-
No
W
Z
Zu
m 121
1. Introduction their simple average structure (body-centered
cubic, bcc, or
which is particularly relevant to the aerospace industry,
buttheir low room-temperature ductility might be a limitationfor
further processing steps. Furthermore, refractory metalsor
alloyshave alsobeenproposed tobe employed for electricalresistors,
medical implants and micro- and nanoelectrome-chanical systems
(MEMS and NEMS) [11,12]. It is thus also
Corresponding authors. Tel.: +41 44 632 66 50 (W. Steurer),
tel.: +4144 632 25 90 (R. Spolenak).
E-mail addresses: [email protected] (W. Steurer),
[email protected] (R. Spolenak).1 These authors
contributed equally to this work.
Available online at www.sciencedirect.com
ScienceDirect
Acta Materialia 65 (2014) 8597High-entropy alloys (HEAs),
conceptualized byYeh et al.in 2004 [1], are usuallymade of ve
ormoremetallic elementswith equimolar or near-equimolar ratios,
where their cong-urational entropy, Sconf, increases with the
number of ele-ments n as DSconf = R ln(n), with R the universal
gasconstant. The high entropy stabilizes solid-solution phasesat
elevated temperatures and single-phase HEAs preventthe formation of
possible intermetallics in these composi-tions [13]. HEAs may have
interesting applications due to
face-centered cubic, fcc), their distorted lattice and low
diu-sion rate in a multi-component system [15]. The mainpotential
applications of HEAs are in the development ofhigh-strength and
high-temperature sustaining alloys [6,7],wear-resistant materials
[2] and diusion barriers [8]. Theconventional HEAs based on Al, Co,
Cr, Cu, Fe and Nihave reached strengths and workability comparable
tothose of steels [6,7]. To achieve higher strengths in the
high-temperature regime above 1100 C, the use of refractorymetals
in HEAs was implemented by Senkov et al. [9,10],Abstract
High-entropy alloys (HEAs) are evolving multi-component
intermetallic systems, wherein multiple principal elements tend to
formsingle solid-solution-like phases with a strong tendency to
solid solution strengthening. In this study, an Nb25Mo25Ta25W25
refractoryHEA was synthesized by arc melting and well homogenized
at 1800 C. Single-crystalline HEA pillars in two orientations
([001] and[316]) and with diameters ranging from 2 lm to 200 nm
were produced by focused ion beam milling and compressed using a
at-punchtip in a nanoindenter. The HEA pillar samples can reach
extraordinarily high strength levels of 44.5 GPa, which is 33.5
timeshigher than that of the bulk HEA; meanwhile the ductility is
signicantly improved. Compared to pure Nb, Mo, Ta and W pillars,the
HEA pillars exhibit higher strengths than any of them in both
absolute and normalized values, and the HEA pillars also show
rel-atively low compressive size eects, as evaluated by the loglog
slope of strength vs. pillar diameter. The higher strength levels
and lowersize dependence for the HEA could be attributed to the
increased lattice resistance caused by localized distortion at
atomic length scales.The correlation between normalized strengths,
length scales and temperatures for body-centered cubic structured
pillars is illustrated,and the relevance of a size-eect slope as
well as the additivity of strengthening mechanisms is critically
discussed. 2013 Acta Materialia Inc. Published by Elsevier Ltd. All
rights reserved.
Keywords: Microcompression; High-entropy alloy; Body-centered
cubic; Size eects; Solid solution hardeningSize-dependent
plasticity in anhigh-entr
Yu Zou a,1, Soumyadipta Maiti b,1,aLaboratory for
Nanometallurgy, Department of Materials, ETHbLaboratory of
Crystallography, Department of Materials, ETH
Received 8 October 2013; received in revised forAvailable
online1359-6454/$36.00 2013 Acta Materialia Inc. Published by
Elsevier Ltd.
Allhttp://dx.doi.org/10.1016/j.actamat.2013.11.049b25Mo25Ta25W25
refractorypy alloy
alter Steurer b,, Ralph Spolenak a,
urich, Wolfgang-Pauli-Strasse 10, CH-8093 Zurich,
Switzerland
rich, Wolfgang-Pauli-Strasse 10, CH-8093 Zurich, Switzerland
7 November 2013; accepted 18 November 2013December 2013
www.elsevier.com/locate/actamatrights reserved.
-
terof great interest to apply refractory HEAs in the
fabricationof micro- or nanodevices. However, to the authors
knowl-edge, so far all the investigations on refractory HEAs
havebeen limited to bulk samples, and no study on the mechani-cal
properties of refractory HEAs at the submicron or nano-meter scale
has been reported.
Small-sized (extrinsic size rather than intrinsic size)metallic
specimens, such as thin lms, wires and pillars,exhibit size-related
strengths in a range from severalmicrons down to a few nanometers
[1315]. Over the lastfew years, great advances have been made to
understandthe mechanical behavior of materials in micron and
sub-micron regimes by applying the microcompression tech-nique to
ion-milled pillars (see reviews in Refs. [16,17]). Ithas been
widely found that the yield or ow strength (r)of the pillar can be
strongly increased when its dimension(D) is decreased, commonly
expressed by a relationshipof r / Dm [18,19], where m is the
size-eect exponent. fccmetals (e.g. Ni, Au, Al and Cu) exhibit a
pronouncedand constant size dependence of plasticity with m in
therange between 0.6 and 0.9 [2022]. bcc metals (e.g.Nb, Mo, V, Ta
and W) have a much more complex size-related behavior with various
m values ranging from0.2 to 0.9, reported by Schneider et al.
