Decrease in the Crystallite Diameter of Solid Crystalline Magnetite Around the Curie Temperature by Microwave Magnetic Fields Irradiation

nanomaterials

Article Decrease in the Crystallite Diameter of Solid Crystalline Magnetite around the Curie Temperature by Microwave Magnetic Fields Irradiation

Takayuki Tsuchida * , Jun Fukushima and Hirotsugu Takizawa

School of Engineering, Department of Applied Chemistry, Tohoku University, Sendai 980-8578, Japan; [email protected] (J.F.); [email protected] (H.T.) * Correspondence: [email protected]; Tel.: +81-22-795-7226

Abstract: A decrease in the crystallite diameter of ferrites irradiated with microwaves has been considered as a non-thermal effect of so-called de-crystallization; however, its mechanism has not been elucidated. We hypothesized that a decrease in the crystallite diameter is caused by interaction between the ordered spins of ferrite and the magnetic ﬁeld of microwaves. To verify this, we focused on magnetite with a Curie temperature of 585 ◦C. Temperature dependence around this temperature and time dependence of the crystallite diameter of the magnetite irradiated with microwaves at different temperatures and durations were investigated. From the X-ray diffraction data, the crystallite diameter of magnetite exhibited a minimum value at 500 ◦C, just below the Curie temperature of magnetite, where the energy loss of the interaction between magnetite’s spins and the

microwaves takes the maximum value. The crystallite diameter exhibited a minimum value at 5 min irradiation time, during which the microwaves were excessively absorbed. Transmission electron

Citation: Tsuchida, T.; Fukushima, J.; microscopy observations showed that the microstructure of irradiated magnetite in this study was Takizawa, H. Decrease in the different from that reported previously, indicating that a decrease in the crystallite diameter is not Crystallite Diameter of Solid caused by de-crystallization but its similar phenomenon. A decrease in coercivity and lowering Crystalline Magnetite around the temperature of Verwey transition were observed, evidencing decreased crystallite diameter. This Curie Temperature by Microwave study can thus contribute to the development of the theory of a non-thermal effect. Magnetic Fields Irradiation. Nanomaterials 2021, 11, 984. https:// Keywords: de-crystallization; microwave processing; magnetite; Curie temperature; non-thermal doi.org/10.3390/nano11040984 effects; ferrites

Academic Editor: Jorge Pasán

Received: 17 February 2021 1. Introduction Accepted: 9 April 2021 Microwave processing exhibits some unique features, such as rapid heating, rapid Published: 11 April 2021 cooling, and selective heating, which are different from conventional processing using an electric furnace. Thus, microwave heating provides many benefits for material processing, Publisher’s Note: MDPI stays neutral such as decreasing the sintering time, synthesizing functionalized nanomaterials, and with regard to jurisdictional claims in published maps and institutional affil- promoting catalytic reactions [1–9]. Additionally, “non-thermal effects”, phenomena of iations. which cannot be explained by thermal effects, have also been reported [10–17]. In the case of solid-state reactions, reported non-thermal effects include promoting the reduction of oxides [10,11], nitriding [12], as well as anisotropic growth [13]. Although these studies indicate unique phenomena due to microwave processing, non-thermal effects are controversial because the mechanism of many of them has still not been clarified. Copyright: © 2021 by the authors. De-crystallization is one of the phenomena considered to be a non-thermal effect [18–26]. Licensee MDPI, Basel, Switzerland. This phenomenon was first discovered by Kimura et al. in 2000; X-ray diffraction showed This article is an open access article distributed under the terms and halo patterns for ferrites irradiated with 28 GHz frequency [18]. In addition to ferrites, de- conditions of the Creative Commons crystallization of n-type Si [22,23], TiO2−x, and Ti0.98Mn0.02O2−x [24] have been reported. Attribution (CC BY) license (https:// Takayama et al. used transmission electron microscopy to investigate the microstructure of creativecommons.org/licenses/by/ magnetite (Fe3O4) irradiated with microwaves, and a 5–20 nm nanodomain structure was 4.0/). observed [25]. In particular, de-crystallization of the ferrites by microwave irradiation is

