Role of magnetism on the martensitic transformation in Ni–Mn-based magnetic shape memory alloys

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Acta Materialia 60 (2012) 459–468 www.elsevier.com/locate/actamat

Role of magnetism on the martensitic transformation in Ni–Mn-based magnetic shape memory alloys V. Sa´nchez-Alarcos a,⇑, V. Recarte a, J.I. Pe´rez-Landaza´bal a, C. Go´mez-Polo 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 D1B–D15, F-38042 Grenoble, France Received 29 July 2011; received in revised form 13 October 2011; accepted 14 October 2011 Available online 16 November 2011

Abstract The effect of magnetism on the martensitic structural transformation has been analyzed through the evolution of the transformation temperatures of several Ni–Mn–Ga and Ni–Mn–In alloys subjected to high-temperature quenching and post-quench annealing thermal treatments. It is found that the atomic order variations associated with the thermal treatments affect the structural transformation in different ways depending on the character of the magnetic ordering in the austenitic and the martensitic phases. In particular, regardless of composition, the variation in the atomic order affects the martensitic transformation temperature only in those alloys in which at least one of the structural phases show magnetic order at the transformation temperature, whereas those transformations taking place between paramagnetic phases remain unaffected. The observed behaviors are explained in terms of the effect of the magnetic exchange coupling variations on the free energy difference between austenite and martensite. The results confirm the key role of magnetism in the martensitic transformation. Ó 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Ni–Mn–Ga; Ni–Mn–In; Atomic order; Martensitic transformation; Ferromagnetic shape memory alloys

1. Introduction Ni–Mn-based Heusler alloys exhibiting both long-range magnetic ordering and thermoelastic martensitic transformation (MT) have been intensively investigated over recent years, from both fundamental and applied points of view, due to the unique properties they show as a result of the coupling between structure and magnetism. In particular, phenomena such as the magnetic shape memory effect, the magnetoresistance or the giant magnetocaloric effect are of great technical interest for practical applications in sensing and magnetic refrigeration [1–4]. These properties have been reported in Ni–Mn–X (X = Ga, In, Sn, Sb) alloys close to the composition Ni2MnX, in which the ⇑ Corresponding author. Tel.: +34 948 169582; fax: +34 948 169565.

E-mail address: [email protected] (V. Sa´nchez-Alarcos).

MT occurs between magnetically ordered phases. These are Heusler compounds showing a cubic L21 crystal structure (space group Fm3m) and next-nearest-neighbor atomic order (L21 order) [5]. Nevertheless, on cooling through the equilibrium phase diagram, Ni–Mn–X alloys do not solidify directly from the melt to the Heusler structure but to a B2 structure (space group Pm3m) 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 [6–11]. 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 [6,11]. The MT takes place from the L21 austenite to a low-symmetry martensitic structure, which, due to the diffusionless character of the transformation, inherits the degree of long-range atomic order (LRO)

1359-6454/$36.00 Ó 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2011.10.026

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of the austenite. This structural transformation is driven by a Jahn–Teller mechanism and its origin relies on the Fermi surface nesting. The MT temperature has been 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, just as it occurs in the Hume–Rothery compounds [12,13]. Likewise, the MT temperature is somewhat affected by the variations on the lattice parameters [14,15]. The magnetic moments in these alloys are mainly confined to the Mn atoms. Since the Mn atoms are not in direct contact, the exchange mechanism is indirect through the conduction electrons and therefore the exchange interactions strongly depend on the interatomic distances [16]. The magnetic character of the Heusler Ni–Mn–X compounds is mainly due to the ferromagnetic coupling between the Mn atoms located in the corresponding Mn sublattice, and, to a lesser extent, to the antiferromagnetic coupling between the Mn atoms in the Mn sublattice and the Mn atoms in the X sublattice [17,18]. Nevertheless, as a consequence of the change of the interatomic distances caused by the MT, the magnetic exchange interactions are modified in such a way that the magnetic properties and even the type of the magnetic ordering of the structural phases (i.e. ferromagnetism, antiferromagnetism, ferrimagnetism, etc.) may be very different depending on the X element [19–21]. Thus, the MT takes place typically from ferromagnetic austenite to ferromagnetic martensite in Ni–Mn–Ga alloys, whereas it occurs between a ferromagnetic austenite and a weak magnetic martensitic phase in Ni–Mn–Z alloys (Z = In, Sn, Sb) [5,22–24]. The peculiar metamagnetic character shown on these later systems is being widely studied nowadays, mainly in the Ni–Mn–In system. In these systems new, interesting phenomena arise such as the magnetic-field induction of the MT, the kinetic arrest of the martensite or the observation of a peculiar isothermal character in some thermoelastic martensitic transformations [25–27]. The structural and magnetic properties of the Ni–Mnbased Heusler alloys depend on the atomic order as long as the variations on the configurational ordering of the constituting elements in the crystal lattice affect both the MT and the alloy magnetic moment. This is related to the modification of both the electronic structure and the lattice site occupancy by the magnetic atoms. The atomic order can be modified either by subjecting an alloy to different thermal treatments or by changing the alloy composition. Nevertheless, this last procedure is not useful when studying the effect of atomic order on the MT since it implies the modification of e/a, which greatly affects the MT. The effect of atomic ordering upon high-temperature quenching and post-quench aging on the MT and the magnetism has been reported in several Ni–Mn–X alloys, although it has been studied systematically only in the Ni–Mn–Ga system [10,28–34]. It has been shown that quenching from high temperatures (around the B2–L21 ordering temperature) allows the low atomic order present

