Dielectric and magnetic properties of NiFe2O4 at 2.45 GHz and heatingcapacity for potential uses under microwaves

Isabelle Polaert a,n, Samuel Bastien b, Benoit Legras a,b, Lionel Estel a, Nadi Braidy b

a LSPC (Laboratoire de Sécurité des Procédés Chimiques). Institut National des Sciences Appliquées INSA Rouen, Franceb Département de génie chimique et de génie biotechnologique, Université de Sherbrooke, Sherbrooke, Québec, Canada J1K 2R1

a r t i c l e i n f o

Article history:Received 1 July 2014Received in revised form9 September 2014Available online 20 September 2014

Keywords:MicrowaveFerriteNiFe2O4

PermittivityPermeability

a b s t r a c t

This paper presents the dielectric and magnetic properties, measured at 2.45 GHz, of a new nickel ferrite,NiFe2O4, synthetized by plasma technology. These properties were measured by the small perturbationmethod in a resonant cavity, from 293 to 513 K. Using these values, the adiabatic heating of nanoparticlesof NiFe2O4 under microwave irradiation was also modeled. The wave propagation equation (Maxwell'sequation) coupled to the heat transfer in the solid was numerically solved. The influence of parameterssuch as the bed volume, its porosity, the microwave incident power or the microwave system geometryis discussed. This study demonstrates that NiFe2O4 nanoparticles can be rapidly heated up to at least513 K under microwaves and can probably achieve higher temperatures according to the thermalinsulation. The magnetic contribution to heating overcomes the dielectric one in the exploredtemperature range. Very efficient energy yield (490%) can then be achieved when the magnetic fieldposition is centered over the bed.

& 2014 Elsevier B.V. All rights reserved.

1. Introduction

Ni-ferrites are characterized by a spinel crystal structure thatoffers some flexibility on the occupancy of each site [1]: on thecationic sites, atomic substitutions are allowed following a given setof rules, while the anionic sites can generally accommodate a fewpercents of vacancies. A range of applications takes advantage of thetunable properties of Ni-ferrites. For example, they are used for somecatalytic reactions [2–4] via a 2-step redox or Mars-van Krevelen-typemechanism in which the oxygen vacancies of the Ni-ferrites tem-porarily collect atomic oxygen from gaseous reactants before releas-ing it. The crystalline nature of Ni-ferrites is responsible for their ionicconduction properties which makes them candidates for anodes ofLi-ion batteries [5,6] or as gas sensors [7,8].

In many applications in which the properties of Ni-ferrites areused, performances are strongly enhanced by elevated temperaturesof operation. Indeed, Ni-ferrites nanoparticles are used for steamreforming of methane at 1073 K [4] while CO2 decomposition withNi-ferrites is performed at �573 K [3]. Similarly, Ni-ferrite's responseas a sensor towards specific gases was shown to increase with tem-perature [7]. In these applications, it would be preferable to selectivelyheat the Ni-ferrites by taking advantage of the high susceptibility

towards microwaves typically expected from ferrites. Several advan-tages are expected from heating Ni-ferrites using microwaves,namely: (i) a fast and site-specific heating method minimizing coldstart-up and (ii) a means to efficiently achieve and maintain a highoperating temperature, especially for endothermic processes.

In order to determine the feasibility of using microwaves to heatferrites for the above-mentioned applications, it is essential toevaluate first, the dielectric and magnetic properties of the material.Although there are few references in literature [9–13], these valuesare not easily available for NiFe2O4 and they strongly depend on theparticle characteristics, temperature and frequency so require anexperimental determination. Second, it is necessary to evaluate themaximum temperatures, spatial uniformity, heating rates and overallefficiency of such a process. In previous papers dealing with othermaterials such as zeolites [14–16] we demonstrated the predominantrole of the dielectric properties on the microwave process efficiency.In the case of ferrites, where magnetic properties are present, we canexpect these benchmarks to be controlled by the geometricaland physical characteristics of the bed (size, dielectric, magnetic andthermal properties, porosity, compaction) and the resonance achievedwithin a given furnace geometry. Given the number, complexity andinterdependency of these parameters, simulations are required tonarrow the parameter space and determine the significant operatingconditions used for preliminary experiments.

