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Contribution of entropy changes to the inverse magnetocaloric effect for Ni46.7Co5Mn33In15.3 Heusler alloy
Solid State Communications 203 (2015) 81–84
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Solid State Communications journal homepage: www.elsevier.com/locate/ssc
Contribution of entropy changes to the inverse magnetocaloric effect for Ni46.7Co5Mn33In15.3 Heusler alloy Zhe Li a,n, Yuanlei Zhang a, Kun Xu a, Taoxiang Yang a, Chao Jing b, Hao Lei Zhang c a College of Physics and Electronic Engineering, Key Laboratory for Advanced Functional and Low Dimensional Materials of Yunnan Higher Education Institute, Qujing Normal University, Qujing 655011, PR China b Department of Physics, Shanghai University, Shanghai 200444, PR China c Institute of Materials Technology and Engineering, Chinese Academy of Sciences, Ningbo 315201, PR China
art ic l e i nf o
a b s t r a c t
Article history: Received 3 September 2014 Accepted 28 November 2014 Communicated by X.C. Shen Available online 5 December 2014
In this paper, the changes of volume fractions between austenitic and martensitic phase have been carefully deduced through magnetization data for polycrystalline Ni46.7Co5Mn33In15.3 alloy during reverse martensitic transformation at different magnetic fields. On this basis, the contributions of the lattice and the spin components to the total entropy changes could be effectively separated by using the Clausius–Clapeyron equation and the Debye theory calculations. It is concluded that the lattice contribution works against the magnetic contribution to the inverse magnetocaloric effect (MCE) in this alloy. Further analysis indicates that the effective inverse MCE comes from field-induced variation of the crystal structure. On the contrary, the change of the magnetic moment alignment in this process yields negative contribution, leading to a reduction of the total inverse MCE by about 33%. & 2014 Elsevier Ltd. All rights reserved.
Keywords: A. Metals and alloys B. Growth from melts C. Martensitic transformation D. Magnetocaloric effect
1. Introduction The magnetocaloric effect (MCE) arises from the entropy (or temperature) changes when a magnetic material is submitted to external magnetic field variations ΔH, and its capability can be described either by the isothermal entropy change ΔST or by the adiabatic temperature change ΔT ad [1]. Since the discovery of the giant MCE in Gd5Si2Ge2 [2], much attention has been focused on this kind of compounds because of their potential application for magnetic refrigeration at room temperature, such as MnAs1 xSbx [3], MnFeP0.45As0.55 [4] and LaFe13 xSix [5]. The mechanism behind the giant MCE is believed to be resulted from the spin orientation, crystallographic distortion and changes in the electronic band structure during the first order magnetostructural transformation [6]. In 2004, a new type of ferromagnetic shape memory alloys have been found in Mn rich Ni–Mn based Heusler alloys, such as Ni–Mn–X(Sn, In, Sb) [7], which also undergoes first order martensitic transformation (MT) from a high-symmetry austenitic phase to a low-symmetry martensitic phase with an abrupt drop of magnetization in the cooling process. Owing to magnetostructural coupling around MT, Krenke et al. first reported a large inverse
n Corresponding author. Permanent Address: College of Physics and Electronic Engineering, Qujing Normal University, Sangjiang Street, Qujing 655011, P. R. China. Tel/fax: þ 86 8748968627. E-mail addresses: [email protected] (Z. Li), [email protected] (K. Xu).
http://dx.doi.org/10.1016/j.ssc.2014.11.023 0038-1098/& 2014 Elsevier Ltd. All rights reserved.
MCE in Ni50Mn50 xSnx alloys [8], and the magnitude of ΔST is comparable to Gd5Si2Ge2 at the similar conditions [2]. Since then, the enhanced ΔST during MT was continuously obtained in other ternary and quaternary Heusler alloys by tuning compositions [9–16]. In the very recent years, Liu et al. further observed a giant inverse MCE with reverse MT in Ni45.2Co5.1Mn36.7In13 alloy, which is entirely contributed from the contribution of lattice entropy change ΔSL , and they explained such phenomenon through an practical assumption, i.e., the magnetic entropy change keeps unchanged when the transformations evolves from a first order to second order (a pure magnetic transition of austenite) [17]. In order to get a deeper understanding of the giant inverse MCE, it is not trivial to directly distinguish the contributions of crystallographic modification and magnetic ordering from MT. In addition, numerous studies proposed that the size of MCE is related to the transformed phase fraction induced by a ΔH at a given temperature [17–22]. Based on this motivation, we attempted to clarify the contributions of various entropy changes from MT through transformed volume fraction by combining the Clausius–Clapeyron (C–C) equation and the Debye theory. In this work, we still took Ni45Co5Mn37In13 as an example, and investigated the evolutional trends between the ΔSL and the magnetic entropy change ΔSstr M upon reverse MT at different magnetic fields in detail. Our results demonstrate that the effective inverse MCE is only contributed from a part of ΔSL ( 77%), while the rest of ΔSL is consumed by opposite contribution of the magnetic moment alignment during reverse MT.