to be partially retained at these temperatures, in such a way that the L21 order degree on the as-quenched alloys is lower than the equilibrium value obtained after a suitably slow cooling treatment. Likewise, if the as-quenched alloys are heated up to temperatures at which atomic diffusion is possible, an ordering process takes place leading to the restoration of the equilibrium atomic order degree of the alloy [10,34]. Recent neutron diffraction measurements, as well as the observation of similar activation energies for the atomic ordering and the Mn atomic self-diffusion processes, have confirmed that the ordering process in Ni– Mn–Ga mainly consists of the diffusion of the Mn (Ga) atoms in the Ga (Mn) sublattice to their own sublattice [34]. Irrespective of the thermal treatments, the MT and Curie temperatures of Ni–Mn–Ga alloys increase with the increasing atomic order. Moreover, 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 can be established [34]. From such correlation, the effect of the L21 atomic order degree on the relative stability between the austenite and martensitic phases has been recently calculated in terms of the free energy change. The saturation magnetization of Ni–Mn–Ga alloys also increases as a consequence of the increase of the L21 atomic order degree [33,35], but, in turn, both the martensitic crystal structure and the lattice parameter seem to be unaffected [30,36]. On the other hand, the effect of atomic order on the metamagnetic alloys (X = In, Sn, Sb) has scarcely been studied. In this respect, it has only been reported that the Curie temperature of Ni–Mn–In alloys also increases as a consequence of the increase on the L21 atomic order, whereas the MT temperature greatly decreases [37,38]. Nevertheless, up to now, the origin of the different behaviors found in the MT temperatures of Ni–Mn–Ga and Ni– Mn–In alloys, and, ultimately, the origin of the effect of atomic order on the MT of Ni–Mn–X alloys, are still unclear. In this work, the effect of magnetism on the martensitic structural transformation has been analyzed through the study of the evolution of the transformation temperatures on several Ni–Mn–Ga and Ni–Mn–In alloys subjected to high-temperature quenching and post-quench annealing thermal treatments. It is found that, regardless of composition or the X element, the atomic order variations associated with the thermal treatments affect the structural transformation in different ways depending on the character of the magnetic ordering in the austenitic and the martensitic phases. The observed behaviors are explained in terms of the effect of the magnetic exchange coupling variations on the free energy difference between austenite and martensite. 2. Experimental Two Ni–Mn–Ga and two Ni–Mn–In polycrystalline ingots were prepared from high-purity elements by arc

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Table 1 Composition, martensitic transformation temperature, magnetic ordering temperatures, saturation magnetization and transformation enthalpy of the studied alloys. Alloy

Ni (at.%)

Mn (at.%)

Ga (at.%)

In (at.%)

Mp (K)

T aust (K) C

T mart (K) C

Msat (emu)

DH (J g1)

