清华材料科学基础课件(英文)skja_03

2020/1/20材料科学基础材料科学基础FundamentalofMaterialsProf:TianMinBoTel:62795426，62772851E-mail:tmb@mail.tsinghua.edu.cnDepartmentofMaterialScienceandEngineeringTsinghuaUniversity.Beijing1000842020/1/20材料科学基础§2.1SpaceLatticeⅠ.Crystalsversusnon-crystals1.ClassificationoffunctionalmaterialsChapterⅡFundamentalsofCrystallographyLessonthree2020/1/20材料科学基础2020/1/20材料科学基础2.ClassificationofmaterialsbasedonstructureRegularityinatomarrangement——periodicornot(amorphous)2020/1/20材料科学基础Crystalline:Thematerialsatomsarearrangedinaperiodicfashion.Amorphous:Thematerial’satomsdonothavealong-rangeorder(0.1～1nm).Singlecrystal:intheformofonecrystalgrainsPolycrystalline:grainboundaries2020/1/20材料科学基础2020/1/20材料科学基础2020/1/20材料科学基础Ⅱ.Spacelattice1.Definition:Spacelatticeconsistsofanarrayofregularlyarrangedgeometricalpoints,calledlatticepoints.The(periodic)arrangementofthesepointsdescribestheregularityofthearrangementofatomsincrystals.2.Twobasicfeaturesoflatticepoints①Periodicity:Arrangedinaperiodicpattern.②Identity:Thesurroundingsofeachpointinthelatticeareidentical.2020/1/20材料科学基础2020/1/20材料科学基础Alatticemaybeone,two,orthreedimensionaltwodimensionsSpacelatticeisapointarraywhichrepresentstheregularityofatomarrangements(1)(2)(3)ab2020/1/20材料科学基础ThreedimensionsEachlatticepointhasidenticalsurroundingenvironment2020/1/20材料科学基础Ⅲ.Unitcellandlatticeconstants1.Unitcellisthesmallestunitofthelattice.Thewholelatticecanbeobtainedbyinfinitiverepetitionoftheunitcellalongit’sthreeedges.2.Thespacelatticeischaracterizedbythesizeandshapeoftheunitcell.2020/1/20材料科学基础2020/1/20材料科学基础Howtodistinguishthesizeandshapeofthedeferentunitcell?Thesixvariables,whicharedescribedbylatticeconstants——a,b,c;α,β,γ2020/1/20材料科学基础LatticeConstantsacbαβγacbαβγ2020/1/20材料科学基础§2.2CrystalSystem&LatticeTypesIfarotationaroundanaxispassingthroughthecrystalbyanangleof360o/ncanbringthecrystalintocoincidencewithitself,thecrystalissaidtohavean-foldrotationsymmetry.Andaxisissaidtoben-foldrotationaxis.Weidentify14typesofunitcells,orBravaislattices,groupedinsevencrystalsystems.2020/1/20材料科学基础Ⅰ.SevencrystalsystemsAllpossiblestructurereducetoasmallnumberofbasicunitcellgeometries.①Thereareonlyseven,uniqueunitcellshapesthatcanbestackedtogethertofillthree-dimensional.②Wemustconsiderhowatomscanbestackedtogetherwithinagivenunitcell.2020/1/20材料科学基础SevenCrystalSystemsTriclinica≠b≠c，α≠β≠γ≠90°Monoclinica≠b≠c，α＝β＝90°≠γα＝γ＝90°≠βOrthorhombica≠b≠c，α＝β＝γ＝90°Tetragonala＝b≠c，α＝β＝γ＝90°Cubica＝b＝c，α＝β＝γ＝90°Hexagonala＝b≠c，α＝β＝90°γ＝120°Rhombohedrala＝b＝c，α＝β＝γ≠90°2020/1/20材料科学基础Ⅱ.14typesofBravaislattices1.DerivationofBravaislatticesBravaislatticescanbederivedbyaddingpointstothecenterofthebodyand/orexternalfacesanddeletingthoselatticeswhichareidentical.2020/1/20材料科学基础7×4＝28Deletethe14typeswhichareidentical28－14＝14+++PICF2020/1/20材料科学基础2.14typesofBravaislattice①Tricl:simple(P)②Monocl:simple(P).base-centered(C)③Orthor:simple(P).body-centered(I).base-centered(C).face-centered(F)④Tetr:simple(P).body-centered(I)⑤Cubic:simple(P).body-centered(I).face-centered(F)⑥Rhomb:simple(P).⑦Hexagonal:simple(P).2020/1/20材料科学基础2020/1/20材料科学基础Crystalsystems(7)Latticetypes(14)PCFIABC1Triclinic√2Monoclinic√√or√(γ≠90°orβ≠90°)3Orthorhombic√√or√or√√√4Tetragonal√√5Cubic√√√6Hexagonal√7Rhombohedral√Sevencrystalsystemsandfourteenlatticetypes2020/1/20材料科学基础Ⅲ.PrimitiveCellForprimitivecell,thevolumeisminimumPrimitivecellOnlyincludesonelatticepoint2020/1/20材料科学基础Ⅳ.ComplexLatticeTheexampleofcomplexlatticeaabc120o120o120o2020/1/20材料科学基础ExamplesandDiscussions1.Whyarethereonly14spacelattices?ExplainwhythereisnobasecenteredandfacecenteredtetragonalBravaislattice.2020/1/20材料科学基础P→CI→FButthevolumeisnotminimum.2020/1/20材料科学基础2.Criterionforchoiceofunitcell•Symmetry•Asmanyrightangleaspossible•Thesizeofunitcellshouldbeassmallaspossible2020/1/20材料科学基础Exercise1.Determinethenumberoflatticepointspercellinthecubiccrystalsystems.Ifthereisonlyoneatomlocatedateachlatticepoint,calculatethenumberofatomsperunitcell.2.DeterminetherelationshipbetweentheatomicradiusandthelatticeparameterinSC,BCC,andFCCstructureswhenoneatomislocatedateachlatticepoint.3.DeterminethedensityofBCCiron,whichhasalatticeparameterof0.2866nm.2020/1/20材料科学基础4.ProvethattheA-face-centeredhexagonallatticeisnotanewtypeoflatticeinadditiontothe14spacelattices.5.DrawaprimitivecellforBCClattice.Thankyou!3