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Z. Li et al. / Solid State Communications 203 (2015) 81–84
2. Experimental details Polycrystalline Ni45Co5Mn37In13 alloy with nominal composition was fabricated by the conventional arc-melting method. The weight loss after melting was found to be less than 1.5%. The obtained ingot was annealed in evacuated quartz capsule for 24 h at 1173 K, and it was subsequently quenched in ice water. Its real composition was determined by energy-dispersive spectrometer (EDS, Tecnai-F20, FEI) analysis corresponding to Ni46.7Co5Mn33 In15.3. The crystal structure was identified by powder x-ray diffraction using a Rigaku Ultima-IV x-ray diffractometer both at 300 K and 410 K, respectively. The microstructure of the specimen was studied by optical microscopy (DM2500-M, Leica). Magnetization data were acquired using a vibrating sample magnetometer (VSM, Versalab, Quantum Design). Examination of heat capacity at low temperature using specimen with a cubic shape of about 1 1 1 mm3, was performed by physical property measurement system (PPMS-9, Quantum Design).
3. Results and discussion Fig. 1 shows the x-ray diffraction patterns of Ni46.7Co5Mn33In15.3 alloy at different temperatures. The reflections of Fig. 1(a) indicate that the sample at 300 K has an L10-type nonmodulated martensitic structure, where a ¼ 0:3926 nm, c ¼ 0:6809 nm and α ¼ 901. The c=a of such tetragonal structure is about 1.7343, and is comparable to that observed in Ni45Co5Mn40In8Sn2 alloy [23]. In the mean time, the microstructure of sample at room temperature is also related to the pure martensitic phase, and its grain size is larger than 150 μm, as shown in the inset of Fig. 1(a). From Fig. 1(b), the reflections indicate that the sample at 410 K has an L21-type austenite structure with lattice parameters a ¼ 0:5955nm and α ¼ 901. For present sample, consequently, the volume change of unit cell between two phases (ΔV=V 0 ¼ 2:56%) is slightly larger than that reported in Ni50Mn37.5Al12.5 alloy, probably because the atom radius of Al is significantly smaller than that of In [24].
Fig. 1. (Color online) X-ray diffraction patterns of Ni46.7Co5Mn33In15.3 alloy at different temperatures. Inset: optical microscopy image of this alloy at room temperature.
Fig. 2(a) illustrates the temperature dependence of magnetization MðTÞ curves for Ni46.7Co5Mn33In15.3 sample on cooling and heating in a magnetic field of 50 mT. When the temperature is above 380 K, a sharp change of magnetization at T AC appears, corresponding to a second order magnetic transition from paramagnetic (PM) austenite to ferromagnetic (FM) austenite. When the temperature lies within the range of 345–375 K, we can see that the forward and the reverse MT occur, i.e., the two transitions take place between FM and PM with an obvious thermal hysteresis, revealing a first order transition feature. Here the Ms and Af denote martensite start temperature and austenite finish temperature, respectively. According to the previous studies [25,26], the MðTÞ data can transform to f ðTÞ, the volume fraction of austenite in the sample at a certain temperature, by assuming that total magnetization is proportional to the phase volume fraction. It is worth noting that we just consider the heating process to avoid influence of thermal hysteresis. To determine f ðTÞ, it is necessary to first obtain the magnetization of pure martensite M M ðTÞ and austenite phases M A ðTÞ at a given temperature, which can be deduced by linearly extrapolating heating curve from transition point (As and Af), as illustrated by the red dashed line in the inset of Fig. 2. By combining M M ðTÞ and M A ðTÞ, the f ðTÞ can be calculated by the following equation: f ðTÞ ¼
MðTÞ M M ðTÞ : M A ðTÞ M M ðTÞ
ð1Þ
The normalized curve f ðTÞ is plotted by the blue solid line in the inset of Fig. 2. Obviously, the shape of f ðTÞ curve follows the MðTÞ from experimental data in the transforming range very well. Based on the magnetization data, we also plotted the f ðTÞ curves at different magnetic fields using the same approach mentioned above, as shown in Fig. 3. For the case of our sample, it can be found that the application of a magnetic field keeps the shape of f ðTÞ curves almost unchanged, but the equilibrium temperature of reverse MT [T 0 ¼ ðAs þ Af Þ=2, denoted as pink star] significantly decreases. The magnetic field dependence of T 0 , which is determined from the intersections of extrapolations from linear regions of M–T curves measured at different fields, is also presented in the inset of Fig. 3. It is clearly seen that the T 0 linearly decreases with the increasing of magnetic field. The slope of this curve (dT 0 =dH) is about 3.2 K/T. Such effect suggests that volume fraction of austenite is added by an applied magnetic field at isothermal condition, which is a key fact that demonstrates why
Fig. 2. (Color online) Thermomagnetic curves for Ni46.7Co5Mn33In15.3 alloy on cooling and heating procedures at 50 mT. Inset: the red dashed line shows linearly extrapolating heating curve (blank pane) from the transition point, and normalized heating curve indicates the volume fraction of austenite in the transforming range (blue solid line).
