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Nanocrystalline High-Entropy Alloys: A New Paradigm in High-

Temperature Strength and Stability

Yu Zou, Jeffrey M. Wheeler, Huan Ma, Philipp Okle and Ralph Spolenak

Version Post-print/Accepted Manuscript

Citation (published version)

Zou Y, Wheeler JM, Ma H, Okle P, Spolenak R. Nanocrystalline high-entropy alloys: a new paradigm in high-temperature strength and stability. Nano letters. 2017 Feb 9;17(3):1569-74.

Publisher’s Statement The article has been published in final form at [10.1021/acs.nanolett.6b04716]

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Nanocrystalline high entropy alloys: A new paradigm in high temperature strength and stability

Yu Zou1, *, Jeffrey M. Wheeler1, Huan Ma1, Philipp Okle1 and Ralph Spolenak1,*

1Laboratory for Nanometallurgy, Department of Materials, ETH Zurich, Vladimir-Prelog-Weg 5, CH-8093 Zurich, Switzerland

Abstract

Metals with nanometer scale grains, or nanocrystalline metals, exhibit high strengths at ambient conditions,

yet their strengths substantially decrease with increasing temperature, rendering them unsuitable for usage

at high temperatures. Here, we show that a nanocrystalline high entropy alloy (HEA) retains an

extraordinarily high yield strength over 5 GPa up to 600 °C – one order of magnitude higher than that of its

coarse-grained form, and five times higher than that of its single-crystalline equivalent. As a result, such

nanostructured HEAs reveal strengthening figures of merit – normalized strength by the shear modulus

above 1/50 and strength-to-density ratios above 0.4 MJ/kg, which are substantially higher than any

previously reported values for nanocrystalline metals in the same homologous temperature range, as well

as low strain-rate sensitivity of ~0.005. Nanocrystalline HEAs with these properties represent a new class

of nanomaterials for high-stress and high-temperature applications in aerospace, civilian infrastructure and

energy sectors.

Keywords: high entropy alloys; nanocrystalline; high temperature; strength; grain boundary; stability

*Correspondence should be addressed to yuzou@mit.edu (Y. Z., current address: Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA) or ralph.spolenak@mat.ethz.ch (R. S.).

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For the past three decades, nanocrystalline (nc) metals have been attractive as potentially useful structural

materials, primarily owing to their high strengths1-4. Their prominent strengths are attributed to a large

volume fraction of grain boundaries as barriers to obstruct dislocation motion. According to the Hall-Petch

law5, such nc-metals, down to the grain sizes of ~40 nm, can attain strength over an order of magnitude

higher than that of coarse-grained ones. Grain boundaries, however, become a vulnerability for metals at

high temperatures; for example, single-crystalline (sx) nickel-based superalloys are more preferred than

polycrystalline ones to be used for gas turbine blades, because of significant grain-boundary diffusion and

sliding in the latter at working temperatures6. In nc-metals, grain-boundary sliding7, diffusion-mediated

plasticity8, and grain-boundary migration9 are even more pronounced, such that grains coarsen even at

ambient or modest temperatures, and, consequently, material strength diminish10, 11. In general, nc-metals

have never been considered to be used at elevated temperatures because of their poor high-temperature

strengths and stability. Hence, developing nc-metallic systems that retain their high strengths over a wide

temperature range has been highly desirable for both scientific interests and demanding applications.

Over the last few years, attention has been focused on solving the problem by two routes: grain boundary

design and alloying design – the first introduces low energy grain boundaries12, for example, nanoscale

twin boundaries13; the second stabilizes grain boundaries by elemental segregation14, 15. Using these

methods, microstructural stability of these nc-metals has been improved for high-temperature, long-

duration conditions. The extant literature, however, reveals a large gap in demonstrating the mechanical

stability of nc-metals under mechanical loading at a relatively high temperature, wherein grain-boundary

motion and diffusion may occur and material strength is decreased. Very recently, Darling et al.16 reported

that an immiscible Cu-Ta nc-metal showed high strength and creep resistance from room temperature to

600 °C, due to nanoscale Ta segregation. These studies have motivated us to achieve even stronger and

more stable nc-metals by virtue of solid-solution strengthening and grain-boundary segregation.

