Long-Range Atomic Order and Entropy Change at the Martensitic Transformation in a Ni-Mn-In-Co Metamagnetic Shape Memory Alloy

The influence of the atomic order on the martensitic transformation entropy change has been studied in a Ni-Mn-In-Co metamagnetic shape memory alloy through the evolution of the transformation temperatures under high-temperature quenching and post-quench annealing thermal treatments. It is confirmed that the entropy change evolves as a consequence of the variations on the degree of L21 atomic order brought by thermal treatments, though, contrary to what occurs in ternary Ni-Mn-In, post-quench aging appears to be the most effective way to modify the transformation entropy in Ni-Mn-In-Co. It is also shown that any entropy change value between around 40 and 5 J/kgK can be achieved in a controllable way for a single alloy under the appropriate aging treatment, thus bringing out the possibility of properly tune the magnetocaloric effect.


Introduction
Ni-Mn-based Heusler alloys exhibiting both long-range magnetic ordering and thermoelastic martensitic transformation (MT) have been intensively investigated in recent years, from both fundamental and applied points of view, due to the unique properties they show linked to the occurrence of a first-order martensitic transformation (MT) between magnetically ordered phases [1].The magnetism in these alloys mainly arises from the coupling between the Mn atoms (in which the magnetic moment is chiefly confined), so the magnetic exchange interactions strongly depend on the Mn-Mn distance [2], and therefore different sequences of magnetostructural transformations can be observed depending on both the X element and the change in interatomic distances caused by the MT.In particular, in the so-called metamagnetic shape memory alloys, Ni 2 Mn 1-x Z 1+x (Z=In, Sn, and Sb), the MT takes place between ferromagnetic austenite and a weak magnetic martensitic phase due to weakening of the exchange interactions (competing ferromagnetic and antiferromagnetic) [3][4][5][6][7][8].The large change of magnetization, ΔM, occurring at the MT in this case allows the induction of the MT by an applied magnetic field, thus giving rise to multifunctional properties (namely giant magnetoresistance [9][10][11][12] magnetic shape memory [13], or large inverse magnetocaloric effect [14,15] of great technical interest for practical applications in sensing and magnetic refrigeration. The magnetostructural MT in metamagnetic shape memory alloys is mainly driven by lattice dynamics and magnetism.Since the free energy of the ferromagnetic phase depends on the magnetization, a magnetic term appears in the energy balance between austenite and martensite due to the variation of the magnetic exchange coupling at the MT.In this sense, the entropy change linked to the MT can be considered as the sum of a vibrational term and a magnetic term (ΔS ≈ ΔS vib + ΔS mag ) as long as there is no configurational contribution to the entropy change (due to the diffusionless character of the MT) and the electronic contribution is expected to be very small in these alloys [16].The magnetic contribution, and therefore the entropy change at the MT, can be modified by the application of an external magnetic field [17] and, taking into account that the magnetic moment depends on the configurational ordering of the magnetic atoms in the crystal lattice, by the variation of the long-range atomic order.In this last respect, it has been recently shown that, for a given alloy composition, the atomic order can be easily modified in Ni-Mn-In alloys by means of different thermal treatments [18,19].In particular, quenching from high temperatures (around the B2-L2 1 ordering temperature) allows to partially retain the low atomic order present at these temperatures, in such a way that the degree of long-range atomic order in the as-quenched alloys is lower than the equilibrium value allowed by the stoichiometry, which can be achieved after a slowly enough cooling.Likewise, the metastable state retained after quenching may evolve to the stable state (that is, the equilibrium atomic order degree of the alloy may be restored) once the alloy is heated up to temperatures at with atomic diffusion is possible, as it occurs in Ni-Mn-Ga alloys [20,21].The increase in atomic order in Ni-Mn-In alloys enhances the magnetic character of the austenite, thus increasing its Curie temperature and lowering the MT temperature.Furthermore, the influence of atomic order on the transformation entropy points out the key role of atomic order on the thermodynamics of the MT in these alloys.In Ni-Mn-Sn and Ni-Mn-Sb, in turn, the L2 1 ordering is stable up to very high temperatures and no variation on the atomic order can be brought by thermal treatments [22].
The addition of Cobalt to Ni-Mn-In has been shown to enhance the magnetism of the austenite and to avoid ferromagnetic ordering in martensite [23,24].This leads to an increase of ΔM at the MT which favors larger magnetically-induced shifts of the transformation temperatures and results in a higher associated magnetocaloric effect [25].In these quaternary alloys, the entropy change at the transformation, ΔS, strongly varies with the degree of atomic order, which can be tailored by means of the thermal treatment [26].The observed evolution of ΔS has been correlated to the difference between the Curie and martensitic transformation temperatures, which also depends on composition.However, up to now, no systematic study on the study of the effect of thermal treatments on the transformation entropy in Ni-Mn-In-Co alloys has been performed.In the present work, the influence of the atomic order on the martensitic transformation entropy change has been studied in a Ni-Mn-In-Co metamagnetic shape memory alloy through the evolution of the transformation temperatures under high-temperature quenching and post-quench annealing thermal treatments.It is confirmed that the entropy change evolves as a consequence of the variations on the degree of L2 1 atomic order brought by thermal treatments, though, contrary to what occurs in ternary Ni-Mn-In, post-quench aging appears as the most effective way to modify the transformation entropy in Ni-Mn-In-Co.It is also shown that any entropy change value between around 40 and 5 J/kgK can be achieved in a controllable way for a single alloy under the appropriate aging treatment, thus bringing out the possibility of properly tune the magnetocaloric effect.

