Effect of chemical ordering annealing on martensitic transformation and superelasticity in polycrystalline Ni–Mn–Ga microwires

Journal of Alloys and Compounds 645 (2015) 335–343

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Effect of chemical ordering annealing on martensitic transformation and superelasticity in polycrystalline Ni–Mn–Ga microwires M.F. Qian a,b,1, X.X. Zhang a,⇑, L.S. Wei a, L. Geng a, H.X. Peng c,⇑ a

School of Materials Science and Engineering, Harbin Institute of Technology, Harbin 150001, PR China Advanced Composites Centre for Innovation and Science (ACCIS), University of Bristol, Queen’s Building, University Walk, Bristol BS8 1TR, United Kingdom c Institute for Composites Science Innovation (InCSI), School of Materials Science and Engineering, Zhejiang University, Hangzhou 310027, PR China b

a r t i c l e

i n f o

Article history: Received 11 March 2015 Received in revised form 28 April 2015 Accepted 14 May 2015 Available online 19 May 2015 Keywords: Ni–Mn–Ga alloys Melt-extraction Chemical ordering annealing Superelasticity Martensitic transformation

a b s t r a c t Polycrystalline Ni–Mn–Ga microwires of diameter 30–80 lm were prepared by melt-extraction technique on a large scale. The rapidly solidified microwires exhibit a fairly high ductility and excellent shape memory property. Here, with the aim to reduce the defect density, internal stress and compositional inhomogeneity in the as-extracted microwires, a stepwise chemical ordering annealing heat treatment was carried out and the effect of annealing on martensitic transformation, magnetic properties and superelastic behavior were investigated. The results indicate that annealing increase the transformation temperature and decrease the transformation hysteresis. These are related to composition homogenization, increase of atomic ordering and decrease in internal stress and defects. During mechanical tests, the stress-induced martensite (SIM) formation took place at a much lower stress after annealing treatment. The annealed microwires also demonstrate a lower superelastic hysteresis and a higher recovery rate compared to the as-extracted microwires. The temperature dependence of SIM stress is weaker after annealing, which is related to the enthalpy change (DH) and phase transformation temperature change according to the Clausius–Clapeyron relation. Ó 2015 Elsevier B.V. All rights reserved.

1. Introduction Ni–Mn–Ga ferromagnetic shape memory alloys (FMSMAs) undergoing a martensitic transformation (MT) from a high-symmetric L21 austenite to low-symmetric martensite are promising candidate materials for new actuators and sensors in which high response frequency and large reversible strain are needed [1]. Ni–Mn–Ga alloys have been demonstrated to exhibit high magnetic-field induced strain (MFIS) [2–6], superelasticity [7–9] and shape memory effect [10] driven by an external magnetic field. On the other hand, they also show well-pronounced superelasticity [11] and shape memory effect [12,13] driven by a thermal field, which is similar to traditional shape memory alloys such as Ni–Ti. In Ni–Mn–Ga single crystals, a shape memory effect (SME) of 6.1% [14] and a superelastic strain of 6% [11] have been achieved.

⇑ Corresponding authors. Tel.: +86 571 87952660, +86 451 86415894; fax: +86 451 86413921. E-mail addresses: [email protected] (X.X. Zhang), [email protected] (H.X. Peng). 1 When the work was carried out, M.F. Qian was a visiting postgraduate at Bristol University. http://dx.doi.org/10.1016/j.jallcom.2015.05.118 0925-8388/Ó 2015 Elsevier B.V. All rights reserved.

A rubber-like behavior with reversible elastic strain >10% at compressive stress of 90 MPa has also been demonstrated in the martensite state of Ni–Mn–Ga single crystals [15]. In polycrystalline Ni–Mn–Ga alloys, a plastic strain of 3.82%, MFIS of 0.82% [16] and a large reversible superelastic strain of 10.9% have been reported [17]. The inertia and eddy current effects decrease with decreasing sample size at high frequency [18], thus, small size Ni–Mn–Ga alloys such as microwire, micropillar, ribbon and film are desirable for applications in micro-actuators and sensors operating at high response frequencies. Our previous work [19] demonstrated that Ni–Mn–Ga microwires prepared by melt-extraction technique exhibited a higher reversible superelastic strain and recoverable shape memory strain compared with bulk parent alloys. The higher strain achieved in Ni–Mn–Ga microwires is related to the low intergranular fracture tendency due to grain refinement caused by the melt-extraction process. MT of Ni–Mn–Ga bulk alloys is significantly influenced by the composition, electron concentration e/a and heat treatment history [20]. Annealing heat treatment of Ni–Mn–Ga alloys may increase the atomic order degree of L21 structure and thus enhances the saturation magnetization, stability of martensite phase and Curie point (Tc) [21,22]. The relationship between the atomic ordering

