An investigation concerning generalized stacking fault behavior of AlCoxCrFeNi (0.25 ≤ x ≤ 2) high entropy alloys: Insights from first-principles study

An investigation concerning generalized stacking fault behavior of AlCoxCrFeNi (0.25 ≤ x ≤ 2) high entropy alloys: Insights from first-principles study

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Journal Pre-proof An investigation concerning generalized stacking fault behavior of AlCoxCrFeNi (0.25 ≤ x ≤ 2) high entropy alloys: Insights from first-principles study Rouzbeh Mayahi PII:

S0925-8388(19)34174-X

DOI:

https://doi.org/10.1016/j.jallcom.2019.152928

Reference:

JALCOM 152928

To appear in:

Journal of Alloys and Compounds

Received Date: 12 August 2019 Revised Date:

8 October 2019

Accepted Date: 5 November 2019

Please cite this article as: R. Mayahi, An investigation concerning generalized stacking fault behavior of AlCoxCrFeNi (0.25 ≤ x ≤ 2) high entropy alloys: Insights from first-principles study, Journal of Alloys and Compounds (2019), doi: https://doi.org/10.1016/j.jallcom.2019.152928. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier B.V.

An investigation concerning generalized stacking fault behavior of AlCoxCrFeNi (0.25 ≤ x ≤ 2) high entropy alloys: insights from firstprinciples study Rouzbeh Mayahi* Department of Materials Engineering, Karaj Branch, Islamic Azad University, Karaj, Iran *Corresponding author: [email protected], Tel.: +98 9381797165

Abstract In current study, the generalized stacking fault curves for AlCoxCrFeNi (0.25 ≤ x ≤ 2) high entropy alloys have been successfully estimated to gain a better understanding on the deformation behavior (slip and twinning phenomena) utilizing first-principles study based on density functional theory. Through this method, four main generalized stacking fault energy parameters (unstable, intrinsic, unstable twinning and extrinsic stacking fault energies), the rivalry between twinning and dislocation mediated slip (crack tip twinning, grain boundary twinning, and critical twin stress) as well as the Rice-criterion were reported. It was found that dislocation mediated slip and martensitic transformation presumably overcome the plastic deformation as Co content increases. To further reveal the nature of strength and ductility, investigation of density of states and electron density difference were carried out to reflect how increasing Co content affect the strength and ductility. The above mentioned calculations provide a beneficial guideline for designing AlCoCrFeNi HEAs in relation with superior properties (special harmony between strength and ductility). Amidst all high entropy alloys in this study, AlCo2CrFeNi alloy exhibits a superior balance between ductility and strength.

Keywords: High entropy alloy; First-principles method; Generalized stacking fault energy; Virtual crystal approximation; Electronic property.

1

1. Introduction Since the appearance of the first results of high entropy alloys (HEAs) also known as multicomponent alloys in 2004 [1-5], these alloys have been demonstrated outstanding potentials in result of their many excellent properties due to the high entropy effect, extreme lattice distortion effect, cocktail effect and sluggish diffusion effect [6,7]. HEAs are categorized as alloys consisting of at least five key elements with equal or near equal atomic percent in which the content of each element ranges from 5 at. % to 35 at. % in virtue of high and stable mixing entropy [8-10]. Amidst all the unique properties, AlCoCrFeNi HEAs have been found very prosperous to expand new-generation low density structural materials for automobile and aerospace applications [11]. The microstructure and mechanical properties of AlxCoCrFeNi HEAs (x = 0~1.8 in molar ratio) at elevated temperatures prepared by vacuum arc melting and casting methods have been reported [12]. The influence of Al element on the structure of AlxCoCrFeNi HEAs also has been studied in order to investigate the creep behavior [13]. Moreover, the effect of Al/Ni ratio and heat treatment on phase transformation and microstructure of AlxFeCoCrNi2-x (x=0.3,1) HEAs have been investigated [14]. There are more various theoretical and experimental publications on AlCoCrFeNi HEAs [15-30]. Despite the extensive investigations, center of the interests is based on the influence of Al and Ni elements on the large elemental compositions on microstructure and properties of AlCoCrFeNi HEAs. Since there are few comprehensive papers focused on the effect of Co content on deformation behavior of AlCoCrFeNi HEAs, some aspects still need more consideration to obtain promising AlCoCrFeNi HEAs. Furthermore, a good harmony between strength and ductility has been achieved using specific amount of Co content in CoCr(FeNi) HEAs [31]. It is also notable that the HEAs with equal molar components may not always exhibit the best properties [30]. According to the large progresses in computation and simulation based on first-principles over past decades [32], utilizing density functional theory (DFT) [33] has recognized as an advantageous tool for anticipating the properties of a material with specified crystal structure. Through DFT, the correlation between the mechanical and structural properties can be calculated in order to study the disordered alloys and solid solutions [34]. First-principles calculations for systems with multiple key elements are hard to perform. Generally, systems with various elements require supercell models comprising randomly distributed atoms which restrict the possibility of computation. In supercell model, the position 2

of each atom possesses many possibilities. Therefore, first-principles calculations based on DFT need some approximations for computation of properties and interactions between different atoms in disorder configurations [35]. In this case, virtual crystal approximation (VCA) method would be accurate and reliable to predict the electronic structure, magnetism and mechanical properties of alloys [36-38]. Employing VCA is considered as a simple method (which benefits the virtual atoms) for analyzing the behavior of atoms in a system under study. The accuracy of this method has been noticed in several papers [35,36,39-41]. The generalized stacking fault energy (GSFE) is a feasible way on understanding the deformation behavior of materials which governs the rivalry between slip and twinning mechanisms (in a bigger frame plastic deformation) rather than the stacking fault energy (SFE) itself [42]. In spite of this fact that the intrinsic stacking fault energy (ISFE) can be calculated experimentally via transmission electron microscopy (TEM) and x-ray powder diffraction (XRD), the unstable stacking fault energy (USFE) can be defined only through first-principles calculations such as DFT [43]. The GSFE curve analysis has been employed as a favored technique on the study of deformation behaviors in some HEAs [43-45]. However, lately, He et al. [46] expressed that the profound perception of micro-alloying in face centered cubic (FCC) HEAs such as stacking fault energy variations, remains unsatisfactory. In this paper, the VCA model for AlCoxCrFeNi HEAs was used to evaluate the nature of deformation behavior. Furthermore, to perceive the relation between slip and twinning phenomena, GSFE was applied to 13 close-packed (111) atomic layers. Then, USF, ISF, UTF and ESF parameters were calculated. Moreover, the surface energies of (111), (110) and (100) planes in AlCoxCrFeNi HEAs were estimated to reveal the analytical results in detail. Finally, the electron density difference and density of states were calculated in order to study electronic properties in AlCoxCrFeNi HEAs. 2. Theoretical methodology All of the first-principles calculations were accomplished based on DFT utilizing the Cambridge sequential total energy package code (CASTEP) [47]. The Pardew-Burke-Ernzerhof (PBE) [48] in the class of the generalized gradient approximation (GGA) was used as the exchangecorrelation functional. Notably, geometry optimization (minimum energy levels of atoms at different volumes) is a necessary condition for simulation. Therefore, the convergence 3

