Accepted Manuscript
Investigation of the critical behavior and magnetocaloric properties in the nano- crystalline CuNi powders
S. Alleg, S. Souilah, K. Dadda, J.J. Suñol, E.K. Hlil, H. Lassri
PII: S0304-8853(17)31112-5
DOI: http://dx.doi.org/10.1016/j.jmmm.2017.08.010
Reference: MAGMA 63044
To appear in: Journal of Magnetism and Magnetic Materials Received Date: 6 April 2017
Revised Date: 20 July 2017 Accepted Date: 2 August 2017
Please cite this article as: S. Alleg, S. Souilah, K. Dadda, J.J. Suñol, E.K. Hlil, H. Lassri, Investigation of the critical behavior and magnetocaloric properties in the nanocrystalline CuNi powders, Journal of Magnetism and Magnetic Materials (2017), doi: http://dx.doi.org/10.1016/j.jmmm.2017.08.010
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Investigation of the critical behavior and magnetocaloric properties
in the nanocrystalline CuNi powders
S. Alleg1,*, S. Souilah1, K. Dadda1, J.J. Suñol2, E.K. Hlil3, H. Lassri4
1Laboratoire de magnétisme et Spectroscopie des Solides, Département de Physique, Université Badji Mokhtar Annaba, BP 12, 23000 Annaba, Algeria.
2Dept. De Fisica, Universitat de Girona, campus Montilivi, 17071 Girona, Spain.
3Institut NEEL, CNRS, Université Grenoble Alpes, 25 rue des Martyrs, BP 166, 38042 Grenoble Cedex 9, France.
4LPMMAT, Faculté des Sciences Aïn Chock, Université Hassan II de Casablanca, B.P.5366 Maârif, Route d'El Jadida, km-8, Casablanca, Maroc.
*Corresponding author e-mail: safia.alleg@univ-annaba.dz (S. Alleg) Tel/Fax: +213 38872770
Abstract
The critical exponents around the ferromagnetic−paramagnetic (PM-FM) phase transition and the magnetocaloric effect in the nanocrystalline (NC) Cu50Ni50 powders have been investigated. The alloy powder exhibits a second order magnetic phase transition. For a field change of 1 and 7 T, −Δ increases from 0.30 to 1.54 J/kg.K, respectively, and the relative cooling power values were found to vary between 43.6 and 271.9 J/kg. The critical behavior has been studied in details by using the modified Arrott plots and critical isotherm plots. The obtained critical exponent values β = 0.505, γ= 1.062 and δ= 3.037 are close to those predicted from the universal theory of mean-field model. This suggests that the magnetic interactions are long range around the Curie temperature, TC. Low cost magnetocaloric NC CuNi powders are good candidates for magnetic cooling applications.
Key words: Magnetic phase transition; Nanostructured materials; Mechanical alloying; Magnetocaloric effect; Critical behavior.
1. Introduction
The magnetocaloric effect (MCE) has attracted much attention during the last decades owing to its potential application in magnetic refrigeration (MR) which is based on the field induced entropy change of magnetic material that serves as refrigeration medium [1]. The MCE is intrinsic to magnetic solids and is a function of both temperature T and magnetic field change ∆H. The MCE has been observed in the magnetic materials possessing a first order magnetic transition (FOMT) [2-8] or a second order magnetic transition (SOMT) [9-12]. The compounds with FOMT are characterized by their large and/or sharp changes in magnetization as well as the strong coupling between crystallographic structure and magnetism such as Heusler- type magnetic shape-memory alloys [2−4], ferrite perovskite [5, 6], (Fe,Mn)2(P, As, Ge, Si) [7, 8], etc. Nonetheless, the phase transition region is narrow and the thermal and/or magnetic hysteresis is significant. Consequently, the life period of refrigerants could be limited [13, 14]. The performances of the materials with SOMT are rather modest compared to those of FOMT. Even though, some magnetic materials with SOMT do not exhibit large magnetic entropy change values (∆SM), but their relative cooling power (RCP) can be larger than those of FOMT due to the wide phase transition [15, 16]. Also, the hysteresis is very small or negligible. Therefore, exploration for new magnetic refrigeration has recently shifted to the composite materials of the SOMT. Since the MCE depends strongly on the type of the magnetic phase transition, a better fundamental understanding of the relationship between the magnetic-phase transitions and the MCE is of prime importance.
