材料科学基础课后习题答案12.docx

材料科学基础课后习题答案12.docx

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材料科学基础课后习题答案12

SolutionsforChapter12

1.Find:

Engineeringapplicationsofattractivemagneticforce.

Solution:

Applicationsinclude:

1）separatingiron（ferrousalloys）fromothercomponentsinasolidwastestream,2）Asanattachmentforcranesusedtopickupcarsinajunkyard,3）closingdevicesoncabinetsandrefrigerators,4）magneticstorageracksforholdingtools,and5）containmentfieldsforfusionreactors.

2.Find:

Engineeringapplicationsofmutualrepulsionoflikemagneticpoles.

Solution:

Applicationsinclude:

1）magneticallylevitatedtrains（andotherlevitationapplications）,2）magneticbearings,and3）magneticstirringdevices.

3.FIND:

Whichclassesofmaterialsdoyouexpecttoshowsignificantmagneticbehavior?

GIVEN:

Magneticpropertiesresultfromthemotionofelectrons.

SOLUTION:

Metalshavehighelectronicmobility,soweexpectmetalstohaveinterestingmagneticproperties.Whenwerealizethatelectronicspinsinmoderate-to-highatomicnumbermaterialsarealsoimportant,thenmetalsagaincometomindaswellassomeceramics.Conductivepolymersmayormaynothaveinterestingmagneticproperties:

wejustcannotsayyet.

4.FIND:

DoesacompassneedlepointdueNorth?

SOLUTION:

Itcertainlydoesnot.Itpointstothenorthmagneticpole,whichisnotthesameastheNorthpole.

COMMENTS:

Compassmeasurementsneedtobecorrectedinordertoprovidetruereadings.Talktoyourlocalsurveyororsatellitedishinstaller.

5.Find:

Similaritiesbetween（B,H,and）and

（I,V,and）.

Data:

Equation12.3-2:

B=oH

Equation10.2-1:

V=IR

Equation10.2-2:

=（A/L）R

Equation10.2-3:

=（1/）

Solution:

Combiningequations10.2-1through10.2-3yieldsV=I（L/A）（1/）whichcanberearrangedtoyield（I/A）=（V/L）.Comparisonofthisequationwithequation12.3-2showsthatthemagneticfieldstrength,H,withunits（A/m）,iscomparabletotheelectricfieldstrengthV/L,withunits（V/m）.Botharemeasuresoftheexternaldrivingforce.ThemagneticinductionB,withunits（T=V-s/m2）,isanalogoustothecurrentdensityI/A,withunits（A/m2）.Botharemeasuresoftheresponseofthematerialtotheexternalfield.Finally,o（andinothermaterials）andarethematerialspropertiesthatdescribetheabilityofaspecificmaterialtorespondtotheexternalfield.

6.

Find:

Relationshipbetweenelectronmotionandmagneticproperties.

Solution:

A.Theorbitalmotionofanelectronaroundtheatomicnucleusalwaysresultsinadiamagneticcontributiontotheresponseofamaterialtoanexternalmagneticfield.

B.Thespinmotionofanelectronmayresultinparamagneticbehaviorifthereareunpairedelectronswithinunfilledinnerelectronshells.

7.Find:

Differencebetweenmagneticinductionandmagneticfieldstrength.

Solution:

Themagneticfieldstrength（H）isthedrivingforcewhilethemagneticinduction（B）isthesystemresponse.Thatis,inmostcasesHistheindependentandBthedependentvariableina

magneticexperiment.

8.Find:

Unitsforandcharacteristicsofmagneticpermeability,relativepermeability,andsusceptibility.

Solution:

A.Magneticpermeability,,hasunitsof（T-m/A）orusingthedefinitionofatesla（T=V-s/m2）.hasunitsof（（V-s）/（A-m）=（-s）/m）.

B.Relativepermeabilityistheratior=/osoitisadimensionlessquantity.

C.Susceptibilityisalsoadimensionlessquantity.Becauserandaredimensionless,theyarethevaluesthataremorelikelytobefoundinhandbooks.Thisisbecausetheyalwayshavethesamevalueregardlessofthesystemofunitsbeingemployed.

9.FIND:

Estimatesforair,water,diamond,alumina,Pyrexglass,andepoxy.Comparetoaccuratevalues.

DATA:

UsethedatainTables11.3-1（）and11.5-1（n）tocomputethevalues.Comparetonumberscomputedfromequation12.3-6（r=1+）andTable12.5-1（）.

SOLUTION:

Webeginbyusingequation12.3-8,whichcanbeusedtoprovideapproximatenumbers:

n=rr=n/.

Thenweuse12.3-6tocalculaterfromvaluesof.Thefollowingtablegivestherawnumbersandthecalculatedvalues:

nr=n/r=1+

air1.01.01.001.0

water1.3380.40.0165-12.9x10-61.0

diamond2.436.00.4-5.9x10-61.0

alumina1.769.00.2-37x10-61.0

Pyrexglass1.475.00.301.0

epoxy1.583.50.4501.0

NotethatIusedof0forair,Pyrexglass,andepoxy.Theyarediamagnetic,sothevaluesareessentiallyzero,asintheothercasesshown.

COMMENTS:

Thisisnotverygoodagreement!

10.Find:

Themagneticfieldstrengthtocreateaninduction

equaltothatoftheearthinMg.

Given:

（Mg）=13.1x10-6

Data:

（earth）=6x10-5T

Equation12.3-5:

=o（1+）H

o=4x10-7（T-m/A）

Solution:

Solvingequation12.3-5forthefieldstrengthHgives:

H=/[o（1+）].

Substitutingthevaluesintheproblemstatementyields:

H=（6x10-5T）/[（4x10-7T-m/A）（1+13.1x10-6）]

H=47.7A/m

11.Find:

RelativepermeabilityandpermeabilityofMg.

