Characteristic strengthening mechanisms in body-centered cubic refractory high/medium entropy alloys

Abstract

The present work reports characteristic strengthening mechanisms of HfNbTaTi, HfNbTiZr, HfNbTi, HfTaTi, and NbTiZr equi-atomic refractory medium entropy alloys (RMEAs). The alloys were processed by high-pressure torsion and subsequent annealing to obtain microstructures with average grain sizes ranging from several hundred nanometers to several tens of micrometers. Their mechanical properties were evaluated by tensile tests at room temperature. Precise Hall–Petch relationships of the RMEAs were acquired based on the tensile yield strength data. Small slopes of the Hall–Petch relationships and weak grain refinement strengthening were clarified to be attributed to their low elastic modulus. In addition, the friction stresses in the RMEAs were higher than those of conventional BCC metals and alloys. By comparing the experimental data and a theoretical model, it was suggested that interaction between severe lattice distortion and elastic field of edge dislocations can largely contribute to the high friction stress of the RMEAs at room temperature.

Full text

Scripta Materialia 231 (2023) 115442
1359-6462/© 2023 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
Characteristic strengthening mechanisms in body-centered cubic refractory
high/medium entropy alloys
Qian He
a
, Shuhei Yoshida
a
,
b
,
*
, Nobuhiro Tsuji
a
,
b
a
Department of Materials Science and Engineering, Kyoto University, 606-8501 Kyoto, Japan
b
Elements Strategy Initiative for Structural Materials (ESISM), Kyoto University, 606-8501 Kyoto, Japan
ARTICLE INFO
Keywords:
Refractory high/medium entropy alloys
Strengthening mechanisms
Grain renement
Hall–Petch relationships
Dislocations
ABSTRACT
The present work reports characteristic strengthening mechanisms of HfNbTaTi, HfNbTiZr, HfNbTi, HfTaTi, and
NbTiZr equi-atomic refractory medium entropy alloys (RMEAs). The alloys were processed by high-pressure
torsion and subsequent annealing to obtain microstructures with average grain sizes ranging from several
hundred nanometers to several tens of micrometers. Their mechanical properties were evaluated by tensile tests
at room temperature. Precise Hall–Petch relationships of the RMEAs were acquired based on the tensile yield
strength data. Small slopes of the Hall–Petch relationships and weak grain renement strengthening were
claried to be attributed to their low elastic modulus. In addition, the friction stresses in the RMEAs were higher
than those of conventional BCC metals and alloys. By comparing the experimental data and a theoretical model,
it was suggested that interaction between severe lattice distortion and elastic eld of edge dislocations can
largely contribute to the high friction stress of the RMEAs at room temperature.
Refractory elements, such as Zr, Hf, V, Nb, Ta, Cr, Mo, W, and Ti,
belong to the groups IVB, VB, and VIB in the periodic table of elements
[1] and possess relatively high melting points. Refractory high entropy
alloys (RHEAs) and refractory medium entropy alloys (RMEAs) are new
classes of refractory alloys consisting of ve or more and three or four
(near-) equi-atomic refractory elements, respectively. Most RHEAs/R-
MEAs have been reported to exhibit single-phase body-centered cubic
(BCC) crystal structure after rapid quenching from high temperatures
above their β-phase solvus temperatures. RHEAs/RMEAs typically show
high yield strengths at a wide range of temperatures [2–4]. However,
owing to the lack of systematic investigations, the reasons for the high
strengths of RHEAs/RMEAs have been unknown. In the previous studies
on RHEAs/RMEAs, as-cast ingots having complex microstructures
composed of grains with a heterogeneous size distribution, second-phase
precipitates, and elemental segregation were used to characterize their
mechanical properties [5]. However, our recent study has veried that
microstructures largely affect the mechanical properties of RHEAs/R-
MEAs, and as-cast materials with complex microstructures are not
suitable for studying their strengthening mechanisms [6].
