of 12
Effect of temperature on small-scale deformation of individual face-
centered-cubic and body-centered-cubic phases of an Al
0.7
CoCrFeNi
high-entropy alloy
Adenike M. Giwa
a
, Zachary H. Aitken
b
,
, Peter K. Liaw
c
,Yong-WeiZhang
b
, Julia R. Greer
a
,
a
Division of Engineering and Applied Sciences, California Institute of Technology, Pasadena, CA 91106, USA
b
Institute of High Performance Computing (IHPC), A*STAR, 138632, Singapore
c
Department of Materials Science and Engineering, The University of Tennessee, Knoxville, TN 37996, USA
HIGHLIGHTS
Both phases of a dual-phase Al
0.7
CoCrFeNi
high entropy alloy display a
smaller is
stronger
size effect at 295 K, 143 K, and
40 K.
The size effect decreases in the face-
centered cubic phase while remaining
constant in the body-centered cubic
phase as temperature decreases.
The decreasing size-effect in the face-
centered cubic phase is a result of increas-
ing lattice friction stress with decreasing
temperature.
GRAPHICAL ABSTRACT
abstract
article info
Article history:
Received 17 December 2019
Received in revised form 18 February 2020
Accepted 27 February 2020
Available online 28 February 2020
Keywords:
High-entropy alloys
Cryogenic temperature
Deformation mechanisms
Al
0.7
CoCrFeNi
Nanopillars
Dislocations
Nanoplasticity
High-entropy alloys (HEAs) represent an important class of structural materials because of their high strength,
ductility, and thermal stability. Understanding the mechanical response of isolated phases of a FCC/BCC dual-
phase HEA is integral to understanding the mechanical properties of these alloys in the bulk. We investigate
the compressive response of single-crystalline cylinders with diameters between 400 nm and 2
μ
m excised
from individual grains within FCC and BCC phases of the dual-phase Al
0.7
CoCrFeNi HEA at 295 K, 143 K, and
40 K. We observed a
smaller is stronger
size effect in the yield strength as a function of pillar diameter, D, of
both alloy phases for all temperatures, with a power-law exponent, m, decreasing with temperature for the
FCC phase, and remaining constant for all temperatures in the BCC phase. We found reduced work-hardening
rates and more extensive strain bursts during deformation at lower temperatures in all samples. We performed
molecular dynamics simulations of similar FCC and BCC HEA compression that displayed deformation dominated
by dislocation slip at all temperatures. We discussed theories of low-temperature strengthening in HEAs, com-
pared them to our experimental data and assessed how they manifest in the observed temperature-dependent
size effect and work-hardening.
© 2020 Published by Elsevier Ltd. This is an open
access article under the CC BY-NC-ND license (
http://
creativecommons.org/li
censes/by-nc-nd/4.0/
).
Materials and Design 191 (2020) 108611
Corresponding authors.
E-mail addresses:
zach-aitken@ihpc.a-star.edu.sg
(Z.H. Aitken),
jrgreer@caltech.edu
(J.R. Greer).
https://doi.org/10.1016/j.matdes.2020.108611
0264-1275/© 2020 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (
http://creativecommons.org/licenses/by-nc-nd/4.0/
).
Contents lists available at
ScienceDirect
Materials and Design
journal homepage:
www.elsevier.com/locate/matdes
1. Introduction
High-entropy alloys (HEAs) are a class of alloys that contain multiple
elements in equi- or near equi-atomic proportions. These alloys were
fi
rst developed by Yeh, et al. and Cantor, et al. in 2004 and found to dis-
play substantially higher strength, ductility, and wear resistance, com-
pared to conventional alloys [
1
5
]. Improved mechanical properties of
HEAs stem from the large lattice distortions and sluggish diffusion
within their atomic microstructures [
6
]. Identifying and predicting sta-
ble HEA compositions and their associated properties have been chal-
lenging because the fundamental properties of individual elements
and phases need to be understood in addition to the complex interac-
tions of their combinations, which could sometimes lead to the forma-
tion of intermetallics and amorphous phases [
7
]. Some attempts have
been made to classify HEAs based on their crystal structures and me-
chanical behaviour [
8
], and several studies on microstructural evolution
with minor-element alloying provide some insights into understanding
stable HEA microstructures [
9
13
]. HEAs often exhibit particularly in-
teresting properties at extreme conditions. Eutectic and near-eutectic
HEAs show good castability and display high strengths and ductility at
elevated and cryogenic temperatures [
14
16
]. The mechanical proper-
ties of these HEAs have also shown to be compositional robust [
15
].
For example, the CrMnFeCoNi HEA undergoes a face-centered-cubic to
hexagonal-close-packed (FCC-HCP) phase transformation induced by
the extensive stacking fault formation at pressures
N
14 GPa [
17
]. The
same CrMnFeCoNi HEA was reported to have a tensile strength of
1 GPa and a fracture toughness of 200 MPa
ffiffiffiffiffi
m
p
, as well as tensile
deformability over a 7% strain at 77 K, compared with 5% at room tem-
perature, enabled by deformation twinning [
18
]. Excellent fracture
toughness at room temperature has also been explained in this same
HEA as a combination of several dislocation mechanisms that include
the partial dislocation slip and dislocation-barrier formation, formation
of stacking-fault parallelepipeds, and nano-scale twinned regions span-
ning the crack tip [
19
]. This feature demonstrates that HEAs make use of
multiple plastic-deformation mechanisms to achieve their favourable
mechanical properties.
To identify and quantify the contributions of different microstruc-
tural parameters, such as the dislocation density, grain size, stacking
fault energy, propensity for twin formation, etc. to the mechanical re-
sponse of bulk metals, conventional practice has been to conduct
systematic experiments on small-scale samples [
20
]. Small-scale exper-
iments are also useful for the design of nanoelectromechanical systems
(NEMS) and microelectromechanical systems (MEMS) [
21
23
]. In addi-
tion to investigating deformation at room temperature, exploring the
effect of temperature on the deformation of HEAs is also essential for
aerospace applications, satellite parts, and tanks for lique
fi
ed gases.
In our earlier work, micro-sized pillars excised from individual FCC
and body-centered-cubic (BCC) phases of the same Al
0.7
CoCrFeNi alloy
were compressed at room temperature and revealed different mechan-
ical behaviour between the two phases. The BCC nano- and micro-
pillars exhibited continuous plastic
fl
ows and high axial strengths, for
example 2.2 ±0.24 GPa for 400-nm-sized [001]-oriented pillars; FCC
samples had stochastic strain bursts throughout deformation and
lower yield strengths, e.g., 1.2 ±0.13 GPa for [324]-oriented pillars of
equivalent size [
24
]. In the present work, we performed in-situ uniaxial
compression experiments on micro- and nano-pillars with diameters
