susceptibility A novel induction-based device for the measurement of the complexmagnetic Sensors and Actuators A: Physical

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Sensors and Actuators A: Physical

jo u r n al hom e p a g e :w w w . e l s e v i e r . c o m / l o c a t e / s n a

A novel induction-based device for the measurement of the complex magnetic susceptibility

Marina Díaz Michelena

, Jose Luis Mesa U ˜ na

, Marina Pérez Jimenez

,

Marco César Maicas Ramos

, Pedro Cobos Arribas

, Claudio Aroca Hernández-Ros

aPayloadsandSpaceSciencesDept.,InstitutoNacionaldeTécnicaAeroespacial,Ctra.Ajalvirkm.4,28850,TorrejóndeArdoz,Spain

bETSIT-ISOM,UniversidadPolitécnicadeMadrid,CiudadUniversitarias/n,28040Madrid,Spain

a r t i c l e i n f o

Articlehistory:

Received29September2016 Receivedinrevisedform3July2017 Accepted10July2017

Availableonline12July2017

Keywords:

Magnetometricdevice Portablesuscetometer Inductivedevice Magneticsusceptibility Complexsusceptibility Inductivemethods Inductivedevices Magneticsurveys Magneticcharacterization Susceptometer

a b s t r a c t

Adevicenamedmagneticsusceptometerforacompletedeterminationofthemagneticcomplexsus- ceptibilityofmaterialsandmineralshasbeenconceivedandmanufacturedasacomplementforthe insitucharacterizationofrocksduringhighresolutionmagneticprospections.Inthisworkadeviceand itscapabilitiesforsusceptibilitymeasurementsaredescribed,thecalibrationperformedwithartificial samples,andthevaluesofrealandimaginarysusceptibilityofnaturalsamplesinarangecomprising:

␹=10⁻⁴to10⁻⁷[SI],representativeofEarthandalsoMarsrocks.

©2017TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBY-NC-ND license(http://creativecommons.org/licenses/by-nc-nd/4.0/).

1. Introduction

Complexmagneticsusceptibilitydeterminationofnaturaland synthetic samples is an important measurement for its com- pletemagneticcharacterization.Magneticlosses,eddycurrents, accumulatedmagneticenergy, and changesonthese andother propertiesundervariationsofamplitudeandfrequencyofanexter- nalmagneticfield maybeof interestin thecharacterizationof syntheticmaterialsfor someapplicationsliketransformers and superconductivity“Singh et al. [1]”, and basicsciencelike spin glasses,phases transitions and superparamagnetism characteri- zation “Mulder et al. [2], and del Barco el al. [3]”. It also can giverelevantinformationoftheconditionsofformation (global magneticfields)orcoolingandalterationprocesses(atmospheric temperatureandenvironmentalconditions)inthestudyofnatu- ralrocks,wheretheremanentmagnetizationmeasurementisnot enoughtoextractrelevantparameters“Pandarinath[4]”.

∗ Correspondingauthor.

E-mailaddress:[email protected](M.DíazMichelena).

The determination ofthecomplex susceptibilityimplies not onlythemeasurementofinitialsusceptibilityanddetermination ofthehysteresisloop“Singhetal.[1],Mulderetal.[2],anddel Barcoetal.[3]”,butalsothebehaviorofthematerialunderthe actionofanalternatingmagneticfield.

Currentmagneticsusceptibilitymeasurementsareperformed indevices“MarconandOstanina[5]”basedonmagneticinduc- tionlikeVibratingSample Magnetometers(VSM)“Foner[6]”or Alternating Force Magnetometers (AFM) as in Vibrating Wire Susceptometerfrom“Astietal.[7]”fortherealpart,andmagneto- optical methods “Motta et al. [8]” as well as Superconducting QuantumInterferenceDevices(SQUID)“Lietal.[9]”candetermine therealandimaginarycomponents.Additionally,othertechniques using Micro-Electro-Mechanical Systems (MEMS) “Drung et al.

[10]”orNuclearMagneticResonance(NMR)“Duyn[11]”havebeen morerecentlyintroduced.Theseexamplesofequipmentprovide high-resolutionsusceptibilityvalues“Mulderetal.[2]”buthave highpowerconsumption,oftenconsistincomplexproceduresand arelimitedtomediumtolargelaboratoryfacilitiesduetothelarge dimensionsofthedevicesandmaintenanceresources.Inallcases, verylittleportableequipmentexists,itisconsideredbulkyand oftenrequires liquid nitrogenfor its operation“Timofeevetal.

http://dx.doi.org/10.1016/j.sna.2017.07.015

0924-4247/©2017TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBY-NC-NDlicense(http://creativecommons.org/licenses/by-nc-nd/4.

0/).

[12]”.Thisisa limitationtostudies,whichneedtheanalysisof naturalsamplesbecauseontheonehandaprocessofsamplecol- lectionandtransportationtothefacilityisneeded,andontheother handbecausetheexhaustiveanalysisofthecollectedsamplecan leadtonon-appropriateconclusionsifitlacksrepresentativeness.

Furthermore,alongthesequenceofprocesses,anygapinthetrace- abilitymightresultinthelossofinformationregardingtheoriginal orientationofthesamples,essentialforpaleomagneticstudiesand withimplicationsonthestructuralanisotropies.

