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Alloy Design Strategies and Future Trends in High-Entropy
Alloys
JIEN-WEI YEH
1,2
1.—Department of Materials Science and Engineering, National Tsing Hua University, 101,
Sec. 2, Kuang-Fu Road, Hsinchu 30013, Taiwan, ROC. 2.—e-mail: jwyeh@mx.nthu.edu.tw
High-entropy alloys (HEAs) are newly emerging advanced materials. In con-
trast to conventional alloys, HEAs contain multiple principal elements, often
five or more in equimolar or near-equimolar ratios. The basic principle behind
HEAs is that solid-solution phases are relatively stabilized by their signifi-
cantly high entropy of mixing compared to intermetallic compounds, especially
at high temperatures. This makes them feasibly synthesized, processed,
analyzed, and manipulated, and as well provides many opportunities for us.
There are huge numbers of possible compositions and combinations of prop-
erties in the HEA field. Wise alloy design strategies for suitable compositions
and processes to fit the requirements for either academic studies or industrial
applications thus become especially important. In this article, four core effects
were emphasized, several misconceptions on HEAs were clarified, and several
routes for future HEA research and development were suggested.
INTRODUCTION
Conventionally, the alloy design, alloy production,
and alloy selection are almost confined by one-ele-
ment or one-compound concept. This alloy concept
obviously limits the degree of freedom in alloy’s
composition and thus limits the development of
special microstructure and properties. It is safer to
say that materials science and engineering of alloys
are still not fully explored because those alloys
outside this conventional scheme have not been in-
cluded. In recognition of this tradition, a brand-new
alloy concept of high-entropy alloys (HEAs) to break
the confinement have been proposed and explored
since 1995.
1–5
Up until now, it has been demon-
strated that the explored alloys in this virgin field
are feasible to be synthesized, processed, and ana-
lyzed contrary to the misconceptions based on tra-
ditional experiences. Moreover, there are many
opportunities in this field for both academic studies
and industrial applications.
As the combinations of composition and process
for producing HEAs are numerous and each HEA
has its own microstructure and properties to be
identified and understood, the research work is
truly limitless. Therefore, in this article, alloy de-
sign strategies and future trends for HEAs were
focused on the technical and scientific viewpoints.
But it is still very important to present basic con-
cepts relating with HEAs in advance, including the
origin of high entropy, definition, four core effects of
HEAs, and misconceptions on HEAs, which are
helpful in alloy design and research for HEAs.
DEFINITION AND THE REASON TO USE
HIGH ENTROPY
The so-called HEAs contain multiple principal (or
major) elements, often five or more in equimolar or
near-equimolar ratios, and minor elements. The
basic principle behind HEAs is that solid-solution
phases are relatively stabilized by their signifi-
cantly high entropy of mixing compared with
intermetallic compounds, especially at high tem-
peratures. This allows them to be feasibly synthe-
sized, processed, analyzed, manipulated, and used
by us. In a broad sense, HEAs are preferentially
defined as those alloys containing at least five
principal elements, each having the atomic per-
centage between 5% and 35%. The atomic percent-
age of each minor element, if any, is hence less than
5%.
Why are the new multicomponent alloys called
HEAs? Let us consider an equimolar alloy at its li-
quid state or regular solid-solution state. Its con-
figurational entropy per mole can be calculated by R
JOM, Vol. 65, No. 12, 2013
DOI: 10.1007/s11837-013-0761-6
2013 The Minerals, Metals & Materials Society
(Published online October 4, 2013) 1759
ln(n) based on the well-known Boltzmann’s
hypothesis on the relationship between the entropy
and the complexion of a system:
DSconf ¼kln w¼R1
nln 1
nþ1
nln 1
nþþ1
nln 1
n
¼Rln 1
n¼Rln n
where Ris gas constant, 8.314 J/K mol, and nis the
number of elements.
4,5
Although total mixing entropy has four contribu-
tions such as configurational, vibrational, magnetic
dipole, and electronic randomness, configurational
entropy is dominant over other three excess contri-
butions.
6,7
Among these three, the excess vibra-
tional entropy at high temperatures could be
calculated from Debye temperatures before and
after mixing.
6
Negative contribution of excess
vibrational entropy to overall mixing entropy might
occur and could be enhanced by attractive interac-
tions between unlike atomic pairs. Table Ilists the
configurational entropies of equimolar alloys in
terms of the gas constant R. The entropy increases
as the number of element increases. From Richards’
rule, the entropy change per mole, DS
f
, from solid to
liquid during melting is about one gas constant Rfor
metals. Moreover, the enthalpy change or latent
heat per mole, DH
f
, can be correlated with DS
f
by
the equation: T
m
DS
f
=DH
f
. Because DH
f
can be re-
garded as the energy required to destroy about one
twelfth of all bonds in the solid, a mixing entropy of
Rper mole due to mixing in an alloy state would be
quite large to decrease the mixing free energy by an
amount of RT at high temperatures, e.g.,
RT = 8.314 kJ/mol at 1000 K, and to compete with
the mixing enthalpy of intermetallic compounds
arising from the interaction between unlike metallic
atoms. That means the tendency to form the mixing
state of constituent elements would be increased by
increased mixing entropy. This tendency will be
further discussed in the ‘‘High Entropy Effect’’ sec-
tion.
It can be seen from Table Ithat configurational
entropy of a three-element equimolar alloy is al-
ready slightly higher than 1Rand that of a five-
element alloy is higher than Rby 61%. Thus, it is
reasonable to think that 1.5R(even not include
other three mixing entropy contributions mentioned
above) is large enough to compete with mixing en-
thalpy, as well as to be used as a border line be-
tween HEAs and medium-entropy alloys. This could
be understood from the fact that if the formation
enthalpies of two typical strong intermetallic com-
pounds such as NiAl and TiAl are divided by their
respective melting points, then the resulting
equivalent DS
conf
, 1.38Rand 2.06R, are in the same
range as the entropy changes of mixing in a system
with more than five elements.
