Microstructure, dielectric and microwave features of [Ni0.4Cu0.2Zn0.4](Fe2−xTbx)O4 (x ≤ 0.1) nanospinel ferrites

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https://www.journals.elsevier.com/journal-of-materials-research-and-technology Availableonlineatwww.sciencedirect.com

Original

Article

Microstructure,

dielectric

and

microwave

features

of

[Ni

0.4

Cu

0.2

Zn

0.4

](Fe

2 −x

Tb

x

)O

4

(x

≤

0.1)

nanospinel

ferrites

M.A.

Almessiere

a,∗

_,

_Y.

_Slimani

a,∗

_,

_B.

_Unal

b

_,

_T.I.

_Zubar

c,d

_,

_A.

_Sadaqat

e

_,

A.V.

Trukhanov

c,d,f

_,

_A.

_Baykal

g

a_Department_of_Biophysics,_Institute_of_Research_and_Medical_{Consultations}_(IRMC)_Imam_Abdulrahman_Bin_Faisal_University,_P.O._BOX

1982,31441,Dammam,SaudiArabia

b_Institute_of_Forensic_Sciences_and_Legal_Medicine,_Institute_of_{Nanotechnology}_and_{Biotechnology,}_Istanbul_University_–_Cerrahpasa,

BuyukcekmeceCampus,34500Buyukcekmece–Istanbul,Turkey

c_SSPA_{“Scientiﬁc}_and_Practical_Materials_Research_Centre_of_NAS_of_Belarus”,_19,_P._Brovki_str.,₂₂₀₀₇₂_Minsk,_Belarus d_South_Ural_State_University,_76,_Lenina_ave._454080,_Chelyabinsk,_Russia

e_Department_of_Mechanical_and_Energy_Engineering,_Engineering_Faculty,_Imam_Abdulrahman_Bin_Faisal_University,_P.O._Box_1982,

31441Dammam,SaudiArabia

f_National_University_of_Science_and_Technology_MISiS,_4,_Leninsky_Prospekt_119049,_Moscow,_Russia

g_Department_of_{Nanomedicine,}_Institute_of_Research_and_Medical_{Consultations}_(IRMC)_Imam_Abdulrahman_Bin_Faisal_University,_P.O.

BOX1982,31441,Dammam,SaudiArabia

a

r

t

i

c

l

e

i

n

f

o

Articlehistory:

Received20June2020 Accepted27July2020 Availableonline8August2020

Keywords: Nanomaterials Spinelferrites Microstructure Microwaveproperties

Domainboundariesresonance Electricalproperties

a

b

s

t

r

a

c

t

Tb-substitutedNi0.4Cu0.2Zn0.4TbxFe2−xO4(0.0≤x≤0.10)nanospinelferriteswereformedby

sonochemicaltechnique.Itwasfirsttimeestablishedcorrelationbetweenchemical com-positionofthenanosizedNiCuZnspinelsandtheirstructural,electricalandmicrowave properties.Thestructureofnanospinelferrites(NSFs)wasprovedthroughXRD. Microstruc-turalwereanalyzedfromSEM.Itwasobserveda non-lineardependenceoftheaverage grainsizewithTbconcentration.Theconductionmechanismanddielectricfunctionhas beenextensivelystudiedasfunctionsoffrequency,temperature,andTbionssubstitution ratiousingcompleximpedancespectroscopy.Itisobvioustoseethatthesubstitutionsratio showedasubstantialinfluenceondielectricfeatures,whileTbionsubstitutionhaslittle butnotableeffectonAC/DCconductivitychange.FromtheArrheniusplots,theactivation energiesforallsubstitutionratioswerecalculated.Thereflectionlossesasafunction fre-quencydependencesofthewerecalculatedfromS-parametersdatawithin1–4.5GHz.The occurrencesoftheelectromagneticabsorptioninthefrequencyintervalof1.85–3.79GHz wereobserved.Non-linearbehaviouroftheamplitude–frequencyfeatureswereverifiedas afunctionofthelevelofchemicalsubstitution(x)withTbionsconcentration.Itwasfound

∗ _{Corresponding}_authors.

E-mails:malmessiere@iau.edu.sa(M.Almessiere),yaslimani@iau.edu.sa(Y.Slimani). https://doi.org/10.1016/j.jmrt.2020.07.094

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j mater res technol.2020;9(5):10608–10623

10609

microstructuralparameters correlateswell withthe mainabsorptioncharacteristics. It was discussed the nature of the electromagnetic absorption for partially substituted nanospinels.Thedeclineofthereﬂectedelectromagneticradiationswasexplicatedalong withdomain-boundaryresonance,whichwellcorrelateswiththemicrostructuredata.The lowdimensionalmagneticoxideshavingthedomain-boundaryresonancehavearolein natureofabsorption.

1. Introduction

Ferritematerialstakeimmenseimportanceduetotheir out-standingelectricandmagneticpropertiesandtheiruses in diverse applications suchas microwave devices,electronic filter, power generation, magnetic switches, electrochemi-caland memory elements forcomputers [1,2]. Particularly, nano-sized spinelferrites take a great concern because of their exclusive features. Thenano-magnetic spinelferrites are very stable in engineering and technological applica-tionslikeinformationstoragesystems,high-frequencypower devices, radar-absorbing materials, pharmaceuticals, drug delivery,medicaldiagnostic,microwaves,sensors,rod anten-nas, transformercores, high-quality filters, radiofrequency, biomedicine,magneticcores,andmagneticresonance imag-ing, etc. [3–5]. Recently, many investigations have been accomplished on the production of NiCuZn nanoferrites withoutstandingelectro-magnetic properties [6].Ni–Zn–Cu ferrites can also be used for transformer cores, recording heads, and multilayer chip inductor, etc. [7]. Liu et al. [8] integrated the radio frequency by preparing thin films of Ni0.4Zn0.4Cu0.2Fe2O4.Nam et al.[9]. Improvedthe electrical

