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Acta Materialia 264 (2024) 119537
Available online 15 November 2023
1359-6454/© 2023 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
Mechanism of elemental segregation around extended defects in
high-entropy alloys and its effect on mechanical properties
Shihua Ma
a
, Weihong Liu
b
, Qian Li
c
, Jun Zhang
a
, Shasha Huang
a
, Yaoxu Xiong
a
, Biao Xu
a
,
Tao Yang
c
,
d
, Shijun Zhao
a
,
d
,
*
a
Department of Mechanical Engineering, City University of Hong Kong, Hong Kong, China
b
School of Materials Science and Engineering, Harbin Institute of Technology, Shenzhen, China
c
Department of Materials Science and Engineering, City University of Hong Kong, Hong Kong, China
d
Hong Kong Institute for Advanced Study, City University of Hong Kong, Hong Kong, China
ARTICLE INFO
Keywords:
High-entropy alloys
Grain boundary
Segregation
Chemical short-range ordering
Decohesion resistance
ABSTRACT
Elemental segregation around extended defects is common in high-entropy alloys (HEAs) composed of multi-
principal elements, which profoundly impacts their mechanical properties. In HEAs, the driving force for
segregation usually competes with chemical short-range ordering (CSRO) formation, making it challenging to
elucidate the segregation mechanisms. In this study, we systematically investigate the chemical composition
changes around extended defects, including dislocations, stacking faults, and grain boundaries (GBs) in CoNiCrFe
HEAs, to explore the chemical-structure-mechanical relationship utilizing hybrid Monte Carlo and molecular
dynamic (MC/MD) simulations and theoretical analysis. We nd a pronounced Cr enrichment and Co/Ni/Fe
depletion around all defects considered in this work. A correlation between the degree of structural disorder and
the chemical segregation/depletion phenomenon in the proximity of extended defects has been uncovered. Our
results show that due to the extreme chemical complexity in HEAs, CSRO inevitably contributes to the elemental
rearrangement and affects segregation. Consequently, the segregation behavior in HEAs is mainly controlled by
interactions between different atomic pairs, and the segregation entropy also plays a dominant role. By
decoupling the strengthening contribution from elemental segregation and CSRO, we demonstrate and highlight
that the strengthening in HEAs can be modulated by elemental segregation. The positive impact of element
segregation on interfacial properties - improved ultimate tensile strength and elongation, has been evidenced
through experimental comparisons of CoNiCrFe with different Fe additions. This work elucidates the mechanism
of heterogenous elemental distributions in HEAs where elemental segregation and CSRO coexist, paving the way
for manipulating their mechanical properties by modulating the compositional variations.
1. Introduction
Extended defects, including dislocations, stacking faults (SFs), and
grain boundaries (GBs), play signicant roles in the performance of
engineering alloys. In practice, these defects are prone to elemental
segregation, referring to increased local compositional concentrations,
which may fundamentally change the mechanical properties of mate-
rials. For high-entropy alloys (HEAs), composed of multiple principal
elements at high concentrations, it has been demonstrated that chemical
segregation around extended defects is more pronounced than conven-
tional alloys, strongly affecting their mechanical properties, such as
decohesion and fracture [1–3]. As the decohesion of GBs controls the
failure mode, i.e., ductile fracture or brittle intergranular fracture,
tuning compositional segregation around GBs is an effective way to
improve the mechanical strength of HEAs [4]. Indeed, elemental
enrichment at GBs can improve cohesive forces by stabilizing GBs in
HEAs [5–7]. Besides segregation at GBs, elemental enrichment around
dislocations and stacking faults also signicantly inuences mechanical
performances by modifying their interactions with constituent atoms
and affecting the deformation mechanism [2,8,9].
Due to the high concentration of all constituted elements in HEAs,
enrichment of a specic elemental species around extended defects
inevitably causes its depletion in the bulk region. On the other hand,
HEAs usually exhibit a certain degree of chemical short-range ordering
* Corresponding author at: Department of Mechanical Engineering, City University of Hong Kong, Hong Kong.
E-mail addresses: taoyang6@cityu.edu.hk (T. Yang), shijzhao@cityu.edu.hk (S. Zhao).
Contents lists available at ScienceDirect
Acta Materialia
journal homepage: www.elsevier.com/locate/actamat
https://doi.org/10.1016/j.actamat.2023.119537
Received 24 February 2023; Received in revised form 23 August 2023; Accepted 14 November 2023
Acta Materialia 264 (2024) 119537
2
(CSRO), even in the absence of extended defects, due to favorable
attractive or repulsive interactions among certain constituent element
pairs [10–12]. Consequently, elemental segregation around extended
defects in HEAs will inevitably be coupled with CSRO formation [13,
14]. Depending on elemental interactions among themselves and with
extended defects, the driving force for CSRO development may promote
or compete with segregation, making it difcult to discern the segre-
gation mechanism in HEAs [11]. The available research on CSRO in
HEAs has proved that elemental rearrangement can change the in-
teractions between constituent elements and dislocations, resulting in a
local energy landscape that raises activation barriers for dislocation
movement, which subsequently inuence the mechanical properties of
HEAs [15–18]. Since both CSRO and elemental segregation contribute to
the mechanical properties of HEAs, it is of great signicance to identify
their individual roles by decoupling these two factors.
Atomistic simulations are powerful techniques to probe the structure
of these extended defects and associated elemental segregation in
metallic alloys [1,13,19,20]. For example, molecular dynamics (MD)
simulations and Monte Carlo (MC) algorithms are widely used to model
and investigate GB segregation at the atomic level [13,21]. In pure
metals, density functional theory (DFT) calculations are extensively
employed to calculate elemental segregation energies around GBs,
which are then used to deduce the elemental enrichment or depletion
tendency based on the modied McLean isotherm [1,20,22]. Nonethe-
less, for HEAs, due to the extreme chemical disorder, interactions be-
tween different constituent elements with extended defects become
complicated, making it challenging to accurately describe the elemental
segregation behavior. In general, the segregation energy, ΔG, is dened
as the Gibbs free energy change when the solute atom located in bulk
swaps its position with an atom at the extended defects: ΔG =ΔH −
TΔS, where ΔH and ΔS are the enthalpy and entropy changes respec-
tively, and T is the temperature. The segregation energy depends on
three factors: elemental concentration [23], solute site preference
(interstitial or substitutional sites) [24], and entropy [25]. Up to now,
theoretical calculations of the segregation energy have been mainly
performed in simple elemental systems and dilute binary alloys [1,26,
27]. Due to the complicated computational procedures, most theoretical
treatments of GB segregation make simplications on the entropy part,
assuming that the segregation energy is temperature independent and
the entropy contribution to segregation is negligible at the temperature
where segregation takes place [28,29], though some studies reported
the irreplaceable role of entropy in GB segregations [25,30]. Specically
for HEAs, the concept of segregation energy may become ill-dened
because of the highly versatile local atomic environments around the
segregation site, making it impossible to identify a reference congu-
ration based on which the segregation energy can be calculated. Besides,
the common simplication of the entropy contribution may fail with
increased chemical complexity.
