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Effect of particle size on the magneto-caloric properties of Ni51Mn34In14Si1 alloy
Journal of Alloys and Compounds 572 (2013) 192–198
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Effect of particle size on the magneto-caloric properties of Ni51Mn34In14Si1 alloy Rahul Das ⇑, A. Perumal, A. Srinivasan Department of Physics, Indian Institute of Technology Guwahati, Guwahati 781039, India
a r t i c l e
i n f o
Article history: Received 5 February 2013 Received in revised form 18 March 2013 Accepted 20 March 2013 Available online 02 April 2013 Keywords: Magnetically ordered materials Magneto-caloric effect Ferromagnetic shape memory alloy Milled powders Particle size Phase transitions
a b s t r a c t We have systematically investigated the effect of particle size on the magneto-caloric properties of Ni51Mn34In14Si1 alloy. Arc melted Ni51Mn34In14Si1 alloy was milled to reduce the average particle size and then vacuum annealed to reduce the strain accumulated in the particles during milling. Annealed particles were sieved and magneto-caloric parameters of the particles of different size ranges were systematically measured. It was observed that with decreasing particle size, the magnetic entropy change (DSM) decreased but the refrigerant capacity (RC) increased to a maximum value and then decreased. The investigations reveal that the magneto-caloric parameters could be tuned over a wide range by changing the particle size of the alloy. RC (DSM) obtained is 40.4 J kg1 (11.2 J kg1 K1) for the alloy with particle size ranging between 600 lm and 710 lm for an applied magnetic field change of 1.2 Tesla. These combined values of DSM and RC are the highest reported for any ferromagnetic shape memory alloy particle. These studies indicate that Ni51Mn34In14Si1 alloy particles with controlled particle size are potential candidates for magnetic refrigeration near room-temperature. Ó 2013 Elsevier B.V. All rights reserved.
1. Introduction Magneto-caloric effect (MCE) which means heating up or cooling down of magnetic materials by an applied magnetic field was first observed by Warburg in 1881 in iron [1]. Later, Giauque and Debye independently explained this phenomenon and suggested its application in magnetic refrigeration [2,3]. MCE is generally measured in terms of isothermal entropy change (DSM) or adiabatic temperature change (DTad) in a magnetic material when it is subjected to a magnetic field. If DSM < 0 (or DTad > 0), the sample heats up upon application of magnetic field (direct MCE). On the other hand, if DSM > 0 (or DTad < 0), the sample cools down when the external magnetic field is applied (inverse MCE) [4]. The current interest in these magnetic refrigerants is due to their environment friendly and energy saving attributes as compared to the gas-compression/expansion technology currently used in commercial refrigeration [5]. For commercial exploitation, the new technology materials exhibiting large MCE parameters such as DSM (or DTad) and refrigerant capacity (RC) near room temperature for relatively low magnetic field change (DH) are required. Generally, ferromagnetic shape memory alloys (FSMAs) show two characteristic temperature induced phase transitions: a magnetic second-order phase transition at the Curie temperature (TC) of the austenitic and martensite phases, and a structural first-order ⇑ Corresponding author. Tel.: +91 361 2582743; fax: +91 361 2690762. E-mail address: [email protected] (R. Das). 0925-8388/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jallcom.2013.03.235
phase transition at the martensitic temperature (Ms), accompanied by a change in magnetization (DM) [6–15]. These FSMAs exhibit compositionally tunable magnetic, electric and structural properties which are important for various technological applications such as shape memory devices [16], magneto-resistive devices [17,18], magnetic field induced actuators [19], and especially, as regenerators in prototype magnetic refrigerators. The latest candidates of FSMAs are Ni–Mn–Sn and Ni–Mn–In based materials of which the characteristic temperatures were first reported by Sutou et al. [6]. Since then, melt-spun ribbons [20–24] and thin films [25,26] of Ni–Mn–In(Sn) alloys have also been studied. Oikawa et al. [8] reported a DSM of 13 J kg1 K1 at MS (190 K) in bulk Ni46Mn41In13 alloys for a high DH of 9 T. It is well known that the properties of FSMAs are sensitive to even a small change in composition. Exploiting this feature, several studies [27–31] of MCE in this alloy system has been carried out. These studies revealed that FSMAs exhibit very large MCE when a sharp change in magnetization occurs with a martensitic phase transformation [9,13]. Typically, Ni50Mn50xInx alloys display maximum RC of 280 J kg1 and 260 J kg1 corresponding to DSM of 6.8 J kg1 K1 and 23 J kg1 K1 near TC and MS, respectively, under DH of 5 T [27]. For the same DH, the RC (DSM) as large as 279 J kg1 (33 J kg1 K1) has been obtained in Ni47Mn38In15 alloy at 285 K [29]. In order to obtain high values of the MCE parameters, most of the investigators have used very high applied magnetic field (>2 T). Since such high fields restrict the commercial viability of these materials, attempts are being made to develop materials
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Fig. 1. Room temperature XRD patterns of bulk and three sets of Ni51Mn34In14Si1 powders with different average particle size (dav).
