFeNix high entropy alloys.

Table 3   Nominal and experimental composition (at.%) of different regions in AlCoCuFeNi3.0 high entropy alloys.

AlloysRegions in Fig. 2AlCoCuFeNi
Ni3.0Nominal14.2914.2914.2914.2942.84
FCC14.7314.9513.6514.4242.25
BCC-----

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Table 4   Mixing enthalpies (kJ/mol) of atomic pairs between elements [26].

ElementAlCoCuFeNi
Al-19-1-11-22
Co6-10
Cu134
Fe-11
Ni

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3.3. Mechanical properties of AlCoCuFeNix HEAs

Fig. 5 shows the compressive engineering stress-strain curves of HEAs measured at room temperature. The yield strength (σ0.2), maximum compressive strength (σmax), fracture strain (εf) and Vickers hardness are summarized in Table 5. With increasing Ni content, the plasticity is enhanced at the cost of yield strength and hardness. Ni0.5 and Ni0.8 alloys show the best yield strength, hardness but the worst ductility. Though Ni2.0 and Ni3.0 alloys exhibit the lowest yield strength, these two alloys do not fracture even the strains of them are over 45%. The yield strength and the hardness of Ni2.0 and Ni3.0 alloys are 544 MPa, 268 MPa, and 299.2 HV, 279.6 HV, respectively. Ni1.0 and Ni1.5 alloys achieve a good combination of strength and ductility, especially for Ni1.5 alloy. Ni1.5 alloy exhibits the biggest maximum compressive strength of 1725 MPa, with a fracture strain of 35.9% and a hardness of 323.8 HV. Plastic deformation periods in strain-stress curves are enlarged with Ni addition. The enhancement of plasticity should be associated with two points, one is the increase of FCC phase volume fraction, the other is the decrease of lattice distortion and solid solution strengthening [27]. However, these two points are actually damaging to the strength and hardness.

Fig. 5.   Engineering stress-strain curves of the as-cast AlCoCuFeNix HEAs compressed at room temperature.

Table 5   Phase structure, mechanical properties and magnetic parameters of AlCoCuFeNix high entropy alloys.

AlloysPhase Structureσ0.2 (MPa)σmax (MPa)εf (%)Hardness (HV)Ms (emu/g)HC
(Oe)
Remanence ratio (Mr/Ms) (%)
Ni0.5BCC + FCC + B2929123113.7430.989.217.300.55
Ni0.8BCC + FCC + B21021146512.3420.083.923.770.29
Ni1.0FCC + BCC + B2994160924.5391.473.735.810.37
Ni1.5FCC + BCC + B2680172535.9323.863.5813.701.40
Ni2.0FCC + BCC + B2544--299.257.4311.120.94
Ni3.0FCC268--279.654.6824.819.35

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To further understand the fracture mechanism of HEAs, SEM images of fracture surface are given in Fig. 6. Ni0.8 and Ni1.5 are selected as examples for two different fracture modes. River-patterns and cleavage steps observed in Fig. 6(a) region A hint that the fracture behavior of Ni0.8 alloy is typical cleavage fracture. Ductile fracture with equal-axis ductile voids can be observed in the Region B for Ni1.5 alloy. In general, fracture mode varies from cleavage fracture for low Ni content AlCoCuFeNix HEAs to ductile fracture at high Ni content. This trend is consistent with the enlargement of plastic deformation regions. Ni element plays a positive role in enhancing plasticity by improving the formation of FCC phase.

Fig. 6.   SEM images of the compressive fracture surface of the as-cast AlCoCuFeNix high entropy alloys: (a) x = 0.8, (b) x = 1.5.