The critical exponent analysis in the vicinity of the ferromagnetic (FM)- paramagnetic (PM) phase transition (Curie temperature, TC) seems to be an effective way of probing the magnetic interactions responsible for the magnetic transitions. The determination of the critical exponents depends on the fitting values that are obtained from the Arrott plot according to Arrott-Noakes equation of state [17]. The critical exponents β and γ can be determined by using different theoretical models [18] such as Landau’s mean-field model, 3D-Heisenberg, 3D-Ising and tricritical mean field [19] which can be used to construct the Arrott plots. The critical values are dependent on the selected model as well as the fitting range [20−22].
Cu−Ni alloys exhibit remarkable properties (electrochemical, mechanical, physical, magnetic, etc.) which make them promising candidates for various
applications such as multi-layered coatings, contact solar cells, tissue engineering and biomedical applications [23−26]. Among the numerous applications of the Cu−Ni system, this paper reveals other possible functionalities such as MCE. Hence, Cu−Ni powder system is a potential candidate for the MR. Therefore, the critical behavior and magnetic entropy changes in the nanocrystalline (NC) Cu50Ni50 powders prepared by mechanical alloying (MA) are discussed. the magnetic entropy changes ∆ from the magnetization data sets. In order to further identify the type of the magnetic phase transition and to explore the MCE, the isothermal magnetization measurements were performed near TC. To the best of our knowledge, only the obtained results in the bulk Ni7Cu3 alloy [27] and electrodeposited Cu-Ni [28] are reported in the literature. No experimental study on the critical behavior and the MCE in the NC Cu−Ni powders has been reported.
2. Experimental details
Mechanical alloying process was used to prepare Cu50Ni50 alloy from elemental Ni (particles size 3−7 µm, purity 99.9%) and Cu (particles size 50 µm, purity 99%) powders in a high energy planetary ball mill Fritsh P7, under argon atmosphere, at ambient temperature. The ball−to−powder weight ratio (BPR) was about 29/5 and the rotation speed was 700 rpm. The milling process was interrupted each 1 h for 30 min to avoid the temperature increase inside the jars.
The magnetization measurements were carried out by means of a BS2 magnetometer developed at the Néel Institute in the temperature range 200–550 K under an applied magnetic field of 0.05 T. For critical exponent’s determination the magnetization isotherms were measured around the PM–FM phase transition, in the temperature range 300–460 K with an interval of 10 K, under applied magnetic fields up to 7 T. Furthermore, the sample used in the study was in the powder form without compacting. Therefore, one expects an insignificant effect of the demagnetization field on the performed analysis. The demagnetization factor D=0.206 was calculated (D=Ha/M) from the slope of the M(Ha) curve near zero field.
Throughout the paper, Ha stands for the applied field and the corrected magnetic field after subtraction of the demagnetization field is H=Ha-HD=Ha−DM.
3. Results and discussion
3.1 Magnetocaloric effect
The temperature dependence of the magnetization (M−T) of the NC Cu50Ni50
powders is shown in Fig. 1. The data were taken, at an applied magnetic field of 0.05 T, in the warming run after zero−field cooling (ZFC) and field cooling (FC), respectively. The M−T curve exhibits a paramagnetic−ferromagnetic (PM−FM) phase transition.From thederivative dM/dT (inset of Fig. 1), the Curie temperature has been determined to be TC~410 K. The decrease of TC compared to that of pure Ni (631 K) is due to the dissolution of Cu atoms into the Ni crystal lattice. This temperature is identical to that obtained for the Cu25Ni75 nanoparticles prepared by MA [26]. The FC curve displays a higher magnetization than the ZFC curve. Due to the irregular multigrain powder, such a behavior may indicate the presence of strong magnetic anisotropy in this powder alloy. The divergence of the FC and ZFC curves is observed around TC. The splitting between the ZFC and FC curves below TC can be attributed to the existence of magnetically inhomogeneous phases and/or clustering. Indeed, for ductile-ductile systems such as Cu−Ni MA process is a competition between fracturing and cold welding of the particles. Further milling duration improves the diffusion process due to the flattening of the particles and the increase of the surface area for contact. The chemical composition of the composite material varies within the particles as well as from particle to particle. Also, according to the Cu-Ni phase diagram, it is expected the formation of two phases α1 and α2 related to Cu-rich Cu(Ni) and Ni-rich Ni(Cu) solid solutions, respectively. This agrees well with the formation of two solid solutions as revealed by the XRD results [29]. Consequently, one expected the presence of magnetically inhomogeneous phases that leads to the variation of the transition temperature from particles to another. Indeed, due to the important powder mass loss after 30 h of milling, the hooked fine powder particles to the inner wall of the vials were recuperated by washing the jars two times with acetone, named hereafter 30h 2 and 30h 3. The hysteresis loops of such powders which exhibit thin shape and reduced saturation magnetization values (Fig. 2) can be attributed to the Cu-rich phases/particles. The ultrafine CuNi powders (30h−3) might be superparamagnetic.
