Solidification Microstructure of AlCoCrFeNi_2.1 Eutectic High Entropy Alloy Ingots

Abstract

AlCoCrFeNi_2.1 eutectic high-entropy alloy (EHEA) ingots were successfully obtained by high-frequency melting and centrifugal metal-mold casting under an Ar flow. The microstructure of the ingots was investigated by trans-scale observations using optical microscopy (OM), scanning electron microscopy (SEM), transmission electron microscopy (TEM), and scanning transmission electron microscopy (STEM). The constituent phases of the ingots were identified as fcc and bcc phases by X-ray diffraction (XRD) analysis, and were not dependent on the position of the ingot. The microstructure was observed to have a primary fcc dendrite and fcc+bcc eutectic structure at the inter-dendrite region, regardless of the position of the ingots. The size of the solidification structure was affected by the cooling rate. Faster cooling rates resulted in finer solidification structures. TEM observations clarified the development of L1₂ ordering structures in the primary fcc dendrite phase, while the ordering peak could not be detected by XRD analysis.

 

This Paper was Originally Published in Japanese in J. JFS 89 (2017) 119–129. In order to more precisely explain the background, the purpose of the study, the experimental procedures, and the results, some parts of the contents were revised. The Refs. 21, 22), and 23) were added to clarify the source of pure elements. The Refs. 12) and 35) were added to discuss the solidification microstructure in more detail. Figure 1 was slightly modified to make the casting process and the position of the ingots clearly understandable. Figure 7 was slightly modified to discuss the solidification microstructure in more detail.

1. Introduction

A new class of metallic materials called high-entropy alloys (HEAs) were developed and are presently attracting considerable interest in the area of materials science and engineering^1–7). The abbreviation “HEA” is roughly used to refer to the metallic materials that are constructed with equal or nearly equal quantities of five or more metals and whose constituent phase is solid solution. Several HEA definitions were suggested, which gives rise to some confusion. Recently, an entropy-based definition was suggested and has been widely adopted, because the phrase “high entropy” suggests a definition based on the magnitude of entropy, as denoted in the literature^5–7). The entropy-based definition is as follows:   

\[ \Delta {\rm S}_{mix} = - R\sum_{i=1}^{n} x_{i} \ln x_{i} \](1)

  

\[ \Delta S_{mix} \ge 1.5R\ ({\rm HEA}) \](2)

where $\Delta S_{mix}$ is the mixing entropy of an ideal solid solution (and regular solid solution), R is the gas constant (8.314 J/K mol), and x_i is the mole fraction of the element i. Based on the $\Delta S_{mix}$, a medium-entropy alloy (MEA) and low-entropy alloy (LEA) can be defined as follows:   

\[ 1.0R \le \Delta S_{mix} \le 1.5R\ ({\rm MEA}) \](3)

  

\[ \Delta S_{mix} \le 1.0R\ ({\rm LEA}) \](4)

The mixing entropy represented by eq. (1) shows the maximum value in the case of an equi-atomic ratio, namely, x_i = 1/n. The maximum mixing entropy in alloys is expressed by eq. (5), and this value increases with an increase in the number of elements.   

\[ (\Delta {\rm S}_{mix})_{\max} = - R\ln n \](5)

The value of (ΔS_mix)_max in a quaternary (4-component) alloy system is 1.39R, and that in a 5-component alloy system is 1.61R. Based on the entropy-based definition of eqs. (1) and (2), only multicomponent alloys with equal and nearly equal quantities of five or more constituent elements can be classified as HEAs. Table 1 lists the mixing entropies calculated for typical traditional alloys and equi-atomic alloys, focusing on cast iron and steel, with some of the data being taken from the literature⁶⁾. A number of previously developed traditional and common alloys cannot attain a value of 1.5R in $\Delta S_{mix}$. This indicates that a value of “5” is not a critical number for an HEA, but a metallic material that is constituted of equal or near-equal quantities of “5” or more metals is important for obtaining alloys for which $\Delta S_{mix} \ge 1.5R$. Recent progress in the taxonomy of HEAs⁷⁾ indicates that not only multicomponent alloys with a single solid-solution phase, but also composites with a main solid-solution phase and minor intermetallic compounds, as well as composites with two solid solutions, and so on, can also be called HEAs. In the present study, the entropy-based definition was adopted for HEAs.

Table 1 Mixing entropies calculated for typical traditional alloys and equiatomic alloys. HEA, MEA, and LEA denote high-entropy alloy, medium-entropy alloy, and low-entropy alloy, respectively.

