Thermo-magnetic properties of ternary polydispersed Mn0.5Zn0.5Fe2O4

ferrite magnetic fluid

Kinnari Parekh n

Dr. K.C. Patel R & D Center, Charotar University of Science & Technology, Changa 388421, Anand District, India

a r t i c l e i n f o

Article history:Received 9 October 2013Received in revised form7 January 2014Accepted 7 February 2014by A.H. MacDonaldAvailable online 18 February 2014

Keywords:A. Magnetic fluidD. Thermal conductivityD. Pyromagnetic co-efficient

a b s t r a c t

Thermo-magnetic properties of ternary Mn0.5Zn0.5Fe2O4 ferrite magnetic fluid is investigated usinga SQUID magnetometer and thermal conductivity analyzer. Crystallite size of the particles is obtained as5.95 nm with size distribution of 0.23. M–T measurement of fluid shows that the system is highlytemperature sensitive with the pyromagnetic co-efficient of the fluid as 2.1 emu/cc K. The Curietemperature of the material was estimated using the Bloch theory, which is 374 K. Thermal conductivityof nanofluid shows 45% enhancement for 10% volume fraction at 25 1C temperature. The increment inthermal conductivity is linear with increase in volume fraction but significantly higher than the predictedMaxwell's theory, Maxwell-Garnett and Bruggeman theory. Even though the nanofluid is highly sensitiveto magnetic field the application of transverse magnetic field does not show any further enhancement inthermal conductivity. These results are explained considering the dipolar coupling co-efficient which inthe present system is lower than unity and hence does not favor the long chain like structures. Thetemperature dependent thermal conductivity shows enhancement of 4% in the temperature range of25–65 1C which makes it an attractive choice for heat transfer devices.

& 2014 Elsevier Ltd. All rights reserved.

1. Introduction

Thermo-magnetic properties of magnetic materials have beenexploited mainly in magnetic refrigeration devices due to variouspossible benefits like (i) its environment friendly technologicalprocesses, (ii) its compactness, (iii) possibility of removing com-pressor with movable components, large rotational speed,mechanical vibration, noise, bad stability and short longevity and(iv) better efficiency around 30–60% of Carnot cycle compared tothat of vapor compression refrigeration [1,2]. These make themagnetic particles a more promising candidate for the purpose.Magnetic refrigerators use a solid refrigerant (either in the form ofspheres or thin sheets) and common heat transfer fluids (e.g.water, water–alcohol solution, air, or helium gas) with no ozone-depleting and /or global-warming effects. The heating and coolingthat occurs in the magnetic refrigeration technique is proportionalto the magnitude of the magnetic moments and to the appliedmagnetic field. This is why research in magnetic refrigeration is atpresent almost exclusively conducted on superparamagneticmaterials and on rare-earth compounds. Since the entropy changecan be controlled by tuning superparamagnetic-blocking transi-tion, the magnetic nanoparticles have also been an attractive

alternative to conventional bulk magnetocaloric materials. Theo-retically, it has been shown that the decrease in particle size closeto the single magnetic domain increases the magnetic entropychange by several orders of magnitude as compared to that in bulkmaterials [3,4]. In addition, the large surface area in nanostruc-tured materials has the potential to provide better heat exchangewith the surrounding materials. By careful design of core–shellstructures, it would be possible to control the heat exchangebetween the magnetic nanoparticles and the surrounding matrix.

In the present work, our approach is to produce such super-paramagnetic particles which have a Curie temperature near to300 K with higher pyromagnetic co-efficient as well as higherthermal conductivity. The particles chosen for the study isMn0.5Zn0.5Fe2O4 because of its lower Curie temperature �340 Kwith moderate magnetization at 300 K. The thermo-magneticproperty of the nanofluid synthesized using these particles havebeen investigated using a SQUID magnetometer and thermalconductivity analyzer LAMBDA system.

2. Experimental

2.1. Materials

The source for initial precursors for Mn2þ , Zn2þ and Fe3þ

were MnCl2 4H2O, ZnCl2 dry and FeCl3 6H2O purchased from

Contents lists available at ScienceDirect

journal homepage: www.elsevier.com/locate/ssc

Solid State Communications

http://dx.doi.org/10.1016/j.ssc.2014.02.0050038-1098 & 2014 Elsevier Ltd. All rights reserved.

n Corresponding author.E-mail address: kinnariparekh.rnd@ecchanga.ac.in

Solid State Communications 187 (2014) 33–37

Sigma-Aldrich and used as received without any further purifica-tion. Oleic acid (90%), acetone and kerosene (reagent grade) werealso purchased from Sigma-Aldrich. Sodium hydroxide used toprecipitate the particles was purchased from SD Fine Chem.Ltd. India.