parameters have been selected when the relaxation of structure was terminated. In this case, the convergence parameters were set as follows: total energy tolerance 10-5 eV/atom, force tolerance 0.03 eV/Å, maximum stress 0.05 GPa, and maximum displacement 0.001 Å. After adequate convergence tests, the Monkhorst-Pack [49] scheme k-points was set as 8×8×8 in the Brillouin zone. Moreover, ultrasoft pseudopotentials were applied and also the plane wave energy cut-off was eventually set as 560 eV. According to selected settings, the error has reached to less than 1% through the convergence of calculated total energy of simulated model. The VCA model which includes a weighted average among various alloying elements in the host Compound, was conducted for all first-principles calculations in order to apply reliable simulation. Additionally, chemical compositions of AlCoCrFeNi HEAs under study are summarized in Table 1. The differences in total energy related to perfect structure and structure with stacking fault have been calculated to model GSFE curve based on first-principles. Fig. 2(a) illustrates the configuration of FCC unit cell with primitive lattice vectors along [111], [110] and [112] directions.

Afterwards, an orthorhombic supercell consists of 13 atomic layers with ABCABCABCABCA

stacking sequence of (111) plane was constructed in virtue of this fact that, mainly, dislocation phenomenon in FCC structures appear in close packed (111) planes. The shearing of structure at (111) plane along [112] slip direction was carried out over two processes for acquiring the GSFE values (Fig. 2(b)). Thus, in the first process, unstable stacking fault (USF) was created at the shear displacement of the upper part along [112] direction from 0.0 to 0.5 with step of 0.1 where Burgers vector (b) is

⁄√6. In the case of intrinsic stacking fault (ISF) with

CABCABABCABCA sequence, the value of shear displacement was increased to 1.0

⁄√6. The

second process was achieved through shifting the lower part with identical distance in opposite direction to form an extrinsic stacking fault (ESF) in sequence of CABCABACABCAB. The GSFE can be calculated with the following equation [42]: = (



)

(1)

is the total energy of supercell with shear displacement, E0 and A represent the total energy of defect free supercell and area of fault plane, respectively. In case of preventing the interactions of atoms in simulated slab with periodic structure, a vacuum spacing of 15 Å was applied. After enough convergence tests on GSFE calculations, the plane wave energy and the Monkhorst-Pack scheme k-points were set as 560 eV and 3×5×1, respectively. 4

3. Results and discussion 3.1. The details of first-principles study and VCA model Among various tested VCA models with different atom occupancy for obtaining a structure with less energy, a FCC primitive cell with 4 atoms has been determined to have more stable structure [50]. Huge amount of computational time due to the low atomic ratio of Co element with minimum size of supercell and difficult determination of the position of Co element in AlCoCrFeNi supercell are two major limitations for creating the conventional AlCoCrFeNi model [51]. In case of investigation the reliability of simulated model, various exchangecorrelation functionals such as GGA-PBE, GGA-PRBE, GGA-PW91 and LDA were applied [43,52-54] as listed in Table 2. It is significant that the values estimated by LDA for lattice constants are lower than that the values resulted from GGA. Performing GGA exchangecorrelation functional has been proposed as an accurate method in comparison with LDA [55], which demonstrates a good agreement with the values obtained from experiments on HEA systems. Yang et al. [51] proposed, GGA-PBE is an advantageous exchange-correlation functional in virtue of structure optimization and energy calculation. The utilized potential V, electronic states D and properties E for virtual atoms (AlαCoβCrαFeαNiα) in VCA model can be obtained by means of weighted average technique in the following equations [51]:

$

=!

= !$

=!

+ #(

+ #($

+

+ #(

+$

+

+

+$

+

+

)

(2)

+$ )

+

)

(3) (4)

The research result indicates that it is entirely possible to develop AlCoCrFeNi HEAs model with VCA method. Therefore, Fig. 1 illustrates FCC unit cell which has derived from VCA method (composition of each atom is identical). In this case, the calculated lattice parameter of 3.5987 Å through VCA model is in a good accordance with 3.591 Å obtained from experimental results in AlCoCrFeNi HEAs [15]. 3.2. The details of generalized stacking fault and surface energies

5

In order to have an accurate anticipation of materials deformation, calculating both USF and ISF energies is vital in consistent with this fact that a material has to prevail the USFE before the lattice shearing happens [43]. The values and curves relevant to GSFE based on first-principles calculations for AlCoxCrFeNi (0.25 ≤ x ≤ 2) HEAs are shown in Table 3 and Fig. 3, respectively. According to the first process which presents in Fig. 3, GSFE curves initiate with a defect free FCC structure at zero shear displacement. As the value of shear displacement along [112] direction increases, the supercell structure would experience an energy barrier at the first

maximum energy point in GSFE curve (energy at unstable SFE,

%& ).

In this case, this energy

barrier is considered as lowest required energy or critical stress for nucleation of partial dislocation. With further shearing, propagation of partial dislocation leads to create intrinsic or stable SFE

%& ,

which referred as the first minimum energy point in GSFE curve. Meanwhile,

SFE formation results in FCC to hexagonal close packed (HCP) phase transformation at room temperature (HCP nucleation in FCC matrix) which also denotes as strain-induced martensitic transformation. The second maximum energy point in GSFE curve corresponds to unstable twinning fault energy

'&

which explains the energy barrier of extrinsic or twinning stacking

fault created from the former ISF [56]. The second minimum energy point defines as extrinsic stacking fault energy

%& .

Additionally, the values of ISF and ESF energies can be calculated

experimentally. As shown in Fig. 3, The USF energy enhances gradually from 98.47 to 143.01 mJ/m2 followed by the increase of Co concentration. It demonstrates that the alloys with higher amount of Co content possess higher resistance to dislocation nucleation. By comparing the intrinsic and extrinsic SFE values, it has been realized that the both experience an enhancement as the Co content increases ( to 35.21 mJ/m2). Furthermore,

%&

%& =

%&

and

-5.58 to 18.06 mJ/m2,

has higher values in contrast with

()*

%& energies %& =

12.48

. It verifies that the ISF

requires less formation energy than ESF. As stated in Ref. [46] the FCC single-phase HEAs have very low or even negative stacking faults energies, which is in good agreement with the results of GSFE curves in current study. Splitting the formation energy from various correlated effects with respect to total energy is considered to be beneficial that validates the accuracy of GSFE calculation based on first-principles over experimental results [42]. Van Swygenhoven et al. [56] confirmed that, selecting SFE as the only criterion for the purpose of identifying deformation mechanisms (twinning and partials dislocation) is inadequate. Thus, the ratio of ISF to USF 6

energies (

%& /

%& )

was used to indicate the trends of full dislocation dissociating to partial

dislocation. Reduction in (

%& /

%& )

ratio leads to a higher tendency of full dislocation

dissociation. In case of propagation of the leading partial dislocations, the trailing partial requires to predominant the energy barrier is associated with the phrase of ( %&

%&

%& .