Alloys		ΔSmix	LEA	MEA	HEA
Cast Iron	Fe-C-Si 　(Fe-3.6C-2.4Si [mass.%])	0.58R	○
	(Fe-3.3C-2.7Si [mass.%])	0.58R	○
	Austenitic cast iron, FCDA-NiMn 13 7 　(Fe-3C-3Si-7Mn-13Cr)	0.88R	○
	Cast stainless steel, SCS16 　(Fe-0.03C-1.5Si-2Mn-12Ni-20Cr-2.5Mo, [mass%])	1.13R		○
	Heat-resistant cast steel, SCH22 　(Fe-0.45C-1.75Si-1.5Mn-22Ni-27Cr, [mass%])	1.29R		○
	Stainless spheroidal carbide cast iron, KSH-C 　(Fe-2.84C-0.95Si-0.61Mn-9.2Ni-17.3Cr-9.34V [mass.%])	1.40R		○
Stainless steel	SUS-304 　(Fe-18Cr-8Ni [mass%])	0.74 R	○
	SUS-316 　(Fe-18Cr-14Ni-3Mo [mass%])	0.94 R	○
Al alloy	A7075	0.43R	○
Mg alloy	AZ91D	0.35R	○
Cu alloy	7-3 brass	0.61R	○
Ni alloy	Inconel 718	1.31R		○
Alnico alloy	Alnico2 　(Fe-10Al-19Ni-13Co-3Cu [mass%])	1.33R		○
	Alnico9 　(Fe-7Al-15Ni-35Co-4Cu-5Ti [mass%])	1.55R			○
Equiatomic alloy	TiNbTaZr	1.39R		○
	CoCrMnFeNi	1.61R			○

HEAs exhibit four effects that differentiate them from other, conventional alloys. In other words, four basic core effects differentiate conventional alloys (namely, LEAs and MEAs) from HEAs^2,5–7). These four core effects are (1) high entropy, (2) severe lattice distortion, (3) sluggish diffusion, and (4) “cocktail.” These four core effects differentiate HEAs from previously developed conventional alloys, intermetallic compounds, and amorphous alloys/metallic glass. Considering that HEAs are cast materials, they exhibit the following three interesting effects: (1) a solid-solution phase can be obtained using a conventional casting process without any need for special techniques, given the high entropy from a thermodynamic aspect and sluggish diffusion from a kinetic aspect, (2) ductile materials can be obtained because of the formation of a solid solution, and (3) high-strength materials are formed as a result of the severe lattice distortion effect. The main route adopted for the fabrication of an HEA specimen is melting and casting because of the need to mix the constituent elements^5–7). While some refractory HEAs^8,9) and bio-HEAs¹⁰⁾, which consist of 4–6 group elements including Ti and others with high melting points, are tried to be fabricated by powder-metallurgy processes with solid-state mixing, melting and casting is the most commonly used technique for fabricating HEAs. When adapting melting and casting processes for the fabrication of HEAs, the following problems should be considered and overcome prior to further development and practical application; (1) the method for melting a mixture of constituent elements, considering the widely varying melting points, the degree of oxidation, the reactivity between the molten metal and the crucible, and the vapor pressure, (2) the general tendency of the heterogeneous properties of the constituent phases and the microstructure, as well as the solidification segregation, has not been clarified for HEAs, and (3) the grain size in HEA specimens obtained by melting and solidification exhibits a tendency to be coarser rather than that of HEA specimens obtained by powder metallurgy. Regarding problem (2), to the best of our knowledge, there have been no systematic studies addressing the solidification segregation in HEAs. Furthermore, the constituent phases and microstructure evaluation were performed mainly by XRD analysis without any consideration of position-dependence. The complexity of the combination of constituent elements in HEAs points to cast products having various type of heterogeneous properties, although little attention has been afforded this topic.

In the present study, the solidification microstructure of AlCoCrFeNi_2.1 eutectic high-entropy alloys (EHEAs) was investigated by trans-scale observation¹²⁾ to clarify the position dependence of the constituent phases and the microstructure of cast products. The present study set out to establish a means of evaluating the solidification microstructure of HEA casting products.

2. Materials and Methods

2.1 Alloy composition and alloy parameters

In is well known that HEAs exhibit the following general tendencies in terms of their mechanical properties: single-phase, bcc-structured HEAs exhibit a relatively high strength but tend to be brittle, while fcc-structured HEAs are ductile but not strong enough to be superior to common alloys developed to date. EHEAs were developed based on the concept of combining bcc- and fcc-structured HEAs to achieve a balance of strength and ductility. The composite structure could be obtained from the eutectic reaction occurring in the thermal melt during solidification^11,12). The fabrication of industrial-scale ingots of AlCoCrFeNi_2.1 EHEAs was attempted to research future applications for engineering cast materials^11,12). However, the possibility of solidification segregation and the position dependence of the constituent phases, as well as the microstructure of the ingots of AlCoCrFeNi_2.1 EHEAs, were not clarified. An AlCoCrFeNi_2.1 EHEA was selected for the investigation because the solidification microstructure can be evaluated easily compared with single-phase HEAs and the applicability of this alloy to engineering applications.

Table 2 lists the nominal alloy composition and the alloy parameters for AlCoCrFeNi_2.1 EHEA. As shown in the nominal alloy composition (Table 2(a)), the atomic composition ratio of Ni is larger than that of the other elements (Al, Co, Cr, and Fe). Based on the weight percentage, the weight ratio of (Ni + Co) is over 50 mass%, and that of (Ni + Co + Cr) is nearly 75%. Various parameters were suggested to predict the formation of the solid-solution phase in multi-component alloys. Table 2(b) lists the parameters for HEAs in AlCoCrFeNi_2.1 EHEA, and the following five parameters (A)–(E) were used in the present study.

