Vapor compression technologies widely used for refrigeration, heating, and air-conditioning have consumed a large fraction of global energy. Efforts have been made to improve the efficiency to save the energy, and to search for new refrigerants to take the place of the ones with high global warming potentials. The solid-state refrigeration using caloric materials are regarded as high-efficiency and environmentally friendly technologies. Among them, the elastocaloric refrigeration using shape memory alloys has been evaluated as the most promising one due to its low device cost and less of a demand for an ambient environment. General caloric materials heat up and cool down when external fields are applied and removed adiabatically (conventional caloric effect), while a few materials show opposite temperature changes (inverse caloric effect). Previously reported shape memory alloys have been found to show either a conventional or an inverse elastocaloric effect by the latent heat during uniaxial-stress-induced martensitic transformation. In this paper, we report a self-regulating functional material whose behavior exhibits an elastocaloric switching effect in Co-Cr-Al-Si Heusler-type shape memory alloys. For a fixed alloy composition, these alloys can change from conventional to inverse elastocaloric effects because of the change in ambient temperature. This unique behavior is caused by the sign reversal of latent heat from conventional to the re-entrant martensitic transformation. The realization of the elastocaloric switching effect can open new possibilities of system design for solid-state refrigeration and temperature sensors.

Since their discovery, various caloric effects in solid-state materials—the barocaloric,1 electrocaloric,2 magnetocaloric,3 and elastocaloric effects (eCE)4—have been expected to be used in high-efficiency and environmentally friendly refrigeration systems as a substitute for the conventional vapor compression refrigeration system.5–9 Among all the alternative non-vapor-compression technologies for refrigeration, the elastocaloric refrigeration technique using shape memory alloys (SMAs) has been evaluated as the most promising one owing to its low device cost and flexibility in ambient environment, which is expected to be useful in various applications in different climates.10 By the martensitic transformation, the temperature of an SMA sample can change when uniaxial stress is applied or removed, even in the absence of heat flow from or to outside. For the thermoelastic martensitic transformation, generally, as shown in Fig. 1(a), the parent phase exists at a higher temperature (high-entropy phase), and a lower temperature favors the martensite phase (low-entropy phase). Moreover, the martensite phase can be stabilized by uniaxial tensile or compressive stresses. Thus, the uniaxial stress promotes the forward martensitic transformation, and a decrease in entropy occurs (ΔS<0). As a result, as shown in Fig. 1(a), under an adiabatic condition, applying uniaxial stress causes the caloric material to heat up (ΔTad>0), whereas it cools down (ΔTad<0) when the uniaxial stress is removed. Until now, the eCE has been reported in many kinds of SMAs, including Ti-Ni-,11,12 Cu-,4,13,14 Ni-,15–17 Fe-Pd-,18 and Co-Ni-based19,20 alloys. All of these alloys show an intrinsically conventional eCE, that is, the loading and unloading processes result in ΔTad>0 and ΔTad<0, respectively,21 as schematically described in Fig. 1(a).

FIG. 1.

Schematic illustrations of entropy and temperature change under uniaxial stresses for (a) conventional and (b) inverse elastocaloric effects (eCEs). Inverse elastocaloric materials cool down and heat up when uniaxial stress is applied and removed, respectively, while conventional elastocaloric materials heat up and cool down in loading and unloading processes of uniaxial stresses, respectively. For the current Co-Cr-Al-Si alloys, the conventional eCE at high temperature switches to the inverse eCE at low temperature. The temperature changes in the unloading process are schematically shown in (c).

FIG. 1.

Schematic illustrations of entropy and temperature change under uniaxial stresses for (a) conventional and (b) inverse elastocaloric effects (eCEs). Inverse elastocaloric materials cool down and heat up when uniaxial stress is applied and removed, respectively, while conventional elastocaloric materials heat up and cool down in loading and unloading processes of uniaxial stresses, respectively. For the current Co-Cr-Al-Si alloys, the conventional eCE at high temperature switches to the inverse eCE at low temperature. The temperature changes in the unloading process are schematically shown in (c).

