Elastocaloric Effect in Aged Single Crystals of Ni₅₄Fe₁₉Ga₂₇ Ferromagnetic Shape Memory Alloy

Abstract

In the present study, the effect of γ′-phase dispersed particles on both the L2₁(B2)-10M/14M-L1₀ martensitic transformations and the elastocaloric effect in aged Ni₅₄Fe₁₉Ga₂₇ single crystals oriented along the [001]-direction was investigated. It was experimentally shown that aging strongly affects the elastocaloric properties of these crystals. The precipitation of semi-coherent γ′-phase particles up to 500 nm in size in the crystals aged at 773 K for 1 h leads to a 1.4 times increase in the operating temperature range of the elastocaloric effect up to ΔT_SE = 270 K as compared with the initial as-grown crystals (ΔT_SE = 197 K). The adiabatic cooling values ΔT_ad are similar for the as-grown crystals ΔT_ad = 10.9 (±0.5) K and crystals aged at 773 K ΔT_ad = 11.1 (±0.5) K. The crystals containing incoherent γ′-phase particles sized 5–35 μm (after aging at 1373 K for 0.5 h) possess an operating temperature range of ΔT_SE = 255 K with slightly smaller adiabatic cooling ΔT_ad below 9.7 (±0.5) K. The aged [001]-oriented Ni₅₄Fe₁₉Ga₂₇ single crystals demonstrate high cyclic stability: the number of cycles does not influence the adiabatic cooling values and parameters of loading/unloading curves regardless of the particle size. The ways to improve the elastocaloric cooling parameters and stability of the elastocaloric effect by means of dispersed particles in the NiFeGa ferromagnetic shape memory alloy were discussed.

1. Introduction

Developing eco-friendly materials for solid-state cooling systems is a promising solution to the global warming problem. The main operating principle of solid-state cooling systems is based on the caloric effect that is associated with a reversible change in the entropy or temperature of a solid body caused by the influence of external fields (electric E, magnetic H, mechanical σ, or hydrostatic pressure P) under isothermal or adiabatic conditions, respectively. New materials should possess significant cooling capability, high reliability, stability, and durability, as well as satisfy the economic requirements in order to be used as efficient solid-state cooling systems [1,2].

Shape memory alloys (SMAs) are widely used for engineering such devices because of the promising elastocaloric effect (EC effect). The EC effect is accompanied by a giant value of adiabatic cooling up to 31.5 K per working cycle [3]. Moreover, it is easier to create conditions for the implementation of the EC effect during loading/unloading cycles in SMAs than in magneto-caloric or electro-caloric materials.

Ferromagnetic NiFeGa-based SMAs with L2₁(B2)-10M/14M-L1₀ martensitic transformations (MTs) are one of the most promising materials possessing functional properties required for solid-state cooling systems. Single crystals of such SMAs are characterized by a wide superelasticity (SE) temperature interval, which is also the working range of the EC effect. To date, the EC effect has been studied only in as-grown NiFeGa single crystals without additional heat treatments. It was shown that the best properties were found in high-strength crystals oriented along the [001]_L21-direction: adiabatic cooling ΔT_ad reaches 8.4–9.8 K for one loading/unloading cycle with narrow stress hysteresis in a wide temperature range of 190–200 K in compression [4,5,6,7].

Improving functional properties in NiFeGa crystals by aging is a topical task. Improvements will strengthen materials, expand a working temperature range, and ensure high cyclic stability of functional properties. It is known that the precipitation of γ(γ′)-phase particles with the face-centered lattice or ordered L1₂-structure occurs in NiFeGa SMAs after austenite aging [8,9,10]. Thus, aging in austenite enables the creation of heterophase crystals whose matrix undergoes thermoelastic MT, whereas precipitated dispersed particles do not undergo MT, they act as elastic elements that store elastic energy, and they contribute to the development of reversible thermoelastic MT. It is assumed that, in aged NiFeGa alloys containing dispersed particles, necessary conditions will be created to obtain the wide operating temperature range and high cyclic stability of the EC effect. It should be noted that the precipitation of γ(γ′)-phase particles in Ni₄₉Fe₁₈Ga₂₇Co₆ and CoNiAl single crystals decreases stress hysteresis, increases the SE temperature interval, and improves the SE cyclic stability [9,10,11,12].