3.4. Magnetic performances of AlCoCuFeNix HEAs

To investigate the effect of Ni element on magnetic properties, the magnetic hysteresis curves of these AlCoCuFeNix high entropy alloys are measured at room temperature and displayed in Fig. 7. The saturation magnetization (Ms), coercivity (HC) and remanence ratio (Mr/Ms) are summarized in Table 5. All the six alloys exhibit excellent soft magnetic properties with high Ms, low HC and low Mr/Ms (<2%). Fig. 8 presents the composition dependence of Ms for HEAs. When a large amount of Ni element is added into the alloy, the value of Ms falls rapidly, and HC is generally increasing. Ni0.5 alloy possesses the best soft magnetic properties, for which Ms is 89.21 emu/g, HC is 7.30 Oe, and Mr/Ms is 0.55%. Ni3.0 alloy, by contrast, shows the smallest Ms (54.68 emu/g) and the largest HC (24.91%). The variations of Ms and HC indicate the soft magnetic property of Ni3.0 alloy is worse than that of the former five alloys. Comparison of the magnetic parameters for serval reported metals is summarized in Table 6. AlCoCuFeNix HEAs show better soft magnetic properties than many other HEAs.

Fig. 7.   Magnetic hysteresis curves of the as-cast AlCoCuFeNix high entropy alloys at room temperature.

Fig. 8.   Composition dependence of Ms of the as-cast AlCoCuFeNix high entropy alloys at room temperature.

Table 6   Comparison of saturation magnetization (Ms) and coercivity (HC) for HEAs.

AlloysPhase structureMs (emu/g)HC (Oe)Reference
AlCoCuFeNi0.5BCC + B2 +FCC77.681.24Current study
AlCoCrFeNiBCC64.7152[16]
AlCoCrFeNb0.75NiLaves+(Laves + BCC)10.3194[16]
CoCrCuFeNiTiFCC + Laves + Amorphous1.511-[28]
FeCoNiFCC155.72.37*[29]
FeCoNiMn0.25Al0.75FCC1013.37[19]
CoCrFeNiCuAlordered BCC + FCC38.1845[30]
CoCrFeCuNiFCC53.41166[31]

*H = 1 (Oe) = 79.6 (A/m).

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The saturation magnetization is mainly dependent on composition and crystal structure. Thus, the decrement of Ms will be analyzed from the following several parts.

First, based on Cullity and Graham [32], the experimental magnetic moment per atom μH for Fe, Co, Ni, Cu is 2.22 μB, 1.72 μB, 0.6 μB, 0 μB respectively and Al element is non-polarized [33]. Therefore, in this alloy system, Al and Cu play a dilution effect. If we consider only the change of ferromagnetic element content, the mean magnetic moment per atom $\bar{\mu}$H and x have an inverse relationship, as Eq. (1):

$\bar{\mu}_{H}$ =∑ai×1/(4+x)×μH,i=0.60+1.54/(4+x) (1)

where ai is the molar ratio of Fe, Co, Ni in AlCoCuFeNix HEAs, x is the value in AlCoCuFeNix, μH,i is the experimental magnetic moment per atom μH for Fe, Co, Ni.

Based on μH, the value of Ms (calculated Ms) can be calculated by Eqs. (2) and (3) [31].

σ0=μN/A (2)

μH=μ/β (3)

where σ0 is the saturation magnetization (calculated Ms), N is Avogadro’s Number, A is the atomic weight, and β is Bohr magnetron (9.273 × 10-21 erg·G-1).

The results of $\bar{μ}_{H}$$H and calculated Ms are presented in Fig. 8. For convenience, experimental Ms is fitted to compare with $\bar{μ}_{H}$ and calculated Ms, as shown in Fig. 8. The Adj. R. Square (0.946) for fitting formula is close to 1, verifying the accuracy of the fitted curve. It can be easily seen that experimental Ms has the similar tendency with the calculated Ms. Fitting curve and Eq. (1) have the same general formula: y=a+b/(c+x), where a, b, c are positive numbers. It shows the fact that the Ms and $\bar{μ}_{H}$ are closely connected. The total molar sum of ferromagnetic elements (Fe, Co, Ni) is larger than 50 at.% and increases as the further addition of Ni element. But the very small μH,Ni lead to the decline of $\bar{μ}_{H}$ and Ms for HEAs. Increasement of Ni atoms cannot offset the total magnetic moment damage for the loose of Fe and Co.