Table 2 (a) Alloy composition and (b) alloy parameters of AlCoCrFeNi_2.1 eutectic high-entropy alloys.

(a) Alloy composition
	Al	Co	Cr	Fe	Ni
atomic ratio	1	1	1	1	2.1
at%	16.39	16.39	16.39	16.39	34.43
mass％	8.51	18.59	16.40	17.62	38.88
(b) Alloy parameters
ΔSmix	ΔHmix	δ	Ω	VEC
[kJ/mol K]	[kJ/mol]
0.0129	−11.9	5.3	1.8	7.70

(A) Mixing entropy, ΔS_mix

The mixing entropy was easily calculated using eq. (1). The value of ΔS_mix of AlCoCrFeNi_2.1 EHEA is 1.55R (Table 2(b)).

(B) Mixing enthalpy, ΔH_mix

Mixing enthalpy was used to predict the tendency to form a solid-solution phase, together with the glass forming ability (GFA) in multicomponent alloys^{2,3,5,6,14–16)}. The mixing enthalpy was expressed as:   

\[ \Delta H_{mix} = \sum_{i=1}^{n} \sum_{j \ne i}^{n} 4\Delta H_{ij} x_{i} x_{j} \](6)

where ΔH_ij is the mixing enthalpy of an X-Y binary system at an equi-atomic composition (X₅₀Y₅₀) for the liquid phase. The value of ΔH_ij is taken from the literature¹⁶⁾.

(C) Delta parameter, δ

The atomic size difference in a multi-component alloy is also an important parameter for predicting the formation of the solid-solution and amorphous phases. The δ parameter for discussing the atomic size differences is as follows^3,5,6,17):   

\[ \delta = \sqrt{\sum_{i=1}^{n} x_{i} \left( 1 - \frac{r_{i}}{\bar{r}} \right)} \times 100 \](7)

  

\[ \bar{r} = \sum_{i=1}^{n} x_{i} r_{i} \](8)

where r_i is the atomic radius of i-th element and $\bar{r}$ is the average atomic radius. The value of r_i was again taken from the literature¹⁶⁾.

(D) Omega parameter, Ω

The Ω parameter¹⁷⁾ contains both ΔS_mix and ΔH_mix for predicting the formation of a solid solution, and is expressed as follows:   

\[ \Omega = \frac{T_{m} \cdot \Delta S_{mix}}{|\Delta H_{mix}|} \](9)

  

\[ T_{m} = \sum_{i=1}^{n} x_{i} \cdot (T_{m})_{i} \](10)

where (T_m)_i is the melting temperature of the element i, T_m is the average melting temperature which is derived from the rule governing a mixture of pure elements and their melting temperatures.

(E) Valence electron concentration parameter, VEC

VEC is a frequently used parameter for predicting the phase stability of fcc and bcc structures in HEAs, and is expressed as follows^7,18,19),   

\[ VEC = \sum_{i=1}^{n} c_{i} \cdot VEC_{i} \](11)

where VEC_i is the value of VEC for a pure element. The literature discusses the use of VEC or the electrons per atom ratio (e/a) for predicting the phase stability of HEAs in detail⁷⁾. We opted to use VEC in the present study. The fcc phases occur at VEC > 8.0, and the bcc phases at VEC ≦ 6.87, with a mixture of bcc and fcc phases being obtained at 6.87 ≦ VEC < 8.0. There are some exceptions to the VEC rule, however, which provide a convenient means of designing fcc- and bcc-based HEAS, as well as those which are a composite of bcc and fcc HEAs.

Zhang et al. reported that a solid-solution phase tended to form when −20 ≦ ΔH_mix ≦ 5 [kJ/mol], δ ≦ 6.4, 0.012 ≦ ΔS_mix ≦ 0.0175 [kJ/mol]³⁾. Guo et al. suggested that the following conditions promote the formation of solid solutions: −11.6 ≦ ΔH_mix ≦ 3.2, δ ≦ 6.6²⁰⁾. Yang et al. suggested that δ ≦ 6.4 and Ω ≧ 1.1 should be used to predict the formation of the solid-solution phases¹⁷⁾. Although some inconsistencies are observed between the above-mentioned criteria, they are helpful for predicting the formation of solid-solution phases in multicomponent alloys. Table 2(b) lists the values of the ΔS_mix, ΔH_mix, δ, and Ω parameters for an AlCoCrFeNi_2.1 alloy. The 0.0129 kJ/mol of ΔS_mix corresponds to 1.55R. All the values exhibit a strong solid-solution formation tendency in an AlCoCrFeNi_2.1 alloy. The VEC value of an AlCoCrFeNi_2.1 alloy is 7.7, indicating the formation of a mixture of fcc and bcc phases.