Further determination of the nature of the magnetic phase transition responsible for the MCE was conducted through the isothermal magnetization versus applied magnetic field around TC as shown in Fig. 3. The MCE can be evaluated by calculating the magnetic entropy change (Δ) upon an application of magnetic field using the thermodynamic Maxwell’s equations:
Δ(, = (, − (, 0 = (1)
!"(,
= (, (2) The magnetic entropy change can be deduced from the magnetic isotherms by using the succeeding equation:
−∆(, = ∑ $%$&'
$&'%$ ∆
( (3) Mi and Mi+1 are the magnitude of magnetization at the temperatures Ti and Ti+1, respectively, under a magnetic field Hi. Fig. 4a shows the −Δagainst T plots for field changes (∆H) ranging from 1 to 7 T. One observes that −Δ increases continuously with increasing the field change from 0.30 to 1.54 J/kg.K for 1 T and 7 T, respectively. Comparable values were obtained in the bulk Ni7Cu3 alloy prepared by arc melting [27].
The relative cooling power (RCP) can be used to select the better refrigerants materials. Indeed, the better magnetocaloric materials commonly have large RCP values and consequently, have high cooling efficiency. RCP is defined as the product of −Δ and the full width at half maximum (FWHM) in the −∆SM(T) curve [30]:
)*+ = |∆| · ./0 (4)
Where |∆| and δTFWHM are the maxima value of the ∆SM(T) and FWHM, respectively. Fig. 4b displays −Δ and RCP as a function of magnetic field change. RCP increases from 43.6 to 271.9 J/Kg for a field change of 1 to 7 T, respectively. The RCP values might be affected by the distribution of the crystallite size of the ball milled powders (15−66 nm) which gives rise to a narrow distribution of TC. It has been reported that the average NC size and size distribution can be used as control parameters to, respectively, tune the peak value ∆and the width-at- half-maximum of the isothermal magnetic entropy change (./0 or the adiabatic temperature change during the magnetization process (MCE) [31]. Consequently, the
crystallite size distribution can be used to achieve reasonably high RCP over a wide temperature range at moderate fields and to reach high cooling power near room temperature.
3.2 Critical behavior 3.2.1 Arrot plots
The critical behavior of a magnetic system showing a SOMT near the Curie point TC is characterized by a set of interrelated critical exponents : β, γ and δ associated, respectively, with the spontaneous magnetization Ms, the initial magnetic susceptibility, χ0, and the critical magnetization isotherm at TC. Physically, β describes how the ordered moment grows below TC, γ designates the divergence of the magnetic susceptibility above TC, and δ defines the curvature of M(H) at TC [32].
If the system obeys to the Landau’s mean-field theory, the relationship of 12 versus /1 (Arrott plot) should be shown as a set of parallel straight lines around TC from which the order of the magnetic transition can be determined. The magnetic phase transition is first order if the slope of the Arrott plot is negative and second order if it is positive [33]. Nonetheless, Franco et al have proposed a more accurate method in which a phenomenological universal curve of the field dependence of the magnetic entropy change can correctly distinguish the order of the magnetic phase transition [33, 34].
From the Arrott plot (Fig. 5) one observes that the slope of the 14 versus 12 curves for NC Cu50Ni50 powders is positive indicating that the alloy exhibits a SOMT according to Banerjee’s criteria [35]. In order to better comprehend the nature of the FM interactions, the critical behavior in the NC Cu50Ni50 powders has been investigated through the modified Arrott plots (MAPs) method [17]. Hence, the critical behavior of a continuous phase transition near TC can be described by the critical exponents β, γ and δ according to the scaling hypothesis. In the high magnetic field region, the effect of charge, lattice and orbital degrees of freedom are suppressed in a ferromagnet and the order parameter can be identified with macroscopic magnetization [36].
