High-Entropy Alloys: Formation and Propertiesproceedings.asmedigitalcollection.asme.org/data/conferences/asmep/... · entropy alloys (< four elements) have been melted using eletroslag

HIGH-ENTROPY ALLOYS: FORMATION AND PROPERTIES

Michael C. Gao1,2, Paul D. Jablonski1, Jeffrey A. Hawk1, and David E. Alman1 1National Energy Technology Laboratory, Albany, OR, USA

2AECOM, Albany, OR, USA

ABSTRACT

This paper presents ongoing research at NETL aimed at gaining fundamental understanding of high-entropy alloys (HEAs) formation and their properties, and developing high-performance HEAs for high-temperature fossil energy applications. First-principles density functional theory (DFT), Monte Carlo simulation, and molecular dynamics simulation are carried out to predict enthalpy of formation, the entropy sources (i.e., configurational entropy, vibrational entropy, and electronic entropy), and elastic properties of model single-phase HEAs with the face-centered cubic, body-centered cubic and hexagonal closed-packed structures. Classical elastic theory, which considers the interactions between dislocations and elastic fields of solutes, has also been used to predict solid solution strengthening. Large-size (~7.5 kg) HEAs ingots are produced using vacuum induction melting and electroslag remelting methods, followed by homogenization treatment resulting in greater than 99% homogeneity. Subsequent thermomechanical processing produces fully-wrought face-centered cubic microstructures. The tensile behavior for these alloys have been determined as a function of temperature, and based on these results screening creep tests have been performed at selected temperatures and stresses.

INTRODUCTION

The core of the concept of high-entropy alloys (HEAs) [1, 2] lies in the assumption that an alloy would reach its maximumideal configurational entropy if the atomic concentration of all constituent elements is equal (i.e., NRS conf lnmax = , where N is the total number of components in the solution and R is the ideal gas constant). While traditional alloy design focus on an edge, or a corner, of a phase diagram, HEAs are comprised of compositions located at the center of multicomponent composition spaces, which until recently have rarely been studied. As a result, HEAs have stimulated increasing interest from academia and industry, not just as a scientific curiosity, but for understanding how the

concept can be used to improve existing alloy classes as well as exploring the unlimited potential of combining elements in ways never before envisioned, and in doing so, achieving improved physical, mechanical, and functional properties [3, 4].

However, many challenges still remain. In practice entropy and enthalpy contribute to phase stability, but they are not independent of each other. Manipulating the entropy by changing the number of components and their relative compositions inevitably causes a change in the enthalpy, and the contribution from entropy may not always dominate. As a result, the vast majority of reported equi-, or near-equi-, molar multicomponent compositions do not result in the formation of a single-phase solid solution alloy. As a matter of fact, the total number of single-phase HEAs in the face-centered cubic (FCC), body-centered cubic (BCC), and hexagonal close-packed (HCP) structures is very limited [5].

Formation of single-phase HEAs have recently been reviewed [4-6]. Gao et al. [5] concluded that those proposed empirical parameters based on thermodynamic, physical, and geometric properties of pure elements and binary alloys can be used to quickly identify single-phase HEA compositions, but they are not sufficient for determining the single phase nature of the combination of elements in the alloy. The threshold values of those empirical parameters may also vary depending on the range of the surveyed experimental data. More importantly, many empirical parameters have scientific flaws in their hypotheses [5].

This report first reviews recent progress in computational prediction of thermodynamics, elasticity, and solid solution strengthening of select single-phase HEAs by the present authors. Then manufacturing of FCC HEAs and characterization of the microstructure and mechanical behavior are presented. To date, seventeen (17) heats of FCC single phase alloys of high entropy nature have been manufactured in the vacuum induction furnace as ~7.5 kg ingots. These ingots have been homogenized using the best thermodynamic and kinetic databases available. The ingots were then converted to fully wrought structures using a combination of hot forging and hot rolling into plate suitable for production of full size tensile specimens. In addition, medium

1 Copyright © 2018 ASME

Proceedings of the ASME 2018 Symposium on Elevated Temperature Application of Materials for Fossil, Nuclear, and Petrochemical Industries

ETAM2018 April 3-5, 2018, Seattle, WA, USA

ETAM2018-6732

This work was authored in part by a U.S. Government employee in the scope of his/her employment. ASME disclaims all interest in the U.S. Government’s contribution.

