Dependence of the martensitic transformation and magnetic transition on the atomic order in Ni–Mn–In metamagnetic shape memory alloys

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Acta Materialia 60 (2012) 1937–1945 www.elsevier.com/locate/actamat

Dependence of the martensitic transformation and magnetic transition on the atomic order in Ni–Mn–In metamagnetic shape memory alloys V. Recarte a,⇑, J.I. Pe´rez-Landaza´bal a, V. Sa´nchez-Alarcos a, J.A. Rodrı´guez-Velamaza´n b,c a

Departamento de Fı´sica, Universidad Pu´blica de Navarra, Campus de Arrosadı´a, 31006 Pamplona, Spain b Instituto de Ciencia de Materiales de Arago´n, CSIC—Universidad de Zaragoza, Zaragoza, Spain c Institut Laue-Langevin, CRG’s D1B, F-38042 Grenoble, France Received 2 November 2011; received in revised form 22 December 2011; accepted 12 January 2012 Available online 1 March 2012

Abstract The analysis of atomic order and its influence on the magnetic and structural properties of Ni–Mn–In metamagnetic shape memory alloys has been performed. The effect of the different thermal treatments on the magnetic and structural transformation temperatures, as well as on the thermodynamics of the martensitic transformation, has been made by calorimetric measurements. The evolution of the degree of long-range atomic order with temperature has been determined by neutron diffraction experiments, thus confirming the effect of thermal treatments on the atomic order. Calorimetric and structural results allow thermal treatments to be directly related to atomic order, and to allow the effect of the atomic order on the martensitic and magnetic transformations in Ni–Mn–In alloys to be quantified. The thermodynamics of the martensitic transformation depends on the atomic order as indicated out by its influence on the transformation entropy. In addition, a correlation between the transformation entropy and changes in the magnetic-field-induced transformation temperatures has been found through the evolution of the atomic order. Ó 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Metamagnetic shape memory alloys (MSMAs); Martensitic phase transformation; Long-range ordering; Neutron diffraction

1. Introduction Ni–Mn-based Heusler alloys exhibiting both long-range magnetic ordering and thermoelastic martensitic transformation (MT) have been intensively investigated for a number of years, both from fundamental and applied points of view, since a giant magnetic field-induced strain associated with the rearrangement of martensitic variants (103 times the magnetostriction in Terfenol-D, the most magnetostrictive material) was first reported in Ni–Mn–Ga alloys close to the stoichiometric alloy composition Ni2MnGa [1]. Alongside magnetically induced deformation, other interesting properties recently observed in these alloys, such as magnetoresistance or the giant magnetocaloric effect, also ⇑ Corresponding author. Tel.: +34 948 169578; fax: +34 948 169565.

E-mail address: [email protected] (V. Recarte).

related to the coupling between structure and magnetism, are being widely studied due to their potential for practical applications in sensing and magnetic refrigeration [2–4]. In addition, interesting new phenomena such as magnetic field induction of the MT, kinetic arrest of the martensite or the observation of a peculiar isothermal character in some thermoelastic martensitic transformations, arise in the socalled metamagnetic shape memory alloys (MSMAs, i.e. Ni–Mn–In, Ni–Mn–Sn and Ni–Mn–Sb systems) [5–7]. These additional properties are linked to the occurrence of a MT between a ferromagnetic austenite and a weak magnetic martensitic phase [8–11]. The MT in Ni–Mn–X (X = Ga, In, Sn, Sb) alloys takes place from a cubic austenitic phase, showing L21 Heusler crystal structure (space group Fm3m) and next-nearestneighbor atomic order, to a low-symmetry martensitic structure [8–11]. Due to the diffusionless character of the

1359-6454/$36.00 Ó 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2012.01.020

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V. Recarte et al. / Acta Materialia 60 (2012) 1937–1945