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As an evolving field of metallurgy, high entropy alloys (HEAs) generally consist of five or more equiatomic

elements and form a single solid-solution phase17, 18. A variety of interesting and useful properties emerge

in face-centered cubic (fcc) coarse-grained HEAs including high fracture resistance19, high strengths20, and

enhanced thermal stability21. Two typical body-centered cubic (bcc) refractory HEAs exhibit a yield

strength of ~500-700 MPa at 1200 °C, even surpassing conventional nickel-based superalloys22. Mechanical

properties of both fcc and bcc HEAs have been studied at macroscopic and microscopic levels23, 24. In such

a chemically enriched system, multiple principle elements tend to strengthen materials markedly by the

solid-solution hardening mechanism, meanwhile randomly distributed elements in grain interiors may

lower relative grain-boundary energy, minimizing thermodynamic driving force for grain-boundary

diffusion and migration. In addition, segregation may occur at grain boundaries and work as barriers to

prevent grain-boundary motion. Our previous work demonstrates that, at room temperature, nc-HEAs

(Nb25Ta25Mo25W25) exhibit higher strength than sx-HEA equivalents by a factor of two, due to grain-

boundary strengthening24, 25. Now, the question arises: Will the nc-HEAs retain their superior strength even

at elevated temperatures, when their large volume fraction of grain boundaries becomes a manifest

weakness?

Sx-HEA pillars were produced by focused ion beam milling from a ⟨011⟩-orientated coarse grain within a

bulk HEA specimen. Nc-HEA pillars, which were milled from HEA films, consist of strongly <011>

textured columnar grains with an average grain size (diameter) of ~70-100 nm. We conducted compression

tests on the sx- and nc-HEA micro-pillars (Supplementary Information Fig. S1) using a diamond flat punch

over a temperature range from room temperature to 600 °C (Fig. 1). The sx-HEA pillars that are deformed

at 25-400 °C show single slips with wavy morphologies (Figs. 1a-1c), while those deformed at 600 °C

reveal sharper slip traces (Fig. 1d and Supplementary Information Fig. S2). After deformation, the nc-HEA

pillars exhibit parallel wavy slip lines intersecting with grain boundaries after they were deformed from

25°C to 600 °C. The nc-HEA pillars that are deformed at 600 °C show more homogeneous deformation

with fewer cracks, suggesting enhanced ductility at a higher test temperature (Fig. 1h). We also find that

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the grain sizes remain consistent (~70-100 nm) after deformation (Supplementary Information Fig. S2), as

compared with those without deformation27. With increasing temperature, the yield strength of the sx-HEA

pillars decrease from ~2 GPa at room temperature to ~1 GPa at 600 °C, with a relatively higher magnitude

of stress drops (Fig. 1i); while the strength of nc-HEA pillars only decrease from ~7 GPa at room

temperature to ~5 GPa at 600 °C, with a relatively consistent magnitude of stress drops (Fig. 1j).

Fig. 2a summarizes temperature dependence of yield strengths of the sx- and nc-HEA pillars. At 600 °C,

the nc-HEA pillars still exhibit a high yield strength of ~5 GPa, which is nearly fivefold greater than that

of the sx-HEAs and one order of magnitude higher than that of the bulk coarse-grained ones. The percentage

of strength reduction as a function of temperature indicates that the strength softening behavior of a material

is due to temperature increase. Fig. 2b shows that the bulk-HEAs22, sx-HEAs, and nc-Cu-Ta alloys16 exhibit

a reduction of strength by ~50% at 600 °C, while the strength of the nc-HEAs is only reduced by ~20%.

