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uu.Crystal structure is the real arrangement of atom in crystals Crystal structure Crystal structure Space lattice+BasisSpace lattice+Basis or structure unit or structure unit2.3 Crystal Structure and Complex Lattice第1页/共27页.Crystal structure is the rea1 1+=第2页/共27页+=第2页/共27页2 2Fe:Al=1:1Fe:Al=1:1F Fe eA Al lThe difference between space lattice and crystal structure 第3页/共27页Fe:Al=1:1FeAlThe differe3 323 atoms/cell第4页/共27页23 atoms/cell第4页/共27页4 41.BCC 1.BCC Example:-Fe,V,Nb,Ta,Cr,Mo,W,alkali metals n=2 atoms/cell CN=8 The number of nearest neighbours around each atom is called Coordination Number.uu.Typical crystal structures of metals第5页/共27页1.BCC Coordination Number.5 5 Packing fraction To determine,The atom is looked as a hard sphere,and the nearest neighbours touch each other.For BCC,Volume of atoms/cellVolume of atoms/cell Volume of unit cell Volume of unit cell第6页/共27页 Packing fractionVolume of at6 62.FCC2.FCC Example:-Fe,Al,Ni,Pb,Cu,Ag,Au,stainless steal n=81/8+61/2=4 atoms/cell CN=12 第7页/共27页2.FCC第7页/共27页7 73.HCP3.HCP Example:Be,Mg,Zn,Cd,Zr,Hf Ti(low temperature)n CN12 0.74第8页/共27页3.HCP 8 8StructureStructurea a0 0 vs.vs.r rAtoms Atoms per cellper cellCoordination Coordination NumberNumberPacking Packing factorfactorExamplesExamplesSC160.52Polonium(Po),-MnBCC280.68Fe,Ti,W,Mo,Nb,Ta,K,Na,V,Zr,CrFCC4120.74Fe,Cu,Au,Pt,Ag,Pb,NiHCP2120.74Ti,Mg,Zn,Be,Co,Zr,Cd4.Summary4.Summary第9页/共27页Structurea0 vs.rAtoms per cel9 92.4 Interstices in typical crystals of metalsuu.Two types of Interstitials in typical crystals Octahedral interstitialOctahedral interstitial Tetrahedral interstitialTetrahedral interstitialDefinition:In any of the crystal structures,there are small holes between the usual atoms into which smaller atoms may be placed.These locations are called interstitial sites.第10页/共27页2.4 Interstices in typical cr10101.Octahedral interstitial1.Octahedral interstitialBCCBCC第11页/共27页1.Octahedral interstitialBCC第1111FCCFCC第12页/共27页FCC第12页/共27页1212HCPHCP第13页/共27页HCP第13页/共27页13132.Tetrahedral interstitial2.Tetrahedral interstitialBCCBCC第14页/共27页2.Tetrahedral interstitialBCC1414FCCFCC第15页/共27页FCC第15页/共27页1515HCPHCP第16页/共27页HCP第16页/共27页1616uu.Determination of the sizes of interstitialsDefinition:By size of an interstitial we mean diameter of the maximum hard sphere which can be accommodated in the interstitial without distorting the lattice.didadiameter of interstitial atomdiameter of atom in lattice point第17页/共27页.Determination of the sizes o17171.Octahedral interstitialOctahedral interstitial condition for touching 第18页/共27页Octahedral interstitial第18页/共21818For BCCFor BCCFor FCCFor FCC第19页/共27页For BCC第19页/共27页19192.Tetrahedral interstitialTetrahedral interstitialH HL LA AD DC CB Binterstitialinterstitialhost atomhost atom第20页/共27页Tetrahedral interstitialHLADCB2020For BCCFor BCCFor FCCFor FCC第21页/共27页For BCCFor FCC第21页/共27页21213.SummarySummaryn nCNCNintersticesdi/daoct.oct.tete.tete.oct.oct.tete.tete.BCCBCC2 28 80.680.686 66/2=6/2=3 3121212/2=12/2=6 60.150.150.290.29FCCFCC4 412120.740.744 44/4=4/4=1 18 88/4=8/4=2 20.410.410.220.22HCPHCP6 612120.740.746 66/6=6/6=1 1121212/6=12/6=2 20.410.410.220.22第22页/共27页SummarynCNintersticesdi/daoct2222Examples and Discussions1.Both FCC and BCC are close-packed Both FCC and BCC are close-packed structures while BCC is more open?structures while BCC is more open?2.The interstitial atoms most likely occupy the The interstitial atoms most likely occupy the oct.interstitial position in FCC and HCP,while oct.interstitial position in FCC and HCP,while in BCC two types of interstitial can be occupied in BCC two types of interstitial can be occupied equally.equally.第23页/共27页Examples and DiscussionsBoth F23233.3.The solid solubility in BCC is much lower than The solid solubility in BCC is much lower than in FCC.in FCC.4.4.Diffusion of interstitial atoms in BCC diffusion is Diffusion of interstitial atoms in BCC diffusion is much faster than in FCC or HCP at same much faster than in FCC or HCP at same temperature.temperature.5.5.Determine the relationship between the atomic Determine the relationship between the atomic radius and the lattice parameter in SC,BCC,radius and the lattice parameter in SC,BCC,and FCC structures when one atom is located and FCC structures when one atom is located at each lattice point.at each lattice point.第24页/共27页3.The solid solubility in BCC24246.6.Determine the density of BCC iron,which has Determine the density of BCC iron,which has a lattice parameter of 0.2866nm.a lattice parameter of 0.2866nm.Solution:Solution:For a BCC cell,Atoms/cell=2 a0=0.2866nm=2.866108cm Atomic mass=55.847g/mol Volume of unit cell=a03=23.5410 24cm3/cell Density第25页/共27页6.Determine the density of BC2525Exercise1.Determine the coordinates of centers of both Determine the coordinates of centers of both the octahedral and the tetrahedral interstitials the octahedral and the tetrahedral interstitials in HCP referred to in HCP referred to a a,b b and and c c.a ab bc c120120o o第26页/共27页ExerciseDetermine the coordina2626Thank you!4 第27页/共27页Thank you!4 第27页/共27页2727
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