Aninsituprospectionincludingsusceptibilityaswellasmag- neticfieldvectormeasurementsishighlyrecommendedbecause magneticsignaturesandpropertiesofoutcrops,whenmeasured inthenature,aretheresultofthecontributionnotonlyfromsur- facerocks,butalsofromthemagneticpropertiesofthesubsurface andsurroundings“MichelenaandKilian[13]”.Therefore,comple- mentaryinsituanalysesarehighlydesiredandtheysupposeavery powerfultoolfromwhichmanyscientificandindustrialsectorslike Paleomagnetism,Geology,Geophysics,Mining,OilIndustry,Arque- ology,etc“Clark[14]andMurdocketal.[15]”canbebenefited.

Thepresenteddevicehasbeenconceivedasapartofacompact andportablemultisensormagneticinstrument,withthecapabil- itytomeasurethemagneticfieldandthereforeanestimationof thevector(threeaxes):NaturalRemanentMagnetization(NRM)+ inducedmagnetization,theMagneticSusceptibilityandtheminor hysteresisloopsoftheminerals“Day[16]andDunlop[17]“.Inthis workwefocusonthecapabilityofthedevicetomeasurethemag- neticsusceptibility,andthereforenamethedevicesusceptometer.

2. Methodology

Thesusceptometerisbasedonaninductivecircuitcomprising anautoinductionwithanHshapedferritecore(Fig.1)andtwo capacitorsconnectedinseriesandparallelwiththecoil(Fig.2).The circuitisbroughttothenaturalRLCresonance,whichminimizes itspowerconsumption.Inthesecircumstances,alongtheworking cycles,thecapacitorC1 (inparalleltotheautoinduction)sources ahighcurrenttothecoil,whichgeneratesfieldsinthegapofthe magneticcircuitintheorderof30mT.

Whenamagneticormetallicmaterialisapproachedtothebot- tomgapoftheferrite,themagneticinduction(B)inthispartofthe magneticcircuitchanges,asaconsequenceofthedifferentrela- tiverealpermittivity(␮’)ofthematerialrespecttotheair(upper gap).Evenmore,duetothecomplexnatureofthepermeability (composedbyareal:␮’andanimaginarypart:␮”),otherdissipa- tionprocessesmightbeunchainedinthegap,likeeddycurrentsor processesofspinrelaxation.

Thechangeinthemagneticcircuitgapinductionresultsina variationoftheautoinductance,whichcanbeeasilymeasuredby thecorrespondingchangeofresonancefrequencyoftheelectrical circuit.Additionally,thedissipationeffectsarereflectedinthefields involvedinthemagneticcircuitaswellasinachangeofthevoltage dropintheinputresistance(R_in).Theferritecorehasacoupledpair ofsecondarycoilsthatmeasurethevariationofthemagneticfield onthetwoedges,whenasampleispresentedtooneofthem.The variationintheamplitudeandphaseofthefieldmeasuredwiththis secondarycoilscorrespondswiththedifferencebetweenrelative realandimaginarycomponentsofthesusceptibilityoftheairand thesample.

Therefore measuring these parameters experimentally, it is possibletoobtainavalueofthemagneticcomplexrelativeper- meability.(=␮’+i␮”)i.e.susceptibility(␹=␹’+i␹”=␮−1inthe InternationalSystem).

Also,thesystemisprovidedwithseveralsetsofcapacitorsto performcomplexsusceptibilitymeasurementsasafunctionofthe frequencyintherangebetween10and100kHz.

Fig.1.SchemeoftheautoinductancebasedonaU-shapedferritecore.Primarycoils areconnectedinseries.SecondarycoilsareconnectedinserieswithineveryUbut inoppositionbetweentheupperandlowerpartsoftheH.

Fig.2. Schemeoftheelectricalcircuit.Amodifiedtankcircuit.

2.1. Mathematics

Inthissectionweintroducetheexpressionstoderivethereal andimaginarypartsofthepermeabilityasafunctionoftheindirect measurementsperformedintheelectricalcircuit.

ThetotalimpedanceofcircuitinFig.1is:

ZT=Rin+[(ZC1)⁻¹+(ZL+ZC2+RL)⁻¹]⁻¹ (1) whereZC1 =_iωC¹₁,ZC2= _iωC¹₂ andZL=RL+iωL.

Table1

PropertiesofthesensorheadcapacitorsC1andC2andcurrentamplificationrationintheresonantcircuit.

fr(kHz)^a C(F)^b Lx(mm²)^c Tol.(%)^d Disipation^e IAmpl.Ratio^f

14.21 4.700 37×27.0 ±20 ≤6×10⁻² 1:06

31.42 1.000 44×20.0 ±10 ≤5×10⁻⁴ 1:12

56.80 0.330 33×17.5 ±10 ≤5×10⁻⁴ 1:37

afristheresonancefrequencyofthecircuit.

bCisthecapacitanceofthecapacitorsinthesensorheadresonantcircuit.

c Dimensionsofthecapacitors:ListheLengthand␾isthediameter/size.

d Sizetoleranceofthecapacitance.

eDisipationratioofthecapacitors(dimensionless)at1kHzandroomtemperature(+25^◦C±5^◦C).

f Iiselectricalcurrent.Ampl.IsAmplification.Thisvaluereferstothecurrentthroughthecoilachievedwhen1ApassesthroughRin.