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and magnetic coupling of Mn atoms occupying different sites in Ni–Mn–Ga alloys has been systematically studied [23]. MT in small size Ni–Mn–Ga microwires, ribbons or films is more complicated, because these materials are usually prepared under an in-equilibrium state, such as rapid solidification, and is size dependent because of the large specific surface area. An enhancement of magnetization and a reduction of MT hysteresis were observed in Ni–Mn–Ga microwires after annealing at 800 °C. The improved MT and magnetic characteristics are related to the improvement of antiferromagnetic Mn–Mn exchange interactions associated with reduction in the density of defects (such as vacancies, atomic disorder and antiphase boundaries) [24]. Besides, internal stresses developed during the fabrication processes exert a profound effect on the properties of small size shape memory alloys [25]. The internal stresses formed during the fabrication of glass-coated microwires have been calculated in Ref [26]. In comparison with glass-coated microwires, internal stresses in melt-extracted microwires are likely: (1) the radial stresses caused by the high overcooling of the copper wheel; (2) the axial stresses produced by the extracting of the microwires. As annealing reduces the defect density and internal-stress, it may increase the elastic strain energy storage and reduce the energy dissipation, which may affect the superelasticity. In the present work, non-stoichiometric Ni–Mn–Ga microwires with diameters of 30–80 lm were prepared by melt-extraction and then subjected to a chemical ordering heat treatment. The effects of chemical ordering on the MT, magnetic properties and superelasticity were systematically investigated.

2. Experimental details Ni–Mn–Ga alloy ingots with a nominal composition of Ni50.6Mn28Ga21.4 (numbers indicate atomic percent) were prepared by induction melting pure Ni (99.99%), Mn (99.98%) and Ga (99.99%) under argon atmosphere and mold casting. The synthesis process for Ni–Mn–Ga microwires by melt-extraction technique has been reported in Ref. [19]. The as-extracted microwires were sealed in a quartz ampoule, backfilled with argon atmosphere and stepwise heat treated at 725 °C for 2 h, 700 °C for 10 h and 500 °C for 20 h. To avoid oxidation and Mn vaporization during the heat treatment, pure Mn particles and Ti foils were sealed in the tube along with the microwires. The microstructure of the microwire was examined with a scanning electron microscope (SEM) equipped with an energy dispersive spectrum (EDS) and a Tecnai G2 F30 transmission electron microscopy (TEM). XRD analysis was undertaken using a Philips X’Pert Pro instrument with Cu Ka radiation (k = 1.54 Å) for phase identification. A TTK 450 low temperature chamber was used for sample cooling for low temperature phase identification. The scan speed was 0.005°/s with a step size of 0.02°. MT temperatures and enthalpy changes of the microwires were measured by a TA Q2000 differential scanning calorimeter (DSC) with cooling and heating rates of 5 °C/min. Transformation temperature and Curie point of the microwires were also confirmed with a vibrating sample magnetometer (VSM, DSM Model 10) under a magnetic field of 0.025T, by heating the sample from 18 °C to 125 °C at 8.5 °C/min, maintaining this temperature for 5 min and cooling to 18 °C at 8.5 °C/min. The magnetization curves were obtained using a Quantum Design MPMS XL5 VSM. The microwire axis was oriented along the magnetic field direction. In order to determine the martensitic transformation temperature of each microwire and select the superelastic test temperatures, the internal friction vs temperature curve (tan d  T) of the microwire was obtained using Q800 DMA and then the same microwire was subjected to superelastic cycles at different temperatures. An as-extracted and an annealed microwire, with martensite starting temperature Ms 14.7 °C and 36.9 °C, respectively, were chosen for superelastic tests. The as-extracted microwire were heated to 80 °C and kept at this temperature for 12 min, then cooled to 15 °C (slightly higher than Ms) and subjected to a tensile loading–unloading cycle with a rate of 0.02 and 0.04 N/min, respectively. After a superelastic cycle at 15 °C, the microwire was heated to 80 °C and kept for 12 min for a second time, then cooled to a second temperature of 18 °C for a second superelastic cycle. The processes were repeated at 15, 18, 20, 23, 25, 28, 30, 33 °C for the as-extracted microwire and 37, 40, 42, 45, 47, 50 °C for the annealed microwire. The heating and cooling rates during the superelastic tests were 5 °C/min. For convenience, Ttest–Ms (0, 3, 5, 8, 10, 13 and 15 °C for both microwires) is introduced to denote the temperature level for the superelastic tests.