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entropy alloys (< four elements) have been melted using eletroslag remelting and the resulting ingot has been converted to wrought product. Both melting practices are scalable to commercial practice. Mechanical properties for a couple of alloys will be presented here to illustrate what is possible with these alloys.

COMPUTATIONAL DETAILS

The first-principles density functional theory (DFT) calculations were performed using VASP (Vienna Ab Initio Simulation Package) [7, 8]. The special quasi-random structure (SQS) method [9, 10] was used to mimic the disordered atomic structures for equimolar HEAs as previously reported by Gao et al. [11]. More details on the DFT calculations are described elsewhere [5, 6]. The enthalpy of formation (ΔHss) was calculated by subtracting the composition–weighted total energies of the constituent elements in their ground state from the total energy of the alloy.

In general, the total entropy of a solid solution phase may consist of the contributions from lattice vibration ( ), configuration ( ), electron excitation ( ), and magnetic spin fluctuations ( ). The entropy sources are temperature and volume dependent. It is assumed that the magnetic entropy term contribution to FCC CoCrFeNi and CoCrFeMnNi should be small at T ≥ 293 K because their critical magnetic ordering temperatures are well below room temperature [12, 13].

The harmonic approximation was used for phonon calculation. The vibrational entropy ( ) was calculated using: 3 ( + 1)ln( + 1) − ln (1) where is the phonon density of states (DOS), and is the Bose-Einstein distribution function.

The electronic entropy ( ), was determined by: −2 ln + (1 − )ln(1- ) (2) where is the electron density of states, and is Fermi-Dirac distribution function.

Single-crystal elastic constants ( ) were derived by performing six finite distortions of the lattice using the basic elastic stress-strain relationship: σ = (3) where σ , and , are the elastic stress, strain, and tensor in the Voigt notation, respectively. The methods to calculate the average elastic properties of cubic polycrystalline materials are described in [6, 14].

In order to calculate the configurational entropy, the hybrid Monte Carlo / molecular dynamics (MC/MD) method [15, 16] was used to simulate the atomic structures at various temperatures. The simulations were done by alternating molecular dynamics at each temperature with Monte Carlo swaps, each performed from first principles using VASP [5, 6, 15-17]. The reduction in configurational entropy due to short-range chemical order can be calculated using the pairwise truncation of the Kikuchi cluster variation method (CVM) [18]: = ∑ ⁄, (4)

where is the near neighbor correlations, and and are the mole fractions of elements i and j, respectively.

EXPERIMENTAL PROCEDURES

References [19-21] explain the details of the manufacturing process, including the homogenization procedure. However, in general terms the manufacturing process and homogenization heat treatment are described thusly.

High purity starting materials were used to formulate VIM melts of two alloys with nominal compositions CoCrFeNi (designated as HEA 1A) and CoCrFeMnNi (designated as HEA 2A). [Note: High purity in this sense means “high purity” from a commercial alloy feedstock perspective, not ultra-high purity used in academic studies.] Approximately 7,800 g of raw materials were pressed into compacts that would fit into the furnace crucible. Some feedstock, such as electrolytic Mn, was resistant to compaction and was charged loosely in the crucible while other feedstock such as electrolytic Ni, or electrolytic Co, were melt consolidated prior to incorporation in the furnace crucible. The initial feedstock charge was loaded in the crucible to enhance electro-magnetic coupling and to facilitate subsequent feedstock addition during melting. Each alloy ingot was induction melted under Ar and poured into 75 mm diameter cylindrical graphite mold with a zirconia coating on the inner mold surface to minimize carbon pickup.

The “C” heats were melt processed similarly, however extra steps were taken to reduce S to low levels. Sulfur comes from the Co, Cr and Mn additions. In the case of Co and Cr, master alloys of Ni-Co-Cr were Electro-slag Remelted (ESR) to reduce the S to a low level as discussed in [22]. In the case of HEA 2 which contains Mn, the Ni-Co-Cr master alloy was utilized along with additions of elemental Fe and Mn (which contributed S) to produce a primary consolidation melt. This material was remelted with the addition of 21.2 g of Fe40Y (by weight) to remove excess S as discussed in [23]. This material was in turn remelted with an addition of NiO to remove excess Y. The series of HEA 2 melts were designated HEA 2C1, 2C2 and 2C3.