ForsimplicityweassumethatC1=C2=C,whichisinagreement withthevaluesofTable1.Theelectricalcircuithastworesonance states:oneatω0=



LC,whichminimizesthelossesinthebranch oftheferriteandthepowerconsumptionandanotheratω1=



LC, whichmaximizesthem.Thedeviceisdrivenat␻0,forwhichthe capacitorsandtheautoinductancemaintainahighcurrentthrough theresonatingbranchwitharelativelowinputcurrent(uptoI₁: I_in=37:1factors).

Therealpartofthesusceptibility␹’ismeasuredbythechange ofresonantfrequencyofthecircuit,giventhefactthattheresonant frequencyisdirectlyrelatedtotheautoinductanceoftheelectrical circuit,and thisisproportional tothepermeabilitythroughthe reluctanceofthecircuit.

Intheabsenceofamagneticsample,themagneticcircuitiscon- stitutedbytheferritecore(indicatedwiththesubindex“F”)and anairgap(subindex“a”).Inthepresenceofanapproachingsam- ple,themagneticcircuitisconstitutedbytheferritecoreandthe samplewithintheterrain(subindex“s”).Inbothcases,thecircuit isdescribedby:

Rm=NI (2)

Ф^{beingthemagneticflux,R}mthemagneticreluctance,Nthe numberofturnsandItheelectricalcurrent.

Therefore,theautoinductanceL=N^d

dl canbecalculatedasLi=

N

R_i,whereRi=_S^lF_F¹_F +_S^li_i¹_i andthesubindex“i”isassociatedto theairortotheterrainsample(i=a,s),whichclosesthemagnetic circuit.

Takingthisintoaccountandduetothefactthatthepermeability oftheairisconsidered␮0,theexpressionoftherealpartofthe permeability(␮’s)andthesusceptibility(␹’s)asafunctionofthe frequencyis:

’s= 2²N²C^SF_l^F

F f_0,a² −1 2²N²C^SF_l^F

F f_0,s² −1 (3)

and

’s= f_0,a² −f_0,s² f_0,s² −_22N^l2FCS_F_F

(4)

where:f_0,a/s=^ω0,a/s_2 ,l_Fisthelengthofthecircuitintheferrite:

l_F=2h+w,l_a/sisthelengthofthemagneticcircuitintheair/soil l_a/s= ^l₄^F,Nisthenumberofturns,Cisthecapacitorsofthecir- cuit,␮Fisthepermeabilityoftheferriteandithasbeenassumed forsimplicitythattheferriteandair/samplesurfacesareequal:

S_F=S_a=S_s=d₁*d₂(Fig.1).Thesectionoftheferriteisnotexactlyof thesamedimensionsofthesurfacecomprisingthefieldlinesin theair/soil(Fig.1).Incontrast,thislastoneisestimatedtobe3 timeshigherthanthatoftheferrite.Additionally,theairandsoil surfaceswillnotbenecessarilybethesameeither.Thisquestionis discussedinsectionV.

Tomeasuretheimaginarypartofthepermeability(␮”)orsus- ceptibility(␹”)wefocusonthelossesofthecircuitandthechange oftheselossesinthepresenceofthesample.

Onewaytomeasuretheimaginarysusceptibilityistomeasure thechangeinvoltagedropthroughR_ininthepresenceandabsence ofsample:V (Rin),becausethepowerdissipatedinthisresistor P (Rin)=IinV (Rin) isareflectionofthepowerlosesintheresonat- ingcircuit.Thismethodisappropriatewhentheimaginarypartis significant.Fornaturalsamplesthisisnotgenerallythecaseand therefore,andamethodwithbetterresolutionwouldbepreferable.

Anotherwaytoquantifytheimaginarysusceptibility,whenthe susceptibilityoftheferriteisknownandtherealpartofthesuscep- tibilityofthesamplehasbeenalreadydetermined,istomeasure themagneticfieldinthemagneticcircuit.Themagneticinduction intheferritebottomsideincontacttothesample(B_F-s)isafunc- tionofknownparametersandtheimaginarysusceptibilityofthe sample(␹s”):BF−s=^B_S^sS_F^s

Forananalyticalsolution,themagneticcircuitissolved.Starting fromfluxconservationinthecontactsurfacebetweencoreand sample,BF=Bs,andusingthemagnetomotiveforce(equation2)to findthemagneticfieldinthecircuit,itisfinallyfoundthatHs=

0NI l_F (1+_F)

5+F+4s,whatleadsto:

BF−s= 0NI lF

(1+s)(1+F) 5+F+4s

(5)

Thisresultisobtainedgiventheapproximationl_a/s=^l4^Fandthat themagneticfluxinthejunctionbetweenthetwoUcoresistwice thefieldproducedineachone.Intheoppositeside(upperside accordingtoFig.1)themagneticinduction(BF-a)intheferriteis directlyrelatedtothesusceptibilityoftheair(approximatedby thatofthefreespace),andthemagneticBF−a=^B_S^s_F^Ssinductioncan beapproachedby:

BF−a=0NI lF

(1+F) 5+F

(6)

Giventhatthesusceptibilityoftheferrite(␹f=2000)ischosen tobe>6ordersofmagnitudehigherthanthepermeabilityofnat- uralsamples,wecanassumethatBF-s=BF-a.Thephase(␪)induced intheelectromotiveforceofthesecondarycoilsinadifferential acquisitioncanbeconsideredasduetothebreakofthesymmetry whenthesampleisapproached(almosttocontact)tothecoreand dependsontheimaginarycomponentofthecomplexsusceptibility ofthesoilapartfromotherparameters.