In this work, we use finite-element simulations to model theheating of NiFe2O4 nanocrystals with microwaves. The nanocrystals

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Journal of Magnetism and Magnetic Materials

http://dx.doi.org/10.1016/j.jmmm.2014.09.0270304-8853/& 2014 Elsevier B.V. All rights reserved.

n Corresponding author: Tel.: þ33 0 232 956 668; fax: þ33 0 232 956 652.E-mail address: isabelle.polaert@insa-rouen.fr (I. Polaert).

Journal of Magnetism and Magnetic Materials 374 (2015) 731–739

were produced using a plasma method described in a previous paper[17]. We then report on the dielectric and the magnetic propertiesobtained using the method of small perturbation in a resonant cavity.[18,19] We then performed COMSOL Multiphysicss finite-elementadiabatic simulations to determine the influence of the NiFe2O4

powder parameters (total mass and porosity), bed geometry (dia-meter, piston position) and microwave parameters (power, irradiationtime) on the maximum achievable temperature, temperature uni-formity of the bed and discuss their influence on the overall processefficiency.

2. Experimental

2.1. Materials

Nickel ferrite (NiFe2O4) nanopowder was synthesized using asolution-spray radio-frequency inductively coupled plasma reactordescribed in details in an earlier publication [17]. Briefly, the nano-powder was synthesized by injecting a solution of aqueous nickel andiron nitrates (Ni/(NiþFe) ratio of 1/3) into an O2/Ar thermal plasma.Tests were performed on a mixture of condensed powder collectedfrom both the filters and the main reactor of the plasma reactor. TheNi-ferrite thus synthesized is only composed of a single spinelcrystallographic phase. The powder exhibits two types of morpholo-gies: a highly faceted, truncated octahedrons morphology with the{100} and {111} facets exposed, and a random agglomerate with nodiscernible shape. The truncated octahedrons have sizes ranging from6 to 160 nm with an average size of about �34 nm, whereas therandom agglomerate has a characteristic length of 3 to 5 nm.

2.2. Apparatus for dielectric permittivity and magnetic permeabilitymeasurement

The dielectric and magnetic properties of NiFe2O4 nanopowderwere measured by the small perturbation method in resonantcavity. [18,19] Among the various available techniques, the cavityperturbation technique is accepted as the most accurate, especiallywhen medium- and low-loss samples are tested and requires onlysmall quantities of samples for measurement. The apparatus usedto acquire dielectric and magnetic properties of NiFe2O4 is ahomemade system (as shown in Fig. 1), consisting in a VectorNetwork Analyzer (VNA) supplied by Agilent (PNA_L seriesN5230A) associated to a resonant cavity, specifically adapted forthe desired measurement. Two cavities were also designed formeasurements at 2.45 GHz 7 1 MHz: one for the dielectricproperties and the other for the magnetic properties [16,20,21].They differ in the cavity length and the position where the sample

is introduced. Both are made with WR340 brass wave guidesdelimited by a shunt inductive iris and an adjustable shortcutcircuit at the other extremity. Only one port is connected to theVNA and an impedance adapter system is used to achieve a betterresonance and a high quality factor of the cavity. The sample isplaced in a quartz tube of 4 mm inner diameter and introduced ina larger quartz tube crossing the cylindrical wave chokes, so-calledthe “chimneys” of the cavity in the paper. The sample is heatedusing a heat gun and the cavity is continuously cooled by a countercurrent cold air circulation in the intermediate space and watercooling of the chimney. The temperatures of the cavity and of thesample are precisely and continuously measured by two Pt-100probes and an optic fiber. Data recorded by the VNA and tem-perature controller are monitored with the Labview© acquisitionsoftware. This system allows an accurate control of the sampletemperature up to 513 K without significant heating and dilatationof the cavity.

