Magnetocaloric Properties of Fe-Ni-Cr Nanoparticles for Active Cooling

Low cost, earth abundant, rare earth free magnetocaloric nanoparticles have attracted an enormous amount of attention for green, energy efficient, active near room temperature thermal management. Hence, we investigated the magnetocaloric properties of transition metal based (Fe70Ni30)100−xCrx (x = 1, 3, 5, 6 and 7) nanoparticles. The influence of Cr additions on the Curie temperature (TC) was studied. Only 5% of Cr can reduce the TC from ~438 K to 258 K. These alloys exhibit broad entropy v/s temperature curves, which is useful to enhance relative cooling power (RCP). For a field change of 5 T, the RCP for (Fe70Ni30)99Cr1 nanoparticles was found to be 548 J-kg−1. Tunable TCin broad range, good RCP, low cost, high corrosion resistance and earth abundance make these nanoparticles suitable for low-grade waste heat recovery as well as near room temperature active cooling applications.

and other systems. Slow heat transfer in bulk solids is one of the most difficult issues which diminish the efficiency of thermal management systems. The dispersion of magnetic particles in a suitable fluid can solve this challenge, the large surface area of nanoparticles and dispersion in fluid results in better thermal contact and therefore faster heat exchange compared to bulk systems. Furthermore, such ferrofluids can be used for self-pumping, automatic, magnetic cooling 28,39,40 .
γ -Fe 80−x Ni x Cr 20 (14 ≤ x ≤ 30) alloys have competing exchange interactions, hence the local spin orientation depends on its environment 41 . The effective exchange interaction can be positive, negative, or nearly zero. This exchange interaction is governed by the concentration, distribution, and strength of the six different exchange interactions (J ij ) between the different magnetic atoms. By using neutron scattering technique, Men'shikov et al. 42  Our earlier studies show that γ -FeNiB nanoparticles are suitable candidates for low grade waste heat recovery while γ -FeNiMn can be used for slightly above room temperature applications 5,13 . On the other hand, alloying of iron based material with Cr will improve corrosion resistance 43 , e.g., increasing Cr content in the magnetic Fe 73.5−x Si 13.5 B 9 Nb 3 Cu 1 Cr x alloy results in a corrosion resistant material for marine or SiO 2 contaminated environments 44,45 . Therefore, Fe-Ni-Cr alloys possess both good corrosion resistance and good magnetocaloric properties.
We report the effect of alloying of Fe 70 Ni 30 with Cr on magnetic phase transition temperature (T C ) and magnetocaloric properties of alloy nanoparticles.  7 were synthesized, the nomenclature is Cr0, Cr1, Cr3, Cr5, Cr6 and Cr7, respectively. The theoretical values of T C were compared with experimental results. In addition, these nanoparticles were coated with oleic acid (80%) and ammonium hydroxide (20%) and dispersed in oleic acid to make the ferrofluid. The ferrofluid was used as a heat transfer medium in a self-pumping magnetic cooling prototype. Figure 1 shows the XRD patterns of Cr0, Cr1, Cr3, Cr5, Cr6 and Cr7 nanoparticles after heating at 700 °C for 2 h followed by quenching. All the samples exhibit three main diffraction peaks (111, 200 and 220) of the γ -FeNi phase with lattice parameter (a) in the range of 3.5919(4)-3.5983(3) Å and space group Fm-3m. Adding Cr to Fe 70 Ni 30 does not shift in the diffraction peak positions much as the atomic radius of Cr does not differ much from the corresponding value for Fe and Ni. The average crystal sizes, calculated by the Scherrer formula after subtracting the instrumental line broadening, were ~9 nm, ~12 nm, ~10 nm, ~13 nm, ~12 nm and ~11 nm for Cr0, Cr1, Cr3, Cr5, Cr6 and Cr7 nanoparticles, respectively. All the samples exhibit asymmetric broadening in the 111 diffraction peak. Figure 2 shows the bright field transmission electron micrograph of Cr3 and Cr5 nanoparticles. The particle size for Cr3 is in the range of 3 nm to 21 nm, with an average size of 9 nm, while the particle size for Cr5 is in the range of 4 nm to 25 nm range, with an average size of 12 nm. These values are close to the value obtained from XRD data. The lattice fringes of 2.1 Å and 2.11 Å for Cr3 and Cr5, respectively, correspond to the 111 planes of the fcc phase (inset of Fig. 2).

X-ray Diffraction and Transmission Electron Microscopy Analysis.