3. Results and discussions 3.1. Microstructural characterization Table 1 summarizes the average composition of the as-extracted and annealed microwires measured on the microwire surface and the fractured cross section. The average compositions and the standard deviations were obtained from six microwires on the surface and four microwires on the cross section. Within the experimental error, the composition change is small after the chemical ordering annealing heat treatment. Cellular grains with a diameter of 1–5 lm on the surface were observed for both as-extracted and annealed microwires, as shown in Fig. 1(a) and (b). Fig. 1(c) and (d) shows the grains in the longitudinal cross section of the microwires. The grains in the as-extracted and annealed microwires have almost the same size and morphology. So the heat treatment at 725 °C did not lead to substantial grain growth. In addition, martensite twins existed in the annealed microwire, indicating that the annealed microwire has a martensite structure at room temperature. Fig. 2 shows two TEM micrographs of the as-extracted (a) and annealed (b) microwires. At the temperature of 15 °C, the as-extracted microwire contains a mixture of martensite and austenite phases. Fig. 2(a) shows the stripe-like martensite twin plates in the microwire. A high density of dislocation is presented in the martensite phase. Fig. 2(b) shows stripe-like martensite twins in the annealed microwire, which contains only martensite phase at the observation temperature. Compared with the as-extracted microwire, the density of dislocation is significantly reduced after annealing. With respect to the crystal structure of the microwires, Fig. 3 shows the XRD patterns of as-extracted and annealed microwires. The as-extracted microwires are L21 austenite (P) at room temperature with a = 5.83 Å. The cell volume is V = 198.16 Å3, and the volume per atom is 12.38 Å3. When the as-extracted microwires were then cooled to 10 °C to reach a martensite state, the 7M incommensurate modulated martensite (‘‘7M’’IC) [27] was obtained with a = 4.23 Å, b = 5.53 Å and c = 41.93 Å. The cell volume is 980.82 Å3 and the volume per atom is 12.26 Å3. For the annealed microwire, the XRD pattern at 25 °C shows a single 5M commensurate monoclinic martensite (‘‘5M’’C) [28] with a = 4.22 Å, b = 5.56 Å and c = 20.96 Å. The cell volume is V = 491.79 Å3, and the volume per atom is 12.29 Å3. The different volume values per atom between as-extracted and annealed microwires at martensite state imply the change of internal stress and defects after annealing. It is interesting to find that the as-extracted and the annealed microwires have different martensite structures, although their compositions are similar. According to Jiang [29], during the austenite to martensite transformation, the volume free energy change DGv can be expressed by:

DGv ¼

DHDT ; T0

ð1Þ

where DGv and DH are changes in volume free energy and enthalpy, respectively. T0 is the phase equilibrium temperature between the two phases, DT is the undercooling (T0  Mp), and approximately equals to (Ap  Mp)/2, where Mp and Ap are the forward and reverse transformation peak temperature, respectively. Therefore,

DGv ¼ DH ðAp  Mp Þ=ðAp þ Mp Þ

ð2Þ

The absolute value of enthalpy change and Ap  Mp are similar and smaller for 5M and 7M compared with the value of Ap + Mp (as shown in Table 2). Therefore,