For dielectric or magnetic properties measurement, the principle ofthe perturbation method is the same. The introduction of a smallsample in the cavity modifies its resonating properties such as theresonant frequency (fr) and the quality factor (Q). In the case ofdielectric properties measurements, the sample has to be introducedat the maximum electric field position, where the magnetic field isnull: only its complex dielectric properties contribute to the complexfrequency shift and one can access to the two parts of the relativecomplex permittivity εr0 and εr″ using Eq. (1). In the case of magneticproperties measurements, the sample has to be introduced at themaximum magnetic field position, and the two parts of the complexpermeability mr0 and mr″ can be calculated using Eq. (2).

ε0r� �

s ¼ 1A

f 0 � f sf s

� �VcV sþ1

ε″r� �

s ¼ 1B

1Q s� 1

Q0

h iVcVs

8><>: ð1Þ

m0r� �

s ¼ 1C

f 0 � f sf s

� �VcVsþ1

m″r� �

s ¼ 1D

1Q s� 1

Q0

h iVcVs

8><>: ð2Þ

where Vs and Vc are the volumes of the sample and of the cavity; fsand Qs are the resonant frequency and quality factor of the cavity withthe sample; f0 and Q0 are the resonant frequency and quality factor ofthe empty cavity.

The factors A, B, C and D were predetermined by a calibrationprocedure. It uses the frequency shift and the quality factormeasured for a standard material which properties are preciselyknown. Methylbenzoate was used as reference material for dielec-tric measurements. Its dielectric properties were previously mea-sured [22] between 278 and 358 K and the values at 291 K are used

Water cooling

Sample tube

Cold air

Quartz pipe

Hot air

Shunt inductive irisVNA

Electric field amplitude

Ferrite sample

Temperature controller

Optic fiber

Fig. 1. Permittivity or permeability measurement setup in resonant cavity.

I. Polaert et al. / Journal of Magnetism and Magnetic Materials 374 (2015) 731–739732

as a standard

ε0r� �

e ¼ 5:573

ε″r� �

e ¼ 1:958

(at T ¼ 291 K

For the magnetic properties, “Ferrite 50”, a lithium nickel zincmanganese ferrite from Trans Tech, was chosen for calibration[23]. Its magnetic properties for a solid density of 4.75 g/cm3 aregiven at 2.454 GHz and 293 K

m0r� �

e ¼ 0:7

m″r� �

e ¼ 2:0

(at T ¼ 293 K

Because we use a fine powder, the porosity of the sample wasprecisely measured and the Lichtenecker [24] mixing law referringto air and particles volume was used to determine the calibrationfactors C and D.

For a better accuracy, the reference materials and samplevolumes were the same: 0.2 mL for dielectric and 0.35 mL formagnetic measurements. They allow a significant, but moderate,frequency shift and attenuation of the quality factor.

Measurements were first made at the reference temperature(29170.1 K or 29370.1 K) and then with different heating rampsup to 51370.1 K. Each series was repeated at least three times.Each data series was computed in order to find the best fit foreach temperature rise, using MATLabs curve fitting toolbox. Theaverage relative error was calculated with

σ ¼ 1N

∑N

i ¼ 1

Fexp�Fcal� �

Fexp100 ð3Þ

where N is the total number of experimental points for theconsidered temperature rise, Fexp and Fcal the experimental andcalculated permittivity or permeability, respectively. Finally, themaximum relative errors on dielectric and magnetic properties are

Δε0r ¼ 6:6% Δm0r ¼ 8:1%

Δε″r ¼ 10:0% Δm″r ¼ 1:5%

2.3. Results

The dielectric and magnetic properties of NiFe2O4 particles synthe-tized by plasma technology are shown in Figs. 2 and 3, respectively.