In the present study, polycrystals of RMEAs (HfNbTaTi, HfNbTiZr,
HfNbTi, HfTaTi, and NbTaTi, which were family of HfNbTaTiZr RHEA)
with BCC single phase composed of simple equiaxed microstructures
were used to quantitatively reveal characteristics of their strengthening
mechanisms. The polycrystal specimens of the RMEAs with a wide range
of mean grain sizes were fabricated and their mechanical properties
were measured by tensile tests at room temperature (RT). Precise
Hall–Petch relationships of the RMEAs were obtained, and their friction
stresses (fundamental resistance to dislocation glide in solid solutions)
and the Hall–Petch slopes were systematically compared. Finally, the
characteristics of the strengthening mechanisms in RHEAs/RMEAs with
BCC structures were discussed based on the contribution of solid solu-
tion strengthening and grain renement strengthening.
Ingots of equi-atomic HfNbTaTi, HfNbTiZr, HfNbTi, HfTaTi, and
NbTiZr RMEAs were produced by vacuum arc-melting of pure metals.
Each arc-melted button was ipped and remelted ve times to homog-
enize elements distribution. Cold rolling with a 90% reduction in
thickness and subsequent homogenization at 1150 ◦C for 24 h under an
Ar atmosphere followed by water quenching were applied to eliminate
complex microstructures in the as-cast materials. Discs with a diameter
of 10 mm and thickness of 0.8 mm were cut, and they were heavily
deformed by high-pressure torsion (HPT) with ve rotations (maximum
equivalent strain of 196 at the edge) at a speed of 0.2 rpm (rotation per
minute) under 7.5 GPa. To obtain the RMEAs with BCC single phase with
a wide range of average grain size, all the RMEAs were subsequently
* Corresponding author at: Department of Materials Science and Engineering, Kyoto University, 606-8501 Kyoto, Japan.
E-mail address: yoshida.shuhei.5s@kyoto-u.ac.jp (S. Yoshida).
Contents lists available at ScienceDirect
Scripta Materialia
journal homepage: www.journals.elsevier.com/scripta-materialia
https://doi.org/10.1016/j.scriptamat.2023.115442
Received 6 December 2022; Received in revised form 27 February 2023; Accepted 20 March 2023

Scripta Materialia 231 (2023) 115442
2
annealed at temperatures ranging from 750 ◦C to 1250 ◦C (corre-
sponding to the BCC single phase region in Fig. S1 in the supplementals)
for short periods (30–120 s).
The annealed disks were mechanically polished, and then electro-
polishing was applied in a solution of 10 vol.% HClO
4
and 90 vol.%
C
2
H
5
OH at 20 V and −30 ◦C for 40 s. Field emission scanning electron
microscopy (FE-SEM) (JEOL, JSM-7800F) equipped with a back-
scattered electron (BSE) detector was used to characterize the micro-
structures observed from the normal direction of the disks. The line
intercept method was applied to the SEM-BSE images to determine the
mean grain sizes.
Tensile tests were conducted on a universal tensile test machine
(SHIMADZU, AG-100 kN Xplus) at a quasi-static strain rate of 8.3 ×10
−4
s
−1
at RT. Tensile test specimens with a gauge dimension of 2 mm ×1
mm ×1 mm were cut from the annealed disks. A CCD video camera
extensometer (SVS625MFCP) was used throughout the tensile tests to
measure the displacement of the gauge section accurately, and the strain
was calculated by the digital image correlation (DIC) technique using
Vic-2D software (Correlated solutions co.) [7,8]. Our previous studies
[9,10] on FCC high/medium entropy alloys have already veried that
the mechanical properties (such as yield strength and Young’s modulus)
obtained by this method using the small-sized specimens are equivalent
to those measured by using standard-sized specimens [11,12]. Tensile
tests were repeated three times for each alloy to ensure the statistical
reliability.
Fig. 1 shows representative SEM-BSE micrographs of the (a)
HfNbTaTi, (b) HfNbTiZr, (c) HfNbTi, (d) HfTaTi, and (e) NbTiZr RMEA
after the HPT and subsequent annealing process. All the alloys showed
single-phase solid solutions of BCC structure. Their mean grain sizes
were ranging from ultra-ne grain (UFG) sizes (e.g., 0.16
μ
m in the
HfNbTiZr RMEA) to ne grain (e.g., 2.4
μ
m in the HfNbTiZr RMEA) and
coarse grain sizes (e.g., 33
μ
m in the HfNbTiZr RMEA). Interestingly,
UFG microstructures, which have been rarely reported in BCC metals
and alloys, could be achieved in all the RMEAs in our study. (See the
supplementals for discussions on the grain growth kinetics.)