Experimental Section
A polycrystalline Ni 45 Mn 36.7 In 13.3 Co 5 (at %) ingot was prepared from high purity elements by arc melting under protective Ar atmosphere.The ingot was remelted several times and then homogenized in vacuum quartz ampoules at 1,173 K during 24 h.Small samples for calorimetric and magnetic measurements were obtained from discs previously cut from the center of the ingots by a slow speed diamond saw, and powder samples for neutron diffraction experiments were elaborated by crushing the samples in an agate mortar.Differential Scanning Calorimetry (DSC) measurements at a heating/cooling rate of 10 K/min were carried out in a TA Q100 DSC to study the thermal behavior of the samples.In order to analyze the effect of high-temperature thermal treatments on the transformation temperatures and the transformation entropy, the alloy was subjected to a 30 minutes annealing treatment at different temperatures (ranging from 773 K to 1173 K) followed by quenching in ice water.On the other hand, 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 atomic order was analyzed by neutron diffraction measurements carried out at the Institute Laue-Langevin (Grenoble, France).In particular, powder neutron diffraction measurements were performed at a wavelength of 1.28 Å.

Results and Discussion
Figure 1 shows the DSC thermograms obtained on a cooling-heating ramp in the vicinity of the martensitic transformation of the as-quenched samples.As indicated, the exothermic and endothermic peaks correspond to the forward and reverse martensitic transformations, respectively, and the λ-type shoulders are associated to the magnetic ordering of the austenite at the Curie temperature, T C .In order to track the evolution of the MT, the temperatures of the MT peaks maxima, T m f °r and T m rev , have been taken as the forward and reverse MT temperature, respectively.As shown in Figure 2a, both the MT and Curie temperatures evolve with the quenching temperature, T quench , though showing a non-monotonous behavior.In particular, the MT temperature T m increases and T C decreases with the increasing T quench for T quench < 900 K, and the opposite behavior, that is, a decrease on T m and a slight increase on T C , is observed when quenching from above 900K.The evolution of the transformation temperatures for T quench < 900 K is similar to that found in ternary Ni-Mn-In, and can be ascribed to a decrease of the retained degree of L2 1 atomic order on increasing the quenching temperature [19].On the other hand, assuming that quenching mainly affects the transformation temperatures due to the modification of atomic order, the behavior of T m and T C for T quench > 900 K could be related to an increase of the retained degree of atomic order with the increasing T quench , promoted by a high vacancies concentration at the quenching temperature that assist the ordering process, as in fact occurs in Ni-Mn-Ga and Ni-Fe-Ga alloys [20,27].In any case, the net variations of the MT temperature (ΔT m ≈ 20 K) are much lower than those found in Ni-Mn-In subjected to exactly the same quenching treatments (ΔT m > 60 K) [19], thus pointing out either a lower effect of quenching on the retained atomic order or a lower influence of atomic order on the MT.From the latent heat estimated from the area bellow the peaks in Figure 1, Q, the corresponding entropy change at the MT has been calculated as ΔS = Q/T m .The absolute values of the entropy change at the forward and reverse MT (ΔS for and ΔS rev , respectively) are plotted as a function of T quench in Figure 2b.Although the absolutes values of ΔS for and ΔS rev are slightly different (as a result of the combination of the strong dependence of the magnetic contribution ΔS mag on the temperature and the hysteresis of transformation) the evolution is almost the same in both cases; ΔS increases with T quench for T quench < 900 K and slightly decreases with T quench for T quench > 900 K. From the values in Figure 2a, it can be seen that the higher is the difference T C -T m the lower the entropy change, in agreement with previous results on similar alloys [26].In this sense, the lower net variations of ΔS under quenching comparing with ternary Ni-Mn-In (Δ (ΔS NiMnInCo ) ≈ 10 J/kgK vss Δ (ΔS NiMnIn ) ≈ 16 J/kgK) can be understood as a direct consequence of the smaller effect of quenching on the transformation temperatures.In order to analyze the effect of thermal treatments on the atomic order, the temperature dependence of long range atomic order has been evaluated from neutron powder diffraction measurements.Figure 3a shows the neutron diffractogram obtained at 400 K (in paramagnetic austenite, to avoid magnetic contributions) on a powder sample quenched from 723 K.The