Materials Equations

7/28/2019 Materials Equations

1/17

MaterialsEquations

Conductors

Fieldwithinaconductor

DriftVelocity

CurrentDensity

ElectricForceactingondueto 4

ElectricFieldintensityduetonpointcharges

4| |

Resistance

1

Voltagegeneratedbyathermocouple


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SemiConductors

Numberofelectronsintheconductionband

4.84 10 BuiltinVoltage

ln

DepletionRegion

Electricfieldindepletionregion

FermiLevel

ln

ln

Momentum

2

Electron/hole

concentration


3/17

Conductivity

1

FillFactor

PowerConversionEfficiency

Magnetism

Ampereslaw

2 2

Magneticfieldintensity

1Susceptibility

Magnetization

HysteresisLoss

, ,

EddyCurrentloss

6

6 /


4/17

DielectricsandInsulators

Fluxdensity

ElectricalDisplacement

Polarization

Capacitors

12

Capacitanceofasinglecorecable

2ln

DielectricStress

in

asingle

core

cable

2

2

Moment

Torque

Workdone

||||


5/17

ClassificationofElectricalandElectronicMaterials

Bondingionic,covalent,metallico Ionic:betweenmetal&nonmetal,electrostaticattraction,achievedviaelectron

transfer

o Covalent:electronsharing,electronisfoundsamedistancefromidenticalatomso Metallic:metalwithmetalinteractionformingmetallicbondso VanDerWaal:weakattraction,mutualattractionofdipoles

Freeelectronmodelo Abilityorinabilitytoconductelectricity.o Accordingtothispropertymaterialsarecategorizedasconductors,semiconductors,

insulators.

o Bondbetweenelectronsandnuclei,strongforinsulators,weakforconductors.

ElectricalConductivityo Underanelectricfieldthefreeelectronsmoveinarandomwayoppositetothe

directionoftheelectricfiled

BandTheoryo Electronsdistributedatdifferentenergylevels.Thesedistinctenergylevels,wideninto

energybands.

These

bands

may

be

overly

separated

or

may

even

overlap.

Last

ground

stateisknownasthevalenceband,containselectronsthatformcovalentbonds

betweenatoms.Permittedenergybandiscalledtheconductionband.

o SemiConductors:AtT=0K,conductionbandisempty.AtT>0K,someelectronsmoveintotheconductionband.

o Theenergydifferencebetweentheconductionbandandvalencebandisknownastheforbiddengap.

o Differencebetweenaninsulatorandasemiconductoristhevalueoftheenergygap.

ConductingMaterials

ConductorinElectricFieldo Aconductorhasalargenumberoffreeelectrons.o Freeelectrons:looselyassociatedwithnucleus,freetowanderthroughtheconductor,

respondstoaninfinitesimalsmallelectricfield.

o Moverandomlywithnonetdriftinanisolatedconductor.o Isolatedconductoriselectricallyneutral.o Withanelectricfieldthenetdriftisintheoppositedirectionoftheelectricalfield.One

side+ve&theotherisve,producesanelectricfieldwithintheconductorwhichis


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equalandoppositetotheexternalelectoralfield.TheKElostduringcollisionsis

changedtoheat.

Applicationsof

Metallic

Conductors

o SilverandGold:Economicallyunviableforuseincables,wires,conductorsandelectricalmachines.Usedasbondwiresinintegratedcircuits.

o Copper&Aluminium:Economicallyviable. Aluminium:Cheaperthancopper,lighterbutmorevolumeisrequiredduetoaworse

conductivity.

o Applications:Highandmediumvoltageoverheadwiring,Rotorsand3phaseinductionmotors,Lowandmediumvoltageundergroundcables.

o Disadvantages:Lowmeltingpoint,lowerthermalconductivitythusworstcaseitcanburn.Whenexposedtoair,anoxidelayerisformedarounditwhichdoesnotconduct

electricity,thusinhibitingelectricalcontact.Slowmaterialcreep,thematerialwillyield

overtime

thus

may

eventually

become

loose

and

lose

contact.

o Mostcommonuse:Overheadcabling:weightisacriticalrole,duetohavingalowerstrengthitmustbereinforcedwithasteelcore.