ranging from 394 nm to 2114 nm made from FCC and BCC phases of
this same alloy at temperatures of 40 K, 143 K, and 295 K to investigate
the relative contributions of temperature and sample size under
compressive loading. Our experiments demonstrate that the yield
strength of 400-nm-sized [324]-oriented FCC pillars deformed at 40 K
is 2.0 ±0.19 GPa and that for [001]-oriented BCC pillars is 3.2 ±
0.28 GPa. We observed power-law strengthening with decreasing sam-
ple size at each temperature, with a size-effect exponent of
m
=0.33at
all temperatures for BCC samples; a decreasing
m
of 0.68 to 0.47 and to
0.38 asthe temperature wasreduced from 298 K to143K and to40 K for
the FCC samples, respectively. Transmission electron microscopy (TEM)
analysis of the deformed pillars shows dislocations and their networks
present in all the samples. To provide insight into the dominant defor-
mation mechanisms present in experiments, we also performed molec-
ular dynamics (MD) simulations of compression on similar FCC and BCC
HEA nanopillars. In simulations, we observed that deformation is driven
by the nucleation of partial dislocations from the surface of these
initially-pristine nanopillars.
2. Materials and methods
The Al
0.7
CoCrFeNi HEA was fabricated using the vacuum arc-melting
method with powders (Al, Co, Cr, Fe, and Ni) of 99% purity in weight
percent. Details of this process are described in [
24
]. The crystallo-
graphic phase and orientation information were identi
fi
ed using the
HKL Electron Back Scatter Diffraction system coupled to a ZEISS Scan-
ning Electron Microscope. The bulk HEA displays a dendritic structure
where dendrite regions have a Fe, Cr, and Co-rich FCC lattice, and
interdendrite regions have an Al, Ni-rich BCC lattice [
24
]. The TEM anal-
ysis of the BCC phase further indicates the presence of a disordered A2
lattice and ordered B2 phases. This microstructure is consistent with
previous reports for the Al
x
CoCrFeNi HEA system [
9
,
13
]. The nanopillars
were fabricated from individual grains with a [324] orientation for the
FCC phase and [001] orientation for the BCC phase using the FEI Versa
three-dimensional (3D) dual scanning electron microscope (SEM)
equipped with a focused ion beam(FIB). Thefabrication details for mak-
ing concentric circular milling pillars with the desired diameters of
394 nm to 2114 nm and a 3 (height): 1 (diameter) aspect ratio can be
found in [
24
]. A typical pillar taper angle was estimated to be 2
3° and
no
N
5° for all pillars of any size.
We conducted nanomechanical experiments in an in-situ instru-
ment, which consists of a nanomechanical module (InSEM
,
Nanomechanics Inc.) inside a SEM (FEI Quanta 200 FEG), with a cryo-
genic assembly (Janis research company), which has a vacuum transfer
line that can be connected to either liquid helium or liquid nitrogen to
control the temperature. This cryogenic assembly is equipped with a
temperature controller containing thermocouples to read the tempera-
ture at the cold
fi
nger entry to the SEM chamber and at the sample
stage. Room-temperature experiments were conducted in the same
setup without the cryogenic assembly. A detailed description of the
cryogenic-testing methodology can be found in Lee, et al. [
23
]. A con-
stant temperature of ~143 K was achieved after 3 h of releasing the liq-
uid nitrogen through the transfer line to the SEM chamber and a
temperature of ~40 K after about 2.5 h was achieved using liquid
helium. Thenanomechanicalexperiments were done2 h after thetarget
temperature was reached.
We used a 5
μ
m-diameter tungsten carbide
fl
at punch indenter tip
coated with 5 nm of Au for the uniaxial compression experiments. The
Au coatingis to prevent chargingof thetip for better SEM imaging. Sam-
ples were compressed at a target strain rate of 10
-3
s
-1
up toa total strain
of 15%. Force and displacement were measured, and engineering stress
and strain were calculated by dividing each by the initial cross-sectional
area and pillar height, respectively. At least 4 samples were compressed
for each set of phase, diameter, and temperature for assuring the accu-
racy of the test data.
The TEM samples of compressed nano-pillars were fabricated using
the lift-out approach by utilizing a FIB, an Autoprobe
nanomanipulator,
and Pt deposition, and the region of interest was removed and fastened
onto a TEM grid. The samples were then thinned using the Ga
+
source
until the sample thickness of 60
65 nm was achieved. For the
fi
nal thin-
ning, a voltage of 8 KeV and a current of 42 pA were used. A FEI TEM
Tecnai TFT 30 operating at 300 KeV w
as employed to study the lamella
containing the deformed pillars. We obtained and indexed diffraction
2
A.M. Giwa et al. / Materials and Design 191 (2020) 108611
patterns of the pillars and collected several bright-
fi
eld, dark-
fi
eld, and
high-resolution images of the deformed microstructure.
We employed MD simulations to investigate atomic-deformation
mechanisms present in a representative FCC and BCC HEA nanopillars
under compression. To construct the initial sample, we created a cylin-
drical geometry with the axis aligned along the [324] crystallographic
direction for the FCC sample and along the [001] crystallographic direc-
tion for the BCC sample to match the experiments. The initial samples
were monatomic, and the HEAs were created by randomly-replacing
atomic species to achieve an equi-atomic composition. The dimensions
of the cylinders were 30 nm in diameter and 90 nm in length. A periodic
boundary condition was prescribed in the direction parallel to the cylin-
der axis; and free surface-boundary conditions were prescribed in the
two directions perpendicular to the axis. The energy of the initial struc-
tures was minimized, following a conjugate gradient scheme. The sys-
tem was assigned a velocity pro
fi
le corresponding to the simulation
temperature of 50 K, 143 K, or 300 K. The pillars were then equilibrated
for 200 ps at the assigned temperature and zero pressure, followed by
the equilibration for 200 ps under the time integration of the
microcanonical ensemble (NVE). All simulations were performed
using an integration time step of 1 fs. Compression was performed by
deforming the simulation box at a strain rate of 10
8
s
-1
up to at least a
total strain of 15%. Such a strain rate is an unavoidable consequence of
the time scales accessible during MD simulations and may over-
predict the initial yield strength in such samples. We thus restrict our
discussion of the simulations to the qualitative comparison.
We implemented the embedded atom method (EAM) potential de-
veloped by Zhou, et al. [
25
] and chose the equi-atomic CoFeNiPd system
as a representative FCC HEA and the equi-atomic AlMoWTa system as
our representative BCC HEA. These systems were chosen based on
(1) similarity to the experimental composition, (2) availability of inter-
atomic potentials, and (3) energetic and mechanical lattice stability. The