2.2. Nanofluid preparation

The Mn0.5Zn0.5Fe2O4 ferrite nano-particles were synthesized byco-precipitation technique followed by digestion. The ratio ofMe2þ (Mn2þ:Zn2þ¼1:1) and Fe3þ was kept as 1:2 and the initialmolarity of the precursor was set as 500 mM. Oleic acid was usedas a surfactant to create steric repulsion between the particles andthen coated particles were dispersed in light hydrocarbon oil. Thenanofluid, thus prepared possesses long-term stability. Thevolume fraction of the particles was determined using the truedensity of carrier ρc, density of particles, ρp and the density of thefluid, ρf. The formula used to calculate the volume fraction fromthe density is given as

φ¼ ðρf �ρcÞðρp�ρcÞ

ð1Þ

2.3. Structural characterization

Rigaku powder X-ray diffractometer (Cu Kα radiation,λ¼1.5414 Å) was used to study the crystal structure of theparticles. The instrument was operated at 40 kV, 40 mA and thedata were recorded in continuous scan mode with steps of 0.02.The size and morphology of the samples were studied usingPhilips Transmission Electron Microscopy model TECNAI F20operated at 200 kV.

2.4. Thermo-magnetic characterization

Magnetic measurement of fluid samples was carried out usingMPMS DC magnetometer. The thermal conductivity of the samplewas measured according to ASTM D2717 standard for fluids usingLAMBDA system (F5 Technologies GmbH, Germany, ModelLAMBDA). The cylindrical vial of ID 30 mm containing the testsample was placed in a circulation thermostat. A Pt 100 thermo-couple inside the vial was used to measure the temperature of thesample. The instrument was calibrated with deionized water,ethanol, and ethylene glycol. Its sensitivity was found to measurethe change within an accuracy of 71%. For application ofmagnetic field, solenoid energized with constant current powersupply was used. The measurement was done after 20 min ofequilibrium i.e., after achieving an equal temperature of the bathand the sample. No variation in thermal conductivity datawas observed with time showing good stability of nanofluidsynthesized.

3. Results and discussion

3.1. Structural characterization

Fig. 1a shows the XRD pattern for Mn0.5Zn0.5Fe2O4 ferritenanoparticles. All the peaks in the XRD pattern correspond tosingle phase spinel ferrite with Fd3m space group. The size of theparticles was calculated using the Scherrer formula using fullwidth half maximum of the most intense (311) plane which comesout to be 5.9570.05 nm. Fig. 1b shows the TEM image. It is seenthat almost all the particles are of similar size with sphericalgeometry. The median size of the particles calculated from theimages is 6.5 nm for Mn0.5Zn0.5Fe2O4 ferrite.

3.2. Thermo-magnetic characterization

MðH; TÞ ¼ nZ Dmax

Dmin

μLðξÞPðDÞdD

¼ nZ Dmax

Dmin

MsV cothMdVHkBT

� �� kBTMdVH

� �1ffiffiffiffiffiffi

2πp

sD

� �

�expInðD=D0Þ2

2s

!dD ð2Þ

Fig. 2a shows the room temperature magnetic response ofmagnetic fluid measured at the applied field of 10 kOe. Themagnetization curve does not show any hysteresis at 300 Kconfirming that the particles are superparamagnetic. Moreover,the magnetic response does not saturate even at the field of10 kOe. This observation matches with that observed for fineparticle magnetic response studied by other researchers [5,6].The nature towards saturation fits with the modified Langevin'stheory which incorporate the log-normal diameter distributionfunction (refer Eq. (2)). Inset of Fig. 2a shows fitting of virgin curve(experimental data points) to Langevin's theory (line) as well asthe distribution in particle size obtained from the fit. The fitparameters thus obtained are the magnetic particle size, Dm,domain magnetization of the particle, Md and the size distribution,s which is 5.3 nm, 210 emu/cc and 0.18, respectively. The differ-ence of 0.65 nm in the diameter is seen from the particle sizeobtained from the magnetic measurement and from X-ray mea-surement. The difference in size can be attributed to the presenceof a magnetic dead layer on particle surface since the particle sizeis in the nanometer range, the ratio of surface area to volumeincreases. At room temperature the moment of the atoms on thesurface of the particles are loosely bound and hence pointing inrandom directions. As a result, they will not contribute to themagnetic response. Only the coherent alignment of the coremagnetic moment will responsible for the magnetic nature. Suchan arrangement is classified as the magnetic core/shell types ofbehavior which follows the model suggested by Kodama et al. [5,6]for magnetic nanoparticles.