Copper:Applications:Alltelecomwiring,Motors,Buildingwire,HVandEHVundergroundcables.

Silver:Lowestcontactresistance. Applications:Brazingfillermetals,electronics,primarybatteries. Gold:Lowelectricalresistivity(onlycopperandsilverarebetter)

Applications:

Microelectronic

circuitry,

wire

bonding

in

ICs

and

connectors,

due

to

resistance

to

corrosion.

EMRelays:Coilwindingmadefromcopper HighResistivityMetals:

o Tungsten:filamentsinelectriclampso Platinum:wirethermocoupleelements,andelectricalcontacts.Itisanexcellent

catalystandistypicallyusedinfuelcellsandthermocouples.

o Constantan:electricalresistorsandthermocouples. Thermocouples:

o ConverttemperaturedifferenceintoEMF.o Temperaturesensorismadebyjoiningtwodissimilarmetalsatoneend.Iftwodifferent

metalsarejoinedatbothendsandhaveadifferenttemperatureacurrentwillbe

createdbytheSeebeckeffect.

SuperConductivity:

Materialswhoseresistivitybecomesextremelysmall(orzero)attemperaturesbelowacriticaltemperatureTc.Consideredasadifferentstateofmatter.Itisareversiblestate.

Ithasahighdegreeoforderthatisentropyiszero,electronsbecomeorderedinthesuperconductivitystate.


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Type1:Destructionbymagneticfield:o Thetransitionbetweenthesuperconductingandnormalstateoccurssharply.

Generallynotusedforcoilsforsuperconductingmagnets.

Type2:o Theeliminationofthesuperconductingstatebyamagneticfieldoccursgradually.

Mainlyusedforsuperconductingmagnetsduetoaddedresistanceagainstthemagneticallyinduceddestructionofsuperconductingstate.

Meissnereffect:AsuperconductorbehavesasifBis0inthesuperconductorwhenanexternalmagneticfieldisappliedonit.Themagnetizationisequalandoppositetheexternalmagnetic

fieldstrength.Theresultisaperfectdiamagnet.

Applicationsofsuperconductors:MRIMedical,particleacceleratorsandsensorselectronics,magnetsandseparationIndustrial

Disadvantages:Coolingofthesuperconductor,complexitiesofthemanufacturingprocessofcertain

components.

Semiconductors

Electricalconductivitymaybechangedasafunctionoftemperature,impuritycontent,excessivecharge

carrierinjectionandopticalexcitation.

IntrinsicSemiConductors:Containsnoimpuritiesordefects.Allelectronsareinthevalencebandat0K.

Temperaturesabove0K,electronsarepromotedtotheconductionband.

ExtriniscSemi

Conductors:

The

availability

of

charge

carriers

in

the

valence

band

and

conduction

band

isgreatlyaffectedbytheintroductionofimpurities.Theseareintroducedtoobtainmaterialsand

deviceswithdesiredproperties.

Introducingimpurities=doping.

Contributeelectrons:donors(intheconductionband)

Contributeholes:acceptors(inthevalenceband)

Ntype:

Eachdonoratomintroducesanextraelectrontothehostcrystalwhichcanparticipateintheconductionprocess,whereasthedonoratombecomespositivelycharged.

Thedonoratomhasahighervalencethantheatomsofthehostmaterial.Ptype:

Acceptoratomintroducesamissingelectron(thusextrahole)whichcancaptureafreeelectrontoformafourthbondwiththesiliconatoms,therebycreatinganimmobilenegativelycharged

acceptoratom.Thisleadstoexcessofholes.

Theacceptorsaresubstitutionalimpuritieswhichhavealowervalencebandthantheatomsofthehostmaterial.

Fermilevelistheenergylevelintheforbiddengapbandfromwhichelectronsareexcitedtobecome

chargecarriers.