choice of a similar system for the BCC phase is further complicated by
the presence of a modulated plate microstructure composed of the or-
dered B2 and disordered A2 lattices [
13
].Despite sucha complicated mi-
crostructure, it has been reported that deformation is concentrated in
the disordered A2 phases [
26
]. Following this observation, we choose
to utilize a disordered A2 lattice in our simulations. All simulations
were performed using the Large-scale Atomic/Molecular Massively Par-
allel Simulator (LAMMPS) molecular dynamics software [
27
], and Open
Visualization Tool (OVITO) software [
28
] was employed for the com-
mon neighbour analysis, calculation of atomic shear strain, and
visualization.
3. Results
3.1. FCC experimental results
Fig. 1
(a
c) show the stress vs. strain data for representative [324]-
oriented FCC nanopillars with diameters ranging from 394 nm to
2114 nm, deformed at 295 K [
Fig. 1
(a)], 143 K [
Fig. 1
(b)], and 40 K
[
Fig. 1
(c)]. These experiments revealed that the yield and
fl
ow stresses
of samples with equivalent diameters were the highest at 40 K and low-
est at 295 K. For example, the ~700 nm-diameter pillars had a yield
strength of ~0.7 GPa at 295 K, 1.4 GPa at 143 K, and 1.6 GPa at 40 K.
The relative increase in the yield stress with temperature appears to
be lower for smaller diameter samples: theyield strength of 2
μ
m-diam-
eter pillars increased by a factor of ~2.0 when temperature was lowered
from 295 K to 143 K and by a factor of ~1.2 from 143 K to 40 K. For the
400-nm-diameter samples, this relative strengthening was ~1.45 and
1.25 for the same-temperature variations. The stress-strain data of the
FCC pillars contains numerous stochastic bursts, whose frequency ap-
pears to increase at smaller pillar sizes and whose magnitude increases
at lower temperatures for the same pillar size.
Fig. 1
(a
c) also show SEM images of the typical deformation mor-
phology of [324]-oriented FCC samples at each temperature, which
contain multiple slip lines denoted by yellow arrows, predominantly
parallel to each other and oriented at ~38° to 48° with respect to the
loading direction, consistent with
011
/{111} slip systems. The primary
slip direction is indicated by the yellow arrows in the post-compressed
pillars. The red arrows in
Fig. 1
(b, c) correspond to the emergence of
secondary slip at the lower temperatures of 143 K and 40 K. These im-
ages andthecompressive stress-strain responsessuggest that thedefor-
mation mechanism remained the same at all these temperatures.
From the stress vs. strain data of the deformed FCC HEA nanopillars
in
Fig. 1
(a
c), we observed intermittent strain bursts at room tempera-
ture and increase in
fl
ow stresses after each burst event. At low temper-
atures, longer strain burst regimes were observed, and we found
Fig. 1.
Representative stress-strain curves of [324]-oriented nanopillars constructed from
the FCC phase of a Al
0.7
CoCrFeNi HEA compressed at (a) 295 K, (b) 143 K, and (c) 40 K.
Typical deformed 2-
μ
m-sized nanopillars are shown as insets in the stress-strain plots at
the test temperatures. The scale bar represents 3
μ
m. Yellow arrows (a, b, c) indicates
the primary slip direction while red arrows (b, c) indicates the secondary slip direction.
(For interpretation of the references to colour in this
fi
gure legend, the reader is referred
to the web version of this article.)
3
A.M. Giwa et al. / Materials and Design 191 (2020) 108611
minimal or no increase at all in the
fl
ow stress until a strain of ~15% was
reached. For example, the stress-strain curves at 295 K in
Fig. 1
(a) showed that the
fi
rst major strain burst event for a 400-nm-sized
pillar occurred at a strain of 2%, then followed by another event at 5, 9,
10, and 12% strains till the unloading event. At 143 K in
Fig. 1
(b), strain
hardening occurred till a 5% strain and no other strain burst activity oc-
curred.At 40K,apartfrom the bursteventsatyield, noother strain burst
events occurred. This trend suggests that though multiple parallel slip
lines were observed in the deformed pillars at the lower temperatures,
these multiple slip events took place within a burst regime.
3.2. BCC experimental results
Fig. 2
(a
c) present the compressive stress-strain response of
nanopillars with diameters between ~400 nm and 1.8
μ
m, fabricated
from the [001]-oriented BCC phase deformed at temperatures of 295 K
[
Fig. 2
(a)],143 K [
Fig. 2
(b)],and 40 K [
Fig. 2
(c)]. We observed a marginal
increase in the yield strength at different temperatures for the same pil-
lar sizes: the yield strength of a 400-nm-diameter pillar increased by
20%, from 2.5 GPa to 3.0 GPa as the temperature was lowered from
295 K to 143 K, and then by an additional 6.67%, from 3.0 GPa to
3.2 GPa as it was further lowered to 40 K. At room temperature, 2
μ
m-sized BCC HEA pillars had yield strengths of ~1.5 GPa, and an in-
crease of 46% was observed in 400-nm-sized BCC HEA pillars having
yield strengths of ~2.2 GPa. The deformation signature of these samples
was apparently different from that of FCC pillars: the stress-strain data
was smoother and less stochastic, especially for samples with diameters
larger than ~2
μ
m.
We calculated the work hardening exponent,
n
,as
n
¼
ln
σ
12
σ
6
ðÞ
ln
ε
12
ε
6
ðÞ
ð
1
Þ
for BCC nanopillars in the strain range of 6 to 12% for all the tempera-
tures.
σ
x
and
ε
x
indicate the measured stress and strain at the strain of
x%. We observed that the work-hardening exponent decreased with de-
creasing temperature [
Fig. 2
(a
c)]. For example, the work-hardening
exponent calculated from the stress-strain data of 2-
μ
m-size BCC pillars
decreased from
n
= 0.27 at 295 K to 0.19 at 143 K and to 0.16 at 40 K.
Fig. 2
(a) shows a continuous plastic behaviour in a 2-
μ
m-sized BCC pil-
lar deformed at room temperature, which is different from the
stochastic-plastic behaviour of smaller pillar sizes of 400 nm to 1
μ
m.
This disparity suggests a transition from the bulk-like deformation in
2-
μ
m-pillars to nanoscale deformation in the smaller pillars.
3.3. Size effect
Fig. 3
(a) shows the plot of the yield stress of [324]-oriented FCC pil-
lars vs. the pillar diameter deformed at each temperature. The yield
strength, which is de
fi
ned as the stress at the
fi
rst displacement burst
following the elastic regime, was determined from the stress-strain
data for each pillar, examples of which are shown in
Fig. 1
(a
c). Error
bars represent the range of stresses for each pillar dimension. This plot
clearly demonstrates that the strength of pillars of all sizes consistently
increased with a reduction in temperature. The highest strength in ex-
cess of 2 GPa was attained by samples with the smallest diameters of
~400 nm at 40 K, while ~2-
μ
m-diameter pillars deformed at room tem-
perature had the lowest strength of ~ 400 MPa.
Fig. 3
(b) shows a log-log
plot of these yield stresses resolved onto {110}/
111
slip systems and
normalized by the shear modulus,