[23,24], Kimand Greer [25], Kim et al. [25,26] and Han et al.
[27].Schneider and his co-workers [23] noticed that various mvalues
in bcc metals could be correlated with dierent crit-ical
temperatures (Tc), above which ow stress becomesinsensitive to test
temperature, and equivalently residualPeierls potentials: the
higher Tc, the lower size dependence.The popular interpretation of
this correlation is that dier-ent non-planar dislocation cores in
bcc metals play impor-tant roles in the mobility of screw
dislocations, whichinuences the size dependence levels of bcc
pillars[17,24,28,29]. Both the simulation [30] and experiment[31]
suggest that bcc and fcc metal pillars dier in the con-trolling
mechanisms of the size eect. However, the exactmechanism which
determines the size-dependent plasticityin bcc metals remains under
debate.
HEAs are essentially solid solutions with a simple fccor bcc
structure. Now, two questions arise: what arethe strength and
ductility of single-crystalline HEAs atmicron and submicron scales,
compared with their bulkforms? And what is the size-dependent
behavior of bccrefractory HEAs, compared with that of pure bcc
met-als? In this study, the mechanical properties of
Nb25-Mo25Ta25W25 HEA pillars with diameters rangingfrom 2 lm to 200
nm were investigated using themicrocompression method. This work
aims to answerthe two questions above and attempts to shed lighton
potential applications of HEAs in micro/nanodevicedesign.
2. Materials and methods
86 Y. Zou et al. / Acta MaCompacted pellets of an approximately
equimolar mix-ture of pure Nb, Mo, Ta and W powders were
arc-meltedin argon atmosphere. A Ti getter was used to consumeany
trace of oxygen in the argon atmosphere. The but-ton-shaped cast
was ipped upside down and re-meltedfour times. The cast alloy was
then sealed inside a Taampoule and homogenized at 1800 C (65% of
the calcu-lated melting temperature [9]) for 7 days. The phase
purityof the homogenized HEA sample was determined by pow-der X-ray
diraction (XRD) (PANalytical XPert PRO dif-fraction system) using
Cu Ka1 monochromatic radiation ina 2h (diraction angle) range from
20 to 120. In order todetermine the atomic displacement parameters
(ADP), apiece of the HEA crystal smaller than 40 lm was extractedto
collect a single-crystal XRD dataset. A single-crystal
dif-fractometer with Mo Ka radiation source and a CCDdetector
(Oxford Diraction, Xcalibur) was used for thedata collection. For
microstructure and composition anal-ysis, a SU-70 Hitachi scanning
electron microscope (SEM)combined with energy-dispersive X-ray
spectroscopy(EDX) (X-MAX, Oxford Instruments) was employed. AFEI
Tecnai F30 high-resolution transmission electronmicroscope (HRTEM)
was used to investigate the struc-tures on sub-micron and nanometer
levels. For the TEMinvestigation, the HEA sample was embedded
inside a cop-per tube, cut into thin discs, ne polished with sand
papers,dimple-polished on both sides with 3 lm diamond suspen-sion
and nally thinned by Ar jet milling.
The hardness of the HEA samples (as-cast and as-annealed for 2,
4 and 7 days) and the pure elemental bccsamples (Nb, Mo, Ta and W
as-annealed for 7 days) wasmeasured in 15 dierent positions using a
Vickers microh-ardness indenter with a load of 200 g and dwell time
of10 s. The HEA sample which was homogenized for 7 dayswas used for
the microcompression tests. The orientationsof the grains were
determined by electron back-scatter dif-fraction (EBSD) using a FEI
Quanta 200 FEG SEM.Before EBSD characterization, the HEA bulk
sample wascross-sectioned using an alumina cut-o wheel
(Struers50A13), polished using 3 lm diamond paste and nallypolished
using 60 nm SiO2 particle suspension. After EBSDcharacterization,
two orientations were selected to producepillars using a focused
ion beam (FIB) system (HeliosNanolab 600i, FEI): [316] orientation
(tolerance angle
-
control mode by feedback mechanism. A strain rate of
300 m
a b
Fig. 1. (a) EBSD inverse pole gure map of the cross-section of
the HEA bulkare indicated by circles: the left one is
[316]-oriented (tolerance angle
-
ter100 m
a
c
88 Y. Zou et al. / Acta Mato be Ut + Us = 0.0037 + 0.0055 =
0.0092 A2, which is
close to the experimental value of 0.0091 A2.
3.2. Compression of pillar samples
As shown in the SEM images (Fig. 5a and b), single slipsare
observed in 2 lm and 1 lm [316]-oriented HEA pillars,which have
slip bands traversing along the gauge length ofthe samples. The
slip bands are oriented at 4070 o theloading axis. A second slip
system could be also activatedwhen the pillars experienced large
strains. Some localizedshear osets along slip planes are observed
at the top partof the pillars (Fig. 5b). For smaller pillars (500
nm and250 nm in diameter, Fig. 5c and d), multiple slips are
usu-ally observed. The multiple slips might be due to a
slightmisalignment between the pillar top and the at punch ordue to
the inuence of the tolerance angle. The multipleslips are expected
to contribute to strain hardening. Asshown in Fig. 5b, occasionally
some degree of bending is
100 m
Fig. 3. SEM images (BSE mode) of the cross-sections of the
NbMoTaW Hgrain boundary. The arrows indicate the line-scans for EDX
analysis. (b and d)in (a) and (c), respectively. The typical EDX
resolution limit is 1.0 at.%.
