Optimization of the refrigerant capacity in multiphase magnetocaloric materials

Optimization of the refrigerant capacity in multiphase magnetocaloric materials R. Caballero-Flores, V. Franco, A. Conde, K. E. Knipling, and M. A. Willard Citation: Applied Physics Letters 98, 102505 (2011); doi: 10.1063/1.3560445 View online: http://dx.doi.org/10.1063/1.3560445 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/98/10?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Characterization of the magnetic interactions of multiphase magnetocaloric materials using first-order reversal curve analysis J. Appl. Phys. 117, 17C124 (2015); 10.1063/1.4919121 Magnetocaloric effect in Fe-Zr-B-M (M = Ni, Co, Al, and Ti) amorphous alloys J. Appl. Phys. 116, 093910 (2014); 10.1063/1.4895048 The effect of distributed exchange parameters on magnetocaloric refrigeration capacity in amorphous and nanocomposite materials J. Appl. Phys. 111, 07A334 (2012); 10.1063/1.3679456 Large magnetocaloric effect and refrigerant capacity in Gd–Co–Ni metallic glasses J. Appl. Phys. 111, 07A919 (2012); 10.1063/1.3673422 Enhanced refrigerant capacity and magnetic entropy flattening using a two-amorphous FeZrB(Cu) composite Appl. Phys. Lett. 99, 232501 (2011); 10.1063/1.3665941 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: 150.214.182.17 On: Wed, 20 Jan 2016 18:12:21 Optimization of the refrigerant capacity in multiphase magnetocaloric materials R. Caballero-Flores,1V. Franco,1,a兲A. Conde,1K. E. Knipling,2and M. A. Willard2 1Dpto. Física de la Materia Condensada, ICMSE-CSIC, Universidad de Sevilla, P.O. Box 1065, 41080 Sevilla, Spain 2Multifunctional Materials Branch, U.S. Naval Research Laboratory, 4555 Overlook Ave. SW, Washington, District of Columbia 20375, USA 共Received 27 December 2010; accepted 2 February 2011; published online 9 March 2011兲 The refrigerant capacity 共RC兲of magnetocaloric materials can be enhanced using multiphase materials or composites, which expand the temperature range over which a significant magnetic entropy change can be obtained. Numerical simulations show that by controlling the parameters of the composite 共the fraction of the different phases and their Curie temperatures兲improvements of RC of ⬃83% are possible. The maximum applied field plays a crucial, nonmonotonic, role in the optimization. As a proof of concept, it is shown that the combination of two Fe88−2xCoxNixZr7B4Cu1 alloys produces an enhancement in RC of ⬃37%, making it ⬃92% larger than that of Gd5Si2Ge1.9Fe0.1.©2011 American Institute of Physics.关doi:10.1063/1.3560445兴 Ambient temperature magnetic refrigeration based on the magnetocaloric effect 共MCE兲has the potential for significantly improved energy efficiency compared with conventional refrigeration techniques based the compression/ expansion of gases.1The MCE arises from the reversible temperature change associated with the application or removal of an applied magnetic field, H, under adiabatic conditions2which is accompanied by a change in magnetic entropy, ⌬SM, leading to a refrigerant capacity, RC, defined as: RC共 ␦ T,Hmax兲= 冕 Tcold Thot ⌬SM共T,Hmax兲dT,共1兲 where ␦ T=Thot−Tcold is the temperature span of the thermodynamic cycle and Hmax is the maximum value of the applied field. There are three principle figures of merit used to evaluate potential refrigerant materials: the magnitude of RC, the peak magnetic entropy change 共⌬SM pk兲, and the adiabatic temperature change 共⌬Tad兲.RC is frequently determined over the temperature range corresponding to the full width at half maximum of the ⌬SM共T兲curve, ␦ TFWHM, and may be estimated 共RCAREA兲as the numerical integration of Eq. 