Nanomaterials 2021, 11, 984. https://doi.org/10.3390/nano11040984 https://www.mdpi.com/journal/nanomaterials Nanomaterials 2021, 11, 984 2 of 9

considered as a non-thermal effect for the following two reasons [21]: First, de-crystallization does not occur via the liquid phase. Second, de-crystallization irradiated with an electric field of microwaves in the single-mode cavity has not been confirmed despite the same temperature processing. These results suggest that de-crystallization is a non-thermal effect; however, the mechanism of de-crystallization has not been determined. We hypothesized that de-crystallization of the ferrites is caused by an interaction between the ordered spins of ferrites and a microwave magnetic field because this phenomenon only occurs under the magnetic field of the single-mode cavity. To verify this hypothesis, the authors focused ◦ on magnetite, with a Curie temperature, TC, of 585 C as the ferrite and investigated the temperature dependence of the interaction between the ordered spins of magnetite and a microwave magnetic field. As a result, a decrease in the crystallite diameter of magnetite was observed, which is not considered to be de-crystallization but its similar phenomenon. In addition, the effect of the duration of microwave irradiation on the crystallite diameters of magnetite was investigated to understand the dynamics of this phenomenon.

2. Materials and Methods Figure1a shows a schematic view of the experimental setup used in this study. We used a 2.45 GHz microwave furnace (Shikoku Instrumentation Co., Ltd., Kagawa, Japan), as used in [16,27], in which a microwave was generated from a magnetron and passed through a TE10 waveguide to a cylindrical applicator (Ø 132 × 200 mm). In the applicator, the H-field and E-field components of microwaves have different distributions, and we used the 3 cm height position where the H-field amplitude was at its maximum. For the raw materials, we selected magnetite powders that exhibit de-crystallization phenomena [21]. Magnetite powder (0.3 g) (99% purity, 1 mm pass, Kojundo Chemical Lab. Co., Saitama, Japan) was placed in a Ø 10 × 8 mm quartz tube and sealed with quartz wool. The tube was surrounded by an alumina insulator. The microwave cavity was evacuated using a rotary pump and subsequently filled with nitrogen gas. A Proportional-Integral- Differential (PID) controller was used to automatically adjust the microwave power to the desired temperature, which was measured using a thermocouple. Each sample was heated from room temperature to a certain constant temperature, which was chosen in the range of 200–1100 ◦C, for a certain duration, which was chosen in the range of 0.2– 60 min, after heating at 900 ◦C/min. After the holding time, the samples were naturally cooled by deactivating the microwave power. As an example, the temperature and power profiles of heating at 500 ◦C for 60 min are shown in Figure1b. The samples irradiated with microwaves were characterized by X-ray diffraction (XRD) with a Co Kα source (λ = 1.78900 Å), and the crystallite diameters, which is the size of single-crystal regions, of the samples were calculated using the Scherrer equation. The microstructure of the samples irradiated with microwaves was observed by transmission electron microscopy (TEM), and the magnetic properties of the resulting samples were evaluated by superconducting quantum interference device (SQUID) measurements. Nanomaterials 2021, 11, x FOR PEER REVIEW 3 of 9