DGP!7M < DGP!5M <0 v v

ð3Þ

M.F. Qian et al. / Journal of Alloys and Compounds 645 (2015) 335–343 Table 1 Composition of the as-extracted and annealed Ni–Mn–Ga microwires. Material state

As-extracted Annealed

Composition (at.%) Ni

DNi

Mn

DMn

Ga

DGa

49.9 50.1

0.3 0.2

28.6 28.5

0.5 0.3

21.5 21.4

0.5 0.3

It can be seen that 7M martensite has a lower free energy than 5M, implying that 7M martensite is more stable than 5M when performing the reverse martensitic transformation [29]. However, the as-extracted microwire exhibits a 7M martensite while the annealed microwire has a 5M martensite. This may be related to the high internal stress formed during the rapid solidification process, which favors the formation of 7M martensite. After annealing and thus internal stress relaxation, 5M structure showed up again in the annealed microwires. 3.2. Martensitic transformation Table 2 shows the transformation temperatures, Ms, Mf, As, Af and Tc, of the as-extracted and annealed microwires obtained both from DSC (Fig. 4(a)) and VSM (Fig. 4(b)). Both forward and reverse MT temperatures shifted towards higher temperatures with reduced transition range (Ms–Mf, Af–As) after annealing. The Tc of the annealed microwire, which can be clearly seen in DSC and VSM, is slightly higher than that of as-extracted ones. All transformation temperatures are in a range typical for modulated martensite. The effect of annealing on MT of the microwires is related to changes of composition (such as Mn evaporation or compositional homogeneity [30]), Ga vacancy concentration [31], long-range atomic ordering [22] and release of internal stress [32]. Table 2 shows that, after annealing, MT transition ranges of both forward and reverse transformation change from 20.4 and 21.0 °C to 4.1 and 4.3 °C after annealing. Aside from the more homogenous composition, the reduced transition range is also likely related to the low internal stress in the annealed microwire.

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In Fig. 5, compared with the as-extracted microwire, the annealed microwire showed a lower saturation field and a higher saturation magnetization, which implies that the annealed microwire has a smaller internal stress as well as diminished defects [30]. During MT of as-extracted microwires, internal stress favors the preferentially oriented martensite variants. As a result, more elastic strain energy forms and thus more undercooling is required leading to a broader transition range. Annealed microwires have a smaller peak to peak hysteresis (10.6 °C) compared with the as-extracted ones (12.2 °C), which is related to two energy dissipative processes: (1) the stored elastic strain energy is dissipated when the coherency strains of martensite–austenite interface relax or bypasses dislocations or precipitates [33,34], (2) frictional work is dissipated to overcome the resistance to interfacial motion. Both dissipation processes may increase the MT hysteresis. After annealing treatment, both frictional work and stored elastic strain energy dissipation are reduced due to decreased internal stresses and defects density. In the as-extracted microwires, the higher internal stress acts as a driving force for reverse MT and thus should decrease the MT hysteresis. However, more stored elastic strain energy is relaxed due to energy dissipation. On the other hand, elastic strain energy is less relaxed in annealed ones, so more stored elastic strain energy is available to assist the reverse transformation, which narrows the MT hysteresis. In addition, frictional work dissipation plays an important part in the hysteresis size as well [35]. Therefore, the hysteresis will be smaller when both dissipation processes are minimized. As shown in Table 2, the enthalpy changes DH for both microwires agree well with that of group II Ni–Mn–Ga alloys [36]. The slight difference of DH during cooling and heating processes is related to the occurrence of the acoustic emission during MT [37]. 3.3. Magnetic properties The initial magnetization curves of the microwires before and after annealing are shown in Fig. 5. Both microwires were tested at temperatures slightly below Ms in their martensite states (0 °C and 25 °C for as-extracted and annealed microwires, respectively).

Fig. 1. Scanning electron micrographs showing surface (a and b) and longitudinal cross-section (c and d) morphologies of as-extracted (a and c) and annealed (b and d) Ni– Mn–Ga microwires. The inset in (d) shows high magnification of twin structures in the annealed microwires.

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Fig. 2. TEM bright field images of (a) as-extracted and (b) annealed Ni–Mn–Ga microwires observed at room temperature (15 °C).

