On the broadening of the magnetic entropy change due to Curie temperature distribution

On the broadening of the magnetic entropy change due to Curie temperature distribution Pablo Alvarez-Alonso, José L. Sánchez Llamazares, César F. Sánchez-Valdés, Gabriel J. Cuello, Victorino Franco, Pedro Gorria, and Jesús A. Blanco Citation: Journal of Applied Physics 115, 17A929 (2014); doi: 10.1063/1.4867346 View online: http://dx.doi.org/10.1063/1.4867346 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/115/17?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Textured Pr2Fe14B flakes with submicron or nanosize thickness prepared by surfactant-assisted ball milling J. Appl. Phys. 115, 17A734 (2014); 10.1063/1.4866879 Crystallographic alignment evolution and magnetic properties of Nd-Fe-B nanoflakes prepared by surfactantassisted ball milling J. Appl. Phys. 111, 07A732 (2012); 10.1063/1.3679414 Optimization of melt spun RE-Fe-B powder composition for fully dense, high energy magnets J. Appl. 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Electricidad y Electr onica, Universidad del Pa ıs Vasco, Barrio Sarriena s/n, 48940 Leioa, Spain 2 Divisi on de Materiales Avanzados, IPCyT, Camino a la presa San Jos e 2055, 78216, San Luis Potos ı, Mexico 3 Institute Laue Langevin, 6 rue Jules Horowitz, 38042 Grenoble, France 4 Dept. F ısica de la Materia Condensada, ICMSE-CSIC, Univ. Sevilla, P.O. Box 1065, 41080 Sevilla, Spain 5 Departamento de F ısica, EPI, Universidad de Oviedo, 33203 Gij on, Spain 6 Departamento de F ısica, Universidad de Oviedo, Calvo Sotelo s/n, 33007 Oviedo, Spain (Presented 7 November 2013; received 23 September 2013; accepted 29 November 2013; published online 3 March 2014) We have studied the correlation between the broadening of the isothermal magnetic entropy change and the Curie temperature (T C ) distribution in nanostructured Pr 2 Fe 17 and Nd 2 Fe 17 alloys produced by high-energy ball-milling after milling times of 10, 20, and 40 h. The changes in the microstructure affect the Fe local environments and as a consequence the magnetic interactions, giving rise to T C distributions centered around 285 K and 330 K for the Pr 2 Fe 17 and Nd 2 Fe 17 alloys, respectively. The width of the distributions enlarges (up to 60 K) as the milling-time increases, and consequently, the isothermal magnetic entropy change curves show an extended full width at half maximum. V C2014 AIP Publishing LLC.[http://dx.doi.org/10.1063/1.4867346] Magnetic refrigeration, the main application of the magneto-caloric (MC) effect, is potentially called to replace conventional vapor-cycle technology due to its higher energy efficiency and because it avoids green-house effect and depletion of ozone. 1–3 Therefore, it is necessary to develop materials with large MC effect in broad temperature intervals around room temperature. The MC materials usually exhibit useful working temperature intervals of about 20 K, 4 under magnetic field changes of 2 T, but often a refrigeration system demands a working temperature range that could reach 50 K or more. Thus, the increase of the temperature range without reducing their refrigerant capacity is a crucial aspect that MC materials must fulfill if their utilization in magnetic refrigeration technology is pursued. One of the material processing methods already used to enlarge the temperature range in which the maximum isothermal magnetic entropy change takes place is the mechanical milling of the MC material. 5–7 In fact, the nanocrystallization of ferromagnetic R 2 Fe 17 compounds (R ¼Pr and Nd) by means of ball milling has been proved as an illustrative example of this method, which leads to the enhancement of the refrigerant temperature range and the refrigerant capacity. 8,9 Moreover, the Curie temperature (T C ) is strongly affected by the modification of the Fe–Fe interatomic distances in a number of Fe-based alloys exhibiting magneto-volume anomalies. 10 Changes in the material microstructure can produce local inhomogeneities around the Fe atoms, and a distribution of Fe-Fe interatomic distances affecting the exchange interactions. The latter would affect the value of the T C in the sense that instead of a unique value for the T C a more reliable picture is to consider also a distribution function for this magnitude in the mechanically treated material. This distribution of T C values can induce a broadening of the magnetic entropy change curves. In this paper, we report on the broadening of the isothermal magnetic entropy change and the Curie temperature distribution in ball-milled Pr 2 Fe 17 and Nd 2 Fe 17 compounds. As-cast pellets and 10, 20, and 40 h ball-milled samples were fabricated following the procedure described elsewhere. 