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Figure 1. (a) Schematic of the experimental setup; (b) Temperature and microwave power profile during processing. Figure 1. (Figurea) Schematic 1. (a) Schematic of the experimental of the experimental setup; (b) Temperaturesetup; (b) Temperature and microwave and microwave power profile power during profile processing. during processing.3. Results 3.1.3. Structure Results 3. Results 3.1. Structure Figure 2a shows the XRD profiles of the samples irradiated with microwaves at var- 3.1. Structure ious temperaturesFigure2a shows from 200 the to XRD 1100 profiles °C for 5 of min. the Diffraction samples irradiated peaks due with to magnetite microwaves were at ◦ Figureclearly 2avarious shows observed temperaturesthe XRD in theprofiles samples from of 200the irradiated tosamples 1100 wiCirradiatedth for microwaves 5 min. with Diffraction microwaves and the peaks raw at material. duevar- to magnetite How- were clearly observed in the samples irradiated with microwaves and the raw material. ious temperaturesever, diffraction from 200 peaks to 1100 due °C to for hematite 5 min. Diffraction(α-Fe2O3) were peaks only due observed to magnetite in samples were irradiated clearly observedHowever, in the samples diffraction irradiated peaks duewith to microwaves hematite (α and-Fe2 Othe3) raw were material. only observed How- in samples with microwaves above 300 °C, indicating◦ partly oxidized samples. Figure 2b shows the ever, diffractioncrystalliteirradiated peaks diameter due with to microwaveshematite of the ma (αgnetite-Fe above2O3 irradiated) were 300 onlyC, indicating with observed microwav partly in sampleses oxidized calculated irradiated samples. from the Figure main2 b with microwavespeaksshows of above magnetite the crystallite 300 °C, using indicating diameter the Scherrer ofpa thertly equation. magnetite oxidized From irradiatedsamples. the results,Figure with microwaves 2b the shows crystallite the calculated diameter from crystallite diameterof the mainsamples of the peaks mahasgnetite of a magnetiteminimum irradiated usingvalue with theof microwav33.1 Scherrer nm at equation.es 500 calculated °C, Fromwhich from the is thesignificantly results, main the crystallite lower diameter of the samples has a minimum value of 33.1 nm at 500 ◦C, which is significantly peaks of magnetitethan that using of the the raw Scherrer material equation. and samples From irradiated the results, with the microwavescrystallite diameter at other tempera- lower than that of the raw material and samples irradiated with microwaves at other of the samplestures. has Therefore, a minimum the decrease value of in 33.1 the nmcrystallit at 500e diameter°C, which of is magnetite significantly occurred lower most at 500 than that of thetemperatures. raw material Therefore, and samples the irradiated decrease in with the microwaves crystallite diameter at other oftempera- magnetite occurred °C. ◦ tures. Therefore,most the at decrease 500 C. in the crystallite diameter of magnetite occurred most at 500 °C.

FigureFigure 2. ( 2.a) (XRDa) XRD patterns patterns of the of the samples samples irradiated irradiated with with microwave microwave at different at different temperatures temperatures for for 5 5 min;min; (b (b) Crystallite) Crystallite diameter diameter of of the the magnetite magnetite calculated calculated by by the the Scherrer Scherrer equation equation as asa function a function of of Figure 2. (a)irradiation XRDirradiation patterns temperature. temperature. of the samples irradiated with microwave at different temperatures for 5 min; (b) Crystallite diameter of the magnetite calculated by the Scherrer equation as a function of irradiation temperature.Figure 3a shows the XRD proﬁles of the samples irradiated with microwaves at 500 ◦C for various durations from 0.2 to 60 min. Magnetite was observed in all samples, including

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Figure 3a shows the XRD profiles of the samples irradiated with microwaves at 500 °C for various durations from 0.2 to 60 min. Magnetite was observed in all samples, including the raw material, and the hematite phase was observed in all samples irradiated with microwaves. The crystallite diameter of the microwave-irradiated magnetite, as shown in Figure 3b, indicated that the minimum value was exhibited for a 5 min duration. Nanomaterials 2021, 11, x FOR PEER REVIEW 4 of 9

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Figure 3a shows the XRD profiles of the samples irradiated with microwaves at 500 °C for various durations from 0.2 to 60 min. Magnetite was observed in all samples, in- cludingthe raw the material,raw material, and theand hematitethe hematite phase ph wasase was observed observed in allin samplesall samples irradiated irradiated with withmicrowaves. microwaves. The The crystallite crystallite diameter diameter of the of microwave-irradiated the microwave-irradiated magnetite, magnetite, as shown as in shownFigure in 3Figureb, indicated 3b, indicated that the that minimum the mini valuemum was value exhibited was exhibited for a 5 for min a duration.5 min duration.

Figure 3. (a) XRD patterns of the samples irradiated with microwave at 500 °C for various durations; (b) Crystallite diameter of the magnetite calculated by the Scherrer equation as a function of irradiation time.