According to the above-mentioned, the aim of the present study is to find out the effect of particles precipitated after austenite aging on the SE and the EC effect in Ni₅₄Fe₁₉Ga₂₇ single crystals oriented along the [001]-direction. Along this direction, the theoretical value of the compressive transformation strain for L2₁(B2)-L1₀ MT is the maximum value of 6.2% [13]. Moreover, this high-strength [001]-orientation is characterized by the absence of detwinning of L1₀-martensite under compressive stress because of the zero Schmid factors for the L1₀-martensite twinning system. In this case, the SE is accompanied by the minimal value of dissipative energy and stress hysteresis Δσ in comparison with the other orientations ([011], [123]), where the detwinning of L1₀-martensite occurs under compressive stress [13,14,15,16]. Therefore, the [001]-direction provides optimal conditions for observing both the SE and the EC effect in studied crystals.

2. Materials and Methods

The single crystals of Ni₅₄Fe₁₉Ga₂₇ (at. %) alloy were grown by Bridgman method in an inert gas atmosphere. For compression testing parallelepiped samples with dimensions of 3 × 3 × 6 mm³ were cut using an electrical-discharge machine ARTA 123 (Delta-Test, Moscow, Russia). The compression axis corresponds to the long side of a sample and possesses the [001]-orientation in austenite. The orientation of single crystals in L2₁(B2)-austenite was defined by a DRON-3 X-ray diffractometer (Burevesnik, St. Petersburg, Russia) using FeKa radiation.

Two aged single crystals were studied in the present research:

−

aged at 773 K for 1 h followed by slow air cooling in order to keep the austenite L2₁-structure (after aging at 773 K);

−

aged at 1373 K for 0.5 h followed by quenching in water.

Such a choice of thermal treatments will allow varying the particle size and austenite structure [8,9,10] in order to create a different degree of particle coherency with austenite and martensite and to study the influence of particle size to EC effect. To compare and find out the effect of dispersed particles on both the EC effect and stress-induced MT, the previously obtained results [17] on the initial [001]_A-oriented Ni₅₄Fe₁₉Ga₂₇ single crystals were used.

Transformation temperatures of L2₁(B2)-10M/14M-L1₀ MT are defined by differential scanning calorimetry (DSC) method using a DSC 404 F1 Pegasus calorimeter (NETZSCH, Bayern, Germany). Temperature M_s, M_f for forward and A_s, A_f for reverse transformation, changes in the entropy ΔS and specific heat capacity at constant pressure C_p were established according to the standard methods after DSC studies, as it was shown in [18].

SE was studied along the [001]-compression axis using an Instron VHS 5969 universal testing machine (Instron, High Wycombe, UK); the instrumental error is ±2 MPa. The adiabatic temperature change ΔT_ad in the single crystals was defined by direct measurement using a highly-sensitive T-type thermal couple (RS International, Northamptonshire, UK) fixed on the sample surface. The mechanical experiments with the EC effect measurement were arranged as follows: first, the sample was loaded with a low strain rate of 2.0 × 10⁻³ s⁻¹ until the given stress was reached; then, the sample was kept at that stress level for about 10 s in order to equalize the sample temperature; the following unloading was performed with a high strain rate of 6.7 × 10⁻¹ s⁻¹ to create the conditions close to adiabatic. The instrumental error for ΔT_ad during the EC effect is ±0.5 K. The data on the change in the sample temperature depending on the test time is recorded by the data acquisition module along with the data on the stress change and strain depending on the test time. This allows us to accurately match two datasets and to establish σ(ε) and ΔT_ad(t) dependences. Transmission electron microscopic studies (TEM) were performed in Krasnoyarsk Science Center SB RAS on transmission electron microscope HT-7700 Hitachi (Hitachi, Tokyo, Japan).

3. Results

The microstructure of the Ni₅₄Fe₁₉Ga₂₇ crystals after austenite aging at 773 K and 1373 K was examined using TEM. It is shown that aging results in the precipitation of γ′-phase particles having the ordered L1₂ crystal structure (Figure 1 and Figure 2).

Aging at 773 K for 1 h leads to the precipitation of γ′-phase particles with the size of 170–500 nm (Figure 1). The particles have the ordered L1₂ crystal structure, which is confirmed by the superlattice reflections of 100 and 110 (Figure 1c). The precipitated particles have an elongated or close to equilateral shape. It is assumed that such particles are semi-coherent. The assumption is confirmed by both the strain contrast near particles and the absence of dislocations at the interphase boundary.

