Shape memory alloys (SMAs) have many unique thermomechanical characteristics such as the shape memory effect, pseudoelasticity, and superelasticity. These alloys can ‘memorize’ their deformation and return to their original form when subjected to thermomechanical or magnetic variations. The non-MSMAs under uniaxial stress undergoes a reversible martensitic transition, which is a first-order structural transition. Because of the large latent heat of the transition, these alloys exhibit the MCE. The lattice distortion associated with the transition is mostly caused by a pure shear. The transition temperature and the MCE are strongly sensitive to uniaxial stress but insensitive to hydrostatic pressure.^[8] Recently, research on the MCE of non-MSMAs has focused on Cu-based and Ti–Ni-based alloys. The thermal effect in single crystals of β-CuZnSn was reported in 1981.^[9] Later experiments^[10–13] have proved that Cu-based alloys such as Cu–Zn–Al single crystal have the MCE. ΔS and ΔT for Cu-based alloys can exceed 20 J·kg⁻¹·K⁻¹ and 14 K, respectively. Because of the large value of ΔS and broad temperature span, the Cu–Zn–Al polycrystal has an enormous relative cooling power for the ECE.^[11] Another important class of non-MSMAs is based on Ti–Ni.^[7,14–22] These alloys transform from a B2 (Pm2m) to a B19′ (P2/m) martensitic phase upon cooling.^[8] The reversible B2→ B19′ transition has a large latent heat, and the transition entropy change is quite high (in the range of 60 J·kg⁻¹·K⁻¹–80 J·kg⁻¹·K⁻¹) at moderate stress (∼ 170 MPa).^[19] ΔT measured by direct methods can reach 25 K for Ni–Ti wires.^[16,17] In addition, the cooling performance of Ni–Ti-based alloys has been studied. One study^[7] revealed that Ni–Ti wires have a quite high cooling efficiency. Furthermore, the values of temperature changes for sputtered NiTi films, especially sputtered NiTiCu films, have good reproducibility even though the alloys have been trained for many cycles.^[15,16] Recently, the ECE caused by the rubber-like behavior of the R-phase nanocrystalline wires of Ti–50.8Ni (at.%) has been reported. Because of the small energy dissipation, the ECE related to the R-phase is more efficient than that induced by the B2 → B19′ transition.^[23] The thermodynamic characteristics are compared for selected non-MSMAs in Table 1.

Table 1.

Table 1.

Table 1. Thermodynamic characteristics for elastocaloric effect compounds. Temperature for the forward (cooling) transition (Tt); transition temperature shift with uniaxial stress (dT/dσ); applied stress (Δσ) to obtain the temperature and entropy changes in this table; adiabatic temperature change measured using direct methods (ΔTd) and estimated from the measured isothermal entropy change (ΔTe); isothermal entropy change determined using indirect methods (ΔSi) and estimated from measured temperature changes (ΔSe). . Compound Sample status Tt/K (dT/dσ)/(K/GPa) |ΔTd|/K |ΔTe|/K |ΔSi|/J·kg−1·K−1 |ΔSe|/J · kg−1 · K−1 Δσ/GPa Reference Cu68.13Zn15.74Al16.13 single crystal 234 500 6 11 20.7 11 0.12 [10,13] Cu68Zn16Al16 ploy crystal 205 513 6 12 17.9 13 0.25 [11] Cu83Al14Ni3 single crystal 250 500 ± 50 14 – – 26 0.15 [93] Ni50.38Ti49.62 single crystal 220 120 14 – – 51 0.5 [14] NiTi wire 300 – 25.5 – – 46 0.55 [16] Ni48.9Ti51.1 wire 295 132 25 – – 46 0.8 [17] Ni47.9Ti52.6 wire 320 200 – 38 60–80 – 0.18 [19] Ni47.9Ti52.6 wire 310 50 – 8 12 — 0.18 [19] Ni50Ti50 film 260 – 16 – – 26 0.3 [94] Fe49Rh51 poly crystal 315 −20 5.2 – – 7 0.53 [44] Fe68.8Pd31.2 single crystal 230 −1000 3 – – 5 0.2 [26] Ni50Fe19Ga27Co4 single crystal 300 400 10 – – 15 0.3 [95] Co40Ni33.17Al26.83 single crystal 303 400 3 – – 5 0.05 [14] Ni43Mn40Sn10Cu7 poly crystal 322 200 – 1.5 2 – 0.01 [28] Ni46Mn38Sb12Co4 poly crystal 300 130 – 15 20 – 0.1 [30] Ni43.5Mn39Sn11Co6.5 poly crystal 260 100 – 6 12 – 0.3 [37] Ni45Mn44Sn11 poly crystal 270 – 6 – – 13 0.26 [36] Ni45Mn36.4In13.6Co5 poly crystal 250 240 4 – – 5 0.15 [33] (Ni50Mn31.5Ti18.5)99.8B0.2 poly crystal 308 31.5 – 45 – 0.7 [92]