resistivityandsaturationmagnetizationwiththeadditionof Cu=0.2withinNiZnspinelferritenanoparticles.Diverse pro-cesseshavebeenemployedinpreparingNiCuZnnanospinel ferritesincludingreversemicelle[10],sol–gel[8],citrate pre-cursor[11]solid-statereaction[12],friendlygelatinprecursor [13],andhydrothermal method[14], etc.Inallthese meth-ods, the ﬁnal productdepends upon the crystallinity, size distribution, and reaction parameters like time, precursor type,temperature,andsolvent,etc.[15,16].Amongthe differ-entsynthesistechniques,thesonochemicalapproachshowed some superiorities including reduced particles/grains size, homogenizeddispersedgrains,higherpurity,lesser agglom-eratedparticles,shortenedinductiontime,preventingextra quantitiesoforganic solventstosupplytogreenchemistry, andsoon[17].

Ontheother hand,thedopingwithrareearth(RE) ions has an extremely crucial role in the improvement of fer-rite performances. There are many publications about the effectsofdifferentREonthefeaturesofMn–Zn[18],Cu–Zn [19],Ni–Zn[20]andMg–Cuferrites[21].REtrivalentelements presentsuperbmagneticandelectric propertieswhenthey are doped within Ni–Cu–Zn ferrites. It has been reported that(Ni0.25Cu0.20Zn0.55)La0.025Fe1.175O4ferritecomposition

dis-played high permeability [22]. They found that there is a substantial rise ininitialpermeability atLa(x=0.025) sub-stitution. The improved in permeability is attributable to

themutualeffectofincreasedgrainsize,speciallyincreased crystallitesize,increaseddensiﬁcation(decreasedporosity), decreased anisotropy and compressive macrostress. How-ever, the Ms diminished withthe incorporation ofLa3+ in

NiCuZnferrites[23].Shirsathandco-workers[24]improved the magnetic features of NiCuZn nanoferrites by using Dy3+ ionsas dopants. Kabburet al. [25]indicated that the (Ni0.25Cu0.30Zn0.45)TbxFe2−xO4 ferrite displayed high electric

andmagneticproperties.Themaincontributionfor increas-ingtheelectricandmagneticfeaturesofspinelferriteresults fromthemicro-strainionicradiidisparityamongferriteand rareearth[24].RE3+_obtains_4f_electrons_and_strong_spin–orbit

angular coupling. Mainly, the 4f shells of REelements are shieldedby5s2_5p6_subshells_and_no_effect_on_the

surround-ingions[25].Recently,weinvestigatedprofoundlythephysical featuresofultrasonicallyproducedNi0.4Cu0.2Zn0.4Fe2−xTbxO4

(x=0.0–0.1) nanospinel ferrites [26]. Compared to undoped sample, Eg (optical band gap) raised slightly from 1.87 to 1.98eVwithdoping.Mössbaueranalysisrevealedthat Tb3+

ionspreferablyresideinOhsites.Ms andMrincreasedwith

risingTbamountuptox=0.06,andafterwarddiminishedwith additionalgrowingxcontent.However,thecoerciveﬁeld(Hc)

showedanoppositevariation.

Thepaperprovidedtheunderstandingoftherelationship between chemical compositions, microstructure, dielectric andmicrowavefeaturesofTbdopedNiCuZnNSFssynthesized viathesonochemicalapproach.Itwasﬁrsttimeestablished correlation betweenchemical compositionofthenanosized NiCuZnspinelsandtheirstructuralparameters,electricaland microwaveproperties.Itwasfoundmicrostructural parame-terscorrelateswellwiththemainabsorptioncharacteristics (amplitudeofresonance,frequencyofresonanceandbandof resonance).Itwasdiscussedthenatureoftheelectromagnetic absorptionforpartiallysubstitutednanospinels.Aftercareful literatureanalysis,weobservedthatthereareno systemati-caldataabouttheimpactoftheTb3+_ions_on_the_properties

evolutionin[Ni0.4Cu0.2Zn0.4](Fe2−xTbx)O4(x≤0.1)NSFs.

2. Experimental

Tb–NiCuZn NSFs were produced by ultrasonication. Raw materialsincludingcopper(II)nitrate,zinc(II)nitrate,nickel(II) chloride(NiCl2),iron(III) nitratenonahydrate,Tb(III)nitrate

were dissolvedin50mlofdeionizedH2Oundercontinuous

stirringandthepHwasattunedto11.5withammonia solu-tion(Eq.(1)).Afterwardtheobtainedsolutionwassubjected toultrasonicirradiationsbyusinganultrasonichomogenizer for45min.Lastly,theﬁnalformwaswashedwithdeionized

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H2Oandthendriedat60◦C[27–29].