2.2 Experimental procedure

Figure 1 is a schematic illustration of the metal mold casting process and the position of the ingot. Figure 1(a), (b) shows the crucible and a mixture of pure element blocks, and the centrifugal-casting equipment, respectively. The schematic illustration of the centrifugal-casting equipment and the position of the ingot for microstructure analysis are shown in Fig. 1(c), (d), respectively. A mixture of pure element blocks, with a total weight of about 80 g was set in the silica-based crucible, as indicated by A in Fig. 1(a). The alloy composition is listed in Table 1(a). Pure Al shots (Purity 99.99%, Mitsuwa Chemical Co., Ltd., Japan²¹⁾), Co flakes (Purity 99.9%, Osaka Asahi Co., Ltd., Japan²²⁾), Cr granules (Purity 99.9%, Mitsuwa Chemical Co., Ltd., Japan²¹⁾), Fe flakes (Purity 99.9%, Toho Zinc Co., Ltd., Japan²³⁾), and Ni grains (Purity 99.9%, Osaka Asahi Co., Ltd., Japan²²⁾), were used as the pure metal blocks in the present study. The crucible (A) and the Cu mold (B) were set in the centrifugal-casting equipment as shown in Fig. 1(b). Thermal melt was obtained by high-frequency melting under an Ar flow. The Ar supply is indicated by C in Fig. 1(b), (c). The ingots were obtained by two different processes to give an “air-cooled ingot” and a “metal-molded ingot.” In the case of the air-cooled specimens, the thermal melt was cooled in the crucible with a slow cooling rate. In contrast, the metal-molded specimens were obtained by centrifugal casting. The metal mold was first heated to remove any moisture. No mold-release agent was used.

Fig. 1

Schematic illustration of metal-mold casting process and ingot position. (a) Schematic illustration of crucible and mixture of pure element blocks, (b) appearance of centrifugal-casting equipment, (c) schematic illustration of centrifugal-casting equipment, and (d) schematic illustration of ingot position for microstructure analysis.

To clarify the position dependence of the constituent phases and the microstructure, the following method was applied in the present study. (1) The ingot was cut into nine part by electro-discharge machining as shown in Fig. 1(d). (2) The specimens were wet-polished by SiC abrasive grinding paper and/or diamond polishing paper. (3) The specimens of No. ① (metal-mold-contacted, top part), No. ② (metal-mold-contacted, middle part), No. ③ (metal-mold-contacted, bottom part), No. ④ (non-contact with metal mold, top part), No. ⑤ (non-contact with metal mold, middle part), No. ⑥ (metal-mold-contacted, bottom part) were selected as typical samples. (4) The constituent phases and the microstructures of specimens ①, ②, ③, ④, ⑤, and ⑥ were investigated by XRD analysis and trans-scale observation¹³⁾ using OM, SEM, EPMA, TEM, and STEM. The thin films required for the TEM and STEM measurements were prepared by mechanical polishing and ion-milling at room temperature. The Micro-Vickers hardness test was performed with a load setting of 1 kgf (9.807 kN).

The cooling rate during the solidification of the ingot prepared by air cooling and metal-mold casting was estimated from the secondary dendrite arm spacing in the Al_95.5Cu_4.5 alloy^24,25). For the air-cooled ingot, the cooling rate was in the order of 1 K/s, regardless of the position of the ingot. The cooling rates in the ingot prepared by metal-mold casting are shown in Fig. 2. The cooling rate in the metal mold ingot points to the position dependence and was estimated to be 100–500 K/s. The cooling rates at positions ③ and ⑥ were higher than those in other positions. Positions ④ and ⑤, which were not in contact with the metal mold, exhibit a relatively low cooling rate. We could consider that the cooling rate shown in Fig. 2 is higher than the typical value calculated by the ratio of the volume and surface area in the ingots fabricated by conventional metal-mold casting²⁶⁾. The difference may be due to the application of the centrifugal casting process, non-use of a mold-release agent, and the use of a Cu mold in the present study.

Fig. 2

Position dependence of cooling rate of ingot prepared by metal-mold casting. The cooling rate was estimated from the spacing of the secondary dendrite arms in the Al_95.5Cu_4.5 (at%) alloy.

3. Results

Figure 3 shows the outer appearance of the AlCoCrFeNi_2.1 EHEA ingots prepared by (a) metal-mold casting and (b) the air-cooling process. The metal-mold ingot exhibits a characteristic metallic luster without any oxide or casting defects such as open cavities or blowholes. In contrast, the air-cooled ingot is covered by an oxide layer. Figure 4 shows a macroscopic view of the solidification structures of the AlCoCrFeNi_2.1 EHEA ingots prepared by (a) metal-mold casting and (b) the air-cooling process. The development of the columnar grains from the surface to the central area, and that of the equi-axial structure in the central region can be seen in the metal mold ingot. In the air-cooled ingot, a large shrinkage cavity can be seen. The size of the solidification structure in the air-cooled ingot was larger than that in the metal-mold ingot. These results indicate that ingots without casting defects can be obtained by high-frequency melting under an Ar flow and by centrifugal casting using a metal mold. It should be emphasized here that the present study focused on the position dependence of the constituent phases and the microstructure in the ingots. The castability and the formation of macroscopic cast defects are an important topic affecting the practical application of HEAs and EHEAs. The formation of a shrinkage cavity in the air-cooled specimens may be prevented by the control of the casting process. However, a detailed study of the formation of shrinkage cavities was not a concern in the present study, but will be addressed in our future work.