FF FP PP1 PP2

49.5 50.5 52.6 52

28.5 33.5 26.7 34

22 – 20.7 –

– 16 – 14

285 223 426 366

351 300 – –

– 218 350 165

72 36 60 12

3.2 3.6 8.7 15.0

melting under a protective Ar atmosphere, and then homogenized in vacuum quartz ampoules at 1173 K for 24 h. The composition of the elaborated alloys was analyzed by energy dispersive X-ray spectroscopy (EDS) in a JEOL JSM-5610LV scanning electron microscope (SEM). As shown in Table 1, the obtained compositions (at.%) were Ni49.5Mn28.5Ga22 (FF alloy), Ni52.6Mn26.7Ga20.7 (PP1 alloy), Ni50.5Mn33.5In16 (FP alloy) and Ni52Mn34In14 (PP2 alloy). The nomenclature corresponds to the magnetostructural transformation observed in each alloy (FF = ferromagnetic austenite to ferromagnetic martensite, FP = ferromagnetic austenite to paramagnetic martensite, and PP = paramagnetic austenite to paramagnetic martensite). In order to modify the long-range atomic order of the alloys, the homogenized samples were subjected to a 30 min high-temperature annealing treatment followed by quenching into ice water. The annealing temperatures were 1173 K in the Ni–Mn–Ga alloys and 1073 K in the Ni–Mn–In alloys, i.e. 100 K above the corresponding B2–L21 transition temperature [6,11]. Small samples for calorimetric and magnetic measurements were obtained from disks previously cut from the center of the ingots with a slow-speed diamond saw. The transformation temperatures were determined from differential scanning calorimetry (DSC) measurements carried out at a cooling/heating rate of 10 K min1 in a TA Q100 calorimeter, and the magnetic characterization (magnetization measurements) was performed by SQUID magnetometry (QD MPMS XL-7 SQUID [39]). The atomic order was determined from neutron diffraction measurements carried out at the Institute Laue–Langevin (Grenoble). In particular, powder neutron diffraction measurements were performed on the quenched FF and FP alloys at the D1B diffractom˚ and 2.52 A ˚ , respectively. eter at a wavelength of 1.28 A 3. Results and discussion Fig. 1 shows the DSC thermograms obtained on a cooling–heating ramp in the vicinity of the martensitic transformation of the as-quenched alloys. The exothermic and endothermic peaks correspond to the forward and reverse martensitic transformations, respectively, and the k-type shoulders are associated with the magnetic transitions. The transformation peaks show the typical thermal hysteresis inherent to the first-order character of the MT whereas, as expected, no hysteresis is observed in the second-order magnetic transition. In order to track the evolution of the

MT with the atomic ordering, the temperature of the forward MT peak maximum Mp has been taken as the transformation temperature. Likewise, the enthalpy change at the MT DH has been determined from the thermograms as the average between the enthalpy changes at the forward and reverse MTs. The obtained Mp and DH values are shown in Table 1. The complete sequences of magnetostructural transformations have been determined from magnetization measurements. The temperature dependence of the low-field magnetization (H = 100 Oe) of the as-quenched alloys is shown in Fig. 2, where the corresponding high-field magnetization heating curves (H = 60 kOe) are shown in the insets. The FF alloy (Fig. 2a) is paramagnetic at high temperatures and orders ferromagnetically at the austenite Curie temperature T aust  350 K. On cooling below the forC ward MT temperature, the magnetization drastically falls as a consequence of the higher magnetic anisotropy of the martensitic phase, whose saturation magnetization Msat is also higher than that of the austenite (see inset). Such a ferromagnetic–austenite to ferromagnetic–martensite transformation sequence is characteristic of Ni–Mn–Ga alloys transforming around or below room temperature, aust in which the conditions M mart and T mart > T aust sat > M sat C C > M p always hold [40]. The transformations sequence in the FP alloy (Fig. 2b) is quite similar, albeit in this case the MT takes place from a ferromagnetic austenite to a paramagnetic martensite which orders magnetically (to a magnetic ordering with coexisting ferromagnetic and antiferromagnetic interactions [21]) on further cooling below T mart  220 K, which has been extrapolated from the C M(T) curve at 6T (see inset) by using the Kuz’min formula [41]. It can be seen that the forward MT is still not completely fulfilled at T mart (compare Figs. 1b and 2b), so the C structural transformation occurs actually between two magnetically ordered phases. In any case, the magnetization in the martensite, and in particular the saturation magnetization, is much lower than in the austenite (see inset), so the MT takes place from a ferromagnetic austenite to a weak-magnetic martensite. This sequence of magnetostructural transformations is typically observed in Ni– Mn–X (X = In, Sn, Sn) metamagnetic alloys, and it 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 [21]. On the other hand, only the magnetization increase associated with the magnetic ordering of the martensite (at

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Fig. 1. DSC thermograms of the quenched alloys: (a) FF, (b) FP, (c) PP1 and (d) PP2 alloys.

