清华大学lesson 26：复习资料

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1、材料科学基础材料科学基础FundamentalofMaterialsFundamentalofMaterialsFundamentalofMaterialsFundamentalofMaterialsProf:TianMinBoTel:62795426，62772851E-mail:tmb@mail.tsinghua.edu.cnDepartmentofMaterialScienceandEngineeringTsinghuaUniversity.Beijing100084ChapterChapterⅥⅥDiffusi

2、oninSolidsDiffusioninSolidsLessontwenty-six§§§§6.1Introduction6.1Introduction6.1Introduction6.1Introduction�ⅠⅠ.Atommovementinsolids.Atommovementinsolidsmechanicalmovementthermalvibration(short-rangemigration)Thermalmotiondiffusion(long-rangemigration)surfacediff

3、usionevaporation&solidificationvolumediffusion�ⅡⅡ.Classificationofdiffusionin.Classificationofdiffusioninsolidssolids∂C1.Accordingto:()∂τSteadystatediffusionandNon-steadystatediffusion∂C2..()=0self-diffusion.bothinpuremetalandin∂xhomogeneousalloy..(∂C)≠0inter-di

4、ffusion.down-hill∂xup-hill3.Accordingtodiffusionpath①Volumediffusion(withgrain,orlattice)②Grainboundarydiffusion③Surfacediffusionshort-cutdiffusion④diffusionalongdislocation4.AccordingtostructureDiffusioninsinglephaseDiffusioninmultiphase�Ⅲ.Significance:.Signifi

5、cance:heattreatment,welding,sintering,corrosion�Ⅳ.Content.Contentphenomenologicaltheorymicroscopictheory§§6.2Fick6.2Fick’’sLawssLaws�ⅠⅠ.Fick.Fick’’sfirstlawsfirstlaw界面C2C1C>C，均为固定值21x∂CForbinary,single-phasesystem∆m∝A∆t∂xdm∆m∂C=lim=−DA—diffusionflowdt∆t→0∆t∂xdm∂

6、CJ==−D—diffusionfluxAdt∂xFor3dimensionaldiffusion:J=−DgradC=−D∇C⎛−Q⎞D=D0exp⎜⎟⎝RT⎠Discussion:1)Itisanempiricalrule2)minussign3)D-materialconstant.4)dimension�ⅡⅡ.Fick.Fick’’ssecondlawssecondlawJ−J∆J12lim=−lim∆x→0∆x∆x→0∆xJxJx+∆x∂J∂C=−=∆xx∂x∂txx+∆x∂C∂(−)∂C∂x=−∂t∂x2∂

7、C∂CifD=const.→=D2∂t∂xFor3dimensionaldiffusion:⎛222⎞∂C∂C∂C∂C2=D⎜++⎟=D∇C∂t⎜∂x2∂y2∂z2⎟⎝⎠1.InCartesiancoordinationsystem∂C∂∂C∂∂C∂∂C=(D)+(D)+(D)∂t∂x∂x∂y∂y∂z∂z222∂C∂C∂C∂CifD=const.=D(++)222∂t∂x∂y∂z2.Forcylindricallysymmetricaldiffusion.2∂CD∂∂C∂CD∂C=(r)=D+2∂tr∂r∂r∂rr∂r

8、3.Forsphericalsymmetricaldiffusion.2∂CD∂2∂C∂CD∂C=(r)=D+222∂tr∂r∂r∂rr∂rRelationbetweenFick’sfirstlawandFick’ssecondlaw§§6.3SteadyStateDiffusion6.3SteadyStateDiffusionF