which exhibit high DSM and RC at lower amenable magnetic fields. For DH of 1T Han et al. [32] obtained high RC (60 J kg1) in Ni45.4Mn41.5In13.1 alloy with a peak DSM of 8 J kg1 K1 and in case of melt spun ribbons Guan et al. [33] showed RC of 42.05 J kg1 with very low DSM (3.9 J kg1 K1) for Ni48Co2Mn35In15 compound. Recently, Ni–Mn–In–Si alloys have been reported to possess excellent magneto-caloric properties at low field [34–36]. Santanna et al. [37] have demonstrated that particle size refinement can enhance RC despite reducing DSM. These reports suggest that particle size refinement of a FSMAs composition exhibiting very high DSM can provide a means to tailor its DSM and RC to required values suitable for magnetic refrigerant application for reasonably low magnetic field change. However, no systematic studies on the effect of particle size over a wide range of particle sizes are available in the literature. In addition, it is important to note that for commercial exploitation of these magnetic refrigerants, large RC and DSM near room temperature for viable magnetic fields (<2 T) are required. This motivated us to perform a systematic investigation of the structural phase transition, magnetic phase transition and magneto-caloric properties of Ni51Mn34In14Si1 alloy with different particle sizes. 2. Experimental Polycrystalline Ni51Mn34In14Si1 alloy ingot was prepared by arc melting high purity (99.99%) elements. To counter preferential loss of Mn during arc-melting, an excess amount (1.2 wt.%) of Mn was taken. After melting several times, weight
loss in the ingot was less than 1.5%. The ingot was sealed in a fused silica ampoule under a pressure of 103 Pa and annealed at 1173 K for 20 h and then quenched in ice water. The annealed ingot was crushed into particles of size <3 mm and milled for 7 h in a planetary ball mill (Insmart make). Hardened steel vial and hardened steel balls were used and 10:1 ball-to-powder weight ratio was maintained during the milling process. The mill was operated at a constant speed of 500 rpm. To avoid overheating of the vial, milling was carried out in cycles of 15 min followed by 10 min of idling. As-milled powders were subjected to the same heat treatment as the original ingot to minimize the strains accumulated during the milling process. Subsequently, the annealed powder was sieved using different pore sized metallic sieves conforming to ASTM standards and classified into different particle size ranges. The alloy powders studied are classified into thirteen sets depending on their size as B (bulk), P1 (850–1180 lm), P2 (710–850 lm), P3 (600–710 lm), P4 (500–600 lm), P5 (425–500 lm), P6 (300–425 lm), P7 (125–300 lm), P8 (106– 125 lm), P9 (90–106 lm), P10 (38–45 lm), P11 (20–38 lm), and P12 (<20 lm). A part of the sorted samples were used for structural analysis using a high power X-ray diffractometer (Rigaku TTRAX 18 kW) using Cu Ka radiation (k = 0.15406 nm). Structural parameters of the samples were obtained from Rietveld analysis of the X-ray diffraction (XRD) patterns. Composition and particle sizes of the powders were verified using an energy dispersive spectrometer (EDS) attached to a scanning electron microscope (SEM, Leo 1430VP). Phase transition temperatures and the magnetization measurements as a function of temperature and magnetic field were performed using a vibrating sample magnetometer (VSM, Lakeshore 7410) equipped with a variable temperature (20–320 K) attachment. Magnetic moment calibration was performed with standard Ni sphere, prior to the magnetization measurements. Isothermal magnetization (M–H)T data were recorded at different temperatures as a function of increasing magnetic field from 0 to 1.2 T and decreasing temperature at 2 K interval. The measurement temperature was reached by cooling the sample from above the austenite finish temperature at zero magnetic fields and the measurements were made after allowing for stabilization of temperature. Heat capacity data at zero magnetic field were obtained using a physical properties measurement system (PPMS, Quantum Design).
3. Results and discussion Fig. 1 depicts the room temperature XRD patterns of the heat treated bulk and three sets of sorted Ni51Mn34In14Si1 alloy powders. All the samples exhibit the cubic L21 structure corresponding space group of austenite phase. No additional (martensite to Fm3m or impurity) phases were found in the XRD patterns. The L21 structure is identified by the characteristic (1 1 1) and (3 1 1) peaks. In case of X2YZ type compound Szytula et al. [38] have shown that the reflections with non-zero structure factors are obtained for the L21 structure when all indices are either even or odd. For first three reflections, the structure factors are F(1 1 1) = 4(fy fz), F(2 0 0) = 4[2fx (fy + fz)], and F(2 2 0) = 4[2fx + fy + fz], where fx, fy and fz are average scattering amplitudes for respective sub-lattices X, Y and Z. Any intermixing between Y and Z atoms can lead to the disordered B2 structure with the absence of F(1 1 1) and reflections with all odd indices. Rietveld analysis of the XRD patterns reveal that alloy particles with sizes larger than 106 lm have the same unit cell dimension with lattice constant a = 0.5974 ± 0.0002 nm.
Table 1 Space group, Wyckoff positions, particle size, measured alloy composition, lattice parameters (a, b and c), unit cell volume (V), and microstrain obtained for bulk and milled Ni51Mn34In14Si1 alloy. Space group Fm3m
Wyckoff positions In (0, 0, 0); Si (0, 0, 0); Mn (0, 0, 0) and (1/2, 1/2, 1/2); Ni (1/2, 1/2, 1/2) and (1/4, 1/4, 1/4).
Alloy ID
Particle size, dav (lm)
Composition from EDS
a = b = c (nm)
V(nm)3
Microstrain 102 (%)
B P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12
Bulk 850–1180 710–850 600–710 500–600 425–500 300–425 125–300 106–125 90–106 38–45 20–38 <20
Ni50.69Mn33.83In14.07Si1.41 Ni50.72Mn33.89In14.00Si1.39 Ni50.65Mn33.85In14.10Si1.40 Ni50.68Mn33.90In14.06Si1.36 Ni50.74Mn33.91In14.03Si1.32 Ni50.66Mn33.80In14.12Si1.42 Ni50.69Mn33.89In14.00Si1.42 Ni50.67Mn33.85In14.07Si1.41 Ni50.70Mn33.87In14.09Si1.34 Ni50.72Mn33.88In14.00Si1.40 Ni50.67Mn33.83In14.09Si1.41 Ni50.68Mn33.84In14.08Si1.40 Ni50.71Mn33.85In14.02Si1.42
0.5974 0.5974 0.5974 0.5974 0.5974 0.5974 0.5974 0.5974 0.5974 0.5975 0.5977 0.5981 0.5992
0.2132 0.2132 0.2132 0.2132 0.2132 0.2132 0.2132 0.2132 0.2132 0.2132 0.2133 0.2140 0.2151
25.9 26.1 26.1 26.2 26.3 26.5 27.0 27.3 28.9 32.5 41.8 52.4 68.9
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Fig. 2. SEM images of sieved Ni51Mn34In14Si1 alloy powders sorted in different size ranges: (a) P12 (<20 lm), (b) P11 (20–38 lm), (c) P8 (106–125 lm) and (d) P3 (600– 710 lm).