Our nc-HEAs are attractive not only due to their higher absolute strength than other nc-metals

(Supplementary information Fig. S3), but also because, in a wide range of temperatures, they offer the

highest normalized strength (i.e., critical resolved shear stress, τ, divided by shear modulus, µ) and specific

strength (i.e., strength-to-density ratio). Fig. 2c illustrates an Ashby-inspired map of the normalized

strengths as a function of homologous temperatures (testing temperature, Tt, over melting temperature, Tm)

for our sx- and nc-HEA pillars, as compared to the literature data for bulk coarse-grained bcc metals and

nc-metals. With respect to compressive strength in the same homologous temperature range, the nc-HEAs

significantly outperforms bulk bcc metals26, other nanostructured metals27-32, high-temperature stable nc-

Inconel 71833, and recently reported nc-Cu-Ta alloys16. Over the temperature range of 0.1-0.3 of Tm, the

strength of our nc-HEAs falls in the ultra-strength regime as ~µ/50-µ/30, approaching its theoretical value

of µ/10. In addition, Fig. 2d highlights the high strength-to-density ratios for the nc-HEAs as structural

materials: our nc-HEAs achieve specific strength or elastic energy density of ~0.4-0.5 MJ/Kg, which

markedly exceeds all nc-metals tested in the same temperature range. Such nc-HEAs exhibit comparable

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specific strength levels to that of carbon lattices and carbon-ceramic lattices (~0.2-0.8 MJ/kg)34,

approaching the lower bound of diamond (~2 MJ/Kg). Although micro-pillar samples exhibit size-

dependent strength26, such size effect in 1-µm refractory HEA pillars (twice strength of that of the bulk

samples) are not as pronounced as that in fcc metal pillars35.

To understand the observed thermal and mechanical stability of nc-HEAs, we pay attention to the

microstructure and stress-strain curves again (Fig. 1). Stress drops during micro-compression are believed

to be attributed to a dislocation avalanche phenomenon, in which dislocations nucleate, propagate, and

escape free surfaces of sx-pillars in a short period of time. In nc-pillars, grain boundaries may prevent such

dislocation avalanches occurring and decrease the magnitude of force drops. It is known that both the low

magnitude of stress drops and wavy slip features indicate that screw dislocations have lower mobility than

edge dislocations – a typical deformation behavior of bcc metals due to the cross slip of screw dislocations36.

The high magnitude of stress drops and sharp slip bands of the sx-HEA pillars at 600 °C indicate that the

mobility of screw dislocations is increased – a deformation feature similar to fcc metals. In addition, we

utilized strain-rate jumps during the micro-compression test37 to determine the strain-rate sensitivity (m) of

the flow stress of the sx- and nc-HEA pillars by measuring the flow stress, σ, as a function of strain rate, 𝜀𝜀̇:

𝑚𝑚 = 𝜕𝜕 𝑙𝑙𝑙𝑙𝜎𝜎𝜕𝜕 𝑙𝑙𝑙𝑙 �̇�𝜀

38. The sx-HEA pillars exhibit decreasing strain-rate sensitivity with increasing temperature –

from ~0.025 at room temperature to ~0.01 at 600 °C, while the nc-HEA pillars show a consistent m value

of ~0.005 (Fig. 3a).

Furthermore, according to the m values, we are able to calculate the apparent activation volume, Va, as 𝑉𝑉𝑎𝑎 =

√3 𝐾𝐾𝐵𝐵𝑇𝑇𝑚𝑚𝜎𝜎

, 38 where kB is the Boltzmann constant of 8.617×10−5 eV/K and T is the absolute temperature. The

value of Va is related to the area swept by dislocation segments during a single thermally activated event

and, more importantly, is indicative of the deformation mechanism. Considering a Burgers vector of 3.229

Å24, we derive the Va for the sx- and nc-HEAs to be ~10 b3 at room temperature (Fig. 3b). This value is