T mart < M p ) can be seen in the M(T) curves corresponding C to the PP1 and PP2 alloys (Fig. 2c and d, respectively). This indicates that in these alloys the MT takes place between paramagnetic austenite and paramagnetic martensite (i.e. M p > T aust and M p > T mart C C ), as usual in most of the Ni– Mn-based Heusler alloys showing large e/a ratios [13]. The magnetic ordering temperatures and the saturation magnetizations (taken as the magnetization at 10 K under 60 kOe) obtained from the magnetization measurements are also shown in Table 1. In order to avoid the possible contribution of magnetically arrested austenite to the saturation magnetization [26], Msat of the FP metamagnetic alloy was determined from low-temperature magnetization measurements performed after zero field cooling. The LRO has been evaluated on the FF and FP alloys from neutron diffraction measurements performed on heating the as-quenched samples up to 1173 K. In particular, the evolution of the L21 atomic order has been estimated from the evolution of the integrated intensity of the austenitic (1 1 1) reflections, which are exclusively linked to that type of ordering [10,34]. The integrated intensity calculated on as-quenched samples (disordered) and on samples slowly cooled from 1173 K (ordered) is shown in Fig. 3 as a function of temperature. In spite of the different quality of the measurements, it can be seen that the behavior is almost the same in both alloys. As expected, the (1 1 1)

intensity (and therefore the L21 atomic order degree) retained by quenching is lower than in the slowly cooled case. The L21 atomic order increases on heating the asquenched samples up to 700 K, where the equilibrium value (that is, that in the ordered samples) is achieved. Finally, the L21 atomic order decreases on further heating until it vanishes at the B2–L21 transition temperature. The observed evolution of the L21 atomic order is similar to that observed in similar Ni–Mn–Ga alloys [10]. For its part, this is the first time the LRO is evaluated in the Ni– Mn–In system in the full temperature range. As previously reported, the metastable-to-stable ordering process taking place below 700 K in the as-quenched samples gives rise to an exothermic peak on the first heating curve of the DSC thermograms, which makes it possible to identify and analyze the ordering process from calorimetric measurements [10,34]. The exothermic peaks associated with the post-quench ordering process taking place on the studied alloys can be seen in the thermograms shown in Fig. 4a. As shown in the inset, the ordering processes occur between 525 K and 625 K, in agreement with previous results in Ni–Mn–Ga alloys and with the temperature range where the increase in the L21 atomic order is detected in Fig. 3. It is worth noting that the temperature of the peak maximum is quite similar in all cases. Taking into account that the ordering temperature depends on the

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Fig. 2. Temperature dependence of the magnetization at 100 Oe: (a) FF, (b) FP, (c) PP1 and (d) PP2 alloys. Inset: heating curve of M(T) at 60 kOe (the onset of the magnetization jump at Tm indicates the beginning of the reverse MT).

quenched L21 atomic order degree (the atomic disorder favors the atomic diffusion assisting the ordering process [34]), this would indicate that the degree of L21 atomic disorder retained by quenching is also similar in all cases. 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 as-quenched samples. The cycles have been carried out at 10 K min1 from a temperature below the MT to a temperature higher in each new cycle, in such a way that each cycle can be considered as a new aging treatment. As shown in Fig. 4b, this procedure makes it possible to observe “in situ” the evolution of Mp and TC as a consequence of the partial development of the ordering process. Similarly, the effect of atomic ordering on the saturation magnetization as well as in those magnetic transitions not detected from the thermogram have been analyzed from magnetization measurements performed on samples subjected to exactly the same postquench thermal cycles. Fig. 5 shows the increment on Mp and TC as a function of post-quench aging temperature Taging (that is, the maximum temperature of the DSC partial cycles). The exothermic peak of the DSC thermogram associated with the ordering process is also plotted in the figure. In the FF case