Fig. 3. XRD patterns of the as-extracted (a and b) (tested at 25 °C and 10 °C) and (c) annealed (tested at 25 °C) Ni–Mn–Ga microwires. The insets show diffraction peaks between 42° and 45.5° of the as-extracted and annealed microwires.

After annealing, the saturation magnetization increased from 40 to 64 emu/g. The saturation magnetic field of the annealed microwire is 7000 Oe, while saturation of the as-extracted microwires cannot be reached at 50,000 Oe. Since the magnetism in Ni–Mn–Ga alloys is thought to be mainly due to the Mn–Mn atomic interaction [38], the different saturation field can be addressed to Mn atoms ordering in the lattice.

As shown in the inset of Fig. 5, the magnetization curve of the as-extracted microwire shows a slope change with increasing field. This implies the occurrence of magnetic-field-induced variant reorientation (MIR) [30]. The result shows that the field for the occurrence of MIR (H⁄) is 4500 Oe for the as-extracted microwire at 0 °C. H⁄ decreases rapidly as the martensite to austenite transformation temperature is approached [31], which is mainly due

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M.F. Qian et al. / Journal of Alloys and Compounds 645 (2015) 335–343 Table 2 Martensitic transformation of the as-extracted and annealed Ni–Mn–Ga microwires from DSC and VSM tests. Material state

As °C

Ap

Af

Ms

Mp

Mf

Hysteresis

Tc

DHcooling (J/g)

DHheating

As-extracted

DSC VSM

15.4 21.7

24.6 –

36.4 31.4

21.9 24.5

12.4 –

1.5 16.4

12.2 5.3

– 87.2

4.5 –

4.9 –

Annealed

DSC VSM

48.6 43.7

51.1 –

52.7 52.3

42.8 44.7

40.5 –

38.5 42.6

10.6 1.1

94.3 98.6

5.5 –

4.5 –

Fig. 4. Heating and cooling (a) DSC plots and (b) VSM measurements (temperature dependence of normalized magnetization, M/M0, where M0 is the maximum magnetization value during each heating–cooling cycle) curves in the as-extracted and annealed Ni–Mn–Ga microwires. The inset figure in (a) shows the 1st derivative of the DSC curves around the Tc (ranging from 90 to 100 °C) of the annealed microwire.

Fig. 5. Magnetization curves of the as-extracted and annealed Ni–Mn–Ga microwires. The inset figure shows the 2nd derivative of the magnetization curve of asextracted microwire at a magnetic field between 2000 and 12,000 Oe.

to the better mobility of the twin boundaries with increasing temperature. In contrast, for the annealed microwire, the magnetization increases rapidly below 500 Oe and then gradually increases to reach the saturated state at 8000 Oe. This indicates that the magnetic anisotropy after chemical annealing is higher than the as-extracted state. Therefore, the MIR may take place at a low field. 3.4. Superelastic behavior of the microwires 3.4.1. Superelastic curves Fig. 6 shows the superelastic curves of both microwires at different temperatures. The ductility of the microwires is enhanced due to the size effect [39]. The maximum stress-induced strains without breaking reach 3.63% at 20 °C under 330 MPa for the as-extracted microwire and 2.06% at 37 °C under 165 MPa for the annealed microwire. The annealed microwire shows smaller