Z. Li et al. / Solid State Communications 203 (2015) 81–84
Fig. 3. (Color online) Temperature dependence of volume fraction of austenite in the transforming range at different magnetic fields for Ni46.7Co5Mn33In15.3 alloy. Inset: field dependence of equilibrium temperature of its reverse martensitic transition [ðAs þ Af Þ=2] together with its best fit line.
the Mn rich Ni–Mn based Heusler alloys exhibit inverse MCE across MT. In this case, the difference between f ðT; H i Þ and f ðT; H f Þ for the ΔH can be quantitatively expressed by the equation
Δf ðT; ΔHÞ ¼ f ðT; Hf Þ f ðT; Hi Þ;
ð2Þ
where both the H i and the H f are defined as the initial and the final magnetic field, respectively. For a completed MT from 100% martensite to 100% austenite, and vice-versa, the total entropy change is corresponding to transition entropy change ΔStr [27], which is often evaluated by C–C equation:
ΔStr ¼
dH ΔM: dT
ð3Þ
Using the ΔM with the value of about 65 emu/g obtained by saturated magnetization between both phases on heating mode, the value of ΔStr for present sample is 20 J/kg K. Combined with Eqs. (2) and (3), the ΔST joined by reverse MT under different ΔH can be easily determined by the approach we proposed, depicted as follows:
ΔST ¼ Δf ðT; ΔHÞΔStr :
ð4Þ
Next, we turn our attention to the lattice entropy of both phases. For one mole Ni46.7Co5Mn33In15.3, in terms of the Debye theory [28], the lattice entropy at pure martensitic state can be estimated by Z ΘM T 3 ΘM =T x3 dx SL ¼ 3NkB ln 1 exp ; þ12NkB expðxÞ 1 T ΘM 0 ð5Þ where N is the number of atoms per mole, kB is the Boltzmann constant and ΘM is the martensite's Debye temperature. By linearly fitting the Cp/T T2 curve at zero magnetic fields (see the inset of Fig. 4), and combining the expression of heat capacity for a metallic crystal, we derived that ΘM is 300 K. Moreover, the relation between ΘM and ΘA can be described from [29] ΔV ΘA ¼ Θ M 1 γ ; ð6Þ V0 where both the ΘA and γ are the austenite's Debye temperature and the Grüneisen parameter respectively. Utilizing the data for the present alloy, that is, ΔV=V 0 ¼ 2:56% and γ ¼ 3 (generally γ should take a value between 1 and 3 for solid materials [30]), the ΘA is 281 K. Substituting the ΘA into Eq. (5), we can also acquire
83
Fig. 4. (Color online) Total lattice entropy change ΔStotal as a function of temperaL ture is deduced by Debye theory. The inset is Cp/T against T2 for the low temperature heat capacity data of zero fields and its best linear fitting.
the lattice entropy at pure austenitic state. Therefore, the temperature dependence of the total lattice entropy change ΔStotal L between pure martensitic and austenitic state is immediately obtained, as illustrated in Fig. 4. It can be observed that the value of ΔStotal in the temperature range of reverse MT almost remains L constant. Such value is close to 30 J/kg K, and it is much higher than ΔStr , indicating that there exists a strong competition between lattice and magnetic entropy changes. By considering that the contribution of ΔStotal should mainly rely on the proporL tion between both phases, the isothermal ΔSL during reverse MT under different ΔH can be solved by the equation
ΔSL ðTÞ ¼ Δf ðT; ΔHÞΔStotal : L
ð7Þ
Here, using Eqs. (4) and (7), both the ΔST and the ΔSL during reverse MT in the different ΔH are illustrated in Fig. 5. For the ΔH ¼ 3 T, the value of ΔST achieves to 15 J/kg K followed by a plateau-like shape. This phenomenon should accurately reflect the intrinsic nature of inverse MCE for this alloy. With the decrease of ΔH, the value of ΔST evidently decreases, and it subsequently shows a sharp peak, which can be interpreted by the fact that a low ΔH can only induce a small part of volume fraction of austenite. Similar results calculated by the Maxwell relation were also observed in Ni45Co5Mn37In13 alloy at same condition [16], proving that the ΔST determined in this way is equitable. Due to negative contribution of magnetic ordering, there is a remarkable difference between ΔST and ΔSL at constant ΔH(see in Fig. 5), and the peak value of ΔSstr M does rapidly increases to 8 J/kg K within the measured magnetic field range (see in the upper panel of Fig. 5). In contrast, the ΔSM , pure magnetic entropy change in the vicinity of T AC , induced by a second order magnetic transition at austenite state retains a linear increment, and the peak value only arrives at 4 J/kg K within the same field range (see in the lower panel of Fig. 5). Such discrepancy could be qualitatively understood by the fact that the arrangement of magnetic moment is much more ordered resulted from the magnetostructural coupling than that resulted from spin fluctuation at similar condition. Furthermore, if an application of ΔH is sufficiently large, we consider that the jΔSstr M j will achieve to a saturated value of 10 J/kg K (expected by jΔStr ΔStotal j). This indicates that about L 33% of lattice entropy change is consumed by the opposite contribution of magnetic entropy in the process of reverse MT. Such value is obviously larger than that ( 23%) speculated in Ni45.2Co5.1Mn36.7In13 using calorimetry based on an assumption [17]. Therefore, the maximizing of the lattice contribution plays a
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Fig. 5. (Color online) Temperature dependence of both the lattice entropy change ΔSL and the entropy change ΔST under different magnetic fields, respectively. Upper panel: A the isothermal magnetic entropy ΔSstr M in the process of reverse martensitic transition. Lower panel: a pure magnetic entropy change ΔSM in the vicinity of T C , which is induced by a second order magnetic transition at austenitic state.