The measured dielectric properties are in the same order ofmagnitude than those given for different types of ferrites [9–13].They are significantly lower than those measured in our apparatusat T¼293 K for Ferrite 50 (Trans Tech) for which εr0 ¼10.3 andεr″¼3.25. The dielectric losses are relatively low (between 0.5 and1) and slightly increase with temperature. The magnetic propertiesexhibited by NiFe2O4 are interesting: the magnetic constant mr0 isclose to 1, indicating neither a paramagnetic nor a ferromagneticbehavior, but the magnetic losses mr″ are relatively high comparedto most ferrites [9–13,21,23]. At 293 K, this value (mr″0 ¼2.0) iscomparable to that of Ferrite 50 (Trans Tech) [23], but remainsconstant with increasing temperature, contrary to Ferrite 50. Thus,microwave interactionwith the magnetic field due to the magneticcharacter of this solid will be maintained even with increasingtemperature, at least up to 513 K.

In conclusion of this section, the magnetic and dielectricproperties of plasma-synthesized NiFe2O4 nanoparticles are quitehigh. This indicates that this material could possibly be heatedrapidly under microwaves.

3. Modeling

Finite-element adiabatic simulations were performed to determinehow the parameters of the NiFe2O4 bed and the microwave irradiation

affect the heating efficiency of the powder. Given that the measuredvalue (Section 2) of εr″ is in the same order of magnitude as mr″, therelative contribution to the powder heating from the interaction withthe electric and magnetic components of the microwave radiationwillalso be determined by the calculations.

3.1. Hypothesis and equations

A model coupling electromagnetic wave propagation and theresulting heat transfer was developed to better understand thephenomena occurring during microwave irradiation of NiFe2O4,evaluate its heating ability under microwaves and simulate newconfigurations of heating processes.

Maxwell's equations were solved to obtain the electric field insidethe wave guide cavity and the ferrite bed and were coupled to a heattransfer model to obtain the 3D temperature distribution inside thebed. Adiabatic conditions were assumed in this model in order tofocus on the material's performances. The numerical computationwas conducted using COMSOL Multiphysicss software.

Fig. 2. Dielectric properties at 2.45 GHz of NiFe2O4 synthetized by plasmatechnology.

Fig. 3. Magnetic properties at 2.45 GHz of NiFe2O4 synthetized by plasmatechnology.

I. Polaert et al. / Journal of Magnetism and Magnetic Materials 374 (2015) 731–739 733

The following geometry was used for the simulations (Fig. 4): abed of ferrite NiFe2O4 is placed in a cylindrical glass reactor andintroduced in the chimneys of a wave guide WR340. Microwavesare generated at one of the two ends of a waveguide at 2.45 GHz,assuming a TE10 rectangular mode. The wave propagates in thewave guide and reflects at the end of an adjustable shortcut circuit.The height of the ferrite bed is 0.04318 m which corresponds tothe wave guide height. The internal reactor diameter is typicallydbed¼0.03 m but was studied as a variable parameter and typicallycorresponds to a NiFe2O4 mass of 38.8 g.

3.1.1. Governing electromagnetic equationsThe electric E and magnetic H field distributions inside the

ferrite bed and the microwave cavity were calculated by solvingthe following 3D Maxwell's equations, with the software COMSOLMultiphysicss. The electromagnetic wave was assumed to propa-gate in a harmonic form in TE10 mode inside WR 340 wave guide,in the y direction defined in Fig. 1, at 2.45 GHz. Each differentialequation for each field can be written as [20]

∇� μ�1∇� E� ��ω2εE¼ 0

∇� ε�1∇�H� ��ω2μH¼ 0;

where ω (rad/s) represents the wave pulsation, ε¼ ε0 � jε″ thecomplex permittivity, and m¼ m0 � jm″ the complex permeability. Therelative permittivity and permeability are such as ε¼ ε0εr; μ¼ μ0μr,with ε0 ¼ 8:854187817� 10�12F=m and μ0 ¼ 4π � 10�7H=m arethe vacuum permittivity and permeability, respectively.

