Thedistancebetweenplanesintheset(hkl),dFortricliniccrystals1.4SimpleCrystalStructures(p.13)1.4.1ClosePackingAclose-packedlayerofsphereswithcentersatpointsAFig.1-19Close-packedstructures:hexagonal(hcp)face-centeredcubic(fcc)hcpfccStackingsequence:ABAB…ABCABC…1.4SimpleCrystalStructures(p.13)1.4.1ClosePackingAclose-packedlayerofsphereswithcentersatpointsAFig.1-19Close-packedstructures:hexagonal(hcp)face-centeredcubic(fcc)hcpfccClose-packedplanes:{0001}{111}1.4.2CharacteristicsofCubicLatticeSimplecubicPrimitivecell=conventionalcellPrimitivevectors:a1aiAa2ajaa3akaLatticepoint/cell=1aeachcellhas8cornerseachatomisshearedby8cellsPackingfractionThemaximumproportionoftheavailablevolumewhichmaybefilledwithhardspheres34a3fVspheres/Vcell/a0.524326Face-centeredcubic(fcc)aPrimitivevectors:a(ij)12aa2(jk)2aaa2a3(ik)2a3a1aNumberofnearestneighbors:12a=48x1/8=16x1/2=3Packingfraction342Vaspheres34f20.7406Body-centeredcubic(bcc)aPrimitivevectors:a(ijk)12aa(ijk)22Aaaa(ijk)32aLatticepoint/cell=2aNumberofnearestneighbors:81.4.3SimpleCrystalStructuresCesiumChlorideStructureExamples:CsCl,CeBr,CeIAlNi,CuZn(b-brass),AgMgFig.1-18-Simplecubic-Basis:Cs+at000andCl-at½,½,½-8nearestneighborsSodiumChlorideStructureExamples:NaCl,KCl,PbSMgO,MnO,Fig.1-15-Spacelattice:face-centeredcubic-6nearestneighbors-Basis:Cl-at000andNa+at½,½,½Whyalkalinehalideshavedifferentstructures?2r32R2R231Rr31R0.73R2R0.73r1Generally:R(Cs+ionicradius174pm,Cl−181pm)2rR222R2rR2Rr/R0.41Generally:0.41r/R0.73(Na+ionicradius102pm,Cl−181pm)Crystalstructureiscloselyrelatedtotheatom(ion)radius:WhenbothionsaresimilarinsizetheCsClstructureisadopted,whentheyaredifferenttheNaClstructureisadoptedDiamondStructureExamples:DiamondCSi,GeSnFig.1-23-Twosetsoffccstructuresdisplacedfrome