transformation, the martensitic phase inherits the degree of long-range atomic order (LRO) of the austenite. Nevertheless, these alloys do not solidify directly from the melt to the Heusler structure but to a CsCl-type B2 structure (space group Pm 3m) with nearest-neighbor atomic ordering. The austenitic L21 structure is then reached through a second-order B2–L21 transition taking place at different temperatures depending on both composition and the X element [12–17]. The ordering temperatures reported in the composition range of interest lie typically around 1050 K in Ni–Mn–Ga alloys, and around 950 K in Ni– Mn–In alloys [12,17]. The MT temperature has been also proved to be very sensitive to composition, and in all cases the compositional dependence can be described as a function of the valence-electron to atom ratio, e/a [18–21]. The configurational ordering of the constituent elements in the crystal lattice affects both the MT characteristics and the magnetic properties of Ni–Mn-based alloys. This is related to the modification of both the electronic structure and the lattice site occupancies. In particular, for a given alloy composition, the LRO can be easily modified by means of various thermal treatments. In this sense, the effect of atomic ordering on high-temperature quenching and post-quench aging on the martensitic, intermartenstic and premartensitic transformations as well as on the magnetism has been systematically studied in the Ni–Mn–Ga system [16,22–29]. It has been shown that quenching from high temperatures (around the B2–L21 ordering temperature) allows to partially retain the low atomic order present at these temperatures, in such a way that the LRO degree of the as-quenched alloys is lower than the equilibrium value allowed by the stoichiometry, which can be achieved after a sufficiently slow cooling. The metastable state retained after quenching may evolve to the stable state (i.e. the equilibrium atomic order degree of the alloy may be restored) once the alloy is heated up to a temperature at with atomic diffusion is possible [16,29]. It has recently been confirmed by neutron diffraction measurements that the post-quench ordering process in Ni–Mn–Ga mainly consists of the diffusion of Mn (Ga) atoms in the Ga (Mn) sublattice to their own sublattice [29], and that, irrespective of the thermal treatments, both the MT and Curie temperatures increase with increasing atomic order. Interestingly, both transformation temperatures show exactly the same linear dependence on the degree of L21 atomic order, and hence a quantitative correlation between the MT temperature and the LRO could be established, thus making it possible to calculate the effect of the L21 atomic order degree on the relative stability between the austenite and martensitic phases in terms of the free energy change [29,30]. On the other hand, the effect of atomic order on MSMAs (X = In, Sn, Sb) has been little studied. It has been recently reported that the MT temperature of Ni– Mn–In alloys decreases greatly as a consequence of the increase in the L21 atomic order, whereas the Curie temperature increases slightly [30–32]; to date, however, no

systematic study has been performed on the effect of atomic order on the transformation temperatures of these alloys. In this work, the analysis of the atomic order and its influence on the magnetic and structural properties of Ni–Mn–In alloys has been performed. On one hand, the effect of different thermal treatments on the magnetic and structural transformation temperatures as well as on the thermodynamics of the MT has been studied from calorimetric measurements. On the other hand, the influence of such thermal treatments on the degree of LRO has been determined from neutron diffraction experiments. Comparison of the calorimetric and structural results allows us to directly relate thermal treatments with atomic order and to quantify the effect of the atomic order on the martensitic and magnetic transformations in Ni–Mn–In alloys. 2. Materials and methods Two similar Ni50.2Mn33.4In16.4 (alloy 1) and Ni50.4Mn33.5In16.1 (alloy 2) polycrystalline alloys were prepared from high-purity elements by arc melting under a protective Ar atmosphere. The composition of the samples was analyzed by energy-dispersive X-ray spectroscopy (EDS) in a scanning electron microscope (JSM-5610LV). The ingots were homogenized in vacuum quartz ampoules at 1173 K for 24 h. In order to retain states with different degrees of LRO, alloy 1 was subjected to a 30 min annealing treatment at three different temperatures, 1173, 823, 723 K (samples labeled AQ1173K, AQ823K and AQ723K), followed by quenching into ice water in a vertical furnace. Another piece of alloy 1 (labeled AQ300K) was slowly cooled from 1173 K for comparison with the quenched samples. On the other hand, alloy 2 was quenched from 1073 K (AQ1073K). Small samples for calorimetric measurements were obtained from a disk previously cut from the ingots with a slow-speed diamond saw. Powder samples for neutron diffraction experiments were produced by crushing the samples in an agate mortar. Differential scanning calorimetry (DSC) measurements at a heating/cooling rate of 10 K min1 were carried out in a TA Q100 calorimeter to study the thermal behavior of the sample. Thermal cycles through the MT after heating up to different temperatures were performed on the as-quenched samples in order to observe “in situ” the evolution of the Curie and MT temperatures with the post-quench thermal treatments. The temperatures of the peak maxima have been taken as the transformation temperature for both the forward MT (FMT), from martensite to austenite, and the reverse MT (RMT), from austenite to martensite. A Quantum Design MPMS XL-7 SQUID magnetometer was used to measure the temperature dependence of the DC magnetization under constant applied magnetic fields of 100 Oe, 10 kOe, 30 kOe and 60 kOe. Magnetic measurements were made on cooling–heating cycles at 1 K min1. The peaks of the derivative curve of the magnetization measurements were used to determine the FMT and RMT temperatures. This criterion is comparable with that used for the calorimetric measurements since in both