The complex permittivity and permeability measured as afunction of temperature in the previous section were used andthe Lichtenecker [24] mixing law referring to air and particlesvolume was applied considering the measured bed porosity. Themicrowave power absorbed per unit volume QMW (W/m3) at anylocation of the medium was calculated from the electric andmagnetic field distribution using Poynting's theorem

QMW ¼ω2

IVðε″jΕ!j2þμ″jΗ!j2Þ dv:

Boundary conditionsThe walls of the wave guide were assumed to be perfect electric

conductors and hence, the tangential component of the electricfield is equal to zero

n� E¼ 0;

where n defines a vector normal to the considered surface.With the TE10 mode propagation, (xoz) becomes a plane of

symmetry and a boundary condition of perfect magnetic conductor

is imposed and can be written as

n� H¼ 0:

At the magnetron side wall, where microwaves are generated,the incident power applied Pi (W) was set at some imposed value,defining a boundary condition on the electric field Ei (consideringa TE10 mode) as

Pi ¼1

Z0 TEEi�� ��2

where Z0 TE defines the characteristic impedance for a propagationmode TE.

At the chimney exit, no electromagnetic wave propagation wasassumed, therefore

n� ∇� Eð Þ� jβg E� n� Eð Þ � nð Þ ¼ 0;

where βg is the propagation constant in the guide.For internal boundaries, field continuities were fixed, so

n� E1�E2ð Þ ¼ 0

and

n� H1�H2ð Þ ¼ 0:

3.1.2. Governing heat transfer equationsAdiabatic conditions for the bed of NiFe2O4 nanoparticles were

considered to isolate the material's performances. The microwavelocal power density was calculated from Poynting's vector and thefollowing thermal balance including conduction in the bed andheat accumulation was solved:

QMW ¼ ρbedCpbed∂T∂t

þ∇� ð�λbed � ∇TÞ

The bed density, ρbed, was calculated using the bed intragranularporosity Abed

ρbed ¼ 1�ϵbedð Þρpþϵbedρair

The particle density ρp was measured as a function of tempera-ture between 293 and 1273 K using a thermogravimetry analyser(TGA). The volume variation of a precise sample mass wasfollowed by the measure of the displacement of a piston placedabove the surface of the ferrite sample. The following experimen-tal law was then obtained, with T expressed in 1C:

ρpkgm3

� �¼ �5:98589� 10�4 � T2�3:21548� 10�1 � Tþ3323

Abed was experimentally estimated by weighing a known volumeof compacted NiFe2O4 nanoparticles. A typical value of 0.63 wasobtained.

Cpbed was obtained from DSC measurements between 293 and1073 K and a mean value of 0.8 kJ/kg/K was considered in thistemperature range.

The effective conductivity of the bed was estimated using the Hsucorrelation [25] and reference values for ferrites [26]. The tempera-ture dependency was considered leading to an effective conductivityof the bed varying from 0.030 to 0.034W/(m�K) between 293 and513 K.

Boundary conditionsAdiabatic conditions were assumed at the reactor wall surface

�n� �k∇Tð Þ ¼ 0:

At the interface between two domains 1 and 2, a continuitycondition was used with the aid of conductivities k1 and k2 definedfor each domain

�n� �k1 ∇T1ð Þ�n� �k2 ∇T2ð Þ ¼ 0:

Fig. 4. Dimensions and geometry of the wave guide and the ferrite bed.

I. Polaert et al. / Journal of Magnetism and Magnetic Materials 374 (2015) 731–739734

3.2. Modeling results and discussion

3.2.1. Influence of the microwave geometryBy varying the shortcut length, it is possible to modify the

electric and magnetic fields distribution and adjust their positionwith respect to the center of the material's bed to be heated. Theeffect of the cavity length was studied between L¼0.40 m andL¼0.48 m with a step of 0.02 m. A length of 0.08 m approximatelyrepresents one half of the wavelength propagating in the guide: itimplies that the electric and magnetic field distributions are thesame for a cavity length modulo of 0.08 m.

Figs. 5 and 6 show the norm of the electric field distribution in thewave guide with respect to the location of the ferrite bed, for twocavity lengths, L¼0.40 m and L¼0.44m, respectively. Similarly,Figs. 7 and 8 show the norm of the magnetic field distribution for

both cavity lengths. In the first case (L¼0.40 m, Fig. 5), the electricfield is centered over the ferrite bed. The maximum value of the normof the electric field is reached at the center of the bed. The field valueis attenuated compared to the one in the waveguide, simply due to themicrowave absorption of the material and its conversion into heat. Atthis position, the norm of the magnetic field is minimal at the centerof the ferrite bed as shown on Fig. 7. On the other hand, when thecavity length is L¼0.44m (Figs. 6 and 8.), the norm of the electric fieldreaches its minimum value at the center of the bed and the norm ofthe magnetic field is then maximum, as shown in Fig. 8.