2.2. Device

2.2.1. Sensorhead

Asithasbeenpreviouslyintroduced,thesusceptometerisbased onaninductivecircuitcomprisinganautoinductionwithaferrite H-shapedcoreandtwocapacitorsconnectedinseriesandparal- lelwiththecoil(Fig.1).ThecircuitisbroughttothenaturalRLC resonance,whichminimizesthepowerconsumption.

Fig.3.SchemeoftheautoinductancebasedonaU-shapedferritecore.

TheautoinductioniscomposedbytwoU-shapedferritecores ofenvelopevolume25.8×22.2×16.0mm³(Fig.2),withd1=6.6, d₂=16,h=13,w=19.2.Thewindingismadewith15turnsofLitz wiretodiminishlosses.Thepermeability(F=’F+i¨F)hasbeen fittedto:

^_F(S.I.) =2000,practically constant in thefrequency range between10and100kHz

^F(S.I.) =0.044f (Hz) +7.55,havingavalueof10±2inthe above-mentionedrange,

whichreproduceswithanerror<1%thecurveprovidedbythe manufacturer.

Thecapacitorshavebeenchosenoffilmtypetosurgethehigh currentneededinthefrequencyrange(10and100kHz).Inpartic- ular,theyareofpolypropylenefoil,tominimizetheinternalohmic lossesandtheparasiticinductance.Itisforeseenasetofbatteries ofcapacitorstotunetheoperationresonantfrequenciesofthecir- cuit.Table1showsthevaluesandmaincharacteristicsofC1and C2capacitors.

Theprototypeconstructedwiththeseelementshasanefficiency incurrent between1:06and 1:37(Table1), achievingcurrents intheorderof10and20Awithaninputcurrent1A.Thesecur- rentsgeneratemagneticfieldsoutsideofthemagneticcircuitin theorderof15/30mT,whichareconsideredenoughtomeasure thesusceptibilityoftheapproachedsample.

2.2.2. Proximitycontrolelectronic

The scheme of the electronics of a laboratory prototype is depictedin Fig.3.Thesystemis controlledby meansofmicro- controller(␮C)MSP430F5438A-EPbyTexasInstruments.The␮C generatesthesignalstotunethefrequencyandselectsthereso- nantcircuit(Res.1–3inFig.3),controlstheconditioningelements, acquiresandprocessestheoutputsignals.

Formerly,the␮Cperformsafrequencysweeptotunetheres- onanceoftheselectedcircuitaccordingtoTable1:14.21,31.42or 56.80kHzwithcontrolledphase.

This is accomplished with an oscillator AD9833 by Analog DevicesandbymeansoftheinstrumentationamplifierTLV5614 byTexasInstruments.Apoweramplifierisusedtoincreasethe currentinjectedinto theresonantcircuitthroughR_in uptothe above-mentionedlevelof1Aapproximately.The␮Ccontrolsthe magnitudeofthiscurrentinaclosedloop.Takingintoaccountthe gainfactorofthecircuit,thiswillestablishacurrentinthebranch ofthecoiloftheresonantcircuitaccordingtoTable1,whichwill createthemagneticfieldintheferritegap.

Therealandimaginarypartsofthesusceptibilityarederived fromthemeasurement oftheresonant frequency shiftandthe phasevariationoftheinducedfieldinthemagneticcircuitswhen thesampleisapproachedtothehead.Thisisperformedbymeans ofaDSPlockin(implementedwithanAD9833oscillatorand a DG211DJZanalogueswitch)thatreceivestheinputsthroughthe instrumentationamplifiersandtheanalogue-to-digitalconverter (ADC)ADS1278byTexasInstruments.

Fig.4. Setupformeasurementsindicatingthemaindevices.Thelockinoscillator isusedforsignalgeneration,thesignalamplifiedisinjectedinthemodifiedtank circuitandthereadingsareperformedwiththelockinamplifierbymeansofaPC code.Theoscilloscopeisonlyforuserverification.

2.3. Operation

Thecompleteset-upispresentedinFig.4.Theprocedureto registerameasurementisasfollows:

Firstly, thesystem is tunedto one of its natural resonance frequencies,and thevalues of:this frequency,thephase ofthe electricalcircuitandthephaseofthesecondarycoilsareacquired (referencevalues).Afterwards,thesensorheadisapproachedto thesample.Andthefollowingparametersareacquired:thevoltage dropthroughR_in(forrefiningpurposesinthefurthercalculations), thephaseofthesecondarycoilsandthedifferentialfieldmeasure- mentbetweenthepartoftheferriteclosedbytheterrain(bottom part)andtheopenone(upperpart).Afterwards,thesystemtunes thenewfrequency,whichmakesresonatethecircuit,andthisnew frequencyisacquired.Frequencysweepisusedtodetermine␹’and thephaseonthesecondarycoilsisusedtocalculate␹”value.

Thedatagivenbythelock-inamplifierareprocessedtoderive thetwocomponentsofthesusceptibility(␹’and␹”)accordingto sectionIIA.Thenthesystemtunesthefollowingresonantfrequen- ciesandrepeatsthissameprocedure.

