Effects of alloying elements concentrations and temperatures on the stacking fault energies of Co-based alloys by computational thermodynamic approach and first-principles calculations

Accepted Manuscript Effects of alloying elements concentrations and temperatures on the stacking fault energies of Co-based alloys by computational thermodynamic approach and firstprinciples calculations Tria Laksana Achmad, Wenxiang Fu, Hao Chen, Chi Zhang, Zhi-Gang Yang PII:

S0925-8388(16)33222-4

DOI:

10.1016/j.jallcom.2016.10.113

Reference:

JALCOM 39280

To appear in:

Journal of Alloys and Compounds

Received Date: 20 July 2016 Revised Date:

11 October 2016

Accepted Date: 13 October 2016

Please cite this article as: T.L. Achmad, W. Fu, H. Chen, C. Zhang, Z.-G. Yang, Effects of alloying elements concentrations and temperatures on the stacking fault energies of Co-based alloys by computational thermodynamic approach and first-principles calculations, Journal of Alloys and Compounds (2016), doi: 10.1016/j.jallcom.2016.10.113. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. 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.

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ACCEPTED MANUSCRIPT

ACCEPTED MANUSCRIPT Effects of alloying elements concentrations and temperatures on the stacking fault energies of Co-based alloys by computational thermodynamic approach and firstprinciples calculations Tria Laksana Achmada,b, Wenxiang Fua, Hao Chena, Chi Zhanga, Zhi-Gang Yanga,* a

Key Laboratory of Advanced Materials, Ministry of Education, School of Materials Science

b

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and Engineering, Tsinghua University, Beijing 100084, PR China

Department of Metallurgical Engineering, Institute Technology of Bandung, Bandung 40132, Indonesia

*

address: [email protected] (Z.-G. Yang).

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Abstract

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Corresponding author. Tel.: +86-10-62795031, 62783848; fax: +86-10-62771160. E-mail

The atomic-scale microstructural and compositional modification of materials are one of the most promising developments of modern materials science. In the present study, we investigate the stacking fault energy (SFE) variations of binary Co-based alloys with different alloying elements (Cr, W, Mo, Ni, Mn, Al and Fe) and concentrations (from 0 to 20 at.%)

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over a broad range of temperatures (from 0 to 1000 K) by computational thermodynamic approach and first-principles density-functional-theory (DFT) calculations combined with quasi-harmonic approximation (QHA). Our work presents a fundamental understanding of the theoretical SFE calculation and the deviations involved in computational thermodynamic

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approach and first-principles calculations systematically for the first time. It concludes that the SFEs of binary Co-based alloys are increased as the increased of temperature, Ni, Mn, Al

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and Fe concentrations while the SFEs are decreased as the increased of Cr, W and Mo concentrations qualitatively. Quantitatively, the SFE differences of these two methods are relatively small (lower than 27 mJ/m2). The SFE variations can be explained regarding the charge density distributions and the atomic bonding. These results also highlight the critical role of Suzuki effect and the key for the SFE variations is the alloying elements only in the vicinity of the fault plane. Keywords: stacking fault energy (SFE); Cobalt-based alloys; computational thermodynamic approach; first-principles density-functional-theory (DFT); quasi-harmonic approximation (QHA). 1

ACCEPTED MANUSCRIPT 1. Introduction Stacking fault (SF) is an important type of planar defect that indicates the interruption in the atomic stacking sequence of a crystal structure induced by shear deformation [1,2]. SFE is a critical intrinsic material parameter that significantly affects the plastic deformation behavior and mechanical properties. Low-SFE materials, like Co-based alloys, enable the

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formations of high densities of stacking faults and twins, which promote partial dislocation accumulation [1,2]. The formation of the stacking fault in fcc crystal on a close-packed (111) stacking plane ABCABC produces the hcp nucleus stacking BCBC in the fcc matrix, which

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is regarded as the beginning of fcc to hcp phase transformation [3]. The fcc to hcp phase transformation of Co-based alloys occurs during plastic deformation at room temperature by

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shear in the a/6[11-2] slip system on (111) planes (a is the lattice constant), also referred as strain-induced martensitic transformation (SIMT). A lower value of SFE results in enhancing both the ductility and fracture toughness without compromising high strengths and also higher strain-hardening and solid solution strengthening coefficients [2,4]. The SFE itself depends on two important metallurgical and thermodynamic parameters;

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composition of the alloys and temperatures. Therefore, SFE can be theoretically modeled as a thermodynamic function based on Olson and Cohen [5] approach, consider that stacking faults (SFs) formation is equivalent to the transformation of a thin plate of fcc to hcp crystal structure. Many researchers use this method to calculate the intrinsic SFE in Fe-based alloys

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[6,7,8] and binary Co-based alloys [9,10]. However, Geissler et. al [11] give critics and ambiguities about thermodynamic methods to model the SFE and its relation to the formation

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of hexagonal ε-martensite in austenitic Transformation and/or Twinning Induced Plasticity (TRIP/TWIP) steels. For example; the inclusion of interfacial energy
/ in the order of 5 – 27 mJ/m2 is inconsistent with the physics of an interface for describing an intrinsic SF, the data as used from computational thermodynamic approach includes extrapolations of mixing parameters to low temperatures are not very reliable. Another method is first-principles density functional theory (DFT) to calculate the intrinsic or stable SFE γsf as a function of alloying elements and temperature that have been applied in pure fcc Ni [12] and dilute Nibase superalloys [1]. Even though with the developments in theoretical calculations of SFE,

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ACCEPTED MANUSCRIPT SFE modeling for Co-based alloys still insufficient. To satisfy this concern, we investigate the intrinsic or stable SFE of binary Co-based alloys by both thermodynamic and firstprinciples method, then compare with available experimental results in literature. The main idea of alloy design is to reduce costs and time required by the traditional (trial and error) method, then finding a new way to develop the efficiency of the alloy design

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is necessary. Experimentally, the value of SFE is hard to measure accurately just by traditional experimental methods, such as transmission electron microscopy (TEM) and Xray Diffraction (XRD) methods [1]. Some authors measured the SFE through TEM

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observations for pure Co and some Co-based alloys under various temperatures [13,14,15]. They reported that increasing temperature will increase the SFE of pure fcc Co [13], Co-8Fe,

decreasing

trends

of

SFE

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Co-33Ni, Co-35Ni and Co-30Ni-15Cr [14,15]. In theoretical calculations, both increasing and with

increasing

temperature

were

observed

[1,6,9,10,12,13,14,15,16,17]. This distinct tendency is due to various influences at high temperatures such as elastic constants, the composition of the alloy, and impurity of dislocations [1]. To deeply understand the SFE under high temperature, the investigation of

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temperature-dependent Gibbs free energy, lattice constants and thermodynamic properties are essential. Through the advance development of the computing techniques, the efficient method for predicting the SFE at finite temperature is the first-principles calculations. Many researchers used the quasi-harmonic approach (QHA) [18] to calculating the effect of

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temperature on the intrinsic SFE of fcc Ni [12,17], Ni-based superalloys [1], and the generalized-stacking-fault-energy of NiAl and FeAl [16].