pivotal role in further improving the inverse MCE for Mn-rich Ni–Mn based Heusler alloy system. 4. Conclusions In summary, the inverse MCE in the case of reverse MT for Ni46.7Co5Mn33In15.3 alloy can be credibly evaluated by C–C equation based on change of volume fraction between both phases. Using this approach as well as the Debye theory, the contributions of the lattice and magnetism to the total entropy change upon this process are effectively separated for present sample. Our results demonstrate that the inverse MCE associated with reverse MT only originates from contribution of lattice entropy change, whereas the magnetic entropy change would be responsible for a counterproductive way. These discussions can also help us to develop more efficiently magnetic refrigerants with such kind of Heusler alloys system. Acknowledgments This work was supported by the National Natural Science Foundation of China (Grant nos. 11364035, 11404186 and 51371111), the Key Basic Research Program of Science and Technology Commission of Shanghai Municipality (Grant no. 13JC1402400), and Project for Innovative Research Team of Qujing Normal University (Grant no. TD201301), and Project for Applied Basic Research Programs of Yunnan Province (Grant nos. 2013FZ110 and 2012FD051). References [1] A.M. Tishin, Y. Spichkin, The Magnetocaloric Effect and its Applications, Institute of Physics Publishing, Bristol, 2003. [2] V.K. Pecharsky, K.A. Gschneidner Jr., Phys. Rev. Lett. 78 (1997) 4494. [3] H. Wada, Y. Tanabe, Appl. Phys. Lett. 79 (2001) 3320.
[4] O. Tegus, E. Bruck, K.H.J. Buschow, F.R. de Boer, Nature (London) 415 (2002) 150. [5] B.G. Shen, J.R. Sun, F.X. Hu, H.W. Zhang, Z.H. Cheng, Adv. Mater. 21 (2009) 4545. [6] R. Zach, B. Malaman, M. Bacmann, R. Fruchart, S. Niziol, G. Le Caer, J. L. Soubeyroux, J. Zukrowski, D. Fruchart, J. Magn. Magn. Mater. 147 (1995) 201. [7] Y. Sutou, Y. Imano, N. Koeda, T. Omori, R. Kainuma, K. Ishida, K. Oikawa, Appl. Phys. Lett. 85 (2004) 4358. [8] T. Krenke, E. Duman, M. Acet, E.F. Wassermann, X. Moya, L. Mañosa, A. Planes, Nat. Mater. 4 (2005) 450. [9] Z.D. Han, D.H. Wang, C.L. Zhang, H.C. Xuan, B.X. Gu, Y.W. Du, Appl. Phys. Lett. 90 (2007) 042507. [10] A.K. Pathak, M. Khan, I. Dubenko, S. Stadler, N. Ali, Appl. Phys. Lett. 90 (2007) 262504. [11] S. Stadle, N. Ali, M. Khan, J. Appl. Phys. 101 (2007) 053919. [12] D.H. Wang, C.L. Zhang, Z.D. Han, H.C. Xuan, B.X. Gu, Y.W. Du, J. Appl. Phys. 103 (2008) 033901. [13] C. Jing, Z. Li, H.L. Zhang, J.P. Chen, Y.F. Qiao, S.X. Cao, J.C. Zhang, Eur. Phys. J. B 67 (2009) 193. [14] A.K. Nayak, K.G. Suresh, A.K. Nigam, J. Phys. D: Appl. Phys. 42 (2009) 035009. [15] A.K. Pathak, I. Dubenko, C. Pueblo, S. Stadler, N. Ali, J. Appl. Phys. 107 (2010) 09A907. [16] L. Chen, F.X. Hu, J. Wang, L.F. Bao, J.R. Sun, B.G. Shen, J.H. Yin, L.Q. Pan, Appl. Phys. Lett. 101 (2012) 012401. [17] J. Liu, T. Gottschall, K.P. Skokov, J.D. Moore, O. Gutfleisch, Nat. Mater. 11 (2012) 620. [18] V.K. Pecharsky, A.P. Holm, K.A. Gschneidner Jr., R. Rink, Phys. Rev. Lett. 91 (2003) 197204. [19] G.J. Liu, J.R. Sun, J. Shen, B. Gao, H.W. Zhang, F.X. Hu, B.G. Shen, Appl. Phys. Lett. 90 (2007) 032507. [20] M. Balli, D. Fruchart, D. Gignoux, R. Zach, Appl. Phys. Lett. 95 (2009) 072509. [21] L. Tocado, E. Palacios, R. Burriel, J. Appl. Phys. 105 (2009) 093918. [22] W.B. Cui, W. Liu, Z.D. Zhang, Appl. Phys. Lett. 96 (2010) 222509. [23] Z.G. Guo, L.Q. Pan, M.Y. Rafique, X.F. Zheng, H.M. Qiu, Z.H. Liu, J. Alloy. Compd. 577 (2013) 174. [24] H.B. Xiao, C.P. Yang, R.L. Wang, V.V. Marchenkov, K. Bärner, J. Appl. Phys. 112 (2012) 123723. [25] P.J. Shamberger, F.S. Ohuchi, Phys. Rev. B 79 (2009) 144407. [26] V. Basso, C.P. Sasso, K.P. Skokov, O. Gutfleisch, V.V. Khovaylo, Phys. Rev. B 85 (2012) 014430. [27] V. Recarte, J.I. Pérez-Landazábal, S. Kustov, E. Cesari, J. Appl. Phys. 107 (2010) 053501. [28] P. Debye, Ann. Phys. 39 (1912) 789. [29] P.J. von Ranke, N.A. de Oliveira, C. Mello, A. Magnus, G. Carvalho, S. Gama, Phys. Rev. B 71 (2005) 054410. [30] C. Kittel, Introduction to Solid State Physics, 5th ed., Wiley, New York, 1976.