Given:

（Mg）=13.1x10-6

Data:

Eqn.12.3-5:

=o（1+）

Eqn.12.3-6:

r=/o=（1+）

o=4x10-7（T-m/A）

Solution:

A.r=（1+）=1+13.1x10-6=1.0000131

B.=o（1+）=（4x10-7T-m/A）（1.0000131）

=1.257x10-6（T-m/A）

12.Find:

MagnetizationandinductanceofMginafieldof

105A/m.

Given:

=13.1x10-6

Data:

Eqn.12.3-1:

M=H

Eqn.12.3-3:

=o（H+M）

o=4x10-7（T-m/A）

Solution:

Usingeqn.12.3-1,themagnetizationis

M=13.1x10-6（105A/m）=1.31A/m.

Usingeqn.12.3-3,theinductanceis

=o（H+M）

=（4x10-7T-m/A）（105+1.31A/m）

=0.1257T

13.FIND:

Howcanyoupickoutasteelwith<1?

GIVEN:

Moststainlesssteelshavethisproperty.

SOLUTION:

Holdamagnetuptothemetals.Anon-magneticsteelisthistypeofstainless.Aliseasytodetectbecauseofitslowdensity.Brassisashadeofyellow.

COMMENTS:

Simpleandeffective

14.FIND:

Wouldagiantferromagneticsinglecrystalincreaseinlengthwhenplacedinamagneticfield?

SOLUTION:

WhileIhaveneverseenanequationthatdescribesthegrowthorshrinkageofamaterialplacedinamagneticfiled,Iexpecttheremightbeachangesindimensionsasthedipolesalign.Theeffectwouldbeverysmall.Sincealargesinglecrystalisnothuge,thechangeinlengthmightbedifficulttomeasure.

15.Find:

Relationshipbetweenvectors,H,andMindia-andparamagneticmaterials.

Solution:

Theexternalmagneticfieldvector,H,andtheinductionvector,B,alwayspointinthesamedirection.Themagnetizationvector,M,alsopointsinthesamedirectionasHinparamagneticmaterialsbutisantiparalleltoHindiamagneticmaterials.

16.Find:

Whydia-andparamagneticfindfewintersectingmagneticapplications.

Solution:

Bothdia-andparamagneticmaterialshavesusceptibilityvaluesverynearzero.Therefore,theirresponsetoamagneticfieldisnearlyindistinguishablefromthatofavacuum（orair）andtheirmagneticpropertiesarenotveryinteresting.

17.Find:

ExplainwhyNaCl,LiF,Si,Ge,Cu,andAgarealldiamagnetic.

Solution:

NaClandLiFareioniccompounds.Afterelectrontransferfromthecationtotheanion,allionshavefilledelectronshells.Thus,therearenounpairedelectronsandbothcompoundsarediamagnetic.SiandGeareGroupIVelements.Bothelementscrystallizeinthediamondcubicstructurebyformingfourcovalentbonds.Assuch,theirelectronshellsarefilled,therearenounpairedelectrons,andSiandGearediamagnetic.CuandAgaremetalsandhavesomeunpairedelectrons.Theirunpairedelectrons,however,areinthevalenceshellanddonotcontributetoparamagneticbehavior.Sincetherearenounpairedelectronsininnerelectronshells,CuandAgarediamagnetic.

18.

Find:

ShowelectronconfigurationforSrthroughCdandpredictmagneticbehavior.

Data:

ElectronconfigurationsinAppendixB.

Solution:

ELEMENTELECTRONCONFIGURATION#OFUNPAIREDMAGNETIC（INNER）e-sCLASS

Sr[Kr]5s20DIA

Y[Kr]4d15s21PARA

Zr[Kr]4d25s22PARA

Nb[Kr]4d45s14PARA

Mo[Kr]4d55s15PARA

Tc[Kr]4d55s25PARA

Ru[Kr]4d75s13PARA

Rh[Kr]4d85s12PARA

Pd[Kr]4d100DIA

Ag[Kr]4d105s10DIA

Cd[Kr]4d105s20DIA

19.

Find:

Can"tin"cansbeseparatedfromawastestreamusingamagnet?

Data:

FromTable12.5-1,Sniseitherdia-orparamagnetic

dependingonthecrystalstructure.

Solution:

Sncan'tbeseparatedfromawastestreamusingamagnet."Sn"cans,however,aremadeofFewithaSnlining,andtheferromagneticFeiseasilyseparatedusingamagnet.

20.

Find:

Contributionofunpairedvalenceelectronstoparamagneticbehavior.

Solution:

Withinasolidthevalenceelectronsofindividualatomsareeithersharedortransferred.Ineithercase,therearenounpairedvalenceelectronswhenthesolidisconsideredasawhole.Thus,thereisnoparamagneticcontributionfromthevalenceelectrons.

21.

Find:

Whyaremostoxidesdiamagneticandarethereanyexceptionstothetrend?

Data:

FromTable12.5-1,weseethatonlyafewoxidessuchasCeO2,CsO2,andCr2O3areparamagnetic.

Solution:

Mostoxidesareeitherionic,covalent,oramixtureofthetwo.Assuchtheywillexhibitfilledvalenceshellsandnounpairedelectrons.Thus,theyarelikelytobediamagnetic.Iftheoxidecontainsatransitionmetalwithanunfilledinnerelectronshell,itmayexhibitparamagneticcharacteristics.

22.

Find:

Mechanismsbywhichanexternalfieldincreasesthemagnetizationofaferromagneticmaterial.

Solution:

InaferromagneticmaterialanexternalfiledcanincreaseMeitherbydomaingrowthorbydipoler