4
That means, 1.5R
could be competitive with most strong bonding
energies of unlike atomic pairs at high tempera-
tures. In addition, 1Rcan be used as the border line
for medium-entropy and low-entropy alloys because
a mixing entropy smaller than 1Ris expected to be
much less competitive with those strong bonding
energies. Table II gives the configurational entro-
pies calculated for typical traditional alloys at their
liquid state or random state. We can see from this
table that most alloys have low entropy, whereas
some concentrated alloys of Ni-base, Co-base su-
peralloys, and bulk metallic glasses (BMGs) have
medium entropy between 1 and 1.5R. That means
very few traditional alloys could have a high mixing
entropy >1.5R. Based on this, the alloy world is
schematically shown in Fig. 1. Previously, the bor-
der lines are set as 0.69Rand 1.61R, respectively,
and thus, they have some difference from the cur-
rent picture. This is simply because the previous
ones are based on the number of principal elements,
i.e., 2 and 5, respectively.
5,8
Based on the defined border lines, the definition of
HEAs in a broad sense can be also understood from
configurational entropy calculation. From the con-
figurational entropy equation, we can obtain that an
element with a concentration of 5 at.% would con-
tribute a mixing entropy of 0.05Rln0.05 = 0.15R,
which is just 10% of minimum requirement of 1.5R
for HEAs. So, we could regard an element in an
amount >5 at.% as a principal element. As for
4 at.%, 3 at%, 2 at.%, and 1 at.%, the contributions
are 0.129R, 0.105R, 0.078R, and 0.046R, respec-
tively, and thus their percentages based on 1.5Rare
8.6%, 7%, 5.2%, and 3.1%, respectively. So, we re-
gard an element in an amount <5 at.% as a minor
element.
A question is raised from the HEAs definition:
What is the upper bound of the number of metallic
principal elements? For 5-element, 10-element, and
12-element alloys, as well as 13-element, 14-ele-
ment, 15-element, 20-element, and 40-element
equal-mole alloys, the total configurational entro-
pies are 1.61R, 2.3R, 2.49R, 2.57R, 2.64R, 2.71R,
3.0R, and 3.69R, respectively. Because the increase
in 0.07R, from a 13- to a 14-element alloy is rela-
tively small (0.07/2.57 = 2.7%), a practical number
of principal element between 5 and 13 was sug-
gested for HEAs.
5
That means more principal ele-
ments will not get a significant benefit from the
Table I. Configurational entropies of equimolar alloys with constituent elements up to 13
n12345678910111213
DS
conf
0 0.69R1.1R1.39R1.61R1.79R1.95R2.08R2.2R2.3R2.4R2.49R2.57R
Yeh1760
high-entropy effect but might increase the com-
plexity in handling raw materials or recycling the
alloys.
Indeed, it is not easy to give a clear-cut composi-
tion definition for HEAs. The composition definition
is just a guideline. An alloy with some deviation
from this composition definition might also be re-
garded as an HEA. For example, an alloy with 21-
element equal-mole alloy is surely an HEA, even
though each element has a concentration smaller
than 5 at.%. In the common definition of low-alloy
carbon steels, they can, from a technical standpoint,
contain about 1 wt.% to 4 wt.% alloying elements.
9
If a higher amount is added, then it is considered as
a different type of steels. Surely, the upper limit of
4 wt.% is also a guideline because 5 wt.% and
8 wt.% were ever proposed from different standing
points.
Under the above definition and practical upper
bound of 13 principal elements, at an arbitrary
choice of a group of 13 metallic elements, we can
obtain a total of 7099 possibilities for designing
equal-mole HEAs systems from 5 to 13 elements
5
:
C13
5þC13
6þC13
7þC13
8þC13
9þC13
10 þC13
11
þC13
12 þC13
13 ¼7099 ð5Þ
We may design an equal-mole AlCoCrCuFeNi al-
loy. We may also design unequal-mole alloys with
minor alloying elements like AlCo
0.5
CrCu Fe
1.5
Ni
1.2
B
0.1
C
0.15
for further modification of micro-
structure and properties. As a result, HEAs are
countless in number.
FOUR CORE EFFECTS OF HEAs
Many factors affect the microstructure and prop-
erties of HEAs. Among these, four core effects are
more basic.
5
For thermodynamics, a high entropy
effect could interfere with complex phase formation.
For kinetics, a sluggish diffusion effect could slow
down phase transformation. For structure, severe
lattice distortion effect could alter properties to an
extent. For properties, the cocktail effect brings
excess quantities to the quantities predicted by the
mixture rule due to mutual interactions of unlike
atoms and severe lattice distortion. The next section
further explains these four effects.
High Entropy Effect
As the name implied, high entropy is the unique and
most important of HEAs because its effect could en-
hance the formation of solution phases and makes the
microstructure much simpler than previously ex-
pected. Why? It is well known that there are three
possible categories of competing states in the solid
state of an alloy, that is, elemental phases, interme-
tallic compounds, and solid-solution phases. The
competition involving liquid phase during solidifica-
tion is not considered. Elemental phase means the
terminal solid solution based on one metal element.
Intermetallic compound means stoichiometric com-
pounds having specific superlattices, such as NiAl
having B2 structure and Ni
3
Ti having D0
24
structure.
Solid solution means the phase with the complete
mixing of all elements or with a significant mixing of
constituent elements in the structure ofbody-centered
cubic (bcc), face-centered cubic (fcc), and hexagonal
close packed (hcp). Intermetallic phases or interme-
diate phases are also included because they are solid
solutions based on intermetallic compounds.