共1兲over ␦ TFWHM.3 Optimizing RC involves increasing the magnitude of ⌬SM pk and broadening the temperature span, ␦ T, thereby increasing the integrated value of ⌬SM. The maximum ⌬Tad experienced by the refrigerant material should not, however, exceed the working temperature span ␦ TFWHM of the cycle since, outside of this temperature range, ⌬SM共T兲vanishes and there is little additional contribution to RC.4For this reason, magnetic materials with tall and narrow ⌬SM共T兲 peaks are generally not optimal magnetic refrigerants. Single-phase materials exhibiting large RC values are rare, and there is considerable research toward expanding ␦ T through various methods, including amorphization by ball milling,5modifying the structure by microalloying6and annealing,7,8nanostructuring,9developing composites10,11 and nanocomposites,12–14 and employing multilayered materials.15,16 All of these methods involve either the existence of a Curie temperature distribution in the magnetic material, or the presence of several phases that contribute to the total ⌬SM. The aim of this work is to study the enhancement of RC in multiphase magnetic systems with different Curie temperatures and analyze the conditions 共i.e., fraction of each phase x, the difference in Curie temperature ⌬TC, and the applied field H兲under which the RC can be optimized. It will be shown that optimum values of these parameters can be found, which maximize the increment of RC 共denoted as RCI兲with respect to the pure constituent phases. Also, contrary to general assumptions, there is an optimum value of H that produces the largest RCI, above which RCI diminishes. Numerical simulations will show that RCIs of ⬃83% are possible. As a proof of concept, a simulated two-phase magnetic material based on experimentally measured properties of two constituent Fe88−2xCoxNixZr7B4Cu1amorphous alloys produces an RCI⬃37%. These values are validated by experimental measurements of a mixture of both phases. The relation between magnetization, M, field, H, and temperature, T, of a second-order magnetic phase transition near TCis given by the Arrott–Noakes equation of state 共AN-EOS兲17共H/M兲1/ ␥ =a共T−TC兲+bM1/ ␤ ,where aand bare characteristic parameters of the material and ␤ and ␥ are the critical exponents. The T and Hdependence of the magnetic entropy change in such a material can be calculated as:18 ⌬SM共T,Hmax兲=− 冕 Ms Mmax a ␥ M共a共T−TC兲+bM1/ ␤ 兲 ␥ −1dM,共2兲 where Ms共T,H=0兲is the spontaneous magnetization and Mmax共T,H=Hmax兲is the magnetization at Hmax. For multiphase materials, Eq. 共2兲cannot be used since there is no analytical expression for the EOS of the composite. The magnetocaloric response can be calculated numerically, however, based on the magnetization behavior of each constituent material. We assume that the magnetic phases present in the multiphase composite are noninteracting, which allows the total magnetic entropy change to be expressed as a rule-of-mixtures sum of the entropy change in a兲Electronic mail: [email protected]. APPLIED PHYSICS LETTERS 98, 102505 共2011兲 0003-6951/2011/98共10兲/102505/3/$30.00 © 2011 American Institute of Physics98, 102505-1 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: 150.214.182.17 On: Wed, 20 Jan 2016 18:12:21 the constituent materials. For a two-phase composite 共containing phases Aand B兲, the entropy change is:⌬SM共x,T,Hmax兲=x⌬SM,A+共1−x兲⌬SM,B,where xis the fraction of constituent A. We initially consider a composite composed of two phases with the same AN parameters and critical exponents but with different Curie temperatures. We suppose a typical soft magnetic amorphous alloy, Fe77Cr8B15, where a =1.228 K−1,b=0.0077 共emu cm−3兲−1/ ␤ , ␤ =0.4579, and ␥ =1.5593.19 The Curie temperature of phase A is TC,A =370 K and that of phase B is variable, with TC,B⬍TC,A. The field and temperature ranges used in the numerical calculation are analogous to those explored experimentally 共up to 6 T, in 50 mT increments and from 100 to 700 K, in 1 K increments兲. The entire phase fraction range, 0ⱕxⱕ1, has been examined in increments of 0.01. RCI is defined as the percentage difference of the refrigerant capacity of the composite with respect to the majority phase 共either x=0 or x=1兲: RCI共x,⌬TC,Hmax兲 = 冦 RC共x兲−RC共x=1兲 RC共x=1兲100, if x ⬎0.5 RC共x,⌬TC兲−RC共x=0兲 RC共x=0兲100, if x ⬍0.5 冧 .共3兲 For the constituents chosen presently 共a,b, and the critical exponents are the same for both phases兲, both expressions in Eq. 