Hence, the critical stress for trailing partial propagation %& )

[57]. Besides, a higher distinction between

%&

and

enhances the possibility of stacking fault formation readily followed by dissociation of full

dislocations into partials which reflects the greatest potential in case of FCC to HCP transformation once the energy barrier is dominated by an external force. When (

%& /

%& )

ratio

contains higher values, the required energy barrier to form trailing partial is expected to be minuscule. Thus, observing full dislocation is conceivable. In this case, stacking fault formation and FCC to HCP phase transformation are hard to generate. In contrast, when (

%& /

%& )

ratio

have low values, nucleation the trailing partial occurs with higher required energy [56]. Based on the results from Fig. 3, the ratio of (

%& /

%& )

increases as the Co content increases. Since the

ratios of alloys in the current study have low values (-0.0567 to 0.1299), the propensity for partial dislocation mechanism and FCC to HCP transformation is more favorable and expected to be occurred. Additionally, TEM studies confirmed the formation of partial dislocations in AlCoCrFeNi HEAs [58]. Tadmor et al. [59] offered an expression in which the dominance of mechanical twinning at an ideal crack tip can be measured. Through this method, propensity of partial dislocations to form into full dislocations which results in dislocation mediated slip or mechanical twinning is determined. The relative barrier height is defined as follows [57]: ,-)* = -.*

'&



%&

(5)

The relative barrier height values are positive for all alloys (Table 3), indicating that the energy barrier for the formation of unstable twinning ( propagation of partial dislocation (

%& ).

'& )

is larger than the energy barrier for

On the other hand, the prevailing deformation behavior

from dislocation mediated slip to twinning is not affected by Co content variation. The existence of twin propagation whether from partial dislocation or twinning is associated with (

'& /

%& )

ratio [59] which is expressed in Table 3. The mechanical twinning is preferable when the ratio is lower, that means in alloys with lower Co content, twinning occurrence is more likely. To further

7

study, the tendency of FCC metals to form mechanical twinning was investigated in virtue of using Tadmor et al. [59] criterion in the following equation: γ

γ

τ0 = 11.136 − 0.151 γ 678 9 :γ;78 -)*

[6]

;<8

Where 1.136 and 0.151 are universal coefficients for the FCC lattice. A higher propensity of

twinning is attainable by incremental values of τ0 (Fig. 4). The applied stress intensity on nucleation position of partial dislocations is assumed as a distinguishing agent in case of twinning formation for alloys with low positive values of ,

'& %&

and high values of τ0 [42].

Asaro et al. [60] introduced an alternative parameter denoted by τ, which reflects the competition between the propagation of dislocation and mechanical twinning from grain boundary sources, and can be expressed as: τ = =(1 + 2β)

?;78

?;<8

[7]

In this equation, γ %& ⁄γ

%&

= 1 − β. The twinning phenomenon is considered as leading

mechanism compared with partial dislocation if the value of τ becomes greater than 1.

Noticeably, this value for all alloys is greater than 1. Moreover, the value of τ decreases as Co content increases, which indicates a reduction in propensity for twinning phenomenon in alloys with higher Co concentrations (Fig. 4). To have more accurate perspective, according to the importance of stress intensity at nucleation position for twinning formation, Kibey et al. [61] offered a quantity for determination of critical twinning stress based on GSFE values in FCC metals which benefits dislocation-based twin nucleation model. The critical twinning stress (referred to τ@ ' ) determined as follows:

τ@

'

=

A

BC


'&

+

GγH78 Iγ678 G

J−

G

KC
(+γ %& )

[8]

Since in FCC structures, shearing along [112] direction on (111) plane leads to the occurrence of

twinning phenomenon, L'M N is defined as ⁄√6. The precision of this quantity has been showed in some FCC metals [61]. Also interesting to note that the validity of τ@ influence of four GSFE values (γ

such case, decreasing τ@

'

%& , γ %& , γ '& , γ %& ),

'

criterion is due to the

instead of considering merely γ %& value. In

results in increasing the tendency of twinning. As shown in Fig. 4, the 8

values of τ@

'

enhance by increasing the Co content, indicating that in alloys with higher amount

of Co, critical twinning stress requires more energy than the lower Co alloys. Furthermore, according to Table 3 and Fig. 4, the HEAs with higher values of ,

'& %&

demonstrate lower values

of τ0 , suggesting that dislocation mediated slip and martensitic transformation presumably

overcome the plastic deformation for these HEAs [43].

To analyze the effect of Co content on ductility of alloys under study, an alternative criterion was utilized which investigates the rivalry between dislocation formation from crack tip and crack cleavage. The Rice-criterion [57] is expressed in the following equation: $ = 0.3 P

P7

(9)

;78

In which, D is considered as ductility parameter and

%

is the surface energy along [111]

direction (explained and measured in the last part of this section) are listed in Table 3. It should be noted that the value of

%

for estimating D was measured in J/m2. In case of $ > 1, the crack

cleavage energy barrier is greater than the dislocation nucleation energy. Thus, the alloys would

experience ductility behavior. But if $ < 0.3, failure due to crack cleavage occurs rather than dislocation mediated slip [43]. According to Fig. 4 and Table 3, results indicate that HEAs with

lower Co content have lower the Rice-criterion ductility, whilst, higher Co content alloys show an increase in ductility. Beyramali Kivy et al. [43] investigated the effects of micro alloying (Al, Ti, Mo, Cu and Mn) on Rice-criterion ($ > 1 for all alloys) for CoCrFeNi based HEAs.

According to their results, the dominance of ductility was found more likely which are in agreement with the results of this paper. Usually, mechanical twinning occurs in body centered cubic (BCC), HCP crystals and materials with lower symmetry. However, this phenomenon has been reported in FCC materials with low stacking faults. Also, twinning is able to produce required slip systems (five slip systems) in order to develop a general slip deformation in alloys and metals with limited slip systems. Furthermore, Kochmann and Le [62] proposed that when the mechanical twinning and the twin boundaries occur, the space for dislocation propagation and dislocation pile-up becomes narrower. In such case, dislocation motion is blocked by twin boundaries which enhances the strength and ductility of crystal structure. To have a better understanding on surface properties of AlCoCrFeNi HEAs, surface energies of (111), (110) and (100) planes were calculated. Fig. 5 demonstrates the defect free slab and surface slab model, including 10 atomic layers. A vacuum space of 8 Å was placed between 9

atomic layers of surface slab model for avoiding the mutual interactions among atoms at the center of slabs. The top and bottom of slabs have been blocked via enough vacuum space to diminish the effects between top and bottom areas. Moreover, the size and shape of slabs were never altered and geometry optimization (structure relaxation) was performed for all slabs. The surface energy %

=

S7;T8 USVHT8

Where,

%

was measured through the following equation [50,63]:

