Supplementary Information

Cryogenic Superelasticity with Large Elastocaloric EffectKodai Niitsu*,†, Yuta Kimura, Toshihiro Omori, Ryosuke Kainuma

Affiliations:

Department of Materials Science, Graduate School of Engineering, Tohoku University, Sendai 980-8579, Japan.

*Correspondence to: niitsu.koudai.8z@kyoto-u.ac.jp, +81-75-753-5481†Present address: Department of Materials Science and Engineering, Kyoto University, Sakyo-ku, Kyoto, 606-8501, Japan.

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Cu–Al–Mn SMA and cyclic heat treatment for abnormal grain growthCu–Al–Mn SMA is characterized by its high cold-workability and

machinability unlike most other SMAs27,S1. According to a previous study27, Cu–Al–Mn alloys with an Al content below 18 at.% undergo the MT for the cubic (L21) parent phase to the monoclinic (18R) martensite phase. The lattice parameters were determined to be a = 0.5864 nm for the parent phase and a = 0.4453 nm, b = 0.5299 nm, c = 3.834 nm and = 89.10° for the martensite phase in a Cu–17Al–10Mn alloy at ambient temperature29. Its superelastic properties are dramatically improved by increasing the grain size relative to the cross-sectional size15, and coarse grains or a single crystal can be obtained using cyclic heat treatment26.

The hot-rolled Cu–17Al–15Mn plates were subjected to the cyclic heat treatment process illustrated in Figure S1a. Cycling between two temperature stages of the (bcc) single-phase region (1143 K) and the (fcc) + two-phase region (773 K) motivates the anomalous grain growth. The obtained plates were composed of coarse grains with an average grain size of ~25 mm (see Figure S1b). The large grains were subjected to tensile tests. Figure S2 presents the electrical resistivity measurements for the obtained Cu–17Al–15Mn. The values were fully reproducible between the cooling and heating sequences, which indicates that this alloy does not undergo the thermally induced MTs over the entire temperature range measured.

Figure S1 (a) Overview of the heat-treatment process. (b) Microstructure of a typical Cu–17Al–15Mn specimen after the heat treatment.

Figure S2 Electrical resistivity measurements for Cu–17Al–15Mn.

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Tensile stress–strain results for specimen #2The tensile stress–strain results for crystal #2, which had a different

crystallographic orientation than that of specimen #1 mentioned in the main text, are presented in Figure S3. The– curves contain many spikes compared with the results presented in Figure 2. These spikes presumably arose from surface roughness and not serration behavior because each spike was similar in shape and position over the wide temperature region, and the spikes were observed even at elevated temperature. SE at 4.2 K was 5.3%.

Serration at cryogenic temperatures is typical in systems showing a drastic increase in hys upon cooling such as Ti-Ni20 and Ni–Co–Mn–In21 SMAs. In these cases, habit plane motion causes a local temperature increase. This invokes an abrupt decrease/increase of Ms/Af during the forward/reverse MTs and serration then occurs. In contrast, Ms and Af in the present Cu–17Al–15Mn were temperature-insensitive over the cryogenic region and the heat dissipation was markedly suppressed. Thus, the smooth flow of the habit planes may be allowed even at cryogenic temperatures.

Figure S3 Tensile – curves for Cu–17Al–15Mn single crystal #2 with initial superelastic plateaus of ~1.5% at various temperatures ranging from 4.2 K to 160 K. The upper inset presents the superelastic curves at 4.2 K. The crystallographic orientation of this crystal in the tensile direction is shown in the inverse pole figure in the lower inset.