FigureFigure 3. (a 3.) XRD(a) XRD patterns patterns of the of samples the samples irradiated irradiated with withmicrowave microwave at 500 at °C 500 for◦ variousC for various dura- dura- tions;Here,tions; (b) (Crystallitebwe) Crystallite discuss diameter diameter whether of the of themagnetite the magnetite decrease calculated calculated in by th the bye crystallite theScherrer Scherrer equation equationdiameter as a asfunction a of function magnetite of of irra- diatedirradiationirradiation with time.microwaves time. is a non-thermal effect. One can consider that it may be caused by a decrease of the lattice volume accompanied by the reduction of the magnetite [28]. Here,Here, we wediscuss discuss whether whether the thedecrease decrease in th ine the crystallite crystallite diameter diameter of magnetite of magnetite irra- irra- Although the lattice constants of the magnetite irradiated with microwaves were slightly diateddiated with with microwaves microwaves is a is non-thermal a non-thermal effect effect.. One One can can consider consider that that it may it may be becaused caused decreased,by bya decrease a decrease suggesting of the of the lattice the lattice volumereduction volume accompan accompanied of magnetitied by bythee,the reductionthe reduction decrease of the of the inmagnetite the magnetite lattice [28]. [28 constant]. of the AlthoughmagnetiteAlthough the theis lattice estimated lattice constants constants to of be the of no the magnetite higher magnetite irradiatedthan irradiated 0.4%. with Therefore, with microwaves microwaves the were decrease were slightly slightly in the crys- tallitedecreased,decreased, diameters, suggesting suggesting as shown the thereduction in reduction Figures of magnetit of 2b magnetite, ande, 3b, the the cannotdecrease decrease be in explainedthe in the lattice lattice constant by constant a decrease of of in the latticethethe magnetiteconstant magnetite isand estimated is estimated caused to beby to beno a nodivisionhigher higher than thanof 0.4%. the 0.4%. totalTherefore, Therefore, volume the thedecrease into decrease more in the in crystallites thecrys- crys- with a tallitetallite diameters, diameters, as shown as shown in Figures in Figures 2b and2b and3b, 3cannotb, cannot be explained be explained by a bydecrease a decrease in the in consequent increase in the number of grain boundaries as shown in Figure 4. In addition, latticethe constant lattice constant and caused and causedby a division by a division of the total of thevolume total into volume more into crystallites more crystallites with a the consequenttemperaturewith a consequent increase during in increase the processing number in the of numbergrain is considerably bo ofundaries grain boundaries as lowershown inthan as Figure shown the 4. melting inIn Figureaddition, 4point. In of magnetitethe addition, (1597temperature °C), the indicating temperatureduring processing that during it is processingdoes considerably not o isccur considerably lower via than the the lowerliquid melting than phase. thepoint melting Therefore, of mag- point it is con- ◦ siderednetiteof magnetitethat(1597 the°C), (1597decreaseindicatingC), indicatingthatin the it does crystallite that not itoccur does divia notameter the occur liquid of via phase.magnetite the liquid Therefore, phase. was it Therefore,caused is con- by a non- it is considered that the decrease in the crystallite diameter of magnetite was caused by a thermalsidered effect. that the decrease in the crystallite diameter of magnetite was caused by a non- thermalnon-thermal effect. effect.

Figure 4. Schematic view of a decrease in the crystallite diameter. FigureFigure 4. Schematic 4. Schematic view view of ofa adecrease decrease inin thethe crystallite crystallite diameter. diameter.

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Figure 5a shows a transmission electron microscopy (TEM) image of the sample irra- Figure5a shows a transmission electron microscopy (TEM) image of the sample diated with microwaves at 500 °C◦ for 5 min. From the image, the sample was composed irradiatedof 0.1–1 mm with size microwaves grains. Figure at 500 5bC forshows 5 min. the From selected the image,area electron the sample diffraction was composed (SAED) ofpatterns 0.1–1 mm of the size magnetite grains. Figuregrains.5 bNo shows ring pa thettern selected derived area from electron the 5–20 diffraction nm nanodomain (SAED) patternsstructure of was the magnetiteobserved, grains.as in a Noprevious ring pattern study [25]. derived Considering from the 5–20that nmthe nanodomainXRD patterns structure was observed, as in a previous study [25]. Considering that the XRD patterns from from crystalline magnetite were observed, it indicates that a decrease in the crystallite crystalline magnetite were observed, it indicates that a decrease in the crystallite diameter diameter of microwave irradiated magnetite is not de-crystallization but its similar phe- of microwave irradiated magnetite is not de-crystallization but its similar phenomenon, nomenon, and the crystallite diameter of magnetite in this study is larger than that re- and the crystallite diameter of magnetite in this study is larger than that reported previously. ported previously. The difference in the crystallite diameters will be discussed in detail The difference in the crystallite diameters will be discussed in detail later. later.