G %

&

and

(10) W

&

are considered as total energies of new surface and free defect crystal

structures, respectively. Fig. 6 illustrates the surface energies for (111), (110) and (100) planes in AlCoCrFeNi HEAs by varying Co content. It is clearly deduced that the lowest surface energy belongs to close-packed (111) plane due to its high density. As Co content increases, surface energy of all three planes tend to increase. Hwang et al. [64] stated that enhancement in surface energy according to crystal re-orientation leads to prevention of deformation twinning which is in accordance with calculated results in Fig. 3 and Table 3. For the purpose of indicating the most sensitive plane to incremental rate of Co content, the differences of surface energies in (111), (100) and (110) planes were evaluated to be 0.783 J/m2, 0.73 J/m2 and 0.291 J/m2, respectively. In this case, (111) plane is found to be more sensitive to higher amounts of Co content. 3.3. The details of electronic properties To clarify the variations of electronic structure of AlCoxCrFeNi HEAs due to presence of various amount of Co concentrations, the density of states (DOS) was estimated. Fig.7 illustrates the DOS of four AlCo0.25CrFeNi, AlCo0.7CrFeNi, AlCo1.2CrFeNi and AlCo2CrFeNi HEAs. The Fermi energy (Ef) was adjusted to 0 eV and signed by dashed line. Furthermore, based on the results of partial density of states (PDOS), the s-orbital and p-orbital states (localized electrons) possess relatively weak values in entire area with respect to d-orbital state compared to total DOS. Close observation of DOS peaks shows that the d-orbital state (delocalized electrons) is considered as a leading role in total DOS in which its values limits between -3.1 to 2.4. The PDOS values for AlCoCrFeNi HEAs are reduced by increasing Co concentration close to Fermi energy line. In such case, AlCo2CrFeNi HEA shows a smaller value of PDOS compared with the other HEAs which implicates that AlCo2CrFeNi HEA has the most stability with respect to other 10

HEAs [65]. The planar projection of electron density difference for (110) plane in AlCoxCrFeNi HEAs is exhibited in Fig. 8. Calculation of electronic density difference is associated with the measurement of difference among atomic densities in FCC unit cell and the VCA model computation. According to electron density difference map, the positive values reflect the greater values of electron density in comparison with the values acquired from matching of original atomic densities [66]. Based on Fig. 8, the amount of charge-transfer increases progressively by enhancing Co concentrations in AlCoCrFeNi HEAs. In this case, through increasing chargetransfer, the bonding between atoms becomes weaker. In case of poor bonding, it was suggested that HEAs are composed of solid solution structure instead of strong bonding compounds [65]. This result is in consistent with the evaluated Ni element (which is next to Co element in periodic table) variations in AlCrFeCuNi HEAs [30]. Pan et al. [67] stated that utilization of a transition metal with high valence electron concentration (VEC) can be considered as a crucial agent on strong chemical bonding formation. Moreover, they suggested that the improvement of strength and ductility for an alloy is based on highly symmetry crystal structure (cubic system) due to the large number of slip systems and utilization of transition metal with high degree of VEC. In order to gain better ductility behavior in intermetallic materials (which have brittle nature and low ductility), a modified crystal structure analogous to above theory has been reported [68]. Additionally, Chen et al. [69] expressed that the variation of VEC possesses crucial impacts on creating harmony between ductility and strength of materials. The valence electron concentrations for AlCoCrFeNi HEAs can be measured through the following equation [65]: X = ∑X (

Where, X and

X)

(11)

X are atomic percent of alloy component i and number of valence electrons,

respectively. High and low values of VEC in comparison to the average VEC of the matrix (Table 4) lead to ductility and strength, respectively. Furthermore, the valence electronic configurations of Al, Co, Cr, Fe and Ni are 3s2 3p1, 3d7 4s2, 3d5 4s1, 3d6 4s2 and 3d8 4s2, respectively. The estimated values of VEC for alloys with various Co content indicate that with increasing Co concentration, the average VEC of the matrix increases. In such case, alloys with higher amount of Co are shown to have more strength than poor Co content alloys and vice versa. Recently, Wei et al. [31] concluded that due to increasing the amount of Co element in 11

CoCrFeNi based HEAs through the range of 35 at. % to 45 at. %, an exceptional combination of both ductility and strength is attainable. Their results demonstrated that the ductility and strength experience an incremental rate without trade-off. In current paper, according to usage of maximum amount of 33.6 at. % Co, the HEA under study shows a similar behavior which is in good accordance with mentioned previous works. In agreement with cited conclusions, the special combination of ductility and strength in AlCoCrFeNi HEAs with higher degree of Co content is due to FCC crystal structure (highly symmetry system), enhancement of the average VEC of matrix compared with the VEC of Co element accompanying with the higher stacking fault energy value for alloy with higher rate of Co concentration. Meanwhile, improvement of ductility (Rice-criterion) which was calculated previously for alloys with incremental rate of Co content is in line with above suggestions. Moreover, altering the deformation mechanism from mechanical twinning toward FCC to HCP martensitic transformation can be considered as another crucial reason in case of special combination of strength and ductility [31]. It also has been proposed that in Al0.75FeNiCrCo HEAs the strength and ductility reduce as a result of Co content removal which validates the accuracy of calculations in this paper [70]. 4. Conclusions The first-principles calculation based on density functional theory has been successfully performed to investigate the deformation behavior (slip and twinning phenomena) through analyzing the generalized stacking fault curves for AlCoxCrFeNi HEAs with various Co contents. The results of current study are summarized as follows: 1. Through the Investigation of virtual crystal approximation method, it was found that the estimated values for calculating lattice constants by GGA-PBE are higher than that the values resulted from LDA and it also shows a slight deviation from experimental results. 2. Evaluation of the GSFE curves according to the ratios of

%& /

%& ,

the twinnabilities

criterions, anticipated twinning stress and ductility parameter (Rice criterion) for alloys with higher Co contents suggests that dislocation mediated slip and martensitic transformation presumably prevail the plastic deformation. Moreover, enhancement in Co at.% in AlCoxCrFeNi (0.25 ≤ x ≤ 2) HEAs is expected to bring a considerable increase in ductility (from 0.57 to 2.09).

12

3. As Co at.% increases, the surface energy values of (111), (110) and (100) planes of HEAs increase. Furthermore, the differences of surface energy values for (111), (100) and (110) planes were calculated to be 0.783 J/m2, 0.73 J/m2 and 0.291 J/m2, respectively. In such case, (111) plane is found to be more sensitive to incremental rate of Co content. 4. The PDOS value for AlCoCrFeNi HEA is reduced by increasing Co concentrations close to Fermi energy line. Moreover, the amount of charge-transfer increases progressively by enhancing Co content which leads to poor atomic bonding. Additionally, the estimated values of VEC for alloys with various Co content indicate that with increasing Co concentrations (from 0.25 to 2), the average VEC of the matrix increases (from 6.885 to 7.506). Thus, the alloys with higher amount of Co are considered to have more strength than low Co content alloys. Consequently, AlCo2CrFeNi HEA exhibits a superior balance between ductility and strength.