3. Calibration

Thecalibrationhasbeencarriedoutbymeansoftheuseofa setofartificialsampleswithknowncompositions.Thesamples weremadeofanon-magneticepoxyresin(ROYAPOX511byRoyal Diamond)withamasspercentagecontentonmagneticmaterial powder,i.e.iron (10and 1wt%),ferrite(1wt%)orpermalloy of compositionFe/Ni19/81%(wt)byMetglas(1wt%).Theartificial samples,withaparallelepipedshapewithaveragedimensionsof 4x3x5cm(60cm³)weremanufacturedinthelaboratorybyusing calculatedcompositionofepoxy,hardenerandmagneticmaterial.

Thesamplepreparationisasfollows.Themixturepreparationis pouredinahandmadecontainerwiththeabove-mentionedshape madeofpolystyrene.Inordertobeabletoremovethesampleeasily whentheepoxyiscured,theinnerwallsofthecontainerarecoated withanaluminumfoilandathinlayerofgrease.Thenthecon- tainerisfixedtoarotatorysystemthatspinsataperiodof12sfor 24htoachieveaproperhomogenizationofthemagneticpowderin theepoxyvolumepreventingitsdepositionontheparallelepiped bottombase.

Theresultsobtainedfortheimaginarypartwillbeconsidered referencevaluesforthemeasurementsofunknownsampleswhilst therealpartresultswillbecalibratedagainstotherequipmentas follows:

Table2

ResultsforRealVolumeSusceptibility(␹’)withdifferentmethods.

RealVol.Susceptibility(10⁻⁶SI)

Sample(wt%) VSM FS(kHz) PS(kHz)

DC 18 52,5 14,21 31,41 56,8

Fe/Ni(19/81)1% 37±2 37±3 30±4 30±3 46±3 35±3

Ferrite1% 33±2 30±3 26±3 45±3 38±3 43±3

Pureiron1% 48±4 54±6 58±5 43±3 34±3 45±3

Pureiron10% 444±7 440±50 430±40 420±30 400±30 370±30

Table3

ResultsforImaginaryVolumeSusceptibility(␹”)withrespecttothevalueofthePureIron10%referencesample.Theseresultshaveacommonmaximumuncertaintyof0.07 a.u.

ImaginaryVol.Susceptibility(a.u.)

FS(kHz) PS(kHz)

Sample(wt%) 18 52,5 14,21 31,41 56,8

Fe/Ni(19/81)1% 0.07 0.08 0.11 0.08 0.07

Ferrite1% 0.05 0.05 0.12 0.10 0.08

Pureiron1% 0.10 0.10 0.12 0.08 0.09

Pureiron10% 1(5,69·10⁻⁵) 1(9,22·10⁻⁵) 1(5,98·10⁻²) 1(5,61·10⁻²) 1(3,36·10⁻²)

Thelow-frequencycalibration,whichisconsideredequivalent toDCmeasurementshasbeenmadebycomparisonwithacom- mercialequipment:

a)twoVSMwithelectromagnet:onebyLakeShoremodel7304at theInstituteofOptoelectronicsandMicroelectronicsSystems intheUPM,andanotherbyADEMagneticsmodelEV-7atthe SpaceMagnetismLaboratory,INTA.

b)aMS2EsusceptometerbyBartington.

Thehigherfrequency calibration(10kHz–100kHz)hasbeen performed by comparison withCobos et al. equipment “Cobos etal.[18]”,designedtodeterminethemagneticlossesoncopper nanoparticles,modifiedandcalibratedforthispurpose.Fromnow onwewillreferCobosetal.equipmentasthefixedsusceptome- ter(FS)andthepresenteddeviceastheportablesusceptometer (PS)referringtothefactthattheformerispartofthelaboratory equipmentandthelatterisahandhelddevice.

Thiscalibrationconsistsintwosteps.1)Aformercalibrationof theFSdevicebycomparisonofthe15kHzmeasurementswitha calibratedVSM(giventhatthelossesat15kHzonpermalloyFe/Ni (19/81),ferriteandpureironarenegligibleincomparisonwiththe resolutionofthedevice),and2)thecomparisonofthemeasure- mentswiththepresentedsusceptometerandFSintheircommon frequencyrange.

Two of the frequencies selected for this FS prototype were almostthesameasfortheportablesusceptometer,sothatadirect comparisonoftheresultsforbothdevicescanbedonetoprove reliabilityoftheresultsandcalibration.Theresultsareshownin Fig.5AandB,andpresentedinTables2and3.

TheerrorsbarsinFig.5Acorrespondtotheuncertainty.This hasbeencalculatedasthemaximumvalueofexperimentaland theoreticalerrorsi.e.theexperimentaldeviationrespecttotheref- erencetechniques(VSMandFS),andthemathematicalpropagation oftheerrorinthedifferentcontributionsinequation4.

Thevaluesoftheimaginarycomponentwerenormalizedwith respecttothesamplewitha10%inironpowdercontenttoavoid themeasurementoftheimaginarysusceptibilityintherelatively highrangeoffrequencies,whichisverycomplicated.

Despiteofthis,theinter-comparisonofthedifferentresultsfor thedifferentsamplesproves thecapabilityoftheinstrumentto measurerelativevaluesandtheirtrendwithfrequency.