10,11
In
such phases, different constituent elements tend to
occupy different sets of lattice sites. According to the
Thermodynamic Second Law, the state having the
lowest mixing free energy DG
mix
among all possible
states would be the equilibrium state. To elucidate a
high entropy effect in enhancing the formation of so-
lid-solution phases and inhibiting the formation of
intermetallic compounds, HEAs composed of constit-
uent elements with stronger bonding energies be-
tween each other are considered. By the comparison in
Table III, which does not consider strain energy con-
Table II. Configurational entropies calculated for
typical traditional alloys at their liquid state or
random state
Systems Alloys
DS
conf
at liquid
state
Low-alloy steel 4340 0.22Rlow
Stainless steel 304 0.96Rlow
316 1.15Rmedium
High-speed steel M2 0.73Rlow
Mg alloy AZ91D 0.35Rlow
Al alloy 2024 0.29Rlow
7075 0.43Rlow
Cu alloy 7-3 brass 0.61Rlow
Ni-base superalloy Inconel 718 1.31Rmedium
Hastelloy X 1.37Rmedium
Co-base superalloy Stellite 6 1.13Rmedium
BMG Cu
47
Zr
11
Ti
34
Ni
8
1.17Rmedium
Zr
53
Ti
5
Cu
16
Ni
10
Al
16
1.30Rmedium
Fig. 1. Alloy world based on configurational entropy.
Alloy Design Strategies and Future Trends in High-Entropy Alloys 1761
tribution (due to atomic size difference) to mixing en-
thalpy for simplicity, elemental phases based on one
major element have small DH
mix
and DS
mix
,and
compound phases have large DH
mix
but small DS
mix
;
on the other hand, solid-solution phases containing
multiple elements have medium DH
mix
and high
DS
mix
. As a result, solid-solution phases become highly
competitive for equilibrium state and more stable
especially at high temperatures. It should be ex-
plained why multielement solid solutions have med-
ium DH
mix
. This is because a proportion of unlike
atomic pairs exists in solution phases. For example, a
mole of atoms, N
0
, of NiAl intermetallic compound
(B2) in completeordering has (1/2) 98N
0
Ni-Al bonds,
whereas a mole of NiAl random solid solution would
have (1/2) 9(1/2) 98N
0
Ni-Al bonds. That means the
mixing enthalpy in the random state is half that of the
completely ordered state. Similarly, for a five-element
equimolar alloy, the ratio is 4/5 and for an eight-ele-
ment equimolar alloy, the ratio is 7/8 assuming that all
heats of mixing for unlike atom pairs are the same. In
brief, a higher number of elements would allow the
random state to have the mixing enthalpy closer to
that of the completely ordered state and to become
even more competitive with the ordered state under
the aid of its high mixing entropy.
In general, if the heats of mixing for unlike atomic
pairs do not have large difference, simplesolid solution
phase would be dominant in the equilibrium state. For
example, the FeCoCrMnNi alloy can form a simple fcc
solution even full-annealed at all temperatures.
12,13
The ductile refractory HfNbTaTiZr alloy having the
melting point around 2250C as predicted by the rule
of mixture hasa simple bcc phase in the as-cast state.
14
Conversely, a large difference might generate more
than two phases. For example, Al has stronger bond-
ing with transition metals, but Cu has no attractive
bond with most transition metals. As a result, AlFe-
CoCrCuNi alloy forms Cu-rich fcc + multi-element
fcc + multi-element bcc (A2) at high temperatures
above 600C, and has B2 precipitates in the Cu-rich fcc
and spinodally decomposed structure of A2 + B2
phases from A2 phase during cooling. The B2 solid
solution containing multielements is in fact derived
from the NiAl-type compound.
15
Even larger differ-
ence as found in the alloys containing O, C, B, or N
would generate oxides, carbides, borides or nitrides in
the microstructure.
To include the effect of atomic size difference, Zhang
et al.
16
first proposed the forming trend of disordered
solid solutions, ordered solid solution, intermediate
phases, and BMG by comparing DS
mix
,DH
mix
,and
atomic size difference (d). Guo and Liu
17
also used
these factors to lay out the phase selection rule for such
kinds of phase. Moreover, Yeh,
18
Chen and Yeh,
19
and
Yang and Zhang
20
used dand the ratio of TDS
mix
to
DH
mix
to describe the order–disorder competition in
HEAs and the existing range of intermetallics and
BMG. All these studies pointed out that solution-type
phases including disordered and intermediate phases
tend to form in highly alloyed multicomponent alloys.
Disordered solutions preferentially form under smal-
ler d, smaller DH
mix
, but higher DS
mix
, i.e., a higher
ratio of TDS
mix
to DH
mix
.
In summary, a high entropy effect is important
for HEAs to avoid the formation of many different
kinds of stoichiometric compounds, which are very
brittle and complex to analyze and understand.
Conversely, it enhances the formation of solution-
type phases and thus reduces the number of phases
as predicted by Gibbs phase rule which permits the
number of phases in equilibrium to increase with
the number of components.
Sluggish Diffusion Effect
We know that the formation of new phases re-
quires cooperative diffusion of many different kinds
of atoms to accomplish the partitioning of composi-
tion in HEAs. However, the vacancy concentration
for substitutional diffusion is still limited in HEAs
as found in traditional alloys because each vacancy
in crystalline HEAs is also associated with a posi-
tive enthalpy of formation and an excess mixing
entropy, which render a minimum free energy of
mixing at a certain equilibrium concentration for a
given temperature.
21
A vacancy in the whole-solute
matrix is in fact surrounded and competed by dif-
ferent-element atoms during diffusion. It has been
proposed that slower diffusion and higher activation
energy would occur in HEAs due to larger fluctua-
tion of lattice potential energy (LPE) between lattice
sites.
13
The abundant low-LPE sites can serve as
traps and hinder atomic diffusion, leading to the
sluggish diffusion effect.
To verify this effect, a near-ideal solution system
of Co-Cr-Fe-Mn-Ni with stable single fcc solid solu-
tion was selected by Tsai et al.
