**Phases, Microstructures and Mechanical Properties of CoCrNiCuZn High-Entropy Alloy Prepared by Mechanical Alloying and Spark Plasma Sintering**

#### **Yuchen Sun, Boren Ke, Yulin Li, Kai Yang, Mingqi Yang, Wei Ji \* and Zhengyi Fu \***

State Key Laboratory of Advanced Technology for Materials Synthesis and Processing, Wuhan University of Technology, Wuhan 430070, China; 15370786151231@whut.edu.cn (Y.S.); ke@whut.edu.cn (B.K.); 1422915370@whut.edu.cn (Y.L.); yangletian@whut.edu.cn (K.Y.); mingqi.yang@whut.edu.cn (M.Y.)

**\*** Correspondence: jiwei@whut.edu.cn (W.J.); zyfu@whut.edu.cn (Z.F.)

Received: 14 November 2018; Accepted: 26 January 2019; Published: 29 January 2019

**Abstract:** In the study, an equiatomic CoCrNiCuZn high-entropy alloy (HEA) was prepared by mechanical alloying (MA) and the phases, microstructures, and thermal properties of the alloy powder were explored. The results suggest that a solid solution with body-centered cubic (BCC) phase and a crystalline size of 10 nm formed after 60 h of milling. Subsequently, the alloy powder was consolidated by spark plasma sintering (SPS) at different temperatures (600 ◦C, 700 ◦C, 800 ◦C, and 900 ◦C). Two kinds of face-centered cubic (FCC) phases co-existed in the as-sintered samples. Besides, Vickers hardness and compressive strength of the consolidated alloy sintered at 900 ◦C were respectively 615 HV and 2121 MPa, indicating excellent mechanical properties.

**Keywords:** high-entropy alloy; spark plasma sintering; mechanical alloying; mechanical property; microstructure

#### **1. Introduction**

Conventional alloy is generally composed of one or two main elements and a small amount of other elements, to enhance its mechanical properties, such as steel and NiAl intermetallics [1,2]. The emergence of high-entropy alloys (HEAs) [3] has broken this traditional notion. A HEA is loosely defined as alloy composed of more than five principal elements with an equimolar ratio (5–35 at.%). High-entropy alloy has high entropy effect, lattice distortion effect, sluggish cooperative diffusion effect, and cocktail effect. It often has simple solid-solutions or amorphous structure [4]. Well-designed HEAs have good mechanical properties including high hardness, high strength, good corrosion, and wear resistance [5].

HEAs can be prepared by various routes, such as vacuum arc-melting and casting [6,7]. However, these routes are not suitable for HEA systems which contain elements with very different melting points. For example, the melting temperature of Cr is 1000 ◦C above the atmospheric boiling point of Zn, so some systems such as CoCrNiCuZn high-entropy alloy cannot be synthesized by arc-melting route. Besides, arc-melting is not suitable for industrial manufacturing and final products have some limitations in shape and size [8]. Mechanical alloying (MA) is a convenient route to synthesize nanocrystalline HEAs materials. MA can reduce the preparation cost of nanocrystalline materials [9,10]. In addition, HEAs can be easily consolidated from the as-milled powders with spark plasma sintering (SPS) technique [11–13].

In this study, we synthesized the CoCrNiCuZn high-entropy alloy by MA and SPS. The phases, microstructures and mechanical properties of the consolidated alloys were also explored.

#### **2. Experimental**

Metal powders (Co, Cr, Ni, Cu, and Zn with a purity of more than 99.5 wt.% and a particle size of ~45 μm) were mixed according to the equiatomic composition and milled in a planetary ball-miller (300 rpm for 60 h, argon atmosphere) with stainless steel vials and balls as milling media (a ball-to-powder mass ratio of 20:1). N-heptane was used as the processing controlling agent (PCA) to avoid cold welding and oxidation. The MA process was monitored with an interval of 6 h. After 60 h of ball milling, the powder was consolidated by SPS (Dr. Sinter-3.20 MKII, Sumitomo, Osaka, Japan) at different temperatures (600 ◦C, 700 ◦C, 800 ◦C, and 900 ◦C) under 30 MPa with dwell time of 10 min in argon atmosphere.

The phases of ball milled (QM-BP, Nanjing Nanda Instrument Plant, Nanjing, China) alloys were characterized by X-ray diffractometer (XRD, Rigaku Ultima III, Tokyo, Japan) with a Cu Kα radiation to investigate the crystal structure. The microstructure was analyzed by a scanning electron microscope (SEM, Hitachi 3400, Tokyo, Japan) and a transmission electron microscope (TEM, JEOL JEM-2010HT, Tokyo, Japan). The thermal analysis of as-milled powder was conducted by a differential scanning calorimeter (DSC, NETZSCH 449C, Selb, Germany) heating the alloy to 1500 ◦C (5 ◦C/min) in flowing argon atmosphere. According to the Archimedes principle, the density of HEA was determined. The hardness of sectioned and polished specimens was determined by vickers hardness tester (Wolpert-430SV, Aachen, Germany). The compressive properties at room temperature were determined by a MTS810 testing machine (MTS 810, MTS Systems Corporation, Eden Prairie, MN, USA) with a loading rate of 1 mm/min. The dimensions of sample is 2 mm × 2 mm × 5 mm. The fracture surface was analyzed by SEM. A thin foil of sintered material obtained by mechanical thinning and ion milling was analyzed by TEM. At least 5 measurements were performed to calculate the means of vickers hardness and compressive strength.

#### **3. Results and Discussion**

#### *3.1. Mechanical Alloying of CoCrNiCuZn HEAs*

#### 3.1.1. X-Ray Analysis

The XRD patterns of the CoCrNiCuZn high-entropy alloy (Figure 1) indicated that a major peak formed after 30-h milling. The diffraction patterns of all alloying elements can be observed in the XRD patterns of primitive blending powder. After 6-h MA, the diffraction peaks of the principle elements were still observed, but the intensity was dramatically decreased. With the increase in milling time to 18 h, some peaks were significantly broadened and some peaks were invisible. After 30-h milling, only 3 peaks of a BCC structure ((1 1 0), (2 0 0), (2 1 1)) could be identified, indicating the formation of a simple solid solution. The BCC solid-solution had a lattice parameter of 2.8831 Å. After 60 h MA, the XRD patterns showed no obvious change. In the milling process, the decreased intensity, broadened or disappeared peak might be caused by high lattice strain, refined crystallite size, and decreased crystallinity [14,15].

The crystallite size (CS) and lattice strain (LS) of CoCrNiCuZn HEA obtained after milling for different time were calculated by Scherrer's formula after eliminating the interferences of instruments and strain [16,17]. The CS of the BCC phase was significantly refined to 19 nm after 18-h MA and then decreased to 13 nm after 30-h milling (Table 1). Further increasing of milling time had no significant influence on the crystallite size. The equilibrium between crystalline refinement and cold welding of BCC phase might be reached after 30-h milling. The lattice strain of milled powders increased with milling time and reached 0.70% after 60 h milling [18].

**Figure 1.** The change of XRD patterns of CoCrNiCuZn high-entropy alloy (HEA) powder obtained after milling for different time (from 0 h to 60 h).

**Table 1.** Crystallite size (CS), lattice strain (LS), lattice parameter (LP) of CoCrNiCuZn HEA obtained after milling for different time (0 h to 60 h).


#### 3.1.2. Microstructure and Composition

Figure 2 shows the microstructure of CoCrNiCuZn HEA powder obtained after ball milling for different time (0 h, 6 h, 18 h, 30 h, and 60 h). The non-milled powder has a different particle size. Through the MA process, milled HEA powder agglomerated into an elliptical shape with the size of ~3 μm and the elliptical particles evolved into ~1 μm thick sheets. The nanocrystalline nature of CoCrNiCuZn HEA obtained after 60 h MA was characterized by the selected area electron diffraction (SAED) pattern and TEM bright field image (Figure 3). The crystal size measured from bright field TEM image was approximately 10 nm, which was consistent with the calculation results by the Scherrer's formula. The existence of nanoscaled crystallite indicated that the microsized alloy particles in SEM images were the aggregates of nanosized grains.

The rings in the SAED pattern (Figure 3) indicated that the nanocrystalline HEA powder after 60 h milling only consisted of a BCC phase. The result was consistent with XRD analysis results. The results confirmed that the CoCrNiCuZn high-entropy alloy with a structure of simple BCC solid solution had been successfully fabricated by mechanical alloying.

Zhang and Guo proposed the criteria for the formation of solid solution and phase stability of HEA prepared by casting [19–23]. According to the results, the as-calculated values of <sup>Δ</sup>*Smix* (J·K−<sup>1</sup> mol<sup>−</sup>1), <sup>Δ</sup>*Hmix* (kJ·mol−1), and *<sup>δ</sup>* for CoCrNiCuZn HEA were respectively 1.61*R*, 0.96 and 4.4%, which were consistent with the formation criteria of HEAs. Table 2 shows mixing enthalpies of atomic pairs in the CoCrNiCuZn alloy system [24,25]. The main advantage of MA is the extension of solid solubility. Therefore, the simple solid solution is more likely formed in the as-milled HEA than that in the as-cast HEA. The calculated values of Δ*Smix*, Δ*Hmix* and *δ* for CoCrNiCuZn HEA indicated that the simple solid solution should be formed in the MA process.

**Figure 2.** SEM images of CoCrNiCuZn HEA powder obtained after milling for different time: (**a**) 0 h, (**b**) 6 h, (**c**) 18 h, (**d**) 30 h, and (**e**) 60 h.

**Figure 3.** TEM image and selected area electron diffraction (SAED) pattern of CoCrNiCuZn HEA powder obtained after 60 h milling.


**Table 2.** Enthalpies (kJ·mol<sup>−</sup>1) between every two elements in CoCrNiCuZn HEA.

#### 3.1.3. Thermal Analysis

Figure 4 shows the DSC results of the CoCrNiCuZn high-entropy alloy powder obtained after 60 h milling. The first endothermic peak at around 100 ◦C is related to the energy absorption of the PCA evaporation [15]. Then the evaporated matter was eliminated by the flowing argon during testing. In the temperature range of 200~400 ◦C, the curve was relatively stable. When the temperature was

above 600 ◦C, an endothermic line is observed, indicating that phase changes started at around this temperature. Two endothermic peaks at 1244.8 ◦C and 1321.8 ◦C were considered as the melting points of different phases [26], proving that there were two phases after the phase change occurred.

**Figure 4.** The trend and peaks of the thermal analysis curves (DSC, Mass) of CoCrNiCuZn HEA powder after 60 h ball milling.

#### *3.2. Consolidation by SPS*

#### 3.2.1. X-Ray Analysis

Figure 5 shows the XRD patterns of the HEA powder after 60 h ball milling and the samples sintered at 600 ◦C, 700 ◦C, 800 ◦C, and 900 ◦C, respectively. Two FCC phases were formed at 900 ◦C and respectively recorded as FCC1 and FCC2. This is consistent with thermal analysis results.

**Figure 5.** XRD patterns of CoCrNiCuZn HEA powder after 60 h ball milling and CoCrNiCuZn HEA samples fabricated by SPS at different sintering temperatures (600–1000 ◦C).

The above results indicated that both the as-milled CoCrNiCuZn powders and the as-sintered CoCrNiCuZn samples mainly had simple solid solution structures. This phenomenon can be explained by the Gibbs free energy of mixing defined as:

$$G\_{\rm mix} = H\_{\rm mix} - TS\_{\rm mix} \tag{1}$$

where *Hmix* is the mixing entropy; *Gmix* is the Gibbs free energy of the mixture; *Smix* is the mixing entropy and *T* is absolute temperature. The entropies of solid solution phases were much higher than those of the intermetallics. The increase in the mixing entropy largely decreased Gibbs free energy. Therefore, especially at high temperatures, the solid solution phases were preferentially formed rather than intermetallics and other complex phases [27].

#### 3.2.2. Microstructure

The densities of alloys sintered at 600 ◦C, 700 ◦C, 800 ◦C, and 900 ◦C are respectively 5.26 g/cm3, 6.26 g/cm3, 7.84 g/cm3, and 7.89 g/cm3 measured by Archimedes principle. Figure 6 shows TEM bright field image and corresponding SAED patterns of CoCrNiCuZn HEA obtained after SPS at 900 ◦C. In the TEM image, two different morphologies were observed. Corresponding SAED patterns in Figure 6b,c indicated that the larger particles had a FCC1 structure, whereas the smaller ones had an FCC2 structure. The result was consistent with the XRD results.

**Figure 6.** TEM image and SAED patterns of the CoCrNiCuZn HEA bulk obtained after SPS at 900 ◦C: (**a**) TEM bright field image of bulk CoCrNiCuZn HEA after SPS, (**b**) and (**c**) corresponding SAED patterns respectively indicate Region A with a FCC1 phase and Region B with an FCC2 phase.

Figure 7 shows the corresponding fractographic feature of the alloys sintered at 700 ◦C, 800 ◦C, and 900 ◦C, respectively. Section structure and stepped structure can be respectively observed in Figure 7a,b. The bulk alloys sintered at 900 ◦C showed a significant plasticity trend because the FCC phase exhibited a higher plasticity than BCC phase [15].

**Figure 7.** Slip fracture morphology of CoCrNiCuZn HEA samples fabricated by SPS at different sintering temperatures: (**a**) 700 ◦C, (**b**) 800 ◦C, and (**c**) 900 ◦C.

#### 3.2.3. Mechanical Properties

Figure 8 shows the room-temperature compressive properties of the CoCrNiCuZn HEA consolidated at different temperatures. The strength increases with increasing of sintering temperature. The compressive strength of the sample sintered at 900 ◦C reached 2121 MPa, which was higher than that of most previously reported HEAs [6,27]. The Vickers hardness of HEA bulk sintered at 900 ◦C reached 615 HV, which was also superior to most commercial hard facing alloys [28]. The high compressive strength and high hardness are ascribed to the ultrafine grains (as shown in Figure 6a) and solid solution strengthening.

**Figure 8.** Compressive strain–stress curves at room temperature of CoCrNiCuZn HEA samples fabricated by SPS at different sintering temperatures (600 ◦C–900 ◦C).

#### **4. Conclusions**

The equiatomic CoCrNiCuZn HEA powder was successfully synthesized by MA. After 30-h ball milling, a BCC phase structure with a grain size of 10 nm was formed. The thermal analysis curve proved that the BCC phase structure gradually converted into FCC phase at above 600 ◦C. The XRD and TEM results demonstrated that the high-entropy alloy obtained after sintering had two FCC phases. The sample sintered at 900 ◦C had a Vickers hardness of 615 HV and a compressive strength of 2121 MPa. The combination of mechanical properties is superior to most of reported HEA systems and commercial hard facing alloys.

**Author Contributions:** Conceptualization, W.J. and Z.F.; methodology, Y.S. and B.K.; investigation, Y.S. and Y.L.; analysis, K.Y. and M.Y.; writing—original draft preparation, Y.S. and W.J.; writing—review and editing, W.J. and Z.F.; supervision, W.J. and Z.F.; project administration, W.J.; funding acquisition, Z.F.

**Funding:** This research was funded by the National Natural Science Foundation of China, grant numbers 51521001 and 51832003, the Students Innovation and Entrepreneurship Training Program of WHUT, grant numbers 2018CLA127 and 20181049701037, and the Self-Determined and Innovative Research Funds of WHUT, grant numbers 2018III020 and 2018IVA094.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

<sup>1.</sup> Greer, A.L. Confusion by design. *Nature* **1993**, *366*, 303–304. [CrossRef]


© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

### *Article* **Lattice Distortion and Phase Stability of Pd-Doped NiCoFeCr Solid-Solution Alloys**

**Fuxiang Zhang 1,\*, Yang Tong 1, Ke Jin 1, Hongbin Bei 1, William J. Weber 1,2 and Yanwen Zhang <sup>1</sup>**


Received: 12 November 2018; Accepted: 21 November 2018; Published: 25 November 2018

**Abstract:** In the present study, we have revealed that (NiCoFeCr)100−*x*Pd*<sup>x</sup>* (*x*= 1, 3, 5, 20 atom%) high-entropy alloys (HEAs) have both local- and long-range lattice distortions by utilizing X-ray total scattering, X-ray diffraction, and extended X-ray absorption fine structure methods. The local lattice distortion determined by the lattice constant difference between the local and average structures was found to be proportional to the Pd content. A small amount of Pd-doping (1 atom%) yields long-range lattice distortion, which is demonstrated by a larger (200) lattice plane spacing than the expected value from an average structure, however, the degree of long-range lattice distortion is not sensitive to the Pd concentration. The structural stability of these distorted HEAs under high-pressure was also examined. The experimental results indicate that doping with a small amount of Pd significantly enhances the stability of the fcc phase by increasing the fcc-to-hcp transformation pressure from ~13.0 GPa in NiCoFeCr to 20–26 GPa in the Pd-doped HEAs and NiCoFeCrPd maintains its fcc lattice up to 74 GPa, the maximum pressure that the current experiments have reached.