13

References [1] B. Cantor, I.T.H. Chang, P. Knight, A.J.B. Vincent, Microstructural development in equiatomic

multicomponent

alloys,

Mater.

Sci.

Eng.

A.

375

(2004)

213-218.

https://doi.org/10.1016/j.msea.2003.10.257. [2] D.B. Miracle, O.N. Senkov, A critical review of high entropy alloys and related concepts, Acta Mater. 122 (2016) 1-16. https://doi.org/10.1016/j.actamat.2016.08.081. [3] T.K. Chena, T.T. Shunb, J.W. Yehc, M.S. Wonga, Nanostructured nitride films of multielement high-entropy alloys by reactive DC sputtering, Surf. Coat. Technol. 188-189 (2004) 193200. https://doi.org/10.1016/j.surfcoat.2004.08.023. [4] P.K. Huang, J.W. Yeh, T.T. Shun, S.K. Chen, Multi‐principal‐element alloys with improved oxidation and wear resistance for thermal spray coating, Adv. Eng. Mater. 6 (2004) 74-48. https://doi.org/10.1002/adem.200300507. [5] J.W. Yeh, S.K. Chen, J.Y. Gan, S.J. Lin, T.S. Chin, T.T. Shun, C.H. Tsau, S.Y. Chang, Formation of simple crystal structures in Cu-Co-Ni-Cr-Al-Fe-Ti-V alloys with multiprincipal metallic

elements,

Metall.

Mater.

Trans.

A.

35

(2004)

2533-2536.

https://doi.org/10.1007/s11661-006-0234-4. [6] K.Y. Tsai a, M.H. Tsai b, J.W. Yeh, Sluggish diffusion in Co–Cr–Fe–Mn–Ni high-entropy alloys, Acta Mater. 61 (2013) 4887-4897. https://doi.org/10.1016/j.actamat.2013.04.058. [7] S. Huang, W. Li, S. Lu, F. Tian, J. Shen, E. Holmström, L. Vitos, Temperature dependent stacking fault energy of FeCrCoNiMn high entropy alloy, Scripta Mater. 108 (2015) 44-47. https://doi.org/10.1016/j.scriptamat.2015.05.041. [8] J. Li, Q. Fang, B. Liu, Y. Liu, Transformation induced softening and plasticity in high entropy alloys, Acta Mater. 147 (2018) 35-41. https://doi.org/10.1016/j.actamat.2018.01.002. [9] Y.P. Cai, G.J. Wang, Y.J. Ma, Z.H. Cao, X.K. Meng, High hardness dual-phase high entropy alloy thin films produced by interface alloying, Scripta Mater. 162 (2019) 281-285. https://doi.org/10.1016/j.scriptamat.2018.11.004. 14

[10] S. Yadav, A. Kumar, K. Biswas, Wear behavior of high entropy alloys containing soft dispersoids

(Pb,

Bi),

Mater.

Chem.

Phys.

210

(2018)

222-232.

https://doi.org/10.1016/j.matchemphys.2017.06.020. [11] C. Zhang, F. Zhang, H. Diao, M.C. Gao, Z. Tang, J.D. Poplawsky, P.K. Liaw, Understanding phase stability of Al-Co-Cr-Fe-Ni high entropy alloys, Mater. Des. 109 (2016) 425-433. https://doi.org/10.1016/j.matdes.2016.07.073. [12] W.R. Wang, W.L. Wang, J.W. Yeh, Phases, microstructure and mechanical properties of AlxCoCrFeNi high-entropy alloys at elevated temperatures, J. Alloys Compd. 598 (2014) 143152. https://doi.org/10.1016/j.jallcom.2013.11.084. [13] T. Cao, J. Shang, J. Zhao, C. Cheng, R. Wang, H. Wang, The influence of Al elements on the structure and the creep behavior of AlxCoCrFeNi high entropy alloys, Mater. Lett. 164 (2016) 344-347. https://doi.org/10.1016/j.matlet.2015.11.016. [14] H.R. Sistla, J.W. Newkirk, F.F. Liou, Effect of Al/Ni ratio, heat treatment on phase transformations and microstructure of AlxFeCoCrNi2-x (x= 0.3, 1) high entropy alloys, Mater. Des. 81 (2015) 113-121. https://doi.org/10.1016/j.matdes.2015.05.027. [15] Ł. Rogal, Z. Szklarz, P. Bobrowski, D. Kalita, G. Garzeł, A. Tarasek, M. Kot, M. Szlezynger, Microstructure and mechanical properties of Al–Co–Cr–Fe–Ni base high entropy alloys

obtained

using

powder

metallurgy,

Met

Mater

Int.

25

(2019)

930-945.

https://doi.org/10.1007/s12540-018-00236-5. [16] Q. Li, W. Chen, J. Zhong, L. Zhang, Q. Chen, Z.K. Liu, On sluggish diffusion in Fcc Al– Co–Cr–Fe–Ni high-entropy alloys: an experimental and numerical study, metals. 8 (2018) 1-14. https://doi.org/10.3390/met8010016. [17] C. Chen, S. Pang, Y. Cheng, T. Zhang, Microstructure and mechanical properties of Al20xCr20+0.5xFe20Co20Ni20+0.5x high entropy alloys, J. Alloys Compd. 659 (2016) 279-287. https://doi.org/10.1016/j.jallcom.2015.10.258. [18] H.P. Choua, Y.S. Changa, S.K. Chenb, J.W. Yeha, Microstructure, thermophysical and electrical properties in AlxCoCrFeNi (0≤x≤2) high-entropy alloys, Mater. Sci. Eng. B. 163 (2009) 184-189. https://doi.org/10.1016/j.mseb.2009.05.024. 15

[19] Z. Fu, W. Chen, H. Wen, Z. Chen, E.J. Lavernia, Effects of Co and sintering method on microstructure and mechanical behavior of a high-entropy Al0.6NiFeCrCo alloy prepared by powder

metallurgy,

J.

Alloys

Compd.

646

(2015)

175-182.

https://doi.org/10.1016/j.jallcom.2015.04.238. [20] K. Jasiewicz, J. Cieslak, S. Kaprzyk, J. Tobola, Relative crystal stability of AlxFeNiCrCo high entropy alloys from XRD analysis and formation energy calculation, J. Alloys Compd. 648 (2015) 307-312. https://doi.org/10.1016/j.jallcom.2015.06.260. [21] J. Joseph, T. Jarvis, X. Wu, N. Stanford, P. Hodgson, D.M. Fabijanic, Comparative study of the microstructures and mechanical properties of direct laser fabricated and arc-melted AlxCoCrFeNi

High

entropy

alloys,

Mater.

Sci.

Eng.

A.