Resultsshowsufficientresolutiontodistinguishmaterialsand composition,highrepeatabilityandhighstability.Regardingthe realpartofthesusceptibility,valuesofVSMandthePSareinvery goodconcordanceasitisshowninFig.5A.Regardingtheimag- inarypart,thedeviationbetweenthe PSand theFS responses, at the same frequencies, is attributed to the fact that the FS measuresaverysmallportionofthesamples(m∼0.2gandvol- ume∼8mm³)andthePSaveragesthesusceptibilityina larger volume (volume∼60cm³ i.e. 30·10³mm³: 2cm thickness, and 3×5cm²surface).Thesizeoftheferriteisdirectlyrelatedtothe volumeofactionofthePSandthisopensafieldofnumerousappli- cations,asitwillbediscussedlaterinthiswork.

Despitethecalibrationmaterialshavehighsusceptibility,their percentagesareverylow(between1and10%),whichmeansthat theintegratedsusceptibilityofthereferencesamplesshouldbeone tenthoronehundredththatofthematerialssusceptibility.Thisis fullyrepresentativeoftherangeofnaturalrocks.

Regarding theimaginary part,the values show ananalogue behaviorofthevaluesmeasuredwiththereferencesusceptometer (FS)buttheyareinthelimitofresolutionoftheapparatus.This isalsoduetothefactthattheexpectedvaluesoftheimaginary componentofthereferencesamplesareexpectedtobeverylow.

4. Results

ThenaturalsamplesweresuppliedbythegroupofPaleomag- netismoftheEarth,AstronomyandAstrophysicsDepartmentof theComplutenseUniversityofMadrid,andwerechosentocover awiderangeofmagneticsusceptibility:fromahighsusceptibility samplefromabasaltdyketoanexpectedlowsusceptibilitygreen clay,includinganarcheologicclay,andarepresentativesampleof aterracefromRíoTintoterrestrialanalogueofMars.

Incomparisonwiththeresultsofcalibration(withartificialand homogeneoussamples),theresultsofthemeasurementofnatu- ralsamplesshowidenticalrepeatabilityandstability.Ithasbeen performedaclassificationintwogroups:group1comprisingVSM andFS,andgroup2comprisingPSandMS2Ecorrespondingtothe differentintegrationvolumesofthesample:volumeofgroup1in theorderof1mm³,andvolumeofgroup3ordersofmagnitude higher.Thisquestionhasamoreimportantinfluenceinthecaseof sampleswithinhomogeneities,whereahighervariabilityisshown intheresultsofFig.6A.Thisvariabilityisparticularlyremarkable inthecaseoftheperidotite,whichispartiallyserpentinizedgiv-

Fig.5.A:Calibrationof␹’vs.thereferencesamples.Thedifferentdotsrepresentmeasurementswiththedifferenttypesofequipmentatseveralfrequencies,B:Stablishment ofreferencevaluesof␹”withrespecttocalibrationsampleIron10%.Figureshowsthenormalizedvaluesfortheimaginarycomponentofthesusceptibility.Theresultsare groupedtogetherinthecomparablefrequenciesforabettercomparison.Theuncertaintyisestimatedin0.1a.u.

Table4

ResultsforRealVolumeSusceptibilitywithdifferentmethods.

RealVol.Susceptibility(10⁻⁶SI)

VSM FS(kHz) PS(kHz) MS2E

Sample(wt%) DC 18 52,5 14,21 31,41 56,8 2kHz

BasaltDyke 15±1 45±2 65±2 130±30 108±30 123±30 107±2

Peridotite(1) ... ... ... 775±3 805±3 844±3 101±2

Peridotite(2) 11±1 12±1 102±3 54±3 3±3 3±3 ...

RedClay 5±1 7±1 5±1 9±3 8±3 3±3 6±2

RioTintoTerrace 1±1 3±1 1±1 3±3 3±3 8±3 2±2

GreenClay 0,8±1 3±1 ... 3±3 1±3 8±3 1±2

ingrisetoatwoverydifferentrealsusceptibilityvaluesinthearea undertest,namedperidotiteintrusionfortheserpentinizedarea andperidotite(2)fornotserpetinizedarea(Tables4and5).

5. Discussion

Themagneticpropertiesofnaturalsamplesaredominatedby thepresenceofmagneticmaterialssuchasiron,nickel,etc.and

Fig.6.A:Measurementof␹’ofnaturalsamples.Thelabelscorrespondtotheaverageddataofthemeasuredfrequencies.Therearetworesultsrepresentationsforthe peridotite,giventhatthissamplepresentsaintrussionofhighsusceptibilitymaterial.Theinsetimagesshowthedifferentsurfacedistributionsoftworepresentative samples:thebasaltdykeandtheperidotite,whereincanbedistinguishedtheserpenizedmaterialintrussionB:Stablishmentof␹”forthenaturalsampleswithrespect tocalibrationsamples.Figureshowsthenormalizedvaluesfortheimaginarycomponentofthesusceptibility.Theseparetedgraphicsrepresenttheresultsforimaginary componentwiththeFSandPSatequivalentfrequenciesinarbitraryunits.

Table5

ResultsforImaginaryVolumeSusceptibility(␹”)withrespecttothevalueofthePureIron10%referencesample.Theseresultshaveacommonmaximumuncertaintyof0.07 a.u.

ImaginaryVol.Susceptibility(a.u.)