Curie temperature. The Curie temperature is the temperature at which the ferromagnetic phase changes to the paramagnetic phase. For MCE applications, we need to determine the T C of that material. It should be noted that the MCE is maximum at its T C and relatively small or almost zero (depending on the T C distribution and the order of the phase transition) at temperatures away from T C . Fig. 3(a,b,c) shows the temperature dependence of magnetization, M(T) (left) and dM/dT (right) for (Fe 70 Ni 30 ) 100−x Cr x (x = 0, 1, 3, 5, 6 and 7) nanoparticles, measured upon cooling under a field of 0.1 T. The Curie temperatures (T C ) of Cr0, Cr1, Cr3, Cr5, Cr6 and Cr7 were found to be 438 K, 398 K, 323 K, 258 K, 245 K and 215 K, respectively. T C was determined from the minima of the plot of dM/dT versus T. The reduction of T C can be understand from the mean field model T C = J(r) eff Z T S (S + 1)/3k B , where J(r) eff is the effective exchange interaction, Z T is coordination number, S is the atomic spin quantum number and k B is the Boltzmann constant 5 .
The Bethe-Slater curve qualitatively describes the variation in strength of direct exchange as a function of the ratio of the interatomic distance to diameter of the 3d electrons (r a /r 3d ) 46 . A pair interaction of two atoms sharing two electrons can be used to explain the trend of this curve. A value of 1.5 for ferromagnetic spin coupling was assumed empirically in this curve to separate positive from negative exchange interactions (Jex) 46 (Fig. 4(a)). For a ratio r a /r 3d less than 1.5, when the electrons from two neighbouring atoms are close to each other, the Pauli Exclusion Principle requires the spins of these electrons to be antiparallel, which results in antiferromagnetic interaction between these atoms. If the ratio r a /r 3d is greater than 1.5, 3d electrons can be further away from each other, filling two different orbital states, resulting in ferromagnetic interactions. After reaching a maximum value, the exchange coupling starts to decrease because of decreasing spatial overlap of the wave functions of the electrons. For the same value of x, T C for (Fe 70 Ni 30 ) 100−x Cr x is lower than that of (Fe 70 Ni 30 ) 100−x Mn x alloys 5,31 . This  is because the value of J CrCr is more negative than that of J MnMn . Hence, the effective exchange interaction (J(r) eff ) is less in the case of (Fe 70 Ni 30 ) 100−x Cr x . The coordination number (Z T ) is the same in both cases (due to the same crystal structure), which results in a reduction in T C .
The experimental values of T C were compared with values calculated from the expression T C = T C1 + (dT C /dc) c, T C1 is the Curie temperature of the parent alloy Fe 70 Ni 30 , dT C /dc is the rate of change of Curie temperature with concentration (c) 46 . The dT C /dc value for Cr is − 3.2 × 10 3 K/at % 46 . A value of T C for Fe 70 Ni 30 was obtained from the binary Fe-Ni phase diagram. This is close to the experimental value of 438 K. Fig. 4(b) shows the change in Curie temperature with Cr% in the ternary system (Fe 70 Ni 30 ) 100−x Cr x .
The dashed blue line and red square represent the expression T C = T C1 + (dT C /dc) c and experimental data, respectively. The experimental T C values for Cr0, Cr1, Cr3, Cr6 and Cr7 are reasonably close to those calculated from the expression. This facile tuning of T C makes these alloys useful for near room temperature cooling. Magnetocaloric Effect. Figure 5(a,b,c,d,e) show the temperature dependence of the magnetic entropy change (− ∆ S M ) under a range of magnetic fields, ranging from 0.5 T to 5 T for Cr1, Cr3, Cr5, Cr6 and Cr7 alloy, respectively. In all cases, the − ∆ S M versus T curves are very broad, exhibiting a table-like shape. There are several reports of the desirability of such table-like shape in magnetocaloric materials for real applications 47,48 . Comparing our data to the literature, the − ∆ S M and RCP values were calculated at T C . For 1 T applied magnetic field, ∆ S M for Cr1, Cr3, Cr5, Cr6 and Cr7 at their T C was found to be 0.38 J-kg −1 K −1 , 0.27 J-kg −1 K −1 , 0.37 J-kg −1 K −1 , 0.29 J-kg −1 K −1 and 0.28 J-kg −1 K −1 , respectively. When the field was increased to 5 T, ∆ S M for Cr1, Cr3, Cr5, Cr6 and Cr7 was found to be 1.58 Relative cooling power (RCP) is an important performance metric, it is defined as the product of the maximum change in entropy (∆ S M ) and the full width at half maximum (δ T FWHM ) of the entropy versus temperature curve, i.e., RCP = ∆ S M × δ T FWHM . Figure 6(a) shows the variation of δ T FWHM , also known as working temperature span, with applied magnetic field.
