Experimental and first-principles investigation of high entropy superalloys produced by powder injection moulding method

In the present study Al-Co-Cr-Fe-Mn-Ni-Ti based HESA were produced. Table 1 shows the chemical compositions of the HESA. Al, Co, Cr, Fe, Mn, Ni and Ti elements were selected due to their melting temperature, electrical conductivity, density, corrosion resistance, mechanical properties, price. Al, Co, Cr, Fe, Mn, Ni and Ti elements were used in the range of 3–38 wt%. Al, Co, Cr, Fe, Mn, Ni, Ti elements were selected in order to develop light, cheap HESAs with creep resistance and strength. HESA includes more light elements (Al and Ti), and lesser expensive elements (Co and Ni). Also, there is no heavy and expensive refractory elements (W, Nb, Mo, Ta).

Entropy of mixing (ΔS _mix), enthalpy of mixing (ΔH _mix), atomic size misfit (δ), parameter Ω, VEC parameters could be used in order to evaluate high entropy alloy formation. Entropy of mixing (ΔS _mix) of the proposed HESAs is calculated by equation (1), where R is the gas constant and C _i is the atomic ratio (molar fraction). There is no any interaction forcess between alloy atoms in the ideal solid solutions. The mixing enhalpy is zero, and the mixing entropy is given by the configurational entropy of the alloying atoms. In addition, interaction forces are insufficient to affect the mixing entropy in the regular solid solution. In the HESAs mixing entropy (ΔS _mix) must be in the range of 11 ≤ ΔS _mix ≤ 19 (J/K mol) for solid solution formation rather than intermetallic formation. ΔS _mix is the highest for alloys with nearly equal atomic ratios. ΔS _mix has vibrational, electronic, configurational, and magnetic components. In the present study, only configurational entropy is considered [18,19]. (1) Δ S mix = − R ∑ i n C i ln C i . \text{Δ}{S}_{\text{mix}}=-R\mathop{\sum }\limits_{i}^{n}{C}_{i}\hspace{.25em}\mathrm{ln}\hspace{.25em}{C}_{i}.

The atomic size misfit parameter (δ), which estimates the amount of lattice strain in the alloy, is calculated by equation (2), where r _i is the atomic radius. Atomic size misfit (δ) parameter must be in the range of 0 ≤ δ ≤ 8.5 for solid solution formation. High δ parameter leads distortion in the lattice, by increasing the free energy, which decrease the stability of solid solution [18,19]. (2) δ = ∑ i n C i ( 1 − r i / r ) 2 . \delta =\sqrt{\mathop{\sum }\limits_{i}^{n}{C}_{i}{(1-{r}_{i}/r)}^{2}}.

VEC parameter of the HESAs is calculated by equation (3) by using VEC values of atoms. Crystal structure of the alloys can be predicted by VEC value. Crystal structure types are as follows: VEC > 8.00 fcc (face centered cubic), VEC < 6.87 bcc (body centered cubic), 6.87 < VEC < 8.00 fcc-bcc dual phase [8,9,18,19]. (3) VEC = ∑ i n C i ( VEC ) i . \text{VEC}=\mathop{\sum }\limits_{i}^{n}{C}_{i}{(\text{VEC})}_{i}.

The enthalpy of mixing (ΔH _mix) is calculated by equation (4), where ΔH _mix is mixing; and C _i and C _j are the atomic ratios of the ith and jth components. For a binary mixture, ΔH _mix is negative if the A and B atoms are attractive to each one. ΔH _mix is positive if the atoms are repulsive. Criteria for solid solution is −10 < ΔH _mix <5 (kJ/mol). A high negative ΔH _mix increases the likelihood of formation of intermetallics. Positive ΔH _mix indicates lower mixing of different atoms in the liquid state, which leads to separation of alloying elements in the solid state. Only if enthalpy of mixing is close to zero alloying elements could be distributed and could form solid solution [18,19]. (4) Δ H mix = ∑ i < j 4 H i j c i c j . \text{&#x0394;}{H}_{\text{mix}}=\sum _{i\lt j}4{H}_{ij}{c}_{i}{c}_{j}.

Dimensionless stability parameter (Ω) is calculated by using equation (5), where T _m is the melting temperature. Ω > 1 means that the effect of the ΔS _mix is greater than ΔH _mix, and the high-entropy phase tends to form. Solid solution formation is possible only if Ω > 1 is satisfied [18,19]. (5) Ω = ∑ c i T m , i ( Δ S mix ) ∣ Δ H mix ∣ . \text{&#x03A9;}=\left(\phantom{\rule[-0.75em]{}{0ex}}\sum {c}_{i}{T}_{m,i}\right)\frac{(\text{&#x0394;}{S}_{\text{mix}})}{| \text{&#x0394;}{H}_{\text{mix}}| }.