13
to make diffusion
couples and analyze the diffusion data of each ele-
ment in the matrix. Four quasi-binary diffusion
Table III. Comparisons of DH
mix
,DS
mix
, and DG
mix
between elemental phases, compounds, and solid solutions
Possible states Elemental phases Compounds Solid solutions
DH
mix
0 Large negative Medium negative
TDS
mix
00RTln(n)
DG
mix
0 Large negative Large negative
Strain energy from atomic size difference is not included in DH
mix
.
Yeh1762
couples were made as listed in Table IV. In the two
end members of each couple, only two elements
differed in concentration. The diffusion couple was
tightly fixed in a molybdenum tube, which was
further sealed in a vacuum quartz tube. From the
concentration profiles obtained after diffusion at
different elevated temperatures, 1173 K, 1223 K,
1273 K, and 1323 K, diffusion coefficients and acti-
vation energy were obtained. The results showed
that the sequence in the order of decreasing diffu-
sion rate was Mn, Cr, Fe, Co, and Ni. It was also
found that diffusion coefficients of each elements at
T/T
m
in the Co-Cr-Fe-Mn-Ni alloy system were the
smallest in similar fcc matrices including Fe-Cr-Ni
(-Si) alloys and pure Fe, Co, and Ni metal. In addi-
tion, the melting point normalized activation ener-
gies, Q/T
m
, in the HEA were the largest as shown in
Fig. 2. These figures show direct evidence for the
sluggish diffusion effect in HEAs. It was also noted
that for the same element, the degree of sluggish
diffusion is related to the number of elements in
that matrix. For example, the Q/T
m
values in the
present HEAs are the highest, those in Fe-Cr-Ni
(-Si) alloys are the second, and those in pure metals
are the lowest.
It is expected that sluggish diffusion effect might
provide several important advantages as found in
many related publications
15,22–29
: easy to get super-
saturated state and fine precipitates, increased
recrystallization temperature, slower grain growth,
reduced particle coarsening rate, and increased creep
resistance. These advantages might benefit micro-
structure and property control for better perfor-
mance. For example, Liu et al.
28
studied the grain
growth of cold-rolled and annealed sheet of CoC-
rFeMnNi HEA and found that the activation energy
is much higher than AISI 304LN stainless steels,
which is consistent with the sluggish diffusion effect.
Severe Lattice Distortion Effect
Because the multielement matrix of each solid-
solution phase in HEAs is a whole-solute matrix,
15
every atom is surrounded by different kinds of atoms
and thus suffers lattice strain and stress mainly due
to atomic size difference as shown in Fig. 3. Besides
the atomic size difference, both different bonding
energy and crystal structure tendency among con-
stituent elements are also believed to cause even
higher lattice distortion because non-symmetrical
bindings and electronic structure exist between an
atom and its first neighbors and moreover, this non-
symmetry varies from site to site in the lattice.
13,32
As
a result, the distortion severity of lattice is much
larger than that in conventional alloys that are based
on a major element. In conventional alloys, most
matrix atoms (or solvent atoms) have the same kind
of atoms as their neighbors.
Lattice distortion not only affects properties but
also reduces the thermal effect on properties.
Hardness and strength effectively increase because
of large solution hardening in the heavily distorted
lattice. For example, hardness values of refractory
bcc HEAs: four equimolar alloy NbMoTaW and five
equimolar alloy VNbMoTaW are Hv 4,455 MPa and
5,250 MPa, respectively. These values are three
times that obtained by the mixture rule.
30
In addi-
tion, electrical and thermal conductivity signifi-
cantly decrease due to electron and phonon
scattering.
31
X-ray diffraction peak intensity de-
creases due to x-ray diffuse scattering in the dis-
torted atomic planes.
32
All these properties in HEAs
become quite insensitive to temperature. This is
explainable because the lattice distortion caused by
thermal vibration of atoms is relatively small com-
pared with the severe lattice distortion.
32
For
Table IV. The concentrations of end members of
three diffusion couples
13
Couple Alloy
Composition (at.%)
Co Cr Fe Mn Ni
Cr-Mn 1 22 29 22 5 22
22217221722
Fe-Co 3 33 23 11 11 22
41123331122
Fe-Ni 5 23 24 30 11 12
62324121130
Fig. 2. Melting-point normalized activation energy of diffusion for Cr,
Mn, Fe, Co, and Ni in different matrices.
13
Alloy Design Strategies and Future Trends in High-Entropy Alloys 1763
example, Lu et al.
33
studied the thermal diffusivity
as a function of temperature for four HEAs and pure
Al as shown in Fig. 4. It was found that the thermal
diffusivities of HEAs are positively small and
insensitive to temperature, whereas that of con-
ventional metal is positively large and sensitive to
temperature.
33
Cocktail Effect
The term ‘‘multimetallic cocktails’’ was first pro-
posed by Ranganathan
34
to emphasize alloy plea-
sures in alloy design and development. To treat
AIDS, cocktail treatment was invented by David Ho
using the concept of three-drug therapy in 1996,
which shows an impressive benefit with a 60–80%
decline in rates of AIDS, death, and hospitalization.
In HEAs, the cocktail effect is also emphasized
majorly because at least five major elements are
used to enhance the properties of the materials. As
stated above, HEAs might have a simple phase, two
phases, three phases, or more depending on the
composition and processing. As a result, the whole
properties are from the overall contribution of the
constituent phases by the effect of phase shape,
phase distribution, phase boundaries, and proper-
ties of each phase. However, each phase is a multi-
element solid solution and can be regarded as
atomic-scale composites. Its composite properties
come from not only the basic properties of elements
by the mixture rule but also the mutual interactions
among all the elements and from the severe lattice
distortion. Interaction and lattice distortion would
bring excess quantities to the quantities predicted
by the mixture rule. As a whole, the ‘‘cocktail effect’’
ranges from an atomic-scale, multielement
composite effect to a microscale, multiphase com-
posite effect. Therefore, it is important for an alloy
designer to understand the related factors involved
before selecting suitable composition and processes.