共3兲give the same result. An alternative definition would be to compare with the phase with the largest RC; however, due to the phases chosen in this work, the results would not differ from those presented here. Figure 1shows ⌬SM共T兲curves of phases Aand Bthat make up the composite 共with TC,A=370 K and TC,B =300 K兲, along with entropy change in the composite 共x =0.6兲. The increased temperature span ␦ TFWHM of the composite is also shown, as compared with that of the pure constituent phases. Three independent parameters 共x,Hmax, and ⌬TC兲determine RCI. Figure 2共a兲displays the surface RCI共x,⌬TC兲for a maximum applied field of 1.5 T, while Fig. 2共b兲shows the surface RCI共x,Hmax兲for ⌬TC=130 K. For a given value of Hmax 关Fig. 2共a兲兴, there exist optimum values xopt 共for each ⌬TC兲and ⌬TC opt 共for each x兲which maximize RCI. These values are indicated by the line overlaid on the surface in Fig. 2共a兲. Note that maximum RCI is always obtained for x ⬎0.5, indicating that the minority phase should have a lower TCthan that of the majority phase in order to maximize the RC of the composite. RCI is negative for large ⌬TC, indicating that RC cannot be improved with a composite whose constituents have too dissimilar TCvalues. The physical reason for this effect is the so-called “sum rule,” which predicts smaller RC values when the ⌬SM共T兲of the two constituents are widely displaced.20 The decrease in RCI for large ⌬TC explained the fact that the partial nanocrystallization of a Finemet-type alloy21 did not produce an increase in RC with respect to the amorphous precursor 共the majority phase has the lower TCand ⌬TCis too large, so that the nanocrystalline phase hardly contributes to MCE兲. It should be noted that, for the parameters used in the simulation, an improvement of RC near 83% can be obtained. For Hmax=1.5 T, xopt=0.6 and ⌬TC opt=195 K. For different values of Hmax, the peak in Fig. 2共a兲occurs at different 共⌬TC opt,xopt兲coordinates. The general rule, however, is that ⌬TC opt increases with increasing Hmax, and the peak value of RCI does not change. Figure 2共b兲shows that, for a given pair of phases for which the optimization of RC is possible 共a given value of ⌬TCwhich is not too large兲, the value of Hmax plays an important role in the optimization. There are three characteristic values of Hmax:Hmax 0is the minimum necessary field to obtain an enhancement in RC 共for lower field values, the ⌬SM共T兲curves of each phase are so narrow that the addition does not cause an enhancement of ␦ T兲;Hmax opt corresponds to the field that produces the largest optimization in RC;Hmax full is the minimum field necessary to have a positive RCI for the whole compositional range. For Hmax⬎Hmax opt the maximum RCI decreases monotonically. This figure shows again the strong asymmetry of RCI共x兲. This is primarily due to the asymmetry of the ⌬SM共T兲curves of the constituent phases. Since ⌬SM共T兲for each phase diminishes rapidly at high temperatures, a relatively large fraction of a second phase 共with FIG. 1. 共Color online兲Temperature dependence of the magnetic entropy change of the two independent phases 共dashed lines兲, and of the biphasic system with fraction x=0.6 共solid line兲. FIG. 2. 共Color online兲Influence of x,⌬TCand Hmax on RCI.共a兲 RCIAREA共x,⌬TC兲surface for a maximum magnetic field of 1.5 T. For each ⌬TCvalue, the maximum RCI is connected through the solid line. 共b兲 RCIAREA共x,Hmax兲surface for ⌬TC=130 K. The characteristic field values Hmax 0,Hmax opt , and Hmax full are marked. 102505-2 Caballero-Flores et al. Appl. Phys. Lett. 98, 102505 共2011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: 150.214.182.17 On: Wed, 20 Jan 2016 18:12:21 larger TC兲is necessary for a broad 共ideally tablelike兲⌬SM共T兲 curve. Similar behavior has been found in these two surfaces when the critical exponents from the mean field and Heisenberg models are considered. Figure 3共a兲shows the variation in the three characteristic fields 共Hmax 0,Hmax opt , and Hmax full 兲with ⌬TC.Hmax 0and Hmax opt have a similar dependence, while Hmax full increases more rapidly with ⌬TC. For magnetic phases with similar TCvalues, the small