材料化学全英文课件PPT课件

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1、材料科学基础FundamentalofMaterialsScienceProf:TianMinBoTel:62795426，62772851E-mail:tmb@mail.tsinghua.edu.cnDepartmentofMaterialScienceandEngineeringTsinghuaUniversity.Beijing100084Lessonfive2.5IndicesofCrystalPlanesandDirections2.5.1What’scrystalplanesanddirections?Theatomicplanesanddirectionspassingthr

2、oughthecrystalarecalledCrystalPlanesandCrystalDirectionsrespectively.1.Stepstodeterminatetheplaneindices:Establishasetofcoordinateaxes.Findtheinterceptsoftheplanestobeindexedona,bandcaxes(x,y,z).2.5.2PlaneindicesacbxyzTakethereciprocalsoftheintercepts1/x,1/y,1/z.Clearfractionsbutdonotreducetol

3、owestintegers.Enclosetheminparentheses,(hkl)Example:1/2,1,2/32,1,3/2(423)Planeindicesreferredtothreeaxesa,bandcarealsocalledMillerIndices.SeveralimportantaspectsoftheMillerindicesforplanesshouldbenoted:Planesandtheirnegativesareidentical.Therefore,.Insomesituation,planesandtheirmultiplesarenoti

4、dentical.Incubicsystems,adirectionthathasthesameindicesasaplaneisperpendiculartothatplane.Total:12Total:4×3！=243.5.3Directionindices1.DerivationforthecrystallographicdirectionAsthefirstabove,settheoriginonthedirectiontobeindexed.Findthecoordinatesofanotherpointonthedirectioninquestions.Reducetoth

5、reesmallestintegers:u,v,w.Encloseinsquarebrackets[uvw].2.Theimportantdirectionincubiccrystals:<100>:crystalaxes<110>:facediagonal<111>:bodydiagonal<112>:apicestooppositeface-centers3.Familyofdirectionsconsistsofcrystallographicallyequivalentdirections,denoted2.6HexagonalAxesforHexagonalCrysta

6、ls2.6.1Whychoosefour-axissystem?Fourindiceshasbeendevisedforhexagonalunitcellsbecauseoftheuniquesymmetryofthesystem.acb2.6.2Planeindices(hkil)Itcanbeproved:i≡－(h＋k)Sofouraxisofplaneindicescanbededuceddirectly.Importantplanes:a1a2a3c2.6.3Directionindices[uvtw]Tomaketheindicesunique,anadditionalcond

7、itionisimposed.----Lett＝－(u＋v)ImportantdirectionsForexample:three-axis:four-axis:,,areallallowed,butnotunique.TransformationofindicesTransformationof3to4indices,orviceversa.Supposewehaveavector,whose3indices[UVW]