Table 1The average values and standard deviations (in MPa) of
the Vickers microhardnfor 2, 4 and 7 days) and pure Nb, Mo, Ta and
W (as-annealed at 1800 C for
Materials Nb 7D Mo 7D Ta 7D W 7D
Average 1086 1898 1488 3714Standard deviation 16 51 52 96b
d
ialia 65 (2014) 8597observed. The data from bent pillars are not
consideredin the analysis.
Compressed [001]-oriented HEA pillars are shown inFig. 6. Wavy
morphologies can be found in both largeand small pillars. This
wavy-slip feature may be attributedto the cross-slip of screw
dislocations along h111i direc-tions, which is commonly observed in
deformed bcc metals[36,37]. This post-deformed morphology of the
HEA pil-lars is similar to that of the W pillars as reported in
Refs.[23,26].
Fig. 7a and b shows engineering stressstrain relation-ships for
the representative [316]- and [100]-orientedHEA pillars,
respectively. Although the crystal orientationsare dierent, the two
groups of pillars exhibit similar fea-tures of both stress
magnitude and characters of curves:the small pillars have higher ow
strengths than the big pil-lars and displacement bursts occurred in
both big and smallpillars, showing a similar phenomenon to that
observed infcc and bcc metal pillars [27,36,37]. The
displacement
EA annealed at 1800 C for 7 days: (a) inside a grain and (c)
including aThe corresponding atomic proportions of the four
elements along the lines
ess of 15 random indents on the HEAs (as-cast and as-annealed at
1800 C7 days).
HEA cast HEA 2 days HEA 4 days HEA 7 days
4853 4766 4803 4515387 362 234 58
-
atera
Y. Zou et al. / Acta Mbursts may be due to a relatively low
feedback rate in dis-placement mode compared with the burst events,
asexplained in Refs. [38,39]. In both orientations, the
smallerpillars exhibit stronger displacement bursts in both
magni-
edc
Fig. 4. High-resolution TEM images of the NbMoTaW HEA
homogenizedaxis and the corresponding electron diraction pattern;
(b) an inverse fast Fouindicated boxes in (b); (d) and (f) show
lattice fringes which are traced for (c)
500 nm
2 m
1 m
a
c
b
d
Fig. 5. SEM images (SE mode) of post-compressed [316]-oriented
HEA pilla250 nm. An enlarged image which presents sharp slip bands
is shown in the inb
ialia 65 (2014) 8597 89tude and frequency; meanwhile the smaller
pillars show ahigher strain-hardening rate than the big pillars,
whichmight be due to more activated and interacting slip systemsin
the small dimension samples. To reduce the inuence of
f
at 1800 C for 7 days: (a) a bright-eld TEM image oriented in
[100] zonerier transform image of the area (a); (c) and (e) are
enlarged images of theand (f), respectively, to indicate the
regions with lattice distortions.
2 m
500 nm
rs with approximate diameters of: (a) 2 lm, (b) 1 lm, (c) 500 nm
and (d)set of (a).
-
ter2 m
500 nm
a
90 Y. Zou et al. / Acta Mathe displacement bursts on analysis
and make a direct com-parison with pure bcc metal pillars in the
references [23,26],the highest ow stress values measured below 5%
strainand 8% strain, which are dened as r0.05 and r0.08,
respec-tively, are used to compare the strengths for dierent
pillardimensions.
The changes of r0.05 and r0.08 due to dierent pillardiameters
for both [316] and [001] orientations are plottedin Fig. 8: for
r0.05, [316] and [001]-orientated HEA pillarshave size-eect
exponents (m) of 0.30 0.02 and0.33 0.02, respectively; for r0.08,
[316] and [001]-orien-tated HEA pillars have m values of 0.32 0.02
and
500 nm
c
Fig. 6. SEM images (SE mode) of post-compressed [001]-oriented
HEA pilla250 nm. An enlarge image which presents a wavy morphology
is shown in the
Fig. 7. Representative engineering stress strain curves for (a)
[316]-orientedranging from 2 lm to 200 nm.1 m
b
ialia 65 (2014) 85970.36 0.02, respectively. The absolute
strength levelsfor the pillars in two orientations are close to
each other.[316]-oriented pillars have a slightly lower size
dependencethan [001]-oriented pillars.
4. Discussion
4.1. Solid solution eect
Some physical properties of Nb, Mo, Ta, W and theHEA are listed
in Table 2. The atomic sizes of Nb andTa are 5% larger than Mo and
W. This atomic size mist
400 nm
d
rs with approximate diameters of: (a) 2 lm, (b) 1 lm, (c) 500 nm
and (d)inset of (a).
and (b) [001]-oriented single crystalline HEA pillars with the
diameters
-
to extremely inhomogeneous stress elds throughout theHEA
specimen.