V. Recarte et al. / Acta Materialia 60 (2012) 1937–1945

cases it corresponds with the maximum transformation rate temperature. Powder neutron diffraction measurements were performed at the beamlines D1B (neutron wavelength ˚ ) and D1A (neutron wavelength 1.907 A ˚ ) at the Insti2.52 A tute Laue-Langevin. The FullProf2000 program [33] was employed to carry out the Rietveld refinement of the different spectra. 3. Results and discussion 3.1. High-temperature thermal treatments Fig. 1a shows calorimetric measurements in the temperature range of the MT for alloy 1 quenched from different temperatures. As indicated, the exothermic peaks observed on the cooling ramps are linked to the FMT, and the corresponding endothermic peaks on heating to the respective RMT. The k-type shoulders observed around 300 K are related to the magnetic ordering of the austenite at the Curie temperature, T aus C . The latent heat linked to the MT, DQ, was estimated from the area below the peaks, and the corresponding entropy change at the MT as DS ffi DQ=T p , where Tp is the peak temperature. The cooling–heating calorimetric cycle through the MT for alloy 2 quenched

Fig. 1. (a) DSC cooling–heating cycles for alloy 1 after quenching from different temperatures. (b) DSC cooling–heating cycle of the quenched alloy 2. Inset: detail of the irreversible exothermic peak associated with the ordering process. FMT and RMT indicate forward and reverse martensitic transformation.

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from 1073 K (Fig. 1b) shows the same features. The Curie temperature, latent heat, entropy change and MT temperatures for both alloys are summarized in Table 1. The differences between the transformation entropy for the FMT and the RMT are due to the outstanding role of the magnetic contribution to the transformation entropy in MSMAs. MT entropy has two main contributions, magnetic and vibrational DS MT ffi DS vib þ DS mag , which have opposite signs [32,34]. As a result of the strong dependence of DS mag on temperature, the hysteresis of transformation and the counterbalance between both contributions, different values of the transformation entropy for the FMR and the RMT are usually determined [32]. As shown in Fig. 2, there is a strong dependence of the MT temperatures on the quenching. In particular, the higher the quenching temperature, the higher the transition temperatures. On the other hand, T aus exhibits the opposite behavior, though C showing a smaller dependence. The lines in Fig. 2 correspond to the linear fitting of the values for alloy 1 (solid symbols). The divergence of the alloy 2 values (open symbols) from the linear trend observed for alloy 1 reflects the fact that the transformation temperatures strongly depend on the alloy composition, even for small variations. In fact, the alloy composition is the main factor controlling the MT temperatures (which show a linear dependence on the electron atom ratio e/a, as a general trend), as has been shown in different magnetic shape memory systems [18,21]. The degree of LRO, which can be easily modified by thermal treatments, is the other relevant factor [16,22–32]. As has been pointed out, systems such as Ni–Mn–X undergo an ordering process from a B2 structure to a L21 at high temperatures (1100–900 K). Although this order–disorder transition cannot be suppressed by quenching, some atomic disorder can be retained in a metastable state after a sufficiently rapid quenching process, and hence the dependence of the transition temperature on the quenching temperature reflects the dependence on the degree of atomic order of the alloy. Neutron diffraction studies have been carried out to determine the degree of LRO as a function of thermal treatment. The observed and calculated neutron diffraction patterns at 320 K (paramagnetic austenite) of a fully ordered sample (alloy 1, AQ300K) are shown in Fig. 3. The structure refinement reveals a L21 structure (space ˚ . In the group Fm3m) with cell parameter a = 6.0058(2) A Ni2MnIn stoichiometric compound, the In atoms occupy the (i) sublattice, Mn atoms the (ii) sublattice, and Ni atoms the (iii) and (iv) sublattices (see inset in Fig. 3). For the composition studied, the refined occupancies show that the (1/4, 1/4, 1/4) positions are occupied by Ni atoms, the (0, 0, 0) positions are occupied only by Mn atoms while at the (1/2, 1/2, 1/2) positions both Mn and In atoms can be found. These occupancies correspond to the maximum degree of atomic order allowed by the stoichiometry, in agreement with the excess of Mn with respect to the stoichiometric content. The evolution of the integrated intensity of the (1 1 1) peak, I111, as a function of temperature of

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Table 1 Data obtained from calorimetric measurements for alloy 1. Curie temperature of the austenite, T aust C , forward and reverse martensite transformation temperatures TFMT and TRMT, latent heat and entropy change for the forward and reverse martensite transformations, QFMT, QRMT, DSFMT and DSRMT. Sample