G
, vs. pillar diameter,
D
, normalized
by the Burgers vector,
b
, at each temperature. We used the Burgers vec-
tor, |
b
|, of 0.2526 nm, calculated based on |
b
|=
a
/2
b
110
N
,where
a
was
taken from previous XRD studies with a value of 0.3572 nm [
13
]. Con-
sidering the FCC phase displays a greater composition of Co, Cr, and Fe
[
24
],
G
was taken as 75 GPa, common for FeCr alloys [
29
]. This plot re-
veals a power-law dependence of
τ
/
G
=
A
(
D
/
b
)
m
, where
m
is the
size-effect exponent that demarks each isothermal size-effect plot. It is
evident that in the FCC samples, the size effect exponent decreased
with temperature: from 0.68 for 295 K to 0.47 for 143 K, and to 0.38
for 40 K. We provide a summary of size-effect exponents in
Table 1
.
Analogously,
Fig. 3
(c) shows the plot of the yield stresses of
001
-
oriented BCC pillars vs. pillar diameter deformed at each temperature.
These yield strengths were de
fi
ned as the stresses at a 0.2% offset strain
in the stress-strain data for each pillar [
Fig. 2
(a
c)]. The BCC data points
representtheaverage values, and theerror bars denote thestandard de-
viation for each pillar dimension. This plot clearly demonstrates that the
Fig. 2.
Representative stress-strain curves of [001]-oriented nanopillars constructed from
the BCC phase of a Al
0.7
CoCrFeNi HEA compressed at (a) 295 K, (b) 143 K, and (c) 40 K.
Typical deformed 2-
μ
m-sized nanopillars are shown in the insets of the stress-strain
plots at the test temperatures. The scale bar represents 1
μ
m. Yellow arrows indicate the
slip traces. (For interpretation of the references to colour in this
fi
gure legend, the
reader is referred to the web version of this article.)
4
A.M. Giwa et al. / Materials and Design 191 (2020) 108611
strengths of the BCC pillars of all the sizes increased with temperature
reduction. The highest strengths in excess of 3.2 GPa were attained by
samples with the smallest diameters of ~400 nm at 40 K, while the larg-
est samples, with ~2-
μ
m-diameters deformed at room temperature had
the lowest strength of ~1.5 GPa.
Fig. 3
(d) shows a log-log plot of these
yield stresses resolved onto the {110}/
111
slip system and normalized
by the shear modulus,
G
, vs. pillar diameter,
D
,normalizedbytheBur-
gers vector,
b
, at each temperature. We used the Burgers vector, |
b
|, of
0.2484 nm, calculated based on
j
b
ffiffiffi
3
p
a
=
2
b
111
N
, where
a
was
taken from previous XRD studies with a value of 0.2868 nm [
13
]. Con-
sidering the BCC phase displays a greater composition of Al and Ni
[
24
],
G
was taken as 70 GPa, common for NiAl alloys [
30
]. This plot
also reveals a power-law dependence of
τ
/
G
=
A
(
D
/
b
)
m
. It is evident
that in contrast to the FCC samples, the size-effect exponent remains
the same at
m=
0.33 for the BCC phase at all the temperatures.
3.4. Molecular dynamics results
To better understand the atomistic mechanisms underlying the
strength and temperature dependence observed experimentally, we
performed molecular dynamics simulations on the compression of our
representative Co
25
Fe
25
Ni
25
Pd
25
FCC and Al
25
Mo
25
W
25
Ta
25
BCC HEA
systems described in the Materials and Method section (
Section 2
).
3.4.1. Simulated compression of the Co
25
Fe
25
Ni
25
Pd
25
FCC HEA
Fig. 4
(a
c) present the local atomic shear strain for the 30 nm-diam-
eter FCC HEA samples compressed at 300 K, 143 K, and 50 K. These
shear-strain snapshots show the accumulated shear strain up to an
axial strain of 3.5% [for details of computed stress-strain data, we refer
the reader to Fig. S5(a)]. Plastic deformation begins in these simulations
via nucleation of a 1/6
112
partial dislocation on the surface of the
initially-pristine nanopillar. A trailing partial nucleates at the same loca-
tion with further straining, which creates a fully-dissociated pair of par-
tial dislocations, which then glide along the (111) slip plane across the
diameter and annihilate at the opposite surface. Further plastic defor-
mation proceeds via the partial dislocation nucleation from the surface
on planes adjacent to the previously-sheared slip planes. Partial disloca-
tions were the primary mechanism of deformation at all the tempera-
tures, and slip occurred on a set of parallel slip planes that correspond
to those with the greatest resolved shear stress. Based on the average
stress at high strains and highly-localized shear pro
fi
les in
Fig. 4
(a
c),
it is clear that the surface steps arising from previously-nucleated dislo-
cations (partials and their pairs) are favourable sources for subsequent
dislocation nucleations, and that no cross-slip of dislocations occurred
at these temperatures, which is likely related to the fact that the disloca-
tion remains dissociated throughout the glide until annihilation at the
opposing surface.
Fig. 3.
(a) Un-normalized size-dependent plot of yield strength vs. pillar diameter of pillars constructed from the FCC phase of a Al
0.7
CoCrFeNi HEA (b) Normalized size-dependent plot of
the resolved shear stress vs. pillar diameter of pillars constructed from the FCC phase of a Al
0.7
CoCrFeNi HEA (c) Un-normalized size-dependent plot of yield strength vs. pillar diameter of
pillars constructed from the BCC phase of a Al
0.7
CoCrFeNi HEA (d) Normalized size-dependent plot of the resolved shear stress vs. pillar diameter of pillars constructed from the FCC phase
of a Al
0.7
CoCrFeNi HEA.
Table 1
Summary of the size-effect exponents for FCC and BCC phases as also indicated in
Fig. 3
.
Size-effect exponent, m
40 K
143 K
295 K
FCC
0.38
0.47
0.68
BCC
0.33
0.34
0.33
5
A.M. Giwa et al. / Materials and Design 191 (2020) 108611
3.4.2. Simulated compression of the Al
25
Mo
25
W
25
Ta
25
BCC HEA
Fig. 4
(d
f) present the atomic shear strain of the BCC HEA sam-
ple compressed at 300 K, 143 K, and 50 K. These shear-strain snap-
shots show the plastic deformation patterns at an axial strain of
~9% [for details of the computed stress-strain data, we refer the
reader to Fig. S5(b)]. Sheared regions correspond to sequences of
(112) planes where partial disloc
ations have nucleated from the
pillar surface and traversed the interior of the nanopillar. The
nucleation of partial dislocations from the surface corresponds to
the beginning of plasticity in these nanopillars. Dislocations
nucleate in groups of adjacent (112) planes and have Burgers
vectors of 1/3
111
,
1/6
111
,and1/3
111
, which result in a 2-
atomic-plane-thick twinned region, similar to the structure of an
I
3
fault [
31
]. This mechanism has been discussed in greater detail
in our previous work [
32
]. Further plastic deformation results in
the nucleation of dislocations from deformed regions and thicken-
ing of twins via the nucleation and glide of 1/3
111
partial disloca-
tions along the boundaries of the twinned region. Due to the high
symmetry of the (001) loading in t
he simulated BCC HEA, several
slip systems are activated simultaneously. The bands of sheared
Fig. 4.