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It is a common practice to modify SFE by the useful alloying element addition. Certain alloying elements could significantly lower the SFE of Co-based alloys from the experiments, such as Cr content in Co-30Ni-15Cr [14], meanwhile another alloying elements like Ni and Fe increase the SFE in binary Co-Ni and Co-Fe alloys, respectively [13,15]. From computational thermodynamic approach, Ishida [7] has calculated the effect of alloying elements on the SFE of cobalt in dilute solution at 700 K, meanwhile Lee et al. [10] calculated the temperature dependences of SFE in pure Co and Co–Cr–Mo–N alloy. Suzuki et. al [19] revealed that alloying elements tend to segregate to stacking faults. Then, the SFE decrease as the alloying elements segregates to such a high concentration. The rapidity of 3

ACCEPTED MANUSCRIPT Suzuki segregation could be improved significantly during deformation at high temperature [20]. Our previous study has been successfully calculated the generalizedstacking-fault-energy (GSFE) for pure Co and Co-9 at% X solid-solutions alloys at 0 K [21]. In the present study, we investigate the change of the SFE of binary Co-based alloys with different alloying elements (Cr, W, Mo, Ni, Mn, Al and Fe) and concentrations (from 0 to 20

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at.%) over a broad range of temperatures (from 0 to 1000 K). The present study would be useful for the further experimental study of high-temperature SFE and for the design of suitable alloys. To further reveal the reasons for the variations of SFE with alloying

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concentrations and temperature, we investigate the electronic structures of pure Co and binary Co-based alloys regarding the charge density difference distributions and the density

the SFE variations. 2. Computational Methodology

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of states (DOS). The result also highlights the critical role of the Suzuki effect and the key for

2.1. Computational thermodynamic approach

Fig. 1 illustrates the stacking sequence of close-packed (111) planes in fcc crystal that

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the normal stacking is a succession of planes ABCABCA. The motion of a single Shockley partial dislocation on a close-packed plane produces a metastable hcp nucleus stacking BCBC in the fcc matrix (Fig. 1), called intrinsic stacking fault (ISF). It is already prevalent to model the SFE with an equilibrium thermodynamic as proposed by Olson and Cohen [5], that

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equivalent to the transformation of a thin plate (n layers) of γ-fcc to ε-hcp crystal structure ∆ → , separated from fcc matrix by a two interfaces
/ [5,6,7,8,11]. The formulation to

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calculate the intrinsic SFE is:  = 2 ∆ → + 2
/

(1)

where γsf is the intrinsic SFE (mJ/m2) of the fault, ∆ → is the Gibbs free energy difference of γ-fcc to ε-hcp phase transformation, and
/ is the interfacial energy per unit area of the phase boundary. The interfacial energy for binary Co-based alloys in the present study was assumed to be a constant value (
/ = 7.5 mJ/m2). The reason for this value and discussion about the interfacial energy are presented in section 3.1. The flowchart in Fig. 2 shows a summary of the equations of the present calculations.

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Fig. 1. Illustration of the intrinsic stacking fault (ISF) formation in fcc crystal and the model of the intrinsic SFE γsf calculation by computational thermodynamic approach. Stacking

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sequence A, B and C are colored in light blue, red and dark blue atoms, respectively.

Fig. 2. The flowchart of intrinsic SFE calculations by computational thermodynamic approach. The lattice parameter a was assumed to be independent of temperature and concentration with the constant value 3.544 Å from the experimental measurement of pure fcc Co at 20 0C in the literature [22]. The thermodynamic data required for the calculations were taken from the literature, mainly from the tables published by the Scientific Group 5

ACCEPTED MANUSCRIPT Thermodata Europe (SGTE) [23], and from publications of computational thermodynamic approach of phase equilibria studies (CALPHAD) [24,25,26,27,28,29]. Table 1 summarizes the thermodynamic data used in this study. →

Table 1. Thermodynamic function describing the change in the Gibbs free energy ∆

of

→

coefficients  Parameter

Thermodynamic function (J/mol)

→ ∆

-427.59 + 0.615T

→ ∆

-2846 - 0.163T

→ ∆

-4550 - 0.629T

1046 + 1.255T

→

-1000 + 1.123T

→

-2243.38 - 4.309T

→ !

2800 + 5T

∆ ∆

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→

∆

[23]

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-3650 - 0.63T

∆

Reference

[23]

→

∆

used in this study.

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the fcc to hcp phase transformation for the pure elements and the excess free energy

[23] [23] [6,7,23] [6,7,23] [6,7,23] [6,7,23]

-4621.59 + 7.32T + (7341.73 – 7.93T)(XCo - XCr)

[24]

→

-820 - 1.65T

[25]

→

-2191.38 + 4.34T + (4068.16 - 3.56T)(XCo – XW) + (7624.18 - 4.53T)(XCo – XW)2

[26]

→

241.4 + 12.8T + (-26593.7 – 17.31T)(XCo – XMo)

[27]

→

13968.75 – 3528.8 (XCo – XFe)2

[28]

→

2756 – 1657 (XCo – XMn)

[29]

" " " "

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"

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→

"

Since both hcp and fcc of Cobalt are ferromagnetic, the calculations must include the

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magnetic properties. When applying the model to binary Co-based alloys, the composition dependence of the magnetic moment of Φ phase (βΦ) and the critical temperature for magnetic ordering of the Φ structure (#$% ), or the Curie temperature for ferromagnetic ordering, must be defined. The formulas for (βΦ) and (#$% ) to calculate the magnetic →

contribution (∆&' ) were directly taken from the reference [23,24,25,26,28,29] and summarized in Table 2. The influence of Al and Mo on the magnetic moment was not taken into consideration. All the thermodynamic data in Table 1 and Table 2 were implemented

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ACCEPTED MANUSCRIPT into a Matlab code, which was programmed for the SFE calculations for binary Co-based alloys. Table 2. The formulas for the magnetic moment of Φ phase (βΦ) and the Curie temperature for magnetic ordering of the Φ structure (#$% ) (K) used in this study. System

Function #$,)*

Co

= 1396

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+,-.