(Fig. 5a) it can be seen that Mp and TC remain constant for Taging < 500 K. In turn, both transformation temperatures increase with the increasing Taging in the Taging range where the ordering process takes place. This parallel behavior means that both Mp and TC increase with the increasing L21 atomic order, as previously demonstrated in similar Ni–Mn–Ga alloys [10,28–34]. Furthermore, the observed variations are very similar in both cases (DMp  15 K and DTC  19 K), in agreement with the recent observation of a common dependence of the structural and magnetic transformation temperatures on the degree of quenched L21 atomic order [34]. The transformation temperatures of the FP alloy also evolve concurrently with the occurrence of the DSC exothermic peak (Fig. 5b). Nevertheless, contrary to the behavior of the FF alloy, Mp and TC show an opposite trend in this Ni–Mn–In alloy. In particular, TC increases, as it does in the FF alloy, whereas, in turn, Mp greatly decreases as a consequence of the atomic ordering. A similar decrease of the MT temperature as a result of the increasing atomic order has been recently reported in Co-doped Ni–Mn–In alloys also transforming from ferromagnetic austenite to a weak magnetic martensite [37,38]. On the other hand, in spite of their compositions being quite close to that of the FF and FP alloys, the transformation temperatures of both the PP1 and PP2 alloys show a

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Fig. 3. Temperature dependence of the integrated intensity of the (1 1 1) austenitic reflection of the as-quenched samples: (a) FF alloy, and (b) FP alloy. Inset: detail of the neutron diffractogram corresponding to the L21 austenitic structure. Lines are visual guides.

rather peculiar behavior upon post-quench aging (Fig. 5c and d, respectively). In these two alloys, TC (which now corresponds to the martensitic phase) also increases with the increasing Taging, as it does in the FF and FP alloy, but, surprisingly, Mp remains constant in the whole temperature range, thus indicating that MT temperatures are unaffected by the variation on the atomic order. In order to better compare the evolution of the transformation temperatures, the increments on the magnetic and martensitic transformation temperatures of the four alloys are shown together in Fig. 6a and b, respectively. In all cases, TC shows a parallel increase as a consequence of the development of the ordering process, though, in genðNi–Mn–GaÞ ðNi–Mn–lnÞ eral, DT mart > DT aust and DT C > DT C . The C C influence of the atomic ordering on the magnetic properties of the Ni–Mn–X Heusler alloys can be explained as a consequence of the coexistence of ferromagnetic and antiferromagnetic Mn–Mn interactions and its dependence on the Mn–Mn distance. The disordered alloy has more Mn atoms in the X sites (the corresponding X atoms occupy

Fig. 4. (a) DSC thermograms obtained on heating the quenched alloys. Inset: detail of the exothermic peak associated with the ordering process. (b) DSC thermograms performed on several consecutive thermal cycles on the FF alloy. The direct heating curve showing the exothermic peak is also plotted for comparison.

the Mn sites) that couple antiferromagnetically to the Mn atoms at the Mn sites, in such a way that the ferromagnetic coupling, and then the effective magnetic moment of the alloy, are reduced. In the same way, the Mn atoms come to occupy their own sublattice as the L21 order degree increases, thus favoring the ferromagnetic coupling between Mn atoms and therefore the increase of the magnetic moment and TC. In this sense, and assuming a similar atomic order variation in all cases, the different DTC values can be attributed to a higher concentration of Mn, leading to a higher antiferromagnetic contribution in the Ni–Mn– In alloys, and to the higher exchange interaction and coordination number between Mn atoms in martensite with respect to those in austenite. As shown in Fig. 7, the increase of the ferromagnetic coupling brought by the atomic ordering also results in a common significant increase of the saturation magnetization. On the other hand, contrary to the case of the magnetic properties, the

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Fig. 5. Increment on the transformation temperatures of the quenched alloys, as a function of the post-quench aging temperature (DSC exothermic peak overlapped). (a) FF, (b) FP, (c) PP1 and (d) PP2 alloys.