Atomic shear strain of the
b
324
N
-oriented 30-nm-diameter Co
25
Fe
25
Ni
25
Pd
25
FCC HEA deformed at (a) 50 K, (b) 143 K, and (c) 300 K to an axial strain of ~ 3.5%. Deformation is
dominated by the nucleation and propagation of 1/6
112
partial dislocations on parallel slip planes that traverse the entire pillar diameter. Atomic shear strain of
b
001
N
-oriented 30-
nm-diameter Al
25
Mo
25
W
25
Ta
25
BCC HEA deformed at (d) 50 K, (e) 143 K, and (f) 300 K to the axial strain of ~9%. Deformation is dominated by the nucleation of 1/3
111
and 1/6
111
partial dislocations that grow into twinned regions and nucleate full dislocations. At 50 K and 143 K, multiple slip systems are activated; slip at 300
K is con
fi
ned to a set of
parallel slip planes.
6
A.M. Giwa et al. / Materials and Design 191 (2020) 108611
regionsintheBCCHEAcanbeaslowas3-nmthickat50Kandupto
13.6 nm thick at 300 K, i.e., 3.33
15 times thicker than sheared re-
gionsseenintheFCCHEA.
4. Discussion
The experimental results described above show three notable features
in the mechanical response of FCC and BCC phases of the Al
0.7
CoCrFeNi
HEA as a function of temperature. With decreasing temperature, there is
(1) a signi
fi
cant increase in the yield strengths of both FCC and BCC sam-
ples, (2) a decrease in the work-hardening exponent in the BCC samples,
and (3) a decrease in the size-effect exponent in the FCC samples.
The possible microstructural origin for these three experimental ob-
servations will be the focus of the current discussion. The initial TEM anal-
ysis indicates the dislocation slip-dominated plasticity (refer to the
supplemental information, S1, Figs. S1
2). We calculated the dislocation
density from the observed dislocation lines in the Dark Field (DF) image
of the deformed FCC nanopillar at 40 K as
ρ
d
=2.28×10
14
m-
2
(see de-
tails in the supplementary information, S2, Fig. S3), which is greater than
pure FCC metals and conventional alloys by two orders of magnitude.
Such a high dislocation density has also been observed for HEAs even at
room temperature [
33
]. We also calculated the dislocation density of
the deformed BCC nanopillar at 40 K as
ρ
d
=1.40×10
14
m-
2
(see details
in the supplementary information, S3, Fig. S4), which is similar to the cal-
culated
ρ
d
in the FCC HEA pillars. The extent of the dislocation density, the
ex-situ nature of the analysis, and artefacts from the TEM lift-out proce-
dure make it dif
fi
cult to uniquely identify a mechanism that attributes
to the observed mechanical behaviour. The surface-dominated nature of
the small-scale samples further complicates the interpretation of defor-
mation mechanisms. We therefore cannot make any comments on the
dominant deformation mechanisms from the TEM analysis alone.
The length scale of MD simulations offers an ideal situation to investi-
gate dislocations in a surface-dominated HEA structure. Below, we con-
sider our MD simulations, discuss how qualitative features of the
simulated FCC and BCC HEAs may give rise to the observed experimental
behaviour and compare our proposed mechanisms to literature reports.
4.1. Yield strength of FCC phase as a function of temperature
Our experiments show that the yield strengths of nanopillars fabri-
cated from the FCC phase of this HEA are the highest at the lowest tem-
perature of 40 K for all sample sizes: we observed the yield strength of
2.0 GPa in 400-nm-sized pillars, 1.6 GPa in 700-nm-sized pillars, and
1.3 GPa in 1
μ
m-sized pillars compressed at 40 K, compared with
1.1 GPa, 0.8 GPa, and 0.6 GPa in equivalent-sized samples compressed
at 295 K.
Fig. 2
(a
c) show that the BCC HEA pillars also exhibit an in-
crease in strength as the temperature is reduced. As the testing temper-
ature is reduced from 295 K to 40 K, the strength of 2
μ
m-sized BCC HEA
pillars increases from 1.5 GPa to 1.8 GPa.
The MD simulations of the representative FCC HEA show that defor-
mation is dominated by the partial dislocation motion. Leading and
trailing partials traverse the entire length of the pillar, annihilating at
the surface, which precludes twinning via successive, adjacent stacking
faults. The dissociation of full dislocations prevents cross-slip in the FCC
HEA, promoting planar, localized plasticity and reducing strain harden-
ing. Such dissociated partial pairs were also suggested in previous ex-
periments on HEAs to prevent cross-slip and promote planar
dislocation structures [
34
36
]. A previous study [
37
]showedthepres-
ence of size effect on the deformation twinning in a FCC HEA. In the
present work, no evidence of deformation twinning in the FCC phase
was observed in the post-deformation TEM analysis.
The assumed dominant deformation mode is the dislocation slip,
and the relevant microstructural quantity related to the temperature-
dependent strength is thus the Peierls barrier. The post-deformation
morphologies of the FCC HEA shown in
Fig. 1
(a
c) are consistent with
such a deformation mechanism. The experimental post-deformation
morphologies indicate that FCC HEA single crystals deform via parallel
planar shear offsets, indicating the highly-localized plasticity at all the
temperatures.
Pure metals have a virtually-non-existent Peierls barrier at low tem-
peratures, and the contribution of lattice resistance to the yield stress
does not change much with temperature [
38
]. Previous reports on
pure metals have reported strengths for FCC metals that do not strongly
depend on temperature [
39
,
40
]. Wu, et al. reported compressive
strengths of bulk Ni of ~0.1 GPa for a temperature range of 77 K to
673 K [
38
]. This feature clearly differs from the strong temperature de-
pendence of FCC HEAs observed here. In contrast, BCC metals have
yield strengths that show a strong dependence upon temperature
[
41
], consistent with BCC results presented here. The BCC metals have
also shown the temperature-dependent tension-compression asymme-
try and dominant slip systems that change with temperature [
42
].
Dilute, binary, FCC solid solutions have been reported to show
temperature-dependent strengths related to solid-solution strengthen-
ing, an increase in the dislocation density and lattice distortion
[
38
,
43
46
]. It was reported that at 77 K, FeNi and NiCo FCC binary alloys
have yield strengths of 0.34 GPa and 0.15 GPa, respectively, while
strengths at room temperature are 0.20 GPa and 0.12 GPa.
It seems reasonable to expect that FCC HEAs, as a multicomponent
alloy, would display a similarly-increased temperature-dependent
strength, as reported for binary FCC alloys. Indeed, signi
fi
cant increases
in strength with decreasing temperature have been reported for a variety
of FCC HEAs [
36
,
38
,
47
53
]. A few models have been proposed for the
temperature-dependent strength in FCC HEAs [
38
,
48
,
54
,
55
]. For the defor-
mation mechanism considered here, the model of the thermally-activated
plastic
fl
ow relates the strength to internal lattice friction as [
56
]:
τ