For example, refractory HEAs developed by Air
Force Research Laboratory have melting points
very much higher than that of Ni-base and Co-base
superalloys.
24,30
This is simply because refractory
elements were selected as constituent elements. By
the mixture rule, four-equimolar-alloy NbMoTaW
and five-equimolar-alloy VNbMoTaW have melting
points above 2600C. As a result, both alloys display
much higher softening resistance than superalloys
and have yield strengths above 400 MPa at 1600C
as shown in Fig. 5.
24
Such refractory HEAs are thus
also expected to have potential applications at very
high temperatures. In another example, Zhang
et al.
35
studied FeCoNi(AlSi)
00.8
alloys for finding
the composition with the optimum combination of
magnetic, electrical, and mechanical properties. The
best was achieved in alloy FeCoNi(AlSi)
0.2
with
saturation magnetization (1.15 T), coercivity
(1,400 A/m), electrical resistivity (69.5 lXcm), yield
strength (342 MPa), and strain without fracture
(50%), which lets the alloy be an excellent, soft
magnetic material for many potential applications.
Obviously, this alloy design relied on the selection of
equimolar ferromagnetic elements (Fe, Co, and Ni)
for forming ductile fcc phase with higher atomic
packing density than bcc, and suitable addition of
nonmagnetic elements (Al and Si having slightly
anti-parallel magnetic coupling with Fe, Co, and Ni)
to increase lattice distortion. It led to a positive
cocktail effect in achieving high magnetization, low
coercivity, good plasticity, high strength, and high
electrical resistance.
Finally, it should be mentioned that the four core
effects are much more pronounced in HEAs and
Fig. 3. Severely distorted lattice in a multielement crystal structure.
Fig. 4. Thermal diffusivities as a function of temperature for pure
aluminum and HEA-a(Al
0.3
CrFe
1.5
MnNi
0.5
), HEA-b(Al
0.5
CrFe
1.5
Mn-
Ni
0.5
), HEA-c(Al
0.3
CrFe
1.5
MnNi
0.5
Mo
0.1
), and HEA-d(Al
0.5
Cr-
Fe
1.5
MnNi
0.5
Mo
0.1
).
32
Yeh1764
strongly influence their microstructure and prop-
erties. Thus, it would become much easier for us to
understand and explain the phenomena in HEAs
through these four effects. In addition, four core
effects are useful guidelines for one to design an
HEA for specific purpose or application.
SEVERAL MISCONCEPTIONS ON HEAs
Several misconceptions about HEAs are as fol-
lows: (I) HEAs have low entropy and complex
microstructure, (II) HEAs are hard and brittle, and
(III) HEAs are expensive and difficult to fabricate.
In the following sections, these misconceptions are
clarified.
Low Entropy and Complex Microstructure
It should be clarified in the first place that mixing
entropy is compared at the liquid solution or ran-
dom solid-solution state. HEAs have a high mixing
entropy at such states compared with those of con-
ventional alloys. Why is high mixing entropy at
such states emphasized? Figure 6shows the phase
evolution during solidification and cooling. If an
alloy has a high mixing entropy, then simple solid-
solution phases will form at high temperatures due
to the large TDS
mix
. During subsequent cooling,
mixing entropy become less important, and short-
range ordering, long-range ordering, or even pre-
cipitation of second phases might occur. But a
sluggish diffusion effect will yield fine precipitates
or inhibit precipitation, which is welcomed for
improving properties.
15
Conversely, if multielement
alloys do not have a high mixing entropy at high
temperatures, then intermetallic phases would form
at high temperatures. In subsequent cooling, the
microstructure would become even more complex.
Such complex microstructures obviously become
very difficult to understand and manipulate, and
they are very brittle to be used. Therefore, the for-
tune to avoid the complexity at low temperatures
essentially comes from the high entropy effect,
which is amplified by high temperatures to compete
with mixing enthalpies of intermetallics.
Hard and Brittle by Nature
It is commonly held that highly alloyed conven-
tional alloys are in general hard and brittle. How-
ever, this is not always true for HEAs. In fact, HEAs
are like conventional alloys: Some are hard and
brittle, while some are softer and ductile. In brief,
fcc phases in HEAs in general possess lower hard-
ness but excellent ductility.
28,36,37
They can be hot
worked and cold worked easily. BCC phases in
HEAs possess a higher hardness but lower ductility.
They can be hot worked and warm worked, while
some can be cold worked. As for the intermediate
phases based on intermetallic compounds, they are
also hard and can increase the alloy hardness by
precipitation hardening or composite strengthening.
If the overall hardness is high, then the slip defor-
mation would become difficult and tend to become
brittle. For such a case, hot forging or hot rolling is
recommended to enhance the deformation and
shaping. If the overall hardness is medium, then the
slip deformation of the matrix is still possible. Cold
working might be feasible. It should be mentioned
that a high entropy effect tends to make all these
phases become multielement solid solutions and to
improve their mechanical properties. For fcc and bcc
phases, solution hardening is known as a good
strengthening mechanism to improve both strength
and ductility. For intermetallic intermediate pha-
ses, multielement substitution will make their su-
perlattices more disordered and enhance slip
deformation and ductility.