T aust ðKÞ C

T FMT ðKÞ

T RMT ðKÞ

QFMT ðJ=gÞ

QRMT ðJ=gÞ

DS FMT ðJ=kg KÞ

DS RMT ðJ=kg KÞ

AQ1173K AQ823K AQ723K AQ300K AQ1073K

295 298 306 312 291

262 226 207 174 223

273 242 223 192 242

6.2 ± 0.2 2.60 ± 0.15 1.7 ± 0.1 1 ± 0.1 3.10 ± 0.15

6.4 ± 0.2 3.30 ± 0.15 2.3 ± 0.1 1.4 ± 0.1 3.60 ± 0.15

23.7 ± 0.8 11.5 ± 0.7 8.2 ± 0.5 5.7 ± 0.6 13.8 ± 0.7

23.4 ± 0.7 13.6 ± 0.6 10.3 ± 0.5 7.3 ± 0.5 14.9 ± 0.8

Fig. 2. Dependence of the Curie temperature of the austenite, T aust (d,s), C the forward martensite transformation temperature TFMT (N,D) and the reverse martensite transformation temperature TRMT (j,h) on the quenching temperature. Solid symbols, alloy 1; empty symbols, alloy 2.

Fig. 3. Measured neutron diffraction pattern (dots), calculated profile (full line) and difference between the measured and calculated profiles (dashed line) for the austenitic phase at 320 K of the ordered sample. Inset: L21 austenitic structure.

both an as-quenched sample (AQ823K) and a slow-cooled sample (AQ300K) was measured in situ on heating from room temperature up to 1000 K at a heating rate of 1 K min1. From these measurements the evolution of the order parameter associated with the L21 structure gL21 can be monitored based in the assumption that it sat1=2 isfies: gL21  ðI 111 Þ [35] (see Fig. 4). In both cases, gL21 experiences a progressive decrease in the temperature range between 700 and 960 K. At this temperature its falling to

Fig. 4. Temperature dependence of the L21 order parameter, gL21 , for the as-quenched (open circles) and ordered (full circles) samples. Dashed lines are visual guides and the solid line is the power-law dependence obtained from the fitting. Inset: log–log plot of gL21 as a function of the reduced temperature.

zero (or the complete disappearance of the (1 1 1) reflection) is linked to the L21 ðFm3mÞ ! B2ðPm3mÞ order–disorder transition leading to the loss of the next-nearest-neighbor atomic order (i.e. sublattices (i) and (ii) are now indistinguishable). According to the evolution of gL21 , the order– disorder transition has a second-order character. In this sense, the behavior of gL21 , when approaching the transition, has been fitted to the power law gL21 ¼ Að1  T = b T ord Þ (the inset in Fig. 4 shows the log–log fit of data). Values of Tord = 965 K, A = 1.44 ± 0.03 and b = 0.33 ± 0.01 have been obtained. The solid line in Fig. 4 represents the power-law dependence of gL21 obtained by taking the values of the fitting. The values of both parameters are consistent with the theoretical ones for a three-dimensional Ising model [36]. Similar behavior has been observed in other Heusler systems such as Cu–Zn–Al [35]. In addition, the value of the transition temperature Tord is in agreement with previous results in Ni–Mn–In alloys [17]. It is worth noting that the ordering temperature is considerably lower than those in Ni–Mn–Ga system [12], as expected from the fact that the typical compositions in that system are closer to the stoichometric one (Ni50Mn25X25). On the other hand, the as-quenched samples also show the L21 structure (next-nearest-neighbor order) since the ordering process cannot be inhibited by the quenching process. It can be seen that, as expected, the intensity at room temperature of the (1 1 1) reflection linked to L21 order is lower in the asquenched sample than in the slowly cooled one. The

V. Recarte et al. / Acta Materialia 60 (2012) 1937–1945

increase of the (1 1 1) intensity upon heating from 300 to 600 K (i.e. in the temperature range for the exothermic peak in Fig. 1b) indicates the occurrence of the above-mentioned post-quench ordering process. The evolution of the magnetization through the MT has been measured for four different applied magnetic fields: 100 Oe, 10 kOe, 30 kOe and 60 kOe. The temperature dependence of the low-field magnetization (H = 100 Oe) curves for alloy 1 are shown in Fig. 5a. Focusing on the AQ1173K curve, the high-temperature cubic phase is paramagnetic at high temperatures and orders ferromagnetically at the austenite Curie temperature, T aust  300 K. On C cooling below the FMT temperature, T FMT ¼ 265 K, the magnetization falls drastically since the MT takes place between a ferromagnetic austenite and a paramagnetic martensite which orders magnetically (coexisting ferromagnetic and antiferromagnetic interactions [37]) on further cooling below T mart  210 K. The thermal hysteresis C observed at T  265 K is a fingerprint of the first-order character of the MT. On the other hand, the magnetic ordering transition of the austenite is second order in nature in agreement with the absence of thermal hysteresis. This sequence of magnetostructural transformations is typ-

Fig. 5. (a) Temperature dependence of the magnetization at 100 Oe for alloy 1 after quenching from different temperatures. (b) Temperature dependence of the magnetization at 100 Oe for alloy 2. Upper inset: heating– cooling cycle of M(T) at 10, 30 and 60 kOe. Lower inset: FMT and RMT vs applied magnetic field.