In bcc metals, edge dislocations move much more easilythan screw
dislocations. Thus, the latter ones mainly con-trol plastic ows, by
a processes of kink nucleation andmotion [44]. The eect of lattice
distortion on plasticstrength may be twofold [45,46]: on the one
hand, the lat-tice distortion, by its stress eld, may facilitate
the nucle-ation of new kink pairs, leading to
solid-solutionsoftening; On the other hand, the propagation of
screw dis-locations is retarded by the stress elds of localized
soluteobstacles along the slip planes, resulting in
solid-solutionhardening. These two mechanisms compete in bcc
solid
Y. Zou et al. / Acta Materialia 65 (2014) 8597 91of the
constituent elements in the HEA can cause a highlydistorted lattice
(Fig. 4) with localized strains throughoutthe whole sample. The
lattice distortion in the HEA speci-men appears as splits in the
atomic positions and localizedshearing of several adjacent lattice
fringes. The calculatedADP was 2.5 times higher than the expected
thermalADP, also suggesting a local lattice distortion due to
thedierence in atomic sizes. The ADP values have been usedas a
measure of the local lattice distortion in a bcc ZrNbHfalloy [43],
where it was observed that the average ADP ofthe alloy was many
times higher than the expected thermalADP. In addition, the thermal
and static components ofthe modeled ADPs, if added up, match the
experimentalrened ADP of the HEA closely. This might validate
thesimple model of calculating static ADPs, and the average
Fig. 8. The relationship between engineering stresses at 5%
strain and 8%strain (r0.05 and r0.08) and pillar diameters for
[316]- and [001]-orientedHEA pillars.static displacement of the
atoms could be 0.074 A. More-over, the modulus mist between the
constituent elementshas a large range: 4% between W and Mo; 70%
betweenW and Nb. Compared with the pure bcc elements, thebinding
forces around dierent solute atoms in the HEAcould vary depending
on surrounding elements. This non-uniform bonding feature at atomic
length level may lead
Table 2Physical properties of pure Nb, Mo, Ta, W and the
HEA.
Metal a (A) q (g cm3) s0 (MPa) G (GPa) s0 (1
Nb 3.301 8.57 415 47.2 [41] 8.7Mo 3.147 10.28 730 158 [24] 4.6Ta
3.303 16.65 340 62.8 [41] 5.4W 3.165 19.25 280350 164 [42] 1.7HEA
calc. 3.229 13.69 114 HEA exp. 3.222
The crystal lattice parameter, a, density, q, and melting
temperature, Tm, of puris collected from Ref. [42], the
corresponding shear modulus, G, is chosen fotemperature, Tc, and
size-eect exponent, m, are chosen from Refs. [23,26]. To gthe
high-temperature linear part and the low-temperature linear part in
the mecalculated due to the rule of mixtures. HEA exp. is the value
measured in thissolutions during plastic deformation. However, the
phe-nomenon of solid-solution softening is mostly observed
atintermediate low temperatures (100250 K) and low con-centrations
(less than 5 at.%). In our study, due to theroom-temperature
measurement and high-concentrationalloying, the solid-solution
hardening eect should be dom-inant in the HEA.
4.2. HEA pillar vs. HEA bulk: ductility and strength
4.2.1. Ductility
Since the concept of HEA design was introduced [1],HEAs have
been considered as potential high-performancestructural materials.
However, a big limitation to usingrefractory HEAs is their low
ductility and toughness atroom temperature. Senkov et al. [10]
found that Nb25Mo25-Ta25W25 and Nb20Mo20Ta20V20W20 HEAs fractured
alonggrain boundaries at 2% compressive strain at room
tem-perature. In Fig. 9a, a fracture surface along the
grainboundaries of the bulk HEA can be seen. Two HEA pillarswith
and without a grain boundary are compared, asshown in Fig. 9b and
c. It is found that a crack that prop-agated along the grain
boundary caused the failure of a3 lm bicrystal pillar (Fig. 9b).
The pillar top area and thecorresponding forcedisplacement curve
are shown in theinsets. Fig. 9c exhibits a post-deformed
[001]-oriented sin-gle-crystalline pillar, which can even bear
large-strain bend-ing (75) without any fracture or crack on the
surface,corresponding to a tensile strain larger than 20% on
one
03) Tm (K) Tc (K) m for r0.05 m for r0.08
2750 350 [23], 290 [26] 0.48 [23] 0.93 [26]2896 480 [23], 465
[26] 0.38 [23] 0.44 [26]3290 450 [23], 440 [26] 0.41[23] 0.43
[26]
2.1 3695 800 [23], 760 [26] 0.21 [23] 0.44 [26]3158 520 [23],
489 [26] 0.37 0.56 9001200 [10] 0.33 0.36
e Nb, Mo, Ta and W are adapted from Table 2 of Ref. [9]; Peierls
stress, s0,r the active slip systems of {112}h111i [24,41,42]; the
values of criticalive an estimation of Tc in the bulk HEA [10], an
intersection point between
asured stresstemperature curve is chosen as the value of Tc. HEA
calc. isstudy.
-
ter400 m
a
c
92 Y. Zou et al. / Acta Maside of the pillar. This comparison
suggests that the elimi-nation of grain boundaries and decrease of
sample sizecould signicantly increase the ductility of HEAs.