way the atomic order affects Mp is not so clear. In fact, the variation of the L21 atomic order affects neither the electron concentration nor the lattice parameters [36] nor the appearing martensitic phase structure [31], which are the main factors affecting the MT temperature in these alloys. Therefore, the origin of the variation of Mp upon postquench aging must rely on another effect associated with the atomic ordering. In this respect, the common dependence of Mp and TC on the degree of L21 atomic order observed in some Ni–Mn–Ga alloys, together with the demonstrated influence of atomic order on the magnetic properties, suggests that the relative stability between the structural phases may be affected by the variations on the magnetism of the alloy, as it has been recently proposed to account for the difference on the MT temperatures observed on quaternary alloys showing the same e/a ratio but different concentrations of magnetic and non-magnetic elements (partial substitutions of Ni by Fe and Co in Ni– Mn–Ga alloys [42] and of Mn by Fe and Cr in Ni–Mn– In alloys [43]). The evolution of the transformation temperatures shown in Figs. 5 and 6 bears out the influence of magnetism on the martensitic transformation. In effect, it can be seen that the ordering process associated with the exothermic peak affects only the MT temperature in the FF

and FP alloys, in which at least one of the structural phases show magnetic order at the transformation temperature. On the contrary, the MT temperatures of the PP1 and PP2 alloys, in which the MT takes place between two paramagnetic phases and therefore no effect of magnetism on the MT is expected, are effectively unaffected by the LRO variations leading to the increase of magnetic moment. It is especially worth noting that the common behavior of the PP1 and PP2 alloys is independent of both the alloy composition and the p-orbital constituent element (In or Ga), in agreement with the hypothesis of the key role of magnetism on the martensitic transformation. As we will see, the variation in the evolution of the MT temperature upon atomic ordering, in particular the different sign and absolute value of the Mp shifts on the FF and FP alloys, can be also explained within the framework of the influence of magnetism on the MT. The schematic model shown in Fig. 8 is proposed to illustrate the effect of magnetism on the relative stability between martensite and austenite. The Gibbs free energies of the martensitic and austenitic phases (Gm and Ga, respectively) have been approximated as linear functions of the temperature, and, as indicated, T0 represents the temperature of thermodynamical equilibrium at which DG = Gm–Ga = 0. First, it is worth noting that the null effect of post-quench aging on Mp (or T0) of

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Fig. 8. Schematic plot of the effect of atomic order on the Gibss free energy of the austenitic and martensitic phases (“ord” = ordered, “dis” = disordered).

Fig. 6. (a) Increment on the magnetic ordering temperature of the studied alloys as a function of the post-quench aging temperature. (b) Increment on the martensitic transformation temperature of the studied alloys as a function of the post-quench aging temperature.

Fig. 7. Increment on the saturation magnetization of the studied alloys as a function of the post-quench aging temperature.

the PP1 and PP2 alloys indicates that the variation on the atomic order does not affect (or equally affects) Gm and Ga in the paramagnetic systems. This means that those contributions to DG other than magnetic can be neglected when analyzing the atomic order effect on the energy balance, in such a way that it can be considered that the increase of the L21 atomic order affects exclusively the free energy of the magnetically ordered phases. In particular, as explained above, the free energy will be reduced upon atomic ordering as a consequence of the increase of the ferromagnetic RKKY-type exchange interaction against the antiferromagnetic exchange one [18]. Thus, in the case of the FP alloy, the atomic ordering will reduce the free energy of the ferromagnetic austenite ðGaord < Gadis Þ while that of the weak magnetic martensite will remain almost unchanged ðGmord  Gmdis Þ. As illustrated in the figure, this makes the equilibrium temperature (and therefore Mp) considerably dis lower in the ordered state ðT ord 0 < T 0 Þ. In the FF alloy, in turn, the free energy of both ferromagnetic austenite and ferromagnetic martensite must diminish with the increasing atomic order ððGaord < Gadis Þ and ðGmord < Gmdis ÞÞ. Nevertheless, since the exchange interaction is stronger in martensite, as inferred from its higher saturation magnetization (see Fig. 2a), Gm experiences a higher decrease than Ga (that is, dGm > dGa), which results in a slight increase of dis equilibrium temperature (T ord 0 > T 0 ). The effect of atomic order on the internal energy has been evaluated from the evolution of the enthalpy change at the MT (DH) upon post-quench aging. In this sense, Fig. 9 shows the enthalpy change at the reverse MT (DHm!a) of the FF and FP alloys as a function of Taging. It can be seen that DHm!a slightly increases in the FF alloy ðdDH m!a < 0;  18Þ whereas it greatly decreases in the FP one ðdDH m!a < 0;  55%Þ. In both cases the variation of the transformation enthalpy takes place on heating up to temperatures inside the DSC exothermic peak, so the observed evolution can be ascribed to the post-quench ordering process. In fact, the evolution of dDHm!a > 0 is