0.4Zn2++0.2Cu2++0.4Ni2++xTb3++(2−x)Fe3+

→[Ni0.4Cu0.2Zn0.4](TbxFe2−2x)O4 (1)

AXRDbyRigakuBenchtopMiniﬂexwithCuK_␣radiationhas beenusedtoidentifythecompositions. Themorphological analyseswereperformedviaaSEMfromFEITitanSTcoupled withEDX.Thedielectric valueswereaccomplished via the NovocontrolAlphaimpedanceanalyzer.TheAlphaanalyzer usedforrelativeimpedance/capacityandtangentlossfactor hasbothbasicaccuracyandresolutionoflessthan3×10−5 and10−5,respectively.Theparticlesizewasanalyzedusing SEMimages.Thestandardcrystallographicmethodwasused tostudy andplottheparticlesizedistributions.An equiva-lentdiscdiameterwasimpliedbyparticlessizeinthepresent paper.Theproportionofparticlearea(Pi)wascalculatedas

[30,31]:

Pi=

d2 ini

4S (2)

wheredi isthe disc diameterofananospinelferrite parti-cle,Sisthefullareaofallparticlesontheanalyzedimage, ni isthenumberofparticleswithagivensize.Theaverage particlesizewasdeterminedasthemaximumvalueofthe ﬁt-tingfunctionthatdescribesthedistributionoraveragevalue ofthetwomaxima(inthecaseofbimodaldistribution)[30]. Thedistributionwidthwasdeterminedathalftheheightof eachﬁttingfunction.Theaccuracyoftheaverageparticlesize measurementswas±4.3nm.

The S-parameters as a function of frequency in the interval of1–4.5GHz were attained via an Agilent network analyzer and calculations were accomplished through the Nicholson–Ross–Weer(NRW)method[32].TheMWreﬂection losswascomputedasfollows[33]:

˙R =

ε−1

ε+1 or| ˙R|=20lg

ε−1

ε+1

indB (3)

Here | ˙R| (in dB) called the reflection coefficient modu-lus.Themeasurementerrorformicrowaveparameterswas insignificantanddeletedatthestageofthecalculationofthe reflectionlossesfromS-parameters.

3. Results

and

discussion

3.1. Microstructure

ThephaseofTb–NiCuZnNSFswasveriﬁedviaXRDpowder patternsasshownfromFig.1.XRDspectraunveiledthe forma-tionofspinelferritestructureaccordingtoICDDcard10-0325. Aminoramountof␣-Fe2O3 phasehasbeendiscernedfrom

x≥0.06 because ofsolubility limits ofrare earth ions into thespinelcrystal[34,35].Inordertoestimatethestructural parameters,weappliedtheRietveldreﬁnementthrough Full-proofprogramme.Thelatticeparameter(a)wasraisedwith growingTbamountasfollows8.370,8.371,8.375,8.383,8.384,

Fig.1–XRDpatternsof[Ni0.4Cu0.2Zn0.4](Fe2−xTbx)O4

(x≤0.1)NSFs.

and 8.389 ˚A. Thisobservation isrelevant tothe lattice dis-tortionbecauseofthelargerionicradiiofTb3+ _ions_{(1.06 ˚}_A)

compared toFe3+ _ions_{(0.64 ˚}_A). _The_crystallites_sizes_(D XRD)

weredeterminedbyusingthewell-knownScherrerequation. DXRDvaluesarefoundbetween13and20nm.TheSEM

micro-graphs ofTb–NiCuZn NSFsare exposed inFig. 2. All ratios showedhighlyaccumulationofcubicparticles.EDXspectra of[Ni0.4Cu0.2Zn0.4](Fe2−xTbx)O4(0.02≥0.1)NSFsisexposedin

Fig.3,whichillustratedthatthecontentsofNi,Cu,Zn,Tb, Fe,andOelementsmatchverywellwiththedesiredchemical compositionofpreparedmaterials.

Fig. 4 illustrates the particles size distributions of Tb–NiCuZnNSFsobtainedbystatisticalanalysisoftheSEM imagesandthecorrespondingfittingfunctions.Thesize dis-tribution of the Tb–NiCuZn NSFs (Fig. 4(a)) has one clear maximum.Thepositionofthefittinglinemaximumexactly correspondstothemostprobableparticlessize,whichcanbe consideredtheaveragesizeinafirstapproximation.So,the averageparticlessizeofthe Tb–NiCuZnNSFsis21nm.The distributionisnarrow,whichmeansacloseparticlesizefrom 5–10to40nm.TheparticlessizedistributionsofTb–NiCuZn NSFs(x=0.02,0.04and0.06)(Fig.4(b)–(d))aremuchwider,i.e.a significantsizedispersionisobservedforthesamples.There

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Fig.2–SEMimagesof[Ni0.4Cu0.2Zn0.4](Fe2−xTbx)O4(x≤0.1)NSFs.

arenoobviousmaximaonthedistributionsforx=0.02and 0.04samples.However,themostprobableparticlessizecan bedeﬁnedasthe maximumofthe ﬁttingfunction. Thisis 29and16nmforx=0.02and0.04samples,correspondingly. Productwithx=0.06differsfrom others inthepresenceof bimodalsizedistributionbehaviour,whichisseeninFig.4(d). Twofunctionmaximaareat82and20nm.Thus,Tb–NiCuZn NSFs(x=0.06)NSFshasahighervalueoftheaverageparticles size,57nm.Fig.4(e)showstheparticlesdistributionforthe samplewithx=0.08.Thisnanospinelferritehasavery

nar-rowpeakwithamaximumat14nm.Thatis,thesamplewith mosthomogeneousmicrostructureisformed(exceptforthe initialcomposition).Thesubstitutiondegreeofx=0.1provides theclassicalunimodalformoftheparticlesizedistribution, whichiswelldescribedbytheGaussianfunction(seeFig.4(f)). Theaverageparticle sizeofthe Tb–NiCuZnNSFs(x=0.1)is 43nm.