Figure 5. (a) TEM image of the sample irradiated with microwaves at 500 °C for 5 min; (b) Selected Figure 5. (a) TEM image of the sample irradiated with microwaves at 500 ◦C for 5 min; (b) Selected area electron diffraction (SAED) patterns of the magnetite grains. area electron diffraction (SAED) patterns of the magnetite grains.

3.2.3.2. MagneticMagnetic PropertiesProperties ToTo obtain obtain evidence evidence of of the the decrease decrease in in the the crystallite crystallite diameter, diameter, the the magnetic magnetic properties properties ofof the the samples samples irradiated irradiated with with microwaves microwaves were were investigated. investigated. First, First, the the authors authors measured measured thetheM M-H-Hloops loops at at room room temperature temperature for for the the raw raw material material and and the the sample sample irradiated irradiated with with microwavesmicrowaves at at 500 500◦ C°C for for 5 5 min, min, as as shown shown in in Figure Figure6a. 6a. An An enlarged enlarged view view of the of coercivitiesthe coercivi- isties shown is shown in Figure in Figure6b. Here,6b. Here, the the magnetization magnetization of theof the samples samples shown shown in in Figure Figure6 is 6 is normalizednormalized withwith saturationsaturation magnetization.magnetization. TheThe resultsresults showshow thatthat thethe coercivitycoercivity ofof thethe samplesample irradiated irradiated with with microwaves microwaves was was smaller smaller than than that that of of the the raw raw material. material. This This result result indicatesindicates that that the the thermal thermal agitation agitation resistance resistance of theof the magnetization magnetization of microwave-irradiated of microwave-irradi- magnetiteated magnetite is lower is thanlower that than of thethat raw of material,the raw material, resulting resulting from a decrease from a in decrease the crystallite in the diametercrystallite of diameter the sample of the irradiated sample irradiated with microwaves. with microwaves. Secondary, Secondary, zero-field zero-field cooling (ZFC) cool- curvesing (ZFC) of the curves sample of irradiatedthe sample with irradiated microwaves with atmicrowaves 500 ◦C for 5at min 500 and°C for the 5 raw min material and the wereraw material also measured were also under measured 10 Oe appliedunder 10 field, Oe applied as shown field, in Figureas shown7. The in Figure differential 7. The coefficientsdifferential ofcoefficients magnetization of magnetization (dM/dT) plotted (dM/d asT) a plotted function as ofa function temperature of temperature are shown are in Figureshown7. in Raw Figure material 7. Raw exhibited material a characteristicexhibited a characteristic peak of d M/d peakT at of 105 dM K./d However,T at 105 K. aslight How- peakever, shift a slight of dM peak/dT shiftto 100 of K d wasM/d observedT to 100 K in was the caseobserved of the microwave-irradiatedin the case of the microwave- sample. Theseirradiated peaks sample. can be These explained peaks by can Verwey be explain transitioned by Verwey and metal-insulator transition and transition metal-insulator of the magnetite.transition of Lee the et magnetite. al. reported Lee that etthe al. Verweyreported transition that the Verwey temperature transitionTV is temperature dependent on TV theis dependent crystallite diameteron the crystallit of magnetitee diameter in the of nanosizedmagnetite rangein the andnanosized that TV rangedecreases and that when TV thedecreases crystallite when diameter the crystallite of magnetite diameter decreases of magnetite [29]. Therefore, decreases it[29]. is considered Therefore, thatit is con- the decreasesidered that in the theT Vdecreaseof the microwave-irradiated in the TV of the microwave-irradiated sample is due to asample decrease is due in the to crystallitea decrease diameter,in the crystallite which corresponds diameter, which to the corresponds XRD measurement. to the XRD measurement.