Second, Ms is profoundly affected by phase structure. The relationship between Ms and phase transformation can be reflected as Eq. (4) [20,21] when 0.5 ≤ x ≤ 3.0:

ΔMs=(Ms,BCC-Ms,FCC)ΔVBCC (4)

where the ΔMs is the change of saturation magnetization, ΔVBCC is the change of the volume fraction of BCC phase, Ms,FCC and Ms,BCC are the saturation magnetization of FCC and BCC phases, respectively.

From above results, the increase of Ni amount retards the formation of BCC phase, so ΔVBCC < 0. The value of Ms declines when the amount of Ni increases from 0.5 to 3.0, meaning ΔMs < 0. Thus, ΔMs will decrease with ΔVBCC declining. In other words, Ms,BCC is larger than Ms,FCC. This result implies that the saturation magnetization of HEA system is closely associated with phase constitution.

Magnetic exchange interaction can be employed to analyze magnetic differences between BCC and FCC. The magnetic exchange interactions from nearest-neighbour Fe-Fe, Fe-Co, Co-Co and Fe-Ni pairs make the maximum contribution to high Ms of HEAs. But, these interactions in BCC are stronger than that in FCC phase [33]. Concluded from Figs .1 and 4, the reduction of BCC volume fraction and the decreasing content of Fe, Co, and Ni elements in BCC restrain the influence of BCC phase on magnetic performance of HEAs. Therefore, it is not hard to understand that the magnetic property of AlCoCuFeNix HEAs is susceptible to the crystal structure.

Third, Al-rich B2 phase is weak ferromagnetic intermetallic and exists in Ni0.5, Ni0.8, Ni1.0, Ni1.5 and Ni2.0 alloys. Thus, Al-rich B2 phase plays a negative role on magnetic properties of HEAs.

Thermomagnetic (M-T) curve is measured at a constant magnetic field of 1 T. Ni0.5 alloy is selected to obtain its Curie temperature (TC), because Ni0.5 alloy exhibits the best soft magnetic properties. The M-T curve demonstrates Ni0.5 alloy exhibits TC of >900 K, which is beyond our test scope. But, TC of Ni0.5 alloy is larger than that of FeCoNiCuGa (800 K), FeCoNiCuMo (657 K) and FeCoNiCuMn (400 K) [34].

3.5. Thermal stability of AlCoCuFeNix HEAs

As shown in Fig. 9, DSC curves make us know the thermal stability of HEAs. There is an obvious endothermic peak locating at 1390 K for Ni0.5 alloy. This endothermic peak is resulted from solid phase transformation and marked as phase transition temperature (TP). More importantly, DSC curves for the six alloys are flat below 1350 K, nonoccurrence of solid solution phase transition demonstrates the great thermal stability of AlCoCuFeNix HEAs, meaning that HEAs can work well in the high-temperature environment.

Fig. 9.   DSC curves (600-1450 K) of the as-cast AlCoCuFeNix high entropy alloys.

4. Discussion

How does Ni element affect microstructure of HEAs? According to many phase formation criteria reported by Zhang [35], Guo [36] and Yang [37], the atomic size difference (δ), the mixing enthalpy (ΔHmix), the mixing entropy (ΔSmix) and valence electron concentration (VEC) are key factors in determining the phase formation. Physical parameter δ is used to estimate the extent of atomic size match. ΔSmix means the extent of atomic disorder in HEAs system. VEC, reflecting the electronic structure of atoms, can affect the type of solid-solution. The electro-negativity difference (Δχ) and melting point (Tm) are also utilized to formulate phase formation rules for HEAs. The values of δ, ΔSmix, ΔHmix, Δχ, VEC and Tm in AlCoCuFeNix HEAs system are defined as follows [5,35,36,38]:

δ=100 $\sqrt{\sum\limits_{i=1}^{n}c_{i}(1-r_{i}/\bar{r})^{2}}$ (5)

ΔSmix=$-R \sum\limits_{i=1}^{n}c_{i}ln c_{i}$ (6)