So,amicrostructureanalysisusingSEMimagesrevealeda non-linearchangeintheaverageparticlessizewith increas-ingTbconcentrationinnanospinelferrites.Fig.5showsthat

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Fig.3–EDXspectraof[Ni0.4Cu0.2Zn0.4](Fe2−xTbx)O4(0.02≤x≤0.1)NSFs.

themaximumvalueoftheaverageparticlessizeisobservedat x=0.06,andthesmallestatx=0.08.Thereisnoclear correla-tionbetweentheaverageparticlessize(basedSEMimages)

and crystallites size obtained using X-ray diffraction data, whichwasdescribedinthepaper[26].Here,thecrystallites sizeincreasesfrom12.4to19.4nmwithincreasingTb

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Fig.4–Particlessizedistributionofthe[Ni0.4Cu0.2Zn0.4](Fe2−xTbx)O4(x≤0.1)NSFs.

centrationfromx=0.0upto0.08,andthenslightlydecreases to18.7nmatx=0.1.

Theconsistentbehaviourwiththeaverageparticles size is observed at the distribution width, the diagram that is showninFig.6.Asarule, thelargertheparticles size,the widerthesizedispersionandthegreaterthesizevariation, which is established fornanospinel ferrite atx=0.06. The minimumparticlessizevariationwasobservedatx=0.08. Pre-viouslywereportedaboutthecorrelationbetweenNi-based [36],Zn-based[37]and NiCuZn-basedspinels[38]with par-tialsubstitution ofthe Feions withthe f-elements.Itwas demonstratedthatlatticeparametersstronglycorrelatedwith

theaverageionradiusofthesubstituent.Themicrostructural parametersalsoasarulechangedgraduallywithincreasing ofthesubstitutionlevel[36–38].

3.2. Impedancespectroscopy

Both electrical conduction mechanism and dielectric func-tion ofTb–NiCuZnNSFs wereevaluated withthehelpofa technique based on the complex impedance spectroscopy. Therefore,somerelatedparameterssuchasdissipation fac-tor,dielectricloss,dielectricconstant,andconductivitywere evaluatedasafunctionofbothtemperatureandfrequencyfor

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Fig.5–Averageparticlesizefor

[Ni0.4Cu0.2Zn0.4](Fe2−xTbx)O4(x≤0.1)NSFsdetermined

usingSEMimages(rightscale)andcrystallitesize determinedusingXRDresultsdescribedin[34](leftscale).

Fig.6–Half-widthdistributionwidth(forparticlesize distributionfromFig.5)for[Ni0.4Cu0.2Zn0.4](Fe2−xTbx)O4

(x≤0.1)NSFs.

variousTbion-substitutionratios,includingactivationenergy withtheeffectofsubstitutionandtemperature.Hereitis obvi-ousthattheanalysisofsuchspinelferritesisimportantfor manytechnologicalapplicationsnowadays[39,40].

3.2.1. ACconductivity

MostoftheNSFsshowagrowthinACconductivitywith fre-quency,whichisthenormaltendencyofferrites.Itiscommon thattheconductionmechanisminferritesmainlycomesfrom theexchange ofchargecarriersbetweenferric and ferrous ions.Itshouldbeemphasizedthattherisesinthefrequency oftheelectricﬁeldappliedexternallyleadanincreaseinthe hoppingofchargecarriersandthusincreasestheconductivity. TheconductivityofTb–NiCuZnNSFsforterbiumion substitu-tionratiosbetweenx=0.00andx=0.10isshowninFig.7asa functionoffrequencyupto3MHzinthetemperatureranges from 20 to 120◦C.The ACconductivity seems to obey the frequencydependenceofthepower-lawwithvarious expo-nents,especiallyatlowertemperatures.Fluctuationtrendin thereferencesampleofx=0.00seemstobeslightlyobvious

comparedwiththelowlysubstitutedTb-NiCuZnNSFs.Highly substitutedTb–NiCuZnNSFs,sayx=0.08and0.10,showsome typeofenvelopebendingalongbothlowestandhighestsides ofthetemperature axisathigherfrequencies.Itisobvious toobservethattheTb3+_{ion-substitution}_ratio_in_NiCuZn_NSFs

provides someinterestingtendenciesinconductivity, espe-ciallytheoneatlowerfrequenciesandalsotheoneathigher frequenciesforhigherTbionratios.Theconductivityin gen-eral,obeystheruleofpower-lawwithanexponent,n,through someangularfrequencyvariationinacertainrangeforany substitutionratioofTbionstoNiCuZnNSFsandthetrendis givenasfollowssimilartoourearlierstudy[41]:

(x,ω,T)=o(x,T)ωn(x) (4)

wherethesubstitutionratio-dependentpowerexponent,n(x) varies around unity between0.8 and 1.2ina certain tem-perature range. Some significant effect is observed in the conduction mechanismdue tothe substitutionratio incre-ment,especiallyatx=0.08,0.10.Yet,slightlymorefluctuation isobservedalongthetemperatureaxisforhighTbsubstitution ratios,whileno majorfluctuations arerecorded in conduc-tivityalongthemediumbandintemperature.Therefore,this trendprovidessomeflexibilitytotheconductivitymechanism byfine-tuningthesubstitutionratiosuitableforavarietyof sensorapplications.

Itisalsonotedthatthepower exponentforeachofthe conductivitycurvesvariesslightlydependingontheresponse timeofthechargecarriersasafunctionofbothfrequency ofthe appliedelectric ﬁeldand the substitutionratio. Itis importanttoseethatACconductivityleadstoa systemati-cally improvedmodiﬁcationwithsomecertainsubstitution ratios in NSFs. Moreover, the increase in AC conductivity with increasing frequencycan actually beconsidered as a source ofbothelectron and polaron-hopping mechanisms. AlthoughthetrendsintheACconductivityare more dom-inant intheelectronhoppingcontribution,it ispossibleto gently associate it with a small polaron type conduction. An increase in DC conductivity with increasing tempera-ture means that the NSFs show electronic semiconductor behaviour[42].