Previous studies on elemental segregation in HEAs are mainly
focused on the Cantor alloy CoNiCrFeMn and its subsystems [31–33]. Li
et al. [34] studied the dependence of GB segregation in CoNiCrFeMn
(co-segregation of Ni and Mn and substantial depletion of Fe, Co, and Cr
from 423 to 623 K) on the GB character (i.e., GB misorientations and
types) experimentally. They found GBs with higher interfacial energy,
which possess lower atomic densities at GBs, exhibit more substantial
segregation. However, different from these segregation behaviors at low
temperatures, as reported from the MD simulations by Wynblatt et al.
[35], Cr emerged as the dominant segregant element instead of Ni in
both GB and free surfaces at high temperatures (above 1000 K). The
inconsistent segregation tendency may be explained by the formation of
new phases facilitated by CSRO domains (Cr-riched BCC phase,
Ni-riched L10 phase, Fe-riched B2 et al.) at low temperatures, which
makes the bulk composition departing from the nominal composition. In
MD simulations for CrCoNi, Cao et al. [13] observed the element
Fig. 1. Schematic of atomic congures without relaxation for (a) Random perfect system, (b) Shockley partial dislocation (SPD), and (c) stacking fault (SF) models;
(d)-(f) are the ATGBs-GB1 (asymmetric tilt GB, ATGB, Σ13<320>), STGB-GB2 (symmetrical tilt grain boundary, STGB, Σ11<332>), and ATGBs-GB3 (ATGB,
Σ13<100>), respectively. The circle in (b) represents the SPD line. The rectangle in (d-f) denotes the enlarged image of the GB region.
S. Ma et al.
Acta Materialia 264 (2024) 119537
3
redistribution around GBs and local phase transitions, mostly reasoned
using the mixing enthalpy argument [36]. However, the mixing
enthalpy of different constituent elements is highly dependent on the
local atomic compositions; it may be inadequate to fully explain
elemental segregation in HEAs [37,38]. Zhao [39] found local elemental
segregation suppress the bias effect of interstitial/vacancy-GBs in-
teractions, promoting efcient effect annihilation within the grain in-
teriors. Recently, Hu et al. developed a machine learning (ML) model
based on MD simulation results to predict GB segregation in quinary
HEAs [40] using the GB structural disorder parameter. Despite the
progress achieved, a fundamental understanding of GB segregation in
multicomponent HEAs is still limited due to the complicated coupling of
interactions among multiple principal elements and their interactions
with extended defects. In addition, the role of CSRO played in the
segregation beharivior remains unexplored.
In this work, we study the mechanism of elemental segregation
around extended defects in CoNiCrFe HEAs with varying Fe concentra-
tions to uncover the interplay between segregation tendency and CSRO.
Typical extended defects are considered, including the line defect (i.e.,
Shockley partial dislocations, SPDs), the planar defect (stacking faults,
SFs), and GBs (i.e., symmetrical tilt GBs and asymmetric tilt GB with
different misorientation angles). In CoNiCrFe, it is known that Cr tends
to segregate around GBs [4]. By tuning the composition of Fe, the degree
of segregation and CSRO can be effectively modied thanks to the sig-
nicant positive mixing enthalpy of Fe-Cr pairs (2.7 kJ/mol based on the
THEMOCALC TCFE9 database [34]). We then systematically analyze the
relation between the chemical segregation and structural disorder pro-
les at different temperatures with varying Fe concentrations. The
importance of structural disorder associated with elemental distribution
around different extended defects in HEA has been uncovered and
highlighted. We further elucidate the contribution of CSRO and segre-
gation to mechanical strength by decoupling these two factors based on
strengthening theories. These results unveil the intricate interplay be-
tween segregation and CSRO in HEAs.
2. Methodology
2.1. Computational methods
The quaternary FCC CoNiCrFe alloy with different Fe atomic con-
centrations, i.e., 0%, 2.5%, 5%, 25%, 50%, 75%, and 90%, was chosen
as model alloys to investigate the segregation trend using the large-scale
molecular dynamics parallel simulation (LAMMPS) software [41].
Correspondingly, these alloys were named as XFe (X is the concentration
of Fe), e.g., 25Fe (Co
25
Ni
25
Cr
25
Fe
25
). The modied embedded atom
method (MEAM) potential developed by B.J. Lee [42] was selected to
describe the atomic interactions. It has been conrmed that this po-
tential can correctly describe the fundamental materials properties and
GB segregation of the CoNiCrFeMn HEA in previous reports [35].
To understand the general segregation mechanism, we constructed
three models with extended defects: SPDs, SFs, and GBs models. Fig. 1a
gives the defect-free random conguration. Fig. 1b and c display the
congurations of SPDs (edge dislocation marked by “⊥”) and SFs,
respectively. In each model, two symmetric defect pairs lying perpen-
dicular to the y-axis were located at ~0.25Ly and ~0.75Ly. The di-
mensions for SPD models are ~14.0 ×34.3 ×12.1 nm
3
with 648,000
atoms. Note that the extra half-atom plane introduced a stress eld be-
tween the two SPD pairs along the y direction. The SFs model was built
with the dimensions of ~19.9 ×24.4 ×17.2 nm
3
with 76,800 atoms. For
GBs, three typical GB models were considered: i.e., GB1 (asymmetric tilt
GB, ATGB, Σ13<320>), GB2 (symmetrical tilt grain boundary, STGB,
Σ11<332>), and GB3 (ATGB, Σ13<100>). The GB disorientation an-
gles and energies were listed in Table S1. The GB system consists of
~20,000 atoms. For all models, periodic boundary conditions (PBC)
were applied in all three dimensions. We have ensured that the sepa-
ration between the two SPDs or GBs is large enough to minimize
interactions between them.
To model elemental segregation, a hybrid MC/MD technique [43]
was carried out to simulate the annealing treatment at 1000 K. The
system was rst equilibrated under the NPT ensemble for 10 ps. The
conjugate-gradient (CG) algorithm was followed to minimize the energy
of the whole system. Then, 20 MC/MD loops, consisting of 2000 MC
swapping, NVT relaxation for 50 ps, and CG minimization, were per-
formed sequentially to obtain equilibrated atomic congurations. In the
following, we denote the segregation models as Seg-Model, e.g.,
Seg-SPD, and the random model as Ran-Model, e.g., Ran-SPD.
For post-processing, the atom volume was calculated by the Voronoi
analysis using OVITO [44]. To characterize the local lattice disorder, we
also measured the centrosymmetric parameters (CSP) [44], wherein a
zero value represents a perfect crystal, and non-zero indicates defects
(details seen in Supplementary Material). In addition, the structure
disorder parameter (
η
Dis
) was calculated to distinguish between ordered
and disordered structures using the method proposed by Chua et al.
[45]. For a perfect crystal without the structural disorder,
η
Dis
=0, while
η
Dis
=1 represents liquid, which completely loses the ordered structure
(Supplementary Material).
The GB energy is the superabundance of energy relative to bulk
materials and is evaluated by
EGB =EGB,sys −EBulk,sys
NBulk
NGB(2A),(1)
where EBulk,sys and EGB,sys are the total energy of the alloy system without
and with two GBs, respectively; NBulk and NGB are the numbers of atoms
in the system without GBs and with GBs, accordingly; A is the area of the
GB plane. Hence, the GB energy for the random system without segre-
gation (EGB,ran) and segregated system (EGB,seg) is calculated as following
Eq. (2) and (3), respectively.