Table 2 shows the parameters of the atoms used in the production of HESA, while Table 3 shows the mixing enthalpy values (kJ/mol) of the binary alloys. In the present study seven HESA were produced. HESA with high VEC value (maximum fcc content) and simultaneously high ΔS _mix was preferred. In general, fcc structure is necessary for creep resistance. ΔS _mix and δ values of the HESA were similar.

Table 4 shows the thermodynamic parameters calculated by equations (1)–(5). As the VEC value is slightly lower than 8.0 and higher than 6.87 for all alloys, bcc and fcc mixed microstructure is supposed to form. As the VEC values of the the alloys are close to fcc microstructure area mainly fcc phase could be formed in the microstructure. The values of atomic size misfit parameters (δ) are within the range of solid solution formation. The values of enthalpy of mixing (ΔH _mix) are within the range of solid solution formation for alloy 1 and alloy 2. Since the system contains seven elements, entropy of mixing (ΔS _mix) is higher than threshold. ΔS _mix values of alloys 1, 2, 3, 4, 5, 6, and 7 are suitable. The values of stability parameter Ω of alloys are within the range of solid solution formation. As a result, the Al₁₅Co₉Cr₁₆Fe₂₀Mn₄Ni₃₃Ti₃ (alloy 1) and Al₁₅Co₄Cr₁₆Fe₂₀Mn₄Ni₃₈Ti₃ (alloy 2) were most suitable for their high VEC value (maximum fcc content), high δ, high Ω, suitable ΔH _mix, high ΔS _mix.

First-principles calculation was used to study the mechanical properties. Cambridge sequential total energy package (CASTEP) code, which is a first-principles quantum mechanical based code, was used for the calculations [20,21,22,23,24,25,26,27,28,29]. CASTEP is a first-principles plane wave pseudo-potentials method based on DFT. Generalized gradient approximation of Perdew-Burke-Ernzerhof was employed in order to describe the exchange correlation energy. Vanderbilt type ultrasoft pseudopotential was used. Cut-off energy is set to 500 eV and 8 × 8 × 8 k-points were used for structure optimization. Face centered cubic structure was used for alloys.

In the present study, seven Al-Co-Cr-Fe-Mn-Ni-Ti based refractory element-free HESA were prepared by MA-PIM. Average particle sizes metal powders were 34 μm. Elemental metal powder mixture was ball-milled (mechanical alloying) with ZrO₂ grinding 6 mmvballs for 35 h at 400 rpm. ZrO₂ to metal ratio was 10/1.

Polymer system contained 70% polyethylene, 28% paraffin, 2% stearic acid. Feedstock consisted of 45% of binder and 55% of metal. PIM was carried out at 185°C. After the PIM step, binder from green specimens was removed in hot hexane (chemical debinding). Thermal removal of the binder from the green specimens was carried out in a furnace at 400°C for 60 min (thermal debinding). Sintering process of the brown specimens was carried out at 1,250°C for 60 min in vacuum (MTI, USA). Figure 1 illustrates the HESA production steps by MA-PIM method.

Figure 1

HESA production by PIM method.

In the present study, heat treatment for production of precipitates consisted of a solution treatment and aging. Solution treatment was carreid out above the solvus temperature at 1,150°C for 8 h for dissolution of alloying elements. Precipitation hardening (aging) was carried out at temperatures between 700 and 1,000°C for 5 h for production of precipitates. Titanum was added to the HESA for the formation of coherent fine intermetallic precipitates. After the solution treatment in the vacuum, alumina tube was removed out from the heating zone and the specimens were quenched. Figure 2 shows the aging heat treatment by using sliding-flange tube furnace.

Figure 2

Aging heat treatment by using sliding-flange tube furnace.

Microstructural characterization of the HESA was performed by scanning electron microscope (SEM). Hardness of the specimens was determined by using a micro-vickers hardness test (Zwick Roell). Wear resistance of the specimens was measured by pin-on-disc method (Devotrans, Turkey). Electrical conductivity was investigated by using eddy current device (WeldCheck). Young’s modulus values of the specimens were determined by using ultrasonic device (General Electric, USA), by using following equation (6). V _T and V _L are transverse and longitudinal velocity, and ρ is density [30]. (6) E = ρ V T 2 3 V L 2 − 4 V T 2 V L 2 − V T 2 . E=\rho {V}_{\text{T}}^{2}\frac{3{V}_{\text{L}}^{2}-4{V}_{\text{T}}^{2}}{{V}_{\text{L}}^{2}-{V}_{\text{T}}^{2}}.