T
ðÞ
τ

0
ðÞ
¼
k
B
T
Δ
E
ln

ε

ε
0

þ
1
;
ð
2
Þ
where
τ
(0) is the athermal strength,
Δ
E is the activation energy required
for a dislocation to overcome the dominant obstacle,

ε
is the experimental
strain rate,

ε
0
is a reference strain rate related to the velocity of mobile dis-
locations, and
k
B
is Boltzmann's constant. Predicting strength as a function
of temperature, according to Eq.
(2)
, requires knowing the athermal
strength,
τ
(0), and the energy barrier to overcome the internal obstacles,
Δ
E.
In conventional metallic solid solutions, the obstacles to dislocation
motion are the solute atoms. No single element dominates in HEAs,
which renders the de
fi
nition of a
solute atom
ambiguous. Most
modelling approaches begin with the classical Labusch model for
strengthening in a binary alloy, which arises from the interactions of a
gliding dislocation with several randomly-dispersed solutes in its glide
plane, and extend it to HEAs [
57
]. The individual solutes in the Labusch
model are not strong-pinning, i.e.,are not suf
fi
cientlystrongtopinadis-
location, but the combined interactions of many solutes act collectively
to obstruct a gliding dislocation. For the application to FCC HEAs,
Varvenne, et al. extended the Labusch model to include interactions of
a gliding dislocation with an arbitrary number of solute atoms in and
outside its glide plane and provided analytic expressions for
τ
(0) and
Δ
E[
55
]. In this model, initially-straight dislocations form
fl
uctuations
in order to reduce their potential energy in the presence of the hetero-
geneous lattice. This wavy dislocation con
fi
guration can be described
by characteristic lengths,
ζ
c
, the length of a pinned segment, and
ω
c
,
the length, which a dislocation segment will bow out in this wavy con-
fi
guration. Analytic expressions for
τ
(0) and
Δ
E are:
τ

0
ðÞ¼
0
:
051
α
1
3
μ
1
þ
ν
1
ν

4
3
f
1
ω
c
ðÞ
δ
mis
b
6

2
3
ð
3
Þ
Δ
E
¼
0
:
274
α
1
3
μ
b
3
1
þ
ν
1
ν

2
3
f
2
ω
c
ðÞ
δ
mis
b
6

1
3
ð
4
Þ
7
A.M. Giwa et al. / Materials and Design 191 (2020) 108611
where
α
is a dimensionless number describing the dislocation line ten-
sion,
μ
is the shear modulus,
ν
is the Poisson's ratio, and
b
is the Burger's
vector.
f
1
(
ω
c
)and
f
2
(
ω
c
) are core coef
fi
cienttermsevaluated atthe char-
acteristic glide length,
ω
c
, and have been shown to be virtually indepen-
dent of the dislocation-dissociation distance and taken as constant, 0.35
and 5.70, respectively [
55
].
δ
mis
is an atomic mismatch parameter over
all alloying elements and de
fi
ned as
δ
mis
¼
X
n
c
n
Δ
V
2
n
þ
σ
2
Δ
V
n

ð
5
Þ
where
c
n
is the concentration of each element,
n
.
Δ
V
n
is the mis
fi
t vol-
ume of the element,
n
,andde
fi
ned as
Δ
V
n
¼
V
n
V
with
V
¼
n
c
n
V
n
.
σ
Δ
Vn
is the standard deviation of the mis
fi
t volume. In the discussion
below, we refer to this model as Model 1.
We would like to obtain values of
τ
(0) and
Δ
E for the FCC phase of
our HEA to compare theoretically-predicted strengths against our ex-
perimental data. Model 1 requires several mechanical properties and
atomic volumes as inputs into the model. For the FCC phase of the
Al
0.7
CoCrFeNi HEA studied here, we take the atomic volumes of
V
Co
=
11.12
Å
3
,
V
Cr
= 12.27
Å
3
,
V
Fe
= 12.09
Å
3
,and
V
Ni
=10.94
Å
3
determined
for a CoCrFeNi alloy [97]. From the EDS analysis of the FCC phase of our
Al
0.7
CoCrFeNi HEA, we use
c
Al
=0.1,
c
Co
=0.23,
c
Cr
=0.26,
c
Fe
=0.27,
and
c
Ni
= 0.14. In order to obtain
V
Al
, we apply Vegard's law, which re-
lates the average atomic volume of an alloy and a solute:
V
Al0
:
7CoCrFeNi
;
FCC
¼
c
Al
;
FCC
V
Al
;
FCC
þ
1
c
Al
;
FCC