The lattice constant a increases to 0.5981 ± 0.0004 nm and 0.5992 ± 0.0002 nm for the finer samples P11 and P12, respectively. This slight variation in the lattice constant could be attributed to the presence of residual stresses in the finer particles even after the annealing treatment. Features in the XRD pattern such as the pronounced asymmetrical tail of (2 2 0) reflection in P11 and P12 samples indicate inhomogenities in the milling. This shows the presence of residual strain in the powder samples even after the annealing treatment. Microstrain estimated using Rietveld analysis of the XRD data was found to increase considerably in powders with dav < 125 lm. The crystallographic data obtained from the analysis are summarized in Table 1. Fig. 2 shows the SEM micrographs of four sets of Ni51Mn34In14Si1 alloy powders sorted by systematic sieving. All the dry milled powders show a typical flake-like morphology as they are subjected to cold welding and fracture inside the vial. The average size (dav) of the particles was measured along the longest side of the flakes. It can be noticed that as the average particle size decreased, the particle shape became more spherical. Composition analysis of the samples by EDS reveal that the final composition of all the samples after milling and annealing is close to the starting composition. The results of the EDS analysis is summarized in Table 1. In order to understand the effect of particle size variation on the magnetic and magneto-caloric properties of the powder samples, temperature dependent magnetic properties were evaluated. Fig. 3 shows the M–T curves of the samples measured during field cooling (FC) and field heating (FH) cycles in a magnetic field of 0.1 T. The observed results reveal that all the samples are in austenite phase above room temperature and with decreasing the temperature, the samples exhibit a magnetic phase transition from the paramagnetic state to ferromagnetic state in austenite phase (marked as TC,A). Below TC,A, the samples order ferromagnetically in the austenite phase until they begin to transform into the martensite phase at the martensite start temperature Ms. On further cooling the samples, they display another magnetic phase transition from the paramagnetic state to the ferromagnetic state in the martensite phase (marked as TC,M). All samples exhibit these two magnetic transitions. The Curie temperature (TC) of the magnetic phase transition is defined as the temperature at which the
@M/@T exhibits a minimum value in FH M–T curve. Only TC,A would be referred in the remaining part of the manuscript since the MCE related to TC,M is considerably smaller and is not of interest to this work. Ms is taken as the temperature at which the maximum magnetization in FC M–T data is observed. Similarly, the austenite start temperature As corresponds to the temperature at which the FH M–T shows a large increase. Both these characteristic temperatures are indicated in Fig. 3. Ms, As, martensite finish temperature (Mf) and austenite finish temperature (Af) of all the samples extracted from the M–T data are listed in Table 2. M–T data recorded under FC condition at a higher magnetic field of 1.2 T is shown as an inset in Fig. 3. Comparison with the data shown in Fig. 3 reveals a slight shift in the martensite transformation temperature towards lower temperatures at the higher applied magnetic field. Such behavior
Fig. 3. Plots of M–T curves of bulk and sorted Ni51Mn34In14Si1 powders recorded under an applied field of 0.1 T. Filled and open symbols represent data recorded during field cooling and field heating, respectively. Curie temperature of martensitic phase (TC,M), martensite start temperature (Ms), martensite finish temperature (Mf), austenite start temperature (As), austenite finish temperature (Af) and the Curie temperature of the austenite phase (TC,A) of the bulk samples are shown. The inset presents the FC M–T curves recorded at an applied field of 1.2 T.
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Table 2 Curie temperature (TC,A), austenite start temperature (As), austenite finish temperature (Af), martensite start temperature (Ms), martensite finish temperature (Mf), thermal hysteresis (DT) obtained at 0.1 T field and magneto-caloric parameters (magnetic entropy change (DSM), full width at half maxima (FWHM) of DSM (T) data, and refrigerant capacity (RC) obtained for 1.2 T field change) of bulk and milled Ni51Mn34In14Si1 alloy. Alloy ID
TC,A (K)
As (K)
Af (K)
Ms (K)
Mf (K)
DT (K)
DSM (J kg1 K1)
FWHM (K)
RC (J kg1)
B P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12
294 294 294 293 293 292 292 290 288 287 285 283 282.6
279 279 279 279 279 278 275 272 268 265 261 260 259
287 287 287 287 287 287 287 286 286 285 284 283 282
278 278 278 278 278 278 278 278 278 278 277 277 276
270 270 270 270 270 265 259 254 250 245 241 238 237
9.0 9.0 9.0 9.0 9.0 11.0 12.5 13.0 13.0 13.5 13.5 14.0 14.0
19.9 17.2 14.6 11.2 10.5 9.4 7.2 6.3 5.7 1.4 0.8 0.5 0.4
2.4 2.8 3.4 4.6 4.6 4.7 5.4 5.7 6.0 8.1 10.5 11.0 11.3
35.9 36.1 36.7 40.4 36.0 33.4 31.5 26.9 21.7 12.2 4.5 4.0 3.5
has also been observed in other FSMAs [39]. TC,A and Ms for the bulk sample are 294 K and 278 K, respectively. In the case of the milled samples, TC,A and Ms do not deviate from the bulk value up to a particle size of 710 lm and 90 lm, respectively. For particles below this size, both TC and Ms decrease with a decrease in particle size (cf. Table 2). Fig. 3 shows another interesting feature, viz., the magnitude of the DM at the martensitic phase transition decreases with decreasing particle size. This may be due to the change in the fraction of the martensite phase and/or the change in the magnetic properties of the sample with decrease in particle size. A thermal hysteresis (DT) observed between the FC and FH curves for all the samples in the temperature range of 230 K to 290 K is attributed to the first-order martensitic transition. DT can be estimated from the characteristic temperature obtained from the M–T curves as DT = (As + Af)/2 (Ms + Mf)/2. DT was close to 9 K for particles with dav down to 500 lm, and then showed a larger increase with further decrease in particle size. Thermal hysteresis effect in the FSMA is a complicated process and is generally related to the nucleation of the new phase and the interaction of interfaces with defects from the microscopic point of view. But from the mesoscopic point of view, the same originates from the formation, annihilation, and rearrangement of elastically interacting domains [30]. In addition, the friction from domain rearrangement and phase boundary motions also contribute to the hysteresis. In other words, DT characterizes the strength of the friction during the transformation. In the present case, the variation of DT with particle size confirms that the friction encountered during the transformation increases with decreasing the particle size. The reduction in the number of domains with reduction in particle size is understandable. However, when one considers the change in the shape of the hysteresis, contributions from the other factors listed above cannot be overruled. One such contribution is the incomplete transformation between the martensite and austenite phases. This can be understood from the non-zero magnetization observed in M–T curves of the powder samples (Fig. 3) in the temperature range TC,M < T < Mf. (M–H)T data of Ni50xMn37+xIn13 alloys [15] show typical paramagnetic behavior in this intermediate temperature range. In order to explore this feature, we obtained isothermal magnetization curve at T = 250 K, where TC,M < T < Mf for our samples. Fig. 4 displays the M–H curves obtained for samples designated as B, P2, P8 and P11. While the bulk (B) sample shows linear field dependence which is characteristic of a paramagnet, the powder samples exhibit a nonlinear behavior at low fields indicating the presence of a small fraction of spontaneous magnetization (or ferromagnetism). Straight lines, passing through the data points are linear fits to the data in the high field region, extrapolated to zero field yield the spontaneous magnetization of the
Fig. 4. Initial magnetization curves recorded at T = 250 K for bulk and sorted milled Ni51Mn34In14Si1 alloy powders. The lines represent linear fits to the data at higher fields.
impurity ferromagnetic phase present in the samples. Fraction of ferromagnetic phase present in the TC,M < T < Mf regime increases with decreasing particle size. The impurity ferromagnetic phase is the residual (untransformed) austenite phase present in the samples. Also, the ratio between the maximum magnetization of FC curve in the austenite phase and the magnetization at the ferromagnetic martensite phase decreases significantly with decreasing particle size. This is mainly due to the increased number of the particle surfaces in a given volume of the sample which tend to reduce the average magnetization of the sample as the particle size is decreased. In order to evaluate the values of DSM and the RC, the (M–H)T curves of all the samples were obtained close to Ms. Fig. 5 displays the (M–H)T curves of Ni51Mn34In14Si1 samples with four different particle size ranges. It is obvious that all the samples are in ferromagnetic state at Ms. However, the magnitude of magnetization decreased not only with decreasing particle size but also with decrease in temperature. The nature of the magnetization curves changes with decreasing particle size and magnetization did not saturate up to an applied field of 1.2 T. This can be attributed either to the reduction in the particle size, which increases the number of particle surfaces and hence each particle would act like a single domain particle, or to the difficulty encountered in magnetization reversal due to the presence of considerable amount of stress in the smaller particles induced by the milling process. Nevertheless,
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Fig. 5. Isothermal initial magnetization curves obtained for bulk and sorted milled Ni51Mn34In14Si1 alloy powders: (a) B (bulk), (b) P2 (710–850 lm), (c) P3 (600–710 lm) and (d) P12 (<20 lm).
