Assignment3

Duedate:2014-11-14

Question1:Computethe(110),(111)and(211)interplanarspacingfortheAlandα-Fe,respectively.(RAl=0.1431nm,Rα−Fe=0.1241nm).Question2:DerivetheBragg’slaw:2dsinθ=λ.

Question3:ForbothFCCandBCCcrystalstructures,theBurgersvectorb

[hkl]whereaistheunitcelledgelengthand[hkl]ismaybeexpressedasb=a2

thecrystallographicdirectionhavingthegreatestlinearatomicdensity.(a)WhataretheBurgersvectorrepresentationsforFCC,BCC,andsimplecubiccrystalstructures?(b)ifthemagnitudeoftheBurgersvector|b|is|b|=a(h2+k2+l2)1/2

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determinethevaluesof|b|forcopperandα-iron.(RCu=0.1278nm,Rα−Fe=0.1241nm)

Question4:(a)Foragivenmaterial,wouldyouexpectthesurfaceenergytobegreaterthan,thesameasorlessthanthegrainboundaryenergy?Why?(b)Thegrainboundaryenergyofasmall-anglegrainboundaryislessthanforahigh-angleone.Whyisthisso?

Question5:Aluminum-lithiumalloyshavebeendevelopedbytheaircraftindus-trytoreducetheweighandimprovetheperformanceofitsaircraft.Acommercialaircraftskinmaterialhavingadensityof2.55g/cm3isdesired.Computethecon-centrationofLi(inwt%)thatisrequired.

Question6:ProvidedthatT3>T2>T1,whichoneofthefollowingpicturesiscorrect,accordingtothetheoryofcrystallization?

Question7:GiventhatthelowestcrystallizationtemperatureofNiisat319oC,computethecriticalradiusofNiatthattimeandcorrespondingcrystalliza-tionenergy.(Tm=1453oC,Hm=-18075J/mol,γ=2.25−5J/cm2,andVmol=6.6cm3/mole)

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*Bonus1:WhatkindofXRDpatternwouldyouexpectfromanamorphousmetal?(explainthereasonbasedonthenatureofnon-crystallinestructureandtheBraggslaw)

*Bonus2:Foracubiccrystalsystem,ifwehavetwopeakslocateatθaandθb(θa<θb)onaXRDspectrum,whichpeakshouldweusetodeterminethelatticeparameterawithbetteraccuracy?

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