Pure

Reference [23]

+ --

#$,)* = 1396 +,-.

= 1.35

+ --

= 1.35

/ /

[23]

+,-.

Co-Cr

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#$,)*+)0 = 1396 XCo - 1109 XCr - 5828.68 XCo XCr + 4873.95 (XCo - XCr) XCo XCr + --

[24]

#$,)*+)0 = 1396 XCo - 1109 XCr - 9392.53 XCo XCr + 8383.04 (XCo - XCr) XCo XCr

+ --

/+ = 1.35 XCo - 2.46 XCr +,-.

Co-W

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+,-.

/+ = 1.35 XCo - 2.46 XCr

[24]

#$,)*+1 = 1396 XCo - 3159.19 XCo XW – 4023.37 (XCo – XW) XCo XW + 200.52 (XCo – XW)2 XCo XW + 5538.65 (XCo – XW)3 XCo XW + --

[26]

#$,)*+1 = 1396 XCo - 3520.31 XCo XW – 4796.2 (XCo – XW) XCo XW – 813.66 (XCo – XW)2 XCo XW + 5699.83 (XCo – XW)3 XCo XW +,-.

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/+ = 1.35 XCo - 2.93 XCo XW – 4.77 (XCo – XW) XCo XW – 4.55 (XCo – XW)2 XCo XW + 10.14 (XCo – XW)3 XCo XW + --

/+ = 1.35 XCo - 2.93 XCo XW – 4.77 (XCo – XW) XCo XW – 4.55 (XCo – XW)2 XCo XW

[26]

+ 10.14 (XCo – XW)3 XCo XW +,-.

Co-Ni

+ --

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#$,)*+23 = 1396 XCo + 633 XNi + 411 XCo XNi – 99 (XCo – XNi) XCo XNi

[23,25]

#$,)*+23 = 1396 XCo + 633 XNi + 411 XCo XNi – 99 (XCo – XNi) XCo XNi +,-.

/+ = 1.35 XCo + 0.52 XNi + 1.046 XCo XNi + 0.165 (XCo – XNi) XCo XNi + --

[23,25]

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/+ = 1.35 XCo + 0.52 XNi + 1.046 XCo XNi + 0.165 (XCo – XNi) XCo XNi

Co-Mn

+,-.

#$,)*+45 = 1396 XCo - 1620 XMn - 2685 XCo XMn + 3657 (XCo – XMn) XCo XMn + --

[29]

#$,)*+45 = 1396 XCo - 1620 XMn - 2685 XCo XMn + 3657 (XCo – XMn) XCo XMn +,-.

/+ = 1.35 XCo - 1.86 XMn - 1.07 XCo XMn

[29]

+ --

/+ = 1.35 XCo - 1.86 XMn - 1.07 XCo XMn Co-Fe

+,-.

#$,)*+67 = 1396 XCo - 253 XCo XFe + 1494 (XCo – XFe) XCo XFe + --

[28]

#$,)*+67 = 1396 XCo - 201 XFe - 283 XCo XFe + 879 (XCo – XFe) XCo XFe +89 /+ = 1.35 XCo + 5.41 XCo XFe – 0.24 (XCo – XFe) XCo XFe +

/+ = 1.35 XCo - 2.1 XFe + 9.74 XCo XFe – 3.516 (XCo – XFe) XCo XFe

7

[28]

ACCEPTED MANUSCRIPT 2.2. First-principles method In the first-principle method, we calculate the differences in total energies associated with the perfect structure and the intrinsic stacking fault structure. The 1x1x4 supercell consists of 22 atoms with 11 layers and ABCABCABCAB stacking sequence of close-packed (111) planes as the perfect or initial structure is presented in Fig. 3(a). Displacement of the

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layers number 7 – 11 along [11-2] will create the intrinsic stacking fault (ISF) or stable SF supercell ABCABC][BCABC. We calculated the total energy of the supercells using the Cambridge Sequential Total Energy Package code (CASTEP) [30] based on density-

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functional theory (DFT) [31]. The exchange-correlation functional was Pardew–Burke– Ernzerhof (PBE) [32] version of the generalized gradient approximation (GGA). In the

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electronic structure calculations, we used the ultrasoft pseudopotential initiated by Vanderbilt [33] to describe the electrons and ion cores interactions. Fully optimized geometry is an essential precondition of calculation (atoms moved until reach minimum energy and forces are zero at different volume). The convergence parameters as follows: total energy tolerance 10-5 eV/atom, force tolerance 0.03 eV/Å, maximum stress component 0.05 GPa and

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maximum displacement 0.001 Å. After enough volumetric relaxation and energy convergence test, the Monkhorst-Pack [34] scheme k-points grid sampling is set as 36 irreducible k-points (11x11x1) in the Brillouin zone and the plane wave energy cut-off is 400 eV. The calculations used a spin-polarized approximation which uniformly distributed over

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the space for pure Co and also for all the alloying elements due to its ferromagnetic nature of Co-based alloy. The predicted spin magnetic moment for Co is 1.65 µB/atom. Then, the

 =

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intrinsic stacking fault energy was calculated by; :;<= +:>

(2)

where Eisf is the total energy of the supercell with intrinsic stacking fault, E0 is the total energy of the perfect fcc supercell, and A is the area of the fault plane (varied according to the equilibrium lattice parameter a0 of the structure). We calculate the effect of supercell size on the stable SFE γsf through the duplication of 1x1x4 supercell along x-axis or [11-2] direction to create a series of 2x1x4 and 3x1x4 supercells with 44 and 66 atoms as shown in Fig. 3(a). The purpose is to analyze the interaction between two-period slabs, especially around the 8

ACCEPTED MANUSCRIPT alloying atoms near the SF planes. Since the main assumption of the SFE formation by computational thermodynamic approach is basically a thin layer of hexagonal close-packed (hcp) phase in an fcc crystal structure (Fig. 1) [5], the alloying atoms position in the supercells structure is ordered in the stacking fault area to represent binary solid solutions. It has been often believed that substitutional alloying atoms are attracted to a stacking fault area

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(Suzuki effect) and change the SFE especially during deformation at high temperature [2,20]. The substitutional alloying atoms have been explicitly assumed to reside in the stacking fault layer in the SFE calculation [2,4,21]. Direct evidence of alloying atoms segregation to the

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stacking fault plane in Co-Ni-Cr based superalloy MP159 have been reported experimentally by Han et al. [20]. For the calculation of binary Co-X alloys, the alloying atoms (Cr, W, Mo,

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Ni, Mn, Al and Fe) substitute two atoms of Co in the 5th and 7th layers as shown in Fig. 3(b). Then the concentration of alloying atoms was about 9 at.%. Substituting another two atoms of Co in 6th and 8th layers create a binary Co-18 at.% X. The alloying atoms selected in these works are forming solid solutions in the alloys based on the binary Co alloys phase diagrams

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[35,36,37] and placed near the SF planes in the low-energy positions [21].