V
CoCrFeNi
;
FCC
ð
6
Þ
We relate theatomic volume tothe latticeparameter for FCC crystals
through
V
n
¼
a
3
4
and use lattice parameters of 0.356 nm and 0.3572 nm
for CoCrFeNi [
13
] and the FCC phase of Al
0.7
CoCrFeNi [
13
], respectively.
This calculation gives
V
Al
=13.71
Å
3
. Following [
55
], we use
α
= 0.123
although in the same analysis, it was reported that at moderate temper-
atures, the predicted strength was insensitive to the line-tension pa-
rameter. Also following [
55
] and DFT calculations that show the
standard deviation of the bond length in an FeCoNiCrCu HEA is only
1.6% of the mean bond length [
58
], we thus neglect
σ
Δ
V
n
from the mis-
match parameter. We apply the isotropic elastic constants of
μ
=75
GPa
and
ν
=0.28[
38
]. Inserting these values into Eqs.
(3) and (4)
,we
obtain
τ
(0) = 103.8
MPa
and
Δ
E = 1.17 eV. These values allow us to
use Eq.
(2)
to predictthe strength asa function of temperature. It should
be noted that these values compare favourably to estimates of the FCC
CrMnFeCoNi HEA with
τ
(0) = 83.0
MPa
and
Δ
E = 1.13 eV [
55
].
The above model assumes that the temperature-dependent strength
arises from thermal contributions to dislocations' ability to overcome
internal obstacles. An alternative temperature-dependent strengthen-
ing model for HEAs has been proposed, where strengthening in FCC
HEAs is assumed to arise from decreasing the dislocation core width
with temperature [
38
]. Within the Peierls-Nabarro (P-N) model,
τ
¼
2
μ
1
ν
exp
2
πω
b