**Keywords:** solid-solution alloys; lattice distortion; phase transformation

#### **1. Introduction**

High-entropy alloys (HEAs) are usually a single-phase solid-solution with multi principle elements randomly distributed in the lattice [1,2]. Due to the size difference of individual atoms, lattice distortion is believed to be one of the core effects, which greatly affects the mechanical and physical properties [3–8]. The distorted local lattice provides pinning sites to slow down dislocation motion and therefore improve the mechanical performance of high-entropy alloys [9–12]. The intrinsic lattice distortion in HEAs can shorten the free-electron migration paths and reduce the electrical and thermal conductivities [1,13,14], which can enhance the recombination of radiation defects due to a strong localized heating effect. In addition, distorted local lattice sites can retard the motion of radiation defects to delay their growth. Therefore, HEAs are strong candidates for nuclear materials by showing excellent radiation resistance [13,15]. However, a quantitative description of the lattice distortion in HEAs is a challenge and previous experimental results are controversial [1,16,17]; especially with respect to alloys with the fcc structure. For example, no obvious lattice distortion was reported previously for a NiCoFeMnCr alloy [17]. Recently, we developed a new analytical method based on atomic pair distribution function (PDF) measurement that can quantitatively describe the local lattice distortion in some high- and medium-entropy alloys [18–20]. PDF analysis has shown that the local lattice distortion in the NiCoFeCr is negligible (< 0.1%), while the NiCoFeCrPd HEA has a very large local lattice distortion (0.79%). Since there is a large mismatch of atomic size between Pd and other atoms, it is interesting to investigate the effect of Pd content on the lattice distortion in (NiCoFeCr)100−*x*Pd*<sup>x</sup>* solid-solution alloys.

Besides atomic size mismatch, different atomic configurations can also affect local lattice distortion in HEAs. For instance, the local bonding environment of individual atoms varies in solid-solution alloys, leading to the fluctuation of nearest atomic pair distances and short-range order [21]. Extended X-ray absorption fine structure (EXAFS) is atomic mass sensitive and is a powerful tool to measure the distance of different atomic pairs in solid-solution alloys. However, some approximations need to be made for those alloys with components that are neighbors in the periodic table. With EXAFS measurement, we have successfully revealed the short-range order in NiPd [22] and NiCoCr [21] solid-solution alloys.

The uncertainty for atoms being located exactly on the lattice sites is another type of structural disorder that contributes to the excess configurational entropy [1,23]. Previous TEM analysis indicated that the lattice distortion destabilized the structure, and phase segregation was observed in solid-solution alloys, such as NiCoFeCrMn [24,25], during annealing and ion irradiation. Under high pressure, the fcc lattice of some alloys can transform to another close-packed hcp structure. However, the phase transformation behavior in the HEAs is not simple. Experiments demonstrated that NiCoFeCr [26] and NiCoFeCrMn [27,28] started to transform to an hcp structure at ~13 GPa, whereas phase transition was not found in NiCoFeCrPd alloy even up to 74 GPa [26]. Moreover, it recognized that magnetic contributions to the free energy may play a critical role. In this paper, the long/short-range lattice distortion and structural stability of Pd-doped (NiCoFeCr)100−*x*Pd*<sup>x</sup>* HEAs were experimentally studied with total X-ray scattering, X-ray diffraction methods and the local bonding environment of atoms in the solid-solution is derived by EXAFS measurements.

#### **2. Materials and Methods**

Elemental metals Ni, Co, Fe, Cr, and Pd (> 99.9% pure) in the designed atomic ratios with the formula of (NiCoFeCr)100−*x*Pd*<sup>x</sup>* (*x* = 1, 3, 5 and 20) were carefully weighed and mixed by arc melting. The arc-melted buttons were flipped and re-melted at least five times before drop casting to ensure the homogeneity. The ambient total scattering measurements were performed at synchrotron beamline F2 of CHESS (Cornell High Energy Synchrotron Source), Cornell University, with an X-ray energy of E = 61.332 KeV and beam size of 500 × 500'μm2. A two-dimensional stationary detector with <sup>200</sup> × 200'μm2 pixel size was placed ∼20 cm behind the sample to collect data. Fit2D software [29] was used to correct for a beam polarization and a dark current. In order to obtain real-space PDF, the measured patterns were Fourier transformed by PDFgetX3 [30] and then normalized reciprocal-space structure function in a Q range of 30 Å<sup>−</sup>1. Using PDFGui software [31], the measured PDFs were refined with the fcc structure models. The in situ high-pressure XRD (X-ray powder diffraction) was conducted with the diamond anvil cell technique in transmission mode at beamline 16-BM-D of the APS (Advanced Photon Source), Argonne National Laboratory. For high-pressure XRD experiments, a methanol/ethanol (4/1) mixture was used as the pressure transition medium. The wavelength of the X-ray was 0.4989 Å and 0.3103 Å for ambient and high-pressure measurements, respectively. For all of the synchrotron XRD experiments, the instrument parameters were calibrated with CeO2 as the standard, and XRD profiles were analyzed with the Rietveld refinement method using the program Fullprof [32]. The EXAFS spectra at the K-edge of elements Ni, Co, Fe, Cr were conducted in a fluorescence mode with a grazing exit configuration (grazing angle of 2–3◦) at beam 13-ID-E of APS, Argonne National Laboratory. Athena program [33] was used for the reduction and analysis of the EXAFS data. The fitting of the EXAFS spectra was conducted with Artemis in Demeter software package [33] in a fixed k-range (3.0–12.0 Å−1) and an fcc structural model was used to simulate the structure of the solid solutions.

#### **3. Results and Discussion**

#### *3.1. Local Lattice Distortion*

The local lattice distortion induced by atomic size mismatch in HEAs has been estimated by a hard sphere model [34]. However, an experimental investigation has revealed that the hard-sphere model considerably overestimated the local lattice distortion in the HEAs. The measurement of the Bragg peak width in XRD or neutron diffraction profiles contains information of both static and dynamic displacements, which, however, cannot be resolved [17]. PDF analysis based on total scattering measurements can effectively reveal the local lattice distortion in terms of variation of local bond distance. Figure 1a shows the observed PDF profile of the NiCoFeCrPd HEA and the calculated one based on a random solid-solution model. Except for the first peak, the calculated pattern matches the observed one very well. The mismatch in the first atomic shell is an indication of local lattice distortion in NiCoFeCrPd. In order to quantitively describe the local lattice distortion in solid-solution alloys, we introduced a local lattice distortion parameter *ε*.

$$\varepsilon = \left( a\_{\text{Dir}} - a\_{\text{av}\%} \right) / a\_{\text{avg}} \tag{1}$$

Where *aavg* is the lattice parameter obtained from fitting the PDF profile over the whole r-range and *avar* is the lattice parameter obtained by fitting the PDF profile from rmin = 1.5 Å (data below this value was excluded because of large oscillations) to the varied rmax value. The local lattice distortion in the fcc HEAs is strongly localized in the first atomic shell, as shown in Figure 1a. Therefore, we only focused on the lattice strain in the first atomic shell, ε1st. Our results show that NiCoFeCr has a negligible ε1st (< 0.1%), whereas the NiCoCr and FeCoNiCrMn possess a small positive ε1st, suggesting that the local bond distances are larger than the expected value from their average structures. NiCoFeCrPd has the largest ε1st (0.79%) (Figure 1b) reported so far. The large lattice strain in NoCoFeCrPd is caused by the large size mismatch between Pd and other elements. With similar analysis of the Pd-doped (NiCoFeCr)100−*x*Pd*<sup>x</sup>* HEAs, the local lattice distortion is found to be proportional to the content of Pd (Figure 1b).

**Figure 1.** (**a**) Pair distribution function of NiCoFeCrPd HEA (high-entropy alloys). The blue symbols are experimental data and the red line is fit to the data using a random solid-solution model. The slight shift of the measured PDF (pair distribution function) from the fitted data (difference shown at *r* from 2 to 3 Å indicates the local lattice distortion; (**b**) Local lattice distortion in the first atomic shell as a function of the Pd concentration in the alloys.

#### *3.2. Long-Range Lattice Distortion*

XRD experimental results have shown that the Bragg peaks are broadened and the intensities are reduced in HEAs [35] because of the larger uncertainty for atoms being exactly on the crystalline lattice sites. No obvious long-range lattice distortion has been observed previously from X-ray or neutron diffraction measurements. For most HEAs, their lattice remains the fcc, bcc or hcp structure. However, long-range lattice distortion is found in Pd-doped (NiCoFeCr)100−*x*Pd*<sup>x</sup>* HEAs from XRD measurement. Figure 2 shows the XRD patterns of (NiCoFeCr)100−*x*Pd*<sup>x</sup>* (*x* = 1, 3, 5 and 20 atom%) HEAs under ambient conditions. The red dots are observed patterns and the green line are calculated patterns based on Rietveld refinement. As shown in the enlarged patterns (Figure 2b), there is a clear deviation at the (200) Bragg peak. The observed (200) peak exhibits a larger d-spacing than the average, whereas all of the other Bragg peaks match the average positions very well. The deviation of the (200) lattice planes is ~0.004 Å. Since XRD reveals the long-range order, the mismatch of the (200) peak indicates that the Pd-doped NiCoFeCrPd*<sup>x</sup>* HEAs have a distorted lattice from the ideal fcc structure, though no peak splitting was observed. Experimental analysis also suggests that the deviation of the (200) peak in the alloys with different concentrations of Pd is nearly the same. Due to the substitution of larger Pd atoms into the structure, it is not difficult to understand the change of lattice constant (Table 1) and local lattice distortion with the Pd content in the solid-solution alloys. It is surprising that even 1atom% Pd-doping in (NiCoFeCr)99Pd1 HEAs can cause a long-range structural distortion on the (200) lattice planes. The systematic larger (200) lattice plane spacing suggests that the large Pd atoms may be not randomly distributed in the lattice. To obtain the short-range order information for these HEAs, a method capable of characterizing the local bonding environment is strongly needed.

**Figure 2.** (**a**) The XRD (X-ray powder diffraction) profiles measured with synchrotron X-rays (*λ* = 0.4989Å). The red symbols are measured data and the green lines are calculated profiles based on Rietveld refinement; (**b**) the enlarged part of the XRD profiles and the observed (200) Bragg peak in all the samples obviously shifted to lower two theta angles with larger d-values.

**Table 1.** The lattice constant and the nearest atomic pair distance in the solid-solution alloys measured with XRD and EXAFS (extended X-ray absorption fine structure).


#### *3.3. Local Bonding Environment*

Neither XRD nor total scattering measurements can give the atomic bonding information in the solid-solution alloys. In order to detect the bond distance in the (NiCoFeCr)100−*x*Pd*<sup>x</sup>* (*x* = 1, 3, 5 and 20 atom%) HEAs, we measured the K-edge X-ray absorption spectrums of Ni, Co, Fe, and Cr elements. Since these four elements have similar X-ray scattering ability, it is difficult to distinguish the individual elements in the solid-solution alloys. As an approximation, we assumed that, except for Pd, the atoms around the core have the same X-ray scattering ability. Figure 3 is the *k*3-weighted FTs of the Fe K-edge EXAFS for the (NiCoFeCr)100−*x*Pd*<sup>x</sup>* (*x* = 1, 3, 5 and 20 atom%) HEAs. We assumed that Pd and Fe atoms are randomly distributed in the fcc lattice and the red dash lines in Figure 3 are the fittings within the first shell in the radial distance of 1–3.5 Å. The first shell peak is generally well fitted with this approximation. The derived average distance between the nearest atomic pairs is shown in Table 1. In general, for the lower Pd-doped alloys, the distance measured with EXAFS is in good agreement with that measured with XRD but for the equiatomic NiCoFeCrPd alloy, the distance measured with EXAFS is obviously smaller (1.7%) than that from the XRD measurement, which suggests that there is a larger lattice strain in the NiCoFeCrPd HEA than the lower Pd-doped alloys. This is in agreement with the total scattering measurements. From the PDF analysis, we have confirmed that the local lattice distortion in NiCoFeCrPd is 3–4 times larger than that in the lower Pd-doped solid-solution alloys [20].

**Figure 3.** The *κ*3-weighted FTs (Fourier Transforms) of the Fe K-edge EXAFS (extended X-ray absorption fine structure) in (NiCoFeCr)100−xPdx solid-solution alloys. The solid blue line is observed and the red dash line is the fitting with the nearest neighbors.

#### *3.4. Structural Stability at High Pressures*

Multi-component concentrated solid-solution alloys can have an fcc, bcc or hcp structure. Theoretical calculations suggested that some fcc HEAs are metastable because their hcp counterparts have similar Gibbs free energies at ambient conditions. Previous experiments have revealed that some of the fcc alloys can transform to the hcp structure under high-pressure conditions, such as NiCoFeCr [26] and NiCoFeCrMn [27,28] alloys that transformed to an hcp structure at ~13 GPa. The hcp structure is quenchable to ambient conditions, though the phase transition is very sluggish. The phase stability is composition sensitive. For FeMnCoCr alloys [36], the hcp structure can coexist with the fcc structure from the sample preparation process. By properly tuning the chemical composition, a dual-phase alloy can possess excellent mechanical properties. For the five-element system of NiCoFeCrPd, the fcc structure is stable up to 74 GPa [26]. The larger size of Pd atoms plays a key role in structural stability. It is thus interesting to study the effect of Pd content on the phase transition. We pressurized the Pd-doped (NiCoFeCr)100−*x*Pd*<sup>x</sup>* HEAs with diamond-anvil cell techniques, and

the experimental results indicate that a small amount of Pd greatly affects the structural stability. The critical pressure for the fcc to hcp phase transition is strongly increased to more than 20 GPa in 1 atom%, 3 atom% and 5 atom% doped (NiCoFeCr)100−xPdx solid-solution alloys. Figure 4 shows the XRD profiles of 3 atom% Pd doped (NiCoFeCr)97Pd3 alloy at different pressures, and the hcp structure starts to appear at 20.9 GPa. The transition is very sluggish, and the amount of the hcp structure is only ~33% at 34.1 GPa. The hcp structure is stable once it is formed, and the quenched alloy has a mixed structure of fcc and hcp. The critical transition pressure is not sensitive to the amount of Pd doped and is observed at 26.0, 20.9, and 21.0 GPa for the 1%, 3% and 5% Pd-doped (NiCoFeCr)100−*x*Pd*<sup>x</sup>* HEAs, respectively. However, no hcp structure was found in the equiatomic solid-solution alloy NiCoFeCrPd up to 74 GPa [26]. Since Pd has a much larger atomic size than other elements in these alloys, the substitution of Pd for other atoms increases the lattice parameter and atomic-pair distances. When the Pd content in the alloys is sufficient, all the smaller atoms will have more free space to move, which may allow adaption to the lattice distortion at high pressures. This may be the main reason why Pd can cause changes in the critical transition pressure for Pd-doped NiCoFeCrPd solid-solution alloys. Therefore, the high local lattice distortion greatly in the equiatomic HEA can enhance the stability of the fcc lattice.

**Figure 4.** The XRD profiles of (NiCoFeCr)97Pd3 measured at different pressures. The fcc lattice starts to transform to hcp structure at 20.9 GPa. The weak diffraction peaks marked with small black arrows are from the W gasket during measurement.

We further analyzed the long-range lattice distortion of (NiCoFeCr)100−*x*Pd*<sup>x</sup>* solid-solution alloys under high pressure, i.e., the deviation at the (200) Bragg peak. Figure 5 shows the deviation of each observed Bragg peaks at different pressures for the 1% Pd-doped NiCoFeCr. The deviation of the (200) Bragg peak obviously increased with pressure. Before the hcp structure starts to form, the deviation of (NiCoFeCr)99Pd1 has reached 0.01 Å. In a strict sense, the structure of the (NiCoFeCr)99Pd1 alloy is not fcc anymore. A similar behavior is also observed in the (NiCoFeCr)97Pd3 and (NiCoFeCr)95Pd5 alloys. Accordingly, the external high pressure can enhance the long-range lattice distortion.

Figure 6 shows the *P-V* curves of Pd-doped NiCoFeCr alloys. As a comparison, the *P*-*V* curves for NiCoFeCr and NiCoFeCrPd are also shown. When fitted with a 3rd Birch-Murnaghan equation of state, the bulk modulus is 190(5), 171(8) and 186(4) GPa for the 1%, 3% and 5% Pd-doped NiCoFeCr solid-solution alloys, respectively. The bulk modulus of the Pd-doped solid-solution alloys is smaller than that of NiCoFeCr (206 GPa) but larger than that of NiCoFeCrPd (168 GPa). The addition for larger Pd atoms makes the alloys more compressible with smaller bulk modulus because the addition of Pd atoms increased the lattice parameters and the smaller atoms, Ni, Co, Fe, and Cr, may have more "free" space to move in order to adapt the structure during pressurization.

**Figure 5.** The deviation of the observed Bragg peaks from the ideal fcc structure at different pressures. The deviation of (200) peak is obvious and it increases with pressure.