EGB,ran =Eran
GB,sys −Eran
Bulk,sys
NB,ran
NGB,ran(2A)(2)
EGB,seg =Eseg
GB,sys −Eseg
Bulk,sys
NBulk,seg
NGB,seg(2A)(3)
To evaluate the GB strength, we calculated the cohesive energy of
GBs. The interfacial cohesive energy is dened as the energy needed to
cleave a crystal along the GB and is calculated by the energy difference
between the system with GB and the system with the two cleaved free
surfaces:
γGB =EFS,1+EFS,2−EGB(2A),(4)
where EFS,1 and EFS,1 are the system energies of crystals 1 and 2 with free
surfaces, respectively.
2.2. Experimental
To examine the segregation around grain boundaries and their in-
uence on mechanical behavior, three alloys with different composi-
tions, namely 2.5Fe (Co
32.5
Ni
32.5
Cr
32.5
Fe
2.5
), 10Fe (Co
30
Ni
30
Cr
30
Fe
10
),
and 25Fe (Co
25
Ni
25
Cr
25
Fe
25
), were produced using the arc melting
technique for experimental analysis. All ingots were subjected to at least
ve ip-melting cycles before being drop-cast into a copper mold (5 ×
10 ×50 mm
3
). Afterward, the as-cast alloys were homogenized at
1200 ◦C for 2 h and cold-rolled longitudinally to a thickness reduction of
approximately 70 %. Later, annealing at 800 ◦C for 1 h resulted in a
single-phase microstructure with equiaxed grains.
Generally, grain boundaries can hinder the movement of disloca-
tions, enhancing the strength and hardness of materials. One traditional
strengthening strategy is grain renement strengthening, which in-
creases the area of grain boundaries and leads to an increase in strength
and resistance to deformation. At room temperature, the strength of
S. Ma et al.
Acta Materialia 264 (2024) 119537
4
ordinary alloys without hydrogen is generally determined by the factors
such as grain size and work hardening rate, et al., rather than the
cohesive strength of grain boundaries [46,47]. However, after being
gassed with hydrogen (H), the embrittlement of GB induced by H makes
them more prone to fracture, thereby the cohesive strength of GB be-
comes a dominant factor that determines the alloy strength [48,49].
Meanwhile, the presence of H, which was charged after annealing
treatment, does not affect the distribution and segregation of elements in
the as-annealed alloy. Therefore, to better investigate the mechanical
property under the inuence of grain boundary segregation from an
experimental perspective, we choose to introduce H into the alloy,
making grain boundaries the determining factor of alloy performance,
and thus revealing the impact of segregation on the grain boundary
strength.
All samples were divided into two groups. One was gassed with
hydrogen at 300 ◦C under a constant pressure of 18 MPa for 336 h,
referred to as the H-charged alloys. The other is H-uncharged alloys
without gaseous hydrogen charging. The H-charged specimens were
immediately stored in liquid nitrogen to retain the hydrogen until tensile
tests. The uniaxial tensile tests were conducted at ambient temperature
in a Material Testing System (MTS, Alliance RT30) tension machine with
a strain rate of 5 ×10
−5
s
−1
. The distribution of elements was analyzed
using energy-dispersive X-ray spectrometry (EDS) on a double
aberration-corrected transmission electron microscope (TEM, Titan
Cubed Themis G2300) operating at 300 kV. Fracture topography anal-
ysis was conducted using a scanning electron microscope (SEM, Quanta
FEG 450).
3. Result
3.1. General segregation phenomenon in HEAs
To elucidate the general segregation phenomena in HEAs, we
compute and construct the segregation diagram by calculating the atom
fraction prole, structural disorder parameter, and CSP in detail for the
models containing line-defect SPDs, planar-defect SFs, and GBs,
respectively.
Fig. 2 shows the typical segregation diagrams of considered defects
in 25Fe at 1000 K. The corresponding relaxed random congurations
without MC/MD procedure are provided in Fig. S1. As the composition
prole shows, a pronounced Cr enrichment and Co/Ni/Fe depletion
around extended defects occur in all the models after the MC/MD
treatment. For all the extended defects, within either bulk region or
extended defect cores, Cr repels Ni/Co/Fe, leaving a pronounced con-
centration gap between Cr and Ni/Co/Fe. In addition to the elemental
segregation around extended defects, several signicant compositional
peaks are evident in the bulk region and induce additional composi-
tional uctuations, especially for GB models. These compositional
changes in the bulk region are contributed from both elemental segre-
gations induced by extended defect structures and CSRO. The atomic
conguration in Fig. 2 shows that the elements in the defect-free bulk
region also exhibit CSRO. Defect-induced elemental segregation alters
the element concentration in the bulk region, leading to deviations from
the original composition. On the other hand, the formation of CSRO can,
in turn, potentially affect compositional distributions. The two
elemental inhomogeneous elemental distributions are coupled with
each other. As displayed in Fig. 2(a), different from planar defects, a
Fig. 2. Typical atomic conguration and corresponding atom fraction, CSP, and structural disorder parameter (
η
Dis
) proles for different defect models in 25Fe
obtained via MC/MD simulations at 1000 K. They are (a) SPD, (b) SF, (c) GB1, (d) GB2, and (e) GB3, respectively. The atomic conguration is illustrated through four
or three color-coded panels of the atom types, stress, CSP, and structure type. The corresponding segregation-related properties change with position, including
composition, CSP, and disorder, are displayed following the atomic conguration view.
S. Ma et al.
Acta Materialia 264 (2024) 119537
5
relatively high-stress eld is introduced between the two SPDs distrib-
uted along the y direction due to the absence of two half-atomic planes.
Cr enrichment occurs in the dislocation core and the high-stress region
between the two SPD pairs. It thus suggests that the high-stress eld also
contributes to the element segregation in HEAs.
To experimentally demonstrate this segregation phenomenon, we
conducted a comprehensive investigation of the element distribution
along GBs using the EDS analysis on a double aberration-corrected TEM,
as shown in Fig. 3. The 25Fe alloy exhibited pronounced Cr segregation
accompanied by Fe and Ni depletion in the vicinity of GBs. As depicted
in Fig. 3b, the brighter blue region indicates an enriched-Cr region,
while the darker green and brown regions represent the depletion of Fe
and Ni, respectively. The specic element fractions are presented in
Fig. 3c. By contrast, the elemental distribution near the GBs in the 10Fe
alloy is much more uniform. Despite the fact that the observed segre-
gation ratio in the experiment was slightly lower than that obtained in
the MD simulation, which can be attributed to the different time and
spatial scales utilized in the experiments and simulations, the results
conrm the segregation trend identied through MD simulations. It
demonstrated that the addition of Fe can increase the degree of
elemental segregation.
This section presents and discusses a detailed exploration and anal-
ysis of the segregation patterns in relation to the structural features,
considering the correlation between the elemental distribution and
microstructure.