11 Scanning (SEM) and transmission (TEM) electron microscopy were used to study the microstructure and morphology of the milled powders. Room temperature x-ray powder diffraction patterns were collected in a highresolution x-ray powder diffractometer (Seifert model XRD3000) using graphite-monochromated Cu Karadiation (k¼1.5418 A ˚). Room temperature neutron powder diffraction patterns were collected on the D1B two-axis neutron diffractometer (ILL, Grenoble, France) using a neutron wavelength of 2.52 A ˚. Le Bail analyses were performed using the FullProf suite package. 12 Magnetization vs. temperature curves under a constant applied magnetic field of l o H¼20 mT in the temperature range 250–400 K were obtained in a Faraday balance. Isothermal M(l o H) curves were measured in two magnetometers, a Lakeshore VSM 7407 (85–420 K) and in a Quantum Design PPMS (200–400 K). The isothermal magnetic entropy change, DS M , was determined through the appropriate Maxwell relation. 13 SEM images reveal that the Pr 2 Fe 17 and Nd 2 Fe 17 milled powders are agglomerations of micronic grains (0.5–10 lm) with rounded borders and narrower size distribution as the milling-time is increased. 8,9 Higher magnification images obtained by TEM show grains formed by crystallites of nanometric size; the histograms describing the crystallite size distribution for the BM-10h and BM-20h compounds (powders ball-milled for 10 and 20 h, respectively) follow log-normal functions with average size of the crystallites below 25 nm (see Table I). For the BM-40h samples, not enough crystallites a) Author to whom correspondence should be addressed. Electronic mail: [email protected]. 0021-8979/2014/115(17)/17A929/3/$30.00 V C2014 AIP Publishing LLC115, 17A929-1 JOURNAL OF APPLIED PHYSICS 115, 17A929 (2014) [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: 150.214.182.116 On: Thu, 28 Jan 2016 14:58:00 appeared in the TEM images to obtain reliable statistical information. The upper right inset in Fig. 1shows a representative TEM image of Nd 2 Fe 17 BM-40h powders. In Fig. 1, the room temperature neutron powder diffraction patterns corresponding to the Nd 2 Fe 17 samples are depicted. All the intensity peaks observed in the pattern of the starting bulk alloy correspond to Bragg reflections belonging to a Nd 2 Fe 17 phase with the rhombohedral Th 2 Zn 17 -type crystal structure; the estimated lattice parameters (see Table I) agree with those previously reported. 14 The ball-milling process maintains the Th 2 Zn 17 -type crystal structure with almost unchanged values of the cell parameters, but alters the microstructure (see Table I). Details of the followed procedure are described elsewhere. 15 Figure 2shows the magnetization as a function of the temperature, M(T) curves. Those curves were composed with the points corresponding to l o H¼1 T of the isothermal M(l o H) measurements. Notice how the shape of the M(T) curves changes as the milling-time increases: the ferro-to-- paramagnetic phase transition becomes poorly defined. However, the position of the dM/dTvs. Tcurve minima (see insets in Figure 2) remains almost unaltered (see Table I). The latter can be attributed to the effect of a change in the local environment of Fe atoms at the grain boundaries, which modifies the magnetic interactions 16 and, thus, the Curie temperature of certain regions. Hence, we could picture the nanostructured powders having a distribution of Fe-Fe interatomic distances around the value for the Bulk alloys giving rise to a distribution of Curie temperature values. 8,9 Then, we describe the temperature dependence of the magnetization M(T) by a superposition of individual power-law functions, according to 17 MT ðÞ ¼m0ðTC TCT TC  b hTCTðÞqTC;a ðÞ dTC:(1) Here, m 0 is a factor proportional to the saturation magnetization, bis the temperature critical exponent of the magnetization, h(x) is the Heavyside function (that ensures vanishing magnetization values at T¼T C ), and q(T C ,a)a sample-specific T C distribution function with parameters set a. For the present case, we have assumed a Gaussian distribution qTC;TC;DTC  ¼1 ffiffiffiffiffiffi 2p pDTC exp 1 2 TCTC  DT2 C ! (2) FIG. 1. Room temperature neutron powder diffraction patterns corresponding to bulk, BM-10h, BM-20h, and BM-40h Nd 2 Fe 17 alloys. Upper left inset: Le Bail fit of the x-ray powder diffraction pattern collected for BM-20h Pr 2 Fe 17 sample. Upper right inset: TEM image of the BM-40h Nd 2 Fe 17 sample. TABLE I. Structural and magnetic data (the crystallographic parameters were obtained from the x-ray and neutron powder diffraction patterns). Pr 2 Fe 17 Nd 2 Fe 17 Bulk BM-10h BM-20h BM-40h Bulk BM-10h BM-20h BM-40h a(A ˚) 8.584(1) 8.580(1) 8. 