ΔHmix=$\sum\limits_{i=1,i\ne j}^{n} {\Omega}_{ij} c_{i} c_{j}$ (7)

Δχ=$\sqrt{\sum_{i=1}^{n}c_{i}(\chi_{i}-\bar{\chi})^{2}}$(8)

VEC=$\sum_{i=1}^{n}c_{i}(VEC)_{i}$ (9)

Tm=$\sum\limits_{i=1}^{n}c_{i}(T_{m})_{i}$ (10)

where n is the number of elements in this HEAs system, ci is the atomic percentages of the ith element, ri is the atomic radius of ith element. $\bar{r}=\sum_{i=1}^{n}$ciri is the average atomic radius. Ωij=4 $ΔH_{i-j}^{mix}$ is the regular melt-interaction parameter between ith and jth elements, $ΔH_{i-j}^{mix}$ is the mixing enthalpy of binary alloys. χi is the Pauling electronegativity of ith element, $\bar{\chi}=\sum_{i=1}^{n}$ciχi is the average Pauling electronegativity for alloys. (VEC)i is the valence electron concentration of ith element. Relevant parameters of Al, Co, Cu, Fe and Ni elements can be obtained from Table 4, Table 7.

Table 7   Parameters of the alloying elements at room temperature [30,31].

ElementCrystal structurer(Å)χVECTm (K)
AlFCC1.431.613933.5
CoHCP1.251.8891770
CuFCC1.281.90111358
FeBCC1.241.8381811
NiFCC1.251.91101728

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Another important parameter Ω is proposed by Yang and Zhang [37] as:

Ω= $\frac{T_{m}ΔS_{mix}}{| ΔH_{mix}|}$ (11)

where ΔSmix, ΔHmix and Tm are provided by Eqs. (6), (7), (10). The calculated values of δ, ΔSmix, ΔHmix, Δχ, VEC, Tm, and Ω are tabulated in Table 8. The absolute value of the mixing enthalpy (|ΔHmix|) can be considered as the obstruction for the formation of solid solution.

Table 8   Values of δ, ΔSmix, ΔHmix, Δχ, VEC, Tm and Ω of AlCoCuFeNix high entropy alloys.

Alloysδ (%)ΔSmix (J·mol-1·K-1)ΔHmix (kJ·mol-1)ΔχVECTm (K)Ω (kJ/mol)
Ni0.55.7013.14-4.540.1148.001497.04.33
Ni0.85.5913.35-5.040.1128.131511.54.00
Ni1.05.5313.38-5.280.1118.201520.13.85
Ni1.55.3613.25-5.690.1098.361539.03.59
Ni2.05.2212.98-5.890.1068.501554.73.43
Ni3.04.9212.27-5.960.1028.711579.53.25

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Smaller Δχ (about 0.11), relative negative ΔHmix (< -3.85) and the decreasing parameter Ω hint the greater likelihood for AlCoCuFeNix HEAs to form intermetallic, as the matrix is solid solution phase [35,37,38]. XRD patterns favour this inference.

The values of VEC increase with the growth of Ni amount. For these six alloys, VEC values are ≥ 8.0. All but Ni3.0 alloy, a single FCC phase alloy, the others are FCC + BCC duplex solid solution structures. Chen and Qin [39] point out that alloy element with a high VEC promotes phase transformation from BCC to FCC. In this study, the VEC of Ni (VECNi = 10) is larger than the average VEC (VECAlCoCuFe = 7.8) for AlCoCuFe matrix. When Ni atoms are further incorporated into AlCoCuFeNix HEAs system, VEC gradually increases, consequently, HAEs tend to form compact, ductile FCC structure, rather than loose, strong BCC structure.

According to the Hume-Rothery rules, atomic size difference and the mixing enthalpy are the two most significant factors that affect the phase formation. The effect of the mixing enthalpy has been discussed in the chapter 3.2. The effect of the atomic size mismatch for AlCoCuFeNix HEAs is the next focus of discussion.