Structural information is depicted using the CSP and structural dis-
order parameter,
η
Dis
. The CSP assesses crystal symmetry, revealing
symmetry-breaking and deviations from an ideal structure. Meanwhile,
the structural disorder parameter measures the level of structural dis-
order. A value of 1 for the disorder parameter indicates a complete loss
of ordered arrangement, resulting in an amorphous state, like a liquid. In
contrast, a value of 0 represents a perfectly ordered crystal. Fig. 2 shows
the related structural disorder parameter measured in Seg-models.
Compared to one-dimensional line defects (i.e., SPD), these two-
dimensional planar defect structures (i.e., SF, GB1, GB2, and GB3)
exhibit signicantly higher but relatively similar CSP peak values,
within the range from 5 to 5.5. The structural disorder parameter en-
ables better quantication of the crystalline ordering of defective
structures, particularly different interface structures with approximately
similar central symmetry. Compared to SF and SPD structures, GB
structures are extended interfaces between two grains, which span
serval atomic planes. This leads to the higher structural disorder
parameter in GB models, due to the stronger disruptive effects of GBs on
the crystal lattice and the resulting higher defect density. The maximal
structural disorder parameter,
η
Dis
follows the order: ATGB-GB3 >
ATGB-GB1 >STGB-GB2 >SF ~ SPD, indicating the decay of structural
disorder in this order (Table 1). The changes in chemical composition
and structural parameters occur almost simultaneously, as depicted in
Fig. 2. This indicates a strong correlation between chemical composi-
tions and structural disorder.
3.2. Correlation between chemical segregation and structural properties
Then we validate the correlation by measuring and analyzing the two
related properties: chemical compositional changes described using Γi
and structural disorder represented via Γtot
Dis. By slicing the system along
the y direction, the chemical absorption amount Γi (i.e., Γi, i=Co, Ni, Cr,
Fe) by extended defects and the structural disorder parameter ΓDis (i.e.,
Fig. 3. The elemental distribution around GB in 25Fe and 10Fe alloys. High-angle annular dark-eld (HAADF) images of GBs in (a) 25Fe and (b) 10Fe HEA, and (b,e)
the corresponding EDS maps. (c,f) The corresponding elements prole across GBs.
Table 1
The maximum value of the structural disorder parameter (
η
Dis, nm
−2
) in 25Fe
Seg-CoNiCrFe at 1000 K.
SPD SF GB1 GB2 GB3
η
tot,max
Dis 0.018 0.018 0.520 0.208 0.679
S. Ma et al.
Acta Materialia 264 (2024) 119537
6
Γtot
Dis and Γi
Dis, i=Co, Ni, Cr, Fe) are collected in all segregation models
with different Fe concentrations at 300 – 1300 K, which are dened by
[40]:
Γi=1
2AΣ
iNi
NA−NBulk
i
NBulk,(5)
Γtot
Dis =
i
Γi
Dis =1
2A
i(
η
i−
η
0).(6)
Here Γi represents the chemical changes of species i relative to the
baseline chemical concentration in bulk regions, and Γi
Dis denotes the
corresponding excess structural disorder parameter for species i. The
information required to obtain these two quantities are the extended
defect area, A; the total number of element i (NBulk
i) and all the elements
in bulk regions (NBulk), respectively; the total number of species i (Ni) and
all atoms in the sampling region (NA), respectively, where the sampling
region is a slice with a width of 2 Å along the y axis; and nally, the
average of disorder parameter of species i in the bulk region (
η
0) and
specic structural disorder of i (
η
i) in the sampling region.
Fig. 4 displays a roughly linear correlation between ΓCr and Γtot
Dis for
all considered extended defect models, though the data points are
scattered in broad regions due to extreme chemical uctuation. Other
related data for Ni, Co, and Fe can be seen in Supplementary Materials.
The positive slope of KCr
Dis indicates the absorption of Cr around the
defect, while the negative Ki
Dis (i=Ni, Co, and Fe) for Co/Ni/Fe agrees
well with the depletion of Co/Ni/Fe. With the temperature increase, Ki
Dis
decays, indicating a decrease in elemental segregation.
Fig. 4a-b shows a relatively linear relationship between SPD and SF
in low-Fe alloys. At higher Fe contents, the presence of single-phase γ-Fe
changes the interactions between elements from mutual interactions to
direct interactions with the phase. This may render the method unsuit-
able for studying the relationship between element composition distri-
bution and structure. The data points in Fig. 4c for GB come from all
three grain boundary types: GB1 (ATGB, Σ13<320>), GB2 (STGB,
Σ11<332>), and GB3 (ATGB, Σ13<100>), which have different
misorientation degrees (as shown in Table S1) and structures (see detail
atomic conguration around GB in Fig. S2). The varying degrees of GB
disorder and structural characteristics result in larger composition
uctuations, leading to the scattered data points in Fig. 4c. Nonetheless,
these results conrm a correlation between composition and structure,
enabling the prediction of composition based on structural characteris-
tics. A similar nding has also been reported in the previous work [40],
where a correlation between composition and structure based on these
two parameters was constructed.
3.3. Segregation modulated mechanical properties
Elemental segregation, as observed, can signicantly affect me-
chanical properties. For dislocations, segregation may regulate the
strength by altering the interactions between the dislocation and local
elements. Regarding interfacial structure (SF and GBs), elemental
segregation inuences the interfacial decohesion resistance of interfa-
cial structures. This section analyses the mechanical strength contrib-
uted by elemental segregation based on established strengthening
theories. The calculated values obtained from theory may show greater
variations than experimental strength changes. Nonetheless, the results
provide valuable insights into how atomic segregation impacts indi-
vidual microstructural defects, from the perspective of atomic in-
teractions, leading to a generalized understanding. Additionally, we
conducted experimental investigations on the inuence of segregation
on interfacial performance in the alloy, to validate the simulation
results.
3.3.1. Mechanical strength contributed from elemental segregation
Segregation around dislocations will change the solute-dislocation
interactions in HEAs, contributing to mechanical strength based on
the strengthening models in random solid solutions [50–52]. Our results
show that elemental segregation and CSRO are coupled together in
HEAs. As it is known that CSRO only in HEAs can have strengthening
effects, we prepare a reference system with SPDs (Ref-SPDs) to distin-
guish the strengthening effects due to both segregation and CSRO. In
Ref-SPDs, dislocation is introduced in a pre-equilibrated CSRO system,
as previously done to study the effects of CSRO [17]. In such a system,
the strengthening effect (
τ
Ref−SPD
dis ) is only from the interaction between
CSRO and solute,
τ
CSRO
dis , as Eq. (7) shows. In contrast, in our Seg-SPDs
system, seen in Eq. (8), the strengthening effect,
τ
Seg−SPD
dis , includes con-
tributions from both the chemical segregation (
τ
Seg
dis ) and CSRO (
τ
CSRO
dis ). In
this work, we consider segregation as elemental rearrangement, similar
to the formation of CSRO, which can be treated in a similar fashion as
CSRO (
τ
Seg,CSRO
dis ).