Close modal

On the other hand, the inverse eCE, that is, the cooling effect on loading and the heating effect on unloading, as shown in Fig. 1(b), has not been easy to realize, although the inverse magnetocaloric,22 inverse barocaloric,23 and inverse electrocaloric24 effects induced by a magnetic field, static pressure, and electrical voltage, respectively, are well-known. The inverse eCE has been realized only in a few alloys, such as Fe-Rh alloys,25,26 coherent-particle-contained Ni-Ti alloys,27 and nanocrystalline Ni-Ti alloys.28 Moreover, all previous elastocaloric materials show either a conventional or an inverse eCE, except for the nanocrystalline Ni-Ti alloys.28 Nanocrystalline Ni-Ti alloys show a conventional eCE at approximately the room temperature (RT ∼300 K) owing to the martensitic transformation, whereas an inverse eCE appears at cryogenic temperatures because of the combination of low specific heat and the large volumetric entropy change in the tensile elastic deformation of the parent phase.28 

Recently, our group has reported novel CoCr-based Heusler-type SMAs showing a unique “reentrant martensitic transformation” behavior,29–31 where the martensite phase induced from the paramagnetic parent phase by cooling transforms back into the ferromagnetic parent phase by further cooling. Due to this unique phase stability relation between the parent and martensite phases, not only the inverse eCE but also some additional functionality on eCE can be expected for the CoCr-based Heusler-type SMAs.

In this paper, we report the elastocaloric switching effect in Co-Cr-Al-Si shape memory alloys. For a fixed alloy composition, the conventional eCE switches to the inverse eCE by the change of ambient temperature. Thus, during the removal of the uniaxial stress, these alloys can provide cooling ability at high temperatures and purvey heating ability at low temperatures, as schematically shown in Fig. 1(c). This abnormal phenomenon originates from the change in sign of the ΔS, which results in a combination of the conventional martensitic transformation at a higher temperature and the reentrant martensitic transformation at a lower temperature in Co-Cr-Al-Si alloys.

Co55Cr23.5Al11.5Si10 and Co55.4Cr23.1Al11.5Si10 alloys were prepared by induction melting in an Ar atmosphere. The critical stresses for the uniaxial-stress-induced martensitic transformation of Co55Cr23.5Al11.5Si10 alloy are slightly higher than those of Co55.4Cr23.1Al11.5Si10 alloy. Thus, for the superelasticity tests, the Co55Cr23.5Al11.5Si10 alloy was used for the temperature range of 153 to 373 K, whereas the Co55.4Cr23.1Al11.5Si10 alloy was used for the temperature range of 10 to 293 K. The ingots were hot rolled at 1473 K with a 20% reduction in thickness. For Co-Cr-Al-Si alloys, single-crystal samples are preferred for mechanical tests, because the samples easily fracture when grain boundaries are included. Moreover, single-crystalline samples are required in order to investigate intrinsic mechanical properties of these alloys. A cyclic heat treatment as shown in Fig. 2, which is similar to the one reported in Cu-Al-Mn,32,33 was conducted to obtain large grains. Specimens of single crystals were cut out by electric discharge machining. By this method, several centimeters of single-crystalline samples were successfully obtained, although they were still too small to perform tensile tests. Therefore, compression tests were conducted for the evaluation of intrinsic elastocaloric properties of these alloys. The crystal orientations in the single-crystalline specimens were determined using the electron backscatter diffraction (EBSD) technique.

FIG. 2.

For Co-Cr-Al-Si alloys, a cyclic heat treatment similar to Cu-Al-Mn alloys32,33 was conducted to obtain large grains. First, samples cut from ingots were solution-heat-treated for 3 h at 1473 K. Consequently, heat treatments indicated by the dashed square were conducted seven times. Finally, these samples were heat-treated for 10 h at 1473 K for grain growth, followed by quenching in water.

FIG. 2.

For Co-Cr-Al-Si alloys, a cyclic heat treatment similar to Cu-Al-Mn alloys32,33 was conducted to obtain large grains. First, samples cut from ingots were solution-heat-treated for 3 h at 1473 K. Consequently, heat treatments indicated by the dashed square were conducted seven times. Finally, these samples were heat-treated for 10 h at 1473 K for grain growth, followed by quenching in water.

Close modal

In this study, three Co55Cr23.5Al11.5Si10 and one Co55.4Cr23.1Al11.5Si10 single-crystalline samples were prepared as a whole. For mechanical tests, two samples, Samples 1 and 2, were used, where Sample 1 was the Co55Cr23.5Al11.5Si10 sized 2.8 × 2.7 × 7.2 mm3 with ⟨7 2 24⟩ in the compressive direction and Sample 2 was the Co55.4Cr23.1Al11.5Si10 sized 2.5 × 2.6 × 6.8 mm3 with ⟨4 2 11⟩. For specific-heat measurements for parent and martensite phases, two Co55Cr23.5Al11.5Si10 samples were quarried from a large single crystal. Sample 3, which is in the parent phase, is an as-quenched sample piece. For the rest of the single crystal, a cyclic compression test with a superelastic strain of 5.2% (full transformation strain) and strain rate of 1.0 × 10−3 s−1 up to 550 times was conducted in ⟨10 5 27⟩ direction at 300 K to stabilize the martensite phase. After the mechanical test, some amount of martensite remained in stress-free condition. Sample 4 is the sample piece in the residual martensite phase cut from the deformed sample.