Of course, the variations of the physico-chemical properties of thematerial with temperature (such as dielectric and magnetic proper-ties, heat capacity, heat conductivity…) have a strong influence onthe fields distribution in the ferrite bed and at the boundaryconditions. But it is important to notice that the irradiation time

Fig. 5. Longitudinal distribution of the electric field norm in the wave guide and the ferrite bed for L¼0.40 m, dbed¼0.03 m, Pi¼50 W, t¼100 s.

Fig. 6. Longitudinal distribution of the electric field norm in the wave guide and the ferrite bed for L¼0.44 m, dbed¼0.03 m, Pi¼50 W, t¼100 s.

I. Polaert et al. / Journal of Magnetism and Magnetic Materials 374 (2015) 731–739 735

does not strongly affect the field distribution in the wave guide in oursimulations. The profiles obtained at t¼100 s are then very similar,whatever the simulation time. This means that the evolution of thephysico-chemical properties of the material with temperature has aweak influence on the fields propagation in the wave guide.

For each of the selected geometry of the wave guide, the heatingresponse of the ferrite was studied with time. The temperaturedistribution in the whole bed was simulated. The absorbed power(Pabs) was calculated using

Pabs Wð Þ ¼ QMWVbed;

where Vbed is the bed volume (m3). The energy yield (Y, in %) isdefined as the absorbed power divided by the incident powerdelivered to the system. The minimum and maximum temperatures(Tmin and Tmax, respectively) within the bed have also been determinedin order to estimate the maximum temperature gradient (ΔTmax)reached in the system, which is an indication on the tempera-ture uniformity. An irradiation power of 50W was first used for all

simulations but was varied as a process parameter (see Section 3.2.4).An irradiation time of 100 s was chosen for all the illustrations.

Figs. 9 and 10 show the temperature profiles in the horizontal andvertical directions at the center of the ferrite bed, where the electricor the magnetic field are centered, respectively. Table 1 outlines thecharacteristic values obtained for different cavity lengths.

When the electric field is centered over the bed (Fig. 9), the highesttemperature is reached on the periphery of the reactor. The tempera-ture is minimal at the center and the maximum thermal gradient isimportant (142 K) within the ferrite bed (Table 1 40 and 48 cm cavitylengths) for 31W of absorbed power. On the other hand, when themagnetic field is centered over the bed, the temperature distribution ismore homogeneous with a maximum temperature gradient of only41 K, with a dissipated power of 33W and with the maximumtemperature in the center or the bed.

These results clearly indicate that the magnetic contribution on theelectromagnetic conversion into heat is predominant for our NiFe2O4

nanoparticles and overcomes the dielectric one. The interaction of the

Fig. 7. Longitudinal distribution of the magnetic field norm in the wave guide and the ferrite bed for L¼0.40 m, dbed¼0.03 m, Pi¼50 W, t¼100 s.

Fig. 8. Longitudinal distribution of the magnetic field norm in the wave guide and the ferrite bed for L¼0.44 m, dbed¼0.03 m, Pi¼50 W, t¼100 s.

I. Polaert et al. / Journal of Magnetism and Magnetic Materials 374 (2015) 731–739736

magnetic field component H with the magnetic NiFe2O4 nanoparticlesis greater than the electric field E one. Both contribute to the sample'sheating but magnetic hysteresis is predominant. This translates into aslightly higher Pabs and yields (Table 1) so into a higher energyabsorption by the medium, and a better temperature homogeneity.

3.2.2. Influence of the bed porosityIn the following sections of this study, the cavity length is fixed

at L¼0.44 m, where the magnetic field is centered on the ferritesample, maximizing the absorbed power and allowing a bettertemperature homogeneity in the ferrite bed.