Fig. 2 shows tensile nominal stress - nominal strain curves of the (a)
HfNbTaTi, (b) HfNbTiZr, (c) HfNbTi, (d) HfTaTi, and (e) NbTiZr RMEAs
with wide ranges of average grain sizes. It was found that all the RMEAs
showed similar mechanical properties, such as high yield strength (>
700 MPa), limited uniform elongation (<2%), and large total elongation
(20–40%). Usually, yield strengths of materials increase, and ductility
decreases with decreasing their average grain sizes. However, as shown
in Fig. 2, changes in the yield strength of each RMEA with varying mean
grain sizes were found to be abnormally small, suggesting that the grain
renement strengthening effect in the RMEAs was signicantly weak
compared with conventional materials.
Grain renement strengthening in polycrystalline metallic materials
is generally described by the Hall-Petch relationship [13,14]:
σ
Y=
σ
0+kHPd−1
2,(1)
where
σ
Y is the yield strength,
σ
0 is the friction stress, kHP is the constant
so-called Hall–Petch slope, and d is the mean grain size of materials. The
σ
0 values can be interpreted as the stress necessary for dislocations to
overcome the energy barrier of the crystal lattice determined from the
Peierls potential and interaction with solutes, for initiating slips on a
large scale with the assistance of thermal activation.
In order to quantitively characterize the grain renement strength-
ening effect of the RMEAs, the yield stress of the (a) HfNbTaTi, (b)
HfNbTiZr, (c) HfNbTi, (d) HfTaTi, and (e) NbTiZr RMEAs were plotted
as a function of reciprocal square roots of the mean grain sizes in Fig. 3.
Note that the yield stress of the materials was determined as the 0.2%
proof stress. The Hall–Petch relationships of each RMEA were obtained
by tting the data using Eq. (1), and the equations are indicated in Fig. 3.
The obtained
σ
0 and kHP of the RMEAs are summarized in Table 1
together with other parameters.
Fig. 4(a) plots the relationship between the experimentally-
measured
σ
0 and kHP of the HfNbTaTi, HfNbTiZr, HfNbTi, HfTaTi, and
NbTiZr RMEAs together with reference values of pure BCC, hexagonal
close-packed (HCP) metals, and other BCC alloys. The
σ
0 of the
HfNbTaTiZr RHEA and all the RMEAs obtained here were much higher
than those of most other materials but comparable to those of pure W
and some beta-Ti alloys with a high concentration of alloying elements
such as Ti
5
Al
5
Mo
5
V
1
Cr
1
Fe
1
, as well as those of RMEAs homogenized at
high temperature shown in our previous paper [6]. At the same time, it
was found that all the RMEAs exhibited lower kHP than other materials
except for interstitial free (IF) steel and pure Ti. To reveal the origin of
the low kHP (i.e., weak grain renement strengthening) in the RMEAs,
the relationship between the kHP and Young’s modulus (E) of the
RMEAs, pure BCC, HCP, face-centered cubic (FCC) metals, and FCC
Fig. 1. Representative SEM-BSE micrographs of the HfNbTaTi RMEA annealed at (a1) 1050
◦C for 30 s, (a2) 1200 ◦C for 30 s, and (a3) 1250 ◦C for 120 s, HfNbTiZr
RMEA annealed at (b1) 750 ◦C for 30 s, (b2) 900 ◦C for 30 s, and (b3) 1200 ◦C for 30 s, HfNbTi RMEA annealed at (c1) 950 ◦C for 30 s, (c2) 1050 ◦C for 30 s, and (c3)
1250 ◦C for 30 s, HfTaTi RMEA annealed at (d1) 1000 ◦C for 30 s, (d2) 1150 ◦C for 30 s, and (d3) 1200 ◦C for 60 s, and NbTiZr RMEA annealed at (e1) 750 ◦C for 30 s,
(e2) 850 ◦C for 40 s, and (e3) 1200 ◦C for 30 s, all after the HPT deformation. Their mean grain sizes (d), determined by the intercept method, are indicated in
each gure.