alloy displays the cubic L2 1 structure typical of Heusler compounds, with lattice parameter a=5.9692Å.The intensity peaks have been indexed according to the associated Bragg reflections.The evolution of the L2 1 atomic order with temperature has been estimated from the evolution of the integrated intensity of the austenitic (111) reflections, which are exclusively linked to that type of ordering (according to the corresponding unit cell structure factor, the L2 1 superstructure reflections are those in which the h, k, l indices are all odd).In particular, the order parameter corresponding to the L2 1 structure,  L21 (which ranges from 0, for the B2 structure, to 1, for the maximum next-nearest-neighbor atomic order allowed by the stoichiometry), has been determined assuming  L21 ~ I 111 1/2 and normalizing to the I 111 value measured at 400 K after slowly cooling from 1,170 K [28].
Figure 3b shows the temperature dependence of the L2 1 order parameter on heating-cooling between 400 K and 1,173 K.The degree of L2 1 atomic order progressively decreases on heating above 700 K, until it becomes zero (the intensity of the (111) reflection completely vanishes) at around 900 K, thus evidencing the occurrence of a L2 1 ↔B2 ordering transition.Since this transition has a second-order character, the behavior of  L21 when approaching the transition has been fitted to the power law  L21 = A (1−T/T ord ) β , obtaining values of T ord = 894 K, A = 1.5 and β = 0.33.The values of A and β parameters are consistent with the theoretical ones for a three-dimensional Ising model [29], and the value of the transition temperature T ord is similar to that observed in the corresponding ternary Ni 50 Mn 37 In 13 alloy [30].The degree of atomic order is close to unity below 750 K and becomes irrelevant above 900 K. Besides, a good agreement between heating and cooling curves is observed.Then, the quenching temperatures where substantial differences could be expected correspond to the 750-900 K temperature range.On the other side, the vacancies concentration at the different temperatures and their evolution must also play an important role during the quenching process and on the final order degree obtained at room temperature.So, the low influence of quenching on the transformation temperatures and on the MT entropy change can be explained since the atomic disorder retained by quenching is almost the same in all samples (except at 753 K where a large order degree is obtained).
Nevertheless, the atomic order can be better correlated with T m , T C and ΔS by means of post-quenched thermal treatments, taking into account that the equilibrium atomic order degree of the alloy may be restored once the alloy is heated up to a temperatures where atomic diffusion is possible.As previously reported in Ni-Mn-Ga and Ni-Mn-In alloys, the metastable-to-stable post-quench ordering process 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.The exothermic peak associated with the post-quench ordering process taking place in the sample quenched from 1,073 K can be seen in the thermogram shown in Figure 4a.The inset shows a detail of the exothermic peaks appearing for different quenching temperatures.In order to determine the effect of the post-quench ordering process on the transformation temperatures and the entropy change, several consecutive heating/cooling DSC thermal cycles have been performed on the as-quenched samples.The cycles have been carried out at 10 K/min 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 Figure 4b, this procedure makes it possible to observe "in situ" the evolution of T m and T C as a consequence of the partial development of the ordering process.
Figure 5a shows the increment on T m rev and T C as a function of post-quench aging temperature, T aging (that is, the maximum temperature of the DSC partial cycles).The DSC exothermic peak associated with the ordering process is also plotted in the figure.T m rev highly decreases (ΔT m rev ≈ 70 K) whereas T C increases (ΔT C ≈ 30 K) with the increasing T aging , concurrently with the occurrence of the exothermic peak.This behavior is very similar to that observed in ternary Ni-Mn-In subjected to exactly the same thermal treatments, though the shifts are considerably lower in this latter case, ΔT m rev ≈ 30 K and ΔT C ≈ 15 K, and it is in agreement with previous results on the effect of atomic order on the MT temperature in Co-doped Ni-Mn-In alloys [26].The increase of the austenite Curie temperature as a result of the atomic ordering process is common to Ni-Mn-Ga and Ni-Mn-In alloys, and it origin relies on the enhancement of the ferromagnetic coupling between Mn atoms as the structure is getting ordered.Likewise, as it has been recently