固体物理+晶体结构

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1、SOLIDSTATECrystalsStructures1.UnitCellCrystalstructurebasicsunitcellssymmetrylatticesSomeimportantcrystalstructuresandpropertiesclosepackedstructuresoctahedralandtetrahedralholesbasicstructuresferroelectricityObjectivesBytheendofthissectionyoushould:beabletoidentifyaunitcellinasymmetricalpat

2、ternknowthatthereare7possibleunitcellshapesbeabletodefinecubic,tetragonal,orthorhombicandhexagonalunitcellshapesWhySolids?mostelementssolidatroomtemperatureatomsin~fixedposition“simple”case-crystallinesolidCrystalStructureWhystudycrystalstructures?descriptionofsolidcomparisonwithothersi

3、milarmaterials-classificationcorrelationwithphysicalpropertiesEarlyideasCrystalsaresolid-butsolidsarenotnecessarilycrystallineCrystalshavesymmetry(Kepler)andlongrangeorderSpheresandsmallshapescanbepackedtoproducesregularshapes(Hooke,Hauy)?GroupdiscussionKeplerwonderedwhysnowflakeshave6corne

4、rs,never5or7.Byconsideringthepackingofpolygonsin2dimensions,demonstratewhypentagonsandheptagonsshouldn’toccur.EmptyspacenotallowedDefinitions1.Theunitcell“Thesmallestrepeatunitofacrystalstructure,in3D,whichshowsthefullsymmetryofthestructure”Theunitcellisaboxwith:3sides-a,b,c3angles-,,Sev

5、enunitcellshapesCubica=b=c===90°Tetragonala=bc===90°Orthorhombicabc===90°Monoclinicabc==90°,90°Triclinicabc90°Hexagonala=bc==90°,=120°Rhombohedrala=b=c==90°2Dexample-rocksalt(sodiumchloride,NaCl)Wedefinelatticepoints;thesearepointswithidenticalenvironmentsC

6、hoiceoforiginisarbitrary-latticepointsneednotbeatoms-butunitcellsizeshouldalwaysbethesame.Thisisalsoaunitcell-itdoesn’tmatterifyoustartfromNaorCl-orifyoudon’tstartfromanatomThisisNOTaunitcelleventhoughtheyareallthesame-emptyspaceisnotallowed!In2D,thisISaunitcellIn3D,itisNOTAllM.C.Escherwor

7、ks(c)CordonArt-Baarn-theNetherlands.Allrightsreserved.SummaryUnitcellsmustlinkup-cannothavegapsbetweenadjacentcellsAllunitcellsmustbeidenticalUnitcellsmustshowthefullsymmetryofthestructurenextsectionCrystalsStructures2:SymmetryBytheendofthissecti