strains at each temperature due to the lower maximum load applied. For both microwires, the elastic deformation of austenite occurred at first stage (part I), after that SIM happened resulting in decrease of the gradient in the superelastic plateau (part II). The slope increased again after the SIM finished and elastic deformation of martensite occurred (part III). Except for the cycle of as-extracted microwire at Ms + 0 °C, which have multi-stages during loading, all other cycles show a one-stage superelastic effect produced by the stress-induced austenite to 7M and austenite to 5M martensitic transformation for microwires before and after annealing, respectively. Upon unloading, the strain partly recovered, either by elastic deformation (part IV) or incomplete martensite to austenite transformation. The remaining strain was completely recovered when the microwire was heated to 80 °C demonstrating no plastic deformation occurred during the loading process. In comparison with as-extracted microwires, the critical SIM stresses for annealed microwire were much lower. As mentioned before, more frictional work was dissipated due to the resistance to interfacial motion in as-extracted microwire because of the higher internal stress and obstacles introduced during fabrication, which compels additional loading to initiate the forward SIM transformation. Fig. 7 displays the slopes in different parts of superelastic deformation curves. The slope of part I represents the elastic modulus of the austenite phase. It can be seen that the slope decreases with decreasing temperature for both microwires, which is consistent with the results reported in Ref. [40]. The elastic modulus softening is related to the soft phonon mode condensation due to the pre-existing modulation of the phase [40]. During SIM process, unlike single crystalline alloys [11], the stress steadily increases, reflecting the polycrystalline nature of the microwire. Furthermore, the annealed microwire exhibited a shallower plateau compared with the as-extracted one at the same temperature levels, as shown in Fig. 7_part II. This may be attributed to the smaller internal stress in the annealed microwire. In the

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Fig. 6. Tensile stress–strain curves of (a) as-extracted and (b) annealed Ni–Mn–Ga microwires at temperature levels (Ttest–Ms) approximately from 0 °C to 15 °C at austenite state (equilibrate at 80 °C, then cool down to Ttest). eirr, ese and eel stand for the irreversible strain (recovered upon heating), strain recovery upon reverse transformation and elastic recovery, respectively.

Fig. 7. Temperature dependence of slopes in different parts of superelastic curves in the as-extracted and annealed Ni–Mn–Ga microwires.

as-extracted microwires, the internal stress restricts the formation of self-accommodate martensite variants. As a result, higher elastic strain energy accumulates in the as-extracted microwire, which acts as resistance to the forward transformation. Accordingly, a higher stress is needed for a complete SIM transformation. In addition, the increase of atomic ordering degree makes shear transformation easier [41], which leads to an SIM formation at low stress since less energy is required. Finally, less defects and composition homogenization after annealing increases the mobility of martensite twin boundaries, which also favors the SIM process.

After the saturation of SIM transformation, the slope of the curve increased again, as shown in Fig. 7_part III. Although this is considered as the martensite elastic deformation part, it does not necessarily involve only one transformation component. Elastic deformation of residual austenite, further SIM transformation or even inter-martensitic transformation (IMT) could occur in this part. This warrants further investigation. In SMAs, reversibility of superelasticity is important for practical applications. Fig. 8 shows the recovery rate of each superelastic cycle for both types of microwires. The relationship between the recovery rate and temperature is divided into three parts, part A, B and C, as shown in Fig. 8. A very slow increase of recovery rate was observed in part A, mainly before Ms + 8 °C. According to Fig. 6, although the annealed microwire showed the reverse transformation at Ms + 0 °C, only a slight slope change appears at the end of the unloading process. For as-extracted one, the reverse transformation occurred until Ms + 8 °C. Therefore, in part A, only eel contributed to the total erec. Furthermore, because of the higher maximum applied stress of the as-extracted microwire, more eel recovered after unloading, contributing to the higher recovery rate of the as-extracted wire than annealed wire. After Ms + 8 °C, a sharp increase of recovery rate can be seen in Fig. 8. With increasing temperature, more external stress was required to initiate the SIM transformation because of the stabilization of the austenite. Therefore, more elastic strain energy was stored during loading to assist the reverse transformation, thus increased the contribution of ese to the total erec. However, eel was still the main part of erec, which led to the higher recovery rate of as-extracted microwire in part B.

M.F. Qian et al. / Journal of Alloys and Compounds 645 (2015) 335–343

Fig. 8. Recovery rate vs temperature relations for as-extracted and annealed Ni–Mn–Ga microwires.