proposed, the enhancement of ferromagnetic coupling brought by the atomic ordering stabilizes the structural phase showing higher magnetic moment (in this case, the ferromagnetic austenite against the paramagnetic martensite) thus giving rise to a decrease of the MT temperature [31].In this sense, the higher influence of post-quench aging on T m and T C observed in Ni-Mn-In-Co (with respect to the ternary alloy [19]) may be a consequence of both a higher retained atomic disorder, which would be in agreement with its lower T ord , and the higher saturation magnetization of the quaternary austenite.In any case, it is worth noting that the post-quench atomic ordering process results in a larger increase of the T C -T m difference, which leads to a considerably higher decrease of the entropy change at the MT (Δ(ΔS NiMnInCo ) ≈ 25 J/kgK vs Δ(ΔS NiMnIn ) ≈ 7 J/kgK), as shown in Figure 5b, where the increment of the entropy change at the MT with respect to the as-quenched state, Δ(ΔS), is shown as a function of the post-quench aging temperature (for the sake of clarity, just the reverse MT is shown).With respect to the effect of atomic ordering on the transformation entropy ΔS, two main contributions, ΔS ≈ ΔS vib + ΔS mag , where ΔS vib is the vibrational contribution and ΔS mag is the magnetic contribution, can be considered (as already said, the electronic contribution ΔS el is expected to be very small, even more if the alloy composition is not modified).In the case of the reverse MT, both terms in the entropy balance have opposite signs; ΔS vib > 0 due to the excess of vibrational entropy of the austenite with respect to the martensite [32], and ΔS mag < 0 as result of a MT from a magnetically disordered phase to an ordered one.Since the austenitic and martensitic overall structures do not evolve with atomic ordering, a similar variation on the density of vibrational states is expected in both phases, and consequently the effect of atomic ordering on ΔS vib can be neglected in a first approximation, so the influence of atomic order on ΔS must be linked just to the change of ΔS mag as a consequence of the variations in the magnetic exchange coupling in the austenitic phase.The comparison between Figure 2b and Figure 5b confirms that post-quench aging is more effective than high temperature quenching to control the entropy change through atomic order variations, contrary to what occurs in the corresponding ternary Ni-Mn-In [18,19].This is quite interesting since it means that almost any ΔS value between around 40 J/kgK and 5 J/kgK can be achieved in a controllable way for a single alloy.In fact, taking into account that the limit value of the magnetocaloric effect is the transformation entropy (if the effect of the magnetic field is strong enough to totally induce the first order transition) [33], this brings out the possibility of properly tune the magnetocaloric effect, which can be tailored in a continuous way by choosing the appropriate aging temperature.Furthermore, the range of achievable entropy values can be broadened by quenching the alloy from different temperatures.In this respect, Figure 6 shows the increments on T m and T C (Figure 6a) and the corresponding absolute values of the entropy change achievable at forward and reverse MT (Figure 6b) for the alloy quenched from 873 K, 973 K, 1,073 K and 1,173 K (from which a similar degree of atomic order is retained) and followed by cyclic post-quench ageing.It can be seen that, in fact, a very large range of entropy change values are obtained for a single alloy from the combination of quenching and post-quench treatments.As stated above, the evolution of the transformation entropy under thermal treatments is caused by the evolution of the magnetic contribution ΔS mag as a consequence of the effect of long-range atomic order on the alloy magnetism.
The role of the magnetic contribution to the transformation entropy becomes evident from the common dependence of the measured ΔS values on the normalized temperature difference, δ A = (T C -T m )/T C , shown in Figure 7.This behavior agrees with the phenomenological model based on a Bragg-Williams approximation recently proposed to describe the evolution of the magnetic contribution to the total entropy change in Ni-Mn-based alloys [34] (a similar behavior has been also reported in Ni-Fe-Ga ferromagnetic shape memory alloys [35]).The absence of a marked change in the slope (previously reported) seems to be due to the paramagnetic nature of martensite in the present Ni-Mn-In-Co alloy.Furthermore, the huge set of values presented in the figure perfectly illustrates the above-mentioned ability of thermal treatments to modify the entropy change at MT as a result of the atomic order variations.