Q. He et al.

Scripta Materialia 231 (2023) 115442
3
HEAs / MEAs [5,10,17] are plotted in Fig. 4(b). Note that the E of the
RMEAs were determined based on the slope in the elastic stage in the
stress-strain curves shown in Fig. 2. It was found that the kHP and E
roughly showed a positive correlation. The reasons can be understood
based on the equations of kHP in several grain renement strengthening
models, summarized in Table S1 in the supplementals. In all the models,
it is obvious that the kHP is a function of the shear modulus (G) and E.
Hence, it could be concluded that the weak grain renement strength-
ening (i.e., low kHP) in the RMEAs was mainly attributed to their low E.
In BCC metals and alloys, their plastic deformation is generally
controlled by the motion of screw dislocations rather than edge dislo-
cations, particularly at RT and low temperatures, due to the non-planar
core structures [28,29]. For evaluating the solid solution strengthening
in conventional BCC dilute alloys, the classical Suzuki model [30] has
been successfully used to simulate solute-dislocation interactions at the
core of a
2[111] screw dislocations. However, the core structure can vary
along the dislocation lines depending on the local chemical environment
in RHEAs/RMEAs, since different elements are distributed in their
crystal lattices [31]. Accordingly, the nucleation and migration barriers
of kinks can vary locally due to the modulation of the local core struc-
tures. Thus, it is not appropriate to simply apply the Suzuki model to
RHEAs/RMEAs [16,32,33]. Recently, some researchers have pointed out
that cross kinks (kinks extended on different slip planes) can sponta-
neously form in screw dislocations of BCC HEAs and MEAs depending on
the local chemical environment. Obviously, the energy barriers for the
glide motion of such cross-kinked screw dislocations in BCC HEAs could
be signicantly higher than those in conventional BCC metals and al-
loys. Maresca et al. [16] proposed a theoretical strengthening model
considering such cross-kinked screw dislocations based on some pa-
rameters extracted from atomistic simulations. However, quantitative
comparison between this theoretical model and our experimental data is
not easy technically.
On the other hand, several analytical solid solution strengthening
models applicable to BCC HEAs and MEAs, such as Toda-Caraballo
model [34] and Maresca-Curtin model [16], have been proposed,
assuming that their plastic deformation is controlled by edge disloca-
tions similar to FCC alloys. The Maresca-Curtin model [16] gives an
analytical expression of the friction stress,
σ
0(T,˙
ε
), at a nite
Fig. 2. Tensile nominal stress (s) – nominal strain (e) curves of the (a) HfNbTaTi, (b) HfNbTiZr, (c) HfNbTi, (d) HfTaTi, and (e) NbTiZr RMEAs with various average
grain sizes obtained from the tensile tests at room temperature. Mean grain sizes of the specimens (d) are also indicated in each graph.
Q. He et al.

Scripta Materialia 231 (2023) 115442
4
temperature, T, and strain rate, ˙
ε
, assuming that the elastic interaction
between edge dislocations and lattice distortion owing to the difference
in atomic sizes of solute atoms is dominant. The expressions are as
follows:
σ
0(0 K) = 0.040M
α
−1
3
μ
1+
ν
1−
ν
4
3ncnΔV2
n
b62
3
,(2)
Fig. 3. Hall-Petch relationships of the (a) HfNbTaTi, (b) HfNbTiZr, (c) HfNbTi, (d) HfTaTi, and (e) NbTiZr RMEAs. Equations of the Hall–Petch relationships, which
were achieved by tting the data points based on Eq. (1), are given as insets in each graph.
Table 1
List of materials parameters of the RMEAs in this study. The lattice constants and Burgers vectors were calculated by the Vegard’s law [15]. The grain size range of the
materials used in the present study is also given. Young’s modulus values were obtained from the elastic stages in the tensile stress strain curves shown in Fig. 2. The
Hall–Petch slopes and the experimental friction stresses were determined from the Hall-Petch relationships shown in Fig. 3, and the theoretical friction stresses were
calculated by the Maresca-Curtin model [16].