Fig. 2b represents the variation of magnetization as a functionof temperature. M (T) measurement was carried out by cooling thesample to 5 K under zero magnetic field and the data wererecorded during warm up under the constant applied field of 1 T.It is seen from the figure that almost 70% of the magnetizationvalue is reduced in the temperature range of 5–300 K indicatingthat the magnetization is highly sensitive to the temperature.In order to find the temperature dependency, the experimentaldata (open symbol) were fitted with the Bloch function defined asMs(T)¼Ms(0) [1�β(T)n], where β is the Bloch constant. The powerof Bloch exponent, n, decides the rate of decrement in magneticmoment which varies between 1.5 and 2 for superparamgneticparticles. In the present system, the best fit value of n is obtainedas 1.5 whereas β is 1.38�10�4 K�1. Using these values (Blochexponent and constant) the value of Curie temperature is calcu-lated which comes out to be 374 K. This value matches with thereported value of Curie temperature for Mn0.5Zn0.5Fe2O4 ferritenanoparticles [7]. The value of pyromagnetic co-efficient, i.e., rateof change of magnetization per degree change in temperatureabove 300 K, is found as 2.1 emu/cc K.

Since the pyromagnetic co-efficient is high for the presentsample, it makes the system interesting for the magneto-caloricenergy conversion devices. If Mn0.5Zn0.5Fe2O4 particles showenhanced thermal conductivity then the rate of heat transfer willbe further improved. In order to check this, the study of thermalconductivity of this fluid has been carried out as a function ofvolume fraction, magnetic field and temperature.

K. Parekh / Solid State Communications 187 (2014) 33–3734

The thermal conductivity as a function of volume fraction,φ, has been investigated with and without the magnetic field.Fig. 3a shows the effect of volume fraction under zero magneticfield. The open symbols (○) in Fig. 3a report the experimentalvalue for Mn0.5Zn0.5Fe2O4 ferrite nanofluid. The fluid shows almostlinear increment in thermal conductivity with increase in volumefraction. This result is similar to that observed for other magneticparticles reported by several researchers [8–10]. The experimentaldata of the percentage enhancement were fitted with Maxwell'stheory of two-component system [11]. It inferred from the figurethat observed enhancement in the fluid is quite higher than thatpredicted by theory. The discrepancy in experimental and theore-tical predicted value can probably due to several factors such as

size, clustering of nanoparticles due to inter-particle interaction,Brownian motion of the particles, particle–carrier interface effect,etc. Maxwell-Garnett (MG) [12] and the Bruggeman approach [13]are two common methods used in effective medium theory totreat the effective transport coefficient of mixture and composites.The MG approach fits well with experimental data for dilute andrandomly distributed components included in a homogeneoushost medium, the particles are considered as to be isolated in thehost medium, no interactions existing among them. While theBruggeman model with mean field approach is used to analyzethe interactions among the randomly distributed particles. TheBruggeman model has no limitation on the concentration ofinclusions, and can be used for particle percolation in suspensions.

20 30 40 50 60

(440)

(511)

(422)(400)

(311)

(220)In

tens

ity

2θ

5.95 nm

40 nm

Fig. 1. (a) Powder X-ray diffraction pattern for Mn–Zn ferrite nanoparticles coated with oleic acid. (b) Morphology of particles studied using TEM.

-10 -5 0 5 10-50

-25

0

25

50

M (e

mu/

gm)

H(kOe)

300K

0 50 100 150 200 250 3000.2

0.4

0.6

0.8

1.0

Mno

rm

T (0C)

Fig. 2. (a) Magnetic measurement of fluid carried out at 300 K. Inset shows the data fitted with Langevin's function and the distribution in particle size obtained using log-normal distribution function. (b) M–T curve for the sample; sample was cooled in zero magnetic field from 300 K to 5 K.