After casting, ingot hot-tops were removed. Metal chemistries were determined using x-ray fluorescence (XRF) on a Rigaku ZSX Primus II, with NIST traceable standards accurate to 0.01 wt%. Carbon and sulfur chemistries were determined using LECO CS444LS while oxygen and nitrogen chemistries were determined on LECO TC436AR. Yttrium was determined by ICP. NIST certified standards were used accurate to 0.0002 wt%. The measured chemistry for HEA1 and HEA2 are reported in Ref. [20].

The sidewalls of the ingots were conditioned on a lathe prior to deformation processing and heat treatment. Each ingot was first given a computationally optimized homogenization heat treatment to reduce residual inhomogeneity to less than ± 1% of nominal: 1100 °C for 1 h + 1180 °C for 3 h + 1200 °C for 5 h. The homogenized ingots were subsequently bagged in stainless steel foil pouches and preheated for 3 hours to provide through ingot thickness heating prior to deformation processing. The “A” heats were hot worked at 800 °C while the “B” heats were hot



worked at 975 °C. Each ingot was forged into a semi-rectangular shape before hot rolling into plate. The final plate thickness was 10 mm. This has been shown to be sufficient to produce a fully wrought-equiaxed microstructure in ingots (~7.5 kg). Note: Specimens for tensile and creep testing were made according to ASTM standards, and tensile and creep testing was performed in accordance with the relevant ASTM test method/standard.

RESULTS AND DISCUSSIONS

Thermodynamic Properties The overall interatomic bond strength of an alloy can be

characterized by the enthalpy of formation (ΔHss). DFT- calculated ΔHss for reported equimolar single-phase HEAs [6] are shown in Figure 1. For FCC and HCP HEAs, the calculated ΔHss are positive, or close to zero. BCC AlNbTiV has the most negative ΔHss at -10.3 kJ/mol, followed by BCC MoNbTaW. Addition of HCP metals such as Hf, Ti and Zr to BCC refractory metals causes a near-zero, or even positive, ΔHss values.

Atomic size difference δ [%]0 1 2 3 4 5 6

Enth

alpy

ΔH

ss [k

J/m

ol]

-10

-5

0

5

10CoCrFeNiCoCrMnNiCoFeMnNiCoCrFeMnNiCoCrFeNiPdAlNbTiVHfNbTaZrMoNbTaVMoNbTaWNbTaTiVNbTaVWNbTiVZrHfNbTaTiZrMoNbTaTiVMoNbTaVWCoFeReRuCoOsReRuMoRhRuPdErGdHoTbYDyGdLuTbTmDyGdLuTbY

Figure 1. DFT-calculated enthalpy of formation of reported single-phase HEAs in the FCC, BCC and HCP structures at zero temperature [6].

Calculated total vibrational and electronic entropies are presented in Ref. [5, 6]. Alloy entropies of mixing ( mixSΔ ) are calculated by subtracting the composition–weighted total entropies of the constituent elements from the entropy of the alloy for total entropy, vibrational entropy, and electronic entropy, respectively. The calculated mixSΔ from various entropy sources for three model HEAs in descending order are: confS >>

vibmixSΔ >> elec

mixSΔ , as shown in Figure 2a [5, 6]. In general,

decreases with deceasing temperature, due to developing chemical short-range order. Note that at room temperature is much lower for MoNbTaW than for the others due to the tendency in forming the ordered BCC (i.e., B2) as revealed by Widom et al. [15, 17].

The vibrational entropies of mixing ( vibSΔ ) approach constant values at temperatures above the Debye temperature (i.e., T ≥ ~400 K), namely, +2.8 J/K/mol, -3.6 J/K/mol and -0.4 J/K/mol for CoCrFeNi, MoNbTaW and CoOsReRu, respectively. This is because the heat capacities approach their classical limit at 3R. In contrast, the calculated elec

mixSΔ values are close to zero. The sum of all entropy sources shows that the total entropy of mixing in descending order for these alloys is: CoCrFeNi > CoOsReRu > MoNbTaW (Fig. 2b).