it may be noted in each of the graphs that at a certain temperature the magnetization increased suddenly [13]. DSM was evaluated as a function of temperature for a magnetic field change (DH) of 1.2 T from (M–H)T curves using the integrated Maxwell’s relation [11,40],
DSM ðT; HÞ ¼
Z 0
H
@MðTÞ dH @T H
ð1Þ
Fig. 6a depicts the temperature dependence of DSM for the powders with different particle sizes. DSM is positive in all the cases because @M/@T is positive at the martensitic phase transition. Positive DSM implies that the sample cools down upon application of external magnetic field [4]. The maximum value of DSM and the full width at half maxima (FWHM) of DSM(T) are the characteristic features of the MCE. DSM and FWHM decreased and increased, respectively, with a decrease in particle size as shown in the Table 2. The temperature at which peak DSM is observed for each set of samples shows a shift towards lower values with a decrease in particle size (cf. Fig. 6a). This feature can be correlated with the corresponding behavior of @M/@T with particle size depicted in Fig. 3. Though the highest peak DSM (=19.9 J kg1 K1) has been observed for the bulk alloy, this sample has the disadvantage of having the narrowest operating temperature range (FWHM = 2.4 K). As can be seen from Fig. 6b and Table 2, this disadvantage can be overcome by optimizing the particle size. An estimate of the adiabatic temperature change (DTad) of these samples would be useful for magnetic refrigerant application of this material. For this, S(T)H curves for H = 0 and H = 1.2 T were obtained using the relations [11,40]:
SðTÞH¼1:2T ¼ SðTÞH¼0 þ DSM ðTÞDH¼1:2T Z T CðTÞH¼0 SðTÞH¼0 ¼ dT þ SðT ¼ 0Þ T 0
ð2Þ
where C(T) is the heat capacity measured at zero magnetic field. Inset in Fig. 7 shows the C(T) data for P3 sample. Isentropic paths from S(T)H=0 curve to S(T)H=1.2T curve at different temperatures result in DTad(T) shown in Fig. 7. The moderate DTad of 1.99 K corresponding to DSM (11.2 J kg1 K1) is exhibited by the P3 powder sample at 278 K for DH = 1.2 T. This value may be compared with DTad = 1.5 K and 1.99 K reported for Ge and Al substituted NiMnIn alloy
Fig. 6. (a) Temperature dependence of magnetic entropy change obtained for 1.2 T field change in bulk and milled Ni51Mn34In14Si1 alloy. (b) Peak DSM (j) and FWHM (N) of Ni51Mn34In14Si1 alloy powders of different particle sizes.
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coupling [37,41], there by leading to an overall increase in MCE. In addition, a survey of the literature and comparison with earlier reports [37,42] shows that these combined values of MCE parameters appear to be highest ever reported for any FSMA powder. Since higher RC signifies a larger heat transport, Ni51Mn34In14Si1 alloy with particle size between 600 lm and 710 lm along with their high DSM for a reasonably small DH of 1.2 T at temperatures close to the ambient show a lot of promise for magnetic refrigeration application. It would also be worthy to investigate the effect of particle shape and its influence on DSM and RC of the powder particles. Particles with appropriate shape may yield higher DSM and RC values. Powder particles have the inherent advantage of being capable of compaction into any desired macroscopic net shape, which may also be an advantage in their application as refrigerant as compared to the inflexible bulk samples. 4. Conclusions Fig. 7. Temperature dependence of adiabatic temperature change obtained for 1.2 T field change. Inset show temperature dependent heat capacity at zero field obtained for Ni51Mn34In14Si1 alloy particles with size in 600–710 lm range.
for DH = 1.8 T, respectively [9]. This comparison serves to highlight the potential of Ni51Mn34In14Si1 alloy for magnetic refrigerant application. RC is another important MCE parameter which is a measure of the amount of heat that can be transferred between hot and cold reservoirs in an ideal refrigeration cycle. If there are two different magnetic refrigerants which differ only in their RC value, then the one with higher RC is expected to perform better because of its capability to transport greater amounts of heat in a real cycle [40]. RC estimated from the following relation [11,40] and depicted in Fig. 8.
RC ¼
Z
T2
DSM ðT; HÞdT
ð3Þ
T1
RC values corresponding to the DSM(T) curves first increased to the highest value and then decreased with particle size. Highest RC (40.4 J kg1) value has been obtained for particles in the size range of 600–710 lm. Particles in this size range also exhibit moderately high values of FWHM (4.6 K), DSM (11.2 J kg1 K1) (cf. Fig. 6b) and DTad (1.99 K). The enhancement in RC values with decreasing particle size range up to 600–710 lm is mainly influenced by the microstructural characteristics of the processed samples, which in turn impose significant control on the magneto-structural
Magnetic and magneto-caloric properties of Ni51Mn34In14Si1 alloys with different particle sizes were studied. The largest value of DSM (19.9 J kg1 K1) was obtained for bulk Ni51Mn34In14Si1 alloy at 279 K for DH = 1.2 T, which was mainly due to the large @M/@T or DM realized at the martensitic phase transition. But, due to the smallest FWHM the bulk sample may not be suitable for magnetic refrigerant application. Compared with the bulk, powdered particles show better magnetic refrigeration ability due to their larger RC as well as FWHM. The present studies on Ni51Mn34In14Si1 alloy show that optimization of the particle size of this alloy can yield powders with the desired combination of large DSM, FWHM and RC near Ms. Particles in the size range of 600–710 lm exhibit moderately high values of FWHM (4.6 K), DSM (11.2 J kg1 K1), RC (40.4 J kg1) and DTad (1.99 K). DSM(T) curves broaden with a decrease in particle size. The largest value of FWHM obtained was 11.3 K for particles with size <20 lm, although they exhibit the lowest DSM (0.4 J kg1 K1) and RC (3.5 J kg1). The high DSM obtained near Ms and the easy tunability of FWHM and RC values with different particle sizes make Ni51Mn34In14Si1 alloy powders an attractive magnetic refrigerant material. Acknowledgements Financial assistance from the Council of Scientific and Industrial Research, India vide Project No: 03(1236)/12/EMR-II is acknowledged. The work present used the infrastructural facilities provided by the Department of Science and Technology, India vide Project Nos.: SR/S2/CMP-19/2006 and SR/FST/PII-020/2009. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]
Fig. 8. Temperature dependence of refrigerant capacity of bulk and milled Ni51Mn34In14Si1 alloy.