To investigate the eCE and superelastic properties at various temperatures, compression tests were performed on the same single-crystal specimen of Co55Cr23.5Al11.5Si10 (Sample 1) with a strain rate of 1.2 × 10−3 s−1, using a universal testing machine (Shimadzu Autograph AG-X 10 kN) equipped with a thermostatic chamber. The strain was measured using a contactless video extensometer (Shimadzu TRViewX240S). The tests were performed in a sequence from the highest (373 K) to the lowest (173 K) temperature with a step of 20 K. At each temperature, the stress–strain curve was measured at first, and then the pseudo-adiabatic temperature change of the sample by the removal of stress was monitored using a T-type thermocouple attached to the surface of the specimen by spot-welding. The superelastic strain was limited to approximately 2.5% to prevent damaging the sample. A strain rate of 1.2 × 10−1 s−1 was employed to approach the adiabatic condition.11 Cyclic compression tests to measure the pseudo-adiabatic temperature change at RT (298 K) and 176 K were carried out for the single-crystal specimen of Co55.4Cr23.1Al11.5Si10 (Sample 2). The strain rates in the loading and unloading processes were approximately 2.5 × 10−2 s−1 and 1.2 × 10−1 s−1, respectively.

The superelastic properties at cryogenic temperatures were investigated by a temperature variable testing machine (Instron 5982 10 kN), with the strain measured using a clipped extensometer (Epsilon 3442–010M-025-LHT). Compression tests were conducted for the single-crystal specimen of Co55.4Cr23.1Al11.5Si10 (Sample 2) with a strain rate of 1.8 × 10−3 s−1 in an order from the lowest (10 K) to highest (275 K) temperature, except for RT (293 K), which was performed first before cooling to 10 K. For this sample, the superelastic strain was set to approximately 0.5% to prevent plastic deformation due to the high critical stress of martensitic transformation.

Specific-heat measurements from 2 to 380 K were conducted on Sample 3 and Sample 4 with the relaxation method using a physical properties measurement system (PPMS, Quantum Design). The volume fraction of the martensite phase was estimated from the magnetization measured by a vibrating sample magnetometer (VSM).

1. Superelastic behavior at around RT

First, we show the superelastic behavior at RT related to the martensitic transformation on a single-crystal Co55Cr23.5Al11.5Si10 alloy (Sample 1) in Fig. 3(a), where the superelastic strains (εSE) of εSE = 2.5%, 3.8%, and 4.6% beyond the elastic regime were applied. The plateaus appear due to the martensitic transformation at around 440 MPa. Subsequently, an increase in stress was found at around εSE = 2.5%. This is not due to the end of the plateaus but to the appearance of other variants of martensite. Therefore, a remarkable increase in stress hysteresis was found when the superelastic strain is greater than 2.5%. From this result, a superelastic strain of εSE = 2.5% was used to evaluate the superelastic behaviors at various temperatures. The superelastic behaviors on Sample 1 from 153 to 373 K are shown in Fig. 3(b). In a wide temperature range, stress plateaus due to the uniaxial-stress-induced martensitic transformation and completely reversible strains upon loading and unloading with stress hysteresis were observed. The critical stresses, that is, the forward martensitic transformation starting stress σMs and the reverse martensitic transformation finishing stress σAf, are determined by extrapolation methods. σMs and σAf are plotted against the temperature in Fig. 3(c). The equilibrium stress σ0, which is assumed to be the average of σMs and σAf,34 is also plotted in Fig. 3(c). Starting from approximately 285 K (above the hatched temperature region), as the temperature increases, one can see that the critical stresses show a mild increasing tendency. However, when the temperature is below approximately 285 K (below the hatched temperature region), the critical stresses increase with decreasing temperature. This behavior is one of the characteristics of an alloy showing reentrant martensitic transformation, such as for Co-Cr-Ga-Si29,30 and Co-Cr-Al-Si with a similar composition to the current alloy.35 

FIG. 3.