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Specific heat and entropy changeThe specific heat (cP) of the Cu–17Al–15Mn and Cu–17Al–12Mn alloys was

measured using a physical property measurement system (PPMS, Quantum Design, Inc., USA), and the results are shown the inset of Figure S4a. cP for Cu–17Al–12Mn shows a cusp at ~165 K because of MT. The temperature dependence of S (Figure S4a) is derived from

S=∫0

T(c P /T )dT

. (S1)

The differential (S) between S for the martensite phase in Cu–17Al–12Mn (SM) and the

parent phase in Cu–17Al–15Mn (SP) is given in Figures S4b and 3c. Furthermore, Q, W,

Tadid, Tfri, Tad

eff, and COPmat can be derived from equation (2), (3), (4), (5), (6), and (7) with the obtained S, respectively, where W and Tfri are derived with constant hys

= 20 MPa and SE = 10%. Their temperature dependences are shown in Figures S4c–e. The curves of Q, W, Tad

id, and Tadeff are also given in Figures 4a-c.

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Figure S4 Temperature dependences of (a) S for Cu–17Al–15Mn (SP) and Cu–17Al–12Mn (SM), derived from equation (S1) with cP shown in the inset, (b) S (= SM–SP), (c) Q and W, (d) Tad

id and Tadeff, and (e) COPmat.

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Reference values and derivations of Q , W , T adid , T ad

eff , and COP mat

Concrete reference values of Q, W, Tadid, Tad

eff, and COPmat are displayed in Figures S5 and S6 together with those for the present Cu–17Al–15Mn (filled plots). In Figures S5a–c, Q, W, Tad

id, and Tadeff for the Cu-based SMAs were obtained from

reference data for Cu–17Al–15Mn30, Cu–17.5Al–11Mn31, Cu–16Zn–16Al35, Cu–33.7Zn–1.7Sn1,36, Cu–27.8Al–3.63Ni1, and Cu–27.7Al–2.7Ni37. Those for the Ni-based Heusler SMAs were obtained from reference data for Ni–5Co–36Mn–14In21, Ni–5Co–36.1Mn–13.9InS2, Ni–5Co–36.5Mn–13.5InS3, Ni–5Co–36.7Mn–13.3InS3-S5, Ni–5.1Co–36.6Mn–13.3InS6, Ni–5.1Co–36.7Mn–13.0InS7, Ni–34Mn–16InS8, Ni–9Co–39Mn–11SbS9,S10, Ni–37Mn–13SbS11, Ni–13.4Co–39.7Mn–13.9GaS12, Ni–20Mn–25GaS13, Ni–7Co–39Mn–11SnS14, and Ni–4Co–19Fe–27GaS15. Those for the Ti–Ni-based SMAs were obtained from reference data for Ti–50NiS16, Ti–51.30Ni20, Ti–51.59Ni20, Ti–51.75Ni19, Ti–50.4Ni filmS17, Ti–32.5Ni–12.6Cu filmS17, and Ti–30.7Ni–12.3Cu–2.3Co filmS18. The properties of the Ni-based Heusler SMAs were derived from the magnetic-field-induced (so-called metamagnetic) MT behaviors except for references 19 and S2. For the metamagnetic MT, W can be determined using

W =∮MdH /2 . (S2)

cP for these alloy systems was preliminarily obtained for representative alloys. If cP was not provided in the literature, we used these representative data.

In Figure S6, the COPmat values for Fe–34Mn–15Al–7.5Ni34, barocaloric La–80.93Fe–3.36Co–8.57SiS19, barocaloric Fe–51RhS20,S21, and Fe–31.2PdS22 are presented in addition to those reported in the aforementioned literature1,19-21,30,31,35-37,S2-S18. For La–Fe–Co–Si, the transformation completion was estimated to be 71% based on the isothermal S reported in the literatureS19. The transformation hysteresis was obtained from the M–H loop for metamagnetic La–Fe–Si–HS23,S24, and COPmat for fully transformed La–Fe–Co–Si was deduced.

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Figure S5 Temperature dependences of caloric properties of (a) –Q and W, (b) Tadid,

and (c) Tadeff alongside concrete plots for References 1, 19-21, 30, 31, 35–37, and S2–

S18.

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Figure S6 Concrete values of COPmat of various caloric materials1,19-21,30,31,34-37,S2-S22.

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