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PNjunction

FormedwhenaPtype&Ntypesemiconductorareincontact. Opencircuit,theFermilevelisuniformthroughoutthestructure.

DepletionRegion:

ElectronsandholesneartheinterfaceinstantlydiffusefromtheN&Ptyperegionsrespectively.Thisflowaddstoformthediffusioncurrent.(Directionfromthepsidetothenside)

Thejunctionthatisdepletedofmobilechargecarriersisknownasthedepletionregion.Abuildupoppositelychargedregionsintheregionaroundthejunctionoccurs,thisresultsinanelectric

fieldthatsweepsoutanyelectronsandholesthatentertheregion.

Driftcurrent:duetothefieldpresentinthedepletionregion.Is=Idforano/c Builtinpotential:Aresultoftheenergydifferencelevelbetweenthentypeandptyperegions. Biasconditions:Netcurrentwillflowinonedirection. Forwardbiased:psideisata+vepotentionwrtnside Reversebiased:nsideisatavepotentialwrtpside. DepletionregionbecomessmallerFB,allowinghigherminoritychargeinjection DepletionregionbecomesbiggerRB,suppressingminoritychargeinjection Presenceofbiaschangestheelectricfieldinthedepletionregion. ReverseBiasnetcurrentstillresultsalthoughthisisextremelysmall. Forwardbiasskipsthresholdvalueandasforwardbiasvoltageisincreasedfurtherthedevices

starttobehavelikearesistor,linearrelation.

ReverseBias:Avalancheeffect:CarriersacceleratedinthefieldcanaccumulateenoughKEthattheycan,throughacollisionprocess,generateelectronholepairsthroughimpactionization.

Thiswillhappenagainandgeneratemorecarriers.Thisisapositivefeedbackmechanismknown

asthe

avalanche

multiplication.

Zenerbreakdown:boththentypeandptypeareheavilydoped.Thewidthifthetransition(depletion)regionissmallandelectronscandirectlytunnelfromtheptypevalencebandtothe

ntypeconductionband.Breakdownvoltageiszenerdiodescanbeaccuratelycontrolled.

o Applications: LED SolarCell TempSensor Frequencymultipliersandmixers Switches(rectifiers,inverters,powersupplies)

PhotovoltaicCell:

APVcellisadevicethatconvertssolarenergyintoelectricitybythephotovoltaiceffect. WhenaPVcellsareexposedtolight:Photonreflection,Photonabsorption,generationoffree

carrierchargeinthesemiconductorbulk,Migrationofthecharge,chargeseparationbymeans

ofanelectricfield.

Pvmaterials:MonoCrystallineSilicon,PolyCrystallineSilicon,AmorphousSilicono MonoCrystalline:Orderedsiliconstructure.Predictablebehaviour,mostexpensivedue

toslowmanufacturingprocess.

o PolyCrystalline:Lower,cost,grainboundariesmakeitlessefficient.


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o Thinfilmcells:Lowerefficienciesbutperfrombetterathighertemperatures.Verycheap.Lowefficiencyduetodanglingbonds.

Dielectrics

Dielectricsareasubsetofinsulatorsthatexhibitdielectricphenomena.Electronsintheoutermostshell

oftheatomsindielectricsinteractwithexternalforcessuchaselectricfields,magneticfields,

electromagneticwaves,mechanicalstress,ortemperature,resultingintheoccurrenceofalldielectric

phenomena.

Fornonmagneticdielectricmaterials,dielectricphenomenainclude:

1. Electricalpolarization2. Resonance3. Relaxation4. Energystorage5. Energydissipation6. Electricalaging7. Destructivebreakdown

Electricalfieldappliedtodielectric:

Asmallofcurrentduetothefreeelectronsinsidethematerial.

Polarization:Displacementofthecommoncentresof+veandveelectricalchargeofthedielectric

atoms

by

a

fraction

of

an

atomic

distance,

thus

producing

an

electric

dipole.