(a) Stress–strain curves up to εSE = 2.5%, 3.8%, and 4.6% (full martensitic transformation) were measured on Sample 1. The plateaus appear due to the martensitic transformation at around 440 MPa. Subsequently, an increase in stress was found at around 3.5% of total strain. This occurred because of the appearance of other variants of martensite. Therefore, a remarkable increase in stress hysteresis was found. (b) Temperature dependence of superelastic properties for Sample 1 under a superelastic strain of εSE = 2.5%. These compression tests were conducted from 373 to 153 K. Forward martensitic transformation starting stress (σMs) and reverse martensitic transformation finish stress (σAf) were defined by the extrapolation method. (c) σMs, σAf, and σ0 = (σMs + σAf)/2 are plotted against the temperature.

FIG. 3.

(a) Stress–strain curves up to εSE = 2.5%, 3.8%, and 4.6% (full martensitic transformation) were measured on Sample 1. The plateaus appear due to the martensitic transformation at around 440 MPa. Subsequently, an increase in stress was found at around 3.5% of total strain. This occurred because of the appearance of other variants of martensite. Therefore, a remarkable increase in stress hysteresis was found. (b) Temperature dependence of superelastic properties for Sample 1 under a superelastic strain of εSE = 2.5%. These compression tests were conducted from 373 to 153 K. Forward martensitic transformation starting stress (σMs) and reverse martensitic transformation finish stress (σAf) were defined by the extrapolation method. (c) σMs, σAf, and σ0 = (σMs + σAf)/2 are plotted against the temperature.

Close modal

2. Superelastic behavior at cryogenic temperatures

The superelastic behavior at cryogenic temperatures was evaluated by the use of a Co55.4Cr23.1Al11.5Si10 single-crystal sample (Sample 2). As shown in Fig. 4(a), the compression tests were performed from 10 to 293 K, where a superelastic strain of εSE = 0.5% was applied. At each temperature, compression tests were conducted more than two times and the last one was shown in Fig. 4(a). Superelasticity was successfully obtained down to 10 K. In Fig. 4(b), σMs, σAf, and σ0 (=(σMs + σAf)/2) were plotted against the testing temperature. The critical stress showed an inverse temperature dependence and continued to increase with decreasing testing temperature until about 10 K. The stress hysteresis σhys (=σMsσAf) gradually increases with decreasing testing temperature below approximately 100 K. A same behavior has also been reported in Ti-Ni36 and Ni-Co-Mn-In37 alloys; however, the tendency of the enlargement of σhys at low temperatures was found smaller in the current Co-Cr-Al-Si alloy.

FIG. 4.

For Sample 2, (a) superelasticity was successfully obtained from 293 to 10 K, where a superelastic strain of εSE = 0.5% was used. Critical stress showed inverse temperature dependence and continued to increase with increasing testing temperature until 10 K. This means ΔS shows positive values, and thus an inverse eCE can be expected until about 10 K. (b) σMs, σAf, σ0 (=(σMs + σAf)/2) and σhys (=σMsσAf) are plotted against temperature.

FIG. 4.

For Sample 2, (a) superelasticity was successfully obtained from 293 to 10 K, where a superelastic strain of εSE = 0.5% was used. Critical stress showed inverse temperature dependence and continued to increase with increasing testing temperature until 10 K. This means ΔS shows positive values, and thus an inverse eCE can be expected until about 10 K. (b) σMs, σAf, σ0 (=(σMs + σAf)/2) and σhys (=σMsσAf) are plotted against temperature.

Close modal

1. Transition from conventional to inverse elastocaloric effect

According to the Clausius-Clapeyron equation38,39

dσ0dT=ΔSPMVεPM,
(1)

the temperature dependence of the transformation critical stress σ0(σMs+σAf)/2 is proportional to entropy change ΔSPMSMSP, where εPM and V are the transformation strain during martensitic transformation and molar volume, respectively. When the slope of σ0 to the temperature changes from positive to negative, as shown in Fig. 3(b), the sign of ΔS changes from negative to positive because both εPM and V are always positive. Thus, the following can be expected from the results in Figs. 3(a) and 3(b).

  • At temperatures above approximately 285 K, applying uniaxial stress results in the PH (parent phase at higher temperatures) → M (martensite phase) transformation. This is a process with decreasing entropy in isothermal condition. Thus, a heating effect (a conventional eCE) is expected under adiabatic condition, as schematically shown in Fig. 1(a).