Fig. 3

Appearance of the AlCoCrFeNi_2.1 eutectic high-entropy alloy ingots prepared by (a) metal-mold casting and (b) air-cooling process.

Fig. 4

Macroscopic view of solidification structures of AlCoCrFeNi_2.1 eutectic high-entropy alloy ingots prepared by (a) metal-mold casting and (b) air-cooling process.

To clarify the position dependence of the constituent phases and the microstructure in the ingot, XRD analysis was performed for specimens ①–⑥. The results for the metal-mold ingot and air-cooled ingot are shown in Figs. 5 and 6, respectively. In the XRD patterns, the intensity is expressed as a linear scale in the left-hand figures and by a logarithmic scale by the right-hand figures to enhance minor peaks. In the metal-mold ingots, the sharp peaks in the XRD patterns of the specimens ①–⑥ can be identified as fcc or bcc phases. The lattice constant of the fcc and bcc was estimated to be 0.358 ± 0.001 [nm] and 0.286 ± 0.001 [nm], respectively, and no position dependence of the lattice constants was observed. The peak intensity of the fcc phase is higher than that of the bcc phase, indicating that the volume fraction of the fcc phase is larger than that of the bcc phase. In the logarithmic scale plot (right side), no minor peaks corresponding to intermetallic compounds were observed. Lu et al. reported the existence of minor peaks corresponding to the B2 ordering phase in the XRD pattern obtained from an weighing 2.5 Kg, while the B2 ordering was not observed in the present study. The peak intensity ratio in the fcc phase is position dependent between (111) and (200). For specimens ③ and ⑥, from the bottom of the metal-mold contacted region, exhibit a peak intensity for (200) that is much higher than that for (111). This can be explained by the crystallographic orientation due to the preferential growth of the primary fcc-dendrite from the metal-mold contacted surface, as described above. The XRD patterns for the air-cooled ingot exhibit the following tendencies which are similar to those of the metal-mold ingot: (1) A composite of the fcc and bcc phases was formed, and the position-dependence of the constituent phases was not observed. (2) The lattice constants of the fcc and bcc phases exhibit no position dependence. (3) The volume fraction of the fcc phases tends to be larger than that of the bcc phase. (4) An ordering peak cannot be seen in the XRD patterns with linear and logarithmic intensity plots of the XRD patterns.

Fig. 5

Position dependence of XRD patterns of AlCoCrFeNi_2.1 eutectic high-entropy alloy ingots prepared by metal-mold casting. (a) Positions ①, ②, and ③; and (b) positions ④, ⑤, and ⑥. The intensity is expressed using a linear scale in the left-hand figures and with a logarithmic scale in the right-hand figures to enhance minor peaks.

Fig. 6

Position dependence of XRD patterns of AlCoCrFeNi_2.1 eutectic high-entropy alloy ingots prepared by air-cooled casting. (a) Positions ①, ②, and ③; and (b) positions ④, ⑤, and ⑥. The intensity is expressed using a linear scale in the left-hand figures and with a logarithmic scale in the right-hand figures.

Figure 7 shows SEM back scattering electron (BSE) images of the solidification structures of the AlCoCrFeNi_2.1 EHEA ingots prepared by (a) metal-mold casting and (b) the air-cooling process. Specimens ④, ⑤, and ⑥ were selected as typical examples. Specimen ⑥ exhibits a fast cooling rate due to its being in contact with the metal mold, while specimens ④ and ⑤ exhibit a lower cooling rate because neither were in contact with the metal mold. The SEM microstructures were observed in the central area of the partitioned specimens, with the lower parts of the SEM images corresponding to the lower parts of the ingots. Figure 7(c) shows the SEM microstructure, focusing on the metal-mold/ingot interface. The black contrast region, a typical example of which is indicated by D, was clarified as being not an inclusion formed through the solidification process but as an artifact introduced during the polishing. The randomly dispersed black particles can be assumed to be SiC and/or SiC-related particles from the SiC abrasive grinding paper. In the metal-mold ingots, the development of the primary dendrite and the eutectic structure at the inter-dendrite region can be seen (Figs. 7(a1)–(a3)). The size of the primary dendrite indicates a position dependence, as follows, ④ > ⑤ > ⑥ (Fig. 7(a1) > Fig. 7(a2) > Fig. 7(a3)). In the air-cooled ingots, the primary dendrite and the eutectic structure in the inter-dendrite region can be seen in the inset of the SEM images for specimens ⑤ and ⑥ (Figs. 7(b2), (b3)), while the development of the dendrite structure was not observed in specimen ④ (Fig. 7(b1)). The area ratio of (primary dendrite)/(eutectic structure in the inter-dendrite region) in the specimens also shows the position dependence as follows: ⑤ > ⑥. The full lamellar structure can be seen for specimen ④. No significant difference in the size of the primary dendrite of specimens ④ and ⑤ was observed. The size of primary dendrite in the air-cooled ingots is much larger than that in the metal-mold ingots, regardless the position in the ingots. A TEM analysis clarified that the primary dendrite phase is an fcc phase, while the eutectic structure is composed of fcc and bcc phases. These are described in detail below. The development of the dendrite was not seen at the metal-mold/ingot interface, and the formation of the eutectic structure in the inter-dendrite region was observed in the region from about 100 μm from the metal-mold/ingot interface. The columnar grain was observed at the metal-mold/ingot interface, which can be explained by the formation of a chill layer and the development of columnar grains at the metal-mold/ingot interface^27–29). The inclusions formed only at the metal-mold/ingot interface region were not seen in the AlCoCrFeNi_2.1 EHEA ingots.