Table 1. Thermodynamic characteristics for elastocaloric effect compounds. Temperature for the forward (cooling) transition (Tt); transition temperature shift with uniaxial stress (dT/dσ); applied stress (Δσ) to obtain the temperature and entropy changes in this table; adiabatic temperature change measured using direct methods (ΔTd) and estimated from the measured isothermal entropy change (ΔTe); isothermal entropy change determined using indirect methods (ΔSi) and estimated from measured temperature changes (ΔSe). .

Magnetic shape memory alloys (MSMAs) are interesting materials with mechano-caloric or multi-caloric effects. In MSMAs, the caloric effect is usually induced by a magnetostructural phase transition. Many characteristics of MSMAs are similar to those of non-MSMAs such as the martensitic transition and shape memory effects; however, the structural transition in MSMAs is accompanied by changes in the magnetism from the antiferromagnetic (AFM) state to the ferromagnetic (FM) state. MSMAs can be divided into two categories: Fe-based alloys, such as Fe–Pt and Fe–Pd, and Ni-based and some Co-based alloys, which are usually Heusler alloys. For MSMAs, the high-temperature phase is not martensitic but cubic and FM. As for the magnetism of the martensitic phase, it depends on whether the martensitic transition temperature is above or below the Curie temperature T_c in a specific material. The martensitic and magnetic transition in Fe-based MSMAs such as Fe–Pt and Fe–Pd were studied many years ago.^[24–26] The martensitic transition from a cubic structure (Fm3m) to a face-centered tetragonal martensitic structure (P4/mmm) occurs on cooling for Fe-based MSMAs. In Fe–Pd alloys, the martensitic transition is weak first-order with a low entropy and small transformation hysteresis.^[26] Because of the small volume changes of the unit cell in this transition, the BCE is not expected. The ECE was studied in Fe–Pd single crystal^[26] and Fe₇Pd₃ polycrystal.^[25] In Fe–31.2Pd (at.%) alloy, a significant ECE was reported. Because of lattice softening caused by a weak first-order martensitic transition near room temperature, an adiabatic temperature change of more than 3 K and ΔS of 4 J·kg⁻¹·K⁻¹–5 J·kg⁻¹·K⁻¹ with excellent reproducibility were observed under uniaxial stress of 200 MPa in this alloy. Apart from Fe-based MSMAs, the MCE for Ni-based MSMAs belonging to Heusler alloys has been heavily investigated.^[14,27–43] Early in their study, these investigated alloys were usually very brittle and could only support very low stresses (≈ 10 MPa).^[42,43] Later, tougher alloys were synthesized using suitable doping or other methods with the maximum applied stresses exceeding 300 MPa. The magnitude of the MCE in these MSMAs depends on the sensitivity of the martensitic transition to hydrostatic pressure or uniaxial stress. The MCE was observed in Ni-based magnetic shape memory alloys and can be compared with giant magnetocaloric effects. Upon uniaxial compression of 100 MPa, the stress-induced entropy change ΔS is 21 J·kg⁻¹·K⁻¹ and the estimated ΔT is approximately 15 K in polycrystalline Ni–Mn–Sb–Co MSMA. The result is better than other reports on the ECE in Ni-based MSMAs.^[24,29,39] For applied hydrostatic pressure, the BCE for Ni–Mn–In MSMA resulted from discontinuities of both the volume of the unit cell and entropy at a magnetostructural transition. This alloy exhibited both barocaloric and magnetocaloric effects. Under hydrostatic pressure of 260 MPa, ΔT can reach 4.5 K and ΔS is approximately 24 J·kg⁻¹·K⁻¹. However, when a magnetic field of 0.94 T is applied, the change of temperature for mCE is only 1.3 K.^[27] It is worth noting that the peak values of ΔT and ΔS increase as pressure increases in the range of 20 MPa–260 MPa. These studies suggest that some magnetocaloric materials could exhibit the BCE. Thermodynamic characteristics are compared for selected MSMAs in Tables 1 and 2.