Dipole:A+vechargeseparatedbyarelativelyshortdistancefromanequalvecharge. Orientationpolarization:Whenanelectricfieldisapplied,thesedipolestendtoorientasa

resultoftorqueexertedonthesedipoles.

Theappliedelectricfieldcanalsoinducepolarizationbydistortionoftheelectroniccloudsandthenucleusoftheatomicstructureofthematter.

Electronicpolarization:Electricfieldcausesdistortionoftheoriginallysymmetricaldistributionoftheelectroncloudsofatoms.(iethedisplacementoftheouterelectroncloudswrttheinner

+veatomiccores)

Ionicpolarization:Electricalfieldcausestheatomsorionsofapolyatomicmoleculetobedisplacedrelativetoeachother.

Orientationalpolarizationhighlytemperaturedependant.Relaxingprocess,mechanicalfrictionduetoresistanceduetothermalagitationandalsoduetotheinertiaresistanceofthe

surroundingmolecules.

Nonpolar:elasticdisplacementelectronicpolarization

Polar:elasticdisplacementofthevalenceelectronclouds.Elasticdisplacementoftherelativepositions

ofions.Electronic&ionicpolarization.

Dipolar:Electronic,ionic,orientationalpolarization.


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Dielectriclosses:

Leakagelosses(I^2)Powerloss,bothDC&ac Hysteresislosses:causedbycyclicpolarizationinthedielectricinsulationbyalternating

electricalfields

ac

only.

Dielectricstrength:theelectricstrengthsufficienttoinitiateabreakdownofthedielectric. Intrinsicstrength:theupperlimitofthedielectricstrengthwhichisreachedrapidlywhenan

impulsevoltageisapplied.

DielectricPhenomena

IntrinsicBreakdown:energygainedbyelectronsfromtheelectricfieldismuchmorethantheycantransfertothelattice,thusbreakingdown.

ElectromechanicalBreakdown:ElectricFieldordielectric,chargesofoppositenatureinducedontheoppositesurfacesofthematerial.Attractiondeveloped,specimenbecomessubjectedto

electrostaticcompressiveforces,thisexceedsmaximumcompressivestrengthcausingthe

materialtocollapse.

ThermalBreakdown:Conditionofinstabilityisreachedduetoconductioncurrentanddielectriclossesduetopolarization,thustemperatureincrease.Heatgeneratedexceedsheatdissipated,

thusthematerialbreaksdown.

Coronadischarge:aselfsustainedelectricaldischargeinwhichthefieldintensifiedionizationislocalizedonlyoverasmallportionofthedistancebetweentheelectrodes.

DielectricApplications:Capacitors,usedtosolvenoiseproblems.

Dielectricscommonlyused:oil,paper,air,mica,variouspolymerfilms,metaloxides.

Capacitors:Ceramic,Aluminium,tantalum

CeramicClass1:o CapdoesnotvarywithVo LowlossesatfrequencyuptotheUHFrange.o HighInsulationResistanceo Applications:resonantcircuits,filters,timingelements.

CeramicClass2:o Higherlosses,relativelyhighcapacitancevaluesevenwithsmallsizecapacitors.o Applications:Coupling,blocking,filtering.

AluminiumCapacitors:o Advantages:Highvolumetricefficiency,upto1Fproduction.Providesahighripple

currentcapabilitytogetherwithahighreliabilityandanexcellentprice/performance

ratio.

TantalumElectrolyticCapacitors:o Highestcapacitanceperunitvolume.Donotsufferfromtheeffectsoftemperature,bias

orvibration.Expensivebutdonotsufferasmuchfromthepiezoelectriceffect.

o Uses:Blocking,bypassing,filtering,decoupling.Piezoelectricmaterials:arematerialsinwhichelectricitycanbegeneratedbyanappliedmechanical

stressoramechanicalstresscanbeproducedbyanappliedelectricfield.

Uses:Cigarettelighters,gasignites,transducersforhighintensityultrasounds,resonators,microphones.