Temperature [K]0 500 1000 1500 2000

Entro

pies

of m

ixin

g [J

/K/m

ol]

-4

-2

0

2

4

6

8

10

12

ΔSvib-CoCrFeNiΔSelec-CoCrFeNiΔSvib-MoNbTaWΔSelec-MoNbTaWΔSvib-CoOsReRuΔSelec-CoOsReRuSconf-CoCrFeNiSconf-MoNbTaWSconf-CoOsReRu

R*ln4(a)

Temperature [K]400 800 1200 1600 2000

Tota

l ent

ropy

of m

ixin

g [J

/K/m

ol]

2

4

6

8

10

12

14

16

CoCrFeNi (FCC)MoNbTaW (BCC)CoOsReRu (HCP)

ideal configurational entropy(R*ln4)

(b)

Figure 2. Calculated (a) configurational, vibrational, and electronic entropies of mixing, and (b) total entropy of mixing for FCC CoCrFeNi, BCC MoNbTaW, and HCP CoOsReRu [5, 6].

Elastic Properties The comparison in lattice parameters and elastic constants

of select single-phase HEAs between DFT prediction [11, 24-26] and average values is documented in Ref. [6]. Overall, the deviation from the average values is not large. For FCC CoCrFeNi and CoCrFeMnNi, DFT calculations overestimated the lattice parameters [6] compared with the averaged values, presumably because the lattice parameter of BCC Cr with two atoms in the unit cell (which is significantly smaller than that of



FCC Cr) was used for the rule of mixtures (ROM). The distribution of bulk modulus, shear modulus and Poisson’s ratio is close to the equality lines with minor scatter (Figure 3).

Figure 3. Comparison between DFT calculations and the ROM [6]: (a) bulk modulus, (b) shear modulus, and (c) Poisson’s ratio [6]. The data shown are taken from the work by Gao et al. [11], Feng and Widom [24], Tian et al. [25] and Ge et al. [26].

Solid Solution Strengthening Lattice distortion is claimed to be responsible for solid

solution strengthening of HEAs [1], which is due to elastic interactions between dislocations and the local stress field of solute atoms [27, 28]. Accordingly, a simple model is used to estimate the value of solid solution strengthening (∆σ) by considering the differences in atomic size and shear modulus between constituent elements:

∆σ = ( ∑∆σi3/2)

2/3 (5)

∆σi = AGfi4/3ci

2/3 (6) Herein, A is a material-dependent dimensionless constant of the order of 0.04 [29], c is the solute concentration, and the fi parameter can be determined by:

fi = + α22

(7)

where δ = 1G

dGdci

is the atomic modulus and δ = 1r

drdci

is the atomic size mismatch. The value for α is a constant which depends on the type of the mobile dislocation. In general, α is 2-4 for screw dislocations; α ≥ 16 for edge dislocations [29].

The calculated yield strength of the alloy can then be roughly estimated using:

σ0.2cal = σ0.2

mix + ∆σ (8) where σ0.2

mix is the yield strength estimated using ROM. This approach was applied to single BCC refractory HEAs

by Yao et al. [30]. Good agreement was obtained between model prediction and experiments as shown in Figure 4. However, caution should be taken that other factors may also influence yield strength, including chemical inhomogeneity, microstructure inhomogeneity, presence of pores and cracks, residual stress, etc. Nonetheless, this simple model serves as useful guide when predicting yield strength without experimental input.

Figure 4. Yield strength of single BCC refractory HEAs: Predicted (σ0.2cal )

vs experiments (σ0.2exp) at room temperature [30].

Average bulk mo dulus [GPa]

120 140 160 180 200 220 240

Cal

cula

ted

bulk

mod

ulus

[GPa

]

120

140

160

180

200

220

240(a) NbT iVZr [Feng]NbTiVZr [ Tian]CrMoNbV [Feng]HfNbTa Zr [Feng]MoNbTaW [Feng]MoNbTiZr [Tian]MoNbTzTiV [Yao]MoNbTiVZr [Tian]CoCrFeNi [Gao]CoCrFeMnNi [Gao]CrMoTi [Ge]MoNbTi [Ge]MoNbV [Ge]MoTiV [Ge]AlMoNbV [Ge]CrMoTiV [Ge]MoNbTiV [Ge]

Average shear modu lus [GPa]

0 20 40 60 80 100

Calc

ulat

edsh

earm

odu

lus

G [G

Pa]

0

20

40

60

80

100(b)NbTiVZr [Feng]NbTiVZr [Tian]CrMoNbV [Feng]HfNbTaZr [Feng]MoNbTaW [Feng]MoNbTiZr [Tian]MoNbTaTiV [Yao]MoNbTiVZr [Tian]CoCrFeNi [Gao]CoCrFeMnNi [Gao]