4.2.2. Strength
Submicron-sized HEA pillars exhibit extraordinarilyhigh
strengths compared to the bulk HEA (44.5 vs.1 GPa [10]). The origin
of the higher strength for theHEA pillars could be the same as the
size-eect phenomenafor the other metal pillars. It is generally
believed that whenthe sample dimension is reduced into micron and
submicronregimes, the strength is increased due to the decreased
aver-age size of dislocation sources. Weinberger and Cai [30]
sug-gest, for bcc pillars, that a single dislocation can
alsomultiply itself repeatedly and forms dislocation segmentsand
hard junctions, contributing to the increased strength.
4.3. HEA bcc pillar vs. pure elemental bcc pillars: size
eects
Size-dependent strengths have been commonly andempirically
characterized by a power-law relation, eitherin a non-normalized
form, r = A(D)m, or in a normalizedform, s/G = A(D/b)m, where s is
the resolved shear stresson primary slip planes, A is a constant, D
is the pillar
Fig. 9. Typical SEM images (SE mode) of: (a) a fracture surface
in the HEApost-deformed HEA pillar that contains a grain boundary
(indicated by arrocurve and the enlarged area of the fracture
region are shown in the insets; (c) awithout any fracture or crack
after deformation.2m
10 mb
ialia 65 (2014) 8597diameter and b is the Burgers vector
[16,17,19,47,48]. Forthe calculation of s in this study, {112} slip
planes are cho-sen [24,41], and the Schmid factors for [316] and
[001] ori-entations are 0.41 and 0.47, respectively. Here, we
applythe power-law ts to the HEA pillars (this study) and
to[001]-oriented Nb, Ta, Mo and W (literature data fromRefs.
[23,26]). In both non-normalized and normalized t-ting lines (Fig.
10ad), the HEA pillars exhibit higherstrength levels than the pure
bcc metal pillars. For exam-ple, the 200 nm HEA pillars have higher
ow strengthsthan pure bcc metal pillars by a factor of 24. In
additionto higher strength levels, the HEA pillars also exhibit
areduced size eect (a smaller absolute value of m) com-pared to the
pure bcc pillars here. The only exception tothis trend is that the
size dependence of the HEA is slightlylarger than that of W
reported by Schneider et al. [23], butit is smaller than that of W
reported by Kim et al. [26](compare Table 2).
Fig. 10e gives a schematic illustration of the normal-ized
strengthdiameter relationship of fcc and bcc pillarssummarized from
Refs. [17,23,26] and the HEA pillarsin this study. In the size
range of a few microns, bccpillars have higher normalized strength
levels than fccpillars, but in the submicron regime the strength
levels
5 m
bulk sample, showing the fracture occurred along grain
boundaries; (b) aws), where the fracture occurred. The
corresponding forcedisplacement2 lm [001]-oriented
single-crystalline HEA pillar, which was severely bent
-
atera
Y. Zou et al. / Acta Mof bcc pillars converge to those of fcc
pillars. The HEAbcc pillars in this study show extraordinarily high
strengthcompared to the pure bcc elements. In order to under-stand
the dierent size eects for pure bcc and HEA
c
e
Fig. 10. Size-dependent strengths for the [316]- and
[001]-oriented HEA pillar[23] and Kim et al. [26]. (a and b) r0.05
and r0.08 vs. pillar diameters (D); (c andG) vs. pillar diameters
normalized by Burgers vector (D/b). (e) Schematic illustrpure fcc
and bcc pillars (data summarized from Refs. [17,23,26]) and the
HEcolored solid ellipse. The HEA bcc pillars exhibit both higher
absolute and nodependence of strengths.b
ialia 65 (2014) 8597 93bcc pillars, we propose a simple analysis
on the resolvedow stress of a pillar sample. The applied resolved
shearstress, s, is traditionally expected to be a sum of
latticefriction, s*, elastic interactions between dislocations
d
s in this study and pure Nb, Mo, Ta and W as reported by
Schneider et al.d) resolved ow strengths normalized by
corresponding shear modulus (s/ation of size-dependent strengths
for dierent metallic systems: FIB-milledA bcc pillars in this
study, and the range of each group is indicated by armalized
strength levels than any other bcc metals but a relatively low
size
-
4.3.1. Pure elemental bcc pillars
In order to illustrate how the three mechanisms underly-ing the
three terms in Eq. (7) inuence the size dependenceof the strength
in bcc metals, the parameters for Mo, whichhave been most
investigated for pillar compression, are cho-sen, as: a 0.5, b
2.728 A, (q0 + qD) 5.0 1012 m2,K 0.5 and k D [48,50,51]. It should
be noted that Kis dependent on Poissons ratio, dislocation type
andanisotropy of dislocation line tension, and k is also inu-enced
by dislocation densities and their distribution [51].Here, we use
the above values to give an estimation of pil-lar strengths. Fig.
11 shows a 3-D graph of normalizedstrength (s/G) vs. normalized
length (D/b) and normalizedtemperature (Tt/Tc) for Mo pillars. The
top surface withcontour lines represents a sum of all the three
mechanismsin Eq. (7). Each mechanism is also plotted in a single
colorbelow separately: s (blue), sG (red) and ssource (green).