The δ T FWHM for Cr1, Cr3, Cr5, Cr6 and Cr7 was found to be 216 K, 220 K, 209 K, 213 K and 166 K at magnetic field of 1 T, respectively. Our δ T FWHM values are higher than those of Gd (~35 K) 49 , Pr 2 Fe 17 (~78 K) 36   and RCP (Fig. 6(c)) at T C results in values of local exponents "n" and "N". The values of local exponent "n" at T C for Cr1, Cr3, Cr5, Cr6 and Cr7 were 0.92, 1.08, 0.84, 0.90 and 0.84 respectively, and the values of local exponent "N" at T C for Cr1, Cr3, Cr5, Cr6 and Cr7 were 1.24, 1.25, 1.05, 1.14 and 1.25, respectively. The variation in local exponent can be attributed to different microscopic interactions due to different Cr % in the alloys. Ferrofluid based magnetic cooling. As mentioned in methods, we prepared a ferrofluid based on our nanoparticles which were synthesized by ball milling. To determine the effect of initial temperature of heat load on cooling, the initial heat load temperatures of 64.4 °C, 53.4 °C and 47.4 °C were used. A magnetic field of 0.25 T was applied near the heat load. Figure 7 shows the temperature profiles for heat load for different initial  These results show that ferrofluid based magnetic cooling is feasible. Our experimental results were in good agreement with the simulations for the same magnetic field, other parameters are the same as those used in the experiments.

Discussion
The (Fe 70 Ni 30 ) 100−x Cr x (x = 1, 3, 5, 6 and 7) exhibits a second order magnetic phase transition that is tunable from ~438 K to ~215 K. The wide Curie temperature distribution and therefore high RCP, is consistent with the asymmetric nature of 111 diffraction peak in XRD, which implies that the alloys exhibit a range of lattice parameters due to the process of ball milling 51 . This lattice distribution gives high distribution of exchange interaction, which leads to a distribution of T C . The reduction in T C and ∆ S M with increasing Cr% is related to the reduction of total exchange energy due to the antiferromagnetic nature of Cr. The Curie temperature and magnetic entropy change of the amorphous alloys Fe 74−x Cr x Cu 1 Nb 3 Si 15.5 B 6.5 (with x = 2, 8, 10, 12, 13, 14 and 20) were also found to decrease with increasing Cr content 52 .
Engelbrecht et al. reported that for practical cooling systems, a material with a broad peak in entropy change (large δ T FWHM ) provides significantly higher cooling power than a material with a sharp peak 53 . The cooling power for a material with low Δ S M and high δ T FWHM is greater than that of a material with high Δ S M and low δ T FWHM . Thus, for a magnetic regenerator, a broad temperature distribution of MCE is more attractive than sharp Δ S M peaks.
One of the main factors for the commercial exploitation of a magnetic material is its cost. Ucar et al., reviewed the RCP in terms of Joule/$ of various magnetocaloric materials and it was found that transition metal based materials have a critical advantage over rare earth based materials 23 . We have estimated the cost of our materials and other relevant magnetocaloric materials. The materials cost of our Fe-Ni-Cr nanoparticles is only about 2% of the cost of pure Gd. Very recently, a transition metal based high entropy alloy NiFeCoCrPd X was introduced as a promising magnetocaloric material. The materials cost of our Fe-Ni-Cr is only about 0.3% of the cost of NiFeCoCrPd 0.50. In addition, our (Fe 70 Ni 30 ) 95 Cr 5 exhibit higher Δ S M (123%) and RCP (180%) compared to NiFeCoCrPd 0.25 ; the T C is almost the same. Table 1 shows the values of ∆ S M , RCP and cost of our alloys and other magnetocaloric materials.
The RCP values for our alloy nanoparticles are comparable with other key magnetocaloric materials, the better corrosion resistance would enhance their suitability for magnetic fluid applications. As mentioned earlier, nanoparticles exhibit additional advantages compared to the bulk, e.g. they can be dispersed in a suitable liquid and used as a ferrofluid for active cooling 40 . Ferrofluid-based self-pumping has novel applications, e.g., for cooling of microelectronic devices and power electronics system 5,54 . Alloy based ferrofluid was used for the first time for magnetic cooling application 55 . The stability of the ferrofluid needs to be improvement for long term application.