0.24 0.28 0.32 0.36 0.40 0.440.24

0.28

0.32

0.36

0.40

0.44NbTiVZr [Feng]NbTiVZr [Tian]CrMoNbV [Feng]HfNbTaZr [Feng]MoNbTaW [Feng]MoNbTiZr [Tian]MoNbTaTiV [Yao]MoNbTiVZr [Tian]CoCrFeNi [Gao]CoCrFeMnNi [Gao]

(c)

Average Poisson's ratio

Cal

cula

ted

Pois

son

'sra

tio



Chemistry The resulting chemistry of the various heats are provided in

Table 1. In general, all the heats met their targeted chemistry. HEA1A picked up a trace of Mn (0.5 wt%) from remnants left in the crucible from the previous melt. The “A” heats contained about 135 ppm S, which is undesirable. As stated earlier, this S comes from the starting materials (Co, Cr, and Mn). The “C” heats have much reduced S with 20 ppm in HEA1C and 60 ppm in HEA2C1. The lower S was a direct result of the use of low S Ni-Co-Cr master alloy material [22]. Note that the use of the master alloy also leads to higher C levels (260-275 ppm vs. 70-80 ppm). The higher C levels come from the Ni-Co-Cr master alloy and are necessary for the efficient removal of S during ESR [22]. The S in HEA2C was further lowered by the addition of Fe40Y to 13 ppm S [23]. However, the excess Y added resulted in 128 ppm Y in heat HEA2C2. Yttrium above about 100 ppm is undesirable since it can lead to incipient melting during hot working. Thus, a third melt of HEA2C was made with the addition of NiO to lower the Y which resulted in HEA2C3 which remained low in S (13 ppm) but Y was reduced to 27 ppm, which is acceptable.

Table 1. Chemistries of the various heats are given below.

HEA Mn Cr Ni Co Fe C N O S Y

wt% ppm 1A 0.5 22.7 25.9 26 24.9 83 67 14 135 NA2A 20.3 19.1 21.5 21.7 17.4 68 64 11 136 NA1C 0.0 22.9 26.4 25.5 25.1 260 60 60 20 NA

2C1 19.7 19.4 21.2 21.5 18.2 200 70 60 60 NA2C2 19.7 19.3 21.3 21.4 18.1 257 85 3 13 1282C3 19.6 19.4 21.3 21.5 18.2 274 84 4 13 27

Microstructure The microstructures of HEA1A and HEA2A are shown in

Figure 5 [20, 21] as substantially single phase and having a mixture of equiaxed recrystallized grains and residual wrought regions. This occurred even though the hot-working temperature of 800 °C is about 0.6-0.7 of the homologous temperature which is sufficient to produce a fully recrystallized microstructure in non-HEA alloys. The grain size of both alloys is less than < 25 μm. As mentioned earlier, heats HEA1C and HEA2C3 were hot worked at 975 °C, which is about 0.74-0.8 of the homologous temperature. This higher hot working temperature resulted in a fully recrystallized, equiaxed microstructure. In addition, the low S and Y levels resulted in microstructures substantially free of secondary phase particles that was observed in the first iteration of these alloys [21].

Figure 6 shows transmission electron microscopy (TEM) images of the HEA1A alloy. The image on the left side shows a low magnification view. It is clear that this material, as well as the others, are single phase. Diffraction imaging verified that the crystal structure was FCC. However, higher magnification

imaging showed clearly that precipitates were present in HEA1A (as well as HEA2A). The “needle-like” precipitate contained Mn and S. Subsequent inspection of other areas of HEA1A and HEA2A indicated a variety of S-rich and Mn-rich precipitates as well as silica (SiO2, approximately) and alumina (Al2O3, approximately). Many of these impurities were very small, i.e., less than 500 nm. The HEA1C and HEA2C variants had much lower S levels so the S-rich compounds in these alloys were less.

Tensile Behavior The tensile properties for HEA1A and HEA2A, i.e., the

initial iteration of these alloys compositions, were first reported in Ref. [21], and are reproduced in Figure 7. In these instances, the microstructures were not fully recovered so yield stress (YS) was relatively high compared to the ultimate tensile strength (UTS) of each respective alloy due to the retained residual strain and associated high dislocation density. This behavior persisted from room temperature through 600 °C. The high work-hardening rate of these two alloys was observed through 600 °C, after which the [YS/UTS] ratio for each alloy began to decrease after yield, and the relative increase in UTS relative to YS was modest [21].