τ
Ref−SPD
dis =
τ
Ref ,CSRO
dis (7)
τ
Seg−SPD
dis =
τ
Seg
dis +
τ
CSRO
dis =
τ
Seg,CSRO
dis (8)
Based on the above consideration, the strengthening effect from the
interaction between solutes and dislocations is mainly attributed to the
Fig. 4. The excess chemical absorption of Cr element (Γ
Cr) vs. excess of structural disorder (Γtot
Dis) at different temperatures for (a) SPD models, (b) SF models, and (c)
all GB models (including GB1, GB2, and GB3). Despite the data points being limited and scattered, the results suggest a possible direct connection between the
heterogeneous distribution of an element and the disorder of the defect structure. For SPD and SF models, the data obtained in low-Fe concentrations models is
marked as the blue region; the other data with high-Fe addition is marked as red. Detailed correlation analysis can be seen in section A.2.3 in supplementary
materials. The more scattered data points in the GBs model are associated with the distinct types of grain boundaries, which stem from three different types of grain
boundaries: ATGB-GB1, STGB-GB2, and ATGB-GB3.
S. Ma et al.
Acta Materialia 264 (2024) 119537
7
local atomic conguration around the 2D line-defect SPD, where
segregation mainly occurs. Such segregation is much stronger than
CSRO. At the same temperature, it is reasonable to assume that the
strength from CSRO in Ref-SPD equals that in Seg-SPD approximatively.
Hence, the strength contributed by segregation can be derived by
eliminating the CSRO strength in Ref-SPD from Seg-SPD.
The elemental redistribution induced by both CSRO and chemical
segregation around the dislocation is described by the local Warren-
Cowley (W-C) parameters [29],
α
n,m=1−pn,mcm,(9)
where p
n,m
is the probability for a species (n) being the rst nearest
neighbor (1NN) to the solute (m) lying in the dislocation, and c
m
is the
global concentration of the species (m) in the entire system. The local
SRO results around dislocations are plotted in Fig. S9.
According to the strengthening theory proposed by Antillon et al.
[50], the strength from the interactions between the dislocation and
CSRO (
τ
CSRO) can be divided into two parts: mist contribution (
τ
y0)
from the elastic interaction between the specic solute and the stress
eld around the dislocation, and the bond-breaking contribution (
τ
b)
from the chemical interaction, i.e.,
τ
CSRO =
τ
y0+
τ
b. Here
τ
y0 is
computed using the strengthening theory demonstrated by Yin et al.
[51]:
τ
y0=A
τ
Γb2−1/3
μ
V1+
ν
V1−
ν
V4/3δ4/3(10)
where the prefactor A
τ
=0.04865[1-(A
z
-1)]/40] and the Zen anisotropy
A
z
=2C
44
/(C
11
–
−C
12
); b is the Burgers vector 1/6<112>; Γ is the
dislocation line tension, dened as Γ=
αμ
110/111
b
2
;
α
=0.125 for most
FCC alloys;
μ
110/111
is the shear modulus for the dislocation slipping
towards 〈110〉on the {111} plane, which can be obtained approx-
imatively according to
μ
110/111
=(C
11
–
−C
12
+C
44
)/3;
μ
V and
ν
V are the
Voigt-averaged values of the shear modulus and Poisson’s ratio,
respectively. Taking CSRO into consideration, the mist term δ is
computed as follows:
δ=
n
cnΔV2
n+
σ
2
ΔVn−Z{111}
n,m
cncm
α
n,mΔVnΔVm0.53Valloy (11)
where Z
{111}
=6 is the number of the 1NN on the {111} plane in FCC
materials; Valloy =3a3/4; ΔVm and ΔVm is the excess volume of solute n
and m to average atomic volume. cn and cm is the local concentration of
the species n and m around the dislocation, respectively. Then, the stress
required to overcome the binding energy barrier
τ
b is computed ac-
cording to:
τ
b=4a2b
3
√
n,m
cncm
α
n,mUn,m(12)
where U
n,m
is the binding energy of n-m pair, and a is the lattice constant.
After obtaining the related materials parameters using our atomistic
data (particularly all the
α
n,m values), we calculate the mechanical
strength in Ref-SPD and Seg-SPD using the above theory. The results are
listed in Table 2. Compared with Ref-SPD only with CSRO, the strength
induced by the interaction between local chemical uctuations and
dislocation in Seg-SPD increases three times. Taking the representative
case, the 25Fe model at 1000 K, as an example, the total strength of the
Ref-SPD system is 152.74 MPa, while Seg-SPD is 434.72 MPa. In this
case, 152.74 MPa in 25Fe Seg-SPD comes from the CSRO part. The
segregation around the dislocation contributes to the remaining ~282
MPa. This pronounced enhancement is predominantly attributed to
τ
b,
which signicantly depends on the local element segregation around the
dislocation. It should be pointed out that the local CSRO values around
the dislocation here were determined based on the local atomic
arrangement around the dislocation core, which only span a few atomic
planes within the cutoff. Such narrowed local-scale statistics may
overestimate the strength difference based on this theory, leading to the
obtained stress being higher than that of the real alloy due to relatively
weak segregationin practice. Thus, the obtained stresses are only used to
highlight the strength contribution from elemental segregation. As seen
in Fig. S9, the CSRO value of Cr-Cr pairs around dislocation in the Seg-
SPD alloy is much larger than that in the Ref-SPD alloy. The binding
energies for all pairs presented in Table 3 (refer to Supplementary Ma-
terial for detailed calculation method) suggest that the most robust bond
in the considered HEA is Cr-Cr, with a binding energy of approximately
−0.018 eV. Therefore, the strength from chemical bond breaking in-
creases essentially. In this segregation-strengthened alloy, eliminating
the CSRO strengthening effect, SPD segregation alone can also enhance
the strength by heightening the bond-breaking resistance thanks to
favored atomic Cr-Cr pairs.
3.3.2. Interfacial decohesion resistance from SF and GB segregation
The interfacial cohesion energy is dened as the energy required to
cleave a crystal along the GB plane, which can be used to evaluate the
embrittlement resistance. It can be calculated according to Eq. (13).
ECoh =EFS,1+EFS,2−ES(2A),(13)
where EFS,1 and EFS,2 are the energies of a system with a single free
surface, respectively. ES is the energy of the same system with the
interface. For random alloys, the three energy terms required are ob-
tained from the alloy with the same elemental distribution. In alloy
systems with interfacial segregation, the cohesive energy of the segre-
gation interface is the energy required to cleave a crystal along the
segregated grain boundary. The energy in Eq. (13) is obtained from the
same segregation system.
We calculate the cohesive energy in random and segregated models
for SF and GB2, as representative cases. As Fig. 5 shows, the cohesion
energy increases both in Seg-SF and Seg-GB2 models, especially for 25
Fe. Models with more Fe content (25Fe) and at a lower temperature
(800 K) exhibit higher cohesive energies due to the relatively stronger
segregation degree. It hence indicates that the interfacial decohesion
resistance is improved by chemical segregation.
To further clarify the contribution of segregation to interfacial
cohesion, we focus on GB models. We dene a chemical strengthening
parameter due to chemical changes in the whole system (i.e., CSRO and
segregation), which is given by the energy difference per unit area ΔEdiff .