FS(kHz) PS(kHz)

Sample(wt%) 18 52,5 14,21 31,41 56,8

BasaltDyke 0.22 0.26 0.39 0.27 0.28

Peridotite(1) 2.97 0.03 0.64 1.19 1.13

Peridotite(2) 0.21 1.10 0.39 0.08 0.55

RedClay 0.07 0.004 0.03 0.02 0.002

RioTintoTerrace 0.03 0.01 0.01 0.01 0.003

GreenClay 0.05 0.004 0.01 0.003 0.01

the structure of thematter. The content in this materials and itsdomainsstructurecanbedelimitedbydeterminingmagnetic propertiessuch assaturationfield, coercive field and magnetic permeability,andcomplementedwithelectricalinformation,i.e.

permittivityandresistivity.

Theproposedfull device(vectormagnetometerand suscep- tometer)measuresthemagneticpropertiesbyanalyzingthemina passiveandinanactiveway,magnetizingthesamplesandcollect- inginformationofthestateofmagnetization.Todirectlydetermine thevolumesusceptibility,thedevicegeneratesamagneticfieldthat penetratesinthesoilandmagnetizeit,sothesoilformspartofthe magneticcircuittogetherwiththeferritecore.

Inthefollowingsomeconsiderationsarediscussed:

• thegeometricalapproximationsdoneinthecalculations.With thisrespect,Fig.7sketchesthemodeloftheferritecore(A),and theresultsofthemagneticmodelsdonewithCOMSOL(BandC).

• andthescopeofthemeasurementsindifferentscenarios.

Regardingthegeometricalapproximations,tocalculatethevol- umeormasssusceptibility,itisrequiredeitherthevolumeorthe massofthemagnetizedsample.Inthecalculationsseveralassump- tionshavebeendoneaffectingthesectionswherethemagnetic fieldlinesareconfinedinthedifferentmediums,andthelengthof theselines.

Oneopenquestioncouldbethehypothesisthat Sa=Ss.Con- cerningthisissue,extrasimulationshavebeendoneusingCOMSOL software.Inthesesimulationsitiscalculatedtheareascomprised byanisodynamicof 1mTin thegapexposed totheairand in thegapclosedbythesoil.Ithasbeenfoundthattheproportion betweenthesetwosurfacesisintheorderof0.89,andtherefore, thehypothesishasbeenconsideredasvalid.

Alltheapproximationsareconsideredinthetheoreticalcalcu- lationoftheerrorintheuncertaintyvaluesoftherealcomponent ofthesusceptibilitymentionedinsectionII.

Theotherquestionconcerningthegeometryisthelengthofthe magneticcircuittohaveanestimationofthepenetrationdepthinto thesoil.Fig.7Bshowstheisolinesdistributionbothintheairandin asamplewithsuscepbitilitiesbetween10⁻⁶and10⁻³(SI).Atthis point,theCOMSOLsimulationhasidentifiedtheisodynamicof1 mT(Fig.7C),andithasbeendoneaplotofthislineinthemagnetic circuit.ThisplothasbeenfittedwithOrigintocalculatethepath numerically.Thispermitstodotheline-integralofthefield.This analysishasbeenusedtovalidatetheassumptionthatthelength ofthemagneticcircuitthroughtheair/soilis1/4ofthelengthof thecircuitintheferrite.

Theotherquestionconcerningthesiteofprospectionislinkedto thislastquestion.Sincethepenetrationdepthislimitedto<1cm, inmanysitesthissusceptibilitymeasurementwouldcastdataof thesoilwhichcoverstherocksandwouldnotbeabletoprovide informationontherocks.Thisrestrictstheareasofapplicationto siteswheretherocksareoutcroppedandnotcoveredbyvegetation orasoil.

Underthe abovementioned constraints,a devicecombining magneticfieldandsusceptibilitymeasurementsisveryusefulfor thehigh-resolutionmagneticsurveysinthecontextoftheEarth prospectionsandtheplanetaryexploration,veryimportantinthe nextdecade“MichelenaandKilian[13];Díaz-Michelenaetal.[19];

Michelenaand Kilian[13]”highlightthatone ofthelimitations toderiveconclusionsofthesurveysisthelackofaninsitumea- surementofthesusceptibility.Thisextrameasurementcanbeof highimportancebecauseitpermitstheinsitudeterminationofthe Koningsbergerratiosandwithhighvaluesoftheserationsonecan usetheinsitumeasurementstoconstrainpropertiesoftheglobal fieldsduringtherocksformation.Alsothedeterminationofthesus- ceptibilityplaysanimportantroleintheidentificationofiron-rich

Fig.7. A.2DModeloftheferritecore,B.Illustrationofthemagneticisolinesinthe airandsamplegaps,C.Sample(10⁻⁶<␹<10⁻³)penetrationdepthfor1mTisoline.

ThecalculationshavebeenperformedwithCOMSOLandadaptedtotheillustration.

mineralsandtheiralterationprocessesaswellastheirstructures in single, multi or pseudo single domain structures. Therefore, theinclusionofsuchmultisensordevice(magnetometer+suscep- tometer)inasuitofinstrumentsincludingspectrometerscanbeof keyimportanceinthesearchofthetinyclueswhichcanevidence extraterrestriallife.Togetherwiththevectormagnetometer,the abilityofthisdevicetoinducemagnetizationwouldalsomakethe dualdevicecapabletosketchminorhysteresiscyclesofthesoils androcks.