**Figure 6.** The pressure dependence of the unit cell volume. The dashed lines *P*-*V* curves which are fitted with 3-rd-order Birch-Murnaghan equation of state

#### **4. Conclusions**

We have systematically studied the effects of Pd doping in *(*NiCoFeCr*)100*−*x*Pd*<sup>x</sup>* solid-solution alloys on lattice distortion and phase stabilities. The short-range order is strongly dependent on the Pd content in the alloys. Both PDF and EXAFS measurements suggest that the lattice is locally strained in the highly Pd doped solid-solution alloys. Even a small amount of Pd addition in the alloys can cause a long-range lattice distortion by showing a larger (200) lattice plan spacing than the expected from the average structure. High-pressure studies revealed that a small amount of Pd in the solid-solution alloys greatly enhanced the phase stability of the fcc structure, and the critical pressure for the fcc to hcp transition increased from ~13 GPa to more than 20 GPa in 1%, 3% and 5% Pd-doped alloys, while the fcc is stable up to 74 GPa in the equiatomic NiCoFeCrPd HEA.

**Author Contributions:** F.Z. and Y.T. performed the experiments, K.J. and H.B. prepared the samples, W.J.W. and Y.Z. contributed to discussion and writing.

**Funding:** This research was funded by US DOE grant number DE-AC05-00OR22725.

**Acknowledgments:** This work was supported as part of the Energy Dissipation to Defect Evolution (EDDE), an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Basic Energy of Sciences under contract number DE-AC05-00OR22725. The X-ray diffraction and total scattering measurement were conducted at the Cornell High Energy Synchrotron Source (CHESS) which is supported by the National Science Foundation and the National Institutes of Health/National Institute of General Medical Sciences under NSF award DMR-1332208. The EXAFS measurement was performed at GeoSoilEnviroCARS (The University of Chicago, Sector 13), Advanced Photon Source (APS), Argonne National Laboratory. GeoSoilEnviroCARS is

supported by the National Science Foundation - Earth Sciences (EAR - 1634415) and Department of Energy-GeoSciences (DE-FG02-94ER14466). This research used resources of the Advanced Photon Source, a U.S. Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under Contract No. DE-AC02-06CH11357.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

### *Article* **Effect of Mn Addition on the Microstructures and Mechanical Properties of CoCrFeNiPd High Entropy Alloy**

#### **Yiming Tan, Jinshan Li \*, Jun Wang and Hongchao Kou**

State Key Laboratory of Solidification Processing, Northwestern Polytechnical University, Xi'an 710072, China; tanym2015@mail.nwpu.edu.cn (Y.T.); nwpuwj@nwpu.edu.cn (J.W.); hchkou@nwpu.edu.cn (H.K.) **\*** Correspondence: ljsh@nwpu.edu.cn

Received: 16 February 2019; Accepted: 12 March 2019; Published: 16 March 2019

**Abstract:** CoCrFeNiPdMn*<sup>x</sup>* (*x* = 0, 0.2, 0.4, 0.6, 0.8) high entropy alloys (HEAs) were prepared and characterized. With an increase in Mn addition, the microstructures changed from dendrites (CoCrFeNiPd with a single face-centered-cubic (FCC) phase) to divorced eutectics (CoCrFeNiPdMn0.2 and CoCrFeNiPdMn0.4), to hypoeutectic microstructures (CoCrFeNiPdMn0.6), and finally to seaweed eutectic dendrites (CoCrFeNiPdMn0.8). The addition of Mn might change the interface energy anisotropy of both the FCC/liquid and MnPd-rich intermetallic compound/liquid interfaces, thus forming the seaweed eutectic dendrites. The hardness of the FCC phase was found to be highly related to the solute strengthening effect, the formation of nanotwins and the transition from CoCrFeNiPd-rich to CoCrFeNi-rich FCC phase. Hierarchical nanotwins were found in the MnPd-rich intermetallic compound and a decrease in either the spacing of primary twins or secondary twins led to an increase in hardness. The designing rules of EHEAs were discussed and the pseudo binary method was revised accordingly.

**Keywords:** high entropy alloys; solidification; alloy design; eutectic dendrites; hierarchical nanotwins

#### **1. Introduction**

High entropy alloys (HEAs) [1] or multi-principal element alloys [2] are now attracting more and more attention [3–10]. In contrast to the traditional alloys with one principal element or two, HEAs have at least four principal elements and usher in an expansive alloy space for exploring potential new materials with brilliant properties [11–26]. Initially, studies of HEAs concentrated to a greater extent on the solid-solution phases, e.g., the HEAs with a single face-centered-cubic (FCC) phase, with a single body-centered-cubic (BCC) phase or with dual FCC and BCC phases. Lots of studies suggested that the high configurational entropy would be able to stabilize thermodynamically the solid-solution phases [1,4,5,27,28]. As the researches move forward, more and more studies suggested that the high configurational entropy alone could not determine completely the constituent phases, because most of the HEAs consisted of multi-phases [29–34].

Although the HEAs with a single solid-solution phase have some advantages (e.g., higher melting points than the HEAs with multi-phases, higher strength for the HEAs with a single BCC phase, better ductility for the HEAs with a single FCC phase etc.), their good properties are usually accompanied by some disadvantages, which are fatal for technological applications. One is that the HEAs with a single solid-solution phase usually have inadequate liquidity, poor castability and hence considerable chemical inhomogeneity [21,35]. The other is that the HEAs with a single solid-solution phase could not achieve a balance between high strength and good ductility (e.g., the HEAs with a single FCC phase were ductile but not strong enough while the HEAs with a single BCC phase were adequately strong but at risk of brittleness [21,35–37]).

To tackle the aforementioned problems, eutectic HEAs (EHEAs) [21] were proposed. On the one hand, EHEAs should have the general character of traditional eutectic alloys. In this sense, EHEAs should have better fluidity and thus better castability and less casting defects [15,35]. On the other hand, EHEAs as one kind of in-situ composites with lamellar or rod-like eutectic microstructures might reach the balance between strength and ductility via mixing the soft FCC phase with the hard BCC phase or intermetallic compound [15,35,38–44]. Some EHEAs indeed have outstanding properties. Lu et al. [15] reported the AlCoCrFeNi2.1 EHEA with simultaneous high strength (944 MPa) and good ductility (25.6%). The excellent mechanical properties do not depend significantly on derivation of eutectic compositions [35]. After cold-rolling and annealing, its strength reached up to 1.2 GPa and its elongation could remain at about 12% [40]. After cryo-rolling and annealing, its strength could reach up to 1.47 GPa while its ductility could even increase to 14% [41]. He et al. [42,43] designed the CoCrFeNiNb*x* EHEAs and found that the microstructures were stable from 600 ◦C to 900 ◦C.

The current work aims to report a new EHEA. From Ref. [45], CoCrFeNiPd is a single FCC solid solution HEA. From the Mn-Pd phase-diagram [46], MnxPdy is a relative stable intermetallic compound. We hence chose CoCrFeNiPd as a FCC solid solution phase and MnxPdy as an intermetallic compound (IMC) phase to design pseudo binary EHEAs via adjusting the content of IMC forming element Mn to finally get the eutectic structure. The effect of Mn addition on the microstructures was investigated and a seaweed eutectic dendrite solidification microstructure was found in the CoCrFeNiPdMn0.8 EHEA. The effect of Mn addition on the mechanical properties was studied by nano-indentation and compression tests. The size effects of primary and secondary twins on the hardness of Mn*x*Pd*y* phase were shown. The designing rules of EHEAs were improved.

#### **2. Materials and Methods**

#### *2.1. Material Preparation*

The ingots were prepared by arc melting under a Ti-gettered, high-purity argon atmosphere. Elements of Co, Cr, Fe, Ni, Mn and Pd with purities better than 99.95 wt.% were chosen as the raw materials. To prevent the mass loss due to evaporation of Mn, a high purity Fe-68.7at.%Mn intermediate alloy was prepared in advance and the total mass loss of each ingot was less than 0.3 wt.%. In order to ensure the chemical homogeneity, electromagnetic stirring was used during the melting process; each ingot was re-melted at least five times in the water-chilled copper crucible, held at a liquid state for at least 5 min and flipped before each melting process. The prepared button-shaped ingots were approximately 20 mm in diameter and 10 mm in thickness.

#### *2.2. Material Characterization*

The crystal structures were analyzed by X-ray diffraction (XRD, DX2700, Fang Yuan Company, Dandong, China) using Co k*α* radiation and a 2θ scattering range of 20◦–120◦. The microstructures were characterized by the field emission scanning electron microscopy (SEM, Zeiss SUPRA 55, Zeiss Inc., Jena, Germany) operated at 15 kV. The SEM samples were first polished and then etched for a few seconds within the solution of hydrochloric acid, sulfuric acid and supersaturated copper sulfuric (30 mL, 10 mL, 1 g). After the SEM observations, the samples for transmission electron microscopy (TEM) analysis were cut from the center of the SEM samples, prepared by mechanically polishing to a thickness of 45 μm, punched into disks with a diameter of 3 mm and then thinned by ion milling (GATAN 691, Gatan Inc., Warrendale, PA, United State). The chemical components and element distributions in different phases were measured by an electron probe micro-analyzer (EPMA, Shimadzu 1720, Shimadzu Inc., Kyoto, Japan) and an energy dispersive spectrometer (EDS) attached to TEM (TecnaiFG2).

The hardness and elastic modulus of constituent phases in the as-cast alloys were investigated by the Nano-indenter XP® system (MTS Inc., Eden Prairie, MN, United State) at room temperature with a diamond Berkovich indenter at a peak load of 20 mN and a load rate of 0.1 mN·s−1. The peak load was held for about 5 s to eliminate the instrument noise and five different points were measured for each phase. The samples for nano-indentation were mechanically polished to 1 mm thickness and then electro-polished in an electrolyte of 90 vol.% ethanol and 10 vol.% perchloric acid, with a voltage of 30 V and a polishing time of about 20 s in Struers LectroPol-5. The compression tests were conducted at room temperature in an electronic testing machine (INSTRON 3382, Instron Inc., Norwood, MA, United State) with a strain rate of 1 × <sup>10</sup>−<sup>3</sup> <sup>s</sup>−1. Cuboid specimens were produced by electric-discharged machining from the cast buttons. The samples were 6 mm in height and 3 mm in length and width, giving an aspect ratio of 2. In order to show the solidification path, the thermal histories of as-cast alloys were measured by a differential scanning calorimetry (DSC, Netzsch 449 C, Netzsch Inc., Selb, Germany) under a flow of purified argon for protection and with a rate of 20 K min<sup>−</sup>1. The mass of samples was about 15 mg.

#### **3. Results**

#### *3.1. Crystal Structures and Microstructures*

Figure 1 shows the XRD patterns of as-cast CoCrFeNiPdMn*x* (*x* = 0–0.8) HEAs. It should be noted that the CoCrFeNiPdMn*<sup>x</sup>* HEA in what follows was denoted as Mn*<sup>x</sup>* for short (e.g., Mn0.2 stands for the CoCrFeNiPdMn0.2 alloy). The Mn0 HEA was of a single FCC phase with a lattice parameter of *a* = 3.669 Å. The Mn0.2, Mn0.4, Mn0.6 and Mn0.8 HEAs had a dual FCC phase and Mn*x*Pd*<sup>y</sup>* intermetallic compound. Because the diffraction peaks of Mn*x*Pd*<sup>y</sup>* intermetallic compound are intensified with increasing Mn addition, one could draw a conclusion that the Mn addition promotes the formation of Mn*x*Pd*<sup>y</sup>* intermetallic compound. However, the diffraction peaks of MnPd, Mn2Pd3 and Mn3Pd5 as well as those of Mn7Pd9 and Mn11Pd21 were quite similar. The XRD results alone were therefore not able to distinguish the crystal structure of the Mn*x*Pd*y* intermetallic compound.

**Figure 1.** XRD patterns of as-cast CoCrFeNiPdMnx (*x* = 0, 0.2, 0.4, 0.6, 0.8) HEAs.

Typical microstructures of as-cast Mn*<sup>x</sup>* (*x* = 0.2–0.8) HEAs are shown in Figure 2. The Mn0 HEA exhibited a single solid-solution phase and the coarse dendrites were of several hundred or even a thousand microns; see Figure 2a,a1 in different magnifications. For the Mn0.2 EHEA, the microstructure consisted of a main FCC solid-solution phase in the dendrite and a sporadic distributed granular Mn*x*Pd*y* intermetallic compound; see Figure 2b. Because the Mn*x*Pd*y* intermetallic compound distributed within the inter-dendrites, it could be reasonable to conclude that the microstructure belonged to divorced eutectics; see Figure 2b1 in which the FCC phase and the Mn*x*Pd*<sup>y</sup>* intermetallic compound are in dark grey and light grey, respectively. It should be pointed out that at the inter-dendrites, a eutectic microstructure could be found but its volume fraction was very small. The microstructure of Mn0.4 EHEA was quite similar to the Mn0.2 EHEA, except that both the volume fractions of eutectics and granular Mn*x*Pd*<sup>y</sup>* intermetallic compound were much larger; see Figure 2c,c1 in different magnifications. The microstructure changes from a hypoeutectic microstructure for the Mn0.6 EHEA (e.g., a primary FCC dendrite around which were the lamellar eutectics) to a fully eutectic microstructure for the Mn0.8 EHEA (e.g., a eutectic dendrite with a fine lamellar spacing around which

were the coarse granular eutectics); see Figure 2d–e1 in different magnifications. In order to show the characteristics of the eutectic dendrite pattern in the Mn0.8 EHEA, two additional figures with different amplifications are shown in Figure 2e2,e3. Figure 2e2 shows an overall view of eutectic dendrites and Figure 2e3 presents some details for tip splitting of eutectic dendrites. Because the tips repeatedly split into several parts and grew on themselves, the microstructure of Mn0.8 HEA belonged to seaweed eutectic dendrites [47,48].

**Figure 2.** SEM images of as-cast CoCrFeNiPdMn*<sup>x</sup>* (*x* = 0, 0.2, 0.4, 0.6, 0.8): Mn0 (**a**,**a1**), Mn0.2 (**b**,**b1**), Mn0.4 (**c**,**c1**), Mn0.6 (**d**,**d1**) and Mn0.8 (**e**,**e1**,**e2**,**e3**).

#### *3.2. Phase Identification*

The TEM results of as-cast Mn*<sup>x</sup>* (*x* = 0.2, 0.4, 0.6, 0.8) HEAs are shown in Figures 3–6. In each figure, the bright-field TEM images (a, d), the selected area electron diffraction (SAED) pattern of FCC (c) and Mn*x*Pd*y* (d) phases, the EDS mapping of Co (e), Cr (f), Fe (g), Ni (h), Pd (i) and Mn (j) elements are shown. To show the effect of Mn addition on the phase transition in the Mn*<sup>x</sup>* HEAs, the chemical compositions of FCC and Mn*x*Pd*y* phases were measured by EDS attached to TEM and EMPA. In the current work, four points were randomly selected for each phase in the fine lamellar region by EDS and five points were measured randomly for each phase in the surrounding coarse granular eutectic region by EPMA. Because the average compositions measured by EDS and EPMA were quite close, only the EPMA results for the FCC solid-solution phase and Mn*x*Pd*<sup>y</sup>* intermetallic compound are summarized in Tables 1 and 2, respectively.

**Table 1.** EPMA results of the FCC phase in the CoCrFeNiPdMn*x* (*x* = 0–0.8) HEAs (in atomic fraction).


**Table 2.** EPMA results of the Mn*x*Pd*y* phase in the CoCrFeNiPdMn*x* (*x* = 0-0.8) HEAs (in atomic fraction).


**Figure 3.** TEM images (**a**) and (**d**), the corresponding SAED patterns of FCC (**b**) and Mn3Pd5 (**c**) phases, and the EDS mapping of Co (**e**), Cr (**f**), Fe (**g**), Ni (**h**), Pd (**i**), Mn (**j**) for the as-cast CoCrFeNiPdMn0.2 HEA.

**Figure 4.** TEM images (**a**) and (**d**), the corresponding SAED patterns of FCC (**b**) and Mn3Pd5 (**c**) phases, and the EDS mapping of Co (**e**), Cr (**f**), Fe (**g**), Ni (**h**), Pd (**i**), Mn (**j**) for the as-cast CoCrFeNiPdMn0.4 HEA.

**Figure 5.** TEM images (**a**) and (**d**), the corresponding SAED patterns of FCC (**b**) and Mn7Pd9 (**c**) phases, and the EDS mapping of Co (**e**), Cr (**f**), Fe (**g**), Ni (**h**), Pd (**i**), Mn (**j**) for the as-cast CoCrFeNiPdMn0.6 EHEA.

**Figure 6.** TEM images (**a**) and (**d**), the corresponding SAED patterns of FCC (**b**) and Mn7Pd9 (**c**) phases, and the EDS mapping of Co (**e**), Cr (**f**), Fe (**g**), Ni (**h**), Pd (**i**), Mn (**j**) for the as-cast CoCrFeNiPdMn0.8 RHEA.