The energy difference in GB systems, ΔEGB
diff , can be evaluated using
energy reduction per unit area in Seg-GBs relative to Ran-GBs, as below:
ΔEGB
diff =EGB
ran,sys −EGB
seg,sys(2A).(14)
Table 2
The strength, including mist (
τ
y0 in MPa) and bond-breaking (
τ
b in MPa)
contributions at 1000 K.
τ
y0 (MPa)
τ
b (MPa)
τ
tot (MPa)
Ref-SPD Seg-
SPD
Ref-SPD Seg-
SPD
Ref-SPD Seg-
SPD
5Fe 45.29
(±1.16)
57.75 80.07
(±9.42)
318.27 125.36
(±9.19)
376.01
25Fe 39.75
(±1.62)
54.13 112.99
(±10.98)
380.59 152.74
(±11.57)
434.72
Table 3
The binding energy (in eV) for 1-NN pairs in random 25Fe.
U
n,m
Co Ni Cr Fe
Co 0.0043 0.0055 0.0072 −0.0169
Ni 0.0117 −0.0065 −0.0106
Cr −0.0184 0.0165
Fe 0.0102
S. Ma et al.
Acta Materialia 264 (2024) 119537
8
Here, the subscript “sys” represents the whole system energy with
the same composition and atomic number, while “ran” and “seg” are the
systems with and without segregation, respectively. ΔEGB
diff represents the
energy reduction caused by the rearrangement of elements during MD/
MC simulations. By comparing ΔEGB
diff , we effectively assess the energy
reduction induced by the inhomogeneous distribution of elements dur-
ing the MC process, including segregation and CSRO.
During MC/MD, the segregation is coupled with CSRO formation,
leading to different atomic compositions in the bulk region from the
original state. It makes CSRO in the GB system different from that in the
GB-free system, even with the same nominal composition, which con-
tributes to energy reduction during MC/MD. Thus, three chemical var-
iations occur in GB models during MC/MD. The rst one is segregation
around GBs. The second is the ideal CSRO state in the GB-free system
with the same nominal composition. The last chemical change can be
regarded as the CRSO deviation from the second due to segregation.
Accordingly, the chemical strengthening contribution due to chemical
change in Seg-GBs can be divided into three parts: the rst is ΔEGB
seg, the
energy change due to GB segregation; the second is ΔEper
CSRO-the energy
contribution due to CSRO in bulk regions, which can be evaluated using
energy reduction in a GB-free system with the same compositions; the
third is ΔEseg
CSRO-the energy change in bulk regions resulting from the
CSRO indued by segregation. Therefore, ΔEGB
diff can be rewritten as:
ΔEGB
diff =ΔEGB
seg +ΔEper
CSRO +ΔEseg
CSRO.(15)
For the rst term in Eq. (15), the energy reduction in GB systems,
ΔEGB
seg , is mainly dependent on the chemical change induced by GBs,
which can be roughly obtained by the GB energy change during MC/MD:
ΔEGB
seg =EGB
seg −EGB
ran
=1
2AEGB,seg −Eper,mc
Nper,mc
NGB,seg−1
2AEGB,ran −Eper,ran
Nper,ran
NGB,ran,(16)
where EGB,seg and EGB,ran are the energy of the GB system after and before
MC, respectively; NGB,seg and NGB,ran are the corresponding total atom
amount, respectively.
The second term comes from CSRO in GB-free system, ΔEper
CSRO, as the
following Eq. (17) shows:
ΔEper
CSRO =Eper
ran,sys −Eper
seg,sys(2A),(17)
where Eper
ran,sys and Eper
seg,sys are system energy in random and MC perfect
models, respectively.
Finally, the contribution ΔEseg
CSRO for the last term can be derived from
the total energy reduction (ΔEGB
diff ) by eliminating ΔEGB
seg and ΔEper
CSRO ac-
cording to Eq. (15).
Here, we take 5Fe and 25Fe as typical examples, which exhibit
different segregation degrees, to demonstrate this strengthening effect.
The obtained results are plotted in Fig 6. It is found that all these three
terms in Eq. (11) contribute considerably to the strengthening effect of
the system. Both in 5Fe and 25Fe, ΔEper
CSRO is higher due to stronger CSRO
at a relatively lower temperature of 800 K, compared with 1000 K.
Similarly, ΔEper
CSRO in 25Fe with stronger CSRO is higher than that in 5Fe,
both at 800 K and 1000 K. For each contribution term, ΔEseg
CSRO is largest,
followed by ΔEper
CSRO and ΔEGB
seg. It is interestingly noted that ΔEGB
seg in GB2
is much smaller than other two terms and it only accounts for a small
fraction of the total energy reduction. For GB1 and GB3, this term
Fig. 5. The interfacial cohesion energy in (a) SF and (b) GB2 models. Ran-models are random systems. Seg-models are systems after MC/MD at 800 K and 1000 K.
Fig. 6. The strengthening effect from CSRO and segregation in Seg-GBs. ΔE
GB
diff is the strengthening contribution in segregated GBs, which is contributed by three
terms: ΔEGB
diff =ΔEGB
seg +ΔEper
CSRO +ΔEseg
CSRO. ΔEGB
seg is the energy contribution due to GB segregation, ΔEper
CSRO-the energy contribution due to CSRO in GB-free system, and
ΔEseg
CSRO is the energy change resulting from CSRO due to segregation.
S. Ma et al.
Acta Materialia 264 (2024) 119537
9
becomes dominant. This is because the GB2 structure is much more
ordered than GB1 and GB3, and the strengthening is relatively limited.
3.4. Mechanical properties in HEAs with GB segregation: an experimental
study
Fig. 7a-c presents the typical engineering stress-strain curves of three
alloys, i.e., 2.5Fe, 10Fe, and 25Fe alloys, tested at room temperature
with and without hydrogen charging. In the stress-strain curve, the
strength is evaluated by ultimate tensile strength (UTS:
τ
UTS
), and
ductility can be assessed by maximum elongation (δ). Compared with
the H-charged samples, the corresponding H-uncharged samples have
larger ultimate tensile strength and better toughness. As observed in
Ref. [4], after charging with H, the strength and toughness of the alloy
generally decrease, and the fracture of the alloy changes from trans-
granular fracture to intergranular fracture. It demonstrated that the
weakness of the alloy in H-charged alloys is the grain boundary. As
Fig. S13c shows, H-charged 2.5Fe suffered severe brittleness along GBs.
By contrast, the H-charged 25Fe alloy (Fig. S13d) shows a ductile frac-
ture surface consisting of numerous dimples, indicating a successful
suppression of hydrogen-induced grain-boundary embrittlement upon
the increased GB segregation.