3.2.2. DCconductivityandactivationenergy

The 2D and 3D Arrhenius plots of DC conductivity of Tb–NiCuZnNSFsasafunctionoftemperatureandfrequency are depictedinFig.8forvariousTbionssubstitutionratios withaninterval of0.02.Itisobvious thatforalmost every Tb–NiCuZnNSFs,exceptfortheunsubstituted,thereare sim-ilartrendsinactivationenergy.Arrheniusplotsgiveustwo activationenergyvaluesforTb–NiCuZnNSFs,whilethereare threeforunsubstitutedNiCuZnNSFs.ForTb3+_{ion-substituted}

NiCuZn NSFsthe activationenergies havevaluesofhigher than400meVonthehigh-temperatureside(70–120◦C),except x=0.10,whilethey ownvalues ofmuchlower onthe low-temperatureside(20–60◦C)asshowninTable1.Forreference, NiCuZnNSFshasanactivationenergyaslowas0.04meVon thelow-temperatureside,whiletherearetwoactivation ener-gies (+435meVand −605meV)higherthan 400meVon the high-temperatureside.ItisevidentthatTb–NiCuZnNSFsare veryimportantintheconductivitymechanism.Forthis

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Fig.7–TheACconductivityof[Ni0.4Cu0.2Zn0.4](Fe2−xTbx)O4(x≤0.1)NSFsasafunctionoffrequencyandtemperature.

son,theconductionmechanisminNiCuZnNSFswithTbion additivecanbeinterpreted bythe Verweymechanism[43], whichrepresentstheexchangeofelectronsorholesbetween thesameelementionsand/orseparatelydisplacedhostand substitutedionsinthe caseofmultiplevalencestates.The activationenergycanbecontrolledundervarioussubstitution ratiosofallTb-substitutedferrites,andtherelaxationprocess canbelinkedtovariousdefectiveeffectsintheconduction mechanismofTbion-associatedchargecarriers.Thus,theDC

conductivityoftheferritesforeachofthesubstitutionratios canbeexpressedasfollows:

dc(x,T)=0(x)exp

−Ea(x) kBT

(5)

whereEaistheactivationenergy,kB istheBoltzmann con-stant and 0 is the conductivity at absolute temperature.

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depend-Fig.8–The2Dand3DArrheniusplotsofDCconductivityof[Ni0.4Cu0.2Zn0.4](Fe2−xTbx)O4(x≤0.1)NSFs.

Table1–ActivationenergyofNi0.4Cu0.2Zn0.4TbxFe2-xO4

(x≤0.10)NSFs.

X Ea(meV)athighT Ea(meV)atlowT

0.00 435(T−)and−605(T+₎ ₀₀₄ 0.02 743 131 0.04 549 131 0.06 537 168 0.08 667 071 0.10 350 063

ingonthetransition(orrelaxation)temperature.Therefore, anychange inthe conductionmechanismdue tothe elec-tron/polaron hopping process occurs on both sides of the transitiontemperature.Forthisreason,itcanbeinterpreted that temperature increase also contributes to drift mobil-ity. Thiscan be attributedtothermal energyexchange for chargecarriersafterthe ferritesare exposedtorising tem-perature.Anappropriateinterpretationcanbemadeforthis conductionmechanismbyconsideringtheiondistributionin tetrahedralandoctahedralregions.Theelectricalconduction canbecausedbyelectronhoppingbetweenferrousand fer-ricions locatedin octahedral regionsofthe NiCuZn NSFs. Whenthevariationofactivationenergyisexaminedinthe substituted NiCuZn NSFs, it is explained that their higher values correspond to the actively exciton/polaron hopping processesbetweenthelocalizedenergybandsofthe param-agneticphase.Itshouldbeemphasizedthatthelowvalues istheresultoftheelectronhoppingofferromagneticphases [41,44].

3.2.3. Dielectricconstant

Thedielectricconstant ofTb-NiCuZnNSFsasafunctionof frequencyandtemperatureisrepresentedinFig.9for vari-ousTbionssubstitutionratiosuptox=0.10withaninterval of0.02. In all substituted NSFs, the value ofthe dielectric constantincreasedbyﬂuctuatingduetoTbionsubstitution rates,and evenchangedinadifferent waywithfrequency

andtemperature.Thedependenceofthedielectricconstant onthetemperatureatlowfrequenciesappearstobehigher forNSFsthanforthosewiththeTbionsubstitution.TheNSFs with twosubstitution ratios of0.08and 0.10 forma valley uptoacertainmediumfrequencyof3kHzwhile establish-ing ahigh-cliff-like fallinthehigher frequencyrange.The rest,includingthosethatarenotsubstituted,indicatessome steadystatedropsacrossfrequenciesupto3MHz.However, thelevelofdependenceinthehigh-andlow-frequencyregion is particularly evident, especially in the high substitution. Also,attentionshouldbepaidtothestateofdependenceon the temperatureandthe rateofcontribution, andit shows asteadydecreaseacrosstheentirefrequency.Thedielectric dispersioninNSFscanbeexplainedinthecontextofspace chargepolarization,whichisanindicationofthepresenceof aconductivephase(grains)attheinsulatinginterfaces(grain boundaries)incomparisonwithourformerstudy,onceagain basedonNiCuZnNSFs[41].Thus,thelocalaccumulationof charge carriers causedbyferric and ferrous can be stimu-latedundertheinﬂuenceoftheexternalelectricﬁeldforthe NSFs.Thedistributioneffectobservedinthecertainfrequency region canbeinterpretedbecauseofMaxwell–Wagnertype interfacepolarizationaccordingtoKoop’sphenomenological theory[45].