Alloys Lattice constant
(Å)
Burgers vector
(Å)
Grain size range
(
μ
m)
Young’s modulus
(GPa)
Hall-Petch slope
(MPa⋅
μ
m
1/2
)
Experimental friction stress
(MPa)
Theoretical friction stress
(MPa)
HfNbTaTi 3.363 2.912 0.344–9.4 100 197 797 758
HfNbTiZr 3.449 2.987 0.160–33 66.7 99 751 683
HfNbTi 3.363 2.912 0.512–19.2 77.4 151 680 623
HfTaTi 3.363 2.913 0.788–12.1 69.6 202 752 511
NbTiZr 3.373 2.921 0.208–21.6 66.7 155 711 618
Q. He et al.

Scripta Materialia 231 (2023) 115442
5
ΔEb=2.00
α
1
3
μ
b31+
ν
1−
ν
2
3ncnΔV2
n
b61
3
,(3)
σ
0(T,˙
ε
) =
σ
0(0 K)1−kT
ΔEb
ln
˙
ε
0
˙
ε
2
3,(4)
where
σ
0(0K)is the friction stress for the glide motion of edge dislo-
cations at 0 K, M is the Taylor factor (=2.733 for BCC metals with
random texture),
α
is a dislocation line tension constant (=0.0833 in
RHEAs/RMEAs),
μ
and
ν
are the shear modulus and the Poisson ratio,
respectively, n is the number of constituent elements, cn (n =1, 2, …, N)
is the concentration of constituent elements in an N-component alloy, b
is the magnitude of the Burgers vector of the alloy, ΔEb is the predicted
energy barrier for dislocation glide, k is the Boltzmann constant, and ˙
ε
0
is the so-called reference strain rate (=10
4
s
−1
). ΔVn is the mist vol-
ume, which is the degree of lattice distortion originating from the dif-
ferences in atomic sizes of alloying elements. The mist volume for the
type-n solute in an N-component alloy can be expressed as:
ΔVn=
∂
Valloy
∂
cn
−
N
m
cm
∂
Valloy
∂
cm
,(5)
where Valloy is the average atomic volume dened as Valloy =a3/4 (a:
lattice constant). In the present study, ΔVn of various BCC alloys were
calculated based on Eq. (5), assuming that the values of Valloy follow
Vegard’s law, similar to previous studies [10]. Theoretical values of the
σ
0 in the alloys were calculated by Eqs. (2) - (4) by using materials
constants extracted from literature [35–41].
Fig. 5 shows a comparison between the experimental
σ
0 acquired
from the Hall–Petch relationships and the theoretical values of
σ
0
calculated by the Maresca-Curtin model, of which values are also sum-
marized in Table 1. It was found in Fig. 5 that in the highly-concentrated
BCC alloys (RHEAs, RMEAs, and binary alloys with a solute content of
more than 25 at.%) the experimental and calculated values are in good
agreement with each other. In contrast, the data points for dilute binary
and ternary BCC alloys largely deviate from the predictions (diagonal
broken line). To bridge between the experimental and theoretical
calculation results for different alloys, we will discuss based on the
difference in the temperature dependence of the strength contribution of
screw and edge dislocations interacting solute atoms.
In any BCC alloy,
σ
0 at 0 K is determined by the contribution of screw
dislocations because they have a much higher critical resolved shear
stress (higher
σ
0(0K)) than that for edge dislocations. At nite tem-
peratures (T),
σ
0 of both screw and edge dislocations decreases because
of thermal activation, and the reduction rate of
σ
0 can be calculated by
differentiating Eq. (4) by T, as shown below.