  • However, at temperatures below approximately 285 K, the loading of uniaxial stress results in the PL (parent phase at lower temperatures) → M transformation. This is a process with increasing entropy, and thus a cooling effect (an inverse eCE) is expected under adiabatic condition, as shown in Fig. 1(b).

For unloading processes, opposite signs of temperature changes are expected.

The elastocaloric properties were experimentally examined via compression tests on Sample 2, where the adiabatic temperature change was monitored by a thermocouple directly spot-welded on the sample. Since a direct evaluation of the eCE requires a condition close to the adiabatic process, a fast loading/unloading of the uniaxial stress is preferred.11 For safety and technical reasons, the strain rates of 2.5 × 10−2 s−1 and 1.2 × 10−1 s−1 in the loading and unloading processes were employed, respectively. Figures 5(a) and 5(b) show the strain profile of the cyclic compression tests and the corresponding temperature changes at 176 K, respectively. The crystal orientation along the loading direction of this sample is shown in the inset of Fig. 4(a). The inverse eCE, where there is a negative temperature change in the loading process and a positive temperature change in the unloading process, was clearly observed at 176 K, even though the sample was heated by the dissipation energy. Note that the absolute value of temperature change tends to be smaller in the loading process because the loading was about one order slower than the unloading for safety reasons, and the test condition was not perfectly adiabatic.11 In addition, temperature changes during the loading and unloading were also monitored at RT (=298 K), and a conventional eCE was confirmed, as shown in Figs. 5(c) and 5(d). Therefore, we can conclude that the eCE of Co55.4Cr23.1Al11.5Si10 intrinsically changes from a conventional eCE to an inverse eCE with decreasing testing temperature.

FIG. 5.

Temperature changes during cyclic compression tests for Sample 2 at 176 K and RT. Inverse elastocaloric effect, where temperature decreased and increased in loading and unloading processes, was clearly obtained at 176 K, as shown in (a) and (b). On the other hand, the conventional elastocaloric effect, where temperature increased and decreased in loading and unloading processes, was observed at RT, as shown in (c) and (d). Here, the difference in temperature change between loading and unloading processes at 176 K is primarily caused by the difference in adiabaticity due to different strain rates between them.11 

FIG. 5.

Temperature changes during cyclic compression tests for Sample 2 at 176 K and RT. Inverse elastocaloric effect, where temperature decreased and increased in loading and unloading processes, was clearly obtained at 176 K, as shown in (a) and (b). On the other hand, the conventional elastocaloric effect, where temperature increased and decreased in loading and unloading processes, was observed at RT, as shown in (c) and (d). Here, the difference in temperature change between loading and unloading processes at 176 K is primarily caused by the difference in adiabaticity due to different strain rates between them.11 

Close modal

2. Temperature dependence of elastocaloric effect

From the results of compression tests on Sample 2, we could confirm that the change from negative to positive ΔTad in unloading process was due to the intrinsic change from conventional to inverse eCE. Therefore, ΔTad was monitored during fast unloading processes to evaluate the temperature dependence of eCE close to the adiabatic process. Here, a same Co55Cr23.5Al11.5Si10 single-crystal sample (Sample 1), on which superelasticity was evaluated in Fig. 3, was used. The ΔTad during the reverse martensitic transformation (εSE = 2.5%) was monitored from 373 to 173 K. As shown in Fig. 6, at temperatures above 273 K, a negative ΔTad was observed, which is a conventional eCE. Although the amount of superelastic strain was kept almost constant, the absolute value of ΔTad decreased when the measurement temperature was lower. At 253 and 233 K, ΔTad was hardly noticeable. However, at low temperatures below 213 K, a positive ΔTad was observed, which indicates the inverse eCE.

FIG. 6.

The eCE during the unloading of compression stresses measured from 373 to 173 K for Sample 1 (Co55Cr23.5Al11.5Si10). Here, the amount of superelastic strain was kept almost constant (εSE = 2.5%). The negative ΔTad (a conventional eCE) at high temperatures switched to a positive ΔTad (an inverse eCE) below approximately 240 K.

FIG. 6.

The eCE during the unloading of compression stresses measured from 373 to 173 K for Sample 1 (Co55Cr23.5Al11.5Si10). Here, the amount of superelastic strain was kept almost constant (εSE = 2.5%). The negative ΔTad (a conventional eCE) at high temperatures switched to a positive ΔTad (an inverse eCE) below approximately 240 K.