Figure 2 shows the microstructure of the Ni₅₄Fe₁₉Ga₂₇ single crystals aged at 1373 K for 0.5 h. There are large incoherent particles with the size of 5–35 μm and volume fraction of (24 ± 5)% in these crystals. It should be noted that the high density of dislocations is observed at the particle–matrix boundary. As mentioned above, the superlattice reflections of 100 and 110 are the evidence of the ordered L1₂ crystal structure in such particles. Some of γ′-phase particles have an elliptical shape and consist of two parts connected by twinning relation (Figure 2c,d), which is consistent with the previous study [19]. The transformation temperatures as well as the heat parameters of MT for all studied Ni₅₄Fe₁₉Ga₂₇ single crystals were defined by DSC method (Figure 3,

Table 1. Characteristic parameters of MT and heat characteristics from DSC response for [001]-single crystals Ni₅₄Fe₁₉Ga₂₇.

Heat Treatment	Ms, (±2) K	Mf, (±2) K	As, (±2) K	Af, (±2) K	Cp, J/(kgK)	ΔSA–M, J/(kgK)	ΔSM–A, J/(kgK)	ΔTadt(A–M), K	ΔTadt(M–A), K
As-grown [17]	276	265	280	289	488	−17.6	16.5	10.2	9.6
Aged at 773 K	259	245	257	270	434	−15.9	14.2	9.7	8.7
Aged at 1373 K	281	261	274	295	418	−14.0	10.1	9.6	7.0

). The single crystals aged at 773 K for 1 h are characterized by lower transformation temperatures as compared with the as-grown crystals or crystals aged at 1373 K, which demonstrate the highest temperatures. The decrease in the MT temperatures in the crystals aged at T = 773 K can occur due to an increase in the degree of order of the high-temperature phase, the effects of dispersion strengthening, and an increase in the elastic and surface energies necessary to maintain the compatibility of the martensitic deformation of the matrix and the elastic deformation of the γ’-phase particles. The increase in the MT temperatures in the crystals aged at 1373 K, firstly, is caused by the change from L2₁ to B2 in the austenite structure. This is in accordance with the previously obtained results [6,20,21]: changes in the austenite structure from L2₁-phase to B2-phase in the NiFeGa alloy occur at 933–978 K. Secondly, the dislocation formation near large γ’-phase particles (Figure 2d), as well as the changing chemical composition of the matrix during the precipitation of large γ’-phase particles (for example the decrease in Fe component by 2 at.%) increases the transformation temperatures [22].

It is experimentally shown that the precipitation leads to a decrease in the magnitude of the change in entropy ΔS^A–M (ΔS^M–A) during both forward and reverse MT (Table 1). It is mainly associated with the increase in the volume fraction of particles that do not undergo transformations. Therefore, the volume of the material undergoing MT decreases. The specific heat capacity C_p also decreases by 54 J/(kgK) in the crystals aged at 773 K and by 70 J/(kgK) in the crystals aged at 1373 K in comparison with the as-grown crystals (Table 1).

Based on the experimental data, it is possible to estimate the maximum theoretical value of adiabatic cooling ΔT_ad during the manifestation of the EC effect [6]:

$$\Delta {\mathrm{T}}_{\mathrm{a}\mathrm{d}}\approx \frac{{\mathrm{T}}_0\Delta \mathrm{S}}{{\mathrm{C}}_{\mathrm{p}}},$$

(1)

where C_p—specific heat capacity, ΔS—entropy change, T₀ ≈ 1/2(M_s + A_f)—equilibrium temperature between austenite and martensite phases.

Theoretical values of the adiabatic temperature change ΔT_ad obtained from DSC assume a small decrease in ΔT_ad by 1–2 K in the aged crystals in comparison with the as-grown ones.

The stress–strain curves at different temperatures in loading/unloading cycles and corresponding sample temperature change for the [001]-oriented Ni₅₄Fe₁₉Ga₂₇ single crystals aged at 773 K for 1 h and 1373 K for 0.5 h are shown in Figure 4. For each test temperature, the red line shows a change in the sample temperature during loading, the blue line shows a change in the sample temperature during unloading. The adiabatic cooling ΔT_ad was measured during loading/unloading cycles under the SE conditions at different test temperatures. The maximum applied stress level was 800 MPa in each cycle at the test temperature from A_f to 473 K. In the studied crystals, the EC effect is also observed at T > 473 K, but to complete the stress-induced MT it is necessary to increase the applied stresses above 800 MPa.

The obtained experimental data show that the working temperature range and the EC cooling in the Ni₅₄Fe₁₉Ga₂₇ single crystals depend on the aging temperature.