Table 2.

Table 2.

Table 2. Thermodynamic characteristics for the barocaloric effect compounds. . Compound Sample status Tt/K (dT/dp)/(K/GPa) |ΔTd|/K |ΔTqd|/K |ΔTe|/K |ΔSqd|/K/J·kg−1·K−1 Δp/GPa Reference Fe49Rh51 poly crystal 310 64 – 9 8 12 0.25 [45] LaFe11.33Co0.47Si1.2 Poly crystal 250 −94 2.2 – 5 8.6 0.2 [48] Mn3GaN – 290 −65 1.3 4.5 14 22.3 0.14 [49] Gd5Si2Ge2 poly crystal 260 35 1 – 10 11 0.2 [50,51] MnCoGe0.99In0.01 poly crystal 310 −77 8.4 18.5 36 52 0.3 [96] (MnNiSi)0.62 Poly crystal 338 -75 3 16 33 74 0.27 [97] (FeCoGe)0.38 Ni49.26Mn36.08In14.66 poly crystal 290 18 – 4.5 18 24 0.26 [27] Ni50Mn33In17 poly crystal 275 19 – 3 9 13 0.25 [34] Ni51Mn33In16 poly crystal 330 18 – 4 29 35 0.25 [34] Ni42.7Co8.87Mn31.67 – 400 30 – – 16 16 0.25 [98] Ga14.98In2.01 BaTiO3 single crystal 400 −55 – 1 2 1.6 0.1 [61] BaTiO3 single crystal 280 −30 – – 1 1.3 0.1 [61] PbTiO3 single crystal 770 −140 2.7 – 1.9 4 0.26 [63] (NH4)2SO4 single crystal 220 −50 ± 10 – – 8 60 0.15 [90] [TPrA]Mn[dac]3 poly crystal 330 231 – 5 – 37 0.007 [66] (NH4)2NbOF5 single crystal 259.3,220.5 −45 – 15 25 100 1 [79] (NH4)2MoOF4 single crystal 271.4 92.8 – 17 17 73 0.9 [80] (NH4)2WOF4 single crystal 201.5 13 – 13 9 40 0.5 [80] (NH4)2SnF6 single crystal 110 ± 1 −157 – 11 11 61 0.14 [99] Rb2KTiOF5 – 215 110 – 18 15 46 0.6 [82] AgI polymorph 420 −128 ± 5 – 18 – 60 0.25 [87] NPG – 320 93 ± 18 – ∼ 45 – ∼ 510 0.6 [89]

Table 2. Thermodynamic characteristics for the barocaloric effect compounds. .