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different from that of fcc metals, but identical to that reported from bulk tensile measurements on W, in

which thermally activated double kink mechanism is believed to be responsible for the motion of screw

dislocations39. With increasing temperature, the Va of the sc-HEA pillars increases to an average value of

~175 b3 at 600 °C, implying that sx-HEAs are deformed by, or partially by, the Peierls mechanism at 600 °C,

which is comparable to the deformation of fcc metals28. The Va of the nc-HEAs slightly increases to ~50 b3

at 600 °C, suggesting the deformation of nc-HEAs could be still dominated by the kink-pair mechanism

rather than the grain-boundary mediated mechanism. This is different from previous studies on fcc

nanocrystalline nickel pillars, in which activation volumes increase with increasing test temperature,

suggesting an enhanced grain-boundary mediated deformation37.

To further understand the role of the grain boundaries on the deformation of nc-HEAs at elevated

temperatures, we used the atom probe tomography (APT) technique to characterize the local chemical

arrangement of both sc- and nc-HEAs (also described in Ref [40]). They both show a uniform distribution

of Nb, Mo, Ta and W without clustering (Figs. 4a and 4c), confirmed by one-dimensional (1D)

concentration profiles (Figs. 4b and 4e). In the nc-HEA sample, we can clearly identify a planar region with

enriched foreign elements (N, C, and O) from the top to bottom of the tip (see Supplementary information

Fig. S4). This band feature with enriched N, C, and O can be correlated to a grain boundary, which is

included in the nc-HEA tip and was observed using a transmission electron microscopy (TEM). At this

grain boundary region, we also observe various nitrides and oxides (TaN, TaO NbN, NbO, and WN) with

the average concentrations of between 1.6 at.-% and 0.05 at.-% (Figs. 4d and 4f). The foreign elements N,

C, and O could be induced from raw materials, and the oxides and nitrides could be formed during sample

preparation. Most importantly, although such nanoscale nitride and oxide clusters at grain boundaries may

sacrifice material ductility, they are able to work as rigid interfaces to impede grain boundary motion,

contributing a kinetic mechanism for enhancing microstructural stability at elevated temperatures. In

addition, due to highly chemically disordered structures in both grain interiors and grain boundaries in the

HEAs, the thermodynamic driving force for boundary motion is low, contributing their enhanced thermal

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stability as well. In addition, the strong texture and low-angle grain boundaries might also play a role in

stabilizing microstructure, and, thus, it would also be interesting to compare thermal and mechanical

stability between columnar nc-HEAs and equiaxed nc-HEAs for future studies.

Looking towards to technological applications, these results demonstrate that nanostructured HEAs permit

access to high-temperature strength and stability of nanocrystalline metals. As a result, some conventional

refractory metals might be replaced by refractory nc-HEAs in future. Their remarkably low strain-rate

sensitivity suggest that they are also capable of creep resistance at elevated temperatures. Combined with

their high strength-to-density ratios, nc-HEAs are potentially interesting for aerospace, automobile, power,

and nuclear industries. Although much work yet remains to optimize nc-HEAs for high-temperature

applications, including improving fracture resistance, verifying creep resistance, and testing fatigue

behavior, the properties demonstrated here offer strong motivation to further pursue their development and

technological usage.

Materials and Methods

Bulk polycrystalline (coarse grained) Nb25Mo25Ta25W25 HEAs were prepared from of an equimolar mixture

of pure Nb, Mo, Ta and W powders (purity of 99.99%, 99.95%, 99.98% and 99.999%, respectively) using

the arc melting technique. Nanocrystalline NbMoTaW HEA films with columnar grains (~70-100 nm grain

size) were deposited using the DC magnetron co-sputtering technique. The details are described in Refs.

[24, 25], respectively. From the obtained HEA bulk and thin films, the pillar specimens were fabricated

using a FIB system (Helios Nanolab 600i, FEI) with a coarse milling condition of 30 kV and 80 pA and a

final polishing condition of 5 kV and 24 pA. The FIB-milled pillars (⟨011⟩ orientation) have a diameter of

approximately 1 μm and aspect ratios of about 3. The tapering angle is ~2–4˚, and the top diameters were

chosen to calculate engineering stresses.