The single crystals aged at 773 K demonstrate a wide SE and EC effect temperature range ΔT_SE = 270 K (from 278 to 548 K), which is 1.4 times greater compared with the as-grown crystals (ΔT_SE = 197 K, from 298 up to 493 K) [17]. This wide temperature range is facilitated, on the one hand, by the lower temperature A_f = 270 K (Table 1). On the other hand, in the crystals aged at 773 K, a higher dislocation slip resistance is observed during the stress-induced MT. The resistance is higher because of the hardening of the matrix by γ’-phase dispersed particles, which expands the SE and EC effect temperature range towards high temperatures. The temperature, at which the irreversible strain more than 0.5% was observed on the σ(ε) curves, was taken as the end temperature of the SE range. In these crystals, aged at 773 K for 1 h, the EC cooling value reaches ΔT_ad = 11.1 (±0.5) K at the test temperature T = 296 K (Figure 4a).

In the single crystals undergoing high-temperature aging at 1373 K, the MT temperatures increase due to the precipitation of incoherent γ’-phase particles, which leads to narrowing of the SE temperature range ΔT_SE = 255 K (from 313 to 568 K) as compared with low-temperature aging at 773 K. The single crystals aged at 1373 K are characterized by wider stress hysteresis because of the presence of a large volume fraction of incoherent γ’-phase particles in the material that do not undergo MT and the stored elastic energy can relax due to plastic deformation of the particles during the forward MT (Figure 4b).

4. Discussion

It has been experimentally established that in the single crystals aged at 773 K for 1 h, the maximum EC cooling value ΔT_ad = 11.1 K is observed. The single crystals with incoherent particles aged at 1373 K for 0.5 h are characterized by the lower maximum values of ΔT_ad = 9.7 K as compared with the crystals aged at 773 K. A decrease in the ΔT_ad value with an increase in the γ’-phase particle size was predicted using the DSC data (Table 1). However, the maximum experimental ΔT_ad values slightly exceed the theoretical estimates of adiabatic cooling ΔT_ad^t(M–A) obtained from DSC (by 1.0–2.5 K). The theoretical values ΔT_ad^t(M–A) are usually greater than the experimental ones because the heat exchange of the sample with testing machine grips is always observed and experimental conditions are not strictly adiabatic.

This difference between the theoretical, i.e., calculated with the DSC data ΔT_ad^t(M–A) for the reverse MT (Table 1), and experimental EC cooling ΔT_ad values is determined by different staging and entropy change for thermal-induced and stress-induced MT in NiFeGa single crystals. It has been found that in the as-grown NiFeGa(Co) crystals [23,24,25], one-stage L2₁-14M MT occurs and a self-accommodated structure of 14M martensite is formed during cooling/heating in the stress-free state. During the stress-induced MT, the growth of oriented L1₀-martensite is observed and L2₁-14M-L1₀ or L2₁-L1₀ MT takes place. Therefore, the magnitude of the entropy change during the stress-induced MT can be estimated using the temperature dependence of the critical stresses σ_Ms(T) or σ_As(T) required for the onset of forward and reverse MT according to the Clausius–Clapeyron equation [17,26]:

$$\Delta {\mathrm{S}}^{\mathrm{A}–\mathrm{M}}=\frac{{\mathsf{\epsilon }}_{\mathrm{tr}}}{\mathsf{\rho }}\frac{{\mathrm{d}\mathsf{\sigma }}_{\mathrm{Ms}}}{\mathrm{dT}}\mathrm{and}\Delta {\mathrm{S}}^{\mathrm{M}–\mathrm{A}}=\frac{{\mathsf{\epsilon }}_{\mathrm{tr}}}{\mathsf{\rho }}\frac{{\mathrm{d}\mathsf{\sigma }}_{\mathrm{As}}}{\mathrm{dT}}$$

(2)

where ε_tr is the transformation strain; ρ = 8450 kg/m³—density [27].

Figure 5 shows the temperature dependence of the critical stresses of forward σ_Ms and reverse σ_As stress-induced MT. For the single crystals aged at 773 K, σ_Ms and σ_As stresses increase linearly with the test temperature. In contrast, a significant deviation of σ_As(T) from the linear dependence is observed in the crystals aged at 1373 K at test temperature T > 450 K.