Fig. 7

SEM-back scattering electron (BSE) images of solidification structures of AlCoCrFeNi_2.1 eutectic high-entropy alloy ingots prepared by (a) metal-mold casting and (b) air-cooling process. (a1) Metal-mold casting–position ④, (a2) ⑤, and (a3) ⑥; and (b1) Air cooling–position ④, (b2) ⑤, and (b3) ⑥. (c) Metal-mold casting–position ⑥ focusing on the mold wall.

To quantitatively evaluate the size of the solidification microstructure, we investigated the relationship between the secondary dendrite arm spacing (DAS) and the cooling rate (K) of the ingots. The results are shown in Fig. 8. The DAS was generally expressed as a function of K using the following equation^{24,25,27–31)}:   

\[ DAS = C \cdot K^{A} \](12)

where A and C are constants. The linear curve in Fig. 8 is the approximate curve based on eq. (12), and the value of A was estimated to be -0.23. The DAS for the AlCoCrFeNi_2.1 EHEA ingots can be evaluated using eq. (12). These results indicate that the solidification microstructure in the AlCoCrFeNi_2.1 EHEA consists of primary fcc dendrite and fcc+bcc eutectic in the inter-dendrite region, while the size of the solidification microstructure increased as the cooling rate fell.

Fig. 8

Secondary dendrite arm spacing of fcc phase as a function of the cooling rate in AlCoCrFeNi2.1 eutectic high-entropy alloy ingots.

We performed SEM-EPMA and STEM-EDS mapping to investigate the distribution of the constituent elements during the solidification. The results are shown in Fig. 9. The EPMA-WDS mapping results (Fig. 9(a)) exhibit the following tendencies: (1) the Al and Ni elements are enriched in the inter-dendrite region, (2) the Co, Cr, and Fe elements are enriched in the primary fcc dendrite. The STEM-EDS mapping results, focusing on the inter-dendrite region, are shown in Fig. 9(b). In the STEM-HAADF image, the white and black contrast regions correspond to the bcc and fcc phases, respectively. The bcc phase exhibits a tendency to be enriched by Al and Ni, while the fcc phases exhibit the opposite tendency in the eutectic region. Table 3 lists the experimental analysis results for the chemical composition of the primary fcc dendrite as evaluated by EPMA-WDS, while the fcc and bcc phases in the eutectic region were evaluated by STEM-EDS. The fcc dendrite appears to be lacking in Al, relative to the nominal composition. For the eutectic region, the following two tendencies can be observed: (1) the Al element is lacking in the fcc phase, relative to the nominal composition, which is similar to the primary fcc dendrite. (2) The Al and Ni elements are enriched in the bcc phase, relative to the primary fcc dendrite and the fcc phase in eutectic region. In other words, the bcc phase in the eutectic region is an Ni- and Al-rich phase. This indicates that the solidification of the AlCoCrFeNi_2.1 EHEA progresses according to the following sequence: (1) fcc dendrite formation and the ejection of Al to the residual liquid, (2) fcc + bcc eutectic structure formation in the inter-dendrite region, resulting in the formation of an Ni/Al-rich bcc phase.

Fig. 9

Element mapping for position ⑤ of AlCoCrFeNi_2.1 eutectic high-entropy alloy ingots prepared by metal-mold casting. (a) SEM-EPMA mapping, (b) STEM-EDS mapping, focusing on the eutectic structure in the inter-dendrite region.

Table 3 Composition analysis results of constituent phases in region ⑤ of AlCoCrFeNi_2.1 eutectic high-entropy alloy ingots prepared by metal-mold casting obtained by EPMA-WDS and STEM-EDS.