3.2.2 Critical exponent’s determination
The critical exponents can be determined from the magnetization measurements by using the following equations:
15( = 1 |6|7, 89: 6 < 0 <= < > (5) ?%@( = AB
B 6C, 89: 6 > 0 <= > > (6) 1 = E@/F, 89: 6 = 0 <= = > (7)
with 6 = ( − > ⁄ >, the reduced temperature and M0, h0 and D, the critical amplitudes. The mean field interaction model for long range ordering (β=0.5, γ=1.0), 3D−Heisenberg model (β= 0.365, γ= 1.336), 3D−Ising model (β=0.325, γ=1.24), and the tricritical mean field model (β=0.25, γ=1.00) (Fig. 6) were used to obtain experimental β and γ values. In order to find the best model that describes the critical behavior in the NC Cu50Ni50 powders, the relative slopes (RS) of the straight lines, defined as RS=S(T)/S(TC) were calculated for each model as shown in Fig. 7. One observes that the RS values of the tricritical, 3D-Ising and 3D-Heisenberg models deviate from 1, while those of the mean field are much closer to 1. Accordingly, the critical behavior in the NC Cu50Ni50 powders can be described by the mean-field model signifying that the magnetic interactions are long range order around TC.
From the MAPs, the linear extrapolation of the high−field straight−line portion of the isotherms yields the spontaneous magnetization 15 (, 0 and the inverse of susceptibility ?%@(, 0 defined as the intercept with the axis 1@/7for < >and ( 1⁄ @/Cfor > >, respectively. The fitting of MS (T,0) and ?%@(, 0 curves to Eqs. (5) and (6), respectively, leads to the determination of new values of β, γ and TC. The optimal values are shown in Fig. 8, with β=0.505, γ= 1.062 and TC= 447 K. The critical exponents are different from those reported for the polycrystalline Ni7Cu3
alloy [27] and pure Ni [37]. Those discrepancies might be attributed to the preparation conditions, sample composition, dimensionality of the system and the range of microscopic interactions.
The third exponent δ can be deduced directly from the critical isotherm M (H, TC) as shown in Fig. 9. The inset displays the Ln(M) against Ln(µ0H) plot. This later gives a straight line with a slope 1/δ according to Eq. 7. The linear fit leads to a value of δ =3.037±0.002. The three critical exponents (β, γ and δ) are related by Widom scaling relation [38, 39]:
. = 1 + I J⁄ (10)
By using the obtained values of β and γ from the MAPs method, δ = 3.103 has been calculated. One notes that the slight differences between the calculated values of δ from the critical isotherms analysis (CI) and the Widom scaling relation can be attributed to the analysis errors.
3.2.2.1 Field dependence of ∆
By using the Arrott-Noakes equation of state, Franco et al. [40] have proposed an expression for the exponent controlling the field dependence of the magnetic entropy change of materials with a SOMT at TC:
K = 1 + 1 .⁄ (1 − (1 J⁄ (11) They also predict: K = 1 +7%@7LC (12)
By using the critical exponents β = 0.505±0.02, γ = 1.062±0.166 and δ =3.037, the use of Eqs. (10) and (11) leads to n=0.68. This value is nearby the predicted n=2/3 by Oesterreicher and Parker [41]. The field dependence of the magnetic entropy changecan be expressed as a power law:
ΔM = <(N O (13)
Where a is a constant and n the local exponent resulting from both temperature and magnetic field variation; n depends on the magnetic state of the sample. The linear fit gives a value of n = 0.83±0.01 (Fig. 10). One observes a linear field dependence of the magnetic entropy change, and the n value is higher than that found from Eqs. (10) and (11). Those discrepancies can be explained by the local inhomogeneity in the NC Cu50Ni50 powders [29].
3.2.2.2 Scaling theory
The reliability of the critical exponents β and γ can be also confirmed by means of the universal scaling hypothesis [42]. In the critical region, the magnetic equation of state can be written as:
1(, 6 = 678 ± ( 6⁄ 7LC (14)
Where ε is the reduced temperature, f+ and f− are regular analytical functions above and below TC, respectively. Eq. 14 suggests that M(H, ε) yields two universal curves for T > TC and T < TC (Fig. 11). The experimental data fall on two universal curves, below and above TC, in agreement with the scaling theory. This means that the
obtained values of the critical exponents and Curie temperature are reliable, and best match the mean-field model.
The critical behavior of the magnetic systems whose undergo a SOMT can be influenced by the disorder in the materials according to the criterion of Harris [43].