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ically observed in Ni–Mn–X (X = In, Sn, Sn) metamagnetic alloys, and is attributed to the weakening of the exchange interactions as a consequence of the abrupt change in the Mn–Mn interatomic distances occurring upon the MT [37]. The magnetic moments in Ni–Mn–X alloys are mainly confined to the Mn atoms, which are not in direct contact, the indirect exchange interactions being strongly dependent on the interatomic distances [38]. The magnetic character is a counterbalance between the ferromagnetic coupling between the Mn atoms located in the corresponding Mn sublattice, and the antiferromagnetic coupling between the Mn atoms in the Mn sublattice and the Mn atoms in the X sublattice [39,40]. As a consequence of the change in the interatomic distances caused by the MT, the magnetic exchange interactions of the martensite are modified with respect to the austenite [37,41,42]. Thus, the MT takes place between a ferromagnetic austenite and a weak magnetic martensitic phase in the case of MSMA (X = In, Sn, Sb) [8–11]. The decrease in the quenching temperatures promotes a shift of the MT cycle to lower temperatures and, consequently, the induced martensite becomes magnetically ordered. Since the applied field is very low, 100 Oe, the influence of the field on the transformation temperatures can be neglected, and hence they can be compared with the transformation temperatures obtained from calorimetric results, showing good agreements. The magnetization curve at H = 100 Oe corresponding to alloy 2 in the as-quenched state (AQ1073K) shows the same behavior (Fig. 5b). The upper inset of Fig. 5b shows the high-field measured magnetization curves in a cooling– heating cycle in the temperature range of the MT. On cooling below the FMT, the magnetization drastically falls as a consequence of the much lower saturation magnetization of the martensite (in agreement with the above-mentioned enhancement of the antiferromagnetic coupling and the weakness of the ferromagnetic exchange upon MT in Ni– Mn–In alloys). The shift of the MT cycle to lower temperatures with increasing applied magnetic field indicates a magnetic stabilization of the austenite. The derivative of the transformation temperatures with respect to the applied magnetic field for the FMT and RMT, dT FMT =dH and dT RMT =dH , have been estimated from the linear fitting shown in the lower inset of Fig. 5b. The high-field analysis has been also performed in alloy 1, and the results are summarized in Table 2 and Fig. 6. It can be seen that the lower the quenching temperature, the higher the magnetic fieldinduced temperature shift; or, equivalently, the lower the transformation temperature, the more sensitive the MT is to the magnetic field. On the other side, for a given quenching temperature the derivative is higher for the FMT. 3.2. Low-temperature thermal treatments As an example of this kind of thermal treatment, a DSC thermogram performed on heating the AQ1073K sample is shown in Fig. 1b. An exothermic peak can be detected far

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Table 2 Oe 10 kOe 30 kOe kOe Data obtained from magnetic measurements. Forward martensite transformation temperatures T 100 and T 60 at 100 Oe, 10 kOe, FMT , T FMT , T FMT FMT Oe 10 kOe 30 kOe 60 kOe 20 kOe and 60 kOe. Reverse martensite transformation temperatures T 100 , T , T and T at 100 Oe, 10 kOe, 20 kOe and 60 kOe. Derivative RMT RMT RMT RMT of the forward and reverse martensite transformation temperature with applied magnetic field dT FMT =dH and dT RMT =dH. Sample

Oe kOe kOe kOe Oe kOe kOe kOe T 100 ðKÞT 10 ðKÞT 30 ðKÞT 60 ðKÞT 100 ðKÞT 10 ðKÞT 30 ðKÞT 60 ðKÞdT FMT =dH ðK=10 kOeÞdT RMT =dH ðK=10 kOeÞ FMT FMT FMT FMT RMT RMT RMT RMT

AQ1173K265 AQ823K 230 AQ723K 211 AQ300K 174 AQ1073K229

263 228 207 168 226

258 218 191 148 214

248 200 167 103 195

270 240 225 190 239

268 237 218 185 236

263 229 205 167 224

2.8 ± 0.2 5.2 ± 0.4 7.5 ± 0.4 12 ± 1 5.8 ± 0.3

254 213 185 136 208

2.7 ± 0.1 4.6 ± 0.3 6.65 ± 0.05 9.2 ± 0.6 5.3 ± 0.3

Table 3 Data obtained from calorimetric measurements as a function of the postquench aging temperature for alloy 2. Curie temperature of the austenite, T aust C , reverse martensite transformation temperature TRMT, latent heat and entropy change for the reverse martensite transformation QRMT and DSRMT.