	Al [at%]	Co [at%]	Cr [at%]	Fe [at%]	Ni [at%]	δ
Dendrite-Fcc	7.7	19.9	20.8	19.3	32.4	3.9
Eutectic-Fcc	5.6	18.0	21.5	19.3	35.7	3.3
Eutectic-Bcc	24.7	11.7	7.2	8.9	47.6	6.0

XRD observations (Figs. 5 and 6), SEM observations (Fig. 7), and EPMA/STEM analyses (Fig. 9) clarified that the constituent phases in an AlCoCrFeNi_2.1 EHEA ingot are the primary fcc dendrite and the fcc+bcc eutectic structure in the inter-dendrite region. To investigate the microstructure of the primary dendrite fcc phase, TEM analysis of specimen ⑤ (a typical metal-mold ingot sample) was performed. The results are shown in Fig. 10. In the bright field (BF) image, no inclusions or precipitates were observed. The inset is a BF image focusing on the triple points of the grain boundary. No precipitates can be seen. Figures 10(b1)–(b3) show the [001], [011], and [111] selected area diffraction (SAD) patterns, where Figs. 10(c1)–(c3) and Fig 10(d) are the [001], [011], and [111] key diagrams for the XY₃ compound with an L1₂ structure, and a schematic illustration of the binary XY₃ compound with a L1₂ structure, respectively. In the key diagrams (Figs. 10(b1)–(b3)), ● and ○ represent the fundamental diffraction of the fcc structure and the super-lattice diffraction based on the L1₂ structure, respectively. The SAD patterns (Fig. 10(c1)–(c3)) can be explained as being those of the L1₂ structure. This indicates that the primary fcc phase is not a chemically random fcc solid-solution phase but an fcc phase with weak chemical ordering based on the L1₂ ordering structure, where the chemical ordering was too weak to be detected by XRD analysis.

Fig. 10

TEM microstructure analysis results for position ⑤ of AlCoCrFeNi_2.1 eutectic high-entropy alloy ingots prepared by metal-mold casting. (a) TEM-bright field (BF) image, ((b1)–(b3)) [001], [011], and [111] selected area diffraction (SAD) patterns, ((c1)–(c3)) [001], [011], and [111] key diagrams of XY₃ compound with L1₂ structure, (d) schematic illustration of binary XY₃ compound with L1₂ structure.

Table 4 lists the position dependencies of the Vickers hardness (Hv) of the AlCoCrFeNi_2.1 EHEA ingots prepared by metal-mold casting. The average and standard deviation were evaluated using five data points at positions ①–⑥. The size of the indentation was approximately 40 μm. The value of Hv was obtained from the region consisting of the primary fcc dendrite and the fcc+bcc eutectic in the inter-dendrite region. No significant position dependence of the Hv was observed. Figure 10 shows the Hv of the AlCoCrFeNi_2.1 EHEA ingots prepared by metal-mold casting as a function of the distance from the metal-mold/ingot interface in the specimen. The Hv exhibits a constant value and no position dependence, while anomalous values in the region near the metal-mold/ingot interface were not observed. The Hv values in the AlCoCrFeNi_2.1 EHEA ingots were nearly homogeneous, while the size of the solidification microstructure was found to decrease as the cooling rate increased.

Table 4 Position dependence of Vickers hardness (Hv) of AlCoCrFeNi_2.1 eutectic high-entropy alloy ingots prepared by metal-mold casting. The average and standard deviation were evaluated using 5 data points.

①　267 ± 6.9	④　266 ± 8.5
②　272 ± 7.2	⑤　275 ± 4.4
③　270 ± 10	⑥　280 ± 8.1

4. Discussion

4.1 Homogeneity in solidification microstructure

The constituent phases in the AlCoCrFeNi_2.1 EHEA ingots are a composite of fcc and bcc phases, regardless of the casting processes (air cooling or metal-mold casting). The ingot exhibits a microstructure consisting of primary fcc dendrite and an fcc+bcc eutectic structure in the inter-dendrite region, and the development of a L1₂ ordering structure at the primary fcc dendrite in the metal-mold ingots. The microstructure of a rapidly solidified melt-spun ribbon of AlCoCrFeNi_2.1 EHEA was investigated³²⁾, where the cooling rate in the melt-spinning process was estimated to be in the order of 10⁵ K/s^33,34). The constituent phases in the melt-spun ribbons are a composite of the fcc and bcc phases, where the microstructure of the ribbon is not a typical lamella structure. This indicates that the constituent phases in the AlCoCrFeNi_2.1 EHEA specimens obtained via the solidification route are basically fcc+bcc phases with a wide-ranging cooling rate of 1–10⁵ K/s, and exhibit a weak cooling-rate dependence. Lu et al. reported on the lamella structure formation in ingots with a weight of 2.5 Kg¹¹⁾, although the position was not mentioned in detail. The full lamella structure was also reported for ingots with a size of 15 mm (width) × 90 mm (length) × 3 mm (thickness)³⁵⁾. In the present study, the development of the primary dendrite structure was not observed and a full lamella structure was seen in position ④ in the air-cooled ingots. This implies that the full lamella structure may be obtained in large specimens with a slow cooling rate. Further discussion of the solidification microstructure in AlCoCrFeNi_2.1 EHEAs will be pursued in a subsequent paper. The Hv value for the AlCoCrFeNi_2.1 EHEA ingots has a very low position dependence, as shown in Table 4 and Fig. 11. This can be explained by the lack of position dependence of the constituent phases of the ingots. The properties that change with the size of the solidification microstructure in the AlCoCrFeNi_2.1 EHEA with a cooling rate of 1–500 K/s is not a dominant factor affecting the hardness, and there was no formation of inclusions or precipitates in the region near the metal-mold/ingot interface.