Contents lists available at ScienceDirect
Solid State Communications journal homepage: www.elsevier.com/locate/ssc
Contribution of entropy changes to the inverse magnetocaloric effect for Ni46.7Co5Mn33In15.3 Heusler alloy Zhe Li a,n, Yuanlei Zhang a, Kun Xu a, Taoxiang Yang a, Chao Jing b, Hao Lei Zhang c a College of Physics and Electronic Engineering, Key Laboratory for Advanced Functional and Low Dimensional Materials of Yunnan Higher Education Institute, Qujing Normal University, Qujing 655011, PR China b Department of Physics, Shanghai University, Shanghai 200444, PR China c Institute of Materials Technology and Engineering, Chinese Academy of Sciences, Ningbo 315201, PR China
art ic l e i nf o
a b s t r a c t
Article history: Received 3 September 2014 Accepted 28 November 2014 Communicated by X.C. Shen Available online 5 December 2014
In this paper, the changes of volume fractions between austenitic and martensitic phase have been carefully deduced through magnetization data for polycrystalline Ni46.7Co5Mn33In15.3 alloy during reverse martensitic transformation at different magnetic fields. On this basis, the contributions of the lattice and the spin components to the total entropy changes could be effectively separated by using the Clausius–Clapeyron equation and the Debye theory calculations. It is concluded that the lattice contribution works against the magnetic contribution to the inverse magnetocaloric effect (MCE) in this alloy. Further analysis indicates that the effective inverse MCE comes from field-induced variation of the crystal structure. On the contrary, the change of the magnetic moment alignment in this process yields negative contribution, leading to a reduction of the total inverse MCE by about 33%. & 2014 Elsevier Ltd. All rights reserved.
Keywords: A. Metals and alloys B. Growth from melts C. Martensitic transformation D. Magnetocaloric effect
1. Introduction The magnetocaloric effect (MCE) arises from the entropy (or temperature) changes when a magnetic material is submitted to external magnetic field variations ΔH, and its capability can be described either by the isothermal entropy change ΔST or by the adiabatic temperature change ΔT ad [1]. Since the discovery of the giant MCE in Gd5Si2Ge2 [2], much attention has been focused on this kind of compounds because of their potential application for magnetic refrigeration at room temperature, such as MnAs1 xSbx [3], MnFeP0.45As0.55 [4] and LaFe13 xSix [5]. The mechanism behind the giant MCE is believed to be resulted from the spin orientation, crystallographic distortion and changes in the electronic band structure during the first order magnetostructural transformation [6]. In 2004, a new type of ferromagnetic shape memory alloys have been found in Mn rich Ni–Mn based Heusler alloys, such as Ni–Mn–X(Sn, In, Sb) [7], which also undergoes first order martensitic transformation (MT) from a high-symmetry austenitic phase to a low-symmetry martensitic phase with an abrupt drop of magnetization in the cooling process. Owing to magnetostructural coupling around MT, Krenke et al. first reported a large inverse
n Corresponding author. Permanent Address: College of Physics and Electronic Engineering, Qujing Normal University, Sangjiang Street, Qujing 655011, P. R. China. Tel/fax: þ 86 8748968627. E-mail addresses: [email protected] (Z. Li), [email protected] (K. Xu).
http://dx.doi.org/10.1016/j.ssc.2014.11.023 0038-1098/& 2014 Elsevier Ltd. All rights reserved.