With increasing temperature up to Ms + 13 °C, the increase rate became small, as shown in part C. In this case, external stress required for SIM transformation became even larger, so that only partial SIM transformation was finished because of the smaller maximum stress applied. The increased stored elastic strain energy assisted the reverse transformation, thus, a larger ese was obtained. As shown in Fig. 6(b), the annealed microwire almost completely recovers the deformation strain during unloading at the temperature of about Ms + 13 °C. In contrast, the strain is only partially recovered for the as-extracted microwire. Therefore, a high recovery rate of 97% was obtained in the annealed microwire at Ms + 15 °C. In fact, as described in Section 3.1, 7M martensite is more stable than 5M, thus, a higher external energy is needed for the reverse transformation of 7M martensite [29]. Another factor is related to the higher degree of atomic order, which enhances the reversibility of the annealed microwire as well. In addition, the slopes of part IV decrease with increasing temperature, which is consistent with Ni–Mn–Ga single crystals and other FMSMAs such as Ni–Fe–Ga and Ni–Fe–Co–Ga [19,40,42,43]. The reduced mobility of the martensite at low temperature contributes to the increase in martensite elastic modulus [40]. To gain further insight into the hysteresis behavior, two superelastic stress–strain responses at same temperature level (Ms + 13 °C) were compared in Fig. 6. Here the stress hysteresis is defined at the middle of the loading stress plateau of the hysteresis loops [35]. Obviously, the hysteresis of the annealed microwire is much lower than that of the as-extracted one which is in agreement with the result obtained by DSC, which is due to the low energy dissipation for both resistance to interfacial motion and stored elastic strain energy dissipation. 3.4.2. Temperature dependence of superelastic stress The onset stress for SIM transformation (rMs) follows the Clausius–Clapeyron relationship, with a slope (drMs/dT) of 7.6 MPa/K for the as-extracted microwire and 7.1 MPa/K for the annealed one. Fig. 9 compares the rMs vs temperature diagrams with respect to Ni–Mn–Ga microwires from our previously work [19], Ni–Mn–Ga single crystals [11,41], other FESMAs single crystals [42,44] and the present Ni–Mn–Ga microwires. Clearly, Ni–Mn–Ga single crystals possess lower temperature dependence than polycrystalline alloys. The differences can be explained according to the generalized Clausius–Clapeyron equation, shown as follows:

drMs DHq ¼ dT eT 0

ð4Þ

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Fig. 9. SIM critical stress (rMs) vs temperature plots of the as-extracted and annealed Ni–Mn–Ga microwires. Data in Ni–Mn–Ga [11,41] and some other conventional superelastic alloys (single crystals [42,44] and polycrystals [45,46]) are also displayed. The results of polycrystalline Co–Ni–Al and Ti–Nb alloys are presented in inset (I). The inset (II) shows critical stresses (rMs, rMf, rAs and rAf) vs temperature plots in both as-extracted and annealed Ni–Mn–Ga microwires.

where DH and T0 stand for the enthalpy change and phase equilibrium temperature between austenitic and martensitic phases (mentioned in Section 3.1), respectively, and T0 approximately equals to (Ap + Mp)/2, q is the mass density, and e is the theoretical strain in the direction of the applied stress. As shown in Table 2, the average enthalpy change DH of the as-extracted and the annealed microwires obtained from DSC curve are 4.7 and 5.0 J/g, respectively. The value of q is taken as 8.2 g/cm3. T0 temperatures derived from DMA experimental results are 294.2 K for as-extracted and 317.5 K for annealed microwires, respectively. The value of e can be evaluated from the lattice parameters of austenite and certain kind of martensite for single crystal. However, because of the constraints between grain boundaries and the multi-variant state in martensite, the value of e is lower than that in single crystal, which leads to the higher slope. Therefore, different DH, T0 and e for as-extracted and annealed microwires lead to the different values of drMs/dT. The theoretical maximum strains of both microwires, which can be induced either by external stress or magnetic field, can also be calculated using Eq. (4), are 0.017 for as-extracted and 0.018 for annealed microwires, respectively. Obviously, the theoretical strains of polycrystalline microwires are much lower than that of single crystals. The temperature dependence of the SIM stress (rMs/dT  7.6 MPa/K) in the present microwires is larger than that in Ni–Mn–Ga single crystals (2.8 MPa/K along [0 0 1] and 5.2 MPa/K along [1 1 0]) [11,41] and in some other ferromagnetic shape memory single crystals (2.1 MPa/K in Ni–Mn–Co–In and 1.4 MPa/K in Ni–Fe–Co–Ga) [42,44]. Besides, the temperature dependence of SIM stress in other conventional polycrystalline superelastic alloys are presented in inset (I). The temperature dependence of the SIM stress in these alloys (2.5 MPa/K in Co– Ni–Al and 4.4 MPa/K in Ti–Nb [45,46]) are relatively smaller than that in Ni–Mn–Ga microwires, which may be related to the larger grain size (1–5 mm in Co–Ni–Ga alloys) obtained in these alloys. In short, polycrystalline Ni–Mn–Ga microwires exhibit higher temperature dependences compared with Ni–Mn–Ga single crystals and conventional superelastic alloys, which is considered to be related to the small grains achieved by melt-extraction. Temperature dependences of other superelastic stresses, including the forward transformation starting and finishing stresses (rMs, rMf) and reverse transformation starting and finishing stresses (rAs, rAf), are plotted against temperature in the inset (II)