Conclusions
The influence of the atomic order on the martensitic transformation entropy change has been studied in a Ni-Mn-In-Co metamagnetic shape memory alloy.The entropy change evolves as a consequence of the variations on the degree of L2 1 atomic order brought by thermal treatments.In particular, the evolution of ΔS is explained in terms of the variation of the magnetic contribution to the entropy as a consequence of the change in the magnetic exchange coupling in the austenitic phase.
Contrary to what occurs in ternary Ni-Mn-In, post-quench aging appears as the most effective way to modify the transformation entropy in Ni-Mn-In-Co.Almost any entropy change value between around 40 and 5 J/kgK can be achieved in a controllable way for a single alloy under the appropriate aging treatment, thus bringing out the possibility of properly tune the magnetocaloric effect.

Figure 1 .
Figure 1.DSC thermograms corresponding to quenching from different temperatures.

Figure 2 .
Figure 2. Transformation temperatures (a) and absolute value of the entropy change at the MT (b) as a function of the quenching temperature.

Figure 3 .
Figure 3. (a) Neutron diffractogram obtained at 400 K on a powder sample quenched from 723 K. (b) Temperature dependence of the L2 1 order parameter.

Figure 4 .
Figure 4. (a) DSC thermograms obtained on heating the sample just quenched from 1,073 K. Inset: detail of the exothermic peak associated to the ordering process in the samples quenched from different temperatures.(b) DSC thermograms performed on several consecutive thermal cycles on the sample just quenched from 1,073 K.

Figure 5 .
Figure 5. Increment on T m rev and T C (a) and increment on the transformation entropy at the reverse MT (b) in the sample quenched from 1,070K, as a function of post-quench aging temperature.Inset: Increment on the transformation entropy in Ni-Mn-In [19].

Figure 6 .
Figure 6.Increment on T m and T C (a), and increment on the absolute value of the transformation entropy (b), in the samples quenched from different temperatures and followed by cyclic post-quench ageing (for T m and ΔS.closed symbols: direct MT; open symbols: reverse MT).

Figure 7 .
Figure 7. Dependence of the measured entropy change values on the normalized temperature difference, δ A = (T C -T m )/T C .