Atomic size difference plays a vital role in lattice distortion and phase formation. Eq. (5) is the commonly accepted formula to represent the atomic size difference. By randomly replacing the intrinsic atoms in the lattice sites, the addition of impurity atoms can severely distort lattice distortion, destabilize the perfect crystal and even alter the crystal type. Fig. 10 shows the HRTEM image and the inset is the inverse fast Fourier transform (IFFT) images of the Ni0.5 alloy. Severe lattice distortion exists in three small white squares.

Fig. 10.   HRTEM image of Ni0.5 alloy. The inset is the IFFT image of selected area.

The lattice strain (ε) is introduced to estimate the lattice distortion and can be calculated by the following equations [10]:

ε=Δa/a0 (12)

Δa=| a-a0| (13)

where a and a0 are the lattice constant of actual crystal and perfect crystal, respectively.

Ni and Fe elements are selected as the perfect crystal elements for FCC phase and BCC phase, respectively. The corresponding lattice constant for Ni is 0.3524 nm [40] and for Fe is 0.2861 nm [41]. Principles of selecting perfect crystal elements are borrowed from Zhou’s research [10].

The values of δ and ε are calculated and plotted in Fig. 11. The value of δ decreases with the addition of Nickel. This is due to the fact that the atomic radius of Ni is relatively smaller (1.25 Å) than that of Al, Co, Cu, Fe. When x is less than 2.0, ε values of BCC and FCC solid solutions increase as the δ increasing, indicating the correlation between the atomic size difference and lattice distortion. Compared with Ni2.0 alloy, Ni3.0 alloy shows a small increase in the lattice strain of FCC. This is related to the disappearance of BCC solid solution. Because BCC structure has a lower atomic packing density (68%) than FCC structure (74%), BCC structure is much easier to deform to relax the lattice distortion energy [42]. Therefore, the lattice strain of FCC is larger than the counterpart of BCC (shown in Fig. 11). Combing with these analyses, it can be concluded that the close-packed FCC phase is more conducive to stabilize the AlCoCuFeNix HEAs system at the condition of low lattice distortion and low lattice strain, while loose-packed BCC structure is prone to form under the circumstance of a high degree of lattice distortion. Reduced δ might be the main factor in inducing phase transformation between the BCC and FCC solid solutions.

Fig. 11.   Lattice strain curves of FCC and BCC solid solutions as a function of atomic size difference (δ) in AlCoCuFeNix HEAs.

5. Conclusion

In this work, the phase constitution of AlCoCuFeNix (x = 0.5, 0.8, 1.0, 1.5, 2.0, 3.0) HEAs varied from BCC + FCC + B2 triplex phases to a single FCC solid solution. This variation tendency hints that Ni addition can improve the formation of FCC phase. Compared with Al, Co, Cu, Fe elements, Ni has relative smaller atomic size. Therefore, when HEAs contain more Ni atoms, decreasing lattice distortion lead to the breakdown of BCC and formation of FCC. This phase transformation improves plasticity and weakens hardness and strength. Negative mixing enthalpies between Ni and the other elements make components distribute homogeneously and make ordered BCC form in HEAs. Influence of composition and phase constitution is crucial on soft magnetic performance of AlCoCuFeNix HEAs. High content of Fe, Co and high volume fraction of BCC mean stronger saturation magnetization for AlCoCuFeNix HEAs. These HEAs are hardly to occurring solid phase transition below 1350 K. Excellent thermal stability and soft magnetic characteristics make these HEAs high-temperature materials and SMMs. AlCoCuFeNi1.5 HEAs has great compressive performance, for which compressive strength is 1725 MPa, fracture strain is 35.9%, and Ms reaches to 63.58 emu/g.

Acknowledgments

This work was supported by the National Natural Science Foundation of China (NSFC, Nos. 51501085 and 51461030).

Appendix A. Supplementary data

Supplementary material related to this article can be found, inthe online version, at doi:https://doi.org/10.1016/j.jmst.2018.12.014.

The authors have declared that no competing interests exist.


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