Thegraph clearly shows how the local slope, m, increases
inmagnitude with an increase of normalized temperature.According to
this graph, we could make the following pre-dictions: at 0 K, if
the sample size is smaller than 1000b,the strength is
source-controlled, having strong a sizedependence; if the size is
larger than 1000b, the strengthis controlled by the Peierls
potential, showing nearly no sizeeect. However, when Tt equals Tc
(480 K for Mo), if thesize is smaller than 20,000b, the strength is
controlled by
terialia 65 (2014) 8597(i.e., Taylor hardening), sG, and
source-controlledstrength, ssource, expressed as [48,49]:
s s sG ssource 2In Eq. (2), s is the stress required to overcome
the Peierlspotential and arises as a consequence of the
forcedistancerelation between individual atoms in a periodic
latticestructure. s is temperature-dependent and can be ex-pressed
as [50]:
s 1 T tT c
s0 with T t < T c; 3
s 0 with T t P T c 4where Tt is test temperature, usually room
temperature ands0 is the Peierls stress at 0 K. Above Tc, there is
sucientthermal energy to overcome the Peierls barriers by
thermalactivation. The second term in Eq. (2), sG, is an
athermalcomponent, which arises from the resistance to
dislocationmotion due to long-range elastic interactions, such as
theinteractions between dislocations. Here, sG may be
simplyapproximated by using the Taylor-hardening relation as:
sG aGbq0 qD
p 5where a is a constant falling in the range 0.1 to 1.0, q0 is
theinitial dislocation density before pillar compression and qDis
the increased dislocation density due to the compression.For a
small amount of strain, the dislocation density is inthe order of
10121013 m2 for most metals. Unlike in bulkmetals, dislocation
storage in small-scale pillar specimenscould be in a lower level,
because new generated disloca-tions may move out of a pillar more
easily due to a smallconned dimension. Another contribution in Eq.
(2), ssource,is the minimal stress required to operate a
dislocationsource. In bulk samples dislocation segments in the
length104b can act as a FrankRead source [50]. However, in pil-lar
samples the average source length, k, is limited, and it
isproportional to the pillar dimension. Single-ended sourcescould
be dominant in the size range of 0.520 lm(102105b) [51]. The
single-end source has also been seenin aluminum pillars using in
situ TEM [52]. The activationstress of a dislocation source in a
pillar sample has been esti-mated by three-dimensional (3-D)
discrete dislocationdynamics simulations [51] and could be
expressed as:
ssource KG lnk=b
k=b6
where K is the source-strengthening constant in the orderof 0.1.
Although dierent controlling mechanisms couldoperate for bigger
pillars (>20 lm in diameter) and evensmaller pillars (
-
calculated strengthsize curve according to Eq. (7) is com-pared
to the experimental data of [001]-Mo pillars [23,26]and [111]-Mo
pillars [53], as shown in Fig. 12. The dashedlines present the
individual contributions from the latticefriction (s*, blue), the
Taylor hardening (sG, red) and thesource strengthening (ssource,
green) to the overall strength(s, black), respectively. In the case
of Mo, the experimentaldata points are in a good agreement with the
calculatedstrength curve at a reasonable scatter level, especially
forthe sample size larger than 100 nm. Surface image stressesmay
have a large eect at the length smaller than 100 nm.In the region
in which two or three mechanisms are similarin magnitude, the
normalized strength will change by up toa factor of three, compared
to a scenario where only thestrongest strengthening mechanism is
relevant. This is theonly scenario where an understanding of which
strengthen-ing mechanisms are additive and which are not
becomesimportant. If only one mechanism dominates, the distinc-tion
is secondary.
4.3.2. HEA bcc pillar
Here, we attempt to predict a strengthsize curve for theHEA
pillars using Eq. (7). Although there is no experimen-tal data of
the Peierls stress and shear modulus for theHEA, the values of s0=G
are available for Nb, Mo, Taand W [42] (Table 2), which are between
103 and 102.
among the bcc metals, 8.7 103, is chosen to give an esti-mation
for the HEA pillars as well as b of 2.799 A, and Tcof 1050 K (Table
2). As can be seen in Fig. 12, the experi-mental data points are
higher than the predicted curve by afactor of 2. The reason might
be that unlike pure bcc ele-ments the solute atoms in the HEA have
dierent atomicdimensions which can induce signicant localized
latticedistortion (Fig. 4). While the rule of mixtures may
beappropriate for determining the shear modulus, the severelattice
distortions in the HEA are expected to result in asignicantly
higher Peierls potential than for each of theconstituents.
Moreover, the non-uniform stress eldsthroughout the HEA sample
might cause an increaseddynamic drag eect and the following
phenomena mightoccur [46,55,56]: the emission of elastic waves
during thedeceleration and acceleration of dislocation sliding
alonga distorted lattice, the excitation of local vibrations of
sol-ute atoms and the radiation of phonons by dislocation
Y. Zou et al. / Acta Materialia 65 (2014) 8597 95Wang [54] also
calculates s0=G theoretically and estimatesthat the values of s0=G
are 103 for bcc edge dislocationsand 102 for bcc screws. Here, the
maximum s0=G value
source
*
G
Fig. 12. The calculated normalized strength vs. normalized
length for Mopillars at room temperature (300 K) according to Eq.