663

(2015)

184-193.

https://doi.org/10.1016/j.msea.2015.02.072. [22] Y.F. Kaoa, T.J. Chena, S.K. Chenb, J.W. Yeha, Microstructure and mechanical property of as-cast, -homogenized, and-deformed AlxCoCrFeNi (0≤x≤2) high-entropy alloys, J. Alloys Compd. 488 (2009) 57-64. https://doi.org/10.1016/j.jallcom.2009.08.090. [23] Y.F. Kaoa, S.K. Chenb, T.J. Chena, P. C. Chua, J.W. Yeha, S.J. Lina, Electrical, magnetic, and Hall properties of AlxCoCrFeNi high-entropy alloys, J. Alloys Compd. 509 (2011) 16071614. https://doi.org/10.1016/j.jallcom.2010.10.210. [24] N. Kumar, Q. Ying, X. Nie, R.S. Mishra, Z. Tang, P.K. Liaw, R.E. Brennan, K.J. Doherty, K.C. Cho, High strain-rate compressive deformation behavior of the Al0.1CrFeCoNi high entropy alloy, Mater. Des. 86 (2015) 598-602. https://doi.org/10.1016/j.matdes.2015.07.161. [25] C.M. Lin, H.-L. Tsai, Evolution of microstructure, hardness, and corrosion properties of high-entropy

Al0.5CoCrFeNi

alloy,

Intermetallics.

19

(2011)

288-294.

https://doi.org/10.1016/j.intermet.2010.10.008. [26] T.T. Shun, Y.C. Du, Microstructure and tensile behaviors of FCC Al0.3CoCrFeNi high entropy

alloy,

J.

Alloys

Compd.

479

(2009)

157-160.

https://doi.org/10.1016/j.jallcom.2008.12.088. [27] Z. Tang, M.C. Gao, H. Diao, T. Yang, J. Liu, T. Zuo, Y. Zhang, Z. Lu, Y. Cheng, Y. Zhang, K.A. Dahmen, P.K. Liaw, T. Egami, Aluminum alloying effects on lattice types, microstructures, 16

and mechanical behavior of high-entropy alloys systems, JOM. 65 (2013) 1848-1858. https://doi.org/10.1007/s11837-013-0776-z. [28] Q. Tang, Y. Huang, H. Cheng, X. Liao, T.G. Langdon, P. Dai, The effect of grain size on the annealing-induced phase transformation in an Al0.3CoCrFeNi high entropy alloy, Mater. Des. 105 (2016) 381-385. https://doi.org/10.1016/j.matdes.2016.05.079. [29] T. Yang, S. Xia, S. Liu, C. Wang, S. Liu, Y. Zhang, J. Xue, S. Yan, Y. Wang, Effects of Al addition on microstructure and mechanical properties of AlxCoCrFeNi high-entropy alloy, Mater. Sci. Eng. A. 648 (2015) 15-22. https://doi.org/10.1016/j.msea.2015.09.034. [30] P. Jinhong, P. Ye, Z. Hui, Z. Lu, Microstructure and properties of AlCrFeCuNix (0.6≤x≤1.4)

high-entropy

alloys,

Mater.

Sci.

Eng.

A.

534

(2012)

228-233.

https://doi.org/10.1016/j.msea.2011.11.063. [31] D. Wei, X. Li, W. Heng, Y. Koizumi, F. He, W. Choi, B. Lee, H.S. Kim, H. Kato, A. Chiba, Novel Co-rich high entropy alloys with superior tensile properties, Mater. Res. Lett. 7 (2018) 8288. https://doi.org/10.1080/21663831.2018.1553803. [32] G. Kresse, J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using

a

plane-wave

basis

set,

Phys.

Rev.

B.

54

(1996)

11169-11186.

https://doi.org/10.1103/PhysRevB.54.11169. [33] P. Hohenberg, W. Kohn, Inhomogeneous Electron Gas, Phys. Rev. 136 (1964) B864-B871. https://doi.org/10.1103/PhysRev.136.B864. [34] W. Kohn, L. J. Sham, Self-consistent equations including exchange and correlation effects, Phys. Rev. 140 (1965) A1133-A1138. https://doi.org/10.1103/PhysRev.140.A1133. [35] L. Bellaiche, D. Vanderbilt, Virtual crystal approximation revisited: Application to dielectric and piezoelectric properties of perovskites, Phys. Rev. B. 61 (2000) 7877-7882. https://doi.org/10.1103/PhysRevB.61.7877. [36] P.H. Lee, Z.R. Xiao, K.L. Chen, Y. Chen, S.W. Kao, T.S. Chin, The magnetism of Fe (1-x) Cox

B

alloys:

First

principle

calculations,

https://doi.org/10.1016/j.physb.2009.03.029. 17

Physica

B.

404

(2009)

1989-1992.

[37] X. Zhang, J. Liu, Y. Liu, G. Sang, T. Gao, Structural, electronic, dynamic and thermodynamic properties of Zr1-xHfxH2 hydride alloys: A first-principles study based on the virtual

crystal

approximation,

Physica

B.

550

(2018)

217-224.

https://doi.org/10.1016/j.physb.2018.08.030. [38] N.J Ramer, A.M. Rappe, Application of a new virtual crystal approach for the study of disordered

perovskites,

J.

Phys.

Chem.

Solids.

61

(2000)

315-320.

https://doi.org/10.1016/S0022-3697(99)00300-5. [39] S. Bacha, A. Bechiri, F. Benmakhlouf, H. Allouache, N. Bouarissa, Electronic band structure

of

InPxSb1−x

alloys,

Physica

B.

406

(2011)

2021-2024.

https://doi.org/10.1016/j.physb.2011.03.010. [40] B.Winkler, C. Pickard, V. Milman, Applicability of a quantum mechanical virtual crystal approximation'

to

study

Al/Si-disorder,

Chem.

Phys.

Lett.

362

(2002)

266-270.

https://doi.org/10.1016/S0009-2614(02)01029-1. [41] H. Jieqiong, X. Ming, Y. Youcai, Z. Jiming, L. Manmen, C. Yongtai, Virtual Crystal Approximation of Pd-Ru-Zr System, Rare. Metal. Mat. Eng. 44 (2015) 2976-2981. https://doi.org/10.1016/S1875-5372(16)60033-4. [42] T.L. Achmad, W. Fu, H. Chen, C. Zhang, Z.G. Yang, First-principles calculations of generalized-stacking-fault-energy of Co-based alloys, Comput. Mater. Sci. 121 (2016) 86-96. http://dx.doi.org/10.1016/j.commatsci.2016.04.031. [43] M. Beyramali Kivy, M. Asle Zaeem, Generalized stacking fault energies, ductilities, and twinnabilities of CoCrFeNi-based face-centered cubic high entropy alloys, Scripta Mater. 139 (2017) 83-86. https://doi.org/10.1016/j.scriptamat.2017.06.014. [44] S. Huanga, W. Li, S. Lu, F. Tian, J. Shen, E. Holmström, L.Vitos, Temperature dependent stacking fault energy of FeCrCoNiMn high entropy alloy, Scripta Mater. 108 (2015) 44-47. https://doi.org/10.1016/j.scriptamat.2015.05.041. [45] J. Liu, C. Chen, Y.Xu, S. Wu, G. Wang, H. Wang, Y. Fang, L. Meng, Deformation twinning behaviors of the low stacking fault energy high-entropy alloy: An in-situ TEM study, Scripta Mater. 137 (2017) 9-12. https://doi.org/10.1016/j.scriptamat.2017.05.001. 18