Expensive and Difficult to Fabricate
Some elemental raw materials such as Zr, Ti, Co,
and Ni for HEAs are more expensive than Mn, Fe,
Al, and Cu. Hence, the overall material cost could be
intermediate between the most expensive compos-
ing element and the cheapest element based on the
rule of mixture. Therefore, HEAs might be cheaper
than Ti alloys, Ni alloys, and Co alloys, depending
on compositions. Like traditional alloys, HEAs could
be fabricated by selecting suitable processes from
ingot metallurgy, powder metallurgy, and coating
0
200
400
600
800
1000
1200
1400
0 200 400 600 800 1000 1200 1400 1600
Yield Strength (MPa)
Temperature (°c)
Nb Mo Ta W
V Nb Mo Ta W
Inconel 718
Haynes 230
Fig. 5. The temperature dependence of the yield stress of
Nb
25
Mo
25
Ta
25
W
25
and V
20
Nb
20
Mo
20
Ta
20
W
20
HEAs and two super-
alloys, Inconel 718 and Haynes 230.
33
Fig. 6. Phase evolution during solidification and cooling of HEAs
having a melting temperature around 1700 K.
Alloy Design Strategies and Future Trends in High-Entropy Alloys 1765
technology. The selection depends on the fabrica-
bility and purposes. For example, fcc-type HEAs
could be hot forged and cold rolled. Tungsten car-
bides or cermets could use suitable HEAs as binders
replacing Co or Ni. They are inevitably processed by
powder metallurgy. In general, there are many
conventional processes provided for fabricating
HEAs.
ALLOY DESIGN STRATEGIES FOR HEAs
There are numerous combinations of compositions
and processes to generate HEAs. The development
of HEAs should be efficient rather than time and
resource consuming. There are several routes to
develop HEAs: (I) use combinatorial materials syn-
thesis technique; (II) use computational materials
science: ab initio simulation, molecular dynamics
(MD), finite element, New PHACOMP, CALPHAD
method, etc.; (III) use Taguchi method to optimize
the properties; (IV) start from promising alloy sys-
tems; and (V) use alloy design principles of materi-
als science. The following sections describe each
route.
Use Combinatorial Materials Synthesis Tech-
nique
Over the last two decades, combinatorial chemis-
try has altered the drug-development process to
discover new drugs.
38,39
By this encouragement,
materials scientists also apply this methodology to
accelerate the discovery of new compounds for high-
T
c
superconductors, luminescent materials, cata-
lysts, and polymers.
40
They use thin-film technology
to deposit substances sequentially in different
amount layer by layer onto a gridded substrate and
then to mix the elements and create a stable com-
pound by heating. The physical properties of inter-
est are then measured on each composition to find
out the outstanding composition. Basically under
little guidance to predict new materials, this is a
very efficient trial-and-error method to discover new
materials. Nowadays, laser-engineered net shaping
(LENS) in the technology of rapid prototyping can
fabricate HEAs in bulk form directly by injecting
metal powders into the area focused with a high-
powered laser beam. The stacking layer by layer
could be changed in different compositions. For
example, Al content can be varied from 0 to 3 seg-
mentally in a grown Al
x
CoCrCuFeNi alloy rod.
41
Similarly, other elements could be varied to produce
segmentally gradient rods. The analyses become
more efficient on the gradient rods to generate data
for further assessment.
Use Computational Materials Science
New Phacomp was invented in 1984 using the d-
electron concept to define the phase boundaries in
terms of M
d
(metal d-level), especially to define the
critical M
d
value of gamma phase and sigma phase
boundary for predicting sigma phase formation in
Ni-base superalloys.
42
Thermo-Calc software
(Thermo-Calc Software, Stockholm, Sweden) is a
computational tool for calculating phase diagrams.
All these computations could save the experiments
that are time consuming, difficult, or expensive. But
the existing database for HEAs is still lacking in
making predictions with accuracy and thus needs to
be enriched in the future. For simple calculation
and prediction, Guo et al.
43
found that the valence
electron concentration (VEC) is the critical param-
eter controlling the phase stability for fcc (VEC ‡8)
or bcc phase (VEC <6.87). This criterion is useful
to design some HEAs.
As for MD simulation, a many-body tight-binding
potential model has been applied to study the effect
of the number of elements and size difference on the
amorphous structure of HEAs.
44,45
This is simply
because this model treats the interatomic forces
existing between any two unlike atoms as the geo-
metric average of their bonding forces in their
respective pure lattices, and thus it treats the sys-
tems as ideal solutions (i.e., the mixing enthalpy is
zero). In other words, such MD simulation rules out
the effect of actual bonding energy between unlike
atoms and only investigates the effects from the
number of elements and the atomic size. The alloys
simulated were from traditional binary alloys to
HEAs by adding one element in sequence. For
example, Fig. 7shows the initial radial distribution
function curves of the alloys at 300 K before the
system was heated.
44
Thus, we can see that the
patterns of two-element to four-element alloys have
well-defined peaks which indicate an ordered
structure. However, the five-element alloy and six-
element alloy containing large-sized Zr have lower
and broader peaks, which confirm an amorphous
structure. Virtually, this trend apparently shows
that the amorphization is enhanced by the number
of elements and large atomic size difference. When
heated up to the molten state at 2200 K, the pat-
terns typically depict a liquid structure as shown in
Fig. 8a. Moreover, as the number of elements in-
creases, peaks become broader and distance be-
tween peaks also become larger, which indicates
that the liquid structure becomes more disordered.
In the melt-quenched state, five-element and six-
element alloys exhibit liquid-like solid structure as
shown in Fig. 8b. But, two- to four-element alloys
display an amorphous structure because there is a
splitting in their second peaks, which indicates that
the structure is more ordered than the liquid
structure. This again shows an increased number of
elements, and thus a large atomic size difference
could enhance the amorphization. In fact, the shape
and evolution of radial distribution function curves
could be explained from the close-packed hard ball
model as shown in Fig. 9. The splitting of the second
peaks indicates that the second nearest-neighbor
shell is not fully merged with the third shell due to
the insufficiency in the degree of disorder. By the
Yeh1766
hard ball model, the number of atoms and distance
for each shell are shown in the second and third
rows of Table V, respectively. Under a random
occupation of sites by different atoms, the fluctua-
tion range caused by the atomic size difference can
be used to judge the merging of peaks. If the atomic
size difference makes the atomic fluctuation range
in the second and third shells larger than 7.2%, then
the second and third shells or peaks are expected to
merge into each other. It can be seen from Table VI
that only 5- and 6-element alloys with deviation
over 10% can fit this requirement. Because the
deviation between 4th and 5th shell is 6.2%, all the
alloys can have merging of the 4th and 5th peaks.