(7). The solid blackline is a sum of all the mechanisms for Mo and
the contribution of eachmechanism is plotted separately in a dashed
color line: s* (blue), sG (red)and ssource (green). The black
points are the experimental data of [001] Mopillars [23,26] and
[111] Mo pillars [53]. The predicted curve for the HEAusing Eq. (7)
and the experimental data of [001] HEA in this study arealso
plotted. In order to calculate the strength levels of the HEA,
thefollowing parameters are chosen: b 2.799 A, Tc 1050 K (Table 2)
andthe maximum s0=G value among the bcc metals, 8.7 103. (For
interpretation of the references to color in this gure legend,
the readeris referred to the web version of this article.)vibration
like a string. Dierent from pure and lightlyalloyed metals with a
relative ideal lattice, the dynamicdrag eect could be prominent in
the HEA, and thereforethe lattice friction could be signicantly
increased, leadingto strong strengthening. However, to make a
convincingconclusion, a precise experimental evaluation of Tc
ands0=G as well as detailed microstructural analyses andatomic
simulations of the non-planar dislocation corestructure in HEAs
will be a subject for future investigation.
As we have shown in Fig. 11, the apparent size eectexponent m
depends not only on the superposition ofstrengthening mechanisms
but also on the experimentallyaccessible size range. Nevertheless
it is instructive to corre-late m to the normalized temperature, if
the analyzed sizeranges and dislocation densities are comparable.
Here, weadapted the method used by Schneider et al. [23] to
corre-late m and Tt/Tc for pure bcc and HEA bcc pillars. Accord-ing
to Eq. (7), the value of m can be expressed as:
the HEA
W
MoTa
Nb
Fig. 13. The absolute values of m vs. Tt/Tc: the correlation
between the
size eects and the critical temperatures of pure Nb, Mo, Ta and
W pillars[23,26] and the HEA pillars in this study.
-
term ln bD
ln B s
0
GAT tT c
8
where B is a material-independent constant. Because s0=Gis
nearly constant for most bcc metals and in the order of103 to 102,
the m value could be mostly inuenced byTt/Tc. Using the values in
Table 2, Fig. 13 indicates thatthe material that has higher Tt/Tc
is expected to have a low-er size eect. The HEA from this study is
in reasonableagreement with this pattern.
5. Summary
In this work, an Nb25Mo25Ta25W25 refractory HEAwas synthesized
by arc melting and well homogenized at1800 C for 7 days. The HEA
shows a simple bcc struc-ture with the average lattice parameter of
Nb, Mo, Taand W, while localized lattice distortions at atomic
lengthscales were observed using HRTEM. The mechanicalproperties of
[316]- and [001]-oriented HEA pillars havebeen measured using the
microcompression technique.Orientation change has a minor inuence
on the sizedependence of strengths. In both orientations, the
HEApillars exhibit higher strength levels than pure Nb, Mo,Ta and W
pillars by a factor of 25, as well as a rela-tively low size eect
(loglog slope of strength vs. pillardiameter of 0.3). Both the
increased strength levelsand reduced size dependence in the HEA
could be attrib-uted to a higher lattice friction in the HEA than
that inpure bcc metals. In this paper, we also illustrate howthe
normalized strength correlates to the normalizedlength scale and
the normalized temperature for bcc struc-tures, and elucidates the
contributions to the size-depen-dent strength from lattice
resistance, dislocationinteractions and source strength,
respectively. Addition-ally, towards the application, both the
strength and duc-tility of single-crystalline HEA pillar samples
aresignicantly improved compared to polycrystalline bulkforms.
These ndings indicate that refractory HEAs showpromise as potential
structural materials in micro/nanode-vice design.
Acknowledgements
The authors would like to thank P. Gasser, Dr. K.Kunze and Dr.
Fabian Gramm (EMEZ, ETH Zurich)for their help in the sample
preparation using FIB andHRTEM; Huan Ma and Matthias Schamel (LNM,
ETHZurich) for their help in SEM and EBSD characterization;and
Claudia Muller (LNM, ETH Zurich) for proof-readingthe manuscript.
The authors also gratefully acknowledgenancial support through SNF
Grants (200021_143633and 200020_144430).
References
96 Y. Zou et al. / Acta Ma[1] Yeh JW, Chen SK, Lin SJ, Gan JY,
Chin TS, Shun TT, et al. AdvEng Mater 2004;6:299.[2] Huang PK, Yeh
JW, Shun TT, Chen SK. Adv Eng Mater 2004;6:74.[3] Yeh JW, Chen YL,
Lin SJ, Chen SK. Mater Sci Forum 2007;560:1.[4] Senkov ON, Senkova
SV, Woodward C, Miracle DB. Acta Mater
2013;61:1545.[5] Zhu C, Lu ZP, Nieh TG. Acta Mater
2013;61:2993.[6] Tong CJ, Chen MR, Chen SK. Metall Mater Trans A
2005;36A:1263.[7] Tsai CW, Tsai MH, Yeh JW, Yang CC. J Alloy Compd
2010;490:160.[8] Tsai MH, Yeh JW, Gan JY. Thin Solid Films
2008;516:5527.[9] Senkov ON, Wilks GB, Miracle DB, Chuang CP, Liaw
PK.