As it was shown in [17,28,29], the critical stresses for forward σ_Ms and reverse σ_As MT can be expressed as:

$${\mathsf{\sigma }}_{\mathrm{Ms}}\left(\mathrm{T}\right)={\mathsf{\sigma }}_0\left(\mathrm{T}\right)+\mathsf{\rho }\frac{\left|\Delta {\mathrm{G}}_{\mathrm{dis}}\left(0,\mathrm{T}\right)\right|+\left|\Delta {\mathrm{G}}_{\mathrm{rev}}\left(0,\mathrm{T}\right)\right|}{{\mathsf{\epsilon }}_{\mathrm{tr}}\left(\mathrm{T}\right)}$$

(3)

$${\mathsf{\sigma }}_{\mathrm{As}}\left(\mathrm{T}\right)={\mathsf{\sigma }}_0\left(\mathrm{T}\right)-\mathsf{\rho }\frac{\left|\Delta {\mathrm{G}}_{\mathrm{dis}}\left(0,\mathrm{T}\right)\right|+\left|\Delta {\mathrm{G}}_{\mathrm{rev}}\left(0,\mathrm{T}\right)\right|}{{\mathsf{\epsilon }}_{\mathrm{tr}}\left(\mathrm{T}\right)}$$

(4)

Here ΔG_dis(0,T), ΔG_dis(1,T), ΔG_rev(0,T), and ΔG_rev(1,T) are the dissipated and the stored elastic energy (reversible energy) per unit mass at the start (volume fracture δ = 0) and at the end of (δ = 1) stress-induced MT. If we assume that ΔG_rev(0,T) has small values and weakly depends on the test temperature, stress σ₀ can be defined as:

$${\mathsf{\sigma }}_0\left(\mathrm{T}\right)=\frac{{\mathsf{\sigma }}_{\mathrm{Ms}}-{\mathsf{\sigma }}_{\mathrm{Af}}}{2}$$

(5)

If the dissipation energy ΔG_dis and stored elastic energy ΔG_rev do not depend on temperature, the Clausius–Clapeyron slope for forward ${\mathsf{\alpha }}_{\mathrm{Ms}}={\mathrm{d}\mathsf{\sigma }}_{\mathrm{Ms}}/\mathrm{dT}$ and reverse MT ${\mathsf{\alpha }}_{\mathrm{As}}={\mathrm{d}\mathsf{\sigma }}_{\mathrm{As}}/\mathrm{dT}$ is similar. However, there is a strong temperature dependence of both dissipation ΔG_dis and stored elastic ΔG_rev energy in the temperature range of the EC effect in the studied aged single crystals. It is known [17,28,29] that the dissipation energy ΔG_dis is proportional to stress hysteresis Δσ and the stored elastic energy ΔG_rev is proportional to the strain rate hardening θ = dσ/dε during the stress-induced MT.

In the crystals aged at 773 K, the strain rate hardening θ = dσ/dε and, accordingly, the stored elastic energy ΔG_rev increase with the test temperature. That is why, according to Equations (3) and (4), the Clausius–Clapeyron slope for reverse MT ${\mathsf{\alpha }}_{\mathrm{A}\mathrm{s}}={\mathrm{d}\mathsf{\sigma }}_{\mathrm{As}}/\mathrm{dT}=3.1\mathrm{MPa}/\mathrm{K}$ is higher than for the forward one MT ${\mathsf{\alpha }}_{\mathrm{Ms}}={\mathrm{d}\mathsf{\sigma }}_{\mathrm{Ms}}/\mathrm{dT}=2.7\mathrm{MPa}/\mathrm{K}$. A similar dependence was observed earlier for as-grown [001]-oriented crystals [17]. The elastic accommodation of austenite and martensite crystals becomes more difficult during the stress-induced MT with an increase in the test temperature. Therefore, at elevated test temperatures in the as-grown crystals and the crystals aged at 773 K, MT is accompanied by high θ and significant accumulation of stored elastic energy ΔG_rev(1,T), which is the driving force of the reverse MT (Figure 4). As Figure 5 shows, at T > 400 K, the reverse MT begins at critical stresses σ_As higher than for the forward one σ_Ms. For the reverse MT, the temperature dependence of θ = dσ/dε and ΔG_rev (1,T) leads to a sharper increase in critical stresses σ_As with the test temperature and, accordingly, to higher Clausius–Clapeyron slope dσ_As/dT in comparison with the forward one (σ_Ms and dσ_Ms/dT).