Such a disorder is characterized by a critical exponent α reliable to β and γ through the following scaling equation:
Q = 2 − 2J − I (15)
The critical exponent α is correlated to the specific heat (CH) and change in adiabatic temperature (∆ ∝ 1 *⁄ . It has been reported that if α is positive, the disorder modifies the critical exponents, whereas if α is negative, long range disorder will smear the transition but short range order should not affect the sharpness of the transition [44]. Accordingly, the disorder is irrelevant in the NC Cu50Ni50 powders since α is found to be negative (α = −0.172).
4. Conclusion
The magnetocaloric properties and the critical behavior in the NC Cu50Ni50
alloy powders prepared by MA were studied. Both magnetic entropy change and RCP increase with increasing the applied magnetic field. The critical exponents (α, β, γ and δ) were evaluated through the modified Arrott plots and critical isotherm analysis.
The obtained exponents’ values β = 0.505, γ= 1.062 and δ= 3.037 are close to those of the mean field model. The experimental data fall on two universal curves, below TC and above TC, in agreement with the scaling theory. The critical exponent α is found to be negative which means that the disorder is irrelevant. NC CuNi powders are much cheaper and both the MCE and TC can be easily adjusted by tuning the cupper content as well as the crystallites and particles size distribution. NC CuNi powder alloy seems to be a good candidate for magnetic cooling applications.
Acknowledgments
Financial support from the Hubert-Curien ‘‘Maghreb’’ partnership PHC-Maghreb 15 MAG07, the Algerian Ministère de l’Enseignement Supérieur et de la Recherche Scientifique are gratefully acknowledged.
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Figure captions
Figure 1: ZFC and FC magnetization vs. temperature in a magnetic field of 0.05 T.
The inset shows the derivative dM/dT.
Figure 2: Hysteresis curves of the ball milled powders for 30 h revealing the existence of magnetically inhomogeneous phases.
Figure 3: Isothermal magnetization curves vs. applied magnetic field, measured at different temperatures.
Figure 4: Temperature dependence of the magnetic entropy change (−∆SM) under different magnetic fields (a). (b) Variations of −∆M (left scale) and RCP (right scale) as a function of applied magnetic field.
Figure 5: The standard Arrott plot of NC Cu50Ni50 powders at different temperatures.
Figure 6: Modified Arrott plots (MAPs): isotherms of 1@ 7⁄ vs.SB@ C⁄ with the mean-field model, 3D-Ising model, 3D-Heisenberg model and tricritical mean field model.
Figure 7: The relative slope as a function of temperature defined as RS=S(T)/S(TC).
Figure 8: Temperature dependence of the spontaneous magnetization MS(T, 0) and the inverse initial susceptibility χ-1(T), along with the fitting curves based on the power laws for NC Ni50Cu50 powders.
Figure 9: Isothermal M vs. µ0H plot at T=440 K and T=450 K. The inset shows the same plot in log-log scale and the solid line is the linear fit following Eq. (6).
Figure 10: Field dependence of change in entropy −∆M and RCP in ln-ln scale.
The solid lines are the linear fitting curves.
Figure 11: Scaling plots showing two universal curves below and above TC. The inset represents the same plots on a log-log scale.
Table caption
Table 1: Comparison of the critical exponents in the NC Cu50Ni50 powders with those of the theoretical models: mean-field model, 3D-Ising model, 3D-Heisenberg model and Tricritical mean-field model as well as those for Ni7Cu3 and pure nickel.
• Magnetocaloric effect has been observed in nanocrystalline CuNi powders.
• The alloy powder exhibits a second order magnetic transition.
• The critical exponents are close to those of the mean field model.
• The experimental data fall on two universal curves below and above TC.
Figure 1
Figure 2
Figure 3
Figure 4a
Figure 4b
Figure 5
Figure 6
Figure 7
Figure 8
Figure 9
Figure 10
Figure 11
Table 1
Method ββββ γγγγ δδδ δ TC (K) Ref.
MAPs CI (experimental) CI (calculated-MAPS)
Ni7Cu3
Ni Ni
Mean-field model 3D-Heisenberg model
3D-Ising model Tricritical mean-field model
0.505
0.608 0.378 0.395 0.5 0.365 0.325 0.25
1.062
2.138 1.34 1.345
1 1.336
1.24 1
3.037 3.103 4.52 4.58 4.35 3.0 4.8 4.82 4.33
447
293.70 627.40 635.53
This work
[27]
[18]
[37]
[18]
[18]
[18]
[19]