The electrical conduction mechanism of some NiCuZn NSFscanbeexplainedbythepolarizationmechanism. Ori-entationpolarizationisknowntoresultfromtherotational displacementofthedipoles.Therefore,ferriteionsareseen asdipolarduetotheexistenceofbothferricandferrousions. DuetothesubstitutionofTbionsintoNiCuZnNSFs,the fer-ricionswillmovetowardsthetetrahedralregion,resultingin areductionofferricionsintheoctahedralregion. Electron-hoppingmobilityoccurringamongferricandferrousionswill reduceduetoadecreaseinferricconcentrationinthe octahe-dralregion,therebyreducingpolarization.However,formany differentreasons,thedielectricconstantwillﬂuctuatewith anincreaseinTbioncontent.

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Fig.9–Thedielectricconstantof[Ni0.4Cu0.2Zn0.4](Fe2−xTbx)O4(x≤0.1)NSFsasafunctionoffrequencyandtemperature.

3.2.4. Dielectricloss

ThedielectriclossparameterofTb–NiCuZnNSFsasafunction offrequencyandtemperature isdisplayedinthe3D repre-sentationin Fig. 10 for various Tb ions substitution ratios withanintervalof0.02.Threedifferenttrendsareobserved in the dielectric loss, with no substitution, little substitu-tion,andmuchsubstitutionratios.Forthelessersubstituted NiCuZnNSFsofx=0.02–0.06,thelossincreaseswith increas-ingtemperatureatlowerfrequencywhileU-shapevariation isobservedforhighersubstitutionratiosofx=0.08and0.10.

Frequencydependencealongthewholerangescanseemsto bequitedifferentforallcurvesofeachoftheTbionratiosin NiCuZnNSFs.Therefore,thedielectriclossstronglydepends ontheTbionsubstitutionratio.Theelectronexchange inter-actionbetweenferrousandferricionscausesadecreaseina lossinthelow-frequencyrange,whilesubstitutioncancause adecreaseinlossduetothereplacementoftheferricionwith Tb3+_ions._More_Tb3+_ion_substitution_to_NiCuZn_NSFs_causes

ﬂuctuationinthelossparameteracrossthetemperaturerange athigherfrequencies.Inaddition,thenon-substitutedNiCuZn

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Fig.10–Thedielectriclossof[Ni0.4Cu0.2Zn0.4](Fe2−xTbx)O4(x≤0.1)NSFsasafunctionoffrequencyandtemperature.

NSFsasareferenceleadstoalowerpermittivityordielectric loss,andoffersV-shapetrendsalongthefrequencyaxisinthe log-loggraphcomparedtoallTbion-substitutedNiCuZnNSFs [46].ItisalsointerestingtonotethattheNiCuZnNSFsitself showsanincreaseinlossonthehigh-frequencyside,those thatarehighlysubstitutedﬂuctuateandslightlyincreasein thesamefrequencyregion.Itisthereforenoteworthythatthe dielectriclosscanbemodiﬁedagainstfrequencyand temper-aturevariationusingsomevariableparameterssuchasthe substitutionratioformanyapplicationsbasedonTbiondoped NiCuZnNSFs.

3.2.5. Dissipationfactor

ThedissipationfactorofTb–NiCuZnNSFsisshowninFig.11 forthe3Dsemi-logarithmicform,suchasthelns-lnf-Tchart forvariousTbionsubstitutionratioswitharangeof0.02.Itis interestingtoseeﬁrstlythatthelossfactorforallNiCuZnNSFs showsdifferenttrendsalongthefrequencyaxis.Whileless temperaturedependencyisobservedforthereferencedand lower substitutedNiCuZnNSFs,highertemperature depen-denceisavailableforhigherTbratios.Justlikeinthecaseof dielectricloss,thedissipationfactorforallexistingNiCuZn NSFsshowssimilartrends.Therefore,thereasonsfor

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expla-j mater res technol.2020;9(5):10608–10623

10619

Fig.11–Thedissipationfactor(tangentloss)of[Ni0.4Cu0.2Zn0.4](Fe2−xTbx)O4(x≤0.1)NSFsasafunctionoffrequencyand

temperature.

nationsshouldbeemphasizedanditisimportanttoseehow functionaltheTbionisintheferrite.Inotherwords, struc-turally,grain–grainboundaryformationwithTbionadditive affectingdielectricpropertiesbecomessoimportant.Itis par-tiallyclearthatthedissipationfactorreducesexponentially withincreasingfrequencyover agiven rangeand shows a Maxwell–Wagnertypedispersionduetointerfacial polariza-tion.

In the light of the electrical and dielectric parameters above,theeffectsofthesubstitutionratioofTbionsonthe conductivity,activationenergy,dielectricconstant,dielectric loss, andlossfactors ofNiCuZn NSFshavebeen examined indetail.Itisalsoknown thatanyincremental changesin conductivityasafunctionoffrequenciesareassociatedwith bothelectronandpolaronhoppingmechanisms.Thepresence ofpolaronmobilitystandsoutduetotheionswithdifferent

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Fig.12–Frequencydependencesofthereﬂectionlossesof [Ni0.4Cu0.2Zn0.4](Fe2−xTbx)O4(x≤0.1)NSFs.

valencestatesintheequivalentelementregionofvarious fer-rites[47].ItisalsoclearthatDCconductivityincreaseswith theTbsubstitutionratiosforallNiCuZnNSFswhilethe acti-vationenergydecreaseswithanincreaseinsubstitutionratio, exceptfor0.08.Itisknownthatthetunabilitylevelof electri-calconductioniscontrolledbetweenthesubstitutionTbions andthehostionssuchasferrousandferricions.