Therefore, the judgment of peak merging by the
atomic size difference is consistent with the radial
distribution function calculated by MD simulation.
Besides MD simulation, ab initio calculation from
the electron level or directly from the first principles
of quantum mechanics is also powerful to predict
materials behavior and properties. However, ab ini-
tio calculations require a large amount of numerical
computation. The computing time increases rapidly
as the number of atoms increases.
Use Taguchi Method
The Taguchi method is helpful to us in designing
a minimum number of experiments to investigate
how different parameters affect the product quality
or performance and then to find the combination of
parameters for optimum performance.
46
The
experimental design uses orthogonal arrays to
organize the parameters that affect the performance
and the levels at which the parameters vary. This
saves time and resources without doing a lot of
experiments. Similarly, the Taguchi method could
be applied to an HEA system to observe those
compositions that display better properties and
performance. For example, with an aim to optimize
hardness, toughness, and oxidation resistance for
plasma spray coatings on elevated-temperature
components, the best compositions based on a
promising HEA system could be obtained. One of
the best compositions from this method is the non-
equal-mole alloy Al-Co-Cr-Fe-Ni-Si-Ti, which has
been successfully deposited on 304 stainless steels
by plasma spray as shown in Fig. 10. Thus, it dis-
plays good performance with a high hardness of Hv
880, good fracture toughness, and oxidation resis-
tance similar to that of well-known NiCrAlY coat-
ings.
Start from Promising Alloy Systems
We might start HEA research from promising alloy
systems. For each system, equal and nonequal-mole
alloys could be systematically studied. Figure 11
shows an example of a six-element Al-Co-Cr-Fe-Mo-
Ni system,
23,29,47–49
which is thought to be an inter-
esting and promising system because Co, Cr, Fe, and
Ni are the bases for superalloys, Al is critical to in-
crease oxidation resistance at high temperatures,
and Al and Mo are important elements to increase the
temperature capability. Because there are lots of
compositions in this six-element system, a strategy
was used to reduce the number of compositions
investigated and effectively understand the system
in a whole view. Figure 11 shows a center alloy base
in which five elements are in equal mole and Mo is in
02468101214
Ni-Al-Cu-Ti-Zr-V
Ni-Al-Cu-Ti-Zr
Ni-Al-Cu-Ti
Ni-Al-Cu
g(r)=
ρ
(r)/
ρ
0
Radius (A)
o
Ni-Al
300 K
Fig. 7. The radial distribution functions obtained at 300 K for Ni-Al to
Ni-Al-Cu-Ti-Zr-V equimolar alloys by MD simulation.
02468101214
Ni-Al-Cu-Ti-Zr-V
Ni-Al-Cu-Ti-Zr
Ni-Al-Cu-Ti
Ni-Al-Cu
Ni-Al
melting status
g(r)=
ρ
(r)/
ρ
0
radius (A
o)
02468101214
Ni-Al-Cu-Ti-Zr-V
Ni-Al-Cu-Ti-Zr
Ni-Al-Cu-Ti
Ni-Al-Cu
Ni-Al
melt-quenched
g(r)=
ρ
(r)/
ρ
0
Radius (A
o)
(a) (b)
Fig. 8. The radial distribution functions obtained (a) at the melt state of 2200 K, and (b) at the quenched state for Ni-Al to Ni-Al-Cu-Ti-Zr-V
equimolar alloys by MD simulation.
Alloy Design Strategies and Future Trends in High-Entropy Alloys 1767
half amount because of its high cost. Then Al, Co, Cr,
Fe, and Ni contents were varied from 0 to 2 in molar
ratio, respectively, except Mo between 0 and 0.9.
Thus, the center alloy with half Mo is positioned at
the zone center of this alloy system. By this strategy,
it is expected that we can easily understand and
estimate the data for any other compositions such as
X and Y from their neighboring data. Table VII shows
the constituent phases of all alloys. In summary, Al
can enhance bcc phase but inhibit rphase; Co and Ni
enhance fcc phase; Cr and Mo enhance rphase; and
Fe inhibits rphase (also judged by the relative peak
intensities of different phases from XRD patterns).
Figure 12 shows hot hardness as a function of tem-
perature for Fe and Mo. The plots for Al, Co, Fe, and
Ni are not shown but are similar in trend to
Fig. 12.
23,29,47–49
For each element’s variation, three
curves of superalloys IN718, IN718H, and T-800 are
compared. T-800 has much higher hardness in lower
temperature range but rapid softening at tempera-
tures above 800 K. Precipitation hardened IN718 has
medium hardness. Nonhardened IN718 has the
lowest hardness but becomes hardened at tempera-
tures above 900 K. It is interesting to see all these
three commercial alloys approach the same hardness
at 1100 K and soften at the same rate. In contrast,
HEAs have a lower softening rate. Although some
HEAs have lower hardness values than T-800 in a
lower temperature range, a lower softening rate al-
lows them to maintain much higher hardness than T-
800 at temperatures above 1000 K. It is noted that
among these data, some HEAs have a hardness
around Hv 300–400 (or Rockwell hardness 30–40) at
1000C.
As a result, this alloy system provides a wide
range of hardness and displays excellent softening
resistance and oxidation resistance. Thus, they
Fig. 9. Hard ball model showing shells from the first to the fifth.