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Effect of particle size on the magneto-caloric properties of Ni51Mn34In14Si1 alloy Rahul Das ⇑, A. Perumal, A. Srinivasan Department of Physics, Indian Institute of Technology Guwahati, Guwahati 781039, India
a r t i c l e
i n f o
Article history: Received 5 February 2013 Received in revised form 18 March 2013 Accepted 20 March 2013 Available online 02 April 2013 Keywords: Magnetically ordered materials Magneto-caloric effect Ferromagnetic shape memory alloy Milled powders Particle size Phase transitions
a b s t r a c t We have systematically investigated the effect of particle size on the magneto-caloric properties of Ni51Mn34In14Si1 alloy. Arc melted Ni51Mn34In14Si1 alloy was milled to reduce the average particle size and then vacuum annealed to reduce the strain accumulated in the particles during milling. Annealed particles were sieved and magneto-caloric parameters of the particles of different size ranges were systematically measured. It was observed that with decreasing particle size, the magnetic entropy change (DSM) decreased but the refrigerant capacity (RC) increased to a maximum value and then decreased. The investigations reveal that the magneto-caloric parameters could be tuned over a wide range by changing the particle size of the alloy. RC (DSM) obtained is 40.4 J kg1 (11.2 J kg1 K1) for the alloy with particle size ranging between 600 lm and 710 lm for an applied magnetic field change of 1.2 Tesla. These combined values of DSM and RC are the highest reported for any ferromagnetic shape memory alloy particle. These studies indicate that Ni51Mn34In14Si1 alloy particles with controlled particle size are potential candidates for magnetic refrigeration near room-temperature. Ó 2013 Elsevier B.V. All rights reserved.
1. Introduction Magneto-caloric effect (MCE) which means heating up or cooling down of magnetic materials by an applied magnetic field was first observed by Warburg in 1881 in iron [1]. Later, Giauque and Debye independently explained this phenomenon and suggested its application in magnetic refrigeration [2,3]. MCE is generally measured in terms of isothermal entropy change (DSM) or adiabatic temperature change (DTad) in a magnetic material when it is subjected to a magnetic field. If DSM < 0 (or DTad > 0), the sample heats up upon application of magnetic field (direct MCE). On the other hand, if DSM > 0 (or DTad < 0), the sample cools down when the external magnetic field is applied (inverse MCE) [4]. The current interest in these magnetic refrigerants is due to their environment friendly and energy saving attributes as compared to the gas-compression/expansion technology currently used in commercial refrigeration [5]. For commercial exploitation, the new technology materials exhibiting large MCE parameters such as DSM (or DTad) and refrigerant capacity (RC) near room temperature for relatively low magnetic field change (DH) are required. Generally, ferromagnetic shape memory alloys (FSMAs) show two characteristic temperature induced phase transitions: a magnetic second-order phase transition at the Curie temperature (TC) of the austenitic and martensite phases, and a structural first-order ⇑ Corresponding author. Tel.: +91 361 2582743; fax: +91 361 2690762. E-mail address: [email protected] (R. Das). 0925-8388/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jallcom.2013.03.235
phase transition at the martensitic temperature (Ms), accompanied by a change in magnetization (DM) [6–15]. These FSMAs exhibit compositionally tunable magnetic, electric and structural properties which are important for various technological applications such as shape memory devices [16], magneto-resistive devices [17,18], magnetic field induced actuators [19], and especially, as regenerators in prototype magnetic refrigerators. The latest candidates of FSMAs are Ni–Mn–Sn and Ni–Mn–In based materials of which the characteristic temperatures were first reported by Sutou et al. [6]. Since then, melt-spun ribbons [20–24] and thin films [25,26] of Ni–Mn–In(Sn) alloys have also been studied. Oikawa et al. [8] reported a DSM of 13 J kg1 K1 at MS (190 K) in bulk Ni46Mn41In13 alloys for a high DH of 9 T. It is well known that the properties of FSMAs are sensitive to even a small change in composition. Exploiting this feature, several studies [27–31] of MCE in this alloy system has been carried out. These studies revealed that FSMAs exhibit very large MCE when a sharp change in magnetization occurs with a martensitic phase transformation [9,13]. Typically, Ni50Mn50xInx alloys display maximum RC of 280 J kg1 and 260 J kg1 corresponding to DSM of 6.8 J kg1 K1 and 23 J kg1 K1 near TC and MS, respectively, under DH of 5 T [27]. For the same DH, the RC (DSM) as large as 279 J kg1 (33 J kg1 K1) has been obtained in Ni47Mn38In15 alloy at 285 K [29]. In order to obtain high values of the MCE parameters, most of the investigators have used very high applied magnetic field (>2 T). Since such high fields restrict the commercial viability of these materials, attempts are being made to develop materials
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Fig. 1. Room temperature XRD patterns of bulk and three sets of Ni51Mn34In14Si1 powders with different average particle size (dav).
which exhibit high DSM and RC at lower amenable magnetic fields. For DH of 1T Han et al. [32] obtained high RC (60 J kg1) in Ni45.4Mn41.5In13.1 alloy with a peak DSM of 8 J kg1 K1 and in case of melt spun ribbons Guan et al. [33] showed RC of 42.05 J kg1 with very low DSM (3.9 J kg1 K1) for Ni48Co2Mn35In15 compound. Recently, Ni–Mn–In–Si alloys have been reported to possess excellent magneto-caloric properties at low field [34–36]. Santanna et al. [37] have demonstrated that particle size refinement can enhance RC despite reducing DSM. These reports suggest that particle size refinement of a FSMAs composition exhibiting very high DSM can provide a means to tailor its DSM and RC to required values suitable for magnetic refrigerant application for reasonably low magnetic field change. However, no systematic studies on the effect of particle size over a wide range of particle sizes are available in the literature. In addition, it is important to note that for commercial exploitation of these magnetic refrigerants, large RC and DSM near room temperature for viable magnetic fields (<2 T) are required. This motivated us to perform a systematic investigation of the structural phase transition, magnetic phase transition and magneto-caloric properties of Ni51Mn34In14Si1 alloy with different particle sizes. 2. Experimental Polycrystalline Ni51Mn34In14Si1 alloy ingot was prepared by arc melting high purity (99.99%) elements. To counter preferential loss of Mn during arc-melting, an excess amount (1.2 wt.%) of Mn was taken. After melting several times, weight
loss in the ingot was less than 1.5%. The ingot was sealed in a fused silica ampoule under a pressure of 103 Pa and annealed at 1173 K for 20 h and then quenched in ice water. The annealed ingot was crushed into particles of size <3 mm and milled for 7 h in a planetary ball mill (Insmart make). Hardened steel vial and hardened steel balls were used and 10:1 ball-to-powder weight ratio was maintained during the milling process. The mill was operated at a constant speed of 500 rpm. To avoid overheating of the vial, milling was carried out in cycles of 15 min followed by 10 min of idling. As-milled powders were subjected to the same heat treatment as the original ingot to minimize the strains accumulated during the milling process. Subsequently, the annealed powder was sieved using different pore sized metallic sieves conforming to ASTM standards and classified into different particle size ranges. The alloy powders studied are classified into thirteen sets depending on their size as B (bulk), P1 (850–1180 lm), P2 (710–850 lm), P3 (600–710 lm), P4 (500–600 lm), P5 (425–500 lm), P6 (300–425 lm), P7 (125–300 lm), P8 (106– 125 lm), P9 (90–106 lm), P10 (38–45 lm), P11 (20–38 lm), and P12 (<20 lm). A part of the sorted samples were used for structural analysis using a high power X-ray diffractometer (Rigaku TTRAX 18 kW) using Cu Ka radiation (k = 0.15406 nm). Structural parameters of the samples were obtained from Rietveld analysis of the X-ray diffraction (XRD) patterns. Composition and particle sizes of the powders were verified using an energy dispersive spectrometer (EDS) attached to a scanning electron microscope (SEM, Leo 1430VP). Phase transition temperatures and the magnetization measurements as a function of temperature and magnetic field were performed using a vibrating sample magnetometer (VSM, Lakeshore 7410) equipped with a variable temperature (20–320 K) attachment. Magnetic moment calibration was performed with standard Ni sphere, prior to the magnetization measurements. Isothermal magnetization (M–H)T data were recorded at different temperatures as a function of increasing magnetic field from 0 to 1.2 T and decreasing temperature at 2 K interval. The measurement temperature was reached by cooling the sample from above the austenite finish temperature at zero magnetic fields and the measurements were made after allowing for stabilization of temperature. Heat capacity data at zero magnetic field were obtained using a physical properties measurement system (PPMS, Quantum Design).
