The magnetocaloric effect in soft magnetic amorphous alloys

The magnetocaloric effect in soft magnetic amorphous alloys V. Franco,a兲J. S. Blázquez, M. Millán, J. M. Borrego, C. F. Conde, and A. Conde Departmento de Física de la Materia Condensada, ICMSE-CSIC, Universidad de Sevilla, P.O. Box 1065, 41080 Sevilla, Spain 共Presented on 8 January 2007; received 31 October 2006; accepted 17 November 2006; published online 23 March 2007兲 The influence of different compositional modifications on the magnetic entropy change and refrigerant capacity of Finemet, Nanoperm, HiTperm, and bulk amorphous alloys is presented. For all the studied alloys, the field dependence of the magnetic entropy change exhibits a quadratic dependence in the paramagnetic regime, a linear dependence in the ferromagnetic temperature range, and a potential law with a field exponent ⬃0.75 at the Curie temperature. This exponent can be explained using the critical exponents of the Curie transition. It is shown that for alloys of similar compositional series, the magnetic entropy change follows a master curve behavior. © 2007 American Institute of Physics.关DOI: 10.1063/1.2709409兴 Magnetic refrigeration is a field of current interest due to the enhanced performance and reduced environmental impact of these systems when compared with those based on the gas compression-expansion cycle.1–3Although current prototypes are based on rare-earth-based materials,4soft magnetic amorphous alloys have been recently proposed as low cost candidates for high temperature magnetic refrigeration.5–13 Albeit the maximum magnetic entropy change, 兩⌬SM pk兩, for these alloys is modest when compared to that of rareearth-based materials,14,15 the remarkable difference in material costs is an incentive for studying their suitability as magnetic refrigerants. Besides their reduced magnetic hysteresis 共virtually negligible兲, higher electrical resistivity 共which would decrease eddy current losses兲, tunable Curie temperature and, in the case of bulk amorphous alloys, outstanding mechanical properties are beneficial characteristics for a successful application of the material. The field dependence of the magnetic entropy change ⌬SMin materials with a second order phase transition has also been recently studied, demonstrating that a master curve behavior is fulfilled for ⌬SM curves measured up to different maximum fields.16 The aim of this work is twofold: to present a comparison of the relevant characteristics of the magnetocaloric response of selected Finemet, Nanoperm, HiTperm, and bulk amorphous alloys 共BAAs兲prepared in ribbon shape and to demonstrate that ⌬SM共T兲curves of different alloys from the same compositional series can also collapse in a master curve. Amorphous alloys from different compositional series have been prepared in ribbon shape 共⬃25 ␮ m thick兲by melt spinning: FexCoyBzCuSi3Al5Ga2P10 共x,y,z,u=70,0,5,5; 56,14,6,4; 43,26,8,3; 29,40,9,2; 17,52,10,1; 5,63,12,0;兲, denoted as CoBAA;11 Fe65.5Cr4−xMo4−yCux+yGa4P12C5B5.5 共x, y=0; 0.5; 1, x+y艋1兲, denoted as CrMoBAA;12 Fe83−xCoxZr6B10Cu1共x=0, 5兲, denoted as CoNanoperm;10 Fe91−xMo8Cu1Bx共x=15, 17, 20兲, denoted as BNanoperm;17 Fe60−xMnxCo18Nb6B16 共x=0,2,4兲, denoted as MnHiTperm;18 and Fe68.5Mo5Si13.5B9Cu1Nb3, denoted as MoFinemet.8Their amorphous character was checked by x-ray diffraction. The specific heat 共cp兲of the CoNanoperm series has been measured in a Perkin-Elmer DSC-7 differential scanning calorimeter 共DSC兲using 20 K/min scans. Samples were placed in Al pans and the cpabsolute values were obtained after baseline subtraction 共recorded signal of an empty Al pan兲and the calibration of the DSC signal using as a standard a sapphire sample in an Al pan. The field dependence of magnetization was measured in a Lakeshore 7407 vibrating sample magnetometer using a maximum applied field H=1.5 T with field steps of 5 mT, for constant temperatures in the range of 300–720 K with increments of 10 K. Prior to the measurements, the stress of the samples was relaxed by preannealing. The magnetic entropy change due to the application of a magnetic field Hhas been evaluated from the processing of the temperature and field dependent magnetization curves using a numerical approximation to the equation: ⌬SM= 冕 0 H 冉 ⳵ M ⳵ T 冊 H dH,共1兲 where the partial derivative is replaced by finite differences and the integration is performed numerically. In order to compare the performance of different materials, either 兩⌬SM pk兩or the refrigerant capacity 共RC兲is used. The refrigeration at low temperatures requires a narrow temperature span of the refrigeration cycle, making 兩⌬SM pk兩the parameter of choice for comparing low temperature materials, while high temperature refrigeration implies a wider temperature range and, consequently, RC is employed for comparison. According to Wood and Potter,19 the RC of a reversible refrigeration cycle operating between Thand Tc 共the temperatures of the hot and cold reservoirs, respectively兲 is defined as RC=兩⌬SM兩共Th−Tc兲, where 兩⌬SM兩is the magnetic entropy change at the hot and cold ends of the cycle. Moreover, hysteresis losses can be taken into account when evaluating the refrigerant material by subtracting them from the computed RC,15 making the comparison between materia兲Electronic mail: [email protected] JOURNAL OF APPLIED PHYSICS 101, 09C503 共2007兲 0021-8979/2007/101共9兲/09C503/3/$23.00 © 2007 American Institute of Physics101, 09C503-1 [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP: 150.214.147.78 On: Fri, 13 Nov 2015 07:44:50 als with different coercivities more straightforward. The optimal refrigeration cycle is that which maximizes the RC. Figure 1shows the dependence of 兩⌬SM pk兩and RC with the peak temperature Tpk of the ⌬SMcurves. Circles around some of the RC points indicate that for that particular alloy RC does not reach a maximum when measured in the available temperature range due to the proximity between Tpk and room temperature. The optimal materials would be those which maximize both parameters and present a peak temperature close to the desired operational range. For the design of composite materials with a broad operational range, 兩⌬SM pk兩共Tpk兲should remain as flat as possible. For most of the studied alloys, compositional changes that produce a reduction in Tpk also cause a reduction in both 兩⌬SM pk兩and RC. The only discrepancy with this feature corresponds to the BNanoperm series, for which 兩⌬SM pk兩remains practically constant for the studied samples, making it a candidate for constituent of composite refrigerants. This constant value of 兩⌬SM pk兩has been recently ascribed to the increasing effective magnetic moment of Fe with increasing B content in the alloy.17 It is seen that the optimal alloy series of those presented here is the CoNanoperm, as it maximizes the refrigerant capacity maintaining 兩⌬SM pk兩in the upper part of the scale. A simple estimate of the adiabatic temperature change by means of the temperature dependence of the zero field specific heat of the Fe78Co5Zr6B10Cu1sample 共the one with the maximum RC in the present study兲yields a maximum value of 1.3 K for an applied field of 1.5 T 共which, for the sake of comparison with other high temperature magnetic refrigerant materials, extrapolates to 3.2 K for a field of 5 T兲. Despite the diversity in the shape of the ⌬SMcurves for the studied alloys, all of them share the same field dependence, expressed as ⌬SM⬀Hn. As an example, Fig. 2shows the temperature dependence of nfor two CoBAA alloys, showing a quadratic field dependence 共n=2兲in the paramagnetic regime, a linear dependence 共n=1兲in the ferromagnetic temperature range, and a potential law with a field exponent n⬃0.71 at the Curie temperature. These values of nhave been ascribed16 to the Curie-Weiss law at high T,tothe temperature independence of the field dependence of magnetization at low T, and to n=1+共1/ ␦ 兲关1−共1/ ␤ 兲兴 at TC, where ␤ and ␦ are the critical exponents. Taking into account that the critical exponents remain practically constant for alloys of similar compositional series, it is expected that the recently proposed master curve for the field dependence of ⌬SM共Ref. 16兲also holds for different alloys of these series. As an example, Fig. 3shows the normalized magnetic entropy change of the alloys for which 1/2⌬SM pk is inside the experimental temperature range 共CoBAA except x=5; Cr- MoBAA; CoNanoperm; x=20 BNanoperm; MnHiTperm except x=0, and MoFinemet兲as a function of the rescaled temperature ␪ , defined as ␪ = 再 −共T−TC兲/共Tr1−TC兲,T艋TC 共T−TC兲/共Tr2−TC兲,T⬎TC, 冎 共2兲 where Tr1and Tr2are the temperatures of the two reference points of each curve that correspond to 1/2⌬SM pk. The inset shows the original data of the CoBAA series used to construct this master curve. Further work to study the extension FIG. 1. 共Color online兲Relationship between the peak temperature of the magnetic entropy change and the magnitude of the peak 共upper兲and the refrigerant capacity 共lower兲for different alloy series for a maximum applied field of 1.5 T. Lines are a guide to the eyes. FIG. 2. 共Color online兲Temperature dependence of the exponent controlling the field dependence of the magnetic entropy change for Fe29Co40B9C2Si3Al5Ga2P10 共open symbols兲and Fe56Co14B6C4Si3Al5Ga2P10 共solid symbols兲for three values of the maximum applied field. FIG. 3. 共Color online兲Inset: Temperature dependence of the magnetic entropy change of the CoBAA series with x=70, 56, 43, 29, and 17, for a maximum applied field of 1.5 T. Main panel: Master curve behavior of all the alloys for which 1 2⌬SM pk is inside the experimental temperature range 共16 curves兲. 09C503-2 Franco et al. J. Appl. Phys. 101, 09C503 共2007兲 [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP: 150.214.147.78 On: Fri, 13 Nov 2015 07:44:50 of this master curve to different systems with larger differences in the critical exponents is being undertaken. In conclusion, the magnetocaloric response of alloy ribbons from Finemet, Nanoperm, HiTperm, and bulk amorphous families has been presented. The optimal composition of those studied in this paper corresponds to a Co-containing Nanoperm alloy, for which the maximum magnetic entropy change is 1.6 J/共kg K兲for an applied field of 1.5 T, with a corresponding refrigerant capacity of 82 J/kg and an estimated adiabatic temperature change of 1.3 K. These values extrapolate to 3.9 J/共kg K兲, 273 J/kg, and 3.2 K for an applied field of 5 T, respectively. It has also been shown that the field dependence of ⌬SMfollows a general trend for soft magnetic amorphous alloys, giving rise to a master curve behavior for alloys of similar compositional series. This work was supported by the Spanish Government and EU-FEDER 共Project MAT 2004-04618兲and the PAI of Junta de Andalucía. One of the authors 共J.S.B.兲is grateful to Junta de Andalucía for a research contract. 1A. M. 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