清华材料科学基础课件英文skja

材料科学基础

FundamentalofMaterialsLessonfive6/28/2024材料科学基础§2.5IndicesofcrystalplanesanddirectionsⅠ.What’scrystalplanesanddirections?Theatomicplanesanddirectionspassingthroughthecrystalarecalled(crystal)planesanddirectionsrespectively.6/28/2024材料科学基础1.Stepstodeterminatetheplaneindices:

Establishasetofcoordinateaxes

Findtheinterceptsoftheplanestobeindexedona,b

and

caxes(x,y,z).a

c

b

x

y

z

Ⅱ.Planeindices6/28/2024材料科学基础Takethereciprocalsoftheintercepts1/x,1/y,1/z.Clearfractionsbutdonotreducetolowestintegers.Enclosetheminparentheses,(hkl)

Example:1/2,1,2/32,1,3/2(423)

Planeindicesreferredtothreeaxesa,b

and

c

arealsocalledMillerIndices.6/28/2024材料科学基础SeveralimportantaspectsoftheMillerindicesforplanesshouldbenoted:

Planesandtheirnegativesareidentical.Therefore.

Planesandtheirmultiplesarenotidentical.

Incubicsystems,adirectionthathasthesameindicesasaplaneisperpendiculartothatplane.6/28/2024材料科学基础2.Theimportantplanesincubiccrystals(110)(112)(111)(001)6/28/2024材料科学基础3.Afamilyofplanesconsistsofequivalentplanessofarastheatomarrangementisconcerned.Total:6Total:46/28/2024材料科学基础Total:12Total:4×3！=246/28/2024材料科学基础Ⅲ.DirectionIndices1.DerivationforthecrystallographicdirectionAsthefirstabove,settheoriginonthedirectiontobeindexed.Findthecoordinatesofanotherpointonthedirectioninquestions.Reducetothreesmallestintegers:u,v,w.Encloseinsquarebrackets[uvw].6/28/2024材料科学基础2.Theimportantdirectionincubiccrystals:<100>:crystalaxes<110>:facediagonal<111>:bodydiagonal<112>:apicestooppositeface-centers3.Familyofdirectionsconsistsofcrystallographicallyequivalentdirections,denoted<uvw>e.g.

6/28/2024材料科学基础§2.6HexagonalaxesforhexagonalcrystalsⅠ.Whychoosefour-axissystem?

Fourindiceshasbeendevisedforhexagonalunitcellsbecauseoftheuniquesymmetryofthesystem.6/28/2024材料科学基础acb6/28/2024材料科学基础Ⅱ.Planeindices(hkil)Itcanbeproved:i≡－(h＋k)6/28/2024材料科学基础Importantplanes:a1a2a3c6/28/2024材料科学基础Ⅲ.Directionindices[uvtw]

Tomaketheindicesunique,anadditionalconditionisimposed.----Let

t＝－(u＋v)Importantdirections6/28/2024材料科学基础TransformationofindicesTransformationof3to4indices,orviceversa.Supposewehaveavector,whose3indices[uvw],and4indices[uvtw].WehaveSince6/28/2024材料科学基础or:6/28/2024材料科学基础Forexample:6/28/2024材料科学基础1.Quickwayforindexingthedirectionsincubiccrystals:Thevalueofadirectiondependsonitsfeaturewhilethesignondirection.ExamplesandDiscussions6/28/2024材料科学基础2.Thecoordinateorigincanbesetarbitrarily(forexampleonapices,body-center,face-centersetc.),butneveronplaneinquestions,otherwisetheinterceptswouldbe0,0,0.3.Thecoordinatesystemcanbetransferredarbitrarily,butrotationisforbidden.c´

a

c

b

a´

b´

6/28/2024材料科学基础4.Theatomicarrangementandplanardensityoftheimportantdirectionincubiccrystal.planeindicesBCCFCCatomicarrangementplanardensityatomicarrangementplanardensity{100}{110}{111}6/28/2024材料科学基础5.Theatomicarrangementandlineardensityoftheimportantdirectionincubiccrystal.linearindicesBCCFCCatomicarrangementlineardensityatomicarrangementlineardensity<100><110><111>6/28/2024材料科学基础ExerciseCalculatetheplanardensityandplanarpackingfractionforthe(010)and(020)planescubicpolonium,whichhasalatticeparameterof0.334nm.