Theaboveevaluationsofferusthatmoreandmorecharge carriersnecessitatelessenergytoovercometheenergy bar-rier.Adecreaseinabarrierheightagainstelectronsmobility isconsideredtobeduetoadecreaseinthenumberofvoids anddefects.Therefore,theexcavationofelectronsnearthe interfacebetweenthevalencestatesoccursbyincreasingthe substitutionratio,therebyleadingtoanincreaseinDC con-ductivity.Inadditiontotherelevantcommentsabove,itcan beseenthattheNiCuZnNSFssubstitutedwiththeTbionshow varioustrends inthedissipation factor toacertain degree depending on the rationallevel ofthe substitution. These factorscanbeinterpretedbycomparingothersimilarspinel ferrites[48],whichcanbeattributedtoexternallosses asso-ciatedwithimperfections,suchasimpurities,defects,grain boundaries,dislocations,voids,somedislocatedTbions.In otherwords,alldielectricparametersstudiedhereshow vari-oustemperatureandfrequencydependenciesduetodifferent typesofimperfectionscausedbyanysubstitutionsand dis-placementcompoundsaddedintospinelferrites.Theeffect ofacertainTbionsubstitutionratioonbothdielectric proper-tiesandconductionmechanismshowsusthatNiCuZnNSFs isasuitablesubstanceformanyspintronicapplicationsand varioussensortechnologies[49].

3.3. Microwaveproperties

ToinvestigatethemicrowavepropertiesofTb–NiCuZnNSFs, S-parameterswerecomputedusingco-axialsystem.To deter-minethereﬂectionlosses,thefrequencydispersionsofthe permittivity and permeability in the frequency range of 1–4.5GHz were taken. The reﬂection losses the frequency dependenceshavebeengiveninFig.12,whichalso demon-stratesthefrequencydependencesofFig.12showedvaluesof

reﬂectionlosseswithabsorptionprocesseswithin1.8–3.8GHz. The resonance of the domain boundary can be used to understand thenature ofelectromagneticabsorption.Each domain boundary possessesown oscillationfrequency, the forcing EMR approaches the frequency of its own oscilla-tions ofaparticulardomain boundarywhenthefrequency increases,whichcausestoresonantabsorptionof electromag-neticenergy.Thenatureoftheboundary(thelengthofthe domain walland itselasticity)leadtothe frequencyofthe boundaryresonance.Therefore,asthedomainsizedecreases, the length ofthe domainwall decreases,and its elasticity increases. The resonance ofthe domain boundary caused theshorterinlengthofthedomainboundaryandhigherits elasticity, higher infrequency ofresonantEMR absorption. Subsequently,thelongerthedomainboundarylengthandthe loweritselasticity,itwillreducethefrequencyofthedomain boundaryresonance.Therefore,varyingtheaveragedomain size(changingtheparametersofthedomainwall)allows con-trollingthefrequencyofthedomainboundaryresonance.The changing indomain sizeaccoured bychange the intensity ofexchangeinteractions duetofrustrationofthemagnetic structure(violationofthelong-rangeorderofexchange inter-actions) and alteration in DXRD. This effect due to change

inthechemicalcompositionofthematerial(replacementof magneticionswithionshavelargerradii).Inthecaseof Tb-substituted NiCuZnspinels,weobservedagoodcorrelation betweenchemicalcomposition(leveloftheTbions),average crystalsize,andmicrowaveproperties.

Theglobalminimumofthereﬂectionlossesnamedasthe amplitudeofresonance(RAmp)andthefrequency,which

cor-respondstothevalueRAmp–frequencyofresonance(RFreq).

The width ofthe peak is (width at1/2 valueof the RAmp)

bandofresonance–Rband.Themaximalvalueofabsorption

(RAmp=−59.01dB)wasobservedat3.79GHz(RFreq)forthe

sam-plewithTbconcentrationx=0.08.However,Tb3+_ions_induced

non-linearchangesintheresonantfrequency(RFreq)andinthe

resonantamplitude(Ramp).TheRfreq(orpositionofthelocal

minimum)linkedwiththefrequencyatwhichthemaximum absorption was detected.In this case, theresonant ampli-tude(RAmp)ofthesamplescorresponded totheamountof

absorbedEMRenergy.AnincreaseintheTb3+_{concentration}

fromx=0.00to0.02;0.1and0.06inNSFscausesandecrease inRfreqvaluefrom2.56to2.44;2.01and1.85GHzrespectively.

AtthesametimechangesinTb3+_{concentration}_from_x₌_0.00

to0.04and0.08inNSFscausesanincreaseintheRFreqvalue

from2.56to2.94and3.8GHzrespectively.Itwasfoundthatthe substitutionofTb3+_does_not_critically_change_R

Ampfor

sam-pleswithx=0.00to0.02;0.1and0.06andinducedsigniﬁcant increase inthe absorbed electromagneticenergy(Ramp)for

sampleswithx=0.04and0.08(seeFig.13).Itisinterestingfact thatincreaseoftheEu3+_substitution_for_NiCuZn_ferrites_[38]

leadstomonotonicincreaseoftheresonantfrequencydueto domainboundariesresonance.Inpresentpaperweobserved non-linearbehaviouroftheresonantfrequencyandresonant amplitude.Itcanberesultofthemicrostructurefeatures.