0 300 600 900

130

140

150

160

170

180

0

10

20

30

40φ = 10 %

φ = 2.5 %K(m

W/m

-K)

H(Oe)

% e

nhan

cem

ent

0 2 4 6 8 10 12

1.0

1.1

1.2

1.3

1.4

1.5

Bruggeman theory

Maxwell & MG theory

K/k

base

Vol. fraction φ (%)(%)

Fig. 3. (Color online) (a) Thermal conductivity as a function of volume fraction for Mn0.5Zn0.5Fe2O4 nanofluid (symbol). Blue line represents Maxwell and Maxwell-Garnettheory whereas red line represents the thermal conductivity calculated using Bruggeman model. (b) Thermal conductivity as a function of transverse magnetic field forMn0.5Zn0.5Fe2O4 nanofluid (open symbol). Right axis shows percentage enhancement (black line) in it.

K. Parekh / Solid State Communications 187 (2014) 33–37 35

For low concentration, the Bruggeman model shows similar resultsas to MG model. When the particle concentration is sufficientlyhigh, the MG model fails to predict precisely the experimentalresults, while the Bruggeman model can still fit well with experi-mental data. In present case, both the models along with Maxwelltheory were fitted with the experimental data. We found that theMaxwell theory and Maxwell-Garnett theory fails to predict theobserved value of Mn0.5Zn0.5Fe2O4 ferrite system. The largestdiscrepancy at the highest volume concentration supports thisargument. The Bruggeman model though does not fit too with theexperimental data but gives closer value to the experimentalobserved results. This indicates that the particles are interactingamong themselves and forming some types of structure within themedium.

Fig. 3b shows the effect of transverse magnetic field appliedthrough the solenoid to the system. The direction of the magneticfield is parallel to the hot wire and transverse to the direction ofheat flow. Fig. 3b shows that transverse magnetic field does notgive any significant enhancement in thermal conductivity. Thesimilar results are observed for increasing volume fraction of theparticles. It is obvious that the magnetic effect on the thermalconductivity of the magnetic fluid at a higher particle concentra-tion is stronger than that at a lower particle concentration. Butapplication of transverse magnetic field up to concentration of 10%does not lead to show any effect on thermal conductivity. It is to benoted, that the data were taken after 20 min of application ofmagnetic field, which is quite long to form any structures underthe influence of magnetic field [14]. The similar field independentthermal conductivity of magnetic fluid was observed by severalauthors [15–17].

In our earlier study on Fe3O4 nanofluid under the transversemagnetic field of 1 kOe, almost 30% enhancement was observed inthermal conductivity at 4.7% volume fraction [8]. Li et al. [16] havereported hardly 2% change in thermal conductivity when the fluidis subjected under transverse magnetic field, whereas about 30%enhancement was seen when magnetic field was longitudinal.Shima et al. [17] on their experiment on hexadecane-based Fe3O4

nanofluid found similar results when experiment with directiondependent magnetic field. They reports 240% enhancement whenthe field direction was exactly parallel to the thermal gradient,whereas practically no enhancement when the field was perpen-dicular to thermal gradient. A gradual reduction in the thermalconductivity enhancement was observed as the field direction wasshifted from parallel to perpendicular direction with respect tothermal gradient.

The magnetic field dependent response can be explained basedon the competing interaction between Zeeman energy, interpar-ticle interaction energy and Brownian energy. In the absence ofmagnetic field, the thermal motion exceeds the magnetic dipolarattraction. Thus, magnetic moments are oriented randomly due tothe effect of the Brownian motion. If an external magnetic field isapplied, the magnetic inter-particle interaction energy becomesgreater enough to counteract the Brownian motion of the particlesand the nanoparticles with the magnetic moments start to alignthemselves in the direction of the magnetic field. As the magneticfield increases, the particles start to form doublets, triplets andshort chains in the direction of the magnetic field. Such alignmentserves as bridges in the thermal transport process. As a result thethermal conductivity enhances beyond the Maxwell limit due tothe chain-like structures of magnetic nanoparticles in the fluid.When direction of magnetic field is transverse to the thermalgradient, the energy transport inside the fluid suppress along thetemperature gradient compared to that along the field direction.This weakens the transport process in the perpendicular magneticfield. Clearly, when the particle volume fraction increases, chainformation becomes denser and the heat conduction through the

chain-like structures becomes more evident, resulting in a higherthermal conductivity. But this is observed only when the dipolarcoupling co-efficient λ, defined as λ¼μ0Md