3. Results and discussion Fig. 1 depicts the room temperature XRD patterns of the heat treated bulk and three sets of sorted Ni51Mn34In14Si1 alloy powders. All the samples exhibit the cubic L21 structure corresponding space group of austenite phase. No additional (martensite to Fm3m or impurity) phases were found in the XRD patterns. The L21 structure is identified by the characteristic (1 1 1) and (3 1 1) peaks. In case of X2YZ type compound Szytula et al. [38] have shown that the reflections with non-zero structure factors are obtained for the L21 structure when all indices are either even or odd. For first three reflections, the structure factors are F(1 1 1) = 4(fy fz), F(2 0 0) = 4[2fx (fy + fz)], and F(2 2 0) = 4[2fx + fy + fz], where fx, fy and fz are average scattering amplitudes for respective sub-lattices X, Y and Z. Any intermixing between Y and Z atoms can lead to the disordered B2 structure with the absence of F(1 1 1) and reflections with all odd indices. Rietveld analysis of the XRD patterns reveal that alloy particles with sizes larger than 106 lm have the same unit cell dimension with lattice constant a = 0.5974 ± 0.0002 nm.
Table 1 Space group, Wyckoff positions, particle size, measured alloy composition, lattice parameters (a, b and c), unit cell volume (V), and microstrain obtained for bulk and milled Ni51Mn34In14Si1 alloy. Space group Fm3m
Wyckoff positions In (0, 0, 0); Si (0, 0, 0); Mn (0, 0, 0) and (1/2, 1/2, 1/2); Ni (1/2, 1/2, 1/2) and (1/4, 1/4, 1/4).
Alloy ID
Particle size, dav (lm)
Composition from EDS
a = b = c (nm)
V(nm)3
Microstrain 102 (%)
B P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12
Bulk 850–1180 710–850 600–710 500–600 425–500 300–425 125–300 106–125 90–106 38–45 20–38 <20
Ni50.69Mn33.83In14.07Si1.41 Ni50.72Mn33.89In14.00Si1.39 Ni50.65Mn33.85In14.10Si1.40 Ni50.68Mn33.90In14.06Si1.36 Ni50.74Mn33.91In14.03Si1.32 Ni50.66Mn33.80In14.12Si1.42 Ni50.69Mn33.89In14.00Si1.42 Ni50.67Mn33.85In14.07Si1.41 Ni50.70Mn33.87In14.09Si1.34 Ni50.72Mn33.88In14.00Si1.40 Ni50.67Mn33.83In14.09Si1.41 Ni50.68Mn33.84In14.08Si1.40 Ni50.71Mn33.85In14.02Si1.42
0.5974 0.5974 0.5974 0.5974 0.5974 0.5974 0.5974 0.5974 0.5974 0.5975 0.5977 0.5981 0.5992
0.2132 0.2132 0.2132 0.2132 0.2132 0.2132 0.2132 0.2132 0.2132 0.2132 0.2133 0.2140 0.2151
25.9 26.1 26.1 26.2 26.3 26.5 27.0 27.3 28.9 32.5 41.8 52.4 68.9
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Fig. 2. SEM images of sieved Ni51Mn34In14Si1 alloy powders sorted in different size ranges: (a) P12 (<20 lm), (b) P11 (20–38 lm), (c) P8 (106–125 lm) and (d) P3 (600– 710 lm).
The lattice constant a increases to 0.5981 ± 0.0004 nm and 0.5992 ± 0.0002 nm for the finer samples P11 and P12, respectively. This slight variation in the lattice constant could be attributed to the presence of residual stresses in the finer particles even after the annealing treatment. Features in the XRD pattern such as the pronounced asymmetrical tail of (2 2 0) reflection in P11 and P12 samples indicate inhomogenities in the milling. This shows the presence of residual strain in the powder samples even after the annealing treatment. Microstrain estimated using Rietveld analysis of the XRD data was found to increase considerably in powders with dav < 125 lm. The crystallographic data obtained from the analysis are summarized in Table 1. Fig. 2 shows the SEM micrographs of four sets of Ni51Mn34In14Si1 alloy powders sorted by systematic sieving. All the dry milled powders show a typical flake-like morphology as they are subjected to cold welding and fracture inside the vial. The average size (dav) of the particles was measured along the longest side of the flakes. It can be noticed that as the average particle size decreased, the particle shape became more spherical. Composition analysis of the samples by EDS reveal that the final composition of all the samples after milling and annealing is close to the starting composition. The results of the EDS analysis is summarized in Table 1. In order to understand the effect of particle size variation on the magnetic and magneto-caloric properties of the powder samples, temperature dependent magnetic properties were evaluated. Fig. 3 shows the M–T curves of the samples measured during field cooling (FC) and field heating (FH) cycles in a magnetic field of 0.1 T. The observed results reveal that all the samples are in austenite phase above room temperature and with decreasing the temperature, the samples exhibit a magnetic phase transition from the paramagnetic state to ferromagnetic state in austenite phase (marked as TC,A). Below TC,A, the samples order ferromagnetically in the austenite phase until they begin to transform into the martensite phase at the martensite start temperature Ms. On further cooling the samples, they display another magnetic phase transition from the paramagnetic state to the ferromagnetic state in the martensite phase (marked as TC,M). All samples exhibit these two magnetic transitions. The Curie temperature (TC) of the magnetic phase transition is defined as the temperature at which the
@M/@T exhibits a minimum value in FH M–T curve. Only TC,A would be referred in the remaining part of the manuscript since the MCE related to TC,M is considerably smaller and is not of interest to this work. Ms is taken as the temperature at which the maximum magnetization in FC M–T data is observed. Similarly, the austenite start temperature As corresponds to the temperature at which the FH M–T shows a large increase. Both these characteristic temperatures are indicated in Fig. 3. Ms, As, martensite finish temperature (Mf) and austenite finish temperature (Af) of all the samples extracted from the M–T data are listed in Table 2. M–T data recorded under FC condition at a higher magnetic field of 1.2 T is shown as an inset in Fig. 3. Comparison with the data shown in Fig. 3 reveals a slight shift in the martensite transformation temperature towards lower temperatures at the higher applied magnetic field. Such behavior
Fig. 3. Plots of M–T curves of bulk and sorted Ni51Mn34In14Si1 powders recorded under an applied field of 0.1 T. Filled and open symbols represent data recorded during field cooling and field heating, respectively. Curie temperature of martensitic phase (TC,M), martensite start temperature (Ms), martensite finish temperature (Mf), austenite start temperature (As), austenite finish temperature (Af) and the Curie temperature of the austenite phase (TC,A) of the bulk samples are shown. The inset presents the FC M–T curves recorded at an applied field of 1.2 T.