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Fig. 3. The geometry of the computational cell used in the first-principles calculations, (a) to calculate the effect of the supercell size with 1x1x4, 2x1x4 and 3x1x4 supercell, (b) to calculate the effect of the alloying elements concentration, (c) to calculate the effect of the

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temperatures. Intrinsic stacking fault (ISF) or stable SF supercell was created by displacing layers numbered 7-11 along [11-2]. Stacking sequence A, B and C are colored in light blue,

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red and dark blue atoms, respectively. Gray atoms are Co atoms and green atoms are the alloying atoms.

It is worth noting that the total energy calculations above only at 0 K without any thermal effects included, called the cold energy or the 0-K total energy. To calculate the thermal properties such as the entropy, enthalpy, lattice heat capacity and Gibbs free energy at finite temperatures, the influence of lattice thermal vibration is essentials. The regularly recognized method is the phonon approach within the harmonic or quasi-harmonic

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ACCEPTED MANUSCRIPT approximation (QHA). Based on the quasi-harmonic approximation (QHA) [18], the Helmholtz free energy F(V,T) at volume V and temperature T can be approximated as: ?@A, #B = C@AB + ?! @A, #B + ?DE @A, #B

(3)

E(V) is the 0-K total energy (without zero-point vibrational energy) at volume V. Fel(V,T) represents the thermal electronic contribution to free energy on the corresponding V and T.

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Fvib(V,T) is the vibrational contribution to free energy, usually described by phonon calculations.

We calculate the phonon dispersion and phonon density of states using the density

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functional perturbation theory (DFPT) through the finite displacements method (known as the supercell method) [38]. In the phonon calculations, we used the cutoff radius of 5.0 Å and the

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exchange-correlation potential is the Ceperley–Alder type [39] parameterized by Perdew and Zunger [40] within the local density approximation (LDA) with the energy cut-off of 400 eV. A 9 × 9 × 2 Monkhorst-Pack mesh is used in the calculation of the phonon density of states. We found that these parameters are sufficient for obtaining well-converged results. For the thermodynamic properties calculation of pure Co at different temperatures, we used 2x2x2

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fcc unit cell with 32 atoms. Meanwhile, for the stable SFE calculations, we used 20 atoms supercell with 5 layers The alloying atoms substitute four atoms of Co in the 5-8 layers and the concentration was about 20 at.% as shown in Fig. 3(c). 3. Results and Discussions

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3.1 Interfacial energy of γ-fcc and ε-hcp interphases F/ of Co-based alloys The interfacial energy of γ-fcc and ε-hcp interphases
/ is temperature and

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composition-dependent parameter. But, it is commonly assumed as a constant value in the SFE calculations by computational thermodynamic approach in Eq. 1. Curtze et al. [6] was assumed the interfacial energy
/ to be 8 mJ/m2, which is a typical value reported for similar chemical compositions of austenitic steels. For pure Co and various Co-based alloys, the interfacial energy term is assumed to be 2
/ = 15 mJ/m2 [9,10,13]. In the present study, we assumed the interfacial energy to be a constant value
/ = 7.5 mJ/m2 based on indirect measurement using experimental SFE values γexp. The formulation to indirectly calculate
/ using γexp is: 11

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/ = IJ. − 2 ∆ → L

(4)

H

Fig. 4(a) shows the available experimental SFE values γexp of pure Co and some Co-based alloys at different temperatures from TEM observations [13,14,15]. By using Eq.4 and ∆ → as described in Fig.2, the calculated interfacial energy
/ as a function of

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temperatures for different Co-based alloys are obtained and presented in Fig. 4(b). It shows that the calculated interfacial energies
/ are decreased as the increase of temperatures, except for Co-35 at.% Ni. The average values of interfacial energies
/ are 7.5 ± 2.5 mJ/m2 (a gray area in Fig. 4(b)). Based on this result, the interfacial energy is taken as a constant

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value and equal to
/ = 7.5 mJ/m2.

Fig. 4. (a) The experimental SFE values γexp of some Co-based alloys at different

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temperatures [13,14,15], (b) the calculated interfacial energy
/ by indirect calculations

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from experimental SFE values γexp. The solid and dashed lines represent the linear regression to shows the trends of the values.

3.2 Effect of supercell size The effect of the supercell size on the stable SFE γsf of pure Co and binary Co-based alloys from first-principles calculation are presented in Fig. 5(a). The γsf variations of pure Co between 1x1x4 supercell (22 atoms) and 3x1x4 supercell (66 atoms) are fairly small, 0.15 mJ/m2 and -1.94 mJ/m2, respectively. The similar results are also detected for alloying with Ni and W atoms at different concentrations, the variations of γsf with supercell size are lower than 1.5 mJ/m2. It indicates that the values of the γsf is constant with supercell size along x-

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and two-layers twinning SFE 2γtsf of pure Co and Co-9 at.% Ni is fairly small with the supercell size [21]. Zhang et al. [41] noted that the calculated SFE of pure Mg convergence against the supercell size along z-axis and tend to be stabilized when the distance between two stacking fault interfaces is not less than 10 layers. The average γsf values of pure Co with

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different supercell sizes at 0 K are -0.74 mJ/m2, meanwhile the γsf of fcc Co at 0 K from the linear regression of the experimental measurement values in Fig. 4(a) is around -5 mJ/m2

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[13]. From the other theoretical calculations by the computational thermodynamic approach, the SFE of pure Co can be negative (around -1 mJ/m2) at room temperature when the fcc

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phase is regarded as a matrix [10].

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ACCEPTED MANUSCRIPT Fig. 5. The first-principles calculated stable SFE γsf of binary Co-based alloys with (a) number of atoms variations in the supercell and (b) alloying atoms concentration variations. (c) The computational thermodynamic approach of intrinsic or stable SFE γsf of binary Cobased alloys with alloying atoms concentration variations. (d) Plot of the calculated stable

3.3 Effect of alloying elements concentrations

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SFE γsf from first-principles versus from the computational thermodynamic approach.

