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: steurer@mat.ethz.ch (W. Steurer), ralph.spolenak@-mat.ethz.ch (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