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Insulators

GasInsulatorso GasesUsed:

Air Oxygen Hydrogen Nitrogen CO2 Sulfurhexafluoride

o Propertiesrequired Highdielectricstrength Thermalandchemicalstability NonInflammability Highthermalconductivity Arcextinguishingcapabilities

Substationso Airinsulatedsubstations

Usesairatatmosphericpressure Everythingisvisibleandinstalledoutdoors Requirelargeareastoobtaintheclearancesrequired

o Gasinsulatedsubstations UsesSF6atmoderatepressure Everythingisinsidegroundedmetalenclosures SF6canachieveincmwhatairachievesinm. Substationsaresmaller Moreexpensivethanair SF6decomposesinthehightemperatureofanarcbutrecombinesback StrongGreenhousegasthathasaverylonglifeinatmosphere CanberecycledfromGIS SF6hashighinsulationcapabilityandhigharcextinctioncapability

LiquidInsulatorso OrganicConsistofcarboncompounds,mostimportantaremineraloils.o InorganicConsistofliquefiedgaseslikenitrogen,oxygenetco MineralOilInsulators

Propertiesdependonchemicalcomposition Usedintransformers(usedforbothelectricalinsulationandheattransferfluid),

oilfilledcablesandcapacitors.

Presenceoffinewaterdropletsaffectthedielectricstrengthofoil SolidInsulators

o Mustbecapableofsupportingandisolatingconductorsatdifferentpotentialso Requirements

Highinsulationresistance Highdielectricstrength Goodmechanicalproperties


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Shouldnotbeaffectedbychemicalsaroundit Nonhygroscopic

o XLPEis theprimeextrudedmaterialusedfortransmissiono ExtrudedPolymers

Polyethylene Hydrocarbonmadeofcarbonandhydrogen Alongerchainofpolyethylenehasahighermolecularweightthana

shorterchain.

Polyethyleneiscomprisedofpolymerchainsthathaveadistributionofmolecularweights.

Polymerchainshaveatendencytocoil. Thisinfluencesthemechanicalpropertiesofthepolymer,butdonothaveamajorinfluenceon

electricalproperties.

Classifiedinto4maincategories:o LowDensityo MediumDensityo HighDensity(providesbestmechanicalproperties)o LinearLowdensity

Hasthebestmoistureresistanceofanynonmetallicmaterial Poorflameresistance

o CopolymersEPR Materialsmanufacturedbyincorporatingmorethanonemonomerintothe

polymerizationprocess.

Properties

Shortchainbranches Noncrystallineamorphousstructure Requiresreinforcingfillers Needstobecrosslinked

Usedasjacketsinlowvoltageapplicationwhenflameresistancehasbeencompoundedintothematerial.

o CrossLinkedPolyethylene(XLPE) Crosslinkingistheprocessofjoiningdifferentpolyethylenechainstogetherby

chemicalreaction

BranchesareconnectedtoadifferentPEchaininsteadofhangingloose. Crosslinkingadvantages

Resistancetodeformationandstresscracking Improvedtensilestrengthandmodulus Electricalpropertiesofpolyethylenearenotnecessarilyimprovedby

crosslinking.

Additionofcarbonprovidessunlightresistanceo PolyvinylChloride(PVC)

Usedinlowvoltagefieldasinsulationandjacket Cannottakehightemperatures Lowcost,easyprocessing


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Fireandchemicalresistance Possessesgoodphysicalstrength,moistureresistance,oilresistance,good

flameresistanceandexcellentresistancetoweathering

Tendencytocreepundercontinuouspressure Tendencytomeltanddeformwhenheatedtohightemperature Chlorinecanbereleasedduringafire,whichwhencombinedwithmoisture

formshydrochloricacid.