Close modal

For a quantitative understanding of the occurrence of conventional and inverse eCEs, the specific heats under constant pressure CP of both the parent (CPP) and martensite phases (CPM) are required. Here, two Co55Cr23.5Al11.5Si10 samples of Sample 3 and Sample 4, which are in parent and martensite phases, respectively, were used. For this alloy system, the parent and the martensite phases exhibit ferromagnetism and paramagnetism, respectively.40 Thus, the volume fraction of the martensite phase was estimated by the saturation magnetization method, which is commonly used for austenitic steels for the evaluation of the volume fractions of the ferromagnetic martensite phase and the paramagnetic austenite phase.41Figure 7(a) shows the magnetization curves of the two samples at RT. The spontaneous magnetizations were determined by the Arrott plot42 to be 42.14 and 8.75 × 10−2 emu/g for Sample 3 and Sample 4, respectively. Therefore, it can be concluded that Sample 3 (undeformed sample) is in full parent phase, and Sample 4 (deformed sample) is in almost full martensite phase. Thus, specific heat measurements were conducted on these two samples.

FIG. 7.

(a) Magnetization measurements at the room temperature for Sample 3 and Sample 4 prepared for specific-heat measurements. Sample 3 (undeformed sample) is in ferromagnetic parent phase (shown as a red line), whereas Sample 4 (deformed sample) is in paramagnetic martensite phase (shown as blue line). Refer to the text for details. (b) CP of parent (Sample 3) and martensite (Sample 4) phases for the Co55Cr23.5Al11.5Si10 alloy. (c) The plot of CP/T vs T2 of parent (red) and martensite (blue) at lower temperatures. While a linear relationship was observed for the parent phase, a non-linear relationship was confirmed for the martensite phase.

FIG. 7.

(a) Magnetization measurements at the room temperature for Sample 3 and Sample 4 prepared for specific-heat measurements. Sample 3 (undeformed sample) is in ferromagnetic parent phase (shown as a red line), whereas Sample 4 (deformed sample) is in paramagnetic martensite phase (shown as blue line). Refer to the text for details. (b) CP of parent (Sample 3) and martensite (Sample 4) phases for the Co55Cr23.5Al11.5Si10 alloy. (c) The plot of CP/T vs T2 of parent (red) and martensite (blue) at lower temperatures. While a linear relationship was observed for the parent phase, a non-linear relationship was confirmed for the martensite phase.

Close modal

The results of specific heats are shown in Fig. 7(b). It was found that, at temperatures higher than 130 K, the relationship of CPP > CPM holds, whereas CPP < CPM was found at temperatures lower than 100 K. A critical temperature, where ΔCP(=CPMCPP) becomes zero, was found in the temperature range of 100 to 130 K (shown as the hatched region). The relationship between CP/T and T2 at low temperatures is shown in Fig. 7(c). CPM/T is about two times greater than CPP/T at low temperatures. A linear relationship holds well for parent phase, and this can be written as

CPCV=γT+βT3,
(2)

where CV is the specific heat at constant volume.43 Conventionally, the first and second terms on the right-hand side of Eq. (2) are considered to be the electronic and lattice contributions, respectively, where γ is the electronic coefficient. The apparent Debye temperature is estimated by using

θD=12π4R5β3,
(3)

where R is the gas constant. From the result of Fig. 7(c) and the use of Eqs. (2) and (3), γ and θD of the parent phase were estimated to be 7.56 mJ mol−1 K−2 and 378 K, respectively. However, on the other hand, a non-linear CP/T vs T2 relationship was confirmed for the martensite phase. Although the details are still unknown and remain a future work, some other factors are considered to contribute to the specific heat of martensite.43 

The results of specific heat measurements are used to evaluate the entropy change ΔS using the following relationship:

ΔS=SMSP=0TCPMCPPTdT.
(4)

The temperature dependence of ΔS is shown in Fig. 8 as black dots. As expected, ΔS is positive at low temperatures, with a maximum value appearing at approximately 120 K. ΔS begins to decrease as the temperature increases above 120 K, and eventually turns into negative values above approximately 240 K. We reported ΔS in a similar composition of Co56.5Cr22.5Al10.5Si10.5 alloy in a previous work, by differential scanning calorimetry (DSC) measurements.35 Those results were plotted in Fig. 8 as orange diamonds. ΔS estimated from specific heat measurements is well-matched to the previous results.

FIG. 8.