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FigureFigure 6. 6. ( a(()a a)M) MM-H-H- Hloops loopsloops measured measured measured at at 300 at300 300 K K of of K the ofthe raw the raw rawmateri materi materialalal and and the and the sample sample the sample irradiated irradiated irradiated with with mi- withmi- ◦ crowavemicrowavecrowave at at 500 at500 500°C °C for forC 5 for 5min; min; 5 min; ( b(b) )the ( bthe) theenlarged enlarged enlarged view view view around around around the the thecoercivities. coercivities. coercivities.

FigureFigure 7. 7.7. Zero Zero field ﬁeldfield cooling coolingcooling curve curvecurve of ofof the thethe ( a((a)a ))raw rawraw material materialmaterial and andand ( (b(bb)) )sample samplesample irradiated irradiatedirradiated with with with micro- microwave microwave(MW)wave (MW) (MW) at 500 at ◦at C500 500 for °C 5°C min.for for 5 5 Themin. min. differentials The The differentials differentials of the of magnetization of the the magnetization magnetization dM/d Td dMasM/d a/dT functionT as as a afunction function of temperature of of tem- tem- peratureareperature also are inserted. are also also inserted. inserted.

4.4. Discussion Discussion TheThe mechanism mechanismmechanism of ofof the thethe decrease decrease in in thethe the crystallitecrysta crystallitellite diameterdiameter diameter of of of magnetite ma magnetitegnetite is is discussedis discussed discussed in inthisin this this section. section. section. First, First, First, we we we considered considered considered the the the temperature te temperaturemperature dependence dependence dependence of of of the the the crystallite crystallite crystallite diameter. diame- diame- ter.Accordingter. According According to to Roy to Roy Roy et et al.,et al., al., de-crystallization de-crystallizatio de-crystallization ofn of of magnetite magnetite magnetite occursoccurs occurs onlyonly only at at the thethe maximum maximummaximum intensityintensityintensity of ofof the thethe microwave microwavemicrowave magnetic magneticmagnetic field fieldfield in inin a aa single-mode single-modesingle-mode cavity cavitycavity [21]. [[21].21]. From FromFrom this, this,this, it itit is isis consideredconsidered that thatthat the thethe decrease decrease inin in thethe the crystallitecrystallite crystallite diameter diameter diameter is is dueis due due to to theto the the interaction interaction interaction between between between the thespinsthe spins spins of magnetiteof of magnetite magnetite and and and the the magneticthe magnetic magnetic field field field of theof of the microwaves.the microwaves. microwaves. Tanaka Tanaka Tanaka et al.et et simulatedal. al. simulated simulated the theenergythe energy energy loss loss loss based based based on on the on the interactionthe interaction interaction between betw between theeen the spinthe spin spin of theof of the magnetitethe magnetite magnetite and and theand the magneticthe mag- mag- field of microwaves and reported that the energy loss takes a maximum value at 500 ◦C, less neticnetic field field of of microwaves microwaves and and reported reported that that the the energy energy◦ loss loss takes takes a a maximum maximum value value at at 500 500 than the Curie temperature of magnetite (TC = 585 C) [30]. We hypothesize that the reason °C,°C, less less than than the the Curie Curie te temperaturemperature of of magnetite magnetite ( T(TC C= = 585 585 °C) °C) [30]. [30]. We We hypothesize hypothesize that that why the crystallite diameter of magnetite most decreased at 500 ◦C was that the energy loss thethe reason reason why why the the crystallite crystallite diameter diameter of of magnetite magnetite most most decreased decreased at at 500 500 °C °C was was that that of the interaction between the spin of the magnetite and magnetic field of microwaves was thethe energy energy loss loss of of the the interaction interaction between between the the spin spin of of the the magnetite magnetite and and magnetic magnetic field field of of largest at 500 ◦C. Consequently, microwave energy was efficiently absorbed by magnetite.