ComparisonSummaryo Advantagesofpolyethylene

Lowepermittivity(lowdielectricconstant) Lowtandelta(lowdielectriclosses) Highinitialdielectricstrength

o AdvantagesofXLPE(inadditiontoonesabove) Improvedmechanicalpropertiesatelevatedtemperatures Nomeltingabove105butthermalexpansionoccurs Reducedsusceptibilitytowatertreeing

o AdvantagesofTRXLPE Evenbetterresistancetowatertreeing

o AdvantagesofEPR ReducedthermalexpansionrelativetoXLPE Reducedsensitivitytowatertreeing Increasedflexibility

HighVoltageCableso Usedwhenundergroundtransmissionisrequiredo Needcompleteinsulationo Differentvoltagesareinducedatdifferentpointsonthesheathwhichcauseeddy

currentstoflowinthesheaths. Thesedependon:

Frequency Distancebetweencables Meanradiusofsheath Resistivityofsheathmaterial

o Powerlosscanoccurdueto: Dielectriclosscausedbyvoltageacrosstheinsulation ConductorlossesCurrentpassingthroughtheresistanceoftheconductor SheathlossesCausedbyinducedcurrentsinthesheath Intersheathlossescausedbycirculatingcurrentsinloopsformedbetween

sheathsofdifferentphases.

o Stressdistribution Theinsulationisfullystressedattheconductorwhilenearthesheaththe

insulationisunnecessarilystrongandthusneedlesslyexpensive.

Capacitivegradingisused Consistsofmakingtheinsulationaroundtheconductorwithvarious

layershavingdifferentpermittivities.


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Ceramicso Crystalsmixedwithaglassyphasewhichhelpsintheprocessingoftheceramicandalso

helpsholdthecrystalstogether.

o Havehighmechanicalstrengthandlowpermittivityo Thebreakdownstrength,whencomparedtootherinsulators,islow,butremains

unaffectedoverawiderangeoftemperaturevariation.

o Inerttoalkalisandacidso Alumina

Oneofthebestelectricalinsulators Meltsathightemperatures Poorheatconductor Transparenttovisiblelight Veryhardbutbrittle Stableinoxidizingmedium,sinceitisalreadyoxidized.

o Mica Thinlayersofmicaarelaminatedwithsuitableresinorvarnishtomakethick

sheetsofmica.

Micacanbemixedwiththerequiredtypeofresintoobtaintherequiredcharacteristics.

Usedasfillersininsulatorstoimprovetheirdielectricstrengthandheatresistance.

Highdielectricstrength Lowdielectriclosses Goodmechanicalstrength

MagneticMaterials

Magneticdipoleo Themagneticfieldofacurrentloopcanbeconsideredascomingfromadistributionof

magneticdipolesoverasurfacespanningtheclosedloop.

o Thesurfacecanbedividedintomanysmallloopsandonemayassumethatacurrentflowsineachloop.

o Thesecurrentswillcanceleachotheroutonalltheinteriorboundaries,butnotattheouterboundary.

o Eachofthesmallloopsproducedamagneticdipole Magneticmomentduetoelectronorbit

o Themagneticfieldsthatresultduetocurrentloopscanbeappliedtothesimplemodeloftheatom.

o Theorbitingelectronsareconsideredasanelementarycurrentloop.o Inanexternalfield,electronsexperiencetorquewhichtendstoalignthemagneticfield

producedbytheorbitingelectronwiththeexternalmagneticfield.

o Allorbitingelectronsinthematerialwouldshiftinsuchawaysoastoaddtheirmagneticfieldstotheexternalfield.

o Theresultantmagneticmomentduetoelectronorbitistemperaturedependent.


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Magneticmomentduetoelectronspino Anelectronspinningaboutitsownaxisgeneratesamagneticdipolemoment.o Thespincanbepositiveornegativevalued,thereforethemagneticfieldcaneitheraid

oropposetheexternalfield

o Theresultantmagneticmomentduetoelectronspinistemperaturedependent. Magneticmaterials

o Ferromagnetic(strong) AferromagnetbecomesparamagneticaboveitsCurietemperatureTC. AssumptionsbyWeiss

Amolecularfieldactsintheferromagneticsubstance,andthatthisfieldissostrongthatitcanmagnetizethesubstancetosaturationevenin

theabsenceofanappliedfield.

Aferromagnetinthedemagnetizedstateisdividedintoanumberofsmall

regions

called

domains.