[46] F. He, Z Wang, B. Han, Q. Wu, D. Chen, J. Li, J. Wang, C.T. Liu, J.J. Kai, Solid solubility, precipitates, and stacking fault energy of micro-alloyed CoCrFeNi high entropy alloys, J. Alloys Compd. 769 (2018) 490-502. https://doi.org/10.1016/j.jallcom.2018.07.336. [47] M.D. Segall, P.J.D. Lindan, M.J. Probert, C.J. Pickard, P.J. Hasnip, S.J. Clark, M.C. Payne, First-principles simulation: ideas, illustrations and the CASTEP code, J. Phys.: Condens. Matter. 14 (2002) 2717-2744. https://doi.org/10.1088/0953-8984/14/11/301. [48] J.P. Perdew, K. Burke, M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77 (1996) 3865-3868. https://doi.org/10.1103/PhysRevLett.77.3865. [49] H.J. Monkhorst, J.D. Pack, Special points for Brillouin-zone integrations, Phys. Lett. B. 13 (1976) 5188-5192. https://doi.org/10.1103/PhysRevB.13.5188. [50] Y. Udagawa, M. Yamaguchi, H. Abe, N. Sekimura, T. Fuketa, Ab initio study on plane defects in zirconium–hydrogen solid solution and zirconium hydride, Acta Mater. 58 (2010) 3927-3938. https://doi.org/10.1016/j.actamat.2010.03.034. [51] J. Yang, Y. Wang, J. Huang, W. Wang, Z. Ye, S. Chen, Y. Zhao, First-principles calculations on interface structure and fracture characteristic of TiC/TiZrC nano-multilayer film based

on

virtual

crystal

approximation,

J.

Alloys

Compd.

775

(2018)

211-223.

https://doi.org/10.1016/j.jallcom.2018.05.009. [52] X. Li, D.L. Irving, L. Vitos, First-principles investigation of the micromechanical properties of

fcc-hcp

polymorphic

high-entropy

alloys,

Sci.

Rep.

8

(2018)

1-8.

https://doi.org/10.1038/s41598-018-29588-z. [53] T. Borkar B. Gwalani, D. Choudhuri, C.V. Mikler, C.J. Yannetta, X. Chen, R.V. Ramanujan, M.J. Styles, M.A. Gibson, R. Banerjee, A combinatorial assessment of AlxCrCuFeNi2 (0 < x < 1.5) complex concentrated alloys: Microstructure, microhardness, and magnetic

properties,

Acta

Mater.

116

(2016)

63-76.

https://doi.org/10.1016/j.actamat.2016.06.025. [54] N.D. Stepanova, D.G. Shaysultanova, M.A. Tikhonovskyb, S.V. Zherebtsova, Structure and high temperature mechanical properties of novel nonequiatomic Fe-(Co, Mn)-Cr-Ni-Al-(Ti) high

19

entropy

alloys,

Intermetallics.

102

(2018)

140-151.

https://doi.org/10.1016/j.intermet.2018.09.010. [55] S. Ghosh, Calculation of phonon spectrum and elastic constants of FePd intermetallics: Performance

of

LDA

and

GGA,

Intermetallics.

17

(2009)

708-713.

https://doi.org/10.1016/j.intermet.2009.02.011. [56] H.V. Swygenhoven, P.M. Derlet, A.G. Frøseth, Stacking fault energies and slip in nanocrystalline metals, Nat. Mater. 3 (2004) 399-403. https://doi.org/10.1038/nmat1136. [57] J.R. Rice, Dislocation nucleation from a crack tip an analysis based on the peierls concept, J. Mech. Phys. Solid. 40 (1992) 239-271. https://doi.org/10.1016/S0022-5096(05)80012-2. [58] X. Gao, Y. Lu, B. Zhang, N. Liang, G. Wu, G. Sha, J. Liu, Y. Zhao, Microstructural origins of high strength and high ductility in an AlCoCrFeNi2.1 eutectic high-entropy alloy, Acta Mater. 141 (2017) 59-66. http://dx.doi.org/10.1016/j.actamat.2017.07.041. [59] E.B. Tadmor, S. Hai, A Peierls criterion for the onset of deformation twinning at a crack tip, J. Mech. Phys. Solid. 51 (2003) 765-793. https://doi.org/10.1016/S0022-5096(03)00005-X. [60] R.J. Asaro, S. Suresh, Mechanistic models for the activation volume and rate sensitivity in metals with nanocrystalline grains and nano-scale twins, Acta Mater. 53 (2005) 3369-3382. https://doi.org/10.1016/j.actamat.2005.03.047. [61] S. Kibey, J.B. Liu, D.D. Johnson, H. Sehitoglu, Predicting twinning stress in fcc metals: linking twin-energy pathways to twin nucleation, Acta Mater. 55 (2007) 6843-6851. https://doi.org/10.1016/j.actamat.2007.08.042. [62] D.M. Kochmann, K.C. Le, A continuum model for initiation and evolution of deformation twinning, J. Mech. Phys. Solid. 57 (2009) 987-1002. https://doi.org/10.1016/j.jmps.2009.03.001. [63] Q. Zhao, J. Li, Q. Fang, H. Feng, Effect of Al solute concentration on mechanical properties of AlxFeCuCrNi highentropy alloys: A first-principles study, Physica B. 566 (2019) 30-37. https://doi.org/10.1016/j.physb.2019.04.025.

20

[64] B. Hwang, M. Kang, S. Lee, C.R. Weinberger, P. Loya, J. Lou, S. Ho Oh, B. Kim, S. Min Han, Effect of Surface Energy on Size-Dependent Deformation Twinning of Defect-Free Au Nanowires, Nanoscale. 38 (2015) 15657-15664. https://doi.org/ 10.1039/C5NR03902A. [65] Y. Mu, H. Liu, Y. Liu, X. Zhang, Y. Jiang, T. Dong, An ab initio and experimental studies of the structure, mechanical parameters and state density on the refractory high-entropy alloy systems, J. Alloys Compd. 714 (2017) 668-680. http://dx.doi.org/10.1016/j.jallcom.2017.04.237. [66] Z.S. Nong, J.C. Zhu, Z.H. Lai, Y. Liu, Structure and stability of as cast AlCrFeMnNiTi high entropy

alloy,

Mater.

Sci.

Technol.

31

(2015)

1153-1158.

http://dx.doi.org/10.1179/1743284714Y.0000000741. [67] Y. Pan, W.M. Guan, Probing the balance between ductility and strength: transition metal silicides,

Phys.

Chem.

Chem.

Phys.