In this section, we compare the calculated stable or intrinsic SFE γsf from both first-

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principles calculations and computational thermodynamic approach with alloying elements concentration variations as shown in Fig. 5(b) and Fig. 5(c), respectively. The γsf of binary

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Co-based alloys varies in a broad range which increased with the alloying of Fe, Al, Ni and Mn atoms. Meanwhile, alloying with Cr, W and Mo atoms decreased the γsf. The effect on the γsf becomes stronger with the increase of alloying elements concentration until 20 at.%. Alloying with Fe atom has the strongest influence on increasing the γsf followed by alloying with Al, Ni and Mn atom. Meanwhile, alloying with Mo atom has the strongest influence on

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decreasing the γsf followed by alloying with Cr and W atom. These tendencies are consistent with the computational thermodynamic approach. Interesting to note that from first-principles calculations, the γsf of Co-9 at.% Cr is slightly higher than Co-9 at.% W, but at high

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concentration, the γsf of Co-18 at.% Cr is lower than Co-18 at.% W. Then, we expect that there is an intersection of the Co-X at.% Cr and Co-X at.% W curves at around 11 at.% (Fig.

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5(b)). The computational thermodynamic approach also expect this intersection at around 11 at.%. Based on these results, we can conclude that a good qualitative correlation between computational thermodynamic approach and first-principles calculations of the γsf of binary Co-based alloys was obtained. Quantitatively, the differences between the calculated γsf from computational thermodynamic approach and first-principles calculations are relatively small, lower than 15 mJ/m2 except for Co-X at.% Mo as shown in Fig. 5(d). Although Ishida [7] only shows the computational thermodynamic approach at 700 K, but the result is consistent with the present study. Ishida [7] shows that the γsf of Co is increased by increasing atomic fractions of Mn, Ni and Fe, meanwhile increasing atomic fractions of Cr, W and Mo 14

ACCEPTED MANUSCRIPT decreased the γsf. the calculated γsf at high temperature by computational thermodynamic approach and first-principles calculations are presented in section 3.4. The electronic structures are usually calculated to further understand the bonding characteristics and further reveal the reasons for the variations of SFE of alloys. In order to

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investigate the electronic structures of pure Co and binary Co-based alloys, we calculate the charge density difference distributions and the density of states (DOS) [21]. The evidence of the Suzuki effects would seem to be clearly from the charge density and atomic bonding analysis. Fig. 6 shows the charge density difference contour in δρ/Å3 of the stable SF

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structure. Positive values (indicated by the red, orange and yellow contours) denote charge accumulation, whereas negative values (indicated by the blue and green contours) denote

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charge depletion. The stable SF structure in Fig. 6(a) shows that the directional bonding between Co-Co atoms is turn around at the ISF planes together with charge redistribution. When alloying atoms enter into the Co matrix, they will inevitably cause the electron charge distribution and bonding in Co to change. Alloying with Mo atoms reveals the loss of charge from the alloying atoms core indicated by the blue boat-like area. This charge is redistributed

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into the interstitial regions and increased the charge accumulation surrounding the alloying atoms indicated by a red boat-like area. Meanwhile, alloying with Fe atoms increased a green

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and yellow boat-like charge depletion area especially around the ISF area [21].

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Fig. 6. Effect of the alloying elements concentration on charge density difference contour (in

δρ/Å3) associated with the stable SF structure, (a) two dimension (2D) plane from the

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supercell’s slice in [11-2] and [111] directions as illustrated in the left side of this figure, (b) charge density difference field distributions in the entire structure.

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From the charge density difference field distributions (Fig. 6(b)), increasing the concentration of Mo atoms until 18 at.% increased both red-boat like charge accumulation

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area from 13 to 30% and blue-boat like charge depletion area from 11 to 18%. More charges accumulated between the SF planes compared with pure Co tend to decrease stable SFE, consistent with the Suzuki effect and the decreasing γsf trend in Co-X at.% Mo (Fig.5 (b)). This tendency is similar with alloying of Cr and W atoms. In contrast, increasing the concentration of Fe atoms until 18 at.% decreased the high charge accumulation (red-boat like area) from 13 to 8%. Then, the reduction of the charge accumulation area compared with pure Co leading to larger stable SFE. The similar tendency is shown in alloying with Mn and Ni atoms.

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ACCEPTED MANUSCRIPT The density of states (DOS) is the visual reflection of energy band structure and defines the number of states at each energy level, which is available and to be occupied. A high DOS at a certain energy level indicates that there are more states available for electrons to occupy [42]. The DOS value at the Fermi level (EF) could estimate the relative bonding electron numbers. A higher number of bonding electrons exhibits a stronger charge interaction [43].

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The Co atom itself has an outer electronic configuration of 3d7 4s2. Alloying atoms will disturb the distribution of free electrons for Co atoms on the SF planes, which further has an effect on the atomic bonding in slip layers [21]. Fig. 7(a) shows the effect of alloying

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elements concentration on the total DOS curves (only show the spin-up curve) associated with the stable SF structure. The Fermi level (EF) is set to 0 eV and marked by gray dashed

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lines in Fig. 7. It is interesting to note that with the alloying of Mo atom (and also for Cr and W), the energy range of total DOS expanded associated with the s-states (from -80 until -60 eV) and p-states (from -50 until -30 eV) [21]. However, these states have little effects on bonding as they are far away from the EF. Around EF, the peak of total DOS dominated by dstates. The valence electronic configurations of Cr, W and Mo are 3s2 3p6 3d5 4s1, 5s2 5p6 5d4

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6s2 and 4s2 4p6 4d5 5s1, respectively, while for Mn, Ni, Al and Fe are 3d5 4s2, 3d8 4s2, 3s2 3p1, and 3d6 4s2, respectively. Alloying with Mo atoms and increasing concentrations of Mo atoms until 18 at.% decrease the total DOS around the EF of pure Co (Fig. 7(a)) indicating a lower atomic bonding then decreased the stable SFE. Meanwhile, alloying with Fe atoms and

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increasing concentrations until 18 at.% increase the total DOS around the EF indicating a

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stronger atomic bonding and a higher stable SFE.