Furthermore, the average width ofthe absorption band (Rband) insufﬁciently ﬂuctuated. This correlates well with

microstructureanalysis(inSection3.1)andtheexplanation providedearlier.FromourpointofviewvalueofRFreq

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10621

Fig.13–Frequencydependencesofthemain amplitude–frequencycharacteristicsofthe

[Ni0.4Cu0.2Zn0.4](Fe2−xTbx)O4(x≤0.1)NSFs:(a)amplitudeof

resonance–RAmp;(b)frequencyofresonance–RFreq;(c)

widthofthepeakorbandofresonance–Rband.

domainsizeandbythepeculiaritiesofthedomainwall.Atthe sametime,valueRAmpdeterminedbythefeaturesofthe

mag-neticstructure(intensityoftheexchangeinteractiondueto Tbionsdistributionandfrustrationofthemagneticstructure). ThevalueoftheRBandorwidthofthepeakdependsonaverage

grainsizedispersion.Allmaterialsarecharacterizedby disper-sioninthevalueoftheaveragegrainsize–thatis,thematerial containsgrainsofdifferentsizes,accordingly,domain bound-ariesthatdifferinsize.Thereareoscillationfrequencyforeach domainboundary.Therefore,theareaofmagneticlossesof electromagneticenergyconsistsofasetofpeaksofindividual boundaries.Thus,thegreaterthedispersion(variationinsize)

andthenumberofcrystallitefractionswithdifferentgrainsize values,thewidertheareaofthereﬂectioncoefﬁcientofthis materialwillbe,whichwillbecausedbytheblurringofthe peakoftheresonanceofthedomainboundaries.

4. Conclusion

Nanospinel ferrites with nominal composition Ni0.4Cu0.2Zn0.4TbxFe2-xO4 (0.0≤x≤0.10) NSFs were

pro-ducedbythecitratesol–gelauto-combustiontechnique.The microstructure analysisusing SEM imagesrevealed a non-linearchangeintheaverageparticlesizewithincreasingTb concentrationinnanospinelferrites.Microstructureanalysis showsthatthemaximumvalueoftheaverageparticlesizeis observedatx=0.06,andtheminimumatx=0.08.Thereisno clearcorrelationbetweentheaverageparticlesize(basedSEM images)andcrystallitesizeobtainedusingX-raydiffraction data,whichwasdescribedindetailinourpreviouspaper.The electricalcharacterizationand dielectric propertiesofNSFs havebeenextensivelyinvestigatedintermsoftheeffectof various Tbionsubstitution ratioson theactivation energy, electricalconductivity,dielectricconstant,dielectricloss,and dissipationfactor.InallNSFs,DCconductivityissummarized usingArrheniusplots,whereatransitiontemperatureof60◦C andtwoactivationenergiesinthehighandlow-temperature regionarerecorded.ForTb3+_{ion-substituted}_NiCuZn_ferrites

theactivationenergieshavevaluesofhigherthan400meVon the high-temperatureside(70–120◦C), exceptx=0.10,while theyownvaluesofmuchloweronthelow-temperatureside (20–60◦C).Forreference,NSFshasanactivationenergyaslow as0.04meVonthelow-temperatureside,whiletherearetwo activation energies (+435meV and −605meV) higher than 400meVonthehigh-temperatureside.Ithasbeenobserved that AC conductivity increases with increasing frequency of compliance with power-law and exhibits a dominant electron, partlypolaron-hoppingmechanisms.In NSFs,the increaseinconductivitywiththeincreaseintemperatureis anindicatorofthepresenceofsemiconductorbehaviour.It hasbeennotedthattheeffectsofTbionsubstitutionrateon dielectric constant,dielectric loss,and lossfactorare quite high. Itisimportant thatthe dissipation factor fallsdown exponentiallywithanincreaseinfrequencyonacertainrange scaleandproducesasuitableMaxwell–Wagnertypedielectric dispersion due to interfacial polarization. The frequency dependences ofthe mainelectrodynamic parameterswere investigatedinthefrequencyrange1–4.5GHzusingaco-axial line and calculated by the Nicholson–Ross–Weer method. Thereﬂectionlossesinthefrequencyrangeof1–4.5GHzwas determinedbyfrequencydispersionsofthepermittivityand permeability.Calculatedvaluesofreﬂectionlossesindicated absorption processesintherange of1.8–3.8GHz.The reso-nanceofthedomainboundarywasconsideredtoexplained the nature of electromagnetic absorption. In the case of Tb-substitutedNSFs,weobservedagoodcorrelationbetween chemicalcomposition(leveloftheTbions),averagecrystal size,and microwaveproperties. Itwasobservednon-linear changes in the main amplitude–frequency characteristics (RAmp;RFreqandRband)asafunctionoftheTbions

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thefeaturesofmicrostructureand asresultbythedomain sizeandbythepeculiaritiesofthedomainwall.Atthesame timevalueRAmpdeterminedbythefeaturesofthemagnetic

structure(intensityoftheexchangeinteractionduetoTbions distributionandfrustration ofthemagneticstructure).The valueoftheRBand orwidthofthepeakdependsonaverage

grain size dispersion. The obtained ﬁndings exposed the possibilityforfeasibleapplicationsofthesenanomaterialsin operatingradio-electronicdevices.

Conﬂicts

of

interest

The authors declare that they have no known competing ﬁnancialinterestsorpersonalrelationshipsthatcouldhave appearedtoinﬂuencetheworkreportedinthispaper.

Acknowledgments

This work was supported by the Deanship for Scientiﬁc Research (Project application No 2020-164-IRMC) of Imam Abdulrahman BinFaisal University (IAU–SaudiArabia). The workwaspartiallysupportedbyAct211Governmentofthe RussianFederation,contractNo02.A03.21.0011(inSouthUral StateUniversity).

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