2V/24kBT is greater thanunity. In the present case, λ is much lesser than unity forMn0.5Zn0.5Fe2O4 ferrite (0.088) at room temperature. This is dueto the fact that the particle size of Mn0.5Zn0.5Fe2O4 ferrite issmaller than 10 nm and the domain magnetization, Md, of thematerial is also relatively lesser (210 emu/cc) than that of Fe3O4

particles (300 emu/cc). As a result the initial susceptibility definedas χi¼8φλ does not allow to form chain like structures and henceno further increase in thermal conductivity is observed even for10% concentration. It is reported, that for λo2, the systemregarded as being in a homogeneous ‘gas like’ state with veryfeeble magnetic interaction. This will hardly support the aggrega-tion or field induced structures of nanoparticles [18]. Thus weconclude that even though the thermal conductivity of magnetite(5 W/m K) is lesser than Mn0.5Zn0.5Fe2O4 ferrite (29 W/m K), thehigher value of coupling coefficient for 10 nm size particles (0.682)makes it responsive under transverse magnetic field and make ita better choice under transverse magnetic field. However, as theMn0.5Zn0.5Fe2O4 ferrite has higher thermal conductivity and thedomain magnetization increases with increasing size, the resultswill be different for relatively larger size of the particles. It isinteresting to study the thermo-magnetic properties ofMn0.5Zn0.5Fe2O4 ferrite as a function of different size ranging fromsuperparamagnetic to single domain region.

The effect of temperature on thermal conductivity of magneticfluid is also studied for two concentrations. Fig. 4 shows the effectof temperature on the thermal conductivity of nanofluid. Figureshows the increase in thermal conductivity of nanofluid as thetemperature rises from 25 to 65 1C. After correcting, the data forthe temperature dependence variation in carrier 1% enhancementis observed a low volume fraction while for the higher volumefraction fluid 4% enhancement is seen. The increase in thermalconductivity with increase in temperature can be due to theincreasing Brownian motion of the particles [19,20] as well asdue to the temperature dependent thermal conductivity of oxidespinel. The heat carrier in oxide solids is due to transport ofphonons. The mean free path of phonon decreases with increase intemperature. As a result, the overall increase in thermal conduc-tivity of nanofluid at lower volume fraction has reduced comparedto the higher volume fraction. For magnetite, magnetic fluid theincrease in temperature does not enhances the thermal conduc-tivity [8,21–23]. However, for the present case we see thesignificant enhancement in Mn0.5Zn0.5Fe2O4 ferrite based mag-netic fluid. We attribute this enhancement as the material proper-ties. The particular reason for the observed enhancement is at

20 30 40 50 60 70 80

11.8

12.0

12.2

12.4

12.6

12.8

46

48

50φ = 10 %

(%) e

nhan

cem

ent

(%) e

nhan

cem

ent

T(0C)

φ = 2.5 %

Fig. 4. Percentage enhancement in thermal conductivity as a function of tempera-ture for two different volume fractions of Mn0.5Zn0.5Fe2O4 nanofluid.

K. Parekh / Solid State Communications 187 (2014) 33–3736

present not clear to us but it is really an interesting future study tosee the effect of size, temperature and the resulting behavior ofmagnetic field on the structure formation due to the modifiedinteractions discussed above.

4. Conclusion

Thermo-magnetic properties of ternary polydispersedMn0.5Zn0.5Fe2O4 ferrite magnetic fluid have been evaluated usinga SQUID magnetometer and Thermal conductivity analyzer systemLAMBDA. At room temperature, the particles are superparamag-netic obeying Langevin's nature with zero remanence and zerocoercivity. M–T measurements made at 1 T magnetic field showsalmost 70% drop in magnetization within 5–300 K temperatureregime. The estimated Curie temperature of the material foundfrom the fit of Bloch's function is 374 K. Thermal conductivity ofnanofluids shows 45% enhancement at 10% volume fraction. Theincrement in thermal conductivity is linear but significantly higherthan the predicted Maxwell's theory, Maxwell-Garnett and Brug-geman's model. Though the nanofluid is highly sensitive tomagnetic field, the application of transverse magnetic field doesnot show any further enhancement in thermal conductivity. Thepossible reason for this can be due to the lower value of thedipolar coupling co-efficient, which does not favor the long chainlike structures. The temperature dependent thermal conductivityshows enhancement of 4% in the temperature range of 25–65 1Cwhich makes it an attractive choice for heat transfer devices.

Acknowledgments

Author is thankful to the GUJCOST-1418, Gandhinagar and DSTCMP-54 project sponsored by DST, New Delhi, Government of India.

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