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Table 2 Curie temperature (TC,A), austenite start temperature (As), austenite finish temperature (Af), martensite start temperature (Ms), martensite finish temperature (Mf), thermal hysteresis (DT) obtained at 0.1 T field and magneto-caloric parameters (magnetic entropy change (DSM), full width at half maxima (FWHM) of DSM (T) data, and refrigerant capacity (RC) obtained for 1.2 T field change) of bulk and milled Ni51Mn34In14Si1 alloy. Alloy ID
TC,A (K)
As (K)
Af (K)
Ms (K)
Mf (K)
DT (K)
DSM (J kg1 K1)
FWHM (K)
RC (J kg1)
B P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12
294 294 294 293 293 292 292 290 288 287 285 283 282.6
279 279 279 279 279 278 275 272 268 265 261 260 259
287 287 287 287 287 287 287 286 286 285 284 283 282
278 278 278 278 278 278 278 278 278 278 277 277 276
270 270 270 270 270 265 259 254 250 245 241 238 237
9.0 9.0 9.0 9.0 9.0 11.0 12.5 13.0 13.0 13.5 13.5 14.0 14.0
19.9 17.2 14.6 11.2 10.5 9.4 7.2 6.3 5.7 1.4 0.8 0.5 0.4
2.4 2.8 3.4 4.6 4.6 4.7 5.4 5.7 6.0 8.1 10.5 11.0 11.3
35.9 36.1 36.7 40.4 36.0 33.4 31.5 26.9 21.7 12.2 4.5 4.0 3.5
has also been observed in other FSMAs [39]. TC,A and Ms for the bulk sample are 294 K and 278 K, respectively. In the case of the milled samples, TC,A and Ms do not deviate from the bulk value up to a particle size of 710 lm and 90 lm, respectively. For particles below this size, both TC and Ms decrease with a decrease in particle size (cf. Table 2). Fig. 3 shows another interesting feature, viz., the magnitude of the DM at the martensitic phase transition decreases with decreasing particle size. This may be due to the change in the fraction of the martensite phase and/or the change in the magnetic properties of the sample with decrease in particle size. A thermal hysteresis (DT) observed between the FC and FH curves for all the samples in the temperature range of 230 K to 290 K is attributed to the first-order martensitic transition. DT can be estimated from the characteristic temperature obtained from the M–T curves as DT = (As + Af)/2 (Ms + Mf)/2. DT was close to 9 K for particles with dav down to 500 lm, and then showed a larger increase with further decrease in particle size. Thermal hysteresis effect in the FSMA is a complicated process and is generally related to the nucleation of the new phase and the interaction of interfaces with defects from the microscopic point of view. But from the mesoscopic point of view, the same originates from the formation, annihilation, and rearrangement of elastically interacting domains [30]. In addition, the friction from domain rearrangement and phase boundary motions also contribute to the hysteresis. In other words, DT characterizes the strength of the friction during the transformation. In the present case, the variation of DT with particle size confirms that the friction encountered during the transformation increases with decreasing the particle size. The reduction in the number of domains with reduction in particle size is understandable. However, when one considers the change in the shape of the hysteresis, contributions from the other factors listed above cannot be overruled. One such contribution is the incomplete transformation between the martensite and austenite phases. This can be understood from the non-zero magnetization observed in M–T curves of the powder samples (Fig. 3) in the temperature range TC,M < T < Mf. (M–H)T data of Ni50xMn37+xIn13 alloys [15] show typical paramagnetic behavior in this intermediate temperature range. In order to explore this feature, we obtained isothermal magnetization curve at T = 250 K, where TC,M < T < Mf for our samples. Fig. 4 displays the M–H curves obtained for samples designated as B, P2, P8 and P11. While the bulk (B) sample shows linear field dependence which is characteristic of a paramagnet, the powder samples exhibit a nonlinear behavior at low fields indicating the presence of a small fraction of spontaneous magnetization (or ferromagnetism). Straight lines, passing through the data points are linear fits to the data in the high field region, extrapolated to zero field yield the spontaneous magnetization of the
Fig. 4. Initial magnetization curves recorded at T = 250 K for bulk and sorted milled Ni51Mn34In14Si1 alloy powders. The lines represent linear fits to the data at higher fields.
impurity ferromagnetic phase present in the samples. Fraction of ferromagnetic phase present in the TC,M < T < Mf regime increases with decreasing particle size. The impurity ferromagnetic phase is the residual (untransformed) austenite phase present in the samples. Also, the ratio between the maximum magnetization of FC curve in the austenite phase and the magnetization at the ferromagnetic martensite phase decreases significantly with decreasing particle size. This is mainly due to the increased number of the particle surfaces in a given volume of the sample which tend to reduce the average magnetization of the sample as the particle size is decreased. In order to evaluate the values of DSM and the RC, the (M–H)T curves of all the samples were obtained close to Ms. Fig. 5 displays the (M–H)T curves of Ni51Mn34In14Si1 samples with four different particle size ranges. It is obvious that all the samples are in ferromagnetic state at Ms. However, the magnitude of magnetization decreased not only with decreasing particle size but also with decrease in temperature. The nature of the magnetization curves changes with decreasing particle size and magnetization did not saturate up to an applied field of 1.2 T. This can be attributed either to the reduction in the particle size, which increases the number of particle surfaces and hence each particle would act like a single domain particle, or to the difficulty encountered in magnetization reversal due to the presence of considerable amount of stress in the smaller particles induced by the milling process. Nevertheless,
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Fig. 5. Isothermal initial magnetization curves obtained for bulk and sorted milled Ni51Mn34In14Si1 alloy powders: (a) B (bulk), (b) P2 (710–850 lm), (c) P3 (600–710 lm) and (d) P12 (<20 lm).