Here, we compare the inuence of grain boundary element segre-
gation on hydrogen embrittlement-induced failure by calculating the
decrease in UTS (Δ
τ
UTS =
τ
H−Charged
UTS −
τ
H−Uncharged
UTS ) and elongation
(Δδ
loss
) before and after charging with H. As shown in Fig. 7d-f, Δ
τ
UTS
becomes smaller with the increase of Fe content. After charging with H,
Δ
τ
UTS changes following the order: −143 MPa (2.5Fe), −40 MPa (10Fe),
and +20 MPa (25Fe). This indicates that grain boundary segregation can
signicantly impede the strength decrease caused by H embrittlement
and maintain the strength of the grain boundary. In addition, ductility is
signicantly inuenced by segregation. Here, we evaluated the ductility
change using the total elongation loss rate (Δδ
loss
), which is dened as
Δδloss = (δCharged −δUncharged)/δUncharged . The results presented in Fig. 7f
indicate that after charging with gaseous H, there is a decrease in Δδ
loss
with an increase in Fe concentration, i.e., −61.7 % (2.5Fe), −35.3 %
(10Fe), and −4.6 % (25Fe). This nding suggests that Fe signicantly
inhibits the detrimental inuence of H on alloy toughness. As shown in
the results of section 3, there is obvious segregation of elements at grain
boundaries, and within the range of Fe concentration from 2.5 % to 25
%, the higher the Fe content, the more pronounced the element segre-
gation in the alloy. Therefore, we experimentally validate that element
segregation in CoNiCrFe alloy can improve the interfacial strength of the
alloy, and such improvement in interfacial performance increases with
the degree of element segregation.
In summary, this study compares three different alloy compositions
experimentally and demonstrates that element segregation improves
both interfacial strength and ductility. The results indicate a positive
impact of element segregation on interfacial properties, leading to
improved ultimate tensile strength and elongation. These ndings
contribute to our understanding of the relationship between element
segregation and the mechanical behavior of alloys, emphasizing the
importance of considering inhomogeneous element distribution to
optimize material properties.
4. Discussion
4.1. Segregation energy in HEAs
The general isotherm proposed by Donald McLean is widely used to
discuss segregation in alloys [53]:
XGB
i
1−XGB
i=XB
i
1−XGB
i
exp−ΔGo
RT ,(18)
where ΔGo is the standard Gibbs free energy for segregation; XB
i and XGB
i
are the atomic ratios of solute i in bulk and at GB, respectively.
According to thermodynamic principles, the standard Gibbs energy
of solute i at GB is dened as:
ΔGo
i=ΔHo
i−TΔSo
i+pΔV.(19)
Here ΔHo
i is the standard segregation enthalpy. ΔSo
i consists of
Fig. 7. The engineering stress-strain curves of three alloys in (a) H-charged and (b) -Uncharged states. (c) Comparison of the stress-strain curves before and after H
charging. (d) The ultimate tensile strength (
τ
UTS
) and (e) elongation (δ) variation with Fe concentration before and after H charging. (f) The loss rate of elongation
and reduction in ultimate tensile strength for different alloys after H charging.
S. Ma et al.
Acta Materialia 264 (2024) 119537
10
several terms: mixing entropy, vibrational, anharmonic, multiplicity,
magnetic, and electronic entropy. For solids, pΔV is nearly 0. Due to the
lack of precise routines for the theoretical calculation of entropy, most
studies usually simplify the entropy terms or even ignore them. In this
case, the segregation energy is often represented only by the segregation
enthalpy ΔHo
i.
Based on the above consideration, the segregation energy is often
computed to represent Gibbs free energy for segregation using the in-
ternal energy change when swapping a solute in bulk with a solvent
atom at GBs:
ΔGseg =Ei
GB −EGB−Ei
bulk −Ebulk.(20)
Here, Ei
bulk and Ei
GB are the energy of the system where an atom i is in
bulk and at GB, respectively. Ebulk and EGB are the energy of the pristine
bulk and GB systems, correspondingly. The calculation in Eq. (20) only
holds for the segregation site at the same type (interstitial/substitutional
sites) in the bulk and GB.
On the other hand, if the atomic concentration prole is known,
according to Eq. (18), ΔGseg can be obtained directly by:
ΔGseg = − kBTlnXGB (1−XB)
XB(1−XGB).(21)
Here we compare the segregation energy calculated by MS (indicated
as ΔGseg
th , Eq. (20)) and measured using the concentration proles from
MC/MD (described as ΔGseg
md, Eq. (21)) in Fig. 8. For ΔGseg
md, Co and Ni
display positive segregation energies in the whole GB range. The pro-
nounced negative segregation energy of Cr is consistent well with its
enrichment around GBs. However, the segregation energy calculated for
Fe contradicts the concentration prole in Fig. 2. While MS predicts
strongly negative segregation energy of Fe, the isothermal equation
suggests that the segregation energy of Fe should be positive in the
whole range. This contradiction is attributed to the stronger interactions
between Fe and the other three elements. As shown in Table 3, the
binding energies between Fe and other elements are relatively large
compared to the pairs formed by other elements. In particular, the
binding energies are −0.0169 eV (Fe-Co), −0.0106 eV (Fe-Ni), and
0.0165 eV (Fe-Cr). This suggests that all the other elements have a sig-
nicant inuence on the distribution of Fe, leading to the observed
contradiction of segregation energies for the Fe element. These results
indicate that the segregation energy measured at 0 K is unsuitable for
predicting segregation in HEA systems. The disagreement denotes the
importance of entropy, especially the congurational entropy at nite
temperatures. We collect and compare the structural disorder and
atomic sites at GB cores in relaxed GB congurations in pure Ni and
CoNiCrFe. As Fig. S12 shows, the atomic sites for segregation in
CoNiCrFe-GBs are much more abundant than those in Ni-GBs. In addi-
tion, the structural disorder in CoNiCrFe-GBs is more pronounced than
Ni-GBs. It indicates a signicant role of congurational entropy in
inuencing the segregation free energies, which cannot be ignored in
HEAs. In addition, from Section 3, we can see that the coupled CSRO is
signicantly pronounced in multicomponent HEAs. Such a local chem-
ical change may also alter the lattice vibrational properties and lead to
an appreciable contribution in entropy. In addition, as Fig. S12 shows,
the atomic sites in CoNiCrFe-GBs are more disordered than in Ni-GBs. It
indicates a signicant role of congurational entropy in inuencing the
segregation free energies, which cannot be ignored in HEAs. These ob-
servations underline the complex entropy contribution at nite tem-
peratures in HEAs, and the enthalpic term alone cannot fully account for
the segregation trend.
From the results in Section 3.2, we can conclude that the structural
disorder parameter displays a good agreement with the chemical
segregation prole for all extended defects examined. The structural
property, Γtot
Dis, correlates well with chemical absorption Γi in low Fe
addition systems, which can be used to predict the chemical change.
What’s more, this correlation can also be used to analyze the additional
chemical uctuation resulting from stress in SPDs. Hence, it can be used
as a powerful parameter to dictate the segregation trend in extended
defects, which can be easily obtained.
4.2. Segregation in HEAs explained by atomic interactions
The main driving forces for segregation include three parts: interfa-
cial energy [54], elastic solute strain energy [27,55], and interaction
energy [5,56]. The surface energies of the phase composed of the four
elements are comparable, suggesting that the rst term is similar for the
four elements in the considered HEA. The second term arises from an
additional mist stress eld and high strain energy, which will attract
elements to reduce the system energy. The third term is contributed by
atomic interactions, which is the most important in governing the
segregation behavior [5]. In the considered HEA, the segregation of Cr
should arise from its particular interaction with the rest three elements.