The crystals with large incoherent γ’-phase particles aged at 1373 K are characterized by wide stress hysteresis Δσ, which is 2–4 times greater than for the as-grown crystals and crystals aged at 773 K and increases sharply at test temperatures T > 450 K (Figure 4). This leads to high energy dissipation ΔG_dis(1,T), and, in accordance with Equation (4), to a sharp decrease in σ_As at test temperatures T > 450 K (Figure 5).

The test temperature grows and alters the values of the stored elastic energy ΔG_rev(1,T) and the dissipated energy ΔG_dis(1,T). These changes contribute to the experimental dσ_As/dT values and the ΔS^M–A values calculated with Equation (2). dσ_As/dT can change sharply with an increase in the strain rate hardening θ = dσ/dε or stress hysteresis Δσ that also change with the test temperature. The conditions for the martensite nucleation and, accordingly, stored elastic ΔG_rev(0,T) and dissipated ΔG_dis(0,T) energy weakly depend on the test temperature. Thus, it is necessary to use ${\mathsf{\alpha }}_{\mathrm{Ms}}$ and ΔS^A–M for forward MT for entropy change during stress-induced MT and EC cooling ΔT_ad^t(A–M) estimations. The calculated values are shown in

Table 2. Maximum theoretical ΔT_ad^t(A–M), calculated by Equations (1) and (2), and experimental ΔT_ad^exp(max) EC effect values for [001]_A-oriented Ni₅₄Fe₁₉Ga₂₇ single crystals.

Heat Treatment	αMs, MP/K	Cp, J/(kgK)	|εrev|max, %	ΔSA–M, J/(kgK)	ΔTadt(A–M), K	ΔTadexp(max), K
Aged at 773 K	2.7	434	5.4	−17.2	10.5	11.1 (±0.5)
Aged at 1373 K	2.5	418	4.7	−13.9	9.6	9.7 (±0.5)

. It can be seen that there is good agreement between the theoretical and experimental values of the EC cooling.

Figure 6 shows the temperature dependence of the adiabatic temperature change ΔT_ad, reversible strain, and stress hysteresis in the aged single crystals in comparison with the as-grown single crystals of the Ni₅₄Fe₁₉Ga₂₇ alloy. The aged crystals demonstrate the similar temperature dependences of the adiabatic temperature change ΔT_ad, which do not depend on the size of the dispersed γ’-phase particles (Figure 6a). There is an increase in ΔT_ad to the maximum values at the start of the SE temperature range. This ΔT_ad(T) dependence behavior is typical for many SMAs [6]. During the test temperature near A_f and the SE manifestation, the sample is locally cooled by ΔT_ad to temperature below A_f. This can inhibit the reverse MT and reduce the ΔT_ad. Therefore, the maximum adiabatic temperature change ΔT_ad is reached at the test temperature T ≥ A_f + ΔT_ad(max). Then almost constant ΔT_ad is achieved in the temperature interval of 50–75 K (Figure 6a). After that, unlike the as-grown crystals, the aged crystals see ΔT_ad decrease linearly with the increasing temperature. In the as-grown crystals, a weak temperature dependence of ΔT_ad in the operating temperature range is observed (Figure 6a).

In the aged crystals, both the adiabatic temperature change ΔT_ad and transformation strain ε_rev decrease with an increase in the test temperature (Figure 6a,b). The maximum transformation strain ε_rev at SE in the single crystals aged at 773 K is equal to ε_rev = 5.4 (±0.3)%. The reversible strain decreases by 2.2 times with an increase in the test temperature in the SE temperature window (ε_rev = 2.3% at T = 548 K). The maximum reversible strain at the SE is less (ε_rev = 4.7 (±0.3)%) in the crystals aged at 1373 K than in the crystals aged at 773 K. This is associated with a large volume fraction of particles (up to 24%) that do not undergo the transformation. The ε_rev in these crystals also decreases by 1.6 times with an increase in the test temperature. At elevated test temperatures T ≥ 448 K, ε_rev is equal to 3.0 (±0.3)% in the crystals aged at 1373 K (Figure 6b). Decreasing transformation strain ε_rev associated with an increase in the test temperature is a distinguishing characteristic of [001]-oriented single crystals of ferromagnetic CoNiGa, CoNiAl, NiMnGa, and NiFeGa(Co) alloys [12,13,17,25,30]. The reason for this ε_rev(T) dependence is the difference between the elastic moduli of austenite and martensite E_A ≠ E_M (Figure 4). This is discussed in detail in our previous work on as-grown [001]-oriented NiFeGa single crystals [17].