Fig. 6. Increment of the forward martensitic transformation temperature as a function of the applied magnetic field for alloy 1 after quenching from different temperatures.

above the MT temperature range (between 400 and 600 K). This peak, which is linked to an irreversible process (the peak appears neither in the cooling ramp nor in the subsequent cycles), appears in all the as-quenched samples but not in the slowly cooled one (AQ300K). If we bear in mind that this is the temperature range in which the intensity of the (1 1 1) diffraction peak of the as-quenched sample increases (see Fig. 4), the exothermic peak can be associated with the ordering process promoted for the recovery of the metastable disorder retained by the quenching (the metastable ! stable ordering process is, in fact, an exothermic process). Above 700 K the order is completely restored and evolves according to the maximum degree of order allowed by the stoichiometry and temperature. A similar recovery of metastable disorder has been observed in Ni–Mn–Ga [16,29]. In order to determine the effect of the post-quench ordering process on the magnetic and structural transformation temperatures, several consecutive heating–cooling DSC thermal cycles have been performed on the asquenched sample AQ1073K. The cycles have been carried out at 10 K min1 from below the MT to a temperature that increases for each new cycle, such that each cycle can be considered as a new aging treatment. This procedure makes it possible to observe “in situ” the evolution of TRMT and T aust C as a consequence of the partial development of the ordering process (see Table 3). Fig. 7 shows the increase of TRMT and T aust as a function of post-quench C

Alloy 2

T aust ðKÞ C

T RMT ðKÞ

QRMT ðJ=gÞ

DS RMT ðJ=kg KÞ

AQ1073K HT423K HT448K HT473K HT498K HT523K HT548K HT573K HT598K HT623K HT648K HT673K

291 291 291 291 291 293 295 299 302 303 303 303

242 242 242 242 242 239 232 220 212 211 210 210

3.60 ± 0.15 3.60 ± 0.15 3.60 ± 0.15 3.60 ± 0.15 3.60 ± 0.15 3.4 ± 0.2 2.90 ± 0.15 2.3 ± 0.2 1.7 ± 0.2 1.6 ± 0.2 1.7 ± 0.2 1.7 ± 0.2

14.9 ± 0.8 14.9 ± 0.8 14.9 ± 0.8 14.9 ± 0.8 14.9 ± 0.8 14.2 ± 0.9 12.4 ± 0.6 10.4 ± 0.8 7.8 ± 1.1 7.8 ± 1.0 7.9 ± 1.0 7.9 ± 1.0

Fig. 7. Increments of the austenite Curie temperature, DT aust C , and the reverse martensitic transformation temperature DT RMT as a function of the post-quench aging temperature (DSC exothermic peak overlapped). Inset: detail of the evolution of the DSC thermograms.

aging temperature, Taging, corresponding to the maximum temperature of the DSC partial cycles (the inset shows the DSC curves where the evolution of both transformations during consecutive cycles can be seen). Both transformation temperatures evolve concurrently with the occurrence of the DSC exothermic peak (also shown, more clearly, in Fig. 7), but showing opposite behavior. In

V. Recarte et al. / Acta Materialia 60 (2012) 1937–1945

particular, T aust increases, whereas, in turn, TMT decreases C ðDT MT  30KÞ as a consequence of the atomic ordering. A similar decrease in MT temperature as a result of the increasing atomic order has been recently reported in Codoped Ni–Mn–In alloys, which also transform from ferromagnetic austenite to a weak magnetic martensite [31,32]. The increase in the Curie temperature is also a consequence of the development of the ordering process. The influence of the atomic ordering on the magnetic properties of the Ni–Mn–X Heusler alloys has its origin in the coexistence of ferromagnetic and antiferromagnetic Mn–Mn interactions. The disordered alloy has more Mn atoms in the In sublattice that couple antiferromagnetically to the Mn atoms at the Mn sites, in such a way that the ferromagnetic coupling, and hence the effective magnetic moment of the alloy, are reduced. Mn atoms come to occupy their own sublattice as the L21 order degree increases, thus favouring the ferromagnetic coupling between Mn atoms and therefore an increase in the magnetic moment and T aust C . With respect to the lowering of the MT temperature upon post-quench heating, it has been recently proposed that the relative stability between the structural phases is affected by the variations in alloy magnetism. In particular, it has been proved that the structural phase showing higher magnetic moment (martensite for Ni–Mn–Ga or austenite for Ni–Mn–In) is stabilized as a result of the enhancement of ferromagnetic coupling brought about by the atomic ordering process [30]. In order to corroborate this assumption in the present case, the evolution of the MT entropy change DS upon post-quench aging has been studied. The absolute value of the RMT entropy of the as-quenched sample has been estimated from the measured transformation enthalpy as jDS RMT j  jDH =T RMT j ¼ 13:8  0:7J kg K. The change in the value of jDS RMT j as a function of post-quench aging temperature, Taging, can be calculated from DSC measurements from the partial thermal cycles as shown in Fig. 8, where the difference of the MT entropy change between the as-quenched state and after heating up to the different aging temperatures aging DðjDS RMT jÞ ¼ jDS aq RMT j  jDS RMT j is shown. The value of DðjDS RMT jÞ diminishes in the temperature range where the increase in the degree of order takes place. Taking into account that, due to the diffusionless character of the MT, there is no configurational contribution to the entropy change, it can be considered that DSMT has two main contributions, DS MT ffi DS vib þ DS mag , where DSvib is the vibrational contribution and DSmag is the contribution from the magnetic subsystem. The electronic contribution is expected to be very small in ferromagnetic Heusler alloys [43], even more if the alloy composition is not modified, and hence DSel can be also neglected. Both terms in the entropy balance have opposite signs: DS vib < 0 due to the excess of vibrational entropy of the austenite with respect to the martensite [44], and DS mag > 0 as result of a MT from a magnetically ordered phase to a disordered one. Since the austenitic and martensitic overall structures do not change as a consequence of the atomic order, a similar