Some magnetic materials also exhibit the MCE because of a first-order magnetostructural transition. The transition can cause changes in the symmetry of the crystal structure or just a uniform expansion or contraction of the unit cell. These compounds, which do not involve changes in the symmetry of the crystal structure, mainly include Fe–Rh, La–Fe–Si, and Mn–Ga–N compounds. The ECE in Fe–Rh alloys was reported early on.^[44] The magnetic transformation from AFM to FM is accompanied by a negative temperature change of 5.2 K under stress of 529 MPa. Later, the BCE with good reproducibility in Fe–Rh alloys was observed.^[45,46] Large values of |ΔT| ∼ 8 K–10 K and |ΔS| ∼ 12 J·kg⁻¹·K⁻¹ were reported under hydrostatic pressure (250 MPa). Another class of these compounds is the La–Fe–Si-based itinerant ferromagnets. The LaFe_{13 – x}Si_x compounds have the cubic NaZn₁₃ structure () and undergo a first-order magnetostructural transition related to BCE from a paramagnetic (PM) phase to FM phase. These contributions of the magnetism, lattice, and electrons to entropy changes in transition reduce the entropy for the FM low-temperature phase. Theoretical calculations indicate that ΔT and ΔS of the BCE can reach 16 K and 55 J·kg⁻¹·K⁻¹, respectively, under a pressure of 450 MPa in La(Fe_0.89Si_0.11)₁₃.^[47] Because of doping with Co to bring the transition temperature close to room temperature, many studies on the BCE in La–Fe–Si have focused on La–Fe–Co–Si compounds. The ΔS obtained using quasi-direct methods and ΔT measured by direct methods can reach 6 J·kg⁻¹·K⁻¹ and 2 K, respectively, under a pressure of 200 MPa in LaFe_11.33Co_0.47Si_1.2.^[48] Mn₃GaN is another itinerant antiferromagnetic system with an antiperovskite structure (). In this compound, a magnetic transition related to the BCE occurs from a PM phase to an AFM phase on cooling near 290 K. The magnetostructural transition enhanced by magnetic frustration leads to an isotropic expansion (∼ 1%) of the unit cell.^[49] ΔS obtained by quasi-direct methods and ΔT measured by direct and quasi-direct methods can reach 22 J·kg⁻¹·K⁻¹, 1.5 K, and 4.5 K, respectively, under a pressure of 150 MPa in Mn₃GaN. Unlike the above magnetic materials, there are some materials whose BCE is accompanied by changes in the crystal structure symmetry. For example, the BCE in Gd₅Si₂Ge₂ compounds was studied under pressure.^[50–52] These compounds undergo a phase transition from a monoclinic (P112₁/a) PM phase toward an orthorhombic (Pnma) FM phase upon cooling.^[53] At 200 MPa, the maximum of the entropy changes of 11 J·kg⁻¹·K⁻¹ and ΔT^d of approximately 1 K are less than those estimated from entropy data. The last mainly magnetic material family with the BCE is the Mn-based ternary compounds whose formula can be expressed as MnTX (T = Ni, Co and X = Si, Ge). These compounds undergo a second-order magnetic phase transition from a PM phase toward another magnetic phase relying on the particular composition. When the temperature drops, there is a structural transition from a Ni₂In-type hexagonal phase (P6₃/mmc) to a TiNiSi-type orthorhombic structure (Pnma) in MnTX. Through doping, varying the composition, and isostructural substitution, the alloys only exhibit a magnetostructural transition. The BCE was reported in MnCoGe_0.99In_0.01 compound.^[54] The BCE induced by magneto-structure transition has a large ΔS (50 J·kg⁻¹·K⁻¹–74 J·kg⁻¹·K⁻¹) and ΔT (16 K–19 K), which were measured using quasi-direct methods at pressures of 300 MPa. ΔT is higher than that measured by direct methods (3 K–8 K) and lower than that estimated from the entropy change (33 K–36 K). The transition temperature, i.e., the work temperature of magnetic materials, can be adjusted by doping or using other methods. The feature is useful under some special conditions. The thermodynamic characteristics are compared for selected materials in Tables 1 and 2.

Perovskite materials have the same crystal structure as calcium titanium oxide, known as the perovskite structure. The general chemical formula for perovskite materials is ABX₃, where A and B are two cations of very different sizes and X is an anion that bonds to both A and B.^[55] For cubic structure stability, the requirement of relative ion size is very stringent. Therefore, slight distortion and deformation can result in several lower-symmetry structures, in which the coordination number of A or B cations or both is reduced. These characteristics lead to a rich phase diagram in perovskite materials. Furthermore, many perovskite ceramics such as BaTiO₃ exhibit ferroelectricity because the complex structure produces electric dipoles. The perovskite materials mentioned in this section are also ferroelectric materials, which were investigated as eCE materials. Because of the strong coupling between polarization and structure, ferroic phase transitions may occur in perovskite materials. Therefore, the MCE is expected in perovskite materials. The MCE of perovskite materials such as BaTiO₃, (Ba_0.85Ca_0.15)(Zr_0.1Ti_0.9)O₃, and PbTiO₃ has been investigated.^[56–64] At high temperature (> 400 K), BaTiO₃ has a centrosymmetric ABO₃ perovskite crystal structure (). When the temperature decreases from above 400 K to below 180 K, this material will exhibit two ferroelectric–structural and three structural phase transitions. At the first ferroelectric phase transition temperature (∼ 400 K), the cubic structure transforms to a tetragonal structure (P4mm) with volume expansion (∼ 0.11%) of the unit cell. The second phase transition occurs at approximately 270 K, and the tetragonal phase transforms toward a ferroelectric orthorhombic phase (Bmm2). The last structure transition is the orthorhombic–rhombohedral transition near 180 K. An entropy change with the BCE has been reported. ΔS for the cubic-tetragonal and tetragonal–orthorhombic transition is 1.7 J·kg⁻¹·K⁻¹ and 1.2 J·kg⁻¹·K⁻¹, respectively, and the values were determined using DSC under hydrostatic pressure of 100 MPa. The MCE was also reported in ferroelectric PbTiO₃. Molecular dynamic simulation predicted the ECE in PbTiO₃ with ΔT of 25 K and 44 K under stresses of 0.5 GPa and 2 GPa, respectively.^[58] The compound is a cubic perovskite structure at much higher temperature (∼ 700 K). On cooling, it exhibits a first-order structural phase transition. This transition between a cubic and tetragonal phase (P4mm) accompanies a paraelectric–ferroelectric transition. The absolute values of ΔT and ΔS for the BCE are 1.9 K and 2.7 J·kg⁻¹·K⁻¹, respectively, under the hydrostatic pressure of 260 MPa.^[63] According to a recent report, the peak values of ΔT for the ECE in lead zirconate titanate are 0.2 K and 1.25 K under stresses of 100 MPa and 400 MPa, respectively, near room temperature (300 K).^[60] In perovskites, the BCE is more significant when the pressure is increased. For example, the maximum ΔT for the BCE in BaTiO₃ single crystals is 2.8 K and 3.6 K when the applied pressure is 0.6 GPa and 2.4 GPa, respectively.^[57] These perovskites exhibit excellent hardness and stability. However, their cooling efficiency is inadequate under low pressure.

