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1、Lecture4:Diffusion:Fick’ssecondlawToday’stopics•LearnhowtodeducetheFick’ssecondlaw,andunderstandthebasicmeaning,incomparisontothefirstlaw.•Learnhowtoapplythesecondlawinseveralpracticalcases,includinghomogenization,interdiffusionincarburizationofsteel,wherediffusionplaysdominantrole.Contin
2、uedfromlastlecture,wewilllearnhowtodeducetheFick’ssecondlaw,andunderstandthemeaningswhenappliedtosomepracticalcases.Let’sconsideracaselikethisWecandefinethelocalconcentrationanddiffusionflux(throughaunitarea)atposition“x”as:So,Fick’sfirstlawcanbeconsideredasaspecific(simplified)formatofth
3、esecondlawwhenappliedtoasteadystate.Now,let’sconsidertworealpracticalcases,andseehowtosolvetheFick’ssecondlawinthesespecificcases.Case1.Homogenization:(non-uniform→uniform)Consideracompositionprofileassuperimposedsinusoidalvariationasshownbelow,wherethesolidlinerepresentstheinitialconcent
4、rationprofile(att=0),andthedashedlinerepresentstheprofileaftertimeτ.Itisanexponentialdecay,thelongerthewavelength(l),thelongertherelaxationtime(τ),thentheslowerdecay.Shortwavelengthdiesfast.That’swhyshakingalwayshelpsspeedupthedispersion,becauseitenableswidespreading(smallerl)ofthestuff(l
5、ikeparticles)youtrytodisperseCase2.Interdiffusion(thecarburizationofsteel):dopingofsteelwithcarbonSituationa):DopingwithfixedamountofdopantConsiderathinlayerofBdepositedontoA,throughannealingathightemperature,wewillbeabletogettheconcentrationprofileatdifferenttimes,fromtherethenwecandeter
6、minethediffusioncoefficient,Dasdeterminedbythisdiffusionkineticsequation,theconcentrationprofileofcarbonasvarioustimeswillbelikethisTheabovediffusionisone-direction(0→+∞).Butifweextendsittotwo-way,from-∞to+∞(likeadropletdissolvedintoasolution)withdopantatx=0,thenwehaveSituationb):Dopingwi
7、thafixedsurfaceconcentration(e.g.carburizationofsteel)Carbonconcentrationprofileshownatdifferenttimes,CarbonizationthicknessisdefinedasThesolutionoftheFick’ssecondlawcanbeobtainedasfollows,thesurfaceisincontactwithaninfinitelongreservoiroffixedconcentrationof,choose