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The FIB-milled pillars were compressed using a custom-modified in situ high-temperature SEM indenter

(Alemnis, Switzerland) in a displacement control mode. Strain-rate jump tests were used for the

measurement of strain-rate sensitivity (2×10-4, 5×10-4 10-3, 2×10-3, and 5×10-3). Testing was carried out at

25, 200, 400, and 600 °C. The morphologies of the pillars were characterized using a high resolution SEM

(Magellan 400 FEI) after compression. The yield strengths of pillars were measured as offset flow stress at

0.2% of strain. The APT tips of sx- and nc-HEAs were prepared using the FIB system and measured using

a LEAP 4000X HR (Cameca) in laser mode with a wavelength of 355 nm, specimen temperature of 40 K,

and pulse frequency of 200 kHz.

References:

1. Gleiter, H., Nanocrystalline materials. In Advanced Structural and Functional Materials, Springer: 1991; pp 1-37.

2. Meyers, M. A.; Mishra, A.; Benson, D. J. Progress in Materials Science 2006, 51, (4), 427-556. 3. Lu, K.; Lu, L.; Suresh, S. Science 2009, 324, (5925), 349-352. 4. Van Swygenhoven, H.; Weertman, J. R. Mater Today 2006, 9, (5), 24-31. 5. Hall, E. Proceedings of the Physical Society. Section B 1951, 64, (9), 747. 6. Reed, R. C., The superalloys: fundamentals and applications. Cambridge university press: 2008.

1-32 7. Van Swygenhoven, H.; Derlet, P. Phys Rev B 2001, 64, (22), 224105. 8. Shan, Z.; Stach, E. A.; Wiezorek, J. M. K.; Knapp, J. A.; Follstaedt, D. M.; Mao, S. X. Science 2004,

305, (5684), 654-657. 9. Rupert, T.; Gianola, D.; Gan, Y.; Hemker, K. Science 2009, 326, (5960), 1686-1690. 10. Gertsman, V. Y.; Birringer, R. Scripta Metall Mater 1994, 30, (5), 577-581. 11. Mathaudhu, S. N.; Boyce, B. L. Jom-Us 2015, 67, (12), 2785-2787. 12. Liu, X. C.; Zhang, H. W.; Lu, K. Science 2013, 342, (6156), 337-340. 13. Zhang, X.; Misra, A. Scripta Materialia 2012, 66, (11), 860-865. 14. Weissmüller, J. Nanostructured Materials 1993, 3, (1–6), 261-272. 15. Chookajorn, T.; Murdoch, H. A.; Schuh, C. A. Science 2012, 337, (6097), 951-954. 16. Darling, K. A.; Rajagopalan, M.; Komarasamy, M.; Bhatia, M. A.; Hornbuckle, B. C.; Mishra, R. S.;

Solanki, K. N. Nature 2016, 537, (7620), 378-381. 17. Yeh, J. W.; Chen, S. K.; Lin, S. J.; Gan, J. Y.; Chin, T. S.; Shun, T. T.; Tsau, C. H.; Chang, S. Y.

Advanced Engineering Materials 2004, 6, (5), 299-303. 18. Cantor, B.; Chang, I. T. H.; Knight, P.; Vincent, A. J. B. Materials Science and Engineering: A 2004,

375–377, (0), 213-218. 19. Gludovatz, B.; Hohenwarter, A.; Catoor, D.; Chang, E. H.; George, E. P.; Ritchie, R. O. Science

2014, 345, (6201), 1153-1158. 20. Li, Z.; Pradeep, K. G.; Deng, Y.; Raabe, D.; Tasan, C. C. Nature 2016. 21. Dolique, V.; Thomann, A. L.; Brault, P.; Tessier, Y.; Gillon, P. Surface and Coatings Technology

2010, 204, (12–13), 1989-1992.