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Fig. 7. Effect of the alloying elements concentration on the spin-up density of states (DOS) curves associated with the stable SF structure, (a) total DOS curves, (b) partial DOS curves of Co atom in a specific layer of pure Co. L6 (L7) is the Co atom at the ISF (layer 6th and 7th) as

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illustrated on the right side of this figure. (c) Partial DOS curves of Co atom of Co-9 at.% Fe and Co-9 at.% Mo in L7 and L4, (d) in L5, L6 and L7 as illustrated on the right side of this

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figure. Alloying atoms are in L7 (at ISF) and L5 (not at ISF) allowing the determination of solute versus solute-fault effects. The Fermi level (EF) is set to 0 eV and marked by the gray dashed lines.

To distinguish whether it is just the alloying atom affecting the variations of the SFE (solute effect) or rather it is the alloying atom only in the vicinity of the SF plane (solute-fault effect) that is the key for the changed of SFE (which is the origin of the Suzuki phenomenon [19,44]), we investigate the partial DOS curve of Co atom in a specific layer (near or removed from solute and near or removed from the ISF plane) as shown in Fig. 7(b-d). In 18

ACCEPTED MANUSCRIPT Fig. 7 (b), the PDOS curves for Co atoms in L6 and L7 (both adjacent to ISF) are the same while L4 is equivalent to the bulk. The PDOS curves in L4 and L5 (far away from ISF) are fairly similar, meanwhile, the PDOS curve in L6 (L7) is changed significantly and the highest at EF due to the interruption in local stacking from fcc to hcp at the ISF, altering mostly the d-band hybridization. The direct effect is an increase in band energy or an energy increase to

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create an intrinsic SF in Co. These results reveal the effects occurring purely due to an ISF formation during the shearing process.

For the combined effect with alloying atoms (solute-fault effect), we analyze the partial

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DOS curves of Co atom of Co-9 at.% Fe and Co-9 at.% Mo in L7 (at ISF, adjacent to alloying atom) compared to L4 (far away from ISF) in Fig. 7(c) and L7 compared to L6 (at

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ISF, no alloying atom) and L5 (not at ISF, adjacent to alloying atom) in Fig. 7(d). Fig. 7(c) shows that the alloying atom at the ISF (L7, a red dashed line curve) still show the signature of the fault, which is increased the peak around Fermi level (EF) in Co-9 at.% Fe (top chart) and decreased in Co-9 at.% Mo (bottom chart). Fig. 7(d) shows that the PDOS curve of Co atom in L7 is the most dominant especially at the peak around EF while the curve in L5 and

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L6 shows some similarity. Obviously, the key for the SFE variations is the alloying atoms only in the vicinity of the ISF plane due to a combination of alloying atoms and shearing process. These results also highlight the critical role of the Suzuki effect, where the alloying atoms are attracted to a stacking fault defect and change the SFE.

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3.4 Effect of temperatures

We have calculated the Helmholtz free energy F(V,T) of the perfect fcc structure and

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the structure with intrinsic stacking fault (ISF) using Eq. (3). The thermal electronic contribution (TEC) Fel(V,T) is defined by Mermin statistics [45] Fel = Eel - TSel. The internal energy due to electron excitations is given by [46], C! @A, #B = M N@O, ABPO QO − M

:R

N@O, ABO QO,

(4)

where N@O, AB is the electronic density of states (DOS), P is the Fermi distribution function, O is the energy eigenvalues and EF is the energy at Fermi level (Fermi energy). The bare electronic entropy Sel is written by [46], S! @A, #B = −TU M N@O, ABVP ln P + @1 − PB ln@1 − PBZQO, 19

ACCEPTED MANUSCRIPT with TU is the Boltzmann’s constant. The electronic density of states (DOS) of 2x2x2 fcc unit cell cobalt at the theoretical equilibrium lattice parameter 3.547 Å [21] (from fitting the total energy versus volume (E–V) data points according to 4-parameter Murnaghan [47] equation of state) is shown in Fig. 8(a). The Fermi level (EF) is set to 0 eV and marked by dashed lines in Fig. 8(a). The calculated LDA spin-polarized DOS curve in the present study is similar

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with the DOS curve of ferromagnetic fcc Co from GGA-PBE calculations in Ref [48]. The electronic density of pure fcc Co around the Fermi level give the non-zero densities, indicating the Helmholtz free energy F(V,T) calculations should consider the thermal

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electronic contribution (TEC) Fel(V,T). Neglecting the TEC may be acceptable at low temperatures (which is usually neglected), but it can be very significant at high temperatures

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and improves the agreement between the calculations and experiments [46]. The Fel(V,T) was calculated from the one-dimensional numerical integration over the electronic density of

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states. In the present study, the TEC will be included but without discussion.

Fig. 8. (a) Spin-polarized total electronic density of states (DOS) per atom of 2x2x2 fcc unit cell cobalt. (b) The predicted phonon dispersion curve of fcc Co together with the experimental measurement for Co0.92Fe0.08 at 296 K [49]. (c) The calculated Helmholtz free energy F(V,T) as a function of lattice parameter a every 200 K from 0 until 1000 K of pure 20

ACCEPTED MANUSCRIPT fcc Co. The minimum value of every fitted curve (the red crosses) is the equilibrium lattice parameter at corresponding temperature. (d) The calculated equilibrium lattice parameter a0 as a function of temperature for fcc Co together with the experimental measurement [51].

The vibrational free energy of the lattice ions Fvib(V,T) is written as follows under the

?DE @A, #B = TU # ∑d ∑j ln ]2 sinh

ℏbc @d,eB Hfg h

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quasi-harmonic approximation [46], i

(5)

where ℏ is the reduced Planck constant and kj @l, AB represents the frequency of the j-th

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phonon mode at wave vector q. The phonon dispersion calculation is important to validate the first-principles phonon calculation. Fig. 8(b) shows the predicted phonon dispersion curve of

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fcc Co at the theoretical equilibrium lattice parameter 3.547 Å together with the neutronscattering experiment for Co0.92Fe0.08 at 296 K [49]. This first-principles phonon dispersion curve had a good agreement with the experiment along high symmetry lines in the Brillouin zone (BZ) and gives a better agreement than embedded-atom method (EAM) potential calculations in Ref [50]. This result verified the qualities of first-principles phonon

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calculation in the present study.

