A strategy of designing high-entropy alloys with high-temperature shape memory effect

Shape memory effect, the ability to recover a pre-deformed shape on heating, results from a reversible martensitic transformation between austenite and martensite phases. Here, we demonstrate a strategy of designing high-entropy alloys (HEAs) with high-temperature shape memory effect in the CrMnFeCoNi alloy system. First, we calculate the difference in Gibbs free energy between face-centered-cubic (FCC) and hexagonal-close-packed (HCP) phases, and find a substantial increase in thermodynamic equilibrium temperature between the FCC and HCP phases through composition tuning, leading to thermally- and stress-induced martensitic transformations. As a consequence, the shape recovery temperature in non-equiatomic CrMnFeCoNi alloys can be increased to 698 K, which is much higher than that of conventional shape memory alloys (SMAs) and comparable to that of B2-based multi-component SMAs containing noble metals (Pd, Pt, etc.) or refractory metals (Zr, Hf, etc.). This result opens a vast field of applications of HEAs as a novel class of cost-effective high-temperature SMAs.

temperature, T 0 , in the various non-equiatomic CrMnFeCoNi HEAs and evaluate the composition dependence of ΔG HCP-FCC using CALPHAD methodology with the TCHEA3 database. Second, we carefully reveal the reversible martensitic transformation between the FCC and HCP phases in the compositionally tuned 3d HEAs using in situ X-ray diffraction (XRD) and thermal analyses. Third, we confirm the shape recovery on heating after pre-deformation in the developed non-equiatomic CrMnFeCoNi HEAs. Indeed, we can manipulate the shape memory effect of the HEAs to have exceptionally wide range of transformation temperatures such as reverse transformation finish temperature from 435 to 698 K. These findings suggest that non-equiatomic CrMnFeCoNi HEAs are promising candidates for cost-effective shape memory actuators even at elevated temperatures.

Results
Design of high-entropy alloys with shape memory effect. Figure 1a shows the predicted ΔG HCP-FCC at 300 K using CALPHAD methodology with the TCHEA3 database in five hypothetical alloy systems of 3d HEAs: (MnFeCoNi) 100-x Cr x , (CrFeCoNi) 100-x Mn x , (CrMnCoNi) 100-x Fe x , (CrMnFeNi) 100-x Co x , and (CrMnFeCo) 100- x Ni x . To evaluate the relative influence of each principal element on ΔG HCP-FCC , the atomic fraction of the fifth element was modified between 10 and 30 at.% while that of other four elements was kept in equimolar ratio. The CALPHAD prediction showed that ΔG HCP-FCC can be significantly reduced when the Ni content decreases or the Co content increases from the equiatomic composition, suggesting that ΔG HCP-FCC is significantly reduced by the replacement of Ni with Co. Figure 1b shows ΔG HCP-FCC for a series of non-equiatomic CrMnFeCoNi alloys with different Cr/Mn ratios from 0.6 to 3, which were predicted to form a single-phase FCC solid solution 28 . All the alloy series exhibited a pronounced decrease in ΔG HCP-FCC as the Ni content was replaced with Co. With an increase in the Cr/Mn ratio up to 3, a more drastic decrease in ΔG HCP-FCC was predicted in the alloys with a lower Ni/Co ratio. Compared with Cr 20 Mn 20 Fe 20 Co 20 Ni 20 alloy, the value of ΔG HCP-FCC in several compositions was calculated to be negative. These results imply that the HCP phase can be favored over the FCC phase at 300 K in a wide composition range of non-equiatomic CrMnFeCoNi HEAs. Figure 1c shows the temperature dependence of ΔG HCP-FCC in the Cr 20 Mn 20 Fe 20 Co 40-x Ni x system (x = 0, 5, 10, and 20 at.