ΔS estimated using the results of CP measurements and the Clausius-Clapeyron equation with the temperature dependence of superelastic critical stress. ΔS of Co-Cr-Al-Si alloys determined by DSC measurements in previous work35 and Co-Cr-Ga-Si alloys29,31,44 are also shown. The sign reversal of ΔS was clearly obtained by this estimation.

FIG. 8.

ΔS estimated using the results of CP measurements and the Clausius-Clapeyron equation with the temperature dependence of superelastic critical stress. ΔS of Co-Cr-Al-Si alloys determined by DSC measurements in previous work35 and Co-Cr-Ga-Si alloys29,31,44 are also shown. The sign reversal of ΔS was clearly obtained by this estimation.

Close modal

On the other hand, the Clausius-Clapeyron equation [Eq. (1)] can be used to evaluate ΔS for the first-order martensitic transformation.38,39 According to the Clausius-Clapeyron equation [Eq. (1)], the temperature dependence of transformation equilibrium stress σ0(σMs+σAf)/2 is proportional to entropy change ΔSSMSP. Here, ΔS was estimated by the Clausius-Clapeyron equation as follows. The crystal structures of parent and martensite phases were reported to be L21 and D022, respectively.40 Their lattice parameters and relating transformation strain vary with temperature. Therefore, in situ x-ray diffraction (XRD) measurements were conducted as shown in the supplementary material, and lattice parameters obtained by in situ XRD measurements were used for calculating εP→M (6.0% – 6.6%, depending on temperature) and V (6.87 × 10−6 – 6.95 × 10−6 m3 mol−1, depending on temperature). Each value of dσ0/dT was assumed by the inclination between adjacent measured values of equilibrium stress in Fig. 3(c) on Sample 1, and ΔS was plotted as red dots in Fig. 8. Furthermore, the results of the stress–strain curves in Fig. 4 on Sample 2 was also used to estimate ΔS. ΔS for low temperatures was plotted as navy blue squares in Fig. 8, where εP→M of 5.7% – 6.5% (depending on temperature) was used.

The values of ΔS obtained from the specific heat measurements (ΔSCP) and the Clausius-Clapeyron relationship (ΔSCC) generally show the same temperature dependence. However, ΔSCC is more scattered, and the absolute values are slightly different from ΔSCP. This difference may originate from the friction between the sample and the jigs during the compression test. In addition, it may be attributed to a stress-dependent transformation strain. Although the reason is not fully clarified, we use ΔSCP for the following discussion because of its higher reliability and lower ambiguity in this situation.

The values of ΔSCP in Fig. 8 were used to evaluate ΔTad as

ΔTad=ΔSCPT+ΔWdisCP,
(5)

where ΔWdis is the dissipation energy due to the stress hysteresis during the martensitic transformation. Here, ΔWdis was characterized by half of the area of the hysteresis loop in the stress (σ)–strain (ε) curves in Figs. 3(b) and 4(a) by the following equation, because the hysteresis loop is caused by both forward and reverse martensitic transformations:

ΔWdis=σεdε2.
(6)

In the practical evaluation, the dissipation energy was timed by five for the stress–strain curves loaded to εSE = 0.5% in Fig. 4(a), in accordance with the curves to εSE = 2.5% in Fig. 3(b). The directly measured ΔTad and estimated ΔTad from specific heats in the unloading process are plotted together in Fig. 9(a). Here, the partial entropy changes of ΔSCP×2.5%εPM were used to estimate ΔTad in Fig. 9, because the ΔTad directly evaluated in Fig. 6 corresponds to the temperature changes associated with the partial martensitic transformation of εSE = 2.5%. Since a good consistency was found at temperatures where ΔTad was experimentally determined, the estimated ΔTad from specific heats below 173 K are also considered reliable. Here, it was observed that the directly measured ΔTad at 373 and 353 K show greater absolute values than those of the estimated ΔTad. This may be the cause of an increased quantity of transformed martensite due to the appearance of another variant [see Fig. 3(a)], although the same superelastic strain of εSE = 2.5% was applied. In Fig. 9(a), ΔTad significantly increases in the temperature region below 100 K due to the combination of increased hysteresis (see Fig. 4) and decreased specific heat [see Fig. 7(b)]. Therefore, this does not mean an increased heating ability for the inverse eCE. The purple dashed line in Fig. 9(a) shows the calculated ΔTad without the ΔWdis term in Eq. (5).

FIG. 9.