MCE in Ni50Mn50 xSnx alloys [8], and the magnitude of ΔST is comparable to Gd5Si2Ge2 at the similar conditions [2]. Since then, the enhanced ΔST during MT was continuously obtained in other ternary and quaternary Heusler alloys by tuning compositions [9–16]. In the very recent years, Liu et al. further observed a giant inverse MCE with reverse MT in Ni45.2Co5.1Mn36.7In13 alloy, which is entirely contributed from the contribution of lattice entropy change ΔSL , and they explained such phenomenon through an practical assumption, i.e., the magnetic entropy change keeps unchanged when the transformations evolves from a first order to second order (a pure magnetic transition of austenite) [17]. In order to get a deeper understanding of the giant inverse MCE, it is not trivial to directly distinguish the contributions of crystallographic modification and magnetic ordering from MT. In addition, numerous studies proposed that the size of MCE is related to the transformed phase fraction induced by a ΔH at a given temperature [17–22]. Based on this motivation, we attempted to clarify the contributions of various entropy changes from MT through transformed volume fraction by combining the Clausius–Clapeyron (C–C) equation and the Debye theory. In this work, we still took Ni45Co5Mn37In13 as an example, and investigated the evolutional trends between the ΔSL and the magnetic entropy change ΔSstr M upon reverse MT at different magnetic fields in detail. Our results demonstrate that the effective inverse MCE is only contributed from a part of ΔSL ( 77%), while the rest of ΔSL is consumed by opposite contribution of the magnetic moment alignment during reverse MT.
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Z. Li et al. / Solid State Communications 203 (2015) 81–84
2. Experimental details Polycrystalline Ni45Co5Mn37In13 alloy with nominal composition was fabricated by the conventional arc-melting method. The weight loss after melting was found to be less than 1.5%. The obtained ingot was annealed in evacuated quartz capsule for 24 h at 1173 K, and it was subsequently quenched in ice water. Its real composition was determined by energy-dispersive spectrometer (EDS, Tecnai-F20, FEI) analysis corresponding to Ni46.7Co5Mn33 In15.3. The crystal structure was identified by powder x-ray diffraction using a Rigaku Ultima-IV x-ray diffractometer both at 300 K and 410 K, respectively. The microstructure of the specimen was studied by optical microscopy (DM2500-M, Leica). Magnetization data were acquired using a vibrating sample magnetometer (VSM, Versalab, Quantum Design). Examination of heat capacity at low temperature using specimen with a cubic shape of about 1 1 1 mm3, was performed by physical property measurement system (PPMS-9, Quantum Design).
3. Results and discussion Fig. 1 shows the x-ray diffraction patterns of Ni46.7Co5Mn33In15.3 alloy at different temperatures. The reflections of Fig. 1(a) indicate that the sample at 300 K has an L10-type nonmodulated martensitic structure, where a ¼ 0:3926 nm, c ¼ 0:6809 nm and α ¼ 901. The c=a of such tetragonal structure is about 1.7343, and is comparable to that observed in Ni45Co5Mn40In8Sn2 alloy [23]. In the mean time, the microstructure of sample at room temperature is also related to the pure martensitic phase, and its grain size is larger than 150 μm, as shown in the inset of Fig. 1(a). From Fig. 1(b), the reflections indicate that the sample at 410 K has an L21-type austenite structure with lattice parameters a ¼ 0:5955nm and α ¼ 901. For present sample, consequently, the volume change of unit cell between two phases (ΔV=V 0 ¼ 2:56%) is slightly larger than that reported in Ni50Mn37.5Al12.5 alloy, probably because the atom radius of Al is significantly smaller than that of In [24].
Fig. 1. (Color online) X-ray diffraction patterns of Ni46.7Co5Mn33In15.3 alloy at different temperatures. Inset: optical microscopy image of this alloy at room temperature.