%). The Cr 20 Mn 20 Fe 20 Co 20 Ni 20 alloy showed a positive value of ΔG HCP-FCC in the considered temperature range, while the other alloys exhibited a negative value of ΔG HCP-FCC at lower temperatures. By replacing Ni    Figure 1d shows the predicted T 0 CAL for the series of the CrMnFeCoNi alloy system shown in Fig. 1b. As the Ni/Co ratio was reduced, T 0 CAL increased from 102 K for the Cr 15 Mn 25 Fe 20 Co 30 Ni 10 alloy and to 666 K for the Cr 30 Mn 10 Fe 20 Co 40 alloy. The range of T 0 CAL was wider than the range of the experimentally measured T 0 in conventional SMAs such as TiNi (227-359 K) 29 , CuAlNi (241-407 K) 30 , and FeMnSi (363-493 K) 31,32 . These predictions suggest the possibility of developing non-equiatomic CrMnFeCoNi HEAs for functional applications employing the shape memory effect (or pseudoelasticity) since the martensitic transformation from the FCC to  Fig. 1c. These HEAs were produced by high-frequency vacuum induction melting and subjected to multi-pass caliber rolling into bars of roughly 14 mm width and annealed at 1373 K for 1 h. XRD (Fig. 2a) and electron backscatter diffraction (EBSD) results ( Fig. 2b-d) show that the as-annealed Ni10 and Ni5 alloys were single-phase FCC solid solutions with an average grain size of ~100 μm, while the as-annealed Ni0 alloy exhibited a dual-phase FCC-HCP structure with an HCP phase fraction of ~40 vol.% from EBSD analysis. Figure 3a shows the XRD patterns of the Ni5 alloy collected in the temperature range from 100 to 700 K. The alloy was initially heated to 700 K under vacuum, then the XRD patterns were obtained during cooling to 100 K and then subsequent heating to 700 K. Compared to the Ni10 alloy, which was a single-phase FCC solid solution during cooling down to 100 K ( Figure S1), the Ni5 alloy exhibited diffraction peaks of the HCP phase when the temperature decreased to 200 K. With further cooling to 100 K, the HCP peaks grew in intensity while those from the initial FCC phase decreased. The HCP peaks remained stable during heating to 400 K, though the HCP phase reverted to the initial FCC phase with heating to 500 K. The unit cell parameters were determined from the XRD pattern at 300 K to be a = 3.58747 ± 0.00001 Å for the FCC phase and a = 2.5369 ± 0.0004 Å and c = 4.0944 ± 0.0018 Å for the HCP phase. The Ni5 alloy cooled by liquid nitrogen exhibited a dual-phase FCC-HCP structure with a thermally induced HCP phase fraction of ~20 vol.% from EBSD analysis and a homogeneous elemental distribution confirmed by electron probe microanalysis ( Figure S2). These results reveal a reversible martensitic transformation between the FCC and HCP phases in the Ni5 alloy.

Reversible martensitic transformation.
A similar phase transition was observed in the Ni0 alloy (Fig. 3b). The alloy showed higher onset temperatures, where the HCP phase appears (300 K) and disappears (700 K), than the Ni5 alloy, indicating an enhanced HCP phase stability, as predicted in Fig. 1c. The unit cell parameters were calculated to be a = 3.58528 ± 0.00001 Å for the FCC phase and a = 2.5363 ± 0.001 Å and c = 4.093 ± 0.005 Å for the HCP phase at 300 K. A small peak around 45°, observed after the initial heating to 873 K, is likely to correspond to a Mn 2 O 3 phase, which is one of the oxides formed on the surface of Cr 20 Mn 20 Fe 20 Co 20 Ni 20 HEA at 873 K 33 . Figure 4a shows the results of thermal analysis of the Ni10, Ni5, and Ni0 alloys measured by differential scanning calorimetry (DSC). An exothermic peak during cooling and an