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Fig. 8. Evolution of the entropy change at the MT as a function of the aging post-quench aging temperature. DðjDS RMT jÞ ¼ jDS aq RMT j  jDS RMT j is the difference of the entropy change between the as-quenched state and after different aging temperatures.

variation in the density of vibrational states is expected in both phases, and consequently the effect of ordering on DS vib can be neglected as a first approximation. The influence of order on DðjDS RMT jÞ must then be linked just to the change in DS mag . The increase in the magnetism of the austenite promoted by the increase in the degree of order raises the magnetic entropy difference between both phases and consequently the net value of DS diminishes. 3.3. Dependence on the long-range order parameter The thermodynamic and magnetic properties at the MT can be tailored by quenching from different temperatures or by post-quenching thermal treatments. In both cases the thermal treatments promote changes in the LRO of the sample, retaining different degrees of disorder by quenching or recovering the order by low-temperature treatments. Both kinds of treatments are equivalent since the final parameter, which controls the MT and magnetic properties, is the degree of LRO [29]. A quantitative correlation between the degree of LRO and the transformation temperatures can be estimated if gL21 is normalized such aq ord ord that gL21 ¼ gaq L21 =gL21 , where gL21 and gL21 are the value of the LRO parameter of the as-quenched and the ordered sample, respectively, and taking into account that gord L21 corresponds to the maximum L21 atomic order degree at each temperature. Fig. 9 shows the shift of the Curie and MT temperatures as a function of the shift of the LRO parameter DgL21 ¼ gL21  goL21 , where goL21 is the value at 450 K. Both temperatures show a linear dependence with DgL21 being negative but more sensitive in the case of the MT temperature. The fitting gives the values for the slopes DT aust ¼ ð140  10ÞDgL21 and DT MT ¼ ð390  40ÞDgL21 . C In a previous work [29] a quantitative correlation between the LRO and the MT and Curie temperatures has been established (irrespective of the thermal treatments) for Ni–Mn–Ga alloys. In that case, both transformation

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Fig. 9. Shift of the transformation temperatures, DT aust and DT MT , as a C function of the increase of the L21 atomic order.

Fig. 10. Evolution of the absolute value of the entropy change at the MT jDS MT j as a function of dtrA . Data from as-quenched samples (solid circles). Data from post-quenching treated samples (open circles).

temperatures show the same linear dependence on the nextnearest-neighbor atomic order parameter DT =DI 111 ¼ 64:5 (I111 was taken as order parameter in this paper). Since DI 111 ¼ 2gL21 DgL21  2DgL21 , a value for DT =DgL21  130 can be estimated for the Ni–Mn–Ga alloys which is close to the DT aust c =DgL21 found in the present work. On the other hand, the opposite behavior shown by the dependence of the MT temperature reflects that the increase in LRO stabilizes the structural phase showing higher magnetic character due to the free energy balance [30]. Regardless of the sign of the MT temperature change, the MT for the Ni–Mn–In alloys is more sensitive to changes in the degree of order than for the Ni–Mn–Ga system, thus indicating that the magnetic contribution to the free energy balance between austenite and martensite is more relevant in the metamagnetic alloys, as can be expected when the MT evolves from a ferromagnetic austenite to a weak magnetic martensite [30]. Recently, a monotonic dependence of the entropy change at the MT, DS MT , on the difference between the Curie temperature of the austenite T aust and the MT temC perature, TMT, for Ni–Mn–In–Co alloys has been

Fig. 11. Shift of the MT temperature with the applied magnetic field dT MT =dH as a function of dtrA .