Conclusions
The magnetocaloric properties of Fe-Ni-Cr nanoparticles were studied. Cr was used to tune the T C of Fe-Ni alloy from more than 400 K to below room temperature. The RCP for Cr1, Cr3, Cr5, Cr6 and Cr7 increased from 82 J-kg −1 , 59 J-kg −1 , 77 J-kg −1 , 62 J-kg −1 and 47 J-kg −1 to 548 J-kg −1 , 436 J-kg −1 , 406 J-kg −1 , 366 J-kg −1 and 306 J-kg −1 J-kg −1 as field increases from ΔH = 1 T to ΔH = 5 T, respectively. The cost of our nanoparticles is only ~2% of the cost of pure Gd and Gd 5 Ge 1.9 Si 2 Fe 0.1 magnetocaloric materials. The magnetocaloric properties, good corrosion resistance and low cost of these nanoparticles makes them attractive for magnetic fluid applications.

Methods
High energy ball milling is a suitable technique for producing large-scale, nano-and micro sized materials. This technique is based on mechanical energy transfer created by the collision of hard phase materials with the reactants. Mechanical alloying consists of flattening, welding, fracturing and re-welding of the powder by hard grinding balls. Therefore, alloying of nanostructured powders with defined stoichiometry and crystalline order can be achieved. the high energy ball milling of Fe-Ni-Cr alloy particles was performed.
Nanoparticles of (Fe 70 Ni 30 ) 100−x Cr x alloy were prepared by high energy planetary ball milling (FRITSCH) at 600 rpm under Ar atmosphere from elemental Fe (99.99%, Sigma Aldrich), Ni (99.998%, Fisher ChemAlert Guide) and Cr (> 99%, Sigma Aldrich) powders. The ball to powder ratio was 10:1. The vials and balls were made of zirconium oxide, and the volume of the vial was 125 ml, which contains 15 balls (10 mm in diameter). To prevent oxidation during heat treatment, the magnetic nanoparticles were sealed under high vacuum (10 −5 torr) in a quartz tube. The sealed tube was heated at 700 °C (γ -phase region) for 2 h and quenched in water 13 . The rate of quenching was ~125 °C/sec. The structure and phase were determined by X-ray diffraction (XRD) using a Bruker D8 Advance diffractometer (CuKα radiation). The composition was confirmed by energy dispersive X-ray spectroscopy using a JEOL JSM-7600F scanning electron microscope. To determine particle size, transmission electron microscopy (TEM) of nanoparticles was carried out on a JEOL 2010 TEM with an operating voltage of 200 kV. Samples for TEM were prepared by ultrasonically dispersing a small amount of powder in hexane, followed by putting a drop of the suspension on a holey carbon-coated copper grid, the sample is then dried overnight in vacuum. The magnetic properties were measured using a physical property measuring system (PPMS) (EverCool-II, Quantum Design), equipped with a vibrating sample magnetometer probe and an oven (model P527). The M (H) isotherms with field from 0 to 5 T in steps of 5 K (near T C ) and 10 K (elsewhere) were recorded for Δ S M measurements. The isothermal magnetic entropy change due to application of magnetic field was calculated using a numerical approximation to the Maxwell equation   Table 1. Curie temperature (T C ), change in magnetic entropy (ΔS M ), relative cooling power (RCP) and cost for selected magnetocaloric materials. The cost of the materials was calculated using pure element cost.
These Fe-Ni-Cr nanoparticles were used to prepare the ferrofluid. (Fe 70 Ni 30 ) 95 Cr 5 nanoparticles were functionalized with oleic acid and ammonium hydroxide and subjected high energy ball milling. Subsequently, these coated nanoparticles were dispersed in oleic acid. This ferrofluid of Fe-Ni-Cr nanoparticles and oleic acid was used as the heat transfer medium to perform magnetic cooling.
A 5.2 mm inner diameter, 60 cm circumference polymer tube was used for circular flow. A heat load (electric heater made by Kanthal wires) and a heat sink (cold water) were placed opposite each other. A permanent magnet, which can provide a maximum field of 0.25 T, was placed close to the heat load. A temperature data logger with SD card was used to record temperature v/s time. The initial temperature was tuned by changing current through the Kanthal wire using a Keithley power supply (Model: 2231 A-30-3). For modelling, COMSOL Multiphysics simulation software version 4.4 was used with finite element method and normal mesh.