endothermic peak during heating were observed for the Ni5 and Ni0 alloys, indicating forward and reverse martensitic transformations, respectively. The martensitic transformation start temperature (M s ), martensitic transformation finish temperature (M f ), reverse transformation start temperature (A s ), and reverse transformation finish temperature (A f ) obtained from the DSC curves are summarized in Fig. 4a. The onset temperatures of the martensitic transformation measured by in situ XRD analysis match well with those measured by DSC analysis. Figure 4b shows the DSC results of Ni0 alloy in five consecutive cycles. A slight increase in M s by the cycling was observed but the transformation heats for forward (~9.0 J·g −1 ) and reverse transformation (~6.0 J·g −1 ) were very stable as compared to Co-32Ni alloy where the transformation peak rapidly decayed by thermal cycling 34 . Thus, the martensitic transformation is highly reversible in the present alloys. We compared the characteristic temperatures of martensitic transformation measured by DSC and a thermo-mechanical analyzer ( Figure S3) with T 0 CAL as a function of Ni content in the Cr 20 Mn 20 Fe 20 Co 40-x Ni x system (Fig. 4c). The thermodynamic equilibrium temperature (T 0 = (M s + A f )/2) was calculated from the DSC results to be 366 and 509 K for the Ni5 and Ni0 alloys, respectively. The predicted T 0 CAL monotonically increased with a decrease in the Ni/Co ratio, and an increasing trend was also seen in the experimentally determined T 0 . In addition to the Ni5 and Ni0 alloys, the Cr 30 Mn 10 Fe 20 Co 40 alloy, which was predicted to show the lowest ΔG HCP-FCC (Fig. 1b) and the highest T 0 CAL (Fig. 1d), exhibited higher M s (479 K), A f (698 K), and T 0 (589 K) than the Ni0 alloy (Fig. 4d). These results validate the CALPHAD prediction in Fig. 1 that the HCP phase stability as well as T 0 can be tailored through composition tuning in 3d HEAs. Figure 5a-c shows the relative change in the specimen length (ΔL/L 0 , where ΔL is the change in length and L 0 is the initial length) of the as-annealed Ni10, Ni5, and Ni0 alloys measured by a thermo-mechanical analyzer. The as-annealed Ni10 and Ni5 alloys exhibited thermal expansion curves similar to the single-phase Cr 20 Mn 20 Fe 20 Co 20 Ni 20 HEA 35 , indicating that no phase transformation occurred during heating to 1000 K and cooling to room temperature. However, the as-annealed Ni0 alloy displayed a dilation during heating and a contraction during cooling. The onset temperatures of the dilation and contraction were 531 and 399 K, respectively.

Shape memory effect.
Figure 5d-f shows the thermal expansion and contraction curves of the pre-strained Ni10, Ni5, and Ni0 alloys deformed with a compressive strain of about 1% at room temperature. In contrast to the pre-strained Ni10 alloy, the pre-strained Ni5 and Ni0 alloys displayed a significant dilation during heating and the pre-strained Ni0 alloy showed a contraction during cooling. The onset temperatures of the dilation for Ni5 and Ni0 alloys and the contraction for Ni0 alloy were 402, 542, and 397 K, respectively. The three as-annealed alloys and the pre-strained Ni10 alloy exhibited a small increase in ΔL/L 0 of less than 5 × 10 −4 (corresponding to 5 μm in specimen length) after cooling. However, the increase in ΔL/L 0 of the pre-strained Ni5 and Ni0 alloys was more than ten times larger than that of the other alloys. The significant increase in specimen length can be attributed to the marked dilation during heating, revealing the shape memory effect of Ni5 and Ni0 alloys.
