材料化学全英文课件PPT课件 30页

'材料科学基础FundamentalofMaterialsScienceProf:TianMinBoTel:62795426，62772851E-mail:tmb@mail.tsinghua.edu.cnDepartmentofMaterialScienceandEngineeringTsinghuaUniversity.Beijing100084Lessonfive 2.5IndicesofCrystalPlanesandDirections2.5.1What’scrystalplanesanddirections?TheatomicplanesanddirectionspassingthroughthecrystalarecalledCrystalPlanesandCrystalDirectionsrespectively. 1.Stepstodeterminatetheplaneindices:Establishasetofcoordinateaxes.Findtheinterceptsoftheplanestobeindexedona,bandcaxes(x,y,z).2.5.2Planeindicesacbxyz Takethereciprocalsoftheintercepts1/x,1/y,1/z.Clearfractionsbutdonotreducetolowestintegers.Enclosetheminparentheses,(hkl)Example:1/2,1,2/32,1,3/2(423)Planeindicesreferredtothreeaxesa,bandcarealsocalledMillerIndices. SeveralimportantaspectsoftheMillerindicesforplanesshouldbenoted:Planesandtheirnegativesareidentical.Therefore,.Insomesituation,planesandtheirmultiplesarenotidentical.Incubicsystems,adirectionthathasthesameindicesasaplaneisperpendiculartothatplane. Total:12Total:4×3！=24 3.5.3Directionindices1.DerivationforthecrystallographicdirectionAsthefirstabove,settheoriginonthedirectiontobeindexed.Findthecoordinatesofanotherpointonthedirectioninquestions.Reducetothreesmallestintegers:u,v,w.Encloseinsquarebrackets[uvw]. 2.Theimportantdirectionincubiccrystals:<100>:crystalaxes<110>:facediagonal<111>:bodydiagonal<112>:apicestooppositeface-centers3.Familyofdirectionsconsistsofcrystallographicallyequivalentdirections,denoted 2.6HexagonalAxesforHexagonalCrystals2.6.1Whychoosefour-axissystem?Fourindiceshasbeendevisedforhexagonalunitcellsbecauseoftheuniquesymmetryofthesystem. acb 2.6.2Planeindices(hkil)Itcanbeproved:i≡－(h＋k)Sofouraxisofplaneindicescanbededuceddirectly. Importantplanes:a1a2a3c 2.6.3Directionindices[uvtw]Tomaketheindicesunique,anadditionalconditionisimposed.----Lett＝－(u＋v)ImportantdirectionsForexample:three-axis:four-axis:,,areallallowed,butnotunique. TransformationofindicesTransformationof3to4indices,orviceversa.Supposewehaveavector,whose3indices[UVW],and4indices[uvtw].WehaveSincelet or: Forexample: 2.6.4DiscussionaboutDirectionindices[uvtw]1.Whyletaccordingtothreeindices:SothedirectionindicesofOPcouldbe:、、、 Tomakethedirectionindicesbeunique,welet:2.Anothermethodtogetdirectionindices[uvtw]Foranypointthatonthedirection,wegetoutitsverticalprojectionona1,a2,a3,c.andmultiplythefirstthreeindicesby2/3.Clearfractionsandreducethemtolowestintegers. 1.Quickwayforindexingthedirectionsincubiccrystals:Thevalueofadirectiondependsonitsfeaturewhilethesignondirection.DiscussionForexample:<100><110><111><112> 2.Thecoordinateorigincanbesetarbitrarily(forexampleonapices,body-center,face-centersetc.),butneveronplaneinquestions,otherwisetheinterceptswouldbe0,0,0.3.Thecoordinatesystemcanbetransferredarbitrarily,butrotationisforbidden.c´acba´b´ 4.Theatomicarrangementandplanardensityoftheimportantdirectionincubiccrystal.planeindicesBCCFCCatomicarrangementplanardensityatomicarrangementplanardensity{100}{110}{111} 5.Theatomicarrangementandlineardensityoftheimportantdirectionincubiccrystal.linearindicesBCCFCCatomicarrangementlineardensityatomicarrangementlineardensity<100><110><111> 6.Calculatetheplanardensityandplanarpackingfractionforthe(010)and(020)planescubicPolonium,whichhasalatticeparameterof0.334nm.Solution However,noatomsarecenteredonthe(020)planes.Therefore,theplanardensityandtheplanarpackingfractionarebothzero. Exercise1.Writeouttheindicesofallthetantamountplanesanddirectionsoffamilyof{123}planeandfamilyof<112>directionincubiccrystals.2.Drawuptheplanesanddirectionsinunitcellofcubiccrystalsasfollow:3.Labeltheindicesofplanesanddirectionsincubiccrystalsbelow.planecenter 4.Writeouttheindicesofalltheplanesanddirectionsinfamilyofplaneandfamilyofdirectioninhexagonalcrystals.5.Drawuptheplanesanddirectionsinunitcellofhexagonalcrystalsasfollow:6.Labeltheindicesofplanesanddirectionsinhexagonalcrystalsbelow. Thankyou!5'