Then, we calculated the equilibrium lattice parameter at temperature T by fitting Helmholtz free energy F(V,T) versus lattice parameter a data points according to the 4-

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parameter Murnaghan [47] equation of state (EOS). Fig. 8(c) shows the F(V,T) as a function of lattice parameter every 200 K from 0 until 1000 K of pure fcc Co. The minimum value of

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every fitted curve (the red crosses) is the equilibrium lattice parameter at corresponding temperature. Fig 8(d) shows that the equilibrium lattice parameter a0 increase with increasing temperature for perfect fcc Co. The a0 versus T curve for fcc Co structure with intrinsic stacking fault (ISF) is slightly lower than perfect fcc Co and the reduction increases with temperature. The experimental measurement shows that the a0 of fcc Co are increased linearly with temperature from 273 K until 1273 K [51]. Meanwhile, the first-principles calculated a0 in the present study are increased slowly below room temperature (0 – 300 K) and increased linearly above room temperature (300 – 1000 K), agree well with the experiments. This tendency is probably as a result of the ferromagnetic effect of Co, 21

ACCEPTED MANUSCRIPT especially below room temperature. The differences between the first-principles calculated a0 of fcc Co with experiments [51] at different temperatures is lower than 0.031 Å. To calculate the thermal expansion, we did not calculate the Grüneisen parameter, which is numerically not always stable since a further derivative of kj @l, AB versus volume V

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must be evaluated [46]. Then, the linear thermal expansion coefficient α at zero pressure is calculated from the V–T relationship [52] or equilibrium lattice parameter a0 versus temperature in Fig. 8(d); G

m = ne p >o

qe>o qh

r

9

(6)

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where Ash is the equilibrium volume at the temperature of interest. Fig. 9(a) shows the linear thermal expansion coefficient α of fcc Co (in 10-6/K) together with the assessed value from

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the experiment [53]. At low temperatures, the calculated α reveals an increase with temperatures (T3) and the increasing trend is gradually smaller (almost linear) at high temperature. This result is in good agreement with experiments data from Touloukian et al. [53] except a few points are higher than the reference by 9% after 700 K. Fig. 9(b) shows the enthalpy of fcc Co at zero pressure (in kJ/mol) obtained by H = F + TS (where S is entropy

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obtained by S = -(∂F/∂T)V). The calculated enthalpy H is increase slowly below 200 K then increases linearly. The differences of our calculations with the recommended values from Barin [54] for fcc Co are lower than 11%. The agreement between the calculation and the

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experiment for α and enthalpy of ferromagnetic fcc Co could have been improved further if

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we included the effect of magnetic transition occurred at ∼700 K.

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Fig. 9. (a) The calculated linear thermal expansion coefficient α of fcc Co and the experiment data from Touloukian et al. [53] (b) The calculated enthalpy of fcc Co and the experiment

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data from Barin [54] (c) The calculated heat capacity at constant volume CV of fcc Co and binary Co-based alloys. The black dashed line is the Dulong–Petit limit of 3R (25 J/K.mol). (d) The calculated heat capacity at constant pressure CP of fcc Co together with the reported

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CP values of Co from Lemke et al. [56].

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Fig. 9(c) shows that the calculated heat capacity at constant volume (CV = T(∂S/∂T)V) was increased rapidly at low temperature (< 100 K), proportional to T3 law. At high temperature (> 300 K), CV tends to be a constant value near 25 J/K.mol, which satisfies the Dulong–Petit law (CV = 3R, where R is the universal gas constant). At intermediate temperatures, the temperature dependence of CV is dominated by the electronic vibrations of the atoms. Then the addition of alloying atoms to pure fcc Co decrease the calculated CV curve at intermediate temperatures. The calculated CV of ferromagnetic fcc Co at different temperatures from quasi-harmonic approximation (QHA) in the present study are slightly higher than the other first-principles calculations with the quasi-harmonic Debye model [55]. 23

ACCEPTED MANUSCRIPT In order to compare with the experimental data, we calculate the heat capacity at constant pressure CP using Eq. 7 [52]: u9 = ue / H v#A

(7)

where β is the volume thermal expansion coefficient which is three times larger than the

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linear thermal expansion coefficient α in Eq. 7, i.e., (β = 3α) and B is the bulk modulus. Fig. 9(d) shows that the calculated CP of fcc Co is in good agreement with the reported CP values of Co from Lemke et al. [56], except a few point at high temperatures (> 500 K) are lower by 6%. Additionally, CV and CP are almost identical at low temperature. Then CP is larger than

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CV and the differences are increased slowly with temperature increasing, mostly due to the thermal expansion coefficient effect.

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Fig. 10 shows the temperature dependence of the calculated intrinsic or stable SFE γsf from computational thermodynamic approach and first-principles calculations together with the available experimental measurement values from TEM observations [13,14,15]. It is obviously seen that the γsf increase with increasing temperature from both theoretical and experimental measurements. The calculated γsf from first-principles calculations (solid lines)

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are increase slowly until 50 K and then increase linearly. Meanwhile, the calculated γsf from computational thermodynamic approach (dashed lines) are increase linearly with temperatures, except for Co-20 at.% Cr (Fig. 10 (b)) and Co-20 at.% W (Fig. 10 (c)) due to →

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the magnetic contribution (∆&' ) around the critical temperature for magnetic ordering (#$% ). Lee et al. [10] also calculated the temperature dependence of SFE of pure Co from

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computational thermodynamic approach and reported the similar result with Fig. 10 (a). Unfortunately, to our knowledge, there are still no experimental or other theoritical calculations of similar alloys and temperatures with our calculations for comparison. But, the calculated γsf values in the present study are reasonable with some experimental measurements, although for Co-Ni and Co-Fe systems are at different concentrations due to the lack data of the γsf from the experimental measurement. It is also shown in Fig. 10 that the differences between the calculated γsf from computational thermodynamic approach and firstprinciples calculations (∆) are relatively small (lower than 27 mJ/m2), except for Co-20 at.% Fe (≤ 39 mJ/m2) and Co-20 at.% Mo alloys (≤ 60 mJ/m2). It is interesting to note that Fe and 24

ACCEPTED MANUSCRIPT Mo atoms give the highest impact in altering the γsf of pure Co due to their electronic structure as discussed in section 3.3 (Fig. 6 and Fig. 7). Then, we can conclude that both computational thermodynamic approach and first-principles methods are capable of calculating the stacking fault energy of Co-based alloys with a highly accurate modeling

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qualitatively and quantitatively (Fig. 5(d) and Fig. 10). Discussion of the deviations that involved in our SFE modeling by computational thermodynamic approach and first-principles

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method are presented in section 3.5.

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Fig. 10. Effect of the temperatures on the stable SFE γsf from computational thermodynamic approach and first-principles calculations of (a) pure fcc Co, (b) Co-20 at.% Cr, (c) Co-20 at.% W, (d) Co-20 at.% Mo, (e) Co-20 at.% Mn, (f) Co-20 at.% Ni, (g) Co-20 at.% Al and (h) Co-20 at.% Fe, together with the available experimental measurements [13,14,15]. ∆

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ACCEPTED MANUSCRIPT represents the differences between the calculated γsf from computational thermodynamic approach and first-principles calculations.

