第二章晶体结构的缺陷h

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1、SOLUTIONThelengthoftheBurgersVectoris:第二章晶体结构的缺陷Chapter2TheCrystalStructuredDefectsProblems1.ConsidertheFCCmetalCu,whichhasalatticeparameteraof0.362nm・a.Calculatethelengthofthelowcst-cncrgyBurgersvectorinthismaterial.b・ExpressthislengthintermsoftheradiusofaCuatom.c.Onwhichfamilyofplaneswillslip

2、occurinthismaterial?Why?ci0.314/n(b)InFCCcrystalstructure,a=2y/2r.SothelengthoftheradiusofaCuatomis:b=a=-x2込r=2r.(c)Slipoccurinthismaterialonthefamilyofplanes{111}.Becausetheintcrplanarspacingin{l11}isthelargest,theforceneedingtoovercomewhileslipoccuristheweakest.2.Thelowest-energyBurgersvector

3、inFCCAghaslength0.288nm.FindthelengthoftheunitcelledgeinAg.SOLUTIONInFCCcrystalstructure,thelowest-energyBurgersVectoris:^=—[no]

4、eparameterainMois0.314nm,determinewhetherMohastheBCCortheFCCcrystalstructure・SOLUTIONTrytofindtherelationbetweentheBuigeisXfectorandthelatticeparametera,dothis:b0272a2w?J3_=_——iiin_=o$66=一，sowecanfirmlybelieveMohastheBCCcrystalstructure.1.Considerthe(ill)planeofanFCCcrystalandadislocationwhoseB

5、urgersvectorisparallelto[TTo].Tliedislocationitselfisparalleltotheintersectionof(ill)and(111).a.GivetheBurgersvectorofthedislocation.b.Indicatethecharacterofthedislocation.SOLUTIONa.TheBurgersVectorofthedislocationis:b.Assumethedirectionoftheintersectionof(1Tl)and(l11)is[uvv.So,therearerelati

6、onsasfollow:=>5v=0Jv=0(abandoned)cos^[TTol[Toi]^=1+0+1J[(-1)2+1+o](l+1+0)aaa亠aaa_222_1[g00]=g[100]Intermsofenergy:工財咖沏2>XbfinalBecause&=60,thedislocationismixeddislocation.2.ShowthatthedislocationreactiongivenbelowisbothvectoriallyproperandenergeticallyfavorableforaBCCmetal:(a/2)[l1l]+(a/2)[ll

7、l]—>a[l00]SOLUTIONIntermsofvector:(d/2)[l11]+(a/2)[111]Sothedislocationreactionisbothvectoriallyproperandenergeticallyfovorable.3.Assumethatthetriangleinthedrawingliesonthe(111)planeofaface-centeredcubiccrystalandthatitsedgesareeq