Intermetallics 2010;18:1758.[10] Senkov ON, Wilks GB, Scott JM,
Miracle DB. Intermetallics
2011;19:698.[11] Kaufmann D, Monig R, Volkert CA, Kraft O. Int J
Plast
2011;27:470.[12] Voyiadjis GZ, Almasri AH, Park T. Mech Res
Commun 2010;37:307.[13] Arzt E. Acta Mater 1998;46:5611.[14] Kraft
O, Gruber PA, Monig R, Weygand D. Annu Rev Mater Res
2010;40:293.[15] Dehm G. Prog Mater Sci 2009;54:664.[16] Uchic
MD, Shade PA, Dimiduk DM. Annu Rev Mater Res
2009;39:361.[17] Greer JR, De Hosson JTM. Prog Mater Sci
2011;56:654.[18] Dimiduk DM, Uchic MD, Parthasarathy TA. Acta
Mater
2005;53:4065.[19] Dou R, Derby B. Scripta Mater 2009;61:524.[20]
Uchic MD, Dimiduk DM, Florando JN, Nix WD. Science
2004;305:986.[21] Greer JR, Oliver WC, Nix WD. Acta Mater
2005;53:1821.[22] Ng KS, Ngan AHW. Acta Mater 2008;56:1712.[23]
Schneider AS, Kaufmann D, Clark BG, Frick CP, Gruber PA, Monig
R, et al. Phys Rev Lett 2009:103.[24] Schneider AS, Frick CP,
Clark BG, Gruber PA, Arzt E. Mater Sci
Eng A Struct 2011;528:1540.[25] Kim JY, Greer JR. Acta Mater
2009;57:5245.[26] Kim J-Y, Jang D, Greer JR. Acta Mater
2010;58:2355.[27] Han SM, Bozorg-Grayeli T, Groves JR, Nix WD.
Scripta Mater
2010;63:1153.[28] Malygin GA. Phys Solid State 2012;54:1220.[29]
Han SM, Feng G, Jung JY, Jung HJ, Groves JR, Nix WD, et al.
Appl
Phys Lett 2013;102:041910.[30] Weinberger CR, Cai W. Proc Natl
Acad Sci 2008;105:14304.[31] Greer JR, Weinberger CR, Cai W. Mater
Sci Eng A Struct
2008;493:21.[32] Denton AR, Ashcroft NW. Phys Rev A
1991;43:3161.[33] Zhou YJ, Zhang Y, Wang FJ, Chen GL. Appl Phys
Lett 2008:92.[34] Sheldrick GM. Acta Crystallogr A 2008;64:112.[35]
Peng LM, Ren G, Dudarev SL, Whelan MJ. Acta Crystallogr A
1996;52:456.[36] Spolenak R, Dietiker M, Buzzi S, Pigozzi G,
Loer JF. Acta Mater
2011;59:2180.[37] Loer JF, Buzzi S, Dietiker M, Kunze K,
Spolenak R. Philos Mag
2009;89:869.[38] Dimiduk DM, Woodward C, LeSar R, Uchic MD.
Science
2006;312:1188.[39] Dimiduk DM, Nadgorny EM, Woodward C, Uchic
MD, Shade PA.
Philos Mag 2010;90:3621.[40] Yeh JW, Chang SY, Hong YD, Chen SK,
Lin SJ. Mater Chem Phys
2007;103:41.[41] Duesbery MS, Vitek V. Acta Mater
1998;46:1481.[42] Suzuki T, Kamimura Y, Kirchner HOK. Philos Mag A
1999;79:1629.[43] Guo W, Dmowski W, Noh JY, Rack P, Liaw PK, Egami
T. Metall
Mater Trans A 2013;44A:1994.[44] Vitek V. Prog Mater Sci
1992;36:1.[45] Butt MZ, Feltham P. J Mater Sci 1993;28:2557.[46]
Neuhauser H, Schwink C. Materials science and technology. Lon-
don: Wiley-VCH; 2006.
ialia 65 (2014) 8597[47] Korte S, Clegg WJ. Philos Mag
2011;91:1150.[48] Lee SW, Nix WD. Philos Mag 2012;92:1238.
-
[49] Parthasarathy TA, Rao SI, Dimiduk DM, Uchic MD, Trinkle
DR.Scripta Mater 2007;56:313.
[50] Hull D, Beacon DJ. Introduction to dislocations. Oxford:
Pergamon;2001. p. 193232.
[51] Rao SI, Dimiduk DM, Tang M, Parthasarathy TA, Uchic
MD,Woodward C. Philos Mag 2007;87:4777.
[52] Oh SH, Legros M, Kiener D, Dehm G. Nat Mater 2009;8:95.
[53] Huang L, Li Q-J, Shan Z-W, Li J, Sun J, Ma E. Nat
Commun2011;2:547.
[54] Wang JN. Mater Sci Eng A Struct 1996;206:259.[55] Alshits
V, Indenbom V. In: Nabarro FRN, editor. Dislocations in
solids, vol. 7. Amsterdam: Elsevier Science; 1986.[56] Natsik
VD, Chishko KA. Cryst Res Tech 1984;19:763.
Y. Zou et al. / Acta Materialia 65 (2014) 8597 97
Size-dependent plasticity in an Nb25Mo25Ta25W25 refractory
high-entropy alloy1 Introduction2 Materials and methods3 Results3.1
Microstructure and phase analysis of bulk specimens3.2 Compression
of pillar samples
4 Discussion4.1 Solid solution effect4.2 HEA pillar vs. HEA
bulk: ductility and strength4.2.1 Ductility4.2.2 Strength
4.3 HEA bcc pillar vs. pure elemental bcc pillars: size
effects4.3.1 Pure elemental bcc pillars4.3.2 HEA bcc pillar
5 SummaryAcknowledgementsReferences