Electrochemical corrosion tests were carred out using a potentiostat (Interface 1000, Gamry) in 5% NaCl solution. Tafel and linear polarization resistance tests were employed for corrosion rate. Electrochemical impedance spectroscopy (EIS) tests were carried out in order to investigate the electrochemical corrosion properties of the HESA specimen and to investigate behaviour of surface. EIS result was fitted by an electrical equivalent circuit model.

Elevated temperature oxidation behaviour of the specimens was studied at 900°C temperature for different durations between 1 and 4 h in air atmosphere. Weight gain values of the specimens were determined by measuring the weight of the specimens before and after the oxidation tests at 900°C in air.

In the present study, first-principles based computational materials science calculations were used in order to study the elastic, physical and mechanical properties. CASTEP software, which is a DFT based code, was used for the calculations. Initially, CASTEP geometry optimization process was carried out by decreasing the magnitude of forces up to they become lower than a defined tolerance value. Figure 13 shows the (a) unit cell and (b) superlattice.

Figure 13

Unit cell (left), and superlattice (right).

Elastic constants should satisfy the mechanical stability criteria for a stable alloy. C ₁₁, C ₁₂ and C ₄₄ are the independent elastic constants for the simple cubic crystal structures. C ₁₁, C ₁₂ and C ₄₄ elastic constants must satisfy the following conditions for mechanical stability according to the Born-Huan criteria [20,21,22,23,24,25,26,27,28,29]. Figure 14 shows the elastic constants of the alloys. C ^I value must be positive for mechanically stability of the crystal structure. As shown in the Figure 14, C ^I values are positive and equations (7)–(10) were satisfied, which means all the alloys are mechanically stable. (7) C I = ( C 11 − C 12 ) 2 , {C}^{I}=\frac{({C}_{11}-{C}_{12})}{2}, (8) C 11 + 2 C 12 > 0 , {C}_{11}+2{C}_{12}\gt 0, (9) C 11 − C 12 > 0 , {C}_{11}-{C}_{12}\gt 0, (10) C 44 > 0 . {C}_{44}\gt 0.

Figure 14

Elastic constants of the high entropy alloys.

Young’s modulus (E), Poisson’s ratio (ρ), bulk modulus (B) and shear modulus (G) can be calculated by the following equations by using C ₁₁, C ₁₂ and C ₄₄ elastic constants for cubic system [20,21,22,23,24,25,26,27,28,29]. In the present study, determination of the mechanical properties was carried out by using of elastic constants (C ₁₁, C ₁₂ and C ₄₄). Figure 15 shows the calculated Young’s modulus (E), shear modulus (G) and bulk modulus (B) values. Highest Young’s modulus was in the alloy-1, while lowest Young’s modulus was in the alloy-3. (11) E = 1 5 ( 3 C 44 + C 11 − C 12 ) , E=\frac{1}{5}(3{C}_{44}+{C}_{11}-{C}_{12}), (12) B = 1 3 ( C 11 + 2 C 12 ) , B=\text{}\frac{1}{3}({C}_{11}+2{C}_{12}), (13) G = C 11 − C 12 + 3 C 44 5 , G=\frac{{C}_{11}-{C}_{12}+3{C}_{44}}{5}, (14) ρ = 3 B − 2 G 2 ( 3 B + G ) . \rho =\frac{3B-2G}{2(3B+G)}.

Figure 15

Young’s (E), shear (G) and bulk (B) modulus values of the alloys.

Figure 16 shows the Poisson’s ratio and G/B ratio (Pugh's ratio) values. Poisson‘s ratio (ρ) determines the shear deformation capacity of alloys. Increasing Poisson’s ratio, increase the plastic deformation capacity and ductility. Ductile materials such as metals have Poisson ratio of 0.30–0.33. Brittle materials such as covalent materials have Poisson’s ratio of 0.20–0.25, while ionic materials have Poisson’s ratio of 0.10–0.15. As the Poisson’s ratio values are 0.30–0.32, all alloys are ductile according to the Poisson’s ratio values. G/B ratio is known as Pugh’s ratio, which is depending on the brittle/ductile nature of metals and can be used for the characterization of ductility. If the Pugh’s ratio is lower than 0.57, the alloy is ductile. If the Pugh’s ratio is higher than 0.57, the alloy is brittle. As the Pugh’s ratio values are about 0.40–0.45, all HESA are ductile. In the present study, mechanical properties were determined by experimental and first principles methods. Difference between the experimental and first principles elastic modulus was 5–20%. Difference was attributed to the presence of porosity and superlattice size used for calculations. Larger superlattice structures could not be calculated due to computer capacity.