For the Mn0.2 EHEA, the FCC phase was rich in Co, Cr, Fe, Ni and Pd but depleted of Mn, whereas for the Mn*x*Pd*y* phase, the compositions of Co, Cr, Fe and Ni were negligible; see Figure 3 and Table 1. According to the SAED patterns taken from the FCC-region and Mn*x*Pd*y*-region, the matrix was of a FCC structure while the Mn*x*Pd*<sup>y</sup>* phase was a Mn3Pd5 intermetallic compound with lattice parameters

of *a* = 0.2285 nm, *b* = 0.1998 nm and *c* = 0.2278 nm, being consistent with the XRD results in Figure 1. It should be pointed out that even though the composition of Pd in the FCC phase (≈13.5%) was much larger than that of Mn (≈2%), it was still considerably smaller than that in Mn3Pd5 intermetallic compound (≈47%). Therefore, the fact that the FCC phase was rich in Pd cannot be shown by the EDS mapping; see Figure 3i. For the Mn0.4 EHEA, the same result could be found from the SAED patterns, i.e., the matrix was the FCC phase and the Mn*x*Pd*<sup>y</sup>* phase was the Mn3Pd5 intermetallic compound. The FCC phase was still a (CoCrFeNiPd)-rich one and similar EDS mappings could be found; see Figure 4e–j.

With the further addition of Mn element, the FCC phases became rich in Co, Cr, Fe and Ni for the Mn0.6 and Mn0.8 EHEAs, while the compositions of Mn (~42.3% and 41.7%) and Pd (~43.7% and ~40.4%) were comparable in the Mn*x*Pd*<sup>y</sup>* phases; see Figures 5e–j and 6e–j, Tables 1 and 2. According to the SAED patterns in Figures 5c and 6c, the Mn*x*Pd*<sup>y</sup>* phase could be the Mn7Pd9 or the Mn11Pd21 intermetallic compound with lattice parameters of *a* = *b* = 0.2267 nm, *c* = 0.203 nm or *a* = *b* = 0.2235 nm, *c* = 0.1816 nm. Because the Mn11Pd21 phase was neither confirmed experimentally nor theoretically [46], the Mn*x*Pd*<sup>y</sup>* phase in the Mn0.6 and Mn0.8 EHEAs was ultimately determined to be the Mn7Pd9 intermetallic compound.

#### *3.3. Solidification Path*

To confirm further the effect of Mn addition on solidification microstructures, the cooling histories were measured by DSC; see Figure 7. For the Mn0.2 (the solid line) and Mn0.4 (the dashed line) EHEAs, two completely separated exothermal peaks could be found during the solidification process. The first and the second peak should correspond to the primary solidification of the FCC phase and following growth of the Mn3Pd5 intermetallic compound or eutectic growth. For the Mn0.6 EHEA (the dotted line), two exothermal peaks still exited during the solidification process but they overlapped with each other. As shown in Figures 1 and 2, an increase of the Mn content promoted the formation of Mn*x*Pd*y* phase, thus intensifying the second exothermal peak during solidification and narrowed the distance between the two peaks as shown in Figure 7. For the Mn0.8 EHEA, only one solidification peak could be found; see the dashed-dotted line in Figure 7. The peak should correspond to eutectic solidification.

**Figure 7.** DSC solidification curves of as-cast CoCrFeNiPdMn*x* (*x* = 0.2–0.8) HEAs. Insert shows the magnified exothermic peaks during solidification.

#### *3.4. Mechanical Properties*

The nanoindentor was used to measure the hardness and elastic modulus of FCC and Mn*x*Pd*<sup>y</sup>* phases; see Figure 8a,b. It should be noted that the lamellar spacing of lamellar eutectics in the Mn0.6 and Mn0.8 EHEAs was so fine that it was beyond the measurability of the nanoindentor. In this case, the coarse granular eutectics were measured. From Figure 8a, it can be seen that with an increase in

the Mn addition, the hardness and elastic modulus of FCC phase first increased and then decreased. From Table 1, the FCC phase was CoCrFeNiPd-rich for the Mn0.2 and Mn0.4 EHEAs while it was CoCrFeNi-rich for the Mn0.6 and Mn0.8 EHEAs. From Ref. [49], the measured hardness of CoCrFeNiPd HEA 3.16 GPa was nearly twice of CoCrFeNi HEA 1.47 GPa. This was the reason why the hardness of Mn0, Mn0.2 and Mn0.4 HEAs was much larger than that of Mn0.6 and Mn0.8 HEAs; see Figure 8a. For the Mn*x*Pd*<sup>y</sup>* phase, the hardness of the Mn3Pd5 intermetallic compound in the Mn0.2 (4.9 GPa) and Mn0.4 (5.3 GPa) EHEAs was much larger than that of the Mn7Pd9 intermetallic compound in the Mn0.6 (3.1 GPa) and Mn0.8 (3.4 GPa) EHEAs. For both the FCC and Mn*x*Pd*<sup>y</sup>* phases, the evolution tendencies of hardness were the same as those of the elastic modulus.

**Figure 8.** Hardness and elastic modulus of FCC phase (**a**) MnxPdy phase (**b**) in the CoCrFeNiPdMn*x* (*x* = 0.2–0.8) HEAs.

To show further the effect of Mn addition on the mechanical properties, compression tests were conducted for the as-cast Mn*<sup>x</sup>* HEAs; see Figure 9 One can see that with the increase of Mn addition, the yielding strength held constantly at about 650 MPa. The fracture strain (strength) decreased from about 50% (2.4 GPa) for the Mn0.2 HEA to about 35% (1.9 GPa) for the Mn0.8 HEA. The current EHEAs had good strength and ductility.

**Figure 9.** Compressive engineering stress-strain curves of as-cast CoCrFeNiPdMn*x* (*x* = 0.2–0.8) HEAs.

#### **4. Discussion**

#### *4.1. Effect of Mn Addition on Microstructures*

With an increase in the Mn content, the microstructures of Mn*x* HEAs changed from dendrites for the Mn0 HEA to divorced eutectics for the Mn0.2 and Mn0.4 EHEAs, to hypoeutectic microstructures for the Mn0.6 EHEA and finally to eutectic dendrites for the Mn0.8 EHEA. The eutectic dendrite solidification pattern in the Mn0.8 EHEA was formed by cooperative growth of the FCC phase and Mn7Pd9 intermetallic compound. From Tables 1 and 2, the FCC phase was lacking Mn while the Mn7Pd9 intermetallic compound was lacking Co, Cr, Fe and Ni. Therefore, lateral solute diffusion of Co, Cr, Fe, Ni and Mn formed the eutectic pattern while longitudinal solute diffusion of Pd made the eutectic interface unstable to a eutectic dendrite.

From Figure 2e2,e3, seaweed eutectic dendrites were found for the Mn0.8 EHEA. Unlike the normal dendrite pattern where the structure branches with pronounced orientation order, the seaweed pattern is characterized by tip-splitting and the key factor for its formation is weak interface energy anisotropy [50]. Generally, the formation of seaweed dendrites is highly related to alloy compositions and solidification conditions [51–54]. For example, the effect of Zn content on the microstructures of directional solidification of Al-Zn alloys was studied by X-ray tomographic microscopy and phase-field simulation [51]. Accordingly, an increase in the Zn content modified the interface energy anisotropy, thus leading to the transition from <100> dendrites at low Zn content to <110> dendrites at high Zn content, between which were the <320> seaweed dendrites. For both the undercooled Cu-8.9 wt.% Ni and Cu-3.98 wt.% Ni alloys [53,54], a transition from <100> dendrites to mixed <100> and <111> seaweed dendrites and then to <111> dendrites was reported.

For eutectic solidification that consisted of at least two solid phases, its morphology was determined by a combination effect of eutectic phases and the formation mechanism became more complex. Eutectic seaweed dendrites were reported in the undercooled Co-24.0at.%Sn eutectic alloy, in which the weak interface energy anisotropy ascribed to an alternate arrangement of lamellae and alloy physical properties [55]. For the current Mn*<sup>x</sup>* HEAs, primary FCC dendrites were found in the divorced eutectics (e.g., Mn0.2 and Mn0.4) and the hypoeutectic microstructures (e.g., Mn0.6), indicated that its interface energy anisotropy was not weak. From Tables 1 and 2, the addition of Mn changed not only the compositions of FCC phase but also those of the Mn7Pd9 intermetallic compound. Therefore, it was quite possible that the addition of Mn influenced the interface energy anisotropy of both the FCC/liquid and Mn*x*Pd*y*/liquid interfaces, thus forming the seaweed eutectic dendrites in the Mn0.8 EHEA.

#### *4.2. Effect of Mn Addition on Mechanical Properties*

Because an increase in Mn addition results in a transition from the CoCrFeNiPd-rich to the CoCrFeNi-rich FCC phase in the Mn*x* HEAs (Table 1) and the hardness of CoCrFeNiPd HEA is much higher than that of CoCrFeNi HEA [49], the hardness of the FCC phase should decrease with increasing Mn addition. This was however, not the case, e.g., the hardness increased first and then decreased; see Figure 8a. The larger hardness of the FCC phase in the Mn0.2 and Mn0.4 EHEAs than that in the Mn0 HEA could be ascribed to the solute strengthening effect. But this effect alone cannot explain the fact that the hardness of the FCC phase in the Mn0.2 EHEA was larger than that in the Mn0.4 EHEA. The TEM results showed that a small amount of Mn addition might promote but a large amount would suppress the formation of nanotwins in the FCC phase; see Figure 10. Abundant nanotwins of about 50 nm could be found in the Mn0.2 EHEA, whereas for the Mn0.4 EHEA, it was almost free of nanotwins and so were the Mn0.6 and Mn0.8 EHEAs (not shown here). Therefore, the solute strengthening effect and the formation of nanotwins made the hardness increase first with increased Mn addition, the suppression of nanotwins then decreased the hardness and finally the transition from the CoCrFeNiPd-rich to the CoCrFeNi-rich FCC phase made the hardness decrease considerably.

Besides, hierarchical nanotwins were found in the Mn*x*Pd*<sup>y</sup>* intermetallic compounds of Mn0.2-Mn0.8 EHEAs; see Figure 10. With the help of Image-Pro Plus software, the spacing of the primary twins (*λ*1) and secondary twins (*λ*2) in the Mn*x*Pd*<sup>y</sup>* intermetallic compound were measured for the Mn0.2-Mn0.8 EHEAs; see Table 3. With an increase in the Mn addition, *λ*<sup>1</sup> decreased but *λ*<sup>2</sup> remained unchanged for the Mn3Pd5 intermetallic compound. For the Mn7Pd9 intermetallic compound, *λ*<sup>1</sup> did not change significantly but *λ*<sup>2</sup> decreased. The measured spacing of primary twins (242.1 nm, 180.3 nm) and secondary twins (10.0 nm, 9.98 nm) in the Mn3Pd5 intermetallic compound were much larger than those in the Mn7Pd9 intermetallic compound (15.0 nm, 15.0 nm for *λ*1, 2.22 nm and 1.46 nm for *λ*2) but the hardness of the former was much larger than that of the latter. However, for the same phase, a decrease of either *λ*<sup>1</sup> or *λ*<sup>2</sup> would increase the hardness of the intermetallic

compound, being consistent with Yuan and Wu [56] who studied the size effects of primary and secondary twins on the atomistic deformation mechanisms in the hierarchically nanotwinned metals.

**Figure 10.** TEM images of FCC phase in the Mn0.2 (**a**) and Mn0.4 (**b**) EHEAs.

**Table 3.** The measured spacing of primary twins (*λ*1) and secondary twins (*λ*2) for the Mn*x*Pd*<sup>y</sup>* phase in the CoCrFeNiPdMn*x* (*x* = 0.2–0.8) EHEAs.


#### *4.3. Designing Rules for EHEAs*

Even though the EHEAs have good processing and mechanical properties, most of the reported EHEAs were found by the trial and error method. Up to now, several studies were carried out for designing EHEAs [42,57–59]. Lu et al. [57] started from their representative AlCoCrFeNi2.1 EHEA. They divided the constituent elements into two different groups, i.e., Al and Ni with very high negative mixing of enthalpy (−22 kJ·mol−1), and Co, Cr and Fe with similar atomic size and very small negative mixing of enthalpy; see Table 4. Their method was to substitute Al by Zr, Nb, Hf and Ta that had very high negative mixing of enthalpy with Ni. After using the enthalpy mixing of equimolar binary alloys to obtain the eutectic points, four new EHEAs, i.e., Zr0.6CoCrFeNi2.1, Nb0.74CoCrFeNi2.1, Hf0.55CoCrFeNi2.1 and Ta0.65CoCrFeNi2.1, were reported. In their subsequent work [58], the eutectic composition containing (Ni, Co, Cr, Fe)-rich solid-solution phase in the (Co, Cr, Fe, Ni)-(Nb, Ta, Zr, Hf) binary systems were averaged to obtain the eutectic compositions of pseudo binary alloy CoCrFeNiM*x* (M = Nb, Ta, Zr and Hf). Consequently, four new EHEAs, i.e., Zr0.51CoCrFeNi, Nb0.6CoCrFeNi, Hf0.49CoCrFeNi and Ta0.47CoCrFeNi, were found. Even though the actual eutectic compositions were very close to the predicted ones using the above simple methods, the former method was based on a known EHEA, which might limit its application [59] and for the latter, there should be a eutectic reaction between the added element and any element in the base alloy which is not always the case for EHEAs. For example, for the CoCrFeNiMnPd*<sup>x</sup>* EHEAs, eutectic reactions happen only in the Mn-Pd and Cr-Pd binary alloys while for the CoCrFeNiPdMn*x* EHEAs, eutectic reactions can be found only in the Pd-Mn binary alloy.

He et al. [42] designed a pseudo binary alloy, i.e., the CoCrFeNi HEA with a single FCC solid-solution phase as the base alloy and Nb as the additional element. Such simple pseudo binary method was followed by Jin et al. [59]. First, they chose one HEA with a single solid-solution phase and one stable binary intermetallic compound. After that, they obtained the HEA with dual phase

by mixing the two phases. To ensure the formation of an eutectic structure, three conditions were proposed: (1) The single solid-solution phase should be stable enough without any segregation and precipitation; (2) the binary intermetallic compound should be stable from room temperature to its melting point; (3) the intermetallic compound must have the most negative mixing of enthalpy among all the binary combinations in the alloy. With CoCrFeNi2, Co2CrFeNi and CoCrFe2Ni as the HEAs with a single FCC solid-solution phase and NiAl as the binary intermetallic compound, they found three new EHEAs.

**Table 4.** The mixing enthalpy <sup>Δ</sup>*Hmix* (kJ·mol−1) of atom pairs in the current CoCrFeNiPdMn*<sup>x</sup>* (*x* = 0.2–0.8) and some other EHEAs.


For the CoCrFeNiMnPd*<sup>x</sup>* and CoCrFeNiPdMn*<sup>x</sup>* EHEAs, CoCrFeNi can be taken to be the HEA with a single FCC solid-solution phase and MnPd can be taken to be the binary intermetallic compound; their mixing led to the CoCrFeNiMnPd EHEA [47]. Even though the mixing enthalpy between Mn and Pd was the most negative one (Table 4), the MnPd intermetallic compound was not stable enough from room temperature to its melting point [46]. As a result, the Mn*x*Pd*<sup>y</sup>* intermetallic compound in the eutectics depending on the compositions could be Mn2Pd3, Mn3Pd5 or Mn7Pd9 [46,47]. In one word, the pseudo binary method could be a simple way for designing EHEAs but the designing rules still need to be studied further to achieve general and effective rules. According to our study, the consistent elements in the EHEAs with a solid-solution phase and an intermetallic compound can be divided into two groups, i.e., two of them with very high mixing of enthalpy forms the intermetallic compound and the rest of them with very small mixing of enthalpy forms the solid-solution phase. There should be a eutectic reaction in the binary alloy system for the two elements in the first group. One of the eutectic phases is the solid-solution phase which should have a good solubility for all the elements in the second group. The other one is the intermetallic compound which might have negligible solubility for all the elements in the second group.

#### **5. Conclusions**

In the current work, the Mn*x* (*x* = 0, 0.2, 0.4, 0.6, 0.8) HEAs were prepared and characterized. Our main conclusions were as follows:

(1) With an increase in Mn addition, the microstructures of CoCrFeNiPdMn*x* HEAs changed from dendrites to divorced eutectics, to hypoeutectic microstructures and finally to eutectic dendrites. For the Mn0.2 and Mn0.4 (Mn0.6 and Mn0.8) EHEA, the FCC phase was a CoCrFeNiPd-rich (CoCrFeNi-rich) phase and the Mn*x*Pd*<sup>y</sup>* intermetallic compound was Mn3Pd5 (Mn7Pd9). Addition of Mn might influence the interface energy anisotropy of both the FCC/liquid and Mn*x*Pd*y*/liquid interfaces, thus forming the seaweed eutectic dendrites in the Mn0.8 EHEA.

