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1、材料科学基础Fundamental of MaterialsProf:Tian Min Bo Tel:62795426，62772851 E-mail:Department of Material Science and EngineeringTsinghua University.Beijing 100084Lesson fouruu.Crystal structure is the real arrangement of atom in crystals Crystal structure Crystal structure Space lattice+BasisSpace lattice
2、+Basis or structure unit or structure unit2.3 Crystal Structure and Complex Lattice+=Fe:Al=1:1Fe:Al=1:1FeFeAl AlThe difference between space lattice and crystal structure 23 atoms/cell1.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 ea
3、ch atom is called Coordination Number.uu.Typical crystal structures of metals 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 cell2.FCC2.FCC Example:-Fe,A
4、l,Ni,Pb,Cu,Ag,Au,stainless steal n=81/8+61/2=4 atoms/cell CN=12 3.HCP3.HCP Example:Be,Mg,Zn,Cd,Zr,Hf Ti(low temperature)n CN12 0.74StructureStructurea a0 0 vs.vs.r rAtoms Atoms per cellper cellCoordination Coordination NumberNumberPacking Packing factorfactorExamplesExamplesSC160.52Polonium(Po),-MnB
5、CC280.68Fe,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.Summary2.4 Interstices in typical crystals of metalsuu.Two types of Interstitials in typical crystals Octahedral interstitialOctahedral interstitial Tetrahedral interstitialTetrahedral interst
6、itialDefinition: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.1.Octahedral interstitial1.Octahedral interstitialBCCBCCFCCFCCHCPHCP2.Tetrahedral interstitial2.Tetrahedral interstitial
7、BCCBCCFCCFCCHCPHCPuu.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 point1.Octahedra
8、l interstitialOctahedral interstitial condition for touching For BCCFor BCCFor FCCFor FCC2.Tetrahedral interstitialTetrahedral interstitialH HL LA AD DC CB Binterstitialinterstitialhost atomhost atomFor BCCFor BCCFor FCCFor FCC3.SummarySummaryn nCNCNintersticesdi/daoctoct.tetetete.octoct.tetetete.BC
9、CBCC2 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 20.410.410.220.22Examples and Discussions1.Both FCC and BCC are close-packed Both FCC and BCC are close-packed structur
10、es 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
11、BCC two types of interstitial can be occupied equally.equally.3.3.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 i
12、n 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 i
13、s located and FCC structures when one atom is located at each lattice point.at each lattice point.6.6.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
14、a0=0.2866nm=2.866108cm Atomic mass=55.847g/mol Volume of unit cell=a03=23.5410 24cm3/cell DensityExercise1.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 oThank you!4