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Most of the absorbed energy is relaxed to thermal energy. However, grain growth will only occur by thermal energy because of the minimization of the boundary energy of the system if sufficient thermal energy is supplied. In a previous study, Fukushima et al. assumed that the grain boundary was formed by H-field irradiation to form a nanodomain structure resulting from the de-crystallization phenomena. If this assumption is correct, we require additional energy for forming grain boundaries [31]. We focused on the time dependence of the crystallite diameter to investigate the additional energy required to form grain boundaries. As shown in Figure3b, the crystallite diameter of the magnetite increased as the irradiation duration increased after 5 min. Focusing on the power profile of the microwave irradiation at 500 ◦C for 60 min, as shown in Figure1b, it is observed that the power of the first 5 min was unstable. Then, the power gradually reached a constant value of approximately 600 W. From these results, it is assumed that the absorbed energy from microwaves was used to form grain boundaries, not via thermalization. The decrease in the crystallite diameter occurred only for the first 5 min; nevertheless, microwave energy was used only to maintain the temperature, and the crystallite diameter of magnetite increased over a duration of more than 5 min. Thus, it is suggested that the decrease in the crystallite diameter of magnetite occurred when the energy loss of the interaction between the spin of the magnetite and the magnetic field of microwaves was directly converted into the formation of grain boundaries. It is sure that the decrease of the crystallite diameter by microwave irradiation was confirmed, a clear difference was acknowledged between the previous study and this study. One of the difference is that the temperature at which the crystallite diameter of the magnetite decreased was considerably lower than that reported in a previous study (>1000 ◦C), and the crystallite diameter of the magnetite was larger than that of de-crystallized magnetite reported in the previous study [25]. The other is the coercivity of the sample irradiated with microwaves. In the study, the value of the coercivity of the sample irradiated with microwaves was around 100 Oe, but the value was around 1.1 Oe in the previous study [32]. These differences may be caused by a significant difference in the microwave cavity because the TE103 single-mode cavity was used for microwave irradiation in the previous study. This difference in the cavities leads to a difference in the quality factor of the cavity, and it is considered that the high-quality factor of the TE103 cavity results in a greater decrease in the crystallite diameter of the magnetite than that of the 2.45 GHz microwave cavity used in this experiment. Further study is required to understand the effect of irradiation methods on the microstructure of the materials by comparison with the quality factor of the cavities.

5. Conclusions In this study, the authors investigated the effects of the irradiation temperature and duration of microwave irradiation on the decrease in the crystallite diameter of magnetite. Consequently, in terms of temperature dependence, the crystallite diameter of the magnetite reaches its minimum value at 500 ◦C, when the energy loss of the interaction between the magnetite spin and the microwave magnetic field becomes maximum. This result indicates that the decrease in the crystallite diameter of magnetite is caused by the interaction between the spin and the magnetic field. In terms of time dependence, it is confirmed that the crystallite diameter of magnetite takes a minimum of 5 min at 500 ◦C irradiation. Based on this result and the power profile of microwave irradiation, it is suggested that the decrease in the crystallite diameter occurs such that the part of energy loss of the interaction between the spin of magnetite and magnetic field of the microwave is directly converted into the formation of grain boundaries. The TEM image and XRD patterns indicate that magnetite irradiated with microwaves in this study is different from that of the de-crystallized magnetite as shown in the previous study, which may be caused by the difference in the microwave cavity. The sample irradiated with microwaves exhibited lower coercivity, and the Verwey transition shifted to a lower temperature compared to the raw material, which can be evidence of the decrease in the crystallite diameter of magnetite. Nanomaterials 2021, 11, 984 8 of 9

The new knowledge of the interaction between microwaves and materials suggested in this study will contribute to the further development of the theory of the non-thermal effect. Future work is required to support this consideration; for example, a theoretical approach using dynamical simulation is necessary.

Author Contributions: Conceptualization, T.T. and J.F.; methodology, T.T. and J.F.; validation, T.T. and J.F.; investigation, T.T.; data curation, T.T.; writing—original draft preparation, T.T.; writing— review and editing, T.T., J.F., and H.T.; visualization, T.T.; supervision, H.T.; project administration, H.T.; funding acquisition, J.F. and H.T. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by a JSPS KAKENHI Grant-in-Aid for Scientific Research (S) Number JP19H05612. Acknowledgments: This work was supported by JSPS KAKENHI Grant-in-Aid for Scientific Re- search (S) Number JP19H05612. The measurements of permittivity were performed at Center for Low Temperature Science, Tohoku University. Conflicts of Interest: The authors declare no conflict of interest.

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