9

22. Senkov, O. N.; Wilks, G. B.; Scott, J. M.; Miracle, D. B. Intermetallics 2011, 19, (5), 698-706. 23. Giwa, A. M.; Liaw, P. K.; Dahmen, K. A.; Greer, J. R. Extreme Mechanics Letters 2016, 8, 220-228. 24. Zou, Y.; Maiti, S.; Steurer, W.; Spolenak, R. Acta Mater 2014, 65, (0), 85-97. 25. Zou, Y.; Ma, H.; Spolenak, R. Nat Commun 2015, 6. 26. Ashby, M. F., Mechanisms of Deformation and Fracture. In Advances in Applied Mechanics, John,

W. H.; Theodore, Y. W., Eds. Elsevier: 1983; Vol. Volume 23, pp 117-177. 27. Lu, L.; Chen, X.; Huang, X.; Lu, K. Science 2009, 323, (5914), 607-610. 28. Wheeler, J. M.; Maier, V.; Durst, K.; Göken, M.; Michler, J. Materials Science and Engineering: A

2013, 585, 108-113. 29. Wang, Y. M.; Hamza, A. V.; Ma, E. Acta Mater 2006, 54, (10), 2715-2726. 30. Maier, V.; Hohenwarter, A.; Pippan, R.; Kiener, D. Scripta Materialia 2015, 106, 42-45. 31. Wei, Q.; Zhang, H. T.; Schuster, B. E.; Ramesh, K. T.; Valiev, R. Z.; Kecskes, L. J.; Dowding, R. J.;

Magness, L.; Cho, K. Acta Mater 2006, 54, (15), 4079-4089. 32. Wei, Q.; Pan, Z. L.; Wu, X. L.; Schuster, B. E.; Kecskes, L. J.; Valiev, R. Z. Acta Mater 2011, 59, (6),

2423-2436. 33. Sh, M.; Ermachenko, A. Journal of Physics: Conference Series 2010, 240, (1), 012118. 34. Bauer, J.; Schroer, A.; Schwaiger, R.; Kraft, O. Nat Mater 2016, advance online publication. 35. Dimiduk, D. M.; Uchic, M. D.; Parthasarathy, T. A. Acta Mater 2005, 53, (15), 4065-4077. 36. Vitek, V. Progress in Materials Science 1992, 36, (0), 1-27. 37. Mohanty, G.; Wheeler, J. M.; Raghavan, R.; Wehrs, J.; Hasegawa, M.; Mischler, S.; Philippe, L.;

Michler, J. Philos Mag 2014, 1-18. 38. Caillard, D.; Martin, J.-L., Thermally activated mechanisms in crystal plasticity. Elsevier: 2003;

Vol. 8. 39. Wei, Q.; Kecskes, L. J. Materials Science and Engineering: A 2008, 491, (1–2), 62-69. 40. Zou, Y.; Okle, P.; Yu, H.; Sumigawa, T.; Kitamura, T.; Maiti, S.; Steurer, W.; Spolenak, R. Scripta

Materialia 2017, 128, 95-99.

Acknowledgements The authors thank S. Gerstl (ScopeM, ETH Zurich) for his help in atom probe analysis, FIRST (ETH Zurich)

for sputtering facility, S. Maiti (Laboratory for Crystallography, ETH Zurich) for supplying the bulk HEA

sample, Y. Xiao (Laboratory for Nanometallurgy, ETH Zurich) for processing micro-compression data.

Y.Z. and H.M. acknowledge financial support through the Swiss National Science Foundation

(200021_143633 and 200021_140532). Y. Z. also acknowledge Swiss SNF Early Postdoc.Mobility

(P2EZP2_165278).