it may be noted in each of the graphs that at a certain temperature the magnetization increased suddenly [13]. DSM was evaluated as a function of temperature for a magnetic field change (DH) of 1.2 T from (M–H)T curves using the integrated Maxwell’s relation [11,40],
DSM ðT; HÞ ¼
Z 0
H
@MðTÞ dH @T H
ð1Þ
Fig. 6a depicts the temperature dependence of DSM for the powders with different particle sizes. DSM is positive in all the cases because @M/@T is positive at the martensitic phase transition. Positive DSM implies that the sample cools down upon application of external magnetic field [4]. The maximum value of DSM and the full width at half maxima (FWHM) of DSM(T) are the characteristic features of the MCE. DSM and FWHM decreased and increased, respectively, with a decrease in particle size as shown in the Table 2. The temperature at which peak DSM is observed for each set of samples shows a shift towards lower values with a decrease in particle size (cf. Fig. 6a). This feature can be correlated with the corresponding behavior of @M/@T with particle size depicted in Fig. 3. Though the highest peak DSM (=19.9 J kg1 K1) has been observed for the bulk alloy, this sample has the disadvantage of having the narrowest operating temperature range (FWHM = 2.4 K). As can be seen from Fig. 6b and Table 2, this disadvantage can be overcome by optimizing the particle size. An estimate of the adiabatic temperature change (DTad) of these samples would be useful for magnetic refrigerant application of this material. For this, S(T)H curves for H = 0 and H = 1.2 T were obtained using the relations [11,40]:
SðTÞH¼1:2T ¼ SðTÞH¼0 þ DSM ðTÞDH¼1:2T Z T CðTÞH¼0 SðTÞH¼0 ¼ dT þ SðT ¼ 0Þ T 0
ð2Þ
where C(T) is the heat capacity measured at zero magnetic field. Inset in Fig. 7 shows the C(T) data for P3 sample. Isentropic paths from S(T)H=0 curve to S(T)H=1.2T curve at different temperatures result in DTad(T) shown in Fig. 7. The moderate DTad of 1.99 K corresponding to DSM (11.2 J kg1 K1) is exhibited by the P3 powder sample at 278 K for DH = 1.2 T. This value may be compared with DTad = 1.5 K and 1.99 K reported for Ge and Al substituted NiMnIn alloy
Fig. 6. (a) Temperature dependence of magnetic entropy change obtained for 1.2 T field change in bulk and milled Ni51Mn34In14Si1 alloy. (b) Peak DSM (j) and FWHM (N) of Ni51Mn34In14Si1 alloy powders of different particle sizes.
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coupling [37,41], there by leading to an overall increase in MCE. In addition, a survey of the literature and comparison with earlier reports [37,42] shows that these combined values of MCE parameters appear to be highest ever reported for any FSMA powder. Since higher RC signifies a larger heat transport, Ni51Mn34In14Si1 alloy with particle size between 600 lm and 710 lm along with their high DSM for a reasonably small DH of 1.2 T at temperatures close to the ambient show a lot of promise for magnetic refrigeration application. It would also be worthy to investigate the effect of particle shape and its influence on DSM and RC of the powder particles. Particles with appropriate shape may yield higher DSM and RC values. Powder particles have the inherent advantage of being capable of compaction into any desired macroscopic net shape, which may also be an advantage in their application as refrigerant as compared to the inflexible bulk samples. 4. Conclusions Fig. 7. Temperature dependence of adiabatic temperature change obtained for 1.2 T field change. Inset show temperature dependent heat capacity at zero field obtained for Ni51Mn34In14Si1 alloy particles with size in 600–710 lm range.
for DH = 1.8 T, respectively [9]. This comparison serves to highlight the potential of Ni51Mn34In14Si1 alloy for magnetic refrigerant application. RC is another important MCE parameter which is a measure of the amount of heat that can be transferred between hot and cold reservoirs in an ideal refrigeration cycle. If there are two different magnetic refrigerants which differ only in their RC value, then the one with higher RC is expected to perform better because of its capability to transport greater amounts of heat in a real cycle [40]. RC estimated from the following relation [11,40] and depicted in Fig. 8.
RC ¼
Z
T2
DSM ðT; HÞdT
ð3Þ
T1
RC values corresponding to the DSM(T) curves first increased to the highest value and then decreased with particle size. Highest RC (40.4 J kg1) value has been obtained for particles in the size range of 600–710 lm. Particles in this size range also exhibit moderately high values of FWHM (4.6 K), DSM (11.2 J kg1 K1) (cf. Fig. 6b) and DTad (1.99 K). The enhancement in RC values with decreasing particle size range up to 600–710 lm is mainly influenced by the microstructural characteristics of the processed samples, which in turn impose significant control on the magneto-structural
Magnetic and magneto-caloric properties of Ni51Mn34In14Si1 alloys with different particle sizes were studied. The largest value of DSM (19.9 J kg1 K1) was obtained for bulk Ni51Mn34In14Si1 alloy at 279 K for DH = 1.2 T, which was mainly due to the large @M/@T or DM realized at the martensitic phase transition. But, due to the smallest FWHM the bulk sample may not be suitable for magnetic refrigerant application. Compared with the bulk, powdered particles show better magnetic refrigeration ability due to their larger RC as well as FWHM. The present studies on Ni51Mn34In14Si1 alloy show that optimization of the particle size of this alloy can yield powders with the desired combination of large DSM, FWHM and RC near Ms. Particles in the size range of 600–710 lm exhibit moderately high values of FWHM (4.6 K), DSM (11.2 J kg1 K1), RC (40.4 J kg1) and DTad (1.99 K). DSM(T) curves broaden with a decrease in particle size. The largest value of FWHM obtained was 11.3 K for particles with size <20 lm, although they exhibit the lowest DSM (0.4 J kg1 K1) and RC (3.5 J kg1). The high DSM obtained near Ms and the easy tunability of FWHM and RC values with different particle sizes make Ni51Mn34In14Si1 alloy powders an attractive magnetic refrigerant material. Acknowledgements Financial assistance from the Council of Scientific and Industrial Research, India vide Project No: 03(1236)/12/EMR-II is acknowledged. The work present used the infrastructural facilities provided by the Department of Science and Technology, India vide Project Nos.: SR/S2/CMP-19/2006 and SR/FST/PII-020/2009. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]
Fig. 8. Temperature dependence of refrigerant capacity of bulk and milled Ni51Mn34In14Si1 alloy.
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