value of Hmax 0indicates that small fields are sufficient to produce an enhancement in RC, and the fact that Hmax opt and Hmax full have similar values indicates that the compositional range over which RC is increased grows quickly with Hmax. However, the differences between these two characteristic fields increase rapidly with increasing ⌬TC. Figure 3共b兲 shows the variation in RCI with xfor ⌬TC=130 K, for the three characteristic values of H, as well as for an intermediate field Hmax opt ⬍Hmax int ⬍Hmax full . Figure 3共b兲clearly shows the decreasing value of the maximum RCI for Hmax⬎Hmax opt . These arguments can be used to understand the reason why the amorphous materials, usually with a Curie temperature distribution, typically have larger values of RC than crystalline phases 共as shown above, a small ⌬TCproduces an enhancement of RC for almost any fraction of phases兲, and why ball milled alloys,5manganite-based composites,10,11 clathrates-EuO composites,14 which involve a combination of phases with different Curie temperatures, may improve RC. We now consider a two-phase magnetic composite based on Fe88−xCoxNixZr7B4Cu1amorphous alloys.22,23 The two phases 共Fe66Co11Ni11Zr7B4Cu1, phase Aand Fe71.5Co8.25Ni8.25Zr7B4Cu1, phase B兲have the following magnetocaloric properties under an applied magnetic field of 1.5 T:TC,A=626 K, ␦ TFWHM,A=74 K, RCAREA,A =97.7 J kg−1 and TC,B=558 K, ␦ TFWHM,B=67 K, RCAREA,B=97.4 J kg−1. Maximum performance is achieved for x=0.65, where ␦ TFWHM =141 K, RCAREA =134 J kg−1, and RCIAREA=37%. These calculated results were verified experimentally by preparing a laminate composite 共layers of melt-spun ribbon pieces of the two compositions in intimate contact兲corresponding to x=0.643. The experimental RCIAREA is 36%, in excellent agreement with the predictions based on the simulated composite.24 This validates the assumption of noninteracting phases. These results represent an improved RC of ⬃92% as compared with Gd5Si2Ge1.9Fe0.1. Further studies to analyze the influence of magnetic interactions between the constituent phases of the composite material are being undertaken, both experimentally and numerically. In conclusion, it has been shown that large enhancements of RC can be obtained by combining different phases in a composite. The parameters controlling this enhancement are the fraction of phases, the difference between their Curie temperatures, and, in contrast with what is usually assumed, the maximum magnetic field. A composite optimized for a particular field range might have diminished properties with respect to the constituent phases when operated at a different field. The increment of RC is asymmetric in the fraction of phases, being more beneficial to have a majority phase with the larger Curie temperature. Increments of RC as large as ⬃83% can be envisioned. Numerical calculations and experimental results for a combination of Fe88−xCoxNixZr7B4Cu1alloys support the validity of this approach. This work was supported by the Spanish Ministry of Science and Innovation and EU FEDER 共Project MAT under Project No. 2010-20537兲, the PAI of the Regional Government of Andalucia, and by the United States Office of Naval Research 共Contract No. N0001410WX30490兲. R.C.F. acknowledges a research fellowship from the Regional Government of Andalucia. 1A. M. Tishin and Y. I. Spichkin, The Magnetocaloric Effect and its Applications, 1st ed. 共Institute of Physics, Bristol, Philadelphia, 2003兲,p.475. 2K. A. 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Phys. Lett. 96, 182506 共2010兲. 24See supplementary material at http://dx.doi.org/10.1063/1.3560445 for a figure including the comparison between model an experiment. FIG. 3. 共Color online兲共a兲Dependence of the characteristic field values with ⌬TC.共b兲Evolution of RCI with the fraction of phase xat ⌬TC=130 K for the characteristic field values and for Hmax opt ⬍Hmax int ⬍Hmax full . 102505-3 Caballero-Flores et al. Appl. Phys. Lett. 98, 102505 共2011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: 150.214.182.17 On: Wed, 20 Jan 2016 18:12:21