Each

domain

is

spontaneously

magnetizedtothesaturationvalue,butthedirectionsofthe

magnetizationaresuchthatthespecimenasawholehasnonet

magnetization.

Theprocessofmagnetizationistheoneofconvertingthespecimenfromamultidomainstateintoasingledomainmagnetizedinthesamedirectionasthe

appliedfield.

o Paramagnetic(weak) Susceptibilityvariesinverselywiththeabsolutetemperature(Curielaw) Paramagneticsaresubstancescomposedofatomsorionswhichhaveanet

magneticmomentduetothenoncancellationofspinandorbitalcomponents.

o Diamagnetic(weak) Nopermanentmagnetism Negativemagnetism Susceptibilitydoesnotvarywithtemperature Monoatomicgasesarealldiamagnetic Covalentbondsalsoleadtoclosedshellsandelementssuchascarbon,silicon

andgermaniumarediamagnetic.

Mostorganiccompoundsarediamagnetico Antiferromagnetic(strong)

Havesmallpositivesusceptibilityatalltemperatures,butitvariesisapeculiarway

with

temperature.

AsthetemperaturedecreasesthesusceptibilityincreasesbutgoesthroughamaximumattheNeeltemperatureTN. ThesubstanceisparamagneticaboveTN

andantiferromagneticbelowit.

Anantiferromagnetichasnonetspontaneousmomentandcanacquireamomentonlywhenastrongfieldisapplied.

o Ferrimagnetic(strong) Exhibitssubstantialspontaneousmagnetizationatroomtemperature,like

ferromagnets


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Consistsofmagneticallysaturateddomainsandexhibitthephenomenaofmagneticsaturationandhysteresis(likeferromagnets)

Theirspontaneousmagnetizationdisappearsabovethecurietemperature,TC,andthentheybecomeparamagnetic.

Ferrimagneticsaresecondonlytoferromagnetics. Thelargeresistivityimpliesthatanappliedalternatingmagneticfieldwillnot

induceeddycurrentsinaferrite.

Bestmaterialsforhighfrequencyapplications MagnetizationCurve

o Ferromagneticmaterialsandferritesarenonlinear.o Astheexternalfieldstrengthisincreasedfrom0,thedomainsthatareinthesame

directionastheappliedfieldincreaseslightlyinsize. Thisprocessisreversibleforsmall

values.

o Asthefieldisincreasedfurther,thedomainsstarttorotateundertheinfluenceofthemagneticfieldandwillkeeprotatinguntiltheseareallalignedwiththeappliedfield. At

thispointthematerialissaturated(temperaturedependent)andfurtherincreasesin

fielddonotincreasethemagnetizationvector.

o Whenthemagneticfieldisremovedthedomainscannotmovebacktotheiroriginalpositionduetofrictionwhenthedomainsrotate.

MinorLoopso Whenthemaximuminductionislessthansaturation,theloopiscalledaminorloop.

Softandhardmagneticmaterialso Soft

Easytomagnetizeanddemagnetize Highpermeability Largemagnetizationforasmallappliedfield FluxMultipliers

o Hard Hardtomagnetizeanddemagnetize HighCoercivity Highresistancetodemagnetization Usedinpermanentmagnets

Magneticlosseso HysteresisLosses

Theareainsidetheloopistheenergyabsorbedbythematerial Thisenergyisdissipatedasheat

o EddycurrentLosses Whenamaterialismagnetizedcyclicallybyasinewavecurrent,therewillbe

voltageinducedinthematerialintheoppositedirectionofthevoltage

producingthemagnetizingcurrent.

Thiswillsetupcircularcurrentsinthematerialswhichproducemagneticfieldsoppositetotheoriginalmagneticfield.

Lossofenergydissipatedasheataddsuptoheatgeneratedbyhysteresisloss. Reductionininternalfluxdensity


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Magnetostrictiono Whenamagneticmaterialismagnetized,asmallchangeindimensionsoccurs.

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Materials Equations