A decreasing transformation strain associated with an increase in the test temperature is observed in both [001]-oriented as-grown and aged crystals. However, the adiabatic cooling ΔT_ad in the as-grown crystals remains constant with a decrease in transformation strain by 2.3–1.6 times [17]. Therefore, a decreasing transformation strain with an increase in temperature due to the difference between the elastic moduli of austenite and martensite cannot be the main reason for the ΔT_ad decrease in [001]-oriented aged NiFeGa crystals.

The γ’-phase precipitation leads to the two-fold increase in stress hysteresis Δσ and, consequently, energy dissipation in the operating cycle in the aged crystals compared with the as-grown ones (Figure 6c). This is due to an increase in the friction force needed for the movement of the interphase boundary in the crystals containing dispersed particles, which do not undergo transformation. Stress hysteresis of Δσ ≈ 60–67 MPa in the single crystals aged at 773 K and of Δσ ≈ 34–40 MPa in the as-grown crystals are independent of the test temperature up to T ≈ 448 K. The SE curves at temperature T > 440 K in the crystals aged at 773 K are characterized by irreversible strain of ε_irr < 0.5% and stress hysteresis increase from 87 MPa (T = 448 K) to 297 MPa (T = 548 K) (Figure 4 and Figure 6c). The crystals with incoherent γ’ phase particles aged at 1373 K are characterized by the maximum stress hysteresis Δσ among the studied crystals. Stress hysteresis increases from 92 MPa to 431 MPa with the growth of the test temperature from T = 398 K to T = 568 K. A sharp increase in stress hysteresis also begins at the test temperature above 450 K in crystals aged at 773 K. Stress hysteresis generates from the energy dissipation not only in the form of frictional work to interfacial motion, but also in the form of plastic relaxation of the coherence stress in the martensite–austenite interface. The plastic relaxation of the coherence stress results in the irreversible strain ε_irr in loading/unloading. The analysis of the obtained experimental results shows that if there is no plastic relaxation of the coherence stress during MT, ΔT_ad weakly depends on stress hysteresis Δσ. However, if irreversible strain ε_irr is observed and stress-induced MT is accompanied by plastic accommodation in the working cycle, the ΔT_ad decreases with increasing Δσ. This is observed in the aged crystals at elevated test temperatures T > 450 K.

The energy dissipation in the operating cycle, which is proportional to stress hysteresis, is an important parameter for practical application and can have a significant influ ence on the cyclic stability of SE and EC effect. The cyclic stability of the SE and the EC effect in 150 loading/unloading cycles was studied in the crystals aged at 773 K at test temperatures near T = 323 K and in the crystals aged at 1373 K at test temperatures near T = 373 K (Figure 7 and Figure 8). This choice of test temperatures allows investigating the cyclic stability of the SE and the EC effect at similar critical stresses for martensite formation in these crystals. The maximum stress in the loading/unloading cycle was 600 MPa. It has been experimentally established that the aged [001]-oriented Ni₅₄Fe₁₉Ga₂₇ single crystals demonstrate high cyclic stability of the SE and the EC effect, which does not depend on the γ’ phase particle size and stress hysteresis Δσ. An increase in the number of loading/unloading cycles, n from 1 to 150, does not affect the value of ΔT_ad = 9.0 (±0.8) K (aged at 773 K for 1 h) and ΔT_ad = 8.5 (±0.8) K (aged at 1373 K for 0.5 h).

A degradation of the critical stresses of martensite formation σ_Ms and stress hysteresis Δσ is observed only in the first three cycles, n = 1−3. The critical stresses σ_Ms go down by 12–13 MPa and stress hysteresis decreases by 20–28 MPa in the second cycle, n = 2, compared with n = 1 in the single crystals aged at 773 K and 1373 K. This is determined by the effect of the first cycle, which is accompanied by irreversible strain less than 0.5% in the first cycle and the formation of a small volume fraction of residual martensite and/or dislocations. This contributes to the creation of favorable internal stress fields for the onset of stress-induced MT during the next cycles and a decrease in energy dissipation due to dislocation hardening, which leads to a decrease in σ_Ms and ∆σ. Such an effect of the first cycle is the common characteristic of SMAs when SE occurs [31].

Thus, despite different stress hysteresis, both aged Ni₅₄Fe₁₉Ga₂₇ single crystals oriented along the [001]-direction and as-grown crystals demonstrate high cyclic stability of SE and EC effect.