As special perovskites, organic–inorganic hybrid perovskites exhibit pressure-induced solid-state cooling effects. This family of materials has the perovskite structure ABX₃, where A is an alkylammonium cation, B is a transition metal cation, and X is a halide or polyatomic bidentate-bridge ligand. A prior review summarized the BCE in more than a dozen hybrid perovskites.^[65] These hybrid perovskites have the following characteristics: (i) a large and reversible entropy change, (ii) a large shift of transition temperature with pressure, and (iii) an adequate transition temperature. A typical example of hybrid perovskites is [TPrA]Mn[dca]₃ (TPrA = (CH₃CH₂CH₂)₄N⁺, dca = [N(CN)₂]⁻).^[66] This material exhibits giant BCEs near room temperature under a pressure of 70 bar (1 bar = 10⁵ Pa).

Unlike the above MCE materials, the MCE materials discussed in this section are amorphous. This type of material can support a dramatic reversible elongation or retraction. The huge deformation results in a huge entropy change. In fact, the first reported material with the ECE is Indian rubber, a randomly oriented polymer.^[1] However, this material was not valued until recently.^[67–70] In natural rubber, the highest temperature change for the ECE is 13.7 K at 674% elongation and the estimated ΔS is 67 J·kg⁻¹ K⁻¹. There are many polymers with the MCE based on ferroelectric polymers such as polyvinylidene fluoride (PVDF).^[71–74] According to results of x-ray diffraction experiments, a crystal transformation from the anti-polar α to the polar β phase was observed in PVDF terpolymers. The transformation can be induced by pressure or an electric field. The elastocaloric properties of PVDF trifluoroethylene chlorotrifluoroethylene (PVDF–TrEE–CTFE) were reported using an infrared imaging camera. ΔT of 2.15 K and ΔS of 11 J·kg⁻¹·K⁻¹ were measured at a strain of 12%. For the BCE, ΔT of 6 K in this polymer was observed under a pressure of 200 MPa at room temperature and increased to approximately 19 K at the phase transition temperature of 368 K.