∂σ
0
∂
T˙
ε
= −
σ
0(0 K)k
ΔEb
ln
˙
ε
0
˙
ε
2
3
T−1
3(6)
The higher
σ
0(0K)in screw dislocations results in a larger reduction in
the contribution to
σ
0, compared to the case of edge dislocations with
lower
σ
0(0K)and smaller reduction rates. Accordingly, at high tem-
peratures, there can be a crossover of contributions between screw and
edge dislocations, and edge dislocations become dominant instead of
screw dislocations. Particularly in highly-concentrated BCC alloys,
σ
0(0K)for screw dislocations can be signicantly higher than that in
dilute alloys owing to the formation of cross-kinks as described above.
Thus, the contribution of screw dislocations to
σ
0 drops very quickly
with increasing temperatures, and there can be a crossover of the con-
tributions (edge dislocations become dominant) even at near RT. Our
systematic comparison between experimental and theoretical values of
the
σ
0 in various BCC alloys shown in Fig. 5 suggests that, at RT, the
glide motion of screw dislocations controls the process of plastic
deformation in pure BCC metals and dilute BCC alloys, while the
contribution of edge dislocations can become comparable or dominant
in high-alloy systems, such as RHEAs/RMEAs. Similar ideas have been
veried in recent studies [16,32,33,42–44]. For example, Han et al.
observed dislocation structures in HfNbTiZr RMEA (one of the present
materials) deformed by nanoindentation at RT and found mixed char-
acter of both screw and edge suggesting that the resistances for screw
and edge dislocations were comparable [42]. Detailed observation of
dislocation structures in the RMEAs is our ongoing work and will be
presented elsewhere in the future. Above all, it can be concluded that
elastic interaction between edge dislocations and alloying elements
having different sizes play an essential role in the solid solution
strengthening of RHEAs/RMEAs at RT. We believe this is one of the
essential characteristics of high-alloy BCC solid solutions.
In conclusion, the present work claried the characteristic
strengthening mechanisms in RHEAs/RMEAs with BCC single phase in
Fig. 4. (a) Relationships between the friction stresses,
σ
0, and the Hall–Petch
slopes, kHP, of the present BCC RHEAs/RMEAs, pure BCC [17], HCP metals
[17], IF steel [18], ferrite steel [19], and other BCC alloys [20–22] represented
by lled red pentagrams, hollow orange triangles, hollow black triangles, and
blue triangles, respectively. (b) Relationship between the Hall–Petch slopes,
kHP, and Young’s modulus, E, of the present RMEAs, pure BCC, HCP, FCC metals
[17,23–27], and FCC HEAs/MEAs [10] represented by lled red pentagrams,
hollow green triangles, hollow blue triangles, hollow black triangles, and hol-
low orange triangles, respectively.
Q. He et al.

Scripta Materialia 231 (2023) 115442
6
terms of grain renement strengthening and solid solution strength-
ening effects. The small Hall–Petch slopes (i.e., weak grain renement
strengthening effect) in the RMEAs could be attributed to their low
elastic modulus. The experimental values of the friction stresses in the
RMEAs were compared with the Maresca-Curtin model. In contrast to
conventional dilute BCC alloys, it was suggested that edge dislocations
could largely contribute to the high strength of BCC RHEAs/RMEAs at
RT due to solute-edge dislocation interactions, as well as screw
dislocations.
Declaration of Competing Interest
The authors declare that they have no known competing nancial
interests or personal relationships that could have appeared to inuence
the work reported in this paper
Acknowledgments
This work was supported by the Elements Strategy Initiative for
Structural Materials (ESISM, No. JPMXP0112101000), JST CREST (No.
JPMJCR1994), the Grant-in-Aid for Scientic Research on Innovative
Area "High Entropy Alloys" (No. JP18H05455), the Grant-in-Aid for
Early-Career Scientists (No. JP22K14501), the Grant-in-Aid for Research
Activity Start-up (No. JP21K20487), and the Grant-in-Aid for JSPS
Research Fellow (No. JP18J20766), all through the Ministry of Educa-
tion, Culture, Sports, Science and Technology (MEXT), Japan. Q.H. was
nancially supported by China Scholarship Council (CSC) for studying
in Kyoto University. All the supports are greatly appreciated.
Supplementary materials
Supplementary material associated with this article can be found, in
the online version, at doi:10.1016/j.scriptamat.2023.115442.
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