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Author Contributions

Y.Z. prepared the micro-pillar samples, analyzed the data, and prepared the manuscript; J.M.W. carried out

the micro-mechanical testing; H.M. sputtered the HEA film; P.O. conducted APT characterization; R.S.

supervised the project; all the authors contributed to the discussion and interpretation of the data and the

revision of the manuscript.

Competing financial interests

The authors declare no competing financial interests

Materials & Correspondence

Correspondence should be addressed to yuzou@mit.edu (Y. Z) or ralph.spolenak@mat.ethz.ch (R. S.).

Supporting Information Available: Supplementary figures are available free of charge via the Internet

at http://pubs.acs.org.

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Fig. 1. Compression results for the sx- and nc-HEA pillars from room temperature to 600 °C. Representative SEM images of the deformed sx-HEA pillars ((a), (b), (c), and (d)) and nanostructured columnar-grained HEA pillars ((e), (f), (g), and (h)). Corresponding engineering stress–strain curves of (i) the sx-HEA and (j) nc-HEA pillars, showing how flow stresses changes by temperature. Strain-rate jump tests are applied to measure the strain-rate sensitivity using initial and final strain rates of 10-3 s-1 and four other strain rates of 2×10-4 s-1, 2×10-3 s-1, 5×10-4 s-1, and 5×10-3 s-1.

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Fig. 2. Comparison of elevated-temperature strengths in nc-metals. a) Yield strength and (b) the percentage of strength reduction (compared to room-temperature strength) as a function of test temperature for sx- and nc-HEA pillars, indicating that the nc-HEAs exhibit substantially lower strength softening at elevated temperatures than the bulk HEAs, the sx-ones, and nc-Cu-Ta alloys16. (c) Normalized critical resolved shear stress (τ/µ) as a function of homologous temperature (Tt/Tm) for the sx- and nc-HEA pillars in this study, bulk coarse-grained (cg) Nb, Ta, Mo, and W (grain sizes of 100 µm)26, nc-Ni29, nanotwinned (nt) Cu27, ultrafine grained (ufg) Al28, ufg-Cr30, nc-W31, nc-Ta32, nc-Inconel 71833, and nc-Cu-Ta alloys16 tested in the strain rate of ~10-3 s, indicating the nc-HEA pillars exhibit the highest normalized strength (~1/50-1/30) among all the bulk and nanostructured metals (τ is critical resolved shear strength, µ is the corresponding shear modulus, Tt is testing temperature, and Tm is melting temperature; a Schmid factor of 0.5 is used here). (d) The Ashby-inspired map of specific strength (strength-to-density ratio) versus test temperature, showing that the nc-HEAs exhibit the highest strength-to-density ratio in all the nc-metals at the same tested temperatures.

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Fig. 3. Evaluation of strain-rate sensitivity (m) and activation volume (Va) as a function of temperature for sx- and nc-HEAs. (a) Strain-rate sensitivity versus temperature, indicating that the m values of sx-HEAs decrease with increasing temperature, while nc-HEAs are strain-rate insensitive with a consistent m value of ~0.005. (b) Activation volume versus temperature, suggesting that the deformation of nc-HEAs is dominated by kink-pair mechanism in a large temperature range, while sx-HEAs are deformed primarily by the Peierls mechanism at 600 °C.

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Fig. 4. Reconstruction of the APT tips showing elemental distribution in sx- and nc-HEAs. The chemical arrangement maps of (a) a sx-HEA tip and (c), (d) a nc-HEA tip. (b), (e), and (f) are corresponding one-dimensional concentration profiles of (a), (c), and (d), respectively. The APT results indicate a homogenous distribution of principle elements (Nb, Ta, Mo, and W) in both the sx-HEA ((a) and (b)) and the nc-HEA ((c) and (e)). Formation of oxides and nitrides (TaN, TaO, NbN, NbO, and WN, see (d) and (f)) and segregation of foreign elements (N, O, and C, see Supplementary information Fig. S4, ((c-f) are adapted from Ref. [40]) are observed at the grain boundary (GB) region.