The MCE of rare-earth compounds as solid-state cooling materials was studied. Because of their 4f electron hybrids, most rare-earth materials have rich magnetic properties that are sensitive to pressure. Some rare-earth compounds such as Ce_x(La, Y)_{1 − x}Sb, HoAs, Ce₃Pd₂₀Ge₆, and EuNi₂(Si_1-xGe_x)₂ have been reported as MCE materials.^[75–78] In these compounds, the entropy changes must take into account that the crystalline electric field splits the (2J + 1)-fold degenerated ground-state J-multiplet of the rare-earth ion into discrete energy levels. In Ce_x(La, Y)_{1 − x}Sb, the PM–AFM transition induced by uniaxial stress was expected to result in a huge entropy change. The in situ experiments revealed ΔT of 0.42 K upon releasing a uniaxial stress of 240 MPa in Ce_0.85(La_0.95Y_0.05)_0.15Sb and ΔT of 2 K upon releasing a uniaxial stress of 500 MPa in CeSb at low temperature (∼ 20 K). The monopnictide HoAs exhibits the ECE resulting from a magnetic–structural phase transition. ΔT for the ECE is over 0.4 K upon the application of uniaxial stress of 300 MPa along the [001] direction. The third material introduced is a heavy-fermion system Ce₃Pd₂₀Ge₆. The |ΔT| of 0.75 K for the ECE was obtained in the Kondo lattice compound Ce₃Pd₂₀Ge₆ because release of the uniaxial stress of 300 MPa leads to a positive shift of the Kondo temperature and splitting of the ground state at 4.4 K. The rare-earth compound EuNi₂(Si_{1 − x}Ge_x)₂ undergoes a first-order valence transition with a thermal hysteresis of 10 K and a huge entropy change from an Eu²⁺ state toward an Eu³⁺ state near 42 K. The sharp valence transition is expected to lead to the BCE.

In the year 2010, the MCE in a series of oxyfluorides was reported. These oxyfluorides have four types, namely (NH₄)₂NbOF₅, (NH₄)₂WOF₄, (NH₄)₂MoO₂F₄, and Rb₂KTiOF₅.^[79–83] The ammonia compound (NH₄)₂NbOF₅ undergoes two phase transitions accompanied by entropy changes. For (NH₄)₂NbOF₅, the disordered phase I transforms into the partially ordered phase II on cooling at 258 K and then transforms to a fully ordered phase III at 220 K.^[84] The strengths of the BCE and ECE are almost equal. The maximum of ΔT and ΔS for the MCE can reach 15 K and 60 J·kg⁻¹·K⁻¹, respectively, upon the application of hydrostatic pressure or uniaxial stress of 1 GPa near the phase transition temperatures. Later, the MCE in (NH₄)₂WOF₄ and (NH₄)₂MoO₂F₄ oxyfluorides was studied. Two phase transitions were reported at 271.4 K and 180 K for the molybdate and at 201.5 K and 161 K for the tungstate. ΔT of 10 K and ΔS of 40 J·kg⁻¹·K⁻¹ for the molybdate and ΔT of 12 K and ΔS of 50 J·kg⁻¹·K⁻¹ for the tungstate were calculated using differential thermal analysis under a force field of 0.5 GPa near the first-order structural phase transitions. Later, the MCE in Rb₂KTiOF₅ was observed near the structural phase transition at 215 K under pressure between 0 and 0.6 GPa. The Rb₂KTiOF₅ undergoes a first-order ferroelastic phase transition that can result in huge entropy changes. ΔT of 16 K and ΔS of 43 J·kg⁻¹·K⁻¹ were calculated from the differential thermal analysis under a pressure of 0.4 GPa. In 2016, a review of the MCE in ferroelastic fluorides and oxyfluorides was published.^[83] This paper reviewed the effects of uniaxial stress and hydrostatic pressure on phase transitions, the MCE, and the experiment methods used to obtain the temperature–pressure phase diagram and entropy under high pressure. The thermodynamic characteristics of selected materials are compared in Table 2. Oxyfluorides have a good cooling efficiency under moderate pressure but are not very stable in air.

Superionic conductors, also known as fast ionic conductors, are a class of solid materials with extremely high ionic conductivity.^[85] According to recent studies of the BCE in fluoride-based and AgI superionic conductors, superionic conductors are expected to be good candidates for MCE materials.^[86,87] The superionic transition in fluorite-structured fast ion conductors such as CaF₂ and PbF₂ results in a large entropy change of over 100 J·kg⁻¹·K⁻¹ under hydrostatic pressure or uniaxial stress. |ΔT| of 20 K in PbF₂ and 3 K in CaF₂ were calculated using density functional theory upon releasing the stress of 0.6 GPa. When the hydrostatic pressure increases to 5 GPa, calculations for the BCE in CaF₂ indicate that |ΔT| and |ΔS| can reach 152 K and 186 J·kg⁻¹·K⁻¹, respectively. Other materials with giant MECs include AgI, which consists of α, β, and γ phases at different temperatures. The structure of the α phase is a body-centered-cubic structure (). The structures of the β and γ phases are a hexagonal-close-packed structure () and a cubic-close-packed structure (), respectively. The first-order structural phase transition from the superionic α phase to a mixed phase of β and γ leads to a disorder–order transition of the silver cations on cooling at approximately 420 K. Because of the first-order reconstructive phase transition with a huge volume change (5%) of the unit cell, the entropy change in the transition can reach 63 ± 4 J·kg⁻¹·K⁻¹. The solid electrolyte AgI exhibits the BCE. ΔT of 18 K and ΔS of 60 J·kg⁻¹·K⁻¹ were observed near the superionic phase transitions. However, AgI and similar superionic conductor such as AgBr and AgCl are unstable owing to photolysis.