Fig. 2(a) illustrates the temperature dependence of magnetization MðTÞ curves for Ni46.7Co5Mn33In15.3 sample on cooling and heating in a magnetic field of 50 mT. When the temperature is above 380 K, a sharp change of magnetization at T AC appears, corresponding to a second order magnetic transition from paramagnetic (PM) austenite to ferromagnetic (FM) austenite. When the temperature lies within the range of 345–375 K, we can see that the forward and the reverse MT occur, i.e., the two transitions take place between FM and PM with an obvious thermal hysteresis, revealing a first order transition feature. Here the Ms and Af denote martensite start temperature and austenite finish temperature, respectively. According to the previous studies [25,26], the MðTÞ data can transform to f ðTÞ, the volume fraction of austenite in the sample at a certain temperature, by assuming that total magnetization is proportional to the phase volume fraction. It is worth noting that we just consider the heating process to avoid influence of thermal hysteresis. To determine f ðTÞ, it is necessary to first obtain the magnetization of pure martensite M M ðTÞ and austenite phases M A ðTÞ at a given temperature, which can be deduced by linearly extrapolating heating curve from transition point (As and Af), as illustrated by the red dashed line in the inset of Fig. 2. By combining M M ðTÞ and M A ðTÞ, the f ðTÞ can be calculated by the following equation: f ðTÞ ¼
MðTÞ M M ðTÞ : M A ðTÞ M M ðTÞ
ð1Þ
The normalized curve f ðTÞ is plotted by the blue solid line in the inset of Fig. 2. Obviously, the shape of f ðTÞ curve follows the MðTÞ from experimental data in the transforming range very well. Based on the magnetization data, we also plotted the f ðTÞ curves at different magnetic fields using the same approach mentioned above, as shown in Fig. 3. For the case of our sample, it can be found that the application of a magnetic field keeps the shape of f ðTÞ curves almost unchanged, but the equilibrium temperature of reverse MT [T 0 ¼ ðAs þ Af Þ=2, denoted as pink star] significantly decreases. The magnetic field dependence of T 0 , which is determined from the intersections of extrapolations from linear regions of M–T curves measured at different fields, is also presented in the inset of Fig. 3. It is clearly seen that the T 0 linearly decreases with the increasing of magnetic field. The slope of this curve (dT 0 =dH) is about 3.2 K/T. Such effect suggests that volume fraction of austenite is added by an applied magnetic field at isothermal condition, which is a key fact that demonstrates why
Fig. 2. (Color online) Thermomagnetic curves for Ni46.7Co5Mn33In15.3 alloy on cooling and heating procedures at 50 mT. Inset: the red dashed line shows linearly extrapolating heating curve (blank pane) from the transition point, and normalized heating curve indicates the volume fraction of austenite in the transforming range (blue solid line).
Z. Li et al. / Solid State Communications 203 (2015) 81–84
Fig. 3. (Color online) Temperature dependence of volume fraction of austenite in the transforming range at different magnetic fields for Ni46.7Co5Mn33In15.3 alloy. Inset: field dependence of equilibrium temperature of its reverse martensitic transition [ðAs þ Af Þ=2] together with its best fit line.
the Mn rich Ni–Mn based Heusler alloys exhibit inverse MCE across MT. In this case, the difference between f ðT; H i Þ and f ðT; H f Þ for the ΔH can be quantitatively expressed by the equation
Δf ðT; ΔHÞ ¼ f ðT; Hf Þ f ðT; Hi Þ;
ð2Þ
where both the H i and the H f are defined as the initial and the final magnetic field, respectively. For a completed MT from 100% martensite to 100% austenite, and vice-versa, the total entropy change is corresponding to transition entropy change ΔStr [27], which is often evaluated by C–C equation:
ΔStr ¼
dH ΔM: dT
ð3Þ
Using the ΔM with the value of about 65 emu/g obtained by saturated magnetization between both phases on heating mode, the value of ΔStr for present sample is 20 J/kg K. Combined with Eqs. (2) and (3), the ΔST joined by reverse MT under different ΔH can be easily determined by the approach we proposed, depicted as follows:
ΔST ¼ Δf ðT; ΔHÞΔStr :
ð4Þ
Next, we turn our attention to the lattice entropy of both phases. For one mole Ni46.7Co5Mn33In15.3, in terms of the Debye theory [28], the lattice entropy at pure martensitic state can be estimated by Z ΘM T 3 ΘM =T x3 dx SL ¼ 3NkB ln 1 exp ; þ12NkB expðxÞ 1 T ΘM 0 ð5Þ where N is the number of atoms per mole, kB is the Boltzmann constant and ΘM is the martensite's Debye temperature. By linearly fitting the Cp/T T2 curve at zero magnetic fields (see the inset of Fig. 4), and combining the expression of heat capacity for a metallic crystal, we derived that ΘM is 300 K. Moreover, the relation between ΘM and ΘA can be described from [29] ΔV ΘA ¼ Θ M 1 γ ; ð6Þ V0 where both the ΘA and γ are the austenite's Debye temperature and the Grüneisen parameter respectively. Utilizing the data for the present alloy, that is, ΔV=V 0 ¼ 2:56% and γ ¼ 3 (generally γ should take a value between 1 and 3 for solid materials [30]), the ΘA is 281 K. Substituting the ΘA into Eq. (5), we can also acquire
83
Fig. 4. (Color online) Total lattice entropy change ΔStotal as a function of temperaL ture is deduced by Debye theory. The inset is Cp/T against T2 for the low temperature heat capacity data of zero fields and its best linear fitting.