582(1) 8.583(1) 8.582(1) 8.580(1) 8.578(1) 8.578(1) b(A ˚) 12.460(1) 12.455(1) 12. 458(1) 12.453(1) 12.459(1) 12.455(1) 12.453(1) 12.454(1) s TEM (nm) … 23(1) 18(1) * … 17(3) 10(2) … s Diff (nm) … 20(1) 17(1) 11(1) … 18(1) 15(1) 11(1)  TC(K) 286(2) 290(5) 290(10) 290(10) 339(2) 340(10) 340(10) 340(10) FIG. 2. Temperature dependence of the magnetization under an applied magnetic field of 1 T for the bulk and BM samples, (a) Pr 2 Fe 17 and (b) Nd 2 Fe 17 . The two insets show the temperature derivatives of the magnetization. 17A929-2 Alvarez-Alonso et al. J. Appl. Phys. 115, 17A929 (2014) [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: 150.214.182.116 On: Thu, 28 Jan 2016 14:58:00 being  TCand DT C the average value and width of the T C distribution. Although the value of T C is unique for any ferromagnetic single-phase alloy and this value must be determined under zero applied magnetic field, if the minimum of the dM/dTvs. Tcurves is chosen as the value for the T C of the material, such minimum of the dM/dT(T) curve exhibits a broadening as the applied magnetic field is increased. The inset in Fig. 3shows the fit obtained for the temperature dependence of the magnetization in bulk Nd 2 Fe 17 alloy for l o H¼0.5 T following this approach. The T C distribution width (see Figure 3) augments with milling-time for each magnetic field. The magnetic field dependence of the width follows a power law, DTCH ðÞ ¼DT0 CþcH1=g, with grelated with the critical exponents of the transition, as Berger et al. have shown. 17 The fit to a power law gives for Nd 2 Fe 17 : g Bulk ¼1.9 60.2, g BM-10h ¼3.0 60.3, g BM-20h ¼2.4 60.2, and g BM-40h ¼2.8 60.3. The differences in these values indicate variations in the magnetic interactions of the alloys and how they are affected by the applied magnetic field. Fig. 4plots the temperature dependence of the magnetic entropy change at l o H¼1.5 T, for the studied samples. The temperatures at which the curves reach their maximum are similar for the four samples (T C ). However, for the milled samples the maximum values of |DS M | diminish with the milling-time because the drop of the magnetization is less pronounced as milling-time increases. In summary, ball-milled Pr 2 Fe 17 and Nd 2 Fe 17 alloys maintain the Th 2 Zn 17 -type crystal structure but their crystallite size is reduced below 25 nm. The local environment of Fe atoms seems to be altered during the nanocrystallization process, giving rise to a Curie temperature distribution around the bulk’s value. Fitting the magnetization vs. temperature curves with a Gaussian-type Curie temperature distribution, we found that the longer milling, the wider the T C distribution, which correlates to the enlargement of the magnetic entropy change full width at half maximum. We thank the financial support from MICINN, Spain (project MAT2011-27573-C04) and from CONACYT, Mexico (CB-2010-01-156932). J.L.S.Ll. thanks the support received from LINAN, IPICyT. We thank ILL and CRG- D1B, the SCTs at the University of Oviedo, and the electron microscopy service of the IPICYT. 1 V. K. Pecharsky and J. Gschneidner, Int. J. Refrig. 29, 1239 (2006). 2 A. Tishin, J. Magn. Magn. Mater. 316, 351 (2007). 3 V. Franco et al., Annu. Rev. Mater. Res. 42, 305 (2012). 4 K. Gschneidner et al., Scr. Mater. 67, 572 (2012). 5 B. Chevalier et al., Appl. Phys. A 80, 601 (2005). 6 P. Gorria et al., J. Phys. D: Appl. Phys. 41, 192003 (2008). 7 J. Gass et al., J. Appl. Phys. 103, 07B309 (2008). 8 P. Gorria et al., Acta Mater. 57, 1724 (2009). 9 P.  Alvarez et al., J. Phys.: Condens. Matter 22, 216005 (2010). 10 P.  Alvarez-Alonso et al., Phys. Rev. B 86, 184411 (2012). 11 P. Alvarez et al., J. Non-Cryst. Solids 354, 5172 (2008). 12 J. Rodr ıguez-Carvajal, Physica B 192, 55 (1993). 13 P.  Alvarez et al., J. Alloys Compd. 504, S150 (2010). 14 G. Long et al., J. Appl. Phys. 76, 5383 (1994). 15 D. Martinez-Blanco et al., J. Phys.: Condens. Matter 20, 335213 (2008). 16 G. Campillo et al., J. Magn. Magn. Mater. 237, 61 (2001). 17 A. Berger et al., J. Appl. Phys. 91, 8393 (2002). FIG. 3. Magnetic field dependence of the DT C for bulk and BM Nd 2 Fe 17 samples. Inset: temperature dependence of the magnetization for the bulk Nd 2 Fe 17 alloy (see text for details). FIG. 4. Temperature dependence of the magnetic entropy change under l o DH¼1.5 T for the bulk and BM Pr 2 Fe 17 and Nd 2 Fe 17 samples. 17A929-3 Alvarez-Alonso et al. J. Appl. Phys. 115, 17A929 (2014) [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: 150.214.182.116 On: Thu, 28 Jan 2016 14:58:00