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of Fig. 9. It can be seen that the temperature dependences are lowered after annealing. The obtained temperature dependences of the superelastic stresses are also larger than conventional superelastic alloys. In particular, the slope of rAs is higher than those of other stresses in both microwires, indicating a higher temperature dependence of the reverse transformation. The slope (drAs/dT) of the annealed microwire, 15.6 MPa/K, is smaller than that of as-extracted one, 17.5 MPa/K, revealing an easier reverse transformation process in the annealed microwire. 4. Conclusions Martensitic transformation, microstructure and superelasticity of Ni–Mn–Ga microwires before and after chemical ordering annealing were comparatively studied. The following conclusions can be drawn: (1) Chemical ordering annealing promotes an increase in MT temperatures, Curie point and saturation magnetization of Ni–Mn–Ga microwires. The changes are related to the increase in the atomic ordering as well as the decrease in internal stress and defect density. In addition, martensite structure changes from 7M to 5M after annealing. (2) The superelasticity can be tailored by chemical ordering annealing. Annealing decreases the SIM stress and the hysteresis, and improves the reversibility during superelastic cycling. After annealing, the stress change amplitude during SIM process is smaller and the temperature dependences of the superelastic stresses become weaker. (3) The annealed Ni–Mn–Ga microwires exhibit lower superelastic stresses, lower temperature dependences, higher superelastic reversibility, higher magnetization (higher Tc) and a near room temperature MT. Besides, the preparation of the microwires is convenient and efficient. Given these properties, the present microwire is expected to be used for practical applications such as superelastic materials, micro-actuator and micro-sensor materials in various fields.

Acknowledgements This work was financially supported by National Natural Science Foundation of China (NSFC) under Grant No. 51001038 and Ministry of Science and Technology Bureau of Harbin under Grant No. 2011RFQXG001. MFQ acknowledges the financial support from the Chinese Scholarship Council (CSC) for her one year exchange at the University of Bristol. The authors are grateful to P. Müllner at Boise State University for the discussion. XXZ thanks C. Witherspoon and A. Rothenbühler at Boise State University for assistance in VSM experiments. References [1] O. Söderberg, I. Aaltio, Y.L. Ge, X.W. Liu, S.P. Hannula, Recent developments of magnetic SMA, Adv. Sci. Technol. 59 (2009) 1–10. [2] S.J. Murray, M. Marioni, S.M. Allen, R.C. O’Handley, T.A. Lograsso, 6% magneticfield-induced strain by twin-boundary motion in ferromagnetic Ni–Mn–Ga, Appl. Phys. Lett. 77 (2000) 886–888. [3] A. Sozinov, A.A. Likhachev, N. Lanska, K. Ullakko, Giant magnetic-field-induced strain in NiMnGa seven-layered martensitic phase, Appl. Phys. Lett. 80 (2002) 1746–1748. [4] M. Chmielus, X.X. Zhang, C. Witherspoon, D.C. Dunand, P. Müllner, Giant magnetic-field-induced strains in polycrystalline Ni–Mn–Ga foams, Nat. Mater. 8 (2009) 863–866. [5] A. Sozinov, N. Lanska, A. Soroka, W. Zou, 12% magnetic field-induced strain in Ni–Mn–Ga-based non-modulated martensite, Appl. Phys. Lett. 102 (2013) 021902.

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