It is known that the energy dissipation and, accordingly, stress hysteresis determine the coefficient of performance (COP). COP is used to classify the EC properties of materials in terms of application efficiency. This coefficient is equal to the ratio of the useful thermal energy obtained from an endothermic reaction of a sample and the environment during cooling to the energy dissipation characterizing the input work in the loading/unloading cycles [32,33]:

$$\mathrm{COP}=\frac{{\mathrm{C}}_{\mathrm{p}}\Delta {\mathrm{T}}_{\mathrm{ad}}}{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathsf{\rho }$}\right.\oint \mathsf{\sigma }\mathrm{d}\mathsf{\epsilon }}$$

(6)

where $2\left|\Delta {\mathrm{G}}_{\mathrm{dis}}\right|=\frac{1}{\mathsf{\rho }}\oint \mathsf{\sigma }\mathrm{d}\mathsf{\epsilon }$ is the energy dissipation in the loading/unloading cycle.

Figure 9 shows the temperature dependence of the COP in the as-grown and aged Ni₅₄Fe₁₉Ga₂₇ crystals. It can be seen that high energy dissipation in the cycle and small specific heat capacity C_p (Table 1) lead to a significant decrease in the COP in the aged crystals compared with the as-grown ones. In the crystals aged at 773 K, the maximum COP reaches 10.6 and remains constant in a wide temperature range from 290 to 425 K. In the crystals aged at 1373 K, the maximum COP goes down and equals to 7.7. The maximum COP remains constant in a narrower temperature range from 313 to 400 K in these crystals. Nevertheless, the COP in the [001]-oriented Ni₅₄Fe₁₉Ga₂₇ crystals aged at 773 K for 1 h is comparable to that obtained earlier in copper alloys (CuAlMn, CuZnAl) and some ferromagnetic NiMnSn, NiMnInCo, and NiFeGaCo SMAs [1,34]. A wide range of operating temperatures and high cyclic stability of the SE and EC parameters allows us to conclude that the crystals aged at 773 K for 1 h have high potential for practical application along with the as-grown crystals.

5. Conclusions

The dependence of the EC effects on test temperature and particles size in the [001]-oriented aged Ni₅₄Fe₁₉Ga₂₇ single crystal undergoing L2₁(B2)-10M/14M-L1₀ martensitic transformations in compression have been studied. The main findings can be summarized as follows:

• It has been shown that aging at 773 K for 1 h and aging at 1373 K for 0.5 h leads to the precipitation of semi-coherent γ’-phase particles up to 500 nm in size and incoherent γ’-phases particles from 5 to 35 microns in size, respectively. Precipitation of γ’-phases particles, which do not undergo transformations, results in a decrease in the transformation entropy changes ΔS^A–M (ΔS^M–A) for both forward and reverse L2₁(B2)-10M/14M-L1₀ martensitic transformations as compared with as-grown single crystals. Moreover, the specific heat capacity C_p also decreases by 54 J/(kgK) in the crystals aged at 773 K and by 70 J/(kgK) in the crystals aged at 1373 K as compared with the as-grown crystals;
• The [001]-oriented Ni₅₄Fe₁₉Ga₂₇ single crystals aged at 773 K for 1 h exhibit the widest temperature range of the superelastic behavior and associated elastocaloric effect ΔT_SE = 270 K with the maximum adiabatic cooling ΔT_ad up to 11.1 (±0.5) K. The crystals with incoherent γ′-phase particles (aging at 1373 K, 0.5 h) show the operating temperature range of ΔT_SE = 255 K with slightly smaller adiabatic cooling ΔT_ad below 9.7 (±0.5) K. In contrast, the temperature range of the elastocaloric effect ΔT_SE = 195–200 K with the maximum adiabatic cooling ΔT_ad up to 10.9 (±0.8) K is smaller in the as-grown crystals than in the aged ones;
• The aged [001]-oriented Ni₅₄Fe₁₉Ga₂₇ single crystals demonstrate high cyclic stability: the adiabatic cooling ΔT_ad and loading/unloading curves do not depend on the number of operating cycles from 3 to 150 regardless of the particle size;
• Wide stress hysteresis and low values of specific heat capacity C_p lead to the decrease in the coefficient of performance (COP = 10.6–7.7) in the aged crystals as compared with the as-grown crystals (COP is up to 21.7). Despite this feature, the wide operating temperature range of the EC effect and excellent reversibility of the EC performance make aged [001]-orientated Ni₅₄Fe₁₉Ga₂₇ single crystals a promising elastocaloric material.