Figure 16

Poisson’s ratio and G/B ratio values of the alloys.

Density of states (DOS) of the materials could be employed in order to determine the stability of the alloy with respect to their behaviour at the Fermi energy level (E _f). Material with the highest DOS at the Fermi energy level is the least stable. Figure 17 illustrates the energy values of the alloys at the Fermi level (E _f). Alloys with lower energy level are more stable. Increasing mixing entropy or mixing enthalpy values increased the energy value and decreased the stability of the alloys. Most stable alloy was alloy-2, while least stable alloys were alloy-4 and alloy-7.

Figure 17

Energy values of the alloys at Fermi level.

Figure 18 shows the effect of (a) heat treatment and (b) composition (alloy type) on the DSC curves of the specimens. DSC curves show the major phase transformations of the HESA specimens. Precipitation hardening (aging) temperature increased the solvus temperature of the γ′ precipitates. The first peaks at temperatures between 720 and 800°C shows the starting of the precipitation of γ′. Second peaks at about 910 and 950°C shows the dissolution of the γ′ intermetallic precipitates. Melting temperature values of alloy 1 and alloy 2 were higher. Highest melting temperature was in te alloy 1, while lowest melting temperature was in alloy 7.

Figure 18

Effect of heat treatment (left), and composition on the DSC curves of the specimens (right).

Traditional alloy design strategy depends on one principal element and addition of secondary minor elements. In the high entropy alloys, fundamental is to add five or more principal elements in equimolar ratios in order to increase the configuration entropy in order to produce a single-phase solid solution. Unfortunately, matrix of a high entropy alloy is not strong enough for elevated temperatures. The heat treatment in order to produce intermetallic precipitates consists of a solution treatment above the solvus temperature and precipitation hardening at lower temperatures in order to produce fine intermetallics. Elevated temperature strength of the superalloys depends on the amount and size of the γ ^I precipitates. Strength of traditional alloys decreases with temperature. But, in the superalloys, strength increases with increasing temperature up to 750–800°C. For elevated temperatures, as the γ ^I precipitates dissolves, the strength decreases [32,33,34,35]. There are two mechanisms for precipitation hardening of the metals by-pass of dislocations (Orowan theory) or shearing of dislocations mechanism [32,33,34,35].

Figure 19 shows the oxidation behaviour test results of the specimens at 900°C for different durations from 1 to 4 h in air atmosphere. Weight of the alloys was increased with the holding time in air at 900°C. As seen, weight gain values of the alloy-5, alloy-6 and alloy-7 were relatively higher. Increasing weight gain in the alloys was attributed to the decreasing Ni, Cr, and Co contents. Highest weight gain value was in the alloy-6, while lowest weight gain value was in the alloy-2.

Figure 19

Oxidation results of the specimens at different durations.

Table 6 shows the density values and price values of the HESA. Table 6 also shows the density and price values of a traditional Ni-based superalloy (Inconel 718) for comparison. Mean cost values of the HESA were calculated by using price of alloying elements (Al is 2,800 US$ per tonne, Co is 4,3720 US$ per tonne, Cr is 7,400 US$ per tonne, Fe is 650 US$ per tonne, Mn is 1,800 US$ per tonne, Ni is 18,250 US$ per tonne, Ti is 8,000 US$ per tonne, Mo is 55,000 US$ per tonne, and Nb is 77,000 US$ per tonne). In addition, mean density values of the HESA were calculated by using density of alloying elements (Al is 2.71 g/cm³, Co is 8.9 g/cm³, Cr is 7.19 g/cm³, Fe is 7.87 g/cm³, Mn is 7.47 g/cm³, Ni is 8.9 g/cm³, Ti is 4.5 g/cm³, Mo is 10.22 g/cm³, and Nb is 8.58 g/cm³) [36,37]. As seen from the Table 6, cost values of the HESA were 32–48% lower than traditional Ni-based superalloy (Inconel 718). In addition, density values of the HESA were 16–23% lower than traditional superalloy (Inconel 718). Especially density and cost values of the alloy-7 (Al₂₅Co₅Cr₁₀Fe₂₅Mn₃Ni₂₇Ti₅) were 48 and 23% lower than the traditional Inconel 718 superalloy.