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Fig. 9. Enthalpy change at the martensitic transformation of the FF and FP alloys, as a function of the post-quench aging temperature.

practically the same as that of Mp (see Fig. 6b). In this respect, it is worth mentioning that DHm!a does not vary with Taging in the PP1 and PP2 alloys either. From the definition of enthalpy, DHm!a = DUm!a + pDVm!a, where DU and DV are the internal energy change at the MT and the volume change at the MT, respectively. Taking into account that the atomic ordering does not affect significantly the lattice parameters (and therefore the volume change at the MT), the increment on DHm!a due to the m!a atomic ordering ðdDH m!a ¼ DH m!a ord  DH dis Þ can be expressed as dDH m!a ¼ dDU m!a þ pdDV m!a  dDU m!a ; m!a

DU m!a ord

ð1Þ

DU m!a dis .

 If we develop the rightwhere dDU hand side term and then we group the austenitic and martensitic terms, Eq. (1) yields dDH m!a ¼ dU a  dU m ;

ð2Þ

where dU = Uord  Udis. Therefore, the effect of atomic ordering on the austenitic and martensitic phases can be compared and evaluated from the experimental measurements of the transformation enthalpies in Fig. 9. Thus, from Eq. (2), the negative increment of the transformation enthalpy observed in the FP alloy (dDHm!a < 0) implies that dUa < dUm. If we take into account that the effect of atomic order on the paramagnetic martensite can be neglected, as stated in the previous paragraph, dUm  0 and then the inequality becomes dUa < 0. This condition means that U aord < U adis and hence that |dUa| > |dUm| in the FP alloy, in agreement with the proposed influence of atomic order on the internal energy. Similarly, the positive increment of the transformation enthalpy observed in the FF case (dDHm!a > 0) implies that dUa > dUm. Since the magnetic ordering decreases the internal energy in both ferromagnetic structural phases (that is dUa < 0, and dUm < 0), dUa > dUm leads to |dUa| < |dUm|, which is again in agreement with the proposed model. Furthermore, the variation

467

of the relative internal energy is considerably higher in the FP alloy than in the FF one (dUa  dUm = 2.0 J/g and dUa  dUm = 0.6 J/g, respectively), according to the higher variation of Mp observed in the former case. The obtained results demonstrate that the increase of the L21 atomic order stabilizes the structural phase showing higher magnetic moment, exactly in the same way as an external magnetic field does [25]. Therefore, it can be concluded that the variation of the MT temperature upon ordering will depend on the difference of magnetic moment between the high and low temperature phases. In fact, after a comprehensive revision in the literature of those Ni–Mnbased alloys which have been subjected to atomic order variations through aging or annealing thermal treatments, it is found that in all cases the transformation temperatures evolve according the proposed influence of magnetism on the MT. This points out the general character of the model, and therefore the key role of magnetism on the relative stability between austenite and martensite. 4. Summary and conclusions The effect of magnetism on the martensitic structural transformation has been analyzed by studying the evolution of the transformation temperatures of several Ni– Mn–Ga and Ni–Mn–In alloys subjected to high-temperature quenching and post-quench annealing thermal treatments. It is found that, irrespective of composition, the variation in the atomic order affects the martensitic transformation temperature only in those alloys in which at least one of the structural phases shows magnetic order at the transformation temperature, whereas those transformations taking place between paramagnetic phases remain unaffected. The observed behaviors are explained as a result of the effect of the magnetic exchange coupling variations on the free energy difference between austenite and martensite. In particular, it is proposed that the increase in the L21 atomic order degree stabilizes the structural phase showing higher magnetic moment. The results obtained demonstrate the key role that magnetism plays in the martensitic transformation. Acknowledgements This work has been carried out with the financial support of the Spanish “Ministerio de Ciencia y Tecnologı´a” (Projects Numbers MAT2009-07928 and MAT200761621). The Institute Laue Langevin–Spanish CRG D1B installation is acknowledged for the allocated neutron beamtime (Exp. 5-24-261 and CRG 1738). References [1] Ullakko K, Huang JH, Kanter 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.

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