Bed porosity was considered as an adjustable parameter in oursystem since the way in which the particles are introduced in thereactor and the bed packing will greatly influence its density. Higherporosity (lower ferrite weight for a given volume) will obviously leadto a weaker interaction with the electromagnetic fields.

As shown in Table 2, lowest bed porosities lead to lower tempera-tures inside the bed and higher temperature gradients, due to lower

absorbed powers per ferrite weight. But the main influence of porosityis on the energy absorption: denser beds lead to higher absorbedpowers and energy yields. Considering these tendencies, a bettermicrowave heating of NiFe2O4 nanoparticles is achieved when max-imizing the bed density and the material weight as well, even ifslightly lower temperatures are achieved.

3.2.3. Influence of the bed diameterTable 3 presents the results obtained for several ferrite bed

diameters and their corresponding ferrite weights. Logically, thehighest temperatures and the best temperature homogeneities areobtained for the smallest diameters, for which the entire volume ofthe reactor is exposed to the highest values of the magnetic field. Butin these cases, the absorbed powers and energy yields are quite lowand perhaps not very interesting from an industrial point of view. Bychoosing a larger reactor, the temperature distribution becomes moreheterogeneous because of the larger variations in the fields of theferrite bed volume. The thermal conduction inside the bed cannot

Fig. 9. Temperature distribution in the ferrite bed after t¼100 s of irradiation for L¼0.40 m, dbed¼0.03 m, Pi¼50 W.

Fig. 10. Temperature distribution in the ferrite bed after t¼100 s of irradiation for L¼0.44 m, dbed¼0.03 m, Pi¼50 W.

I. Polaert et al. / Journal of Magnetism and Magnetic Materials 374 (2015) 731–739 737

compensate the very fast local and heterogeneous microwave heatingof the ferrite by magnetic hysteresis. But for larger beds, the absorbedenergy is maximized leading to a noticeable gain in the overall heatingof the ferrite bed.

3.2.4. Influence of the incident power/or the irradiation timeThe heating rate of NiFe2O4 nanoparticles can be easily controlled

under microwaves by varying the incident power and the irradiationtime. It is obvious that bed temperature will increase with longerirradiation times at a given incident power, especially in adiabaticconditions. Wewere interested in temperatures lower than 500 K thatwere typically achieved with irradiation times �100 s. We thereforefixed the irradiation times at 100 s. As mentioned in Section 2.2, thedielectric and magnetic properties were measured only up to 513 K.Extrapolating these results above this temperature would not berigorous considering the high sensitivity of the conversion and thetemperature profiles on these properties.

Table 4 shows the impact of the incident power on the tempera-ture homogeneity and the influence of the heating rate on the energyyield. As expected, high temperatures (around 510 K) can be rapidlyreached by the ferrite nanoparticles with a maximum temperaturegradient of 116 K with 100W of incident power. The energy yield isnot affected by the power applied. It is worth mentioning that thisresult would not be the same by simulating non adiabatic heating ofthe bed: the thermal losses would play a preponderant role atelevated temperatures. These losses are expected to be higher,especially for longer irradiation times. The highest yields would thenbe obtained for faster heating rates, that is to say, shorter irradiationtimes with higher incident powers.

4. Conclusions

Based on finite-element modeling, we demonstrated that thenovel nickel-ferrite NiFe2O4 nanopowder synthesized using induc-tion thermal plasma could be easily and quickly heated to at least513 K under microwaves with a very good efficiency. These calcula-tions show the potential of using ferrites heated by microwave forvarious applications at moderately elevated temperatures (at least upto 513 K). This material absorbs the electromagnetic energy andconverts it into heat very efficiently, permitting very fast heating andminimizing cold start-up in some industrial processes.