Futureimprovements of this instrument arefocused onthe wideningof itscapability toperform Anhystereticand Isother- malRemanent Magnetizationmeasurements(ARMandIRM).In ordertoachievethis,thecurrentgainratiosinthecircuitneedsto beimprovedandasystemtoincludeaDCfieldwiththeusedof batteriesofcapacitorsisbeingstudied.

6. Conclusions

Thedescribedinstrumentisanovelportabledevicetomeasure themagneticcomplexsusceptibilityofrocksand othersamples insituwithouttheneedtoloadthesampleinasystem.Thewhole instrumenthastwoboxes:onesensorheadandanelectronicbox withmassesof200and250g,volumesof60×60×50mm³ and 60×60×40mm³respectively,andapowerconsumption<6W.

The easiness of use makes it a very good choice for Earth prospectionsandplanetaryexploration.

Thecombinationoftheinstrumentwithavectormagnetome- tercanbeclueintheexplorationofterrainswheretheaccessis complicated,anditscombinationwithgeologicalmodulesinrover canmakeahugestepforwardintheplanetaryexploration.

Thisdeviceaimstocomplementcurrentstateofthearttech- niquesinfieldcampaignsonEarthandplanetaryexploration,and alsointendstobecomealowcost,reliable,robust,andlowmainte- nancecostdeviceforlaboratoriesthatcannothostSQUIDdevicesor largeandhighcostlaboratoryequipmenttomeasurethecomplex magneticsusceptibility.

Acknowledgments

Thisworkhasbeenfunded bytheprojects PRI-PIBUS-2011- 1150, PRI-PIBUS-2011-1182, ESP2015-70184-R and 730041 − NEWTON.

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Biographies

MarinaDíazMichelenaPhDinPhysicsfromPolytechnicUniversityofMadrid (2004).Currentposition:headoftheSpaceMagnetismLaboratoryattheSpanish NationalInstituteorAerospaceTechnology(INTA).Dr.DíazMichelenahasevolveda lineinminiaturizedandcompactmagnetometersforspaceandplanetaryapplica- tions.ThemagnetometersinEarthorbitarecurrentlybeingusedforSpaceweather purposes.Asaresultofthisdevelopmentactivityshehasgrownaninterestinplan- etarymagnetometry.InparticulardevotedtodevelopnewinstrumentsforMars andMoonmagneticmineralogyaswellasintheinvestigationofterrestrialanalogs.

JoséLuisMesaU ˜naPhDStudentattheSpanishNationalInstituteorAerospace Technology(INTA).JoséLuisMesaU ˜nafinishedhisMScinPhysicsintheAutónoma UniversityofMadrid(2012)andiscurrentlydoinghisPhDindevicesdevotedto themeasurementofthemagneticsusceptibility.Themainareaofapplicationisthe planetaryexploration.

MarinaPérezJiménezPhDStudentattheInstituteofOptoelectronicSystemsand Microtechnology(ISOM).MarinaPérezJiménezfinishedhisMScinTelecommuni- cationEngineeringinthePolytechnicUniversityofMadrid(2013)andiscurrently doingherPhDinhighlyspecialisedmagnetometricdevices.

CésarMarcoMaicasRamosPhDinPhysicsfromComplutenseUniversityofMadrid (1996).Currentposition:TitularprofessorontheETSIST,UPMMadrid.Researcherat theInstituteofOptoelectronicSystemsandMicrotechnology(ISOM).Dr.Maicasisa specialistinmagneticsimulationcomprisingfiniteandboundaryelementsmethod.

Presentlyheiscollaboratinginseveralprojectsofdifferentnaturefromspintronics toinstrumentationforplanetaryexploration.

PedroCobosArribasPhDinTelecommunicationEngineeringfromPolytechnicUni- versityofMadrid(2001).Currentposition:TitularprofessorontheETSIST,UPM Madrid.ResearcherattheInstituteofOptoelectronicSystemsandMicrotechnology (ISOM).Dr.CobosArribasdidhisfirstresearchworkwithafluxgateapplication,as hisFinalyearProyect,in1990.Heiscurrentlyinvolvedinthedesignanddevelop- mentofmicrocontrollercircuitssolutionsformagneticapplications,aslinearmotor controllers,magneticdetectorsandmagneticdetectioninstruments.

ClaudioArocaHernández-RosPhDinPhysicsfromtheComplutenseUniversity ofMadrid(1980).Currentposition:Prof.Dr.HeadoftheDepartmentofPhysics AppliedtotheInformationTechnologiesDepartmentofthePolytechnicUniversity ofMadrid.SubdirectoroftheInstituteofOptoelectronicSystemsandMicrotechnol- ogy(ISOM).Prof.Dr.Arocastartedhisresearchinthestudyofmagneticstructures inamorphousmagneticmaterials.Thisresearchderivedinanappliedactivityin thefieldofmagneticsensorsandinstrumentation.AtISOMhehasfocusedonthin filmmaterialsstudy,theexchangeinteractioninthesesystems,anddevelopment ofplanarsensors.Heiscurrentlyinvolvedinthedesignanddevelopmentofspin- tronicbaseddevicesandinthestudyofmagneticnanoparticlesanditsapplication forbiomedicaltechnologiesasNMRcontrastandMEG.