Fig. 11

Vickers hardness (Hv) of AlCoCrFeNi_2.1 eutectic high-entropy alloy ingots prepared by metal-mold casting as a function of the distance from the metal-mold/ingot interface.

4.2 Development of L1₂ structure in primary fcc dendrite phase

The development of the L1₂ ordering structure in primary fcc dendrite can be detected by TEM-SAD pattern analysis (Fig. 10), while the sharp intensity peaks corresponding to the L1₂ ordering structure cannot be seen in the XRD patterns (Fig. 5). The L1₂ ordering in the fcc phase is thought to be too weak to be evaluated in detail only by XRD, while the existence of chemical ordering can be detected in certain observation directions in the SAD patterns in TEM observation. In the following, the development of the L1₂ structure in the fcc phase is discussed from the viewpoint of the alloy parameters for HEAs. The VEC values of the primary fcc dendrite phase, calculated based on an EPMA-WDS analysis (Table 3) was 8.0, with this value being the limit value for the formation of the fcc single phase^7,18,19). However, the application of VEC theory to the phase stability of the solid-solution phase in HEAs focuses on the formation of the fcc phase and bcc phases, not on the formation of the chemical-ordering structure in the fcc and bcc phases. The ordering phase, such as the bcc-based B2 structure and fcc-based L1₂, were formed in a number of HEAs, as reported in the literature⁷⁾, and these are generally called “ordered phases.” In the δ-Ω map suggested by Yang et al.¹⁷⁾, the solid-solution phase exhibits a tendency to be formed at δ ≦ 6.6 and Ω ≧ 1.1, while the ordered phase exhibits a tendency to form at 4 ≦ δ ≦ 6.6 in spite of the solid-solution formation range. In the ΔH_mix − δ map suggested by Zhang et al.³⁾, the ordered phase is likely to form in the region of δ ≧ 4.5. These tendencies were derived from the empirical rules, with both rules exhibiting a tendency for the ordered phases to be formed at relatively high δ values. The δ value of the primary fcc dendrite phase, evaluated by the chemical composition analysis results, is 3.9, as shown in Table 2. This was close to the limit value for the formation of an ordered phase in the δ-Ω map⁷⁾. The δ parameter is used to evaluate the difference in the atomic size effect in HEAs. The L1₂ ordering formation in the primary fcc dendrite phase may be explained by the rejection of the Al content from the fcc phase to the residual liquid and the relaxation of the atomic size differences in the constituent elements. It should be emphasized here that the TEM-SAD pattern analysis is vital to the clarification of the formation of the ordered phase, and the formation of the ordered phase may be predicted by using the alloy parameters for HEAs in AlCoCrFeNi_2.1 and Al-Co-Cr-Fe-Ni based EHEAs.

5. Conclusions

The constituent phases and microstructure of an AlCoCrFeNi_2.1 EHEA were investigated by trans-scale observations covering millimeter-order to nanometer-order scales to evaluate the solidification microstructure in HEAs. The obtained results are summarized as follows:

• (1)   Cast products of AlCoCrFeNi_2.1 EHEA can be successfully obtained by high-frequency melting under an Ar flow and centrifugal casting using a metal mold.
• (2)   The solidification microstructure evaluation for HEAs was discussed. The heterogeneity of the constituent phases and microstructure was investigated using nine partitioned parts obtained from an ingot by using XRD (with linear and logarithmic scales) and trans-scale observations using OM, SEM, EPMA-WDS, TEM, and STEM.
• (3)   The constituent phases in the AlCoCrFeNi_2.1 EHEA were a combination of the bcc and fcc phases. This was not dependent on the position in the ingot.
• (4)   The microstructure of the ingot obtained by centrifugal casting using a metal mold was primary fcc dendrite, with a bcc+fcc eutectic structure in the inter-dendrite regions. The size of the microstructure exhibited a cooling-rate dependence; as the cooling rate increased, the secondary dendrite space arming and lamellar size of the eutectic structure became finer.
• (5)   The development of the L1₂-based ordering structure in the primary fcc dendrite was observed by TEM analysis.

Acknowledgements

This work was partially supported by JSPS KAKENHI (Grant Number 15K06484), by scientific grants from the Japan Foundry Engineering Society (JFS) and by the Organization for Research and Development of Innovative Science and Technology (ORDIST), Kansai University. The authors are grateful to Mr. Kazuki Takahashi of Kansai University for his assistance with the micro Vickers hardness measurements.

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