ð
7
Þ
where
ω
is the dislocation width, and
b
is the Burgers vector, strength is
exponentially related to the dislocation width. In this model, the tem-
perature dependence of the dislocation core width is approximated as
linear [
38
],
ω
¼
ω
0
1
þ
α
T
ðÞð
8
Þ
where
α
is a positive
fi
tting constant, and
ω
0
=
b
. In the discussion
below, we refer to this model as Model 2.
In order to compare our small-scale experimental data against these
theories, we must obtain an estimate of the size-independent strength
contribution. It has been argued that an estimate of the bulk strength
can be obtained from the small-scale data by evaluating the size-effect
power law at a length scale that corresponds to the source length in
bulk materials [
34
]. Following the previous analysis [
34
], we evaluate
τ
=
A
×
D
m
at
D
=20
μ
m
for each isothermal dataset. Fit parameters
as obtained from the experimental data are
A
300
K
= 401.44
MPa
;
A
143
K
= 679.29
MPa
;
A
40
K
= 908.49
MPa
, and
m
300
K
= 0.67;
m
143
K
=
0.47;
and m
40
K
= 0.375. Estimations of bulk strengths are then
τ
300
K
= 53.9
MPa
,
τ
143
K
=166.2
MPa
,and
τ
40
K
= 295.4
MPa
. This
trend gives us an estimate of the bulk strength of the FCC phase of our
HEA and enables us to compare against strengthening theories. We
also
fi
t these estimates to Model 2 and obtain
fi
tting constant,
α
=
0.001
K
1
.
Fig. 5
shows these bulk strength estimates, the predictions from
Model 1, and the curve
fi
t to Model 2. It is seen that Model 1 predicts
the room-temperature strength of the FCC HEA but signi
fi
cantly under-
estimates the strength at cryogenic temperatures. This feature may sug-
gest that at low temperatures, Angstrom-level
fl
uctuations in the
dislocation line (which are neglected in Model 1) become increasingly
important. The consideration of the
fi
tting parameter,
α
= 0.001
K
1
,
in Model 2 suggests a 23% decrease in the dislocation core width from
room to cryogenic temperatures and is several orders of magnitude
greater than the reported thermal expansion coef
fi
cient of
Al
0.7
CoCrFeNi at 14 × 10
6
K
1
[
59
]. This trend suggests that Model 2
cannot capture the physical mechanism of temperature-dependent
strength and is not applicable to this system. Following this analysis, it
seems that Model 1 can capture near-room temperature strength well
with no
fi
tting necessary and is the most promising towards capturing
the relevant underlying dislocation physics. Model 2 does not appear
applicable to this system. Improvements to Model 1 at low tempera-
tures may require the inclusion of
fi
ner
fl
uctuations in the dislocation
line.
4.2. Work hardening of the BCC phase as a function of temperature
The compression experiments show that the work-hardening expo-
nent decreases in the BCC samples, as the temperature is decreased.
Considering the high symmetry of the compression axis of BCC samples,
there should be a greater activation of dislocations and dislocation
sources and thus, the interaction between dislocations. From the pres-
ence of a modulated A2 and B2 microstructure [
13
,
26
], some hardening
from thehard B2phase and dislocation interactionsatphase boundaries
is also expected to contribute to the strength of the BCC samples. The
temperature-dependent hardening exponent suggests that in addition
to these strengthening mechanisms that are present in all samples,
there are dislocation multiplication and storage mechanisms present,
Fig. 5.
Estimated bulk shear strength of the FCC phase of the Al
0.7
CoCrFeNi HEA, compared
to two models of the temperature-dependent strength for FCC HEAs. Model 1 predicts the
strength at room temperature well and signi
fi
cantly under-predicts low-temperature
strengths. The Model 2
fi
t predicts a 23% decrease in the dislocation core width from
room temperature to 0 K.
8
A.M. Giwa et al. / Materials and Design 191 (2020) 108611
which are temperature-dependent. The post-deformation morphology
revealed by SEM provided in
Fig. 2
(a
c) indicates the homogeneous de-
formation in the BCC HEA single crystals at all the temperatures. We
note that previous studies identi
fi
ed dislocation-twin interactions as
the underlying mechanism for work hardening, and hardening was ob-
served to increase with decreasing temperature [
18
]. Considering that
we have observed a decrease in hardening with decreasing tempera-
ture, such a mechanism may not be applicable to this BCC HEA. In con-
trast to previous indentation experiments [
26
], our TEM analysis does
not indicate any phase-transformation plasticity in this BCC phase.
The MD simulations on the representative BCC HEA show highly-
anisotropic dislocations. Partial dislocations are nucleated from the sur-
faceand travel through thepillaralongtheir mixedscrew/edge segment
until encountering the opposing surface or an intersecting dislocation.
The dislocation segment in the propagation direction is chie
fl
yof
mixed character, with the perpendicular segments showing a screw
character. The shape of the dislocation after propagation indicates an-
isotropy in the mobility of the mixed and screw segments resulting in
long, straight extended screw segments. Deformation in this simulated
BCC HEA is clearly dominated by the kink-pair nucleation of screw dis-
location segments. There is no evidence of the promotion of the kink-
pair nucleation of screw segments in regions near solute atoms, as ob-
served in some BCC alloys (as in the case of solid-solution softening)
[
60
,
61
], which would reduce the anisotropic shape of the dislocations.
The anisotropy of the dislocations also suggests that the critical resolved
shearstress (CRSS) of the mixed dislocation segments is not comparable
to that of the screw segments, as has been suggested in MD simulations
of the dislocation motion in BCC HEAs [
62
].
Dislocation-multiplication mechanisms in BCC metals include dou-
ble cross-slip or sources found at strong pinning points (superjogs or
junctions) [
63
65
]. All of these mechanisms rely upon cross-slip of
screw segments to multiply the dislocation content, a feature that has
been noted in discussing the importance of cross-slip on the hardening
behaviour in BCC metals [
63
66
]. As cross-slip of screw segments is a
thermally-activated process, it is reasonable to expect these multiplica-
tion mechanisms to be more active at elevated temperatures and thus
promote hardening at elevated temperatures.
Earlier studies on some refractory BCC HEAs have reported high strain-
hardening rates at room temperature [
67
,
68
] but they did not report the
effect of temperature on the work-h
ardening rate or propose a mechanism
underlying the observed work hardening. A Ti
35
Zr
27.5
Hf
27.5
Nb
5
Ta
5
BCC
HEA was reported to have high room-temperature work-hardening rates
that were attributed to the transformation-induced plasticity, as indicated
from the post-deformation micro
structural characterization [
69
]. No phase
transformation is expected or has been reported in this Al
0.7
CoCrFeNi HEA.
Room-temperature strain hardening reported in a TiZrHfNbTa BCC HEA
was attributed to the build-up of the dislocation density [
70
,
71
].
4.3. Size effect as a function of temperature
In the last decade, studies on deformation of micron- and sub-micron
sized single-crystalline metals reveal a size
effect exponent of the shear
stress (
τ
) with the pillar diameter (
D
), i.e.,
τ
D
m
. In single-crystalline
FCC metals, the power-law size effect has a universal exponent of
m
=
0.66 from simulations and experiments [
72
76
]atroomtemperature,
which correlates well with the room-temperature size effect of
m=
0
.
68
calculated for the FCC HEA nanopillars in this study. The universality
ofthesizeeffectatroomtemperaturei
s explained from the ease of dislo-
cation motion and dislocation annihilation to the free surface in FCC
metals [
76
]. It has also been shown that the sample size-effect is indepen-
dent of orientations in both FCC metals [
77
]andBCCmetals[
78
].
The role of thermally-activated processes in the size effect of a FCC
metal was investigated by Wheeler, et al. who reported a constant size ef-
fect of
m
= 0.65 in the deformed, annealed Cu nanopillars from room
temperatures to 400 °C [
79
]. They attributed the constant size effect to
the limitation of the dislocation-source size and negligible thermally-
activated contributions to stresses within the temperature range [
79
]. In
contrast to the previous report of the temperature insensitivity at high
temperatures, we observed a reduction in the size-effect exponent,
m
,
from 0.68 at 295 K, to 0.47 at 143 K, to 0.38 at 40 K, as well as a systematic
increase in the yield strength with lowering the temperature.
Single-crystalline BCC metals also exhibit a power-law dependence
of the shear stress,
τ
, on size. In this study, BCC HEA pillars show a sim-
ilar size-effect exponent of
m
= 0.33 at test temperatures of 40 K, 143 K,
and 295 K. At room temperature, single crystals of commonly-studied
BCC metals (W, Ta, V, Nb, and Mo) exhibit the variation in the size-
effect exponent,
m
, which is due to differences in their Peierls stresses
and critical temperatures [
76
,
80
]. It was reported that V and Nb have
low stress barriers and low critical temperatures, which enhance the
screw-dislocation mobility, thus having a high size-effect exponent,
m
values of 0.82 at room temperature [
24
,
80
,
81
]. Mo, W, and Ta have the
high Peierls stress and high critical temperature, leading to a reduced
size-effect exponent,
m
(~0.32 to 0.42). The reduced screw-dislocation
mobility was reported in these BCC metals ensuing the continuous plas-
tic deformation [
76
,
78
,
80
83
]. Previous work on the same BCC HEA pil-
lars demonstrated a size-effect exponent of
m
=0.28atroom
temperature [
24
]. Zou, et al. reported that single crystals of the refrac-
tory HEA Nb
25
Mo
25
Ta
25
W
25
exhibited a size-effect exponent of
m
=
0.32 [
24
]. The reduced value of
m
at room temperature in the BCC
HEAs can be attributed to their higher lattice friction than that of the
pure BCC metals. We can also suggest a highly-distorted BCC phase in
which the energy dispersive spectroscopy (EDS) analysis reveals ~
56.9 at.% of Ni and Al [
24
], indicating a heavily-strained phase due to
the differences in the atomic sizes of the major elements in this phase.
Experiments on the BCC HEA pillars at low temperatures of 143 K
and 40 K demonstrated a size-effect exponent,
m
, of 0.34 and 0.33, re-
spectively, which is similar to that at room temperature. These results
are contrary to the size-effect exponents found for pure BCC metals at
low temperatures. Lee, et al. [
23
] reported a signi
fi
cant decrease in
m
for Nb and W at 160 K, for example,
m
for Nb reduced from 0.73 at
room temperature to 0.23 at 160 K, and
m
for W reduced from 0.36 at
room temperature to 0.19 at 160 K. They attributed this change to the
increased intrinsic lattice resistance as a result of the suppressed dislo-
cation multiplication as the temperature reduces. From the results on
compression of the BCC HEA pillars, we can suggest that at low temper-
atures, there is a minimal effect of temperature on the lattice resistance
of BCC HEAs, in contrast to pure BCC metals, where overcoming the in-
trinsic lattice resistance stems almost exclusively from the thermal acti-
vation. In BCC HEAs, the lattice resistance is so high (presumably from
the chemical and energetic directionality of bonds) that even with the
thermal contribution during deformation at room temperature, it is
similar to the deformation resistance at cryogenic temperatures. It can
also be suggested that the dislocation structure in the BCC phase re-
mains relatively stable for the range of temperatures studied, making
the size-effect exponent invariant of temperature. The size-effect expo-
nent can be governed by other phenomena, such as single arm sources
[
84
,
85
].This feature is plausible if thedislocation densities and activated
slip systems during deformation remain the same [
84
]. Clearly, more
work is needed to establish this phenomenon in the BCC HEAs.
In light of the previous discussion on temperature-dependent solu-
tion strengthening in the FCC phase of this HEA, the source of the
temperature-dependent size effect becomes clear. We consider three
signi
fi
cant contributions to the observed strength of the single-phase
FCC HEA: (1) solid-solution strengthening, (2) dislocation-source con-
tribution, which is sample size-dependent, and (3) dislocation forest in-
teractions similar to forest hardening. These contributions to the shear
strength can be represented as [
84
86
]:
τ
¼
τ

þ
τ
G
þ
τ
source
D
m
ð
9
Þ
where
τ
denotes the lattice friction,
τ
G
is the contribution from Taylor
hardening, and
τ
source
D
n
is the contribution from the single
arm
9
A.M. Giwa et al. / Materials and Design 191 (2020) 108611