The Ni10 alloy with a single-phase structure showed no phase transformation, whereas the Ni0 alloy with a dual-phase structure displayed a distinct dilation during heating and contraction during cooling in both the as-annealed and pre-strained states. No phase transformation was observed for the as-annealed Ni5 alloy, but marked dilation was observed for the pre-strained Ni5 alloy. XRD results revealed that the pre-strained Ni5 alloy showed a dual-phase structure while the alloy after heating to 873 K for 10 min showed a single-phase structure 40 Figure 3. In situ XRD patterns at various temperatures. (a) XRD patterns of as-annealed Ni5 alloy between 100 and 700 K. The initial XRD pattern at 700 K corresponds to an FCC single-phase structure. New peaks, corresponding to the HCP phase, appear from 200 K during cooling and fully revert to the initial FCC peaks at 500 K during heating. (b) XRD patterns of as-annealed Ni0 alloy between 100 K and 873 K. The initial pattern at 873 K corresponds to a FCC single-phase structure, but shows a small peak around 45°. This peak likely corresponds to the Mn 2 O 3 phase, which is one of the oxides that forms on the surface of Cr 20 Mn 20 Fe 20 Co 20 Ni 20 alloy at 873 K 33 . HCP peaks appear from 300 K during cooling and revert to the FCC peaks at 700 K during heating. Shifts of all peaks to higher angles during cooling and to lower angles during heating result from the contraction and expansion of the unit cells, respectively. (2019) 9:13140 | https://doi.org/10.1038/s41598-019-49529-8 www.nature.com/scientificreports www.nature.com/scientificreports/ (inset in Fig. 5). The onset temperatures of the dilation and contraction in the dual-phase alloys (Fig. 5c,e,f) agreed well with A s and M s measured by DSC analysis, indicating that the dilation and contraction are associated with the reverse and forward martensitic transformations between the FCC and HCP phases, respectively.
The dilation observed during heating was stronger in the pre-strained Ni5 and Ni0 alloys than the as-annealed Ni0 alloy. The small dilation in the as-annealed Ni0 alloy was due to the reverse martensitic transformation of the thermally induced HCP phase 31 . The significant dilation in the pre-strained Ni5 and Ni0 alloys originated from the reverse martensitic transformation of the stress-induced HCP phase. When the initial FCC phase of the Ni5 and Ni0 alloys was strained, the HCP phase was stress-induced by the movement of Shockley partial dislocations preferentially in the direction of the applied shear stress 36 . The reverse martensitic transformation of the stress-induced HCP phase was achieved by the reverse motion of the partial dislocations along this direction 36,37 . Thus, the shape recovery of the Ni5 and Ni0 alloys can be attributed to the formation of the stress-induced HCP phase during a shape change and the reverse martensitic transformation of the stress-induced HCP phase on heating. www.nature.com/scientificreports www.nature.com/scientificreports/ Recovery strain. Figure 6a-c shows the recovery strain in the Ni10, Ni5, and Ni0 alloys measured by bending rectangular specimens with dimensions of 3 × 0.6 × 40 mm 3 at two different deformation temperatures, room (293 K) and liquid-nitrogen (77 K) temperatures. The Ni10 alloy deformed at 293 K exhibited no recovery strain, while the alloy deformed at 77 K showed a recovery strain with a maximum value of ~1.8%. The Ni5 and Ni0 alloys at both temperatures exhibited recovery strain with maximum values of ~2.0% and ~1.1% when deformed at 293 K and ~1.4% and ~1% when deformed at 77 K, respectively. The Ni5 alloy deformed at 293 K displayed the largest recovery strain among the alloys (Fig. 6d and Supplementary Video 1). The recovery strain in the alloys increased with an increase in the pre-strain, but remained stable after reaching a pre-strain of ~3.0%.
With a decrease in deformation temperature from 293 to 77 K, the recovery strain decreased by ~30% for the Ni5 alloy. The alloy showed a dual-phase structure with an HCP fraction of ~20 vol.% after cooling to 77 K ( Figure S2). Since the thermally induced HCP phase suppresses the stress-induced martensitic transformation 20 and the stress-induced HCP phase interacts with the pre-existing phase boundaries during pre-straining 32 , the stress-induced martensitic transformation and the reverse martensitic transformation of the stress-induced HCP phase are interrupted in the dual-phase alloys. Thus, the Ni5 alloy exhibited a smaller recovery strain when deformed at 77 K. The reason why the recovery strain is almost the same in the Ni0 alloy deformed at both temperatures is unclear, but the smaller recovery strain in the Ni0 alloy than the Ni5 alloy may be associated with the higher fraction (~40 vol.%) of the thermally induced HCP phase at room temperature (Fig. 2d).