Figure 5. SEM backscatter micrographs: (a) HEA1A and (b) HEA2A, showing equiaxed grains, twins, and sulfide stringer inclusions that are rich in Mn and S [20].



The “C” series iterations for HEA1A and HEA2A were fully recrystallized and recovered. As such, the YS was significantly lower, e.g., HEA 1A at RT had a YS equal to 611 MPa while the YS for HEA 1C was equal to 240 MPa. The [YS/UTS] ratio for HEA1A was 0.77 while for HEA1C it was 0.36. The value of [YS/UTS] for the fully recovered HEA1C variant was typical of austenitic stainless steel, where [YS/UTS] varies from about 0.35 (S30403) to 0.44 (S30451 and S31651) depending on the specific alloy. The same relative change occurred for the HEA2 variants. In this case, HEA2A had a [YS/UTS] ratio equal to 0.75 while the HEA2C3 had a ratio of 0.39.

Figure 6. Several small features were observed in HEA1A using TEM, one of which had a needle-like shape, or possibly a plate-like form, that was imaged edge on. One such feature is arrowed, while another one is enlarged in the image on the right. These precipitates were rich in S and Mn.

Temperature [K]300 400 500 600 700 800 900 1000 1100

Stre

ss (Y

S, U

TS, M

Pa)

0

200

400

600

800

1000

Elon

gatio

n (%

), R

educ

tion

in a

rea

(%)

10

20

30

40

50

60

70

80HEA1: YSHEA1: UTSHEA2: YSHEA2: UTSHEA1: ElongHEA1: RAHEA2: ElongHEA2: RA

Figure 7. Tensile behavior for HEA1A and HEA2A as a function of temperature: Yield stress (YS), ultimate stress (UTS), elongation (Elong), and reduction in area (RA), reproduced from Ref. [21].

Probably the most interesting feature in tensile mechanical behavior was the strength of each alloy at 800 °C. Up through tests at 700 °C the YS and UTS for the “A” variants were higher than the “C” variants. For example, at 700 °C HEA1A had YS and UTS equal to 244 and 346 MPa, respectively. For HEA2C the YS and UTS was 148 and 337 MPa, respectively. While the UTS strength values were close (HEA1A was ∼2.5% greater than HEA1C), the YS values were not (here HEA1C was ∼39% greater). This was consistent for these alloys, i.e., HEA1A and HEA2A relative to HEA1C and HEA2C3, from RT through 700 °C. However, at 800 °C the behavior changed for both HEAs. HEA1A had YS and UTS equal to 103 and 174 MPa, respectively. HEA1C had vales equal to 125 and 213 MPa, respectively, so the relative change in YS and UTS for HEA1A compared to HEA1C was ∼21% for YS and ∼22%. This same trend occurred for the HEA2 variants at roughly the same magnitude.

Figure 8 shows TEM images from the gage section of a tensile specimen tested at room temperature. Whereas the wrought HEA material possessed some twins (see Figure 5) tensile deformation and the resulting increase in dislocation density typical of FCC alloys showed that in addition to dislocation glide, fine twinning also occurred as a primary deformation mechanism. TEM inspection of the gage section of HEA1A tested at 800 °C also showed twinning but in this case the twins were much fewer in number and much larger in their dimensions. The dislocation density was also visibly lower, no doubt due to the extended time at 800 °C during the tensile test.

Figure 8. A lot of fine twinning are present in HEA1A, gage section of tensile tested specimen at RT. The twinning width/spacing often is in the 50-100 nm range. The arrows indicate grain high angel boundaries.

Although not shown here, fractography on the tensile and creep tested specimens were also performed. The fracture surfaces showed a nice distribution of very fine dimples interspersed between areas of larger ones. The larger dimples each had at least one large precipitate in at the base of the dimple. The formation of fine and large dimples supports the high elongations at fracture observed in these alloys.