In 2019, colossal BCEs were observed in plastic crystals.^[88,89] Plastic crystals, also known as orientation-disordered crystals, are oriented randomly, whereas the mass center forms symmetric lattices. The reversible first-order transition induced by pressure in plastic crystals induces large amounts of heat changes. In plastic crystals such as 2,2-dimethyl-1,3-propanediol (NPG), 2-methyl-2-nitro-1-propanol (MNP), and pentaglycerin (PG), the solid-state transition enthalpy is equivalent to or even higher than the melting enthalpy of some common solids such as Fe, Ti, and Mn. For the BCE in NPG, MNP, and PG, the maximum of |ΔS| calculated by indirect methods can reach 389, 404, and 493 J·kg⁻¹·K⁻¹, respectively. The value of entropy changes in plastic materials is dozens of times as large as that in previous materials with the MCE. The microscopic origin of colossal BCEs in plastic crystals was revealed through high-resolution quasi-elastic neutron scattering and inelastic neutron scattering experiments under high pressure. These experiments verified that orientational disorder in plastic crystals is restrained by the pressure. Thus, the transition results in huge entropy changes.^[88] Plastic crystals have excellent cooling efficiency; however, the organic part leads to quite large hysteresis.

To date, the MCE has been investigated in SMAs including non-magnetic SMAs and MSMAs, ferroelectric perovskite materials, polymers, rare-earth compounds, oxyfluorides, superionic conductors, plastic crystals, and other materials. Here, we list thermodynamic characteristics for the elastocaloric effect (in Table 1) and barocaloric effect (in Table 2) in selected materials.

Figure 1 shows ΔT and ΔS for selected mechanocaloric materials under hydrostatic pressure or uniaxial stress. These current studies have shown that the application external hydrostatic pressure or uniaxial stress is a very effective and clean method to induce structural transitions and change the entropy and temperature of the crystals or amorphous polymers. In ferromagnetic or ferroelectric materials, the pressure affects the structure, magnetization, or polarization. Generally, the transition temperature shifts under different pressure. The shift coefficient dT/dp or dT/dσ represents the sensitivity of the transition to hydrostatic pressure or uniaxial stress. Many materials with the MCE have been discovered near ferroic phase transitions.^[3] Therefore, we expect the MCE could be observed in magnetocaloric and/or electrocaloric materials. In addition to mechanocaloric materials associated with pure structural, magnetostructural, or electrostructural transitions, polymers and plastic crystals exhibit colossal MCEs associated with disorder–order transitions. The application of pressure suppresses the oriented disorder in polymers and plastic crystals. However, the obvious drawback is a large hysteresis of the disorder–order transition in polymers.^[91] After dozens of minutes, the materials can carry out the next cycle. In addition, the organic matter and superionic conductors are not stable enough in air. According to current research on their mechanical performance, hysteresis, and cooling efficiency, SMAs are good candidates for widespread applications. These alloys have been intensively investigated for a long time. A very recent study reported colossal MCEs with a strikingly high value of 31.5 K in a Ni–Mn-based Heusler SMA.^[92] In fact, the disorder–order transition has a larger value of entropy change than structural transition in this SMA. The potential materials with the disorder–order transition are expected to have a feature that part of the ions or ionic groups can freely move but the remaining ions or ionic groups are stable and maintain structural symmetry. Therefore, these materials should have the advantages of both SMAs and polymers. In this case, the materials will have a small hysteresis and large entropy changes similar to organic–inorganic hybrid materials and superionic conductors.

Fig. 1.

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	Fig. 1. (a) and (b) Absolute value for the isothermal entropy change and adiabatic temperature change, respectively, as a function of the applied uniaxial stress for selected elastocaloric materials. (c) and (d) Absolute value of isothermal entropy change and adiabatic temperature change, respectively, as a function of the hydrostatic pressure for selected barocaloric materials.