determined [32]. Fig. 10 shows jDS MT j as function of the aust normalized difference dtrA ¼ ðT aust C  T MT Þ=T C , where the values for alloy 1 and alloy 2 quenched from different temperatures have been depicted. It should be noted that, regardless of the thermal treatment, jDS MT j shows a single trend as a function of dtrA . In addition, the parameter dtrA is related to the LRO as can be inferred from Fig. 9: an increase in DgL21 implies an increase in the difference between both transformation temperatures, T aust C  T MT , and consequently an increase in dtrA . Then, proportionality between both parameters should be assumed. The absolute value of DS MT diminishes with the increase of dtrA . As has mag been previously argued, jDS MT j ffijDS vib MT þ DS MT j ¼ mag mag vib vib jDS MT j  jDS MT j, with DS MT < 0 and DS MT > 0. Since jDS vib MT j remains constant, the drop in the absolute value tr of DS MT must be due to an increase in DS mag MT with dA or DgL21 . Finally, the derivative of the transformation temperatures with respect to the applied magnetic field, dT MT =dH , shows a monotonic dependence, increasing for increasing dtrA or gL21 (Fig. 11). This behavior can be qualitatively explained according to the Clausius–Clapeyron equation, DT MT =DH ¼ lo DM MT =DS MT , since DM MT remains fairly constant (see upper inset in Fig. 5b) and DS MT diminishes when the MT takes place from a more magnetically ordered austenite (higher dtrA ). Thus, for a given composition the response of the MT to the applied magnetic field can be tailored by thermal treatments. 4. Summary and conclusions The effect of high-temperature quenching and postquench annealing thermal treatments on the martensitic and magnetic transformations has been studied in Ni– Mn–In alloys. The analysis of the evolution of the L21 atomic order during thermal treatments links the evolution of both transformations to the change in the atomic order. Thus, irrespective of the kind of thermal treatment, the L21 atomic order degree is the parameter that controls the magnetic and structural transitions for a given composition. In

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addition, its influence has been quantitatively determined. The increase in atomic order enhances the magnetic character of the austenite, thus increasing its Curie temperature and lowering the MT temperature. The thermodynamics of the MT depends on the atomic order as indicated by its influence on the transformation entropy. In addition, a correlation between the transformation entropy and the magnetic-field-induced transformation temperatures changes has been found through the evolution of the atomic order. Acknowledgements This work has been carried out with the financial support of FEDER and the Spanish “Ministerio de Ciencia y Tecnologı´a” (Project number MAT2009-07928 and MAT2007-61621). The Institute Laue-Langevin D1A installation and the Spanish CRG D1B are acknowledged for allocated neutron beamtime (CRG-1738). References [1] Ullakko K, Huang JK, Kantner C, O’Handley RC, Kokorin VV. Appl Phys Lett 1996;69:1966. [2] Yu SY, Liu ZH, Liu GD, Chen JL, Cao ZX, Gu GH, et al. Appl Phys Lett 2006;89:162503. [3] Krenke T, Duman E, Acet M, Wassermann EF, Moya X, Man˜osa Ll, et al. Nat Mater 2005;4:450. [4] Planes A, Man˜osa Ll, Acet M. J Phys: Condens Matter 2009;21:233201. [5] Kainuma R, Imano Y, Ito W, Sutou Y, Morito H, Okamoto S, et al. Nature 2006;439:957. [6] Ito W, Ito K, Umetsu RY, Kainuma R, Koyama K, Watanabe K, et al. Appl Phys Lett 2008;92:021908. [7] Kustov S, Golovin I, Corro´ ML, Cesari E. J Appl Phys 2010;107:053525. [8] Webster PJ, Ziebeck KRA, Town SL, Peak MS. Phil Mag B 1984;49:295. [9] Krenke T, Acet M, Wassermann EF, Moya X, Man˜osa Ll, Planes A. Phys Rev B 2005;72:014412. [10] Krenke T, Acet M, Wassermann EF, Moya X, Man˜osa Ll, Planes A. Phys Rev B 2006;73:174413. [11] Khan M, Dubenko I, Stadler S, Ali N. Appl Phys Lett 2007;91:072510. [12] Overholser RW, Wuttig M, Neumann DA. Scr Mater 1999;40:1095. [13] Schlagel DL, Wu YL, Zhang W, Lograsso TA. J Alloys Compd 2000;312:84. [14] Khovailo VV, Takagi T, Vasil’ev AN, Miki H, Matsumoto M, Kainuma R. Phys Status Solidi A 2001;183:R1. [15] So¨derberg O, Friman M, Sozinov A, Lanska N, Ge Y, Ha¨ma¨la¨inen M, et al. Z Metallkd 2004;95:724.

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