Creep Behavior Since NETL is interested in these alloys, primarily, as

structural elements, understanding their creep behavior is critical. As such a series of creep experiments have been ongoing at NETL to better understand their creep capability as well as their long-term microstructure stability. HEA3B was examined in detail in creep where experiments were designed to establish the activation energy for creep (i.e., constant stress level but different creep test temperatures) and stress exponent for creep (i.e., constant creep test temperature, chosen as 600 °C, but with different stress levels). While the details of this testing will not be discussed here, one issue arose from inspecting the results. For the first iteration of HEA ingots, it appears that manufacture methodology led to a less than ideal microstructure in terms of thermal microstructure stability. This was noted in the following way: For the activation energy for creep series of tests, since they are performed at the same stress level but at different temperatures, the Larson-Miller Parameter (LMP) should be the same or nearly so within the range of creep testing variability. However, inspection of the data showed that as the duration of the creep test increased, the value of LMP decreased relative to the other creep specimens tested. The decrease was not large but it was consistent, indicating it was other than just random creep variation. Shorter tests, for example, had higher values of LMP. Table 2 provides the numerical values. Figure 9 shows this graphically.

Table 2. Creep screening test for HEA 3 (CoCrFeMnNi with Nb

and C). Test stress was 137.9 MPa.

Temp (°C) LMP Failure Time (h) 650 20.4583 145

637.5 20.4045 255 625 20.3621 469

612.5 20.2946 822 600 20.2616 1,604 600 20.2501 1556

587.5 20.2004 2,959 575 20.1917 6,408

Microstructure inspection using transmission electron

microscopy showed two trends. In the grip section of the HEA3B creep specimen, the general equi-atomic nature of the material was relatively unchanged. That is, there was some minor variation in chemistry around the mean but it was less than 1 to 1.5 atomic percent. However, in the gage section of the creep specimen, there was more inter-diffusion of Cr and Ni relative to Fe, Mn, Co (nearly the same as HEA2 series of alloys but with carbide forming element Nb intentionally added).

For example, in some regions there could be as much as 25 to 30 atomic percent difference from the mean for Cr and about 15 atomic percent difference for Ni. Manganese also showed some variation, usually less than 9 atomic percent with Co and Fe little affected. The inter-diffusion Cr and Ni/Mn leads to the formation of a Cr-rich phase (i.e., high Cr, low Ni), that has been

designated σ [31]. In addition to the σ phase, more normal grains with the equi-atomic chemistry were found as well as some Cr-deficient grains with varying compositions of the other elements.

LMP = (T/1000) x [20 + log t]

18.5 19.0 19.5 20.0 20.5 21.0 21.5

18.5 19.0 19.5 20.0 20.5 21.0 21.5

Stre

ss, M

Pa

50

100

150

200

250

300

HEA3B, Constant TempHEA3B, Constant StressHEA1C, Variable Stress & Temp

Figure 9. LMP data for HEA3B for creep tests performed at constant stress and constant temperature. HEA1C creep tests shown for comparison some of which are still in test.

In addition to the creep testing described, screening creep tests of all manufactured HEAs were performed. Part of the rationale for manufacturing a second iteration of HEAs for HEA1A and HEA2A was to more thoroughly address microstructure instability. Table 3 shows the relative difference in creep life for HEA1A and HEA2A compared to HEA1C and HEA2C3. HEA3B is included for reference. It should be noted that creep testing for HEA1C remains ongoing at 600 °C and 137.9 MPa. Figure 10, however, shows a snapshot of where this testing stands.

Table 3. Relative creep life (hours) for HEA1A and HEA2A relative to HEA1C and HEA2C3 at 600 °C and 137.9 MPa.

Creep life for HEA3B included for reference.

HEA1A HEA1C HEA2A HEA2C3 HEA3B

1,308 10,097* 281 3,435 1,604 1,556

Δ = 10,097 h or 7.72 × Δ = 3,154 h or 12.22 × *test ongoing The results in Table 3 show that changing the manufacturing

process, in this case cleaning up trace impurities in the alloy like S as well as developing a fully recovered and recrystallized microstructure resulted in improvements in creep life for both HEA1C and HEA2C3. From previous testing it is estimated that HEA1C has reached about ½ its creep life at 10,097 h. Elongation at this point is about 12%.

Mechanical behavior for single phase, face centered cubic HEAs behave similarly to 300 series austenitic stainless steels. Fully recovered/recrystallized HEAs have low yield stress, show



a steep work-hardening curve, and possess relatively high ductility. Although not specifically addressed, in uniaxial tensile extension at temperature from room ambient up through 800°C, elongation to failure for HEA1A, HEA2A, HEA1C and HEA2C3 was excellent, with values between 20% (minimum for HEA1A at 600 °C) and 76% (maximum for HEA2C3 at 800°C). Ductility in creep was generally very good with most specimens exhibiting >30% elongation to failure. As in most creep testing there are some specimens that fail at lower elongations. There have only been two tests to date that failed at elongations less than 15%.