We calculate the charge density difference contour and DOS of pure Co at different

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temperatures corresponding to the equilibrium lattice parameter (Fig. 8(d)). Fig. 11 shows the charge density difference contour of the stable SF structure of pure Co at 0, 300, 600 and 1000 K. Increasing temperature from 0 until 1000 K slightly decreased the charge accumulation area (red boat-like area) of [111] and [11-2] plane especially around the ISF

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area (Fig. 11 (a)). It is obviously shown from the charge density difference field distribution (Fig. 11(b)) that the red-boat like area or charge accumulation distributions are decreased

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with temperature. The lower charge accumulation area of the stable SF structure leads to

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larger stable SFE.

Fig. 11. Effect of the temperatures on charge density difference contour (in δρ/Å3) of pure fcc Co associated with the stable SF structure, (a) two dimension (2D) plane on layers numbered

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ACCEPTED MANUSCRIPT 4-9 from the supercell’s slice in [11-2] and [111] directions as illustrated in the left side of this figure, (b) charge density difference field distributions in the entire structure.

Details of the atomic bonding characteristics can be clearly illustrated by the partial density of states. Fig. 12(a) shows that the Co–d state plays a significant role during shearing

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because the Co–s state and the Co–p state are relatively weak in the entire region. As the temperature increases, the total DOS of pure Co (dominated by Co–d state) near the Fermi level (EF) is increased as shown in Fig. 12(b). The increasing of the total DOS and the

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reduction of the charge accumulation indicates the stronger atomic bonding of Co as temperature increases leads to the increase of the stable SFE (Fig. 10 (a)). Furthermore, the

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variation of the charge density difference distributions (Fig. 11(b)) and the shape of the total DOS (Fig. 12(b)) between 0 K and 1000 K are fairly significant, implying the important of

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the thermal electronic contribution (TEC) Fel(V,T) especially at high temperatures.

Fig. 12. (a) Spin-up partial DOS curve of pure fcc Co at 0 K, (b) spin-up total DOS curve of pure fcc Co at different temperatures. The Fermi level (EF) is set to 0 eV and marked by the gray dashed lines.

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ACCEPTED MANUSCRIPT 3.5 Deviations involved in SFE modeling by computational thermodynamic approach and first-principles method Although the theoretical SFE calculation by computational thermodynamic approach and first-principles method are similar in the principle and give a highly accurate modeling, a certain number of deviations are discovered in practice. The deviations are enlarged when the

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temperature and alloying elements concentrations are varied both during experiments and theoretical calculations. In this section, we explained briefly the difficulties or factors that could give rise

to the deviations of the SFE calculations in the present study. From

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computational thermodynamic approach; the interfacial energy
/ should not be assumed as constant value (Eq. 1), extrapolations of the thermodynamic data of mixing parameters

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(Table 1) to low temperatures (below room temperature) are not very reliable, the magnetic contributions (Table 2) are still difficult to account for exactly. From first-principles method; the interaction between alloying atoms could affect the calculations when the concentration of alloying atom is higher than a critical value (for example, higher than 20 at.% [57]), the effect of magnetic transition occurred at ∼700 K had not been accounted. Zhang et al. [41]

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reported that the abnormal variation of SFE of binary Mg-based alloys with some alloying elements when the concentration is 25 at.% was correlated with a tunneling effect. Electron of the alloying atoms could tunnel from one atom to another then interaction between the alloying atoms will get stronger, corresponding to a relatively smaller SFE variation. From

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the experimental measurement, Rémy and Pineau [14] pointed out the theoretical difficulties in determining the variation of SFE with temperature from TEM observations for example;

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changes in elastic constants, change in lattice friction forces, changes in the local or global chemical compositions of alloys and Suzuki segregation to the stacking fault.

4. Conclusions

The concentration and temperature dependencies of the stacking fault energy (SFE) of binary Co-based alloys have been successfully calculated using computational thermodynamic approach and first-principles calculations provide a highly accurate modeling qualitatively and quantitatively. The conclusions of the present study are as follows:

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ACCEPTED MANUSCRIPT 1. A good qualitative correlation between computational thermodynamic approach and firstprinciples calculations of the concentration-dependent SFE γsf of binary Co-based alloys was obtained. Alloying with Fe atom has the strongest influence on increasing the γsf followed by alloying with Al, Ni and Mn atom while alloying with Mo atom has the

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strongest influence on decreasing the γsf followed by alloying with Cr and W atom. The effect on the γsf becomes stronger with the increase of alloying elements concentration until 20 at.%. Quantitatively, the differences between the calculated γsf from

small, lower than 15 mJ/m2 except for Co-X at.% Mo.

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computational thermodynamic approach and first-principles calculations are relatively

2. The effects of temperatures on the thermodynamic properties and the stable SFE γsf have

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been investigated by first-principles calculations combined with quasi-harmonic approximation (QHA) and provide a fairly good agreement with available experimental and other theoretical results in the literature. The γsf of binary Co-based alloys increase with increasing temperature to 1000 K and compared with computational thermodynamic approach, the differences are relatively small (lower than 27 mJ/m2), except for Co-20

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at.% Fe (≤ 39 mJ/m2) and Co-20 at.% Mo alloys (≤ 60 mJ/m2).

3. The variations of the stable SFE γsf with alloying elements concentration and temperatures can be explained regarding the charge density distributions and the atomic bonding

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especially around ISF plane. Increasing concentrations of Mo atoms to 18 at.% will increase charge accumulations in interstitial regions leads to weaker atomic bonding and

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decreases the γsf of pure Co and vice versa in case of alloying with Fe atoms. These results also highlight the critical role of the Suzuki effect, where the alloying atoms are attracted to a stacking fault defect, then change the SFE and the key for the SFE variations is the alloying atoms only in the vicinity of the ISF plane. Meanwhile, increasing temperature from 0 until 1000 K slightly decreased the charge accumulation area leads to stronger atomic bonding and increase the γsf.

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. 30

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Highlights • Stacking fault energy (SFE) variations of Co-based alloys with different alloying elements and concentrations are studied.

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• SFE increase with increasing temperature from theoretical and experimental measurements. • Both computational thermodynamic approach and first-principles methods are capable of calculating the SFE with a highly accurate modeling qualitatively and quantitatively.

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• The critical role of the Suzuki effect and the key for the SFE variations are investigated.