(a) From ΔS expected by CP measurements, the adiabatic temperature changes in the unloading process by a superelastic strain of εSE = 2.5% for Co-Cr-Al-Si were estimated and plotted against testing temperature. Previous reports for other alloy systems were also plotted.13–15,17–19,25,27,28 ΔTad in the loading process is summarized in (b).

FIG. 9.

(a) From ΔS expected by CP measurements, the adiabatic temperature changes in the unloading process by a superelastic strain of εSE = 2.5% for Co-Cr-Al-Si were estimated and plotted against testing temperature. Previous reports for other alloy systems were also plotted.13–15,17–19,25,27,28 ΔTad in the loading process is summarized in (b).

Close modal

As shown in Fig. 9(a), compared to the alloys showing only either a conventional or inverse eCE,13–15,17–19,25,27,28 the current Co-Cr-Al-Si alloy exhibits a conventional eCE at temperatures above approximately 250 K and a robust inverse eCE behavior at lower temperatures. Here, nanocrystalline Ni-Ti alloy also shows a conventional ΔTad at high temperatures and an inverse ΔTad at low temperatures; however, this sign reversal is different in mechanism from that of Co-Cr-Al-Si alloys. For Co-Cr-Al-Si alloy, both conventional and inverse eCEs occur by the latent heat of martensitic transformation. On the other hand, for nanocrystalline Ni-Ti alloy, conventional eCE occurs at around 300 K due to the latent heat of martensitic transformation, whereas the inverse one at cryogenic temperatures is caused by the volumetric entropy change in the tensile elastic deformation. The volumetric entropy change is small; therefore, for nanocrystalline Ni-Ti alloy, inverse temperature change occurs only at cryogenic temperatures where specific heats are small.

Because this abnormal phenomenon is caused by the unique martensitic transformation in Co-Cr-Al-Si alloys, opposite signs of temperature change can also be obtained during the loading. The temperature change in the loading process was estimated by both direct measurements and calculation using ΔS, as shown in Fig. 9(b). This was confirmed by a calculation using the Cp data in which a negative ΔTad appears in the temperature region from 100 to 200 K. The tendency was confirmed by the experimental results at 176 K and RT, as shown in Fig. 5. The reversal from negative to positive of ΔTad at temperatures below approximately 100 K is brought about by the overwhelmed dissipation energy over the latent heat of the martensitic transformation.

In the present Co-Cr-Al-Si alloys, the change from conventional to inverse eCEs occurs at approximately 240 K due to the sign reversal of ΔS from negative to positive. Here, we defined the temperature where ΔS becomes zero as TA. Xu et al. reported ΔS of Co-Cr-Ga-Si alloys,29,31,44 which is shown as a purple line in Fig. 8 with its TA. While the TA of Co-Cr-Al-Si is at approximately 240 K, the TA of Co-Cr-Ga-Si alloys is much higher.31,35 Therefore, TA is considered tunable for the intended use by selecting a proper alloy system and composition.

The elastocaloric cooling techniques using SMAs have been studied not only in materials science but also in system design,9,45,46 owing to their high potential for energy saving.10 Besides, the elastocaloric switching materials can show different signs of ΔTad so that the ambient temperature approaches to a specific critical temperature, and thus, can serve as a self-regulating sensor or a temperature controller. We expect the elastocaloric switching effect may open new possibilities of system design and the abovementioned applications.

The superelastic and elastocaloric properties were investigated on the Co-Cr-Al-Si alloys showing the unique re-entrant martensitic transformation behavior. They show a conventional eCE at high temperatures, whereas the absolute value of the adiabatic temperature change gradually decreases with decreasing testing temperature, and then shows a sign reversal below approximately 240 K. Thus, these alloys show an elastocaloric switching effect, where a conventional eCE switches to an inverse eCE by ambient temperature. From the results of specific heat measurements and temperature dependence of superelastic critical stress with the Clausius-Clapeyron equation, ΔS was found to change from negative to positive values at approximately 240 K, which represents the thermodynamic cause of the unique elastocaloric switching effect.

See the supplementary material for the results of in situ x-ray diffraction measurements and temperature dependence of lattice parameters of a bulk Co56.4Cr22.6Al10.5Si10.5 alloy.

This study was partially supported by Grants-in-Aid (Nos. 19H02412, 18K18933, and 20J11238) from the Japan Society for the Promotion of Science (JSPS). A part of the experiments was performed at the Center for Low Temperature Science, Institute for Materials Research, Tohoku University. This study was also partially supported by a research grant from the Hirose International Scholarship Foundation.

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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Supplementary Material