19

(2017)

19427-19433.

https://doi.org/

10.1039/C7CP03182C. [68] Z.B. Jiao, J.H. Luan, C.T. Liu, Strategies for improving ductility of ordered intermetallics, Prog Nat Sci-Mater. 26 (2016) 1-12. https://doi.org/10.1016/j.pnsc.2016.01.014. [69] R. Chen, G. Qin, H. Zheng, L. Wang, Y. Su, Y. Chiu, H. Ding, J. Guo, H. Fu, Composition design of high entropy alloys using the valence electron concentration to balance strength and ductility, Acta Mater. 144 (2018) 129-137. https://doi.org/10.1016/j.actamat.2017.10.058. [70] Z. Chen, W. Chen, B. Wu, X. Cao, L. Liu, Z. Fu, Effects of CO and Ti on microstructure and mechanical behavior of Al0.75FeNiCrCo High entropy alloy prepared by mechanical alloying and

spark

plasma

sintering,

Mater.

Sci.

https://doi.org/10.1016/j.msea.2015.08.056.

21

Eng.

A.

648

(2018)

217-224.

Figure captions

Fig. 1 The VCA model for AlCoxCrFeNi HEAs with various Co concentrations (0.25 ≤ x ≤ 2). Fig. 2 (a) The atomic configuration of utilized FCC cell with stacking sequence A, B and C in light green, red and dark green, respectively. (b) The supercell consisting 13 atomic layers of (111) plane. The green atoms indicate mixed atoms in VCA model, while the purple atoms demonstrate a group of atoms which imposed a relative translation along [112] direction to create USF, ISF and ESF with 15Å vacuum space to prevent mutual interactions between atoms. Fig. 3 The GSFE curves calculated based on first-principles method for AlCoCrFeNi HEAs. Fig. 4 The estimated ratios of

%& /

%& ,

twinnability for crack tip twinning [0 , twinnability for

grain boundary twinning [, the Rice-criterion for ductility D and anticipated critical stress [@ for AlCoCrFeNi HEAs.

'

Fig. 5 The free defect slab with 10 atomic layers with adequate vacuum space (a, b and c) and surface slab with vacuum space of 8Å at the center (d, e and f) for (111), (110) and (100) planes. (The vacuums which inserted to top and bottom of slabs are identical for all slabs, the variations in atomic distance in various crystal planes lead to change slabs configurations). Fig. 6 Surface energies of (111), (110) and (100) planes in AlCoCrFeNi HEAs. Fig. 7 Total and partial density of states due to incremental rates of Co content in AlCoxCrFeNi HEAs (x=0.25, 0.7, 1.2 and 2). Fig. 8 The planar projection of electron density difference of (110) plane in AlCoxCrFeNi HEAs (x=0.25, 0.7, 1.2 and 2).

22

Table 1 Chemical compositions (in at.%) of AlCoxCrFeNi HEAs. HEAs AlCo0.25CrFeNi AlCo0.50CrFeNi AlCo0.70CrFeNi AlCo1.00CrFeNi AlCo1.20CrFeNi AlCo1.50CrFeNi AlCo1.70CrFeNi AlCo2.00CrFeNi

Al (at.%) 23.5 22.2 21.3 20.0 19.2 18.1 17.5 16.6

Co (at.%) 6.00 11.2 14.8 20.0 23.2 27.6 30.0 33.6

Cr (at.%) 23.5 22.2 21.3 20.0 19.2 18.1 17.5 16.6

Fe (at.%) 23.5 22.2 21.3 20.0 19.2 18.1 17.5 16.6

Ni (at.%) 23.5 22.2 21.3 20.0 19.2 18.1 17.5 16.6

Table 2 Computed lattice parameters (in Å) of HEAs in VCA model with various exchange-correlation functional, compared with available experimental results. HEAs (in fcc phase) CoCrFeNiMn CoCrFeNi AlCrCuFeNi2 Al23Cr18Cu16Fe16Ni27 Al21Cr19Cu15Fe16Ni29 Fe35Co20Cr17Ni12Al12Ti4 Fe36Mn21Cr18Ni15Al10 Fe36Co21Cr18Ni15Al10 * Relative Error

Expt. 3.590 [43] 3.575 [52] 3.618 [53] 3.636 [53] 3.623 [53] 3.588 [54] 3.621 [54] 3.591 [54]

GGAPBE 3.604 3.589 3.619 3.622 3.612 3.575 3.609 3.587

RE* (%) 0.38 0.39 0.02 0.38 0.30 0.36 0.33 0.11

GGAPRBE 3.648 3.601 3.660 3.598 3.640 3.611 3.649 3.637

RE (%) 1.61 0.72 1.16 1.04 0.46 0.64 0.77 1.28

GGAPW91 3.533 3.548 3.559 3.582 3.593 3.565 3.539 3.560

RE (%) 1.58 0.75 1.67 1.48 0.82 0.64 2.26 0.86

LDA 3.414 3.484 3.509 3.525 3.586 3.495 3.443 3.512

RE (%) 4.90 2.54 3.01 3.05 1.02 2.59 4.91 2.19

Table 3 First-principles calculated unstable (mJ/m2), stable (mJ/m2), unstable twinning (mJ/m2), 2 ⁄ twinning (mJ/m ), energy barrier height , parameter, Rice-criterion D and surface 2 energies of (111), (110) and (100) planes (J/m ) in AlCoxCrFeNi HEAs. HEAs (x) 0.25 0.50 0.70 1.00 1.20 1.50 1.70 2.00

98.47 104.46 109.91 118.82 123.97 124.40 132.68 139.01

-5.58 -2.05 1.20 4.33 10.28 13.41 16.55 18.06

127.79 135.96 143.68 154.84 161.33 168.11 179.67 195.48

12.48 19.05 22.27 24.31 29.46 30.32 33.45 35.21

29.32 31.49 33.76 36.02 37.36 43.71 46.99 56.47



D

1.297 1.301 1.301 1.303 1.307 1.351 1.354 1.406

0.577 0.859 1.079 1.404 1.607 1.938 1.979 2.099

(111) 0.189 0.299 0.395 0.556 0.664 0.803 0.875 0.972

(100) 0.367 0.490 0.595 0.756 0.852 0.971 1.026 1.097

(110) 0.836 0.878 0.913 0.971 1.008 1.059 1.087 1.127

Table 4 The calculated valence electron concentrations (VEC) for AlCoxCrFeNi HEAs. HEAs (x)

0.25

0.50

0.70

1.00

1.20

1.50

1.70

2.00

VEC

6.885

7.002

7.083

7.2

7.272

7.371

7.425

7.506

Highlights



Effects of Co content on slip and twinning phenomena were studied.



Dislocation mediated slip prevailed the plastic deformation in Co-rich alloys.



The ductility (Rice criterion) increased in alloys with higher Co at.%.



The high VEC of matrix increased strength in alloys with higher Co at.%.



AlCo2CrFeNi alloy showed an exceptional combination of both ductility and strength.

Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: