Latent heat and hysteresis width

Four material parameters^{Reference Qian, Geng, Wang, Ling, Hwang, Radermacher, Takeuchi and Cui9,Reference Wieczorek, Frenzel, Schmidt, Maaß, Seelecke, Schütze and Eggeler10} are important for elastocaloric cooling performance. The SMA must exhibit large latent heat ΔH; low hysteresis width, which corresponds to a low work input, W; and good functional and structural stability, sufficient for several years of service life (>10⁷ loading/unloading cycles). It also must be able to deliver the elastocaloric effect in an envisaged temperature regime.

It is well known that the martensitic transformation and thus pseudoelastic behavior is governed by alloy composition^{Reference Wieczorek, Frenzel, Schmidt, Maaß, Seelecke, Schütze and Eggeler10,Reference Kim, Jo, Park, Park and Han14} and microstructure.^{Reference Waitz, Kazykhanov and Karnthaler21,Reference Delville, Malard, Pilch, Sittner and Schryvers22} Various research groups^{Reference Wieczorek, Frenzel, Schmidt, Maaß, Seelecke, Schütze and Eggeler10,Reference Sehitoglu, Wu and Ertekin11,Reference Luo, Feng and Verma15} have made attempts to study the effects of alloy chemistry on cooling performance. Both latent heat and hysteresis width react sensitively to compositional changes.^{Reference Wieczorek, Frenzel, Schmidt, Maaß, Seelecke, Schütze and Eggeler10,Reference Frenzel, Wieczorek, Opahle, Maaß, Drautz and Eggeler23–Reference Ball and James29} Latent heats between 8.5 and 35 J/g,^{Reference Frenzel, Wieczorek, Opahle, Maaß, Drautz and Eggeler23} and thermal hysteresis widths ranging from ≈0 K to >70 K,^{Reference Frenzel, Wieczorek, Opahle, Maaß, Drautz and Eggeler23,Reference Zarnetta, Takahashi, Young, Savan, Furuya, Thienhaus, Maass, Rahim, Frenzel, Brunken, Chu, Srivastava, James, Takeuchi, Eggeler and Ludwig26} are reported in the literature. We note that the thermal hysteresis width, which is often used as a preferred indicator in compositional screenings,^{Reference Cui, Chu, Famodu, Furuya, Hattrick-Simpers, James, Ludwig, Thienhaus, Wuttig, Zhang and Takeuchi25,Reference Zarnetta, Takahashi, Young, Savan, Furuya, Thienhaus, Maass, Rahim, Frenzel, Brunken, Chu, Srivastava, James, Takeuchi, Eggeler and Ludwig26} is directly proportional to the mechanical hysteresis width^{Reference Jaeger, Maaß, Frenzel, Schmidt, Seelecke, Kastner and Eggeler27} and thus to the required input work, W (Figure 1a). The results of a recent study^{Reference Frenzel, Wieczorek, Opahle, Maaß, Drautz and Eggeler23} identify a dilemma that may limit the development of new elastocaloric SMAs. Figure 2 shows that a correlation exists between the latent heat and the hysteresis width. It is difficult to obtain the desired combination of small hysteresis width and large latent heat simultaneously. Nevertheless, Wieczorek et al.^{Reference Wieczorek, Frenzel, Schmidt, Maaß, Seelecke, Schütze and Eggeler10} recently found a good compromise in a NiTiCuV SMA with an exceptionally high COP value of 20. This value is about 4× higher than for binary NiTi.^{Reference Qian, Geng, Wang, Ling, Hwang, Radermacher, Takeuchi and Cui9} Schmidt et al.^{Reference Schmidt, Ullrich, Wieczorek, Frenzel, Schütze, Eggeler and Seelecke30} made a first attempt to study the cooling performance of this material.

Figure 2.

Key parameters for ferroic cooling—hysteresis width and latent heat.^{Reference Frenzel, Wieczorek, Opahle, Maaß, Drautz and Eggeler23} Alloy design requires good compromise (small hysteresis width and large latent heat) between both factors.

Functional stability

The lowest functional degradation of the material is very important for any application. For example, a pseudoelastic SMA would have to tolerate >15 million loading/unloading cycles in a cooling device operating at 0.2 Hz over five years with 50% average utilization. Research on quaternary NiTi-based SMAs revealed a pronounced effect of crystallographic compatibility on the hysteresis width and reversibility (i.e., functional stability in thermally induced phase transformations).^{Reference Zarnetta, Takahashi, Young, Savan, Furuya, Thienhaus, Maass, Rahim, Frenzel, Brunken, Chu, Srivastava, James, Takeuchi, Eggeler and Ludwig26} The crystallographic compatibility conditions can be derived from the transformation matrixes between austenite and martensite and are thus purely geometric. For crystallographic compatibility^{Reference Gu, Bumke, Chluba, Quandt and James31} (where the two phases fit without the need for slip or for establishing stressed transition layers), the middle eigenvalue of the transformation matrix λ₂ must equal one. This can be achieved by fine-tuning the composition. This λ₂ = 1 condition affects the heights of the energy barriers between the transforming phases, which determine the width of the transformation hysteresis.

A higher degree of compatibility—so-called supercompatibility—can be obtained by additionally fulfilling other conditions that promote good fit and thus provide an even higher degree of flexibility, as was first demonstrated for Zn₄₅Au₃₀Cu₂₅.^{Reference Song, Chen, Dabade, Shield and James32} The influence of supercompatibility on functional and structural fatigue in stress-induced austenite-martensite transformations has been demonstrated for TiNiCuCo^{Reference Chluba, Ge, de Miranda, Strobel, Kienle, Quandt and Wuttig19} and ZnAuCu,^{Reference Ni, Greer, Bhattacharya, James and Chen33} and it was recently reviewed in Reference Reference Gu, Bumke, Chluba, Quandt and James31. The composition Ti_54.7Ni_30.7Cu_12.3Co_2.3 showed no measurable fatigue for 10 million pseudoelastic cycles^{Reference Chluba, Ge, de Miranda, Strobel, Kienle, Quandt and Wuttig19} (Figure 3). This indicates that supercompatibility between austenite and martensite has an important influence on the fatigue behavior. From investigations of different TiNiCu and TiNiCuCo alloys with a λ₂-value close to one, the functional degradation behavior was found to also depend on microstructural parameters such as grain size^{Reference Chluba, Ge, Dankwort, Bechtold, de Miranda, Kienle, Wuttig and Quandt34} and the nature of precipitates.^{Reference Chluba, Ge, de Miranda, Strobel, Kienle, Quandt and Wuttig19} It was found that Ti₂Cu precipitates, which form in Ti-rich alloys, lead to a near-to-perfect reversibility and repeatability up to >10 million pseudoelastic cycles (Figure 3). The coherency of Ti₂Cu precipitates in both phases, austenite and martensite, accounts for this excellent structural and functional property. These Ti₂Cu precipitates guide the phase transformation in a well-defined manner and thus act like sentinels, assuring that the austenite-martensite transformation repeatedly follows the same path during each cycle.^{Reference Chluba, Ge, de Miranda, Strobel, Kienle, Quandt and Wuttig19}

Figure 3.

Ultralow fatigue of Ti-rich TiNiCu and TiNiCuCo alloys, as demonstrated by next-to-identical first and 10⁷th pseudoelastic transformation cycles.^{Reference Chluba, Ge, de Miranda, Strobel, Kienle, Quandt and Wuttig19} These materials meet requirements for long-term stability in ferroic cooling applications.

Bulk material-based cooling demonstrators

The first successful large-scale elastocaloric cooling devices have been developed and demonstrated.^{Reference Qian, Geng, Wang, Muehlbauer, Ling, Hwang, Radermacher and Takeuchi35} The concept forming the basis of these developments is mechanical loading and unloading of SMA tube elements in compression and use of the absorbed and released latent heats to cool a hydraulic fluid. In contrast, the work presented in this article focuses on NiTi-based ribbons or wires that are loaded in tension to develop scalable air-cooling devices. Inherently coupled to this design goal is the optimization of the process parameters in terms of cooling power and COP. This requires optimization of the amount of straining, the strain rate, and efficient synchronization between mechanical loading/unloading and heat transfer.

Extending the usual framework of calculating COP values, a graphical method similar to that used for conventional vapor compression cycles has been developed to illustrate relevant work and heat quantities in stress/strain and temperature/entropy diagrams.^{Reference Schmidt, Schütze, Seelecke and Johnson36} This helps to predict optimized hybrid cycles by appropriately combining adiabatic and isothermal process branches. A comprehensive test rig was developed^{Reference Schmidt, Schütze and Seelecke17,Reference Schmidt, Schütze, Seelecke and Zagrai37–Reference Schmidt, Schütze and Seelecke39} to experimentally validate process efficiency and to study the effects of material training/functional degradation on mechanical, caloric, and thermal properties (Figure 4).^{Reference Schmidt, Ullrich, Wieczorek, Frenzel, Schütze, Eggeler and Seelecke30} In the device shown in Figure 4a, a pseudoelastic NiTi ribbon is subjected to mechanical cycling. During this process, it moves between two copper blocks, Figure 4b, which act as a heat sink (in contact with the SMA during straining) and a heat source (in contact during unloading of the ribbon), respectively. Figure 4c exemplarily shows a color-coded IR image, which documents temperature changes in the ribbon and the two Cu blocks. A challenge for the design of future elastocaloric cooling devices is the implementation of these concepts into continuously operating units that outperform current vapor compression systems. The first ideas are currently being implemented into a demonstrator with a patent-pending drive element to map experimentally optimized processes.^{Reference Schmidt, Kirsch, Seelecke and Schütze38} Simultaneously, due to the large number of parameters involved in the design, simulation tools have to be developed to narrow the design space.

Figure 4.

Elastocaloric test rig for NiTi ribbon characterization.^{Reference Schmidt, Schütze and Seelecke17} During cyclic operation, a shape-memory alloy (SMA) ribbon moves between two copper blocks, which act as a heat sink (in contact with the SMA during straining) and a heat source (in contact during unloading of the ribbon). (a) Concept sketch with infrared camera, two linear axes for loading/unloading and heat transfer via copper blocks. (b) Ribbon and copper blocks at higher magnification. (c) Thermography image of the setup during operation. A significant temperature difference between both blocks is established after a few elastocaloric cycles.

Thin-film cooling devices

The implementation of elastocaloric cooling on a miniature scale involves opportunities and challenges. The use of freestanding elastocaloric films allows for efficient heat transfer between film and heat sink/-source, which is of critical importance for high cooling performance. However, parasitic heat fluxes are difficult to control in small systems, and system integration is often challenging. In addition, localized phase-transformation events may affect heat transport.^{Reference Ossmer, Lambrecht, Gultig, Chluba, Quandt and Kohl13,Reference Ossmer, Chluba, Gueltig, Quandt and Kohl40,Reference Wendler, Ossmer, Chluba, Quandt and Kohl41} One important feature of film-based SMAs is that they allow for almost pure tensile loading even when subjected to out-of-plane deflection.

Figure 5a shows an example of a miniature cooling device where this loading principle is applied. Heating and cooling power is separated by bringing the SMA film alternatingly in contact with the heat source during unloading, upper position x ₁, and with the heatsink during loading, lower position x ₂. Switching heat fluxes and loading the film in one single mechanism makes the setup simple, which is crucial for miniaturization. A typical elastocaloric cycle includes moving the film up and down, which results in stepwise transfer of heat from the heat source to the heat sink. Thus, the temperature T _source decreases and T _sink increases, as can be seen in Figure 5b for various operation frequencies.

Figure 5.

(a) Schematic of a miniature-scale cooling device.^{Reference Ossmer, Wendler, Gueltig, Lambrecht, Miyazaki and Kohl18} Moving the shape-memory alloy film periodically between the lower (x ₂) and upper (x ₁) position loads/unloads the film, and, thus, heat is generated/absorbed. Due to alternate switching of surface contacts in both positions, the moving film causes a directed heat flux from heat source to heat sink. (b) Experimentally observed temperature changes of the device for various operation frequencies reaching a maximum temperature span of 14 K.

The device reaches a maximum temperature span ΔT of 14 K at room temperature, a maximum cooling power of 18 Wg^–1, and a maximum COP of 6 at zero thermal load neglecting actuation efficiency. Keeping in mind that the film sample has a mass of only 0.015 g, the results in Figure 5b highlight the potential of small-scale elastocaloric cooling devices. Furthermore, it has been shown that work recovery can minimize the required mechanical power input in film-based cooling devices.^{Reference Ossmer, Wendler, Gueltig, Lambrecht, Miyazaki and Kohl18,Reference Bruederlin, Ossmer, Wendler, Miyazaki and Kohl42} For practical applications, the heat-source element can be interconnected to a thermal load (e.g., an electronic chip or a heat-transfer fluid). Currently, the elastocaloric cooling device is limited by the adiabatic temperature span of the SMA material,^{Reference Ossmer and Kohl43} in this case, a NiTiCuCo alloy. This limit can be overcome by cascading several SMA films with tailored phase transition temperatures in a stack.