(2) With an increase in Mn addition, the hardness of FCC phase increased first and then decreased. The solute strengthening effect of Mn and the formation of nanotwins made the hardness increase firstly, the suppression of nanotwins then decreased the hardness and finally the transition from the CoCrFeNiPd-rich to the CoCrFeNi-rich FCC phase made the hardness decrease considerably. For the Mn3Pd5 and Mn7Pd9 intermetallic compounds, a decrease of either *λ*<sup>1</sup> or *λ*<sup>2</sup> would increase the hardness.

(3) The current EHEA system violates to some extent all the designing rules for EHEAs. The pseudo binary method was improved accordingly and the current work might be helpful for accelerating designing of potential EHEAs.

**Author Contributions:** Y.T. and J.L. conceived and designed the experiments; Y.T. performed the experiments; Y.T., J.W., H.K. performed the data analysis and drafted the manuscript. Y.T., J.W., H.K. participated in the data analysis, discussion, and interpretation. Y.T. and J.L. completed the paper.

**Funding:** This research was funded by the National Nature Science Foundation of China, grant number 51571161, 51774240 and 51690163, the Natural Science Basic Research Plan in Shaanxi Province of China, grant number 2016JQ5003 and the Program of Introducing Talents of Discipline to Universities, grant number B08040.

**Conflicts of Interest:** The authors declare no conflicts of interest.

#### **References**


© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

### *Article* **Effect of Atomic Size Difference on the Microstructure and Mechanical Properties of High-Entropy Alloys**

#### **Chan-Sheng Wu 1, Ping-Hsiu Tsai 1, Chia-Ming Kuo 1,2 and Che-Wei Tsai 2,\***


Received: 29 October 2018; Accepted: 10 December 2018; Published: 14 December 2018

**Abstract:** The effects of atomic size difference on the microstructure and mechanical properties of single face-centered cubic (FCC) phase high-entropy alloys are studied. Single FCC phase high-entropy alloys, namely, CoCrFeMnNi, Al0.2CoCrFeMnNi, and Al0.3CoCrCu0.3FeNi, display good workability. The recrystallization and grain growth rates are compared during annealing. Adding Al with 0.2 molar ratio into CoCrFeMnNi retains the single FCC phase. Its atomic size difference increases from 1.18% to 2.77%, and the activation energy of grain growth becomes larger than that of CoCrFeMnNi. The as-homogenized state of Al0.3CoCrCu0.3FeNi high-entropy alloy becomes a single FCC structure. Its atomic size difference is 3.65%, and the grain growth activation energy is the largest among these three kinds of single-phase high-entropy alloys. At ambient temperature, the mechanical properties of Al0.3CoCrCu0.3FeNi are better than those of CoCrFeMnNi because of high lattice distortion and high solid solution hardening.

**Keywords:** high-entropy alloys; mechanical property; recrystallization

#### **1. Introduction**

A multi-principal-element alloying system, developed by Yeh et al. in 2004 [1,2], is called high-entropy alloy (HEA). HEAs are defined as equiatomic or near-equiatomic alloys containing at least five elements, whose atomic concentration ranges from 5% to 35%. The multiprincipal-elemental mixtures of HEAs result in high entropy, lattice distortion, sluggish diffusion, and cocktail effects [3]. High entropy causes single-phase structures to become stable; as such, HEAs usually consist of simple solid solution phases with face-centered cubic (FCC) and body-centered cubic (BCC) structures rather than other intermetallic compounds [2]. A lattice is highly distorted because all atoms are solutes that can disorderly fill in a FCC or BCC lattice, and atomic sizes differ among elements in this alloying system, thereby possessing strengthening effect in high-solid-soluted HEAs [4]. Lattice distortion impedes atomic movement and slows down the diffusion rate of atoms in HEAs; these conditions lead to higher recrystallization temperatures, that is, the activation energies of grain growth in deformed HEAs are higher than those in conventional alloys [1,5].

In FCC single-phase HEAs, CoCrFeMnNi has been widely studied [2,6–11]. The atomic radius of each component in CoCrFeMnNi is close to each other, and the atomic size difference (δ) is approximately 1.18% only. δ is defined as follows:

$$\delta = 100 \sqrt{\sum\_{i=1}^{n} c\_i \left(1 - r\_i/\overline{\tau}\right)^2},\tag{1}$$

where *r* = ∑*<sup>n</sup> <sup>i</sup>*=<sup>1</sup> *ciri* is the average radius, *ci* and *ri* are the atomic percentage and atomic radius of the *i* element, respectively [12–14]. Other reports have also suggested that δ should consider the shear modulus, adjacency, and differences in the modulus of another element in single BCC phase HEA [15]. Moreover, researchers clarified that δ might be dependent on chemical composition of the alloys and the local lattice distortion in HEAs would differ from place to place [16,17].

Grain growth kinetics is usually described by the following equation:

$$d^\text{\tiny\kern-1.2em}\_0 - d\_0^\text{\tiny\text{\tiny\text{\tiny\text{\tiny}}}} = kt,\tag{2}$$

where *d* is the grain size after annealing time *t*, *d*<sup>0</sup> is the initial grain size (this term approaches to zero for the as-rolled state), *k* is a temperature-dependent constant, and *n* is the grain growth exponent. *k* can be described by Equation (3):

$$k = k\_0 e^{-Q/RT},\tag{3}$$

where *k0* is a constant, *R* is Boltzmann's constant, *T* is the temperature, and *Q* is the activation energy of grain growth.

Otto et al. [6] observed that the activation energy of the grain growth of CoCrFeMnNi is 325 kJ/mol. However, the relation between lattice distortion and grain growth activation energy remains unknown. To clarify this phenomenon, other researchers [9,18] added aluminum, whose atomic radius is larger than that of other elements, to CoCrFeMnNi. Al is a BCC stabilizer in HEAs [9,19]. Thus, Al addition is limited to a molar ratio of 0.2 to prevent the formation of dual-phases in CoCrFeMnNi. With a moderate amount of Al addition, a FCC single-phase structure and a high atomic size difference should be obtained in the designed alloy.

Al0.5CoCrCuFeNi high-entropy alloy is composed of matrix and Cu-rich phases, which become a FCC phase after they are treated with a solution [19–23]. A Ni–Al–rich phase precipitates in the matrix phase, and a Cu-rich phase precipitates at midtemperature, leading to the brittleness of the alloy at intermediate temperature. Thus, to design single-phase structures, decreasing the amounts of Al and Cu in Al0.5CoCrCuFeNi is needed.

According to the Hume–Rothery rule, solid solutions can be obtained until the atomic size difference is larger than 15% [24]. In addition, factor Ω can be utilized to predict whether an alloy is solid soluted:

Ω = *Tm* Δ*Smix* |Δ*Hmix*| , (4)

where *Tm* is the melting point (Kelvin) of the alloy, and Δ*S*mix and Δ*H*mix are the mixing entropy and enthalpy of the alloy, respectively [13]. For solid solution formation, Ω should be larger than 1. Δ*H*mix ranging from −15 kJ/mol to 5 kJ/mol is beneficial to obtaining single-phase structures [12].

For high-entropy alloys, an empirical statistical pattern is observed by calculating the valence electron concentration (VEC) to predict the formation of stable phases [25,26]. A phase consists of BCC and FCC when the VEC is below 6.8 and above 8.0, respectively. Otherwise, BCC and FCC phases are formed in HEAs.

In this study, Al0.3CoCrCu0.3FeNi (δ = 3.65%; ΔHmix = −4.38 kJ/mol; Ω = 5.67; VEC = 8.35) is designed to be the FCC single-phase high-entropy alloy. The lattice distortion and activation energy of grain growth in Al0.3CoCrCu0.3FeNi are compared with those of other FCC single-phase HEAs to determine the effect of atomic size difference on microstructure and mechanical properties.

#### **2. Materials and Experimental Methods**

High-entropy CoCrFeMnNi, Al0.2CoCrFeMnNi, and Al0.3CoCrCu0.3FeNi alloys were prepared by arc melting in a vacuum chamber at a pressure of 0.01 Torr, and its constituent elements had at least 99.99 wt.% purity. Melting was performed at a current of 500 A in a water-cooled copper hearth and repeated at least four times to confirm chemical homogeneity. The dimensions of the final solidified ingot were cuboid and had a width of 20 mm, a length of 40 mm, and a height of 10 mm. The ingots were homogenized at 1100 ◦C for 6 h, quenched with water quenching or cooled in a furnace, and cold rolled at a thickness reduction of 70%. The specimens were annealed between 900 ◦C and 1100 ◦C for various times and finally quenched with water.

The specimens were prepared by cutting, grinding, and polishing in a sequence. The crystalline structure of the present alloys was characterized using an X-ray diffractometer SHIMADZU-XRD6000 equipped with Cu-target radiation (Kα = 1.54 Å) at 30 kV and 20 mA. The sample was scanned at 2θ angle from 20◦ to 100◦ at a scanning rate of 2◦/min. The microstructures were observed under a scanning electron microscope (JEOL-5410) at an acceleration voltage of 20 kV for a working distance of 24 mm. All of the specimens were etched with 0.5 g of copper (II) chloride, 10 mL of hydrochloric acid, and 10 mL of ethanol mixing liquid solution to observe the grains. The grain size was calculated and statistically measured using ImageJ. The grain size was also circled at least 400 grains to yield an average grain size for each specimen. For the tensile test, all of the specimens were tested at ambient temperature by Instron 4468 at a stain rate of 10−<sup>3</sup> s<sup>−</sup>1. Figure 1 presents the dimensions of the samples used in the tensile test.

**Figure 1.** Dimensions of tensile specimens (unit: mm).

#### **3. Results**

#### *3.1. Microstructure and Crystalline Structure*

Al0.2CoCrFeMnNi is designed from CoCrFeMnNi by adding 0.2 molar ratio of Al to contribute increased lattice mismatch. Figure 2 shows the X-ray diffraction (XRD) analysis of Al0.2CoCrFeMnNi HEAs in its homogenized state quenched with water and cooled in a furnace. The lattice constant of Al0.2CoCrFeMnNi is 3.582 Å. The atomic size difference of Al0.2CoCrFeMnNi can be calculated by Equation (1), and the value is 2.77%. Figure 3 shows the XRD analysis of the designed Al0.3CoCrCu0.3FeNi HEAs in its homogenized state after water quenching and furnace cooling. The diffraction pattern also clearly reveals the appearance of peaks of the FCC structure only. The lattice constant of Al0.3CoCrCu0.3FeNi is 3.585 Å. The atomic size difference of Al0.3CoCrCu0.3FeNi is 3.65%, which is calculated by Equation (1).

θ **Figure 2.** X-ray diffraction (XRD) patterns of homogenized Al0.2CoCrFeMnNi alloys after water quenching and furnace cooling.

**Figure 3.** XRD patterns of homogenized Al0.3CoCrCu0.3FeNi alloys after water quenching and furnace cooling.

#### *3.2. Grain Growth Activation Energy of Al0.2CoCrFeMnNi and Al0.3CoCrCu0.3FeNi Alloys*

All of the present alloys exhibit only single FCC phases without any other precipitations and show good workability at room temperature. The reduction of thickness can reach 70% without any cracks neither on the rims nor inside the as-rolled specimens. Recrystallization occurs after annealing and is performed above 900 ◦C for various times. The movement of each solute atom is more difficult than that in traditional alloying systems because of sluggish effect in high-entropy alloys. Under this condition, the recrystallization temperature in HEAs becomes higher than that in conventional alloys. Recrystallization takes place in high-lattice-strain energy regions, such as slip band, deformation twin intersections, and grain boundaries, which are the preferred nucleation sites for new strain-free grains. The average grain size of Al0.2CoCrFeMnNi is 42.6 μm after it is annealed at 1000 ◦C for 120 min, water quenching is subsequently performed Figure 4a. The grain sizes at different annealing temperatures for various times are shown in Table 1. The grain growth activation of Al0.2CoCrFeMnNi is calculated with Equations (2) and (3), and the linear fitting result is shown in Figure 5. The slope of the fitting line represents the activation energy (Q) for grain growth, which is 434.4 kJ/mol in Al0.2CoCrFeMnNi.

The grain growth is observed at 900 ◦C in Al0.3CoCrCu0.3FeNi, and the evolution of the microstructure in Al0.3CoCrCu0.3FeNi is shown in Figure 6. High-resolution scanning electron microscopy is utilized after the etching condition is optimized for observation because of the small grain size. The grain sizes at different temperatures in various times are shown in Table 2. The grain growth activation is calculated by Equations (2) and (3), and the fitting result is shown in Figure 7. The activation energy of grain growth is 761.3 kJ/mol.

**Figure 4.** Microstructure of Al0.2CoCrFeMnNi with cold rolling and annealing at (**a**) 1000 ◦C and (**b**) 1100 ◦C for 120 min.


**Table 1.** Grain size of Al0.2CoCrFeMnNi annealed at 1000 ◦C, 1050 ◦C, and 1100 ◦C with different times (unit: μm).

**Figure 5.** Grain growth activation energy of Al0.2CoCrFeMnNi.

**Figure 6.** Microstructure of Al0.3CoCrCu0.3FeNi with cold rolling and annealing at 900 ◦C for (**a**) 120; (**b**) 300; (**c**) 600 and (**d**) 1200 min.


**Table 2.** Grain size of Al0.3CoCrCu0.3FeNi annealed at 900 ◦C, 950 ◦C, and 1000 ◦C at different times (unit: μm).

**Figure 7.** Grain growth activation energy of Al0.3CoCrCu0.3FeNi.

#### *3.3. Relationship between Atomic Size Difference and Grain Growth Activation Energy*

Three high-entropy alloy systems with a single FCC phase are observed: CoCrFeMnNi, Al0.2CoCrFeMnNi, and Al0.3CoCrCu0.3FeNi. These alloys are selected and compared with others. The outstanding phase stability of these HEAs can avoid from the formation of second phases that can influence grain growth at increased temperature.

The calculated results of atomic size difference and grain growth activation is shown in Table 3. The atomic size difference of Al0.3CoCrCu0.3FeNi is 3.65% as calculated by Equation (1). This value is the highest in these three kinds of HEAs, and 2.77% and 1.18% belong to Al0.2CoCrFeMnNi and in CoCrFeMnNi, respectively. The activation energy of Al0.3CoCrCu0.3FeNi for grain growth is also the highest among others.


**Table 3.** Value of atomic size difference and grain growth activation energy.

The mixing enthalpy between each solute element is also shown in Table 4 to determine how the mixing enthalpy affects the activation energy of grain growth. However, the mixing enthalpy of these three HEAs is slightly related to the atomic size difference or the activation energy of grain growth.


**Table 4.** ΔHmix for the element pairs (unit: kJ/mol).

#### **4. Discussion**

#### *4.1. Effect of Atomic Size Difference on Microstructures*

The comparison result of the microstructure between Al0.2CoCrFeMnNi and Al0.3CoCrCu0.3FeNi single FCC-type high-entropy alloys according to XRD analysis in Figures 2 and 3 shows that the as-homogenized state and the furnace-cooled state both have outstanding phase stability without any detrimental non-FCC phases regardless of the cooling condition. Haas, Sebastian, et al. [27] reported that the Gibbs free energy of solid solution alloys is completely due to configurational entropy and contributes to the thermal stability of solid solution alloys. The consequent single FCC phase is gained with a significant sluggish diffusion effect in HEAs [3], and this parameter is beneficial to the following heavily cold-rolling procedure without showing the undesired brittleness and ensuring great workability.

The atomic size difference of Al0.3CoCrCu0.3FeNi is larger than that of Al0.2CoCrFeMnNi. Different grain sizes are found (Tables 2 and 3) when the samples are treated with the same thermomechanical process, that is, 70% cold rolled, annealed at 1000 ◦C for 120 min, and quenched with water. This result reveals that the atomic size difference likely affects the ability of dislocation movement, causing a different grain growth behavior in these two HEAs.

#### *4.2. Effect of Atomic Size Difference on Mechanical Properties*

Large atomic size difference (δ) corresponds to the great amount of activation energy needed for grain growth. Large δ is associated with a high degree of lattice distortion in the single-phase solid solution and cause atoms to spontaneously move at the most stable state, thereby decreasing the potential energy of the existing defects in a low level; that is, defects are found in stable sites. The energy of grain growth comes from the different energy levels between lattice distortion and defects [28]. When the number of alloying elements is low, or the alloy is low entropy, the energy of grain growth in such an alloy, which is nearly pure metal, is attributed to undistorted grain and perfect dislocation, and the energy level difference between the former and the latter can be regarded as the driving force for recrystallization then to make a perfect dislocation being released by a new grain.

In other cases, if the difference between these two energies is insufficient, the driving force for recrystallization is too low to induce dislocation rearrangement. In other words, higher annealing temperature or longer annealing time is needed so that it can enable the recrystallization to start at dislocation site and new grain to grow subsequently.

Table 4 shows that aluminum has the highest binding energy to each element, possibly leading to the solute-pinning effect and making each solute atom suitable to their lattice site. In other words, atoms become self-accommodating to the stable sites. Thus, when a great amount of aluminum is added, the grain is distorted remarkably because of large δ, causing energy level of a grain to be higher

than undistorted one. Also, solute atoms are pinned in their preferred lattice site, and each solute atom can act as an obstacle of the movement of dislocations, thus obtaining the lower energy level of pinned dislocations, that is, dislocations become more stable or immovable.

#### *4.3. Comparison of Tensile Properties with Different HEAs*

Otto et al. [6] reported that the tensile properties of CoCrFeMnNi at different temperatures with different grain sizes are yield strength of 350 MPa, ultimate tensile strength of 650 MPa, and recrystallized grain size of 4.4 μm. With cold rolling and annealing, the grain size of CoCrFeMnNi can be small. The compatible small scale of the grain size of Al0.3CoCrCu0.3FeNi was designed to compare its mechanical properties with those of CoCrFeMnNi. After cold rolling and annealing were performed at 900 ◦C for 5 h and water quenching was conducted, the grain size is approximately 5.13 μm under the optimized thermomechanical treatment. The final microstructure is shown in Figure 6b.

Figure 8 illustrates the tensile stress–strain curves of the designed Al0.3CoCrCu0.3FeNi in the as-homogenized states and 900 ◦C/5 h annealing state. Table 5 shows the comparison of the mechanical properties between CoCrFeMnNi and Al0.3CoCrCu0.3FeNi with different grain sizes. The yield strength and the ultimate tensile strength are 500 and 717 MPa in the annealed Al0.3CoCrCu0.3FeNi, respectively. The elongation of Al0.3CoCrCu0.3FeNi is smaller than that of CoCrFeMnNi, suggesting that the plastic deformation in CoCrFeMnNi is involved in one-to-one atom-vacancy exchange mechanism [29,30]. This finding can be accounted for this high ductility.

**Figure 8.** Mechanical properties of Al0.3CoCrCu0.3FeNi alloy annealed at 900 ◦C for 5 h and the as-homogenized state.



The lattice distortion of Al0.3CoCrCu0.3FeNi is higher than that of CoCrFeMnNi because the former has a larger atomic size difference (δ) than the latter. Different δ can be related to the mechanical behavior, for an example, higher yield and tensile strength in Al0.3CoCrCu0.3FeNi with the same FCC structure and the close value of grain sizes compared with CoCrFeMnNi. The high lattice distortion can introduce the concentrated strain field around the lattice, causing the movement of dislocations to be more difficult. The large amount of the added aluminum can introduce a high degree of interaction to each alloying element, causing the pinning effect on dislocations. Finally, in high-entropy alloys with high lattice distortion, although the lattice distortion effect on properties of HEAs is yet an open question still await to be solved [31], once a large atomic size difference is obtained, the increment of tensile strength can be predicted.

#### **5. Conclusions**

Al0.2CoCrFeMnNi is a single FCC high-entropy alloy structure composed of Al added to CoCrFeMnNi at a molar ratio of up to 0.2. The microstructure of Al0.3CoCrCu0.3FeNi is also a single FCC phase. The recrystallization and grain growth behavior of Al0.3CoCrCu0.3FeNi and Al0.2CoCrFeMnNi are observed. The calculation of the grain sizes under different annealing conditions reveals that the activation energy of the grain growth of Al0.2CoCrFeMnNi is 434.4 kJ/mol with an atomic size difference of 2.77%. The activation energy of the grain growth of Al0.3CoCrCu0.3FeNi is 761.3 kJ/mol with an atomic size difference of 3.65%. A large atomic size difference indicates that a high activation energy is needed for grain growth. The lattice distortion of Al0.3CoCrCu0.3FeNi is much higher than that of single FCC-phase CoCrFeMnNi. The mechanical properties of Al0.3CoCrCu0.3FeNi are superior to those of CoCrFeMnNi under similar conditions. This result is attributed to high lattice distortion and pinning effect on dislocation because of the large atomic size difference in high-entropy Al0.3CoCrCu0.3FeNi alloy.

**Author Contributions:** Conceptualization, C.-W.T.; formal analysis, C.-S.W. and P.-H.T.; data curation, C.-S.W. and P.-H.T.; writing—original draft preparation, C.-S.W.; writing—review and editing, C.-M.K.; supervision, C.-W.T.; project administration, C.-W.T.

**Funding:** This research received no external funding.

**Acknowledgments:** We are pleased to acknowledge the financial support for this research by Ministry of Science and Technology, R.O.C (MOST 104-2218-E-007-017 and 106-2218-E-007-019). The support provided by the High Entropy Materials Center from The Featured Areas Research Center Program within the framework of the Higher Education Sprout Project by the Ministry of Education (MOE) in Taiwan is greatly appreciated.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

### *Article* **Influence of Titanium on Microstructure, Phase Formation and Wear Behaviour of AlCoCrFeNiTix High-Entropy Alloy**

#### **Martin Löbel \*, Thomas Lindner, Thomas Mehner and Thomas Lampke**

Materials and Surface Engineering Group, Institute of Materials Science and Engineering, Chemnitz University of Technology, D-09125 Chemnitz, Germany; th.lindner@mb.tu-chemnitz.de (T.Li.); thomas.mehner@mb.tu-chemnitz.de (T.M.); thomas.lampke@mb.tu-chemnitz.de (T.La.) **\*** Correspondence: martin.loebel@mb.tu-chemnitz.de; Tel.: +49-371-531-31865

Received: 31 May 2018; Accepted: 29 June 2018; Published: 2 July 2018

**Abstract:** The novel alloying concept of high-entropy alloys (HEAs) has been the focus of many recent investigations revealing an interesting combination of properties. Alloying with aluminium and titanium showed strong influence on microstructure and phase composition. However, detailed investigations on the influence of titanium are lacking. In this study, the influence of titanium in the alloy system AlCoCrFeNiTix was studied in a wide range (molar ratios x = 0.0; 0.2; 0.5; 0.8; 1.0; 1.5). Detailed studies investigating the microstructure, chemical composition, phase composition, solidification behaviour, and wear behaviour were carried out. Alloying with titanium showed strong influence on the resulting microstructure and lead to an increase of microstructural heterogeneity. Phase analyses revealed the formation of one body-centred cubic (bcc) phase for the alloy without titanium, whereas alloying with titanium caused the formation of two different bcc phases as main phases. Additional phases were detected for alloys with increased titanium content. For x ≥ 0.5, a minor phase with face-centred cubic (fcc) structure was formed. Further addition of titanium led to the formation of complex phases. Investigation of wear behaviour revealed a superior wear resistance of the alloy AlCoCrFeNiTi0.5 as compared to a bearing steel sample.

**Keywords:** HEA; high-entropy alloy; CCA; compositionally complex alloy; phase composition; microstructure; wear behaviour

#### **1. Introduction**

High-entropy alloys (HEAs) are an emerging class of new materials. Their alloying concept differs from conventional alloys, which are composed of one main element, and an improvement of properties is achieved by adding minor amounts of other elements. In contrast, HEAs are multicomponent alloys comprising at least five elements with approximately equimolar composition [1]. Despite their complex composition, only simple solid solutions with fcc or bcc structure were formed for several alloy systems. The formation of brittle and intermetallic phases can be successfully suppressed. One of the first alloys with a single fcc phase is the equimolar alloy CoCrFeMnNi investigated by Cantor et al. [2]. Due to their unique structure, HEAs exhibit an interesting combination of properties e.g., high hardness and strength in combination with adequate ductility. Furthermore, a high wear and corrosion resistance can be obtained [3–6]. Two main groups can be distinguished: HEAs forming (i) cubic or (ii) hexagonal phases [4].

Detailed structural investigations of HEAs revealed that only a few alloys form a single phase microstructure comprising fcc or bcc phases. Most alloys are composed of more than one phase, partly including complex or intermetallic phases. For these alloys, the term compositionally complex alloys (CCA) was introduced [7].

One of the most intensely investigated HEA systems, primarily forming cubic phases is AlCoCrCuFeNi [8,9]. Due to the positive enthalpy of mixing ΔHmix among Cu and the elements Fe and Cr, segregation was observed, deteriorating mechanical and corrosion properties. Therefore, subsequent investigations focused on the copper-free derivative AlCoCrFeNi [3,10–13]. Early studies concentrated on the equimolar composition. However, investigations showed that optimum properties are usually achieved when choosing a differing chemical composition [14].

Investigating the influence of different alloying elements showed a strong influence of aluminium on the microstructure, phase composition, and properties [15,16]. For a low aluminium content, fcc phases are stabilised, whereas high contents of aluminium act as a strong bcc phase stabiliser [17,18]. In addition, the formation of complex phases can be suppressed for a high aluminium content [19].

Furthermore, the influence of additional alloying elements has been investigated. One element which shows distinct effects on microstructure, phase composition, and mechanical properties is titanium. Due to its large atomic radius, titanium leads to solid solution strengthening, increasing its hardness and strength. However, for a high titanium content, the formation of intermetallic phases and compounds was determined, leading to embrittlement. The alloy system AlCoCrFeNiTi shows high wear resistance also in comparison to conventional steels [20–24].

Detailed investigations on the influence of the alloying element titanium are required for the development of lightweight HEAs. The aim of the present study is the determination of the influence of this alloying element in the alloy system AlCoCrFeNiTix regarding its influence on microstructure, phase composition and wear behaviour.

#### **2. Materials and Methods**

Bulk samples of the alloy system AlCoCrFeNiTix with the molar ratios of x = 0.0; 0.2; 0.5; 0.8; 1.0; 1.5 were produced by arc-melting. Elemental granules with a purity of ≥99.9% were used as raw materials. The elemental granules were weighed and mixed according to the intended molar ratios. Each sample had a total weight of 10 g. Arc-melting of the samples was conducted in a water-cooled copper crucible.

After evacuating and reaching a pressure of 2 × <sup>10</sup>−<sup>4</sup> mbar, the furnace chamber was filled with argon to a pressure of 1.1 bar. A tungsten electrode was used to ignite an arc. All samples were remoulded three times and turned after each step to achieve chemical homogeneity. The resulting samples had a diameter of approximately 20 mm. For the arc furnace, a low cooling rate of <50 K/s was determined in preliminary studies.

Metallographic cross-sections were prepared according to standard metallographic procedures. Investigations of the microstructure were carried out by scanning electron microscopy (SEM) in a LEO 1455VP (Zeiss, Jena, Germany) with an acceleration voltage of 25 kV. For the visualisation of material contrast, a backscattered-electron detector (BSD) was used. The analyses of the overall chemical composition was carried out by energy dispersive X-ray spectroscopy (EDS) with a GENESIS spectrometer (EDAX, Mahwah, NJ, USA) at a magnification of 500× within an analysis area of approximately 43,500 μm2. Three measurements were carried out for every sample. Microhardness measurements (Vickers hardness HV0.5) were conducted with a Wilson Tukon 1102 device (Buehler, Uzwil, Switzerland) in metallographic cross-sections. The average microhardness and standard deviation was calculated from ten single indents. Phase analyses was conducted by X-ray diffraction (XRD) with a D8 Discover diffractometer (Bruker AXS, Billerica, MA, USA) using Co Kα radiation (tube parameters: 40 kV; 40 mA). The diffractograms were measured in a diffraction angle range (2θ) of 20◦ to 130◦ with a step size of 0.01◦ and 3.4 s/step, which corresponds to 653 s/step due to the utilisation of a 1D Lynxeye XE detector. For phase identification, the powder diffraction file (PDF) database 2014 (International Centre for Diffraction Data) was used. The solidification behaviour was investigated by differential scanning calorimetry (DSC) with a STA 409 C device (Netzsch, Selb, Germany) under argon atmosphere in the temperature range from 1800 K to room temperature with a cooling rate of 20 K/min.

To investigate the tribological behaviour under adhesive, oscillating, and abrasive wear conditions, ball-on-disk, oscillating wear and scratch tests have been carried out. For the ball-on-disk tests a Tetra Basalt Tester (Tetra, Ilmenau, Germany) were used. The oscillating wear tests were carried out with a Wazau SVT 40 device (Wazau, Berlin, Germany) and a CSM Revetest-RST device (CSM Instruments SA, Peseux, Switzerland) has been used for the scratch tests. The applied parameters are summarised in Table 1.



The measurements of the resulting wear depths after the ball-on-disk test were conducted by a contact stylus instrument with a Hommel Etamic T8000 device (Jenoptik, Villingen-Schwenningen, Germany). Resulting wear marks of the oscillating wear and scratch tests were analysed by laser scanning microscopy (LSM) with a Keyence VK-X200 device (Keyence, Osaka, Japan) to determine the resulting wear depth. The reference material bearing steel EN 1.3505 (100Cr6) was investigated under identical conditions. Wear marks of the scratch test were investigated with the digital microscope Keyence VHX-500 (Keyence, Osaka, Japan).

#### **3. Results and Discussion**

#### *3.1. Chemical Composition*

The mean chemical composition of all samples was measured. Results are summarised in Table 2.



The chemical composition of the arc-melted samples was in good agreement with the nominal values. Only for the aluminium content did a distinct deviation of >1 at.% occur. The titanium content was in good agreement with the nominal values for all samples.

#### *3.2. Microstructure*

SEM images of the microstructure using a BSD to visualise material contrast with different magnifications are shown in Figure 1.

**Figure 1.** *Cont.*

**Figure 1.** SEM micrographs (BSD detector) of arc-melted AlCoCrFeNiTix samples: (**a**) x = 0.0; (**b**) x = 0.2; (**c**) x = 0.5; (**d**) x = 0.8; (**e**) x = 1.0; (**f**) x = 1.5 with phase declaration (PP: primary phase; CW: cell wall; IP: interdendritic phase). The formation of additional phases and an increase of heterogeneity in the microstructure can be observed for an increased titanium content.

For the alloy without titanium (x = 0.0), a homogeneous microstructure occurred. The grains solidified with no preferred direction. Low differences of the chemical composition were confirmed by a minor BSD contrast. Alloying with titanium causes the formation of a more heterogeneous microstructure. Within the grains, material contrast was observed for the alloy with x = 0.2, indicating differences in the chemical composition. Between both of these areas, no distinct boundaries occurred, indicating a directional solidification with minor change in orientation. During the solidification, the precipitation of the primary phase caused a depletion of alloy elements in the residual liquid phase, causing the precipitation of a secondary phase with a different chemical composition. With further increased titanium content (x = 0.5), a dendritic structure appeared. A bright-appearing phase (interdendritic phase) was observed at the grain boundaries of the primary phase, indicating that this area is rich in elements with a high atomic number. A third phase (cell wall) solidifies as a remainder between the dendritic structures. For the alloy with higher titanium content (x = 0.8), the content of this third phase increased. Also, for the samples with further increased titanium content (x = 1.0 and x = 1.5), a dendritic structure comprising three distinguishable phases appeared. The cross-sections of all arc-melted samples exhibited cavities and shrinkage porosity caused by a different contraction of the present phases, and small amounts of breakouts due to the metallographic preparation or sample production (black areas). The presence of these defects was most distinct for the alloy with the highest titanium content (x = 1.5).

#### *3.3. Solidification Behaviour and Phase Analyses*

The solidification behaviour was determined by DSC measurements. The resulting cooling curves in a temperature range of 1800 K to 800 K are shown in Figure 2.

**Figure 2.** DSC cooling curves of arc-melted AlCoCrFeNiTix samples. A single exothermic reaction can be observed for the alloy without titanium, whereas several exothermic reactions occur for all alloys containing titanium, revealing the formation of additional phases.

The DSC cooling curve of the alloy without titanium (x = 0.0) exhibited one peak at a temperature of 1640 K. All investigated alloys showed a major peak at a temperature above 1600 K, corresponding to the major primarily formed phase. For the alloy with (x = 0.2), two distinct exothermic reactions occurred, showing that two major phases were formed. The similar temperature range indicated a continuous solidification. For the alloys with increased titanium content (x = 0.5 and 0.8), the DSC cooling curves also showed two major exothermic reactions. However, the increasing temperature shift of the peaks indicated a changed solidification behaviour and chemical composition of the second major phases, while the primary phase precipitated at the same temperature. For the equimolar alloy (x = 1.0), a further peak appeared at a temperature of 1470 K, showing that an additional phase was formed. The DSC cooling curve of the alloy with the highest titanium content (x = 1.5) only displayed two exothermic reactions, which can be ascribed to the two major phases also detected for the alloys with lower titanium content. No further peak of another phase visible in the SEM images (Figure 1f) appeared, indicating a small phase content or a similar solidification temperature.

For the assignment of phases, the resulting diffractograms of the XRD phase analyses are shown in Figure 3.

**Figure 3.** XRD diffractograms of arc-melted AlCoCrFeNiTix samples. A single phase is formed for the alloy without titanium, whereas diffraction peaks of additional phases occur for an increased titanium content. Complex phases are formed for x ≥ 0.8.

The diffraction diagram of the alloy without titanium (x = 0.0) exhibited high intensity diffraction peaks which could be ascribed to a chemically ordered bcc phase with B2 structure. Diffraction peaks of this phase appeared for all investigated alloys, which was in accordance with DSC results, revealing that this phase is the primary phase (PP). For all titanium containing alloys, the diffractograms showed an additional phase with a bcc structure: a chemically disordered bcc phase with A2 structure. This phase corresponded to the second exothermic reaction in the DSC measurements, and hence to the interdendritic phase (IP) in the alloys x ≥ 0.2. The stabilisation of bcc phases due to a high aluminium content has been reported elsewhere in detail [19]. For the alloy with the lowest titanium content (x = 0.2), no additional phases were be detected. However, with increased titanium content further diffraction peaks occurred. For all alloys with a titanium content of x ≥ 0.5, an additional peak at a diffraction angle of 31.0◦ appeared. This diffraction angle could be ascribed to an fcc phase. Further diffraction peaks of this phase overlapped with the bcc (B2) phase. Previous investigations of the alloy system AlxCoCrFeNiTi revealed the solidification of the fcc phase as a remainder in the cell walls [19]. The diffraction diagram of the alloy with a titanium content of x = 0.8 exhibited several additional diffraction peaks, which can be assigned to a tetragonal σ phase. This phase has also been detected by Moravcik et al. for the alloy AlCoCrFeNiTi0.5 produced by spark plasma sintering (SPS). Microstructural investigations revealed the formation of this phase embedded in a mixture of other phases around a primary phase. However, subsequent heat treatment resulted in the dissolution of the σ phase, showing that the formation of this phase sensitively depends on manufacturing conditions [25]. For the equimolar alloy (x = 1.0), no diffraction peaks of the σ phase appeared. Additional peaks occurred, which can be ascribed to a centred cluster (cc) with A12 structure type. DSC results also revealed the formation of an additional phase, which solidifies as a remainder after the two major bcc phases and forms cell walls in the microstructure. This phase has been detected in the same alloy system in preliminary studies by Lindner et al. and for a high aluminium content (AlCoCrFeNiTi1.5), the formation of this phase could be suppressed [19]. The diffractogram of the alloy with the highest titanium content (x = 1.5) exhibited diffraction peaks which can be ascribed to the bcc (A2), bcc (B2) and an fcc phase. However, the diffraction peaks at 2θ = 35.4◦; 96.7◦ and 98.9◦ of these phases did not appear. This might be caused by the relatively coarse microstructure and texture of the samples due to the comparatively slow cooling conditions. The diffraction diagram did not exhibit peaks of the σ or cc (A12) phase. Additional diffraction peaks can be ascribed to a hexagonal Laves phase (C14/MgZn2 type). A similar phase with slightly changed lattice parameters has been detected by Zhou et al. [20]. The present phases and corresponding major crystallographic information are summarised in Table 3.


**Table 3.** Summary of phases detected by XRD analyses for arc-melted AlCoCrFeNiTix samples.

In addition to the formation of further phases, a shift of lattice parameters was observed with increasing titanium content. The lattice parameters of the bcc (B2) phase and the fcc (A1) phase were slightly increased. This behaviour indicated that more titanium with a large atomic radius was resolved in these phases.

#### *3.4. Hardness and Wear Behaviour*

The influence of the titanium content on the average microhardness HV0.5 was investigated. The results are summarised in Figure 4.

**Figure 4.** Microhardness of arc-melted AlCoCrFeNiTix samples. Microhardness increases with titanium content, reaching a maximum of 770 HV0.5 for the equimolar alloy.

For the alloy without titanium (x = 0.0), an average microhardness of 550 HV0.5 was measured. With increasing titanium content, an increase of microhardness was observed, reaching a maximum for the equimolar composition with a microhardness of 770 HV0.5. The increasing hardness indicated the formation of additional phases, which was in accordance with microstructural investigations and phase analyses. Furthermore, solid solution strengthening contributes to an increase of hardness—an increase of lattice parameters could be proven for the bcc (B2) and fcc (A1) phases. However, for the alloy with the highest titanium content (x = 1.5), a reduced microhardness of 730 HV0.5 was measured, which might be a result of the increased presence of cavities and shrinkage porosity in that alloy.

The wear behaviour was investigated under adhesive, oscillating, and abrasive wear conditions in ball-on-disk, oscillating wear, and scratch tests. The results are summarised in Figure 5.

**Figure 5.** Wear depths of bearing steel EN 1.3505 and AlCoCrFeNiTix in: (**a**) Ball-on-disk; (**b**) Oscillating wear and (**c**) Scratch tests. The wear depths of AlCoCrFeNiTix are decreased in comparison to EN 1.3505, except under oscillating wear conditions. Overall, the best results are obtained for x = 0.5.

The investigation of the wear behaviour in the ball-on-disk test revealed a high wear depth for the alloy without titanium (x = 0.0). With the addition of titanium (x = 0.2), a slight decrease of wear depth could be achieved. Further increase to x = 0.5 resulted in a distinct decrease of wear depth. The alloy x = 0.5 exhibited a multiphase character, only comprising cubic phases. In comparison to the alloys with lower titanium content, the microhardness was increased, which enhanced wear resistance in ball-on-disk tests. However, further increase of titanium content did not cause a reduction of wear depth or an improvement of the wear resistance. Phase analyses revealed the formation of additional complex phases reducing wear resistance. All samples containing titanium exhibited a lower wear depth in comparison with the bearing steel EN 1.3505, and hence a higher wear resistance in the ball-on-disk test.

In the oscillating wear tests, the highest wear depth was measured for the alloy without titanium (x = 0.0). Adding minor amounts of titanium resulted in a decrease of the wear depth. For the sample x = 0.5, the lowest wear depth was measured, showing that a multiphase character only comprising cubic phases was advantageous under oscillating wear condition. The further addition of titanium led to an increase of the wear depth. Additional tetragonal or cc phases did not contribute to an improvement of wear resistance. For the alloy with the highest titanium content (x = 1.5), a low wear depth was measured, which was in the range of the alloy with x = 0.5. In comparison with bearing steel EN 1.3505, all investigated samples exhibited a higher wear depth, and thereby lower wear resistance under oscillating wear conditions.

Under abrasive tribological conditions in the scratch tests, the lowest wear depth was measured for the sample with a titanium content of x = 0.2. With an increase in titanium content, the wear depth slightly increased. The highest wear depth was measured for the equimolar alloy (x = 1.0). In comparison to the bearing steel EN 1.3505, all investigated samples exhibit a distinctly lower wear depth and thereby higher wear resistance. The wear tracks of all samples were investigated by optical microscopy. In Figure 6 images of the sample surface where the highest load was applied in the progressive mode scratch test are shown.

**Figure 6.** Surface of the arc-melted AlCoCrFeNiTix samples: (**a**) x = 0.0; (**b**) x = 0.2; (**c**) x = 0.5; (**d**) x = 0.8; (**e**) x = 1.0; (**f**) x = 1.5 after progressive mode scratch test. Ductile behaviour occurs for x ≤ 0.5, whereas cracks or spalling of material are visible for x ≥ 0.8.

The investigation of the surface after scratch test under abrasive conditions reveals no cracks or spalling of material along the main scratch for the sample without titanium (x = 0.0) and the two samples with the lowest titanium content (x = 0.2; x = 0.5). However, spalling of material and distinct secondary cracks perpendicular to the main scratch can be observed for all samples with a titanium content exceeding x = 0.5. The formation of secondary cracks and spalling of material indicated the brittle behaviour of these alloys, which is caused by the formation of additional, complex phases—tetragonal, cc and a hexagonal Laves phase for a titanium content x ≥ 0.8. These phases possess low numbers of slip systems, which results in reduced ductility.

#### **4. Summary and Conclusions**

The influence of the alloying element titanium was studied in detail in the alloy system AlCoCrFeNiTix. For the alloy without titanium (x = 0.0), a single chemically ordered bcc phase with B2 structure is formed. In contrast, a multiphase microstructure was revealed for all titanium-containing alloys. With an increase of titanium content, an increase of heterogeneity of the microstructure is observed. Furthermore, the hardness can be distinctly increased, whereas the maximum hardness is achieved for the equimolar composition. Phase analyses prove the formation of two major bcc phases for all titanium-containing samples. One chemically ordered bcc phase with B2 structure and one chemically disordered bcc phase with A2 structure is formed. With an increase in titanium content, additional phases occur. For x ≥ 0.5 a minor fraction of an fcc phase was detected. A further increase in titanium content results in additional, more complex phases. This could also be proved by analysing the solidification behaviour. Analyses of the lattice parameters revealed a shift to bigger values with increasing titanium content, especially for the bcc (B2) and the fcc (A1) phase. The alloy system AlCoCrFeNiTix exhibits an increased wear resistance in comparison with the bearing steel EN 1.3505, except under oscillating wear conditions.

Correlations between phase composition, microstructure, and wear resistance can be concluded. Microstructure design for high wear resistance requires cubic phases. Hereby, a multiple bcc/fcc phase character exhibits an advantageous behaviour. Complex phases (cc and tetragonal) increase the hardness, but should be avoided in order to achieve a high wear resistance, as the presence of these phases causes increased brittleness. AlCoCrFeNiTi0.5 is a promising candidate for wear protection applications in both bulk and coating materials.

**Author Contributions:** M.L. and T.L. (Thomas Lindner) conceived and designed the experiments. M.L., T.L. (Thomas Lindner) and T.M. performed the experiments, analysed the data, and wrote the paper. T.L. (Thomas Lampke) directed the research, and contributed to the discussion and interpretation of the results.

**Acknowledgments:** The publication costs of this article were funded by the German Research Foundation/DFG and the Chemnitz University of Technology in the funding programme Open Access Publishing. The authors thank Benjamin Sattler for sample manufacturing, Marc Pügner for conducting the XRD measurements and Thomas Uhlig for conducting the DSC measurements.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

### *Article* **Prediction of Strength and Ductility in Partially Recrystallized CoCrFeNiTi0.2 High-Entropy Alloy**

#### **Hanwen Zhang 1, Peizhi Liu 2, Jinxiong Hou 1, Junwei Qiao 1,2,\* and Yucheng Wu 2,\***


Received: 24 February 2019; Accepted: 28 March 2019; Published: 11 April 2019

**Abstract:** The mechanical behavior of a partially recrystallized fcc-CoCrFeNiTi0.2 high entropy alloys (HEA) is investigated. Temporal evolutions of the morphology, size, and volume fraction of the nanoscaled L12-(Ni,Co)3Ti precipitates at 800 ◦C with various aging time were quantitatively evaluated. The ultimate tensile strength can be greatly improved to ~1200 MPa, accompanied with a tensile elongation of ~20% after precipitation. The temporal exponents for the average size and number density of precipitates reasonably conform the predictions by the PV model. A composite model was proposed to describe the plastic strain of the current HEA. As a consequence, the tensile strength and tensile elongation are well predicted, which is in accord with the experimental results. The present experiment provides a theoretical reference for the strengthening of partially recrystallized single-phase HEAs in the future.

**Keywords:** high entropy alloys; precipitation kinetics; strengthening mechanisms; elongation prediction

#### **1. Introduction**

High entropy alloys (HEAs), a new class of structural materials, have attracted a great deal of attention in recent years on account of their special intrinsic characteristics [1–9], such as high configuration entropy [10], sluggish atomic diffusion [11], and large lattice distortion [12]. Nevertheless, recent studies indicate that single-phase HEAs, especially single-phase fcc HEAs, the strength is insufficiently for structural applications [13,14]. In other words, strengthening is badly needed so that satisfactory mechanical properties can be achieved. Klimova et al. [15] reported that in the Aland C-containing CoCrFeNiMn-type high-entropy alloy, substructure strengthening was found to be dominated at low rolling reductions (<40%), while grain (twin) boundary strengthening prevailed at higher strains. Chemical short-range order also has an important influence on the mechanical properties of FeCoNi(AlSi)*x* high entropy alloys [16]. Among the numerous strengthening mechanisms, Precipitation hardening is an effective technique widely used for strengthening high entropy alloys [9,17–22]. For example, He et al. [17,23] reported nano-sized L12 coherent precipitates in a face centered-cubic (fcc) NiCoFe alloy with minor additions of Al and Ti, specifically (NiCoFeCr)94Ti2Al4, which exhibits a strength increment of about 327 MPa. It is widely studied that these HEAs are all fully recrystallized, and the grain/grain boundary is thermally stable. In contrast, the partial recrystallized HEAs are rarely studied, the microstructure-property relationship and consequent strengthening mechanism are lacking. In this study, we pay attention to the effect of the partially crystallized microstructure on the mechanical properties. The grain growth mechanisms for the nanoscale precipitation and strengthening mechanisms are fully investigated. In addition, a quantitative model for estimation of tensile ductility is established.

#### **2. Materials and Methods**

The mixture of Co, Cr, Fe, Ni, and Ti with purity of at least 99.9% (weight percent, wt.%) was prepared by arc-melting. Under a Ti-gettered argon atmosphere, the sample was cast into an <sup>85</sup> × <sup>10</sup> × <sup>2</sup> mm<sup>3</sup> copper mould and CoCrFeNiTi0.2 (atomic percent, at.%) alloy ingots were prepared. A stable uniform structure was obtained at 1200 ◦C homogenized for 5 h. The sliced samples were cold-rolled to 75% of the total reduction ratio, and then aged at 800 ◦C for 3 h, 5 h, 8 h, 10 h, 24 h and 48 h respectively, followed by water quenching. The phase identification was carried out by X-ray diffraction (XRD) using Cu Kα radiation. Then, optical microscopy (OM), scanning electron microscopy (ZEISS SUPRA55 SEM) operated at 20 kV, with the working distance of 9.1 mm, energy dispersive spectrometer (EDS), and JEM-2010 transmission electron microscopy (TEM) were used to observe the surface microstructures. Dog-bone-like tensile specimens with a gauge length of 10 mm, a gauge width of 2 mm and a thickness of 0.5 mm were prepared from aged specimens by electrical discharge machining. Instron 5969 universal testing machine was used to carry out quasi-static tensile tests at room temperature at a constant strain rate of 1 × <sup>10</sup>−<sup>3</sup> <sup>s</sup>−<sup>1</sup> greater than or equal to five times.

#### **3. Results and Discussion**

#### *3.1. Precipitation Kinetics*

As can be seen from Figure 1a, the XRD diagrams of homogenized and aged alloys are displayed. In each alloy, a series of fcc diffraction peaks can be found, which indicates that the matrix of the four alloys is composed of the same fcc phase. In aged samples, an extra series of minor peaks, named L12-Ni3Ti, can be detected, which indicates that there is a great probability of the existence of a secondary phase. Figure 2a–e,g–h shows the corresponding SEM micrographs of these HEAs in different statuses. It can be concluded that in Figure 2a, the homogenized alloy demonstrates a single-phase structure, in accordance with the XRD pattern. There are only a few etch pits on the surface probably introduced during electropolishing. After the homogenization process been carried out, the grains are all transformed into equiaxed grains with an average grain size of ~198 μm. Figure 2b exhibits the microstructural feature of the cold-rolled CoCrFeNiTi0.2 HEAs. Because of the large CR reduction, there are serious deformation and elongation of grains in the rolling direction, and a high-density of lamellar deformation bands can be dramatically observed after electro-polishing. Similar microstructures have been reported in Fe34.95Ni27.5Co17.5Al11.5Cr8.5B0.05 HEAs [24]. Since the recrystallization temperature of the present HEA is above 800 ◦C, a large number of slip lines (deformation bands) remain in the matrix. As a consequence, in the recrystallization region, the precipitates spread along the grain boundaries, as shown in Figure 2c. Besides, some plate-shaped precipitates are formed. Generally, upon aging, precipitates often preferentially form at grain boundaries, which is the microstructural heterogeneous site. Moreover, when the aging temperature is low, for instance 800 ◦C here, the diffusion along the grain boundary is much faster than that in the lattice [23]. This is the main reason why the plate-shaped precipitates grow at grain boundaries. Whereas in the area where the grains are not recrystallized, a great many precipitates are uniformly distributed throughout the matrix, as evidenced in Figure 2d. The measured average compositions of the precipitates and fcc matrix in the 800 ◦C/5 h aged alloy, as well as the composition variation across a single precipitate is, as shown in Figure 1b. It indicates that the precipitates are enriched with Ni and Ti, but depleted in Co, Cr, and Fe. Meanwhile a part of Ni is substituted by Co. With the above EDS analysis, it is finally identified that the precipitates in the 800 ◦C/5 h aged alloy is the (Ni,Co)3Ti phase. Figure 2i shows the bright field TEM images of aged alloys at 800 ◦C/5 h. Spheroidal and plate-shaped particles with an average size of 145 nm are found to disperse in a matrix. From the illustration on the right side of Figure 2i, the selected area electron diffraction (SAED) pattern along Z = [011] taken from the precipitates are indexed. The main diffraction points can effectively prove that the matrix does has an fcc structure, whilst additional weak spots observed in the image can

also scientifically prove the existence of precipitates with superlattice L12 structure. Han et al. have identified that L12 phase as (Ni,Co)3Ti type γ phase [25].