The Ni10 alloy exhibited the largest recovery strain among the alloys deformed at 77 K. The pre-strained Ni10 alloy at 77 K exhibited distinct dilation during heating in the thermo-mechanical analysis (Figure S3), indicating a reverse martensitic transformation from the HCP to FCC phase. However, a forward martensitic transformation was not observed in the in situ XRD (Figure S1), DSC analysis (Fig. 4a), and the XRD pattern of the alloy cooled by liquid nitrogen (not shown), implying that M s of the Ni10 alloy was lower than 77 K. Thus, the Ni10 alloy was predominantly deformed by the stress-induced martensitic transformation at 77 K without any thermally induced   Figure 5. Shape memory effect of 3d HEAs. (a-c) Relative change in specimen length (ΔL/L 0 , ΔL is the change in length and L 0 is the initial length) during heating to 1000 K and cooling to room temperature for as-annealed (a) Ni10, (b) Ni5, and (c) Ni0 alloys. Compared with the Ni10 and Ni5 alloys, the Ni0 alloy exhibits a dilation and contraction during heating and cooling, respectively. (d-f) ΔL/L 0 for pre-strained (d) Ni10, (e) Ni5, and (f) Ni0 alloys with a compressive strain of ~1% deformed at room temperature. Compared with the Ni10 alloy, the Ni5 and Ni0 alloys exhibit a drastic dilation during heating. The marked dilation leads to a pronounced increase in specimen length after cooling, demonstrating the shape memory effect of Ni5 and Ni0 alloys. XRD patterns of the pre-strained Ni5 alloy (inset) show an FCC/HCP dual-phase structure before heating but an FCC singlephase structure after heating to 873 K for 10 min, indicating that the shape memory effect is associated with the martensitic transformation between the FCC and HCP phases. (2019) 9:13140 | https://doi.org/10.1038/s41598-019-49529-8 www.nature.com/scientificreports www.nature.com/scientificreports/ HCP phase, which is one of the reasons why the Ni10 alloy deformed at 77 K exhibited a similar recovery strain as the Ni5 alloy deformed at 293 K.

Discussion
In this work, we have developed novel shape memory alloys in the CrMnFeCoNi alloy system using the CALPHAD methodology by calculating the ΔG HCP-FCC variation for a wide composition range of 3d HEAs. In comparison with the previously reported SMAs with martensitic transformation between the FCC and HCP phases, the recovery strain in the Ni5 alloy deformed at 293 K was found to be much larger than that in CoNi 34,38-40 , FeMn 41 , and FeMnC 42 alloys (less than 0.3% 38,42 ) and comparable to that in polycrystalline FeMnSi-based alloys (~2.0% 41 ) containing Si up to about 11 at.% 43,44 , used for industrial applications like pipe joining and seismic damping 44,45 . For CoNi and FeMn binary alloys with a poor shape memory effect, the addition of a significant amount of Si led to a remarkable improvement in the recovery strain. The roles of Si in the shape memory effect have been determined to be 41-46 1) suppressing the magnetic transition from paramagnetism to anti-ferromagnetism, which inhibits the martensitic transformation due to magnetic ordering, 2) enhancing the reversibility of the martensitic transformation by decreasing the volume change between the FCC and HCP phases, and 3) solid-solution strengthening of the FCC phase to suppress the glide motion of dislocations.