the lattice entropy at pure austenitic state. Therefore, the temperature dependence of the total lattice entropy change ΔStotal L between pure martensitic and austenitic state is immediately obtained, as illustrated in Fig. 4. It can be observed that the value of ΔStotal in the temperature range of reverse MT almost remains L constant. Such value is close to 30 J/kg K, and it is much higher than ΔStr , indicating that there exists a strong competition between lattice and magnetic entropy changes. By considering that the contribution of ΔStotal should mainly rely on the proporL tion between both phases, the isothermal ΔSL during reverse MT under different ΔH can be solved by the equation
ΔSL ðTÞ ¼ Δf ðT; ΔHÞΔStotal : L
ð7Þ
Here, using Eqs. (4) and (7), both the ΔST and the ΔSL during reverse MT in the different ΔH are illustrated in Fig. 5. For the ΔH ¼ 3 T, the value of ΔST achieves to 15 J/kg K followed by a plateau-like shape. This phenomenon should accurately reflect the intrinsic nature of inverse MCE for this alloy. With the decrease of ΔH, the value of ΔST evidently decreases, and it subsequently shows a sharp peak, which can be interpreted by the fact that a low ΔH can only induce a small part of volume fraction of austenite. Similar results calculated by the Maxwell relation were also observed in Ni45Co5Mn37In13 alloy at same condition [16], proving that the ΔST determined in this way is equitable. Due to negative contribution of magnetic ordering, there is a remarkable difference between ΔST and ΔSL at constant ΔH(see in Fig. 5), and the peak value of ΔSstr M does rapidly increases to 8 J/kg K within the measured magnetic field range (see in the upper panel of Fig. 5). In contrast, the ΔSM , pure magnetic entropy change in the vicinity of T AC , induced by a second order magnetic transition at austenite state retains a linear increment, and the peak value only arrives at 4 J/kg K within the same field range (see in the lower panel of Fig. 5). Such discrepancy could be qualitatively understood by the fact that the arrangement of magnetic moment is much more ordered resulted from the magnetostructural coupling than that resulted from spin fluctuation at similar condition. Furthermore, if an application of ΔH is sufficiently large, we consider that the jΔSstr M j will achieve to a saturated value of 10 J/kg K (expected by jΔStr ΔStotal j). This indicates that about L 33% of lattice entropy change is consumed by the opposite contribution of magnetic entropy in the process of reverse MT. Such value is obviously larger than that ( 23%) speculated in Ni45.2Co5.1Mn36.7In13 using calorimetry based on an assumption [17]. Therefore, the maximizing of the lattice contribution plays a
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Z. Li et al. / Solid State Communications 203 (2015) 81–84
Fig. 5. (Color online) Temperature dependence of both the lattice entropy change ΔSL and the entropy change ΔST under different magnetic fields, respectively. Upper panel: A the isothermal magnetic entropy ΔSstr M in the process of reverse martensitic transition. Lower panel: a pure magnetic entropy change ΔSM in the vicinity of T C , which is induced by a second order magnetic transition at austenitic state.
pivotal role in further improving the inverse MCE for Mn-rich Ni–Mn based Heusler alloy system. 4. Conclusions In summary, the inverse MCE in the case of reverse MT for Ni46.7Co5Mn33In15.3 alloy can be credibly evaluated by C–C equation based on change of volume fraction between both phases. Using this approach as well as the Debye theory, the contributions of the lattice and magnetism to the total entropy change upon this process are effectively separated for present sample. Our results demonstrate that the inverse MCE associated with reverse MT only originates from contribution of lattice entropy change, whereas the magnetic entropy change would be responsible for a counterproductive way. These discussions can also help us to develop more efficiently magnetic refrigerants with such kind of Heusler alloys system. Acknowledgments This work was supported by the National Natural Science Foundation of China (Grant nos. 11364035, 11404186 and 51371111), the Key Basic Research Program of Science and Technology Commission of Shanghai Municipality (Grant no. 13JC1402400), and Project for Innovative Research Team of Qujing Normal University (Grant no. TD201301), and Project for Applied Basic Research Programs of Yunnan Province (Grant nos. 2013FZ110 and 2012FD051). References [1] A.M. Tishin, Y. Spichkin, The Magnetocaloric Effect and its Applications, Institute of Physics Publishing, Bristol, 2003. [2] V.K. Pecharsky, K.A. Gschneidner Jr., Phys. Rev. Lett. 78 (1997) 4494. [3] H. Wada, Y. Tanabe, Appl. Phys. Lett. 79 (2001) 3320.
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