FUTURE WORK

As an emerging material, HEAs have shown extraordinary fracture toughness (e.g., FCC CoCrFeMnNi [32]), extraordinary impact toughness (e.g., FCC Al0.1CoCrFeNi [33]), good fatigue performance [34], excellent resistance against irradiation [35] and corrosion [36], etc. In order to balance ductility and strength as typically faced in traditional alloys, alloy strategy has been employed to promote precipitation of nano-scale second phase in an FCC [37] or BCC [38] high-entropy solid solution matrix.

However, in order to be used for commercial structural materials, the long-term microstructure stability of HEAs and their corresponding mechanical properties need to be carefully evaluated in the future work. Thermodynamically speaking, all HEAs hitherto reported in the literature may undergo phase decomposition at intermediate or low temperatures, if given sufficient thermal energy and/or time for diffusion. This is because the entropy contribution to the Gibbs free energy is greatly reduced at lower temperatures. For example, precipitation of the σ phase was observed in the well-known CoCrFeMnNi alloy after annealing at 700 °C for 500 days [31]. On the other hand, to date whether high entropy truly slows down atomic diffusion in HEAs compared to low-entropy alloys is still controversial [39].

CONCLUSIONS

Recent computational and experimental work have reviewed formation, thermodynamics, elasticity, fabrication, and mechanical behavior of HEAs at the NETL. The following conclusions were reached: 1) DFT-calculated enthalpy of formation of twenty-one single-

phase solid solution HEAs are between -10.3 kJ/mol and +8.4 kJ/mol.

2) The configurational entropies are close to their ideal value at high temperatures and then decrease as decreasing temperature due to developing chemical short-range order.

3) Configurational entropy is significantly larger than vibrational entropy of mixing, while electronic entropy of mixing is negligible.

4) At T > 400 K, the calculated vibrational entropy of mixing is +2.8, -3.6 and -0.3 J/K/mol for FCC CoCrFeNi, BCC MoNbTaW and HCP CoOsReRu, respectively.

5) The deviation of elastic properties from the averages estimated using ROM is not big. However, certain elements in certain crystal structures are mechanically unstable (e.g., FCC Cr, BCC Hf/Ti/Zr), and this may lead to biased results when comparing with the averages.

6) A simple model is used to predict the solid solution strengthening of HEAs by considering the differences in atomic size and shear modulus between constituent elements. Good agreement in yield strength between model prediction and experiments is obtained for single-phase BCC refractory HEAs.

7) Large ingots of HEA material have been manufactured using commercial melting techniques. This material has been converted into fully recovered/recrystallized single phase, face centered cubic wrought alloy. Chemical homogeneity is very good, typically <1% from nominal.

8) Tensile mechanical and creep screening tests have been performed. Tensile behavior is good, consistent with face centered cubic materials in terms of strength and ductility.

9) Creep screening of 1st iteration HEAs has shown that temperature stability of the HEA material is good. However, in stressed regions at temperature and for long-term exposures, inter-diffusion of Cr and Ni/Mn occurs, leading to σ phase formation. There are also grains that are clearly Cr-deficient.

10) The 2nd iteration of HEAs HEA 1C and HEA 2C3 have resulted in much better creep life due to better control of trace elements and development of a fully recovered/recrystallized microstructure. Tensile strength properties (YS and UTS) are less than in 1st iteration but decrease less with temperature. YS and UTS at 800 °C is better for 2nd iteration HEAs than for 1st iteration ones.

ACKNOWLEDGMENTS

This work was performed in support of the US Department of Energy’s Fossil Energy Crosscutting Technology Research Program. The Research was executed through NETL Research and Innovation Center’s Advanced Alloy Development Field Work Proposal. Research performed by AECOM Staff was conducted under the RES contract DE-FE-0004000.

DISCLAIMER

This project was funded by the Department of Energy, National Energy Technology Laboratory, an agency of the United States Government, through a support contract with AECOM. Neither the United States Government nor any agency thereof, nor any of their employees, nor AECOM, nor any of their employees, makes any warranty, expressed or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily



constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

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High-Entropy Alloys: Formation and Propertiesproceedings.asmedigitalcollection.asme.org/data/conferences/asmep/... · entropy alloys (< four elements) have been melted using eletroslag