To reveal the underlying mechanism, the binding energies for each
atomic pair are evaluated and collected in random 25Fe models by
sampling different local atomic environments (more than 1000 calcu-
lations) around the pairs. The positive binding energy indicates a
repelling force between two species, and the negative suggests attrac-
tion. As shown in Table 3, the binding energy follows the order in 25Fe:
Cr-Fe >Ni-Ni >Fe-Fe >Co-Cr >Co-Ni >Co-Co >0 >Ni-Fe >Co-Fe >
Cr-Cr pair. Here Cr-Cr, Co-Fe, and Ni-Fe display the most potent
attractive forces, while Cr-Fe shows the strongest repulsive interaction.
Thus, Ni and Co prefer to bond with Fe but repel Cr. When Fe concen-
tration is low, some extra Cr will be bonded with Ni/Cr. However, with
increasing Fe, those Ni and Co will be deprived of Fe and prefer to form
Ni-Fe and Co-Fe pairs, leading to the separation of Cr. The combined
effect of the strong binding force of Cr-Cr and the depletion of Ni and Co
due to increasing Fe concentration thus causes strong segregation of Cr.
This analysis is in line with the pair density as described using
α
n,m
Fig. 8. Segregation energy proles for the four different elements in 25Fe at 0 K: (a) GB1, (b) GB2, and (c) GB3. The dot and dash lines are segregation energy
measured using MS (ΔG
seg
md) and classical segregation theory (ΔGseg
th ), respectively. The GB core is marked using a black arrow.
S. Ma et al.
Acta Materialia 264 (2024) 119537
11
(wherein a negative value represents a high fraction of pairs). As seen in
Fig. S10,
α
CrCr,
α
CoFe,
α
NiFe, and
α
NiFe are largely negative, whereas
α
CrFe
and
α
CoCr are positive. It again conrms the preferential formation of
Cr-Cr and Fe-Ni/Co/Cr bonds, and Fe addition facilitates Cr-Cr binding.
The elemental segregation may facilitate the grain boundary
embrittlement or de-embrittlement depending on the nature of the
segregating elements and the composition of the alloy [57,58]. To
further clarify why this alloy exhibits such a signicant strengthening
effect, taking the random 25Fe GB2 models as an example, we collect
and compare the substitutional energy of every substitution type (n/m, n
is replaced to m) in bulk without GB (EBulk
n/m) and all GB sites (EGB
n/m). The
elemental substitutional energy is dened as the energy change when
replacing an atom n to m (expressed as “n/m”), as Eq. (21) shows:
En/m=Em−En,(21)
where En is the energy of the initial system with a xed solute n, and
Emis the energy of the replaced system with the atom m, under same
local atomic environments. For the same substitutional type (n/m), the
energy difference (Em-En) is the same in bulk and GB. When the substi-
tutional energy of n/m is negative, it indicates the repulsion of n and
attraction of solute m, leading to a more stable conguration. The ob-
tained results where the substitution is performed in the bulk region and
GB region are provided in Fig. 9.
As Fig. 9a shows, the average substitutional energy of Ni and Co by
other elements in bulk is negative, indicating that Ni and Co would be
stable in bulk. Fe is close to zero, while Cr is positive, meaning that Cr is
unfavorable in bulk. In GB sites (Fig. 9b), although the substitutional
energy spectrum shows uctuations at different sites, its variation is
small (within the range of 0.2 eV). In particular, the average substitu-
tional energy of Cr is positive at all GB sites, and it is ~0.2 eV lower than
that in bulk. The net substitutional energy difference (ΔE
GB-Bulk
) was
plotted in Fig. 9c. When ΔE
GB-Bulk
of element is below zero, it would be
more favored in GB regions and acts as GB strengthening elements. In
contrast, positive ΔE
GB-Bulk
indicates a strengthened effect in bulk. From
Fig. 9c, Cr is a GB-strengthening element, while Ni and Co are bulk-
strengthening elements. The strengthening effect of Fe is nearly the
same in bulk and GB. The elemental segregation results from Section 3
reveal that Cr segregates towards the extended defect, while simulta-
neously inhibiting the distribution of Co and Ni around it. Consequently,
the strength increases due to the elemental segregation in various defect
structures of the CoNiCrFe HEA, which results from both the enrichment
of strengthening element (Cr) and the suppression of weakening ele-
ments (Co/Ni).
5. Conclusion
In this work, we systematically investigate the segregation phe-
nomena around extended defects: SPD, SF, and GBs in CoNiCrFe HEAs
with different Fe concentrations at a temperature range of 300 ~1300 K.
It allows the following conclusions to be made:
(1) There is strong elemental segregation around extended defects in
CoNiCrFe HEAs. A pronounced Cr enrichment and Co/Ni/Fe
depletion generally occur. Due to the segregation, a distinguished
concentration gap between Cr and Co/Ni/Fe is formed resulting
from the bonding preference among different elements.
(2) Through analysis of the strengthening effects from CSRO and
segregation, we have revealed that segregation is an effective
parameter to regulate the mechanical strength in HEAs. The
dislocation strengthening effect and interfacial embrittlement
resistance are affected by segregation and CSRO.
(3) Comparison of three different alloy compositions, in terms of
ultimate tensile strength and elongation, provides evidence that
element segregation improves both interfacial strength and
ductility in the studied HEA. These ndings highlight the positive
impact of element segregation on interfacial properties, resulting
in improved mechanical performance, in agreement with
simulations.
(4) Based on the comparisons and analysis of segregation energy
obtained from different methodologies, we show that segregation
entropy plays a critical role in governing segregation in HEAs,
which cannot be ignored. The enthalpic term alone cannot fully
account for the segregation trend.
(5) The segregation strengthening can be explained by the relative
contribution to strength in bulk and GB sites. The coupled
strengthening effect of Cr-segregation in GB and Co- and Ni-
enrichment in bulk contribute to the segregation strengthening
in this work.
Declaration of interests
The authors declare that they have no known competing nancial
interests or personal relationships that could have appeared to inuence
the work reported in this paper.
Acknowledgement
This work was supported by the National Natural Science Foundation
of China (No. 11975193), and Research Grant Council of Hong Kong
(No. C1017-21G and No. 11200421). This work was carried out using
the computational facilities, CityU Burgundy, managed and provided by
Fig. 9. The substitutional energy of n/Co (n=Ni, Cr, Fe), n/Ni (n=Co, Cr, Fe), n/Cr (n=Ni, Co, Fe), and n/Fe (n=Co, Ni, Cr), as well as their average in the 25Fe (a)
bulk, and (b) GB2 site along the y direction. The average substitutional energy of species m is the average energy change when m is replaced by n (n∕=m). For
example, Co denotes the average energy of Ni/Co, Cr/Co, Fe/Co. (c) The substitutional energy difference between the average substitutional energy in GB and bulk
(GB-Bulk) in 25Fe.
S. Ma et al.
Acta Materialia 264 (2024) 119537
12
the Computing Services centre at City University of Hong Kong (https:
//www.cityu.edu.hk/)
Supplementary materials
Supplementary material associated with this article can be found, in
the online version, at doi:10.1016/j.actamat.2023.119537.
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