Table V. The number of atoms and distance for each shell in the hard ball model with an atomic size of r
1st shell 2nd shell 3rd shell 4th shell 5th shell
Number of atoms 6 6 6 12 6
Distance (shell radius) 2r 3.46r4r5.29r6r
Mean Distance of two close shells 3.73r5.65r
Deviation from mean 7.2% +7.2% 6.2% +6.2%
Table VI. The merging and atomic size difference for NiAl to NiAlCuTiZrV equimolar alloys based on hard
ball model
Alloys NiAl NiAlCu NiAlCuTi NiAlCuTiZr NiAlCuTiZrV
Atomic size deviation ±6.7% 5.3%, + 8.3% ±7.8% 11%, + 14% 10.4%, + 14.7%
Deviation of 2nd and
3rd shells
±7.2%
Partially merged
±7.2%
Partially merged
±7.2%
Partially merged
±7.2%
Merged
±7.2%
Merged
Deviation of 4th and
5th shells
±6.2%
Merged
±6.2%
Merged
±6.2%
Merged
±6.2%
Merged
±6.2%
Merged
Fig. 10. Typical layer structure of nonequal-mole alloy Al-Co-Cr-Fe-
Ni-Si-Ti deposited on 304 stainless steels obtained by plasma spray.
Yeh1768
might find applications in different environments.
Furthermore, based on these data, where there are
some specific industrial applications requiring im-
proved properties, some of these compositions
studied might be considered or modified. Similarly,
this route could be applied to other promising alloy
systems. In other words, the systematic study of a
system with compositions centered at equal-mole
alloy or near-equal-mole alloy could provide a very
valuable database.
Use Alloy Design Principles of Materials
Science
Using principles of materials science to design
and research new materials is the most basic route
to develop HEAs. This route needs better under-
standing on the features of elements such as melt-
ing point, atomic size, crystal structure, valence
electron, electronegativity, density, elastic con-
stants, interactions in unlike atom pairs, thermo-
dynamics and kinetics, microstructure and
properties relationship, and four core effects of
HEAs. In fact, most HEA researchers have used
such principles to develop new HEAs for desired
properties from the beginning. This route is con-
vincing and would become more effective with in-
creased accumulation of data, knowledge, and
experiences on HEAs. For example, when you
examine an equimolar alloy system such as AlCo-
CrFeNiMnSi and TiCoCrFeNiMnB for high
strength and moderate toughness, you might find
their microstructures containing several solid-solu-
tion phases and also their high hardness but poor
ductility. For such cases, you could further use
scanning electron microscope with energy disper-
sive spectrometer or electron microprobe analyzer to
analyze each phase composition and use a microh-
ardness tester to measure the microhardness.
Thereafter, you could select the phase preferred for
your purpose and property requirement as well as
prepare the second alloy according to its composi-
tion. The monolithic phase displaying high strength
and moderate ductility could be obtained because
those brittle phases have been excluded. It should
be mentioned that by the Gibbs phase rule, the de-
gree of freedom in composition is high. So, you can
further adjust the concentration of each element to
improve some properties but still maintain the
simple phase. Apparently, promising HEAs with
better performance usually have nonequal-mole
compositions. Equal-mole HEAs are in general the
beginning points for understanding new alloy sys-
tems. Fine tuning of composition and process are
always necessary to achieve aimed properties just
like the historical development of high-performance
traditional alloys.
FUTURE TRENDS OF HEAs
Although over 400 HEA papers have been pub-
lished up to now, the understanding of the whole
HEA world is still at the infant stage. However,
several future trends can be pointed out at this
stage:
1. More fundamental and basic science studies are
required. Because materials science and solid-
state physics are mainly based on the research on
conventional materials with one or two principal
elements, what happens in HEAs would be inter-
esting in many aspects and become valuable
academic issues. In the whole-solute matrix, dif-
ferent contributions to mixing entropy, mutual
interactions in unlike atomic pairs, short range
order, lattice distortion, electrical and thermal
conductivity, vacancy concentration, diffusion
coefficients, dislocation energy, staking fault en-
ergy, grain boundary energy, slip, twinning,
strengthening, toughening, creep, wear, corro-
sion, and oxidation are all needed to be understood
with their mechanisms and theories. Whether
they are a simple extension from that of conven-
tional alloys or not is still curious for scientists.
2. More research on promising alloy systems for
better mechanical, chemical, and physical prop-
erties is required. This is in response to the
endless requirements in the improvements of
existing materials. Better performances will
bring cost, energy, and resource savings for us.
3. More research on the performance challenges
unattainable by traditional alloys or materials is
required, such as room-temperature supercon-
ductors, alloys exceeding the performance and
temperature capability of superalloys, and tools
with very high hot hardness and long lifespan.
4. More research on high-entropy nitrides, car-
bides, oxides, and their combinations is required.
A certain amount of such research
50–53
has
indicated that four core effects of HEAs also hold
Fig. 11. Content variation lines of all elements passing through the
center alloy AlCoCrFeNiMo
0.5
, in which Al, Co, Cr, Fe, and Ni con-
tents are varied from 0 to 2 in molar ratio, but Mo is from 0 to 0.9.
Alloy Design Strategies and Future Trends in High-Entropy Alloys 1769
true in such high-entropy ceramics (HECs), and
many promising properties are obtained for
diffusion barriers, hard coatings, and functional
coatings.
5. Assessments of the existing database to find
possible applications are required. It is believed
that HEAs or HECs could solve many bottlenecks
encountered by conventional materials. So, do
not forget to correlate HEAs and HEC data with
industrial applications and exploit their promis-
ing properties. By this effort, one might get closer
to use or modify HEAs and HECs to fit the
application requirements.
CONCLUSIONS
1. High-entropy materials have four core effects:
high entropy, sluggish diffusion, severe lattice
distortion, and cocktail effects, and could provide
a wide spectrum of properties.
2. Like traditional alloys, HEAs have potential
applications in different fields and might replace
traditional materials.
3. Basic science, new HEAs, new HECs, and new
applications are awaiting further research.
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