**Figure 1.** The XRD patterns of the homogenized and the aged alloys (**a**), and EDS-measured composition variation across a single precipitate in the 800 ◦C/5 h aged alloy(**b**).

**Figure 2.** SEM images of the homogenized (**a**), the cold rolled (**b**), the 800 ◦C/3 h aged (**c–d**) alloys and the aged alloy of different aging time: 5 h (**e**), 10 h (**g**), and 48 h (**h**). The left insert in (**e**) is the corresponding enlarged views of the slip lines in 800 ◦C/5 h aged alloy. (**f**) and (**i**) show the TEM image of the L12 precipitates and the slip lines in 800 ◦C/5 h aged alloy, respectively.

As mentioned above, many slip lines remain in the matrix on account of partial recrystallization, which is revealed in Figure 2e. In order to further examine the nature of these slip lines, an enlarged area is selected as exhibited in the left inset of Figure 2e. A significant amount of slip lines along different directions are clearly observed inside the grains. Although the directions of these slip lines are inconsistent, the value of the intersection angle between them is virtually constant as to be about 60◦. Figure 2f is the corresponding TEM image of these slip lines in 800 ◦C/5 h aged alloy. The slip

lines are distributed along different directions, and the intersection angle between one another is about 60◦ as well, which are consistent with SEM images.

To unveil the evolution of precipitation with the time, SEM images for 800 ◦C/5, 10, and 48 h aged alloys are carefully taken. The precipitates in Figure 2e are basically spheroidal and plate-shaped, uniformly distributed throughout the fcc matrix, the volume fraction is about 15.6 %. As time goes on, the shape of the precipitates turns to be droplet-like and plate-shaped. The average size of precipitates is closely related to the aging time. The longer the aging time is, the larger the average size of precipitates will be. For example, after three hours of aging, the average size of particles is 120 nm, but the average value rises to 385 nm after aging for 48h. The size distributions of the two aged alloys are plotted in Figure 3. Moreover, the precipitate number density *nv* is negatively correlated with the aging time. A similar variation of the precipitate with aging time has been reported in many HEAs, such as (NiCoFeCr)94Ti2Al4 [26] and (FeCoNiCr)100-x-*y*Ti*x*Al*<sup>y</sup>* [23] HEAs.

**Figure 3.** The size distributions of the 800 ◦C/3 h aged alloy(**a**) and 800 ◦C/48 h aged alloy(**b**).

The precipitate number density *nv*, was determined from *nv* = *n*a/*d*, where *na* is the areal density of precipitates measured from SEM micrographs. The precipitate size was defined using an area-equivalent diameter (i.e., diameter = 2!( areaπ)) measured from SEM micrographs. The average precipitate size *d*, was calculated according to precipitate size distributions. Dividing the areal density by the precipitate diameter to get the number density in three-dimensional space. It should be noted that many slip lines are clearly revealed in the matrix in 800 ◦C/3 h aged alloy, as shown in Figure 2e. With the aging time, the amount of slip lines is gradually decreased. When the aging time is reached to 48 h, the slip lines do not basically exist in the matrix. This indicates that although the alloy does not fully recrystallize at 800 ◦C, the recrystallization has been going on with the extension of time.

It is very important to study the precipitates growth kinetics in order to further reveal the microstructure-property relationship. The volume fraction (*ϕ*(*t*)), number density (*nv*(*t*)), and average size (*d*(*t*)) are all varies with time, and the relationship is shown in Figure 4a,b, which is corresponding to L12 precipitates in the CoCrFeNiTi0.2 HEAs aged at different times in 800 ◦C. It can be seen from Figure 4a that the value of *ϕ*(*t*) remains constant when the aging time changed from 3 to 48 h. It is pointed out that the nucleation stage of the precipitation process has been bypassed and entered the coarsening stage directly, therefore *ϕ*(*t*) remain stable on its equilibrium value (*ϕeq*) [26]. The stored energy is negatively correlated with the aging time, which is consistent with the theory. With the increase of aging time, the stress concentration is caused by the growth of precipitates, leading to the fracture of the alloy more easily, which is corresponding to the reduction of stored energy. The precipitation number density *nv*(*t*) is a function of aging time, as demonstrated in Figure 4b, which indicates the power-law relationship between the two variables at a given temperature. When the aging time is increased from 3 to 48 h, the number density is accordingly decreased from (5.6 ± 0.3) × <sup>10</sup><sup>20</sup> to (6.4 ± 0.2) × <sup>10</sup><sup>17</sup> <sup>m</sup><sup>−</sup>3. Definitely, the power-law exponent for *nv*(*t*), namely the slope of the linear fitted curve is −0.78. Similar temporal exponents also appear in some Ni-Al-based ternary alloys [27–30]. The size of precipitates also depends on the aging time. It can be concluded from Figure 4b that the average precipitation size *d*(*t*) also follows the power law relationship. The power law index is 0.41.

A model can be used to explain the power-law relationship among the number density, average precipitation size and aging time scientifically and effectively. Philip and Voorhees established the PV model for Ostwald ripening in multi-component systems [31]. According to the model, the coarsening process of precipitates is in accordance with a similar power-law relationship. In other words, the size of precipitates raised to a 1/3 power, due to the increasing aging time. To apply the PV model reasonably to the CoCrFeNiTi0.2 HEA, the first step is to concentrate the chemical composition. The baseline of the alloy is fcc-CoCrFeNi. In addition, Ni is the only element with an fcc structure in the alloy, so it can be treated substantially as a Ni-based alloy. Besides that, the lattice constant of CoCrFeNi (0.3572 nm) is highly close to that of Ni (0.3517 nm) [30]. Hence, it seems logical to treat the CoCrFeNiTi0.2 as a Ni-based pseudo binary Ni-Ti alloy. Therefore, the PV model of stable coarsening reaction can be used to calculate the coarsening behavior of L12 precipitation in CoCrFeNiTi0.2 HEAs [32–35]:

$$d^3(t) - d^3(t\_0) = K(t - t\_0),\tag{1}$$

$$n\_{\overline{v}}(t)^{-1} - n\_{\overline{v}}(t\_0)^{-1} = 4.74 \frac{K}{\varphi\_{eq}}(t - t\_0),\tag{2}$$

where *K* represents the coarsening rate constant, *d*(*t*), and *nv*(*t*) refer to the average size and number density of precipitates at time *t.* Obviously, in Figure 3a,b, the time index for *nv*(*t*) is −0.78, and that for *d*(*t*) is 0.41, which is basically consistent with the predicted values of −1 (Equation (3)) and 1/3 (Equation(2)) corresponding to the PV model. The main reason for the slight deviation is probably caused by the fact that the aging time is within a limited duration, but in principle, the coarsening stage of precipitates cannot reach a stable state [36–39].

**Figure 4.** Temporal evolution of (**a**) volume fraction (*Φ*(*t*)) and stored energy (*E*(*t*)), (**b**) number density (*nv*(*t*)), and average size (d(t)) of L12 precipitates in the CoCrFeNiTi0.2 high entropy alloys (HEA). Tensile stress-strain curves of the homogenized and the annealed alloys(**c**). Detailed tensile strength and the elongation value are plotted in (**d**).

#### *3.2. Strengthening Mechanisms*

In order to study the effect of microstructure on mechanical properties, uniaxial tensile tests were carried out. As can be seen from Figure 4c, the tensile engineering stress-strain curves of the current seven HEAs under room temperature are measured. The homogenized alloy exhibits high ductility, which reaches 48%, but the yield and ultimate strengths of the alloy are low, which are only 315 and 609 MPa, respectively. A similar value of strength is obtained in CoCrFeMnNi HEAs [1]. Compared to the homogenized alloy, the aged alloys (3 h) exhibit a striking improvement in the mechanical performances, the yield and ultimate strength can reach about ~800 and ~1200 MPa respectively, accompanied by ~20% homogeneous elongation. Detailed tensile strength and the elongation of the aged alloys are plotted in Figure 4d. It is noteworthy that both the tensile strength and elongation are gradually decreased with the aging time. The results can be ascribed to the growing up of the second-phase precipitates with the increasing aging time, which can pin the dislocation movement and accordingly promote the dislocation accumulation, leading to stress concentration, which in turn reduce both the strength and ductility [23].

In precipitation hardening alloys, the particles morphological distribution is the main factor of strength, which covers particle size, particle shape and spacing between particles. The classical Orowan bowing/looping and particles shearing are the main models used to describe the precipitation hardening, which mainly includes. Orowan looping often occurs when the radius of the coherent particles exceeds the critical value or when the particles are incoherent with the matrix. Whereas when the precipitates are small and coherent, the shear mechanism takes place. For the current HEA, the sizes of the precipitates are all more than 100 nm, and the particles are not easily plastically deformed. Therefore, it is concluded that L12 particles strengthen the alloy via Orowan mechanism. The critical stress *σ* or can be expressed in the following [40]:

$$
\sigma\_{\mathcal{W}} = M \cdot \frac{0.4Gb}{\pi \sqrt{1-\upsilon}} \cdot \frac{\ln\left(\frac{7}{b}\right)}{\lambda},\tag{3}
$$

where *M* = 3.06 is the Taylor factor, *G* = 87.5 GPa is the shear modulus, υ = 0.31 is the Poisson ratio, and b = <sup>√</sup>2/2 <sup>×</sup> *aCoCrFeNiTi*0.2 = 0.255 nm represents the burger vector for an fcc structure. *<sup>d</sup>* <sup>=</sup> <sup>√</sup>2/3·*<sup>d</sup>* represents the average precipitate diameter on the slip planes. λ = *d*( !*π*/(4f)−1) represents the average interparticle spacing. Orowan stresses for precipitates in the six aged HEA with different volume fractions and sizes are calculated respectively.

As mentioned above, a large number of slip lines exist in the alloys along various directions, due to partial recrystallization. These slip lines can be regarded as sub-grain boundaries. Generally speaking, grain refinement can greatly improve the strength of the alloy. The volume fraction of the grain-boundaries is negatively correlated with the grain size. Smaller grain size offers a higher volume fraction of grain-boundaries, which will hinder the movement of dislocations. So here the extensive slip lines can improve the strength by grain-boundary strengthening. To apply the mechanism to the current CoCrFeNiTi0.2 HEA, let us consider its equivalent grain size. Figure 5a–b is the corresponding schematic illustration. The slip lines within a grain are selected as the statistical target. Draw twelve lines passing through the center of the grain at 30-degree intervals and measure the length of each line, as Figure 5a shows. Then, it is counted how many segments the 12 lines are divided by the slip lines within a grain and how many segments each slip line within a grain are divided by the 12 lines. Accordingly, it is obtained the length of each line being cut off and the average length. From the two dimensions, the equivalent length of the spacing can be obtained between the slip lines, that is, the average grain diameter. In the statistics at least 50 grains were used for counting in different aging times. In this way, the distance between slip lines within the grains is transformed into the average grain diameter of sub-grain boundaries (Figure 5b). Consequently, the strength increment provided by grain-size refinement can be theoretically predicted.

Hall-Petch equation can explain the relationship between yield strength and grain size scientifically [41]:

$$
\sigma\_y = \sigma\_0 + k\_y / d^{\frac{1}{2}},\tag{4}
$$

where *σ<sup>y</sup>* represents the yield stress, *σ*<sup>0</sup> represents the lattice friction stress, *ky* represents the strengthening coefficient, and d represents the average grain diameter. We can express the increase of yield strength caused by grain size difference (Δ*σG*) as:

$$
\Delta \sigma\_{\mathbb{G}} = k\_{\mathbb{Y}} \left( d\_p^{-\frac{1}{2}} - d\_A^{-\frac{1}{2}} \right). \tag{5}
$$

In the formula, *dP* denotes the grain size of the thermo-mechanically processed alloys, and *dA* represents the grain size of the homogenized alloy.

In order to show the conclusion more intuitively and clearly, the histogram, as shown in Figure 5c, is summarized to explain the strength contribution of the above two strengthening mechanisms. The black part represents the intrinsic strength of the alloy, or the so-called lattice friction strength, according to Moon et al [42], the calculated value is 156 MPa. It can be seen from the diagram that the contribution of precipitation strengthening to strength increment is much greater than that of grain-boundary strengthening. However, with the growth of precipitated particles size, the contribution of precipitation strengthening is gradually decreased, similar to the (FeCoNiCr)100-*x*-*y*Ti*x*Al*<sup>y</sup>* HEAs reported before [23]. Moreover, with the aging time, the number of slip lines is decreased, leading to the increased distance between slip lines, thus causing gradually weakened contribution of grain boundary strengthening, which is consistent with the experimental results in Figure 4c.

**Figure 5.** Schematic illustrations showing the slip line be equivalent to sub-grain boundary (**a**) and (**b**). Strengthening contributions from precipitation hardening and grain-boundary hardening in all the aged alloys (**c**). The elongation displayed as a function of the volume fraction and mean particle diameter of L12 phase in the current HEA (**d**).

#### *3.3. Prediction of Elongation*

Compared with the strength which is relatively easy to evaluate in the existing models, it is quite challenging to quantitatively evaluate the tensile ductility. Aging time is one of the important reasons for the variation of tensile ductility in current HEA. It is due to that with the increase of aging time, the L12 particles grow up gradually, leading to stress concentration, which will lead to a significant

reduction in ductility. Here, the present HEAs containing L12 particles can be regarded as ceramic particles-reinforced metal-matrix composites (MMCs) [43]. In discontinuous reinforced metal matrix composites, when the size of the reinforcing phase is micron order and the volume fraction reaches about 20%, the most balanced strength-ductility properties are expected to be exhibited. Similar to metal-based composite alloys, the L12 particles in existing alloys are about 0.1–0.4 μm and the volume fraction is 15.6–19.8%, which appears to be consistent with the model. In order to estimate the elongation of HEAs accurately, a model based on MMCS phenomenologically is adopted [44]:

$$
\varepsilon\_{\varepsilon}/\varepsilon\_{m} = (1 - f)(1 + \varepsilon\_{\text{cav}})(1 - f\_{\text{con}}),
\tag{6}
$$

where *ε<sup>c</sup>* represents the failure strain of the composites, *ε<sup>m</sup>* represents the failure strain of the unreinforced matrix, and f represents the volume fraction of particles. In the equation mentioned above, *εcav* = *f* 4/3/*s* [44] is the contribution to the failure strain from the cavity formation, and *s* represents the aspect ratio of the particles. The parameter *fcon* in Equation (6) represents the ratio of the constrained to the matrix volume, and can be expressed as [44]:

$$f\_{com} = 2s / \left[ 5 \left( f^{-1} - 1 \right) \right]. \tag{7}$$

Combining Equations (6) and (7), it is readily obtained

$$
\varepsilon\_{\varepsilon}/\varepsilon\_{m} = (1 - f) \left( 1 + \frac{f^{4/3}}{s} \right) \left( 1 - \frac{2s}{5(f^{-1} - 1)} \right) = F. \tag{8}
$$

At present, *ε<sup>c</sup>* can be plotted as a function of *F*, and the result is demonstrated in Figure 4d. It is pointed out that there is a good linear relationship with the slope of the curve to be about 0.43. It can be concluded from the Equation (8) that the slope is predicted to be the fracture strain of the unreinforced alloy matrix, *εm*. Compared with the elongation value of homogenized alloy (~0.49), the value of 0.43 is close to the experimental value. The main reason for the slight offset in Figure 4f is the inhomogeneous distribution of L12 particles with non-random orientation. Nevertheless, it can be concluded from Figure 5d that the tensile ductility in HEA is determined by the volume fraction and morphology of L12 precipitates.

#### **4. Conclusions**

In this study, a systematic study of the aging behavior of the CoCrFeNiTi0.2 HEA is conducted. L12 particles are readily precipitated after annealing at 800 ◦C for a different time. The temporal exponents for the average size and number density of precipitates are in reasonable accord with the predictions by the PV model for particle coarsening in the current alloys. The ultimate tensile strength can be greatly improved to ~1200 MPa, accompanied with a tensile elongation of ~20% after precipitation. Both grain boundary and precipitates can contribute to strengthening. The tensile strength and tensile elongation are well predicted, which is consistent with the experimental results. The present experiment provides a theoretical reference for the strengthening of partially recrystallized single-phase HEAs in the future.

**Author Contributions:** Conceptualization, J.Q.; Data curation, P.L.; Project administration, Y.W.; Software, J.H.; Writing-original draft, H.Z.; Writing-review and editing, H.Z.

**Funding:** This work was financially supported by the financial support from National Key Laboratory for Remanufacturing, Academy of Armored Forces Engineering (No. 61420050204).

**Conflicts of Interest:** The authors declare no conflict of interest.

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