The Cr 20 Mn 20 Fe 20 Co 20 Ni 20 alloy was predicted to show a very low magnetic transition temperature of 23 K by the addition of Cr and Mn 47 , implying that the martensitic transformation is not strongly affected by the magnetic transition in the non-equiatomic CrMnFeCoNi HEAs. The volume changes between the FCC and HCP phases calculated from the lattice constants 46 38 ) alloys. The higher yield strength resulted from the enhanced solid solution strengthening of the HEA, which contributes to the stress-induced martensitic transformation as a predominant deformation mode in the pre-straining. Therefore, the large recovery strain in non-equiatomic CrMnFeCoNi HEAs with shape memory effect can be attributed to the reduced volume change between the FCC and HCP phases and the improved yield strength of the FCC phase.   (Fig. 4) and B2-based multicomponent SMAs (TiZrHfNiCu 24 and NiPdTiHfZr 25 alloys), compared with the characteristic temperature range in conventional SMAs such as binary TiNi, ternary CuAlNi, and ternary FeMnSi [29][30][31][32] . Interestingly, similar to the B2-based multi-component SMAs, some of the developed non-equiatomic CrMnFeCoNi HEAs exhibit much higher M s than 373 K, which is regarded as an upper limit of M s in commercial SMAs like binary TiNi alloys 48,49 . Also, the developed non-equiatomic CrMnFeCoNi HEAs exhibit a wider range of transformation temperatures, e.g., from less than 77 to 479 K for M s and from 435 to 698 K for A f than the conventional SMAs. These findings suggest that developed non-equiatomic CrMnFeCoNi HEAs, which have excellent workability, weldability, fracture resistance, and corrosion resistance 12,50-52 , are promising candidates for shape memory actuators at elevated temperatures. It should be noted that much higher M s and A f could be achieved in the CrMnFeCoNi alloy system by exploring a broad range of compositions where FCC phase is predicted to be formed 28 . For the high-temperature applications, the thermal stability of FCC phase at the elevated temperatures is a major issue. Reduced transformation hysteresis (A f -M s ) would be preferred for actuator applications. In general transformation hysteresis is related to the mobility of austenite/martensite interface and more glissile interface may lead to smaller hysteresis. These subjects are currently under investigation.
In conclusion, we have developed novel 3d HEAs with shape memory effect in the CrMnFeCoNi alloy system. The designed non-equiatomic CrMnFeCoNi HEAs displayed thermally-and stress-induced martensitic transformations between the FCC and HCP phases. The appreciable shape memory properties, comparable to those of polycrystalline FeMnSi-based alloys, result from the reverse martensitic transformation of the stress-induced HCP phase, which is predominantly assisted by the enhanced solid solution strengthening of the FCC phase and reversibility of the martensitic transformation between the FCC and HCP phases. The highest M s and A f in the developed non-equiatomic CrMnFeCoNi HEAs were higher than those in conventional SMAs, and these shape recovery temperatures could be made even higher via customized compositional manipulation of the developed HEAs with shape memory effect in a wide composition range. These findings allow us to use the non-equiatomic CrMnFeCoNi HEAs as a new class of potential high-temperature SMAs and offer new insights on how to develop novel HEAs with customized shape memory effect.

Methods
Materials processing. Ingots of a series of Cr 20 Mn 20 Fe 20 Co 40-x Ni x (x = 0, 5, 10, and 20 at.%) and Cr 30 Mn 10 Fe 20 Co 40 alloys, 1 kg in weight, were produced by high frequency vacuum induction melting. The as-cast ingots with cross-sections of 30 × 30 mm 2 were homogenized at 1473 K for 24 h under Ar atmosphere followed by water quenching. The homogenized ingots were subjected to multi-pass caliber rolling at 673 K to form squared bars 53 with cross-sections of 14 × 14 mm 2 , then annealed at 1373 K for 1 h.
Microstructural characterization. The phase constitutions in the temperature ranges 100-700 K for the Ni5 alloy and 100-873 K for the Ni0 alloy were confirmed by low-and high-temperature XRD experiments (SmartLab diffractometer with TTK-600 chamber, Rigaku, Tokyo, Japan) using a Cu Kα 1 X-ray source at 45 kV and 200 mA under vacuum. For the XRD analysis, the surfaces of the as-annealed specimens were pre-etched using aqua-regia (3HCl:1HNO 3 ) solution to remove the oxidized surface. Differential scanning calorimetry (DSC; DSC Q2000, TA Instruments, New Castle, DE, USA) analysis was conducted with a constant cooling/heating rate of 20 K·min −1 . The microstructure was examined by a scanning electron microscope (SEM; JSM-7001F,