The dielectric and magnetic properties of this material wereexperimentally measured at 2.45 GHz and are now available fortemperatures ranging from 293 K to 513 K. Simulations of the adia-batic heating of this Ni-ferrite demonstrate that the interaction of theelectromagnetic field is mainly controlled by the magnetic componentof the field in the studied temperature range (293–513 K). Energyabsorption and conversion into heat are thus maximized where themagnetic field is strongest, although the dielectric losses contribute toa smaller degree to the energy conversion and heating. However, themagnetic losses decline with temperatures approaching the Curietemperature and, based on the measured trends, the electric lossesappear to increase with temperature. Therefore, with higher tempera-tures, the contribution of the electric losses to the heat conversionshould increase. By continuously tuning the cavity during the micro-wave process, it would be possible to take advantage of thebi-functionality of this material from room to high temperature andtherefore maximize the heat conversion of the microwaves for alltemperatures.

Acknowledgments

The authors want to thank J. Gauvrit, E. Receveur, M. Diakhite,J. Renaux and V. Lemarchand, students in chemical engineering andrisk management at INSA Rouen, France, for their contribution to thepermeability measurements and the modeling part of this work.The authors are grateful to the Natural Sciences and EngineeringResearch Council of Canada for support of this research.

References

[1] K.E. Sickafus, J.M. Wills, N.W. Grimes, Structure of spinel, J. Am. Ceram. Soc. 82(1999) 3279–3292.

[2] M.D. Allendorf, R.B. Diver, N.P. Siegel, J.E. Miller, Two-step water splitting usingmixed-metal ferrites: thermodynamic analysis and characterization of synthe-sized materials, Energy Fuels 22 (2008) 4115–4124.

[3] C. Nordhei, K. Mathisen, I. Bezverkhyy, D. Nicholson, Decomposition of carbondioxide over the putative cubic spinel nanophase cobalt, nickel, and zincferrites, J. Phys. Chem. C 112 (2008) 6531–6537.

[4] M. Sturzenegger, L. D'Souza, R. Struis, S. Stucki, Oxygen transfer and catalyticproperties of nickel iron oxides for steam reforming of methane, Fuel 85(2006) 1599–1602.

Table 1Influence of the cavity length on maximum and minimum temperatures, absorbedpower and energy yield. dbed¼0.03 m, ϵbed¼0.63, Pi¼50 W, t¼100 s

Cavity length (cm) Tmin (K) Tmax (K) Pabs (W) ΔT max(K) Yield (%)

40 323 465 31 142 6242 333 454 32 121 6444 368 409 33 41 6646 340 433 32 93 6448 323 465 31 142 62

Table 2Influence of the bed porosity on maximum and minimum temperatures, absorbedpower and energy yield. L¼0.44 m, dbed¼0.03 m, Pi¼50 W, t¼100 s.

Bed porosity(dimension less)

Ferriteweight, m(kg)

Tmin

(K)Tmax

(K)Pabs(W)

Pabs/m(W/kg)

DTmax(K)

Yield(%)

0.5 0.0485 342 403 39.6 816 61 790.6 0.0388 358 416 32.9 848 58 660.7 0.0291 365 421 28.3 972 56 570.8 0.0194 372 425 20.5 1057 53 41

Table 3Influence of the bed diameter on maximum and minimum temperatures, absorbedpower and energy yield. L¼0.44 m, ϵbed¼0.63, Pi¼50 W, t¼100 s.

Bed diameter(m)

Ferrite weight(kg)

Tmin

(K)Tmax

(K)Pabs(W)

ΔTmax(K)

Yield(%)

0.015 0.0097 384 411 9 27 180.020 0.0172 381 412 16 31 320.025 0.0269 376 412 24 36 480.030 0.0388 368 409 33 41 660.035 0.0528 355 401 41 46 820.040 0.0690 338 395 45 57 90

Table 4Influence of the incident power on maximum and minimum temperatures,absorbed power and energy yield. L¼0.44 m, ϵbed¼0.63, dbed¼0.03 m, t¼100 s.

Incident power (W) Tmin (K) Tmax (K) Pabs (W) ΔT max(K) Yield (%)

10 310 323 6.5 13 6630 343 371 20 28 6650 368 409 33 41 66

100 430 546a 66 116 66

a Order of magnitude.

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