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1、C h a p t e r 3/Structures of Metals and CeramicsC h a p t e r 3 Structures of Metals and CeramicsHigh velocity electron beams wavelike.wavelengths shorter than interatomic spacings,diffraction by atomic planes in crystalline materials,As x-raysC h a p t e r 3/Structures of Metals and CeramicsWhy St

2、udy Structures of Metals and Ceramics?properties of some materialscrystal structuresdirectly related byFor example:Magnesium(Mg)Beryllium(Be)Having same crystal structuremore brittlethanGold(Au)Silver(Ag)Having same crystal structureCrystallineand NoncrystallineDifferentpropertyhaving the same compo

3、sition but different structure3.1 INTRODUCTIONC h a p t e r 3/Structures of Metals and CeramicsChapter 2 was concerned atomic bonding.the electron structure of the individual atoms.In this chapternext level of the structure of materials the arrangements of atoms in the solid stateIntroducing the con

4、ceptscrystal and noncrystalFor crystal structureunit cellcrystallographic directions and planesmetals and ceramicsSingle crystals and polycrystalline非晶体晶体晶胞单晶体多晶体C h a p t e r 3/Structures of Metals and Ceramics3.2 Fundamental ConceptsCrystalline.The state of a solid material characterized by a peri

5、odic and repeating three-dimensional array of atoms,ions,or molecules.long-range orderthe atoms will position themselves in a repetitive three-dimensional pattern,in which each atom is bonded to its nearest-neighbor atoms.All metals,many ceramic materials,and certain polymers form crystalline struct

6、uresMaterialscrystallineNoncrystalline or amorphousNo long-range atomic order长程有序C h a p t e r 3/Structures of Metals and CeramicsThe description of crystallineatomic hard sphere modelUnit Cells晶胞晶胞3.3 Unit Cellshard sphere lattice unit cells晶格晶格C h a p t e r 3/Structures of Metals and Ceramicsatomi

7、c hard sphere model:atoms(or ions)are thought of as being solid spheres having well-defined diameters.lattice.The regular geometrical arrangement of points in crystal space.(means a three-dimensional array of points coinciding with atom positions)unit cells:The basic structural unit of a crystal str

8、ucture.It is generally defined in terms of atom(or ion)positions within a parallelepiped or prisms volume.the lattice parameters:The combination of unit cell edge lengths and interaxial angles that defines the unit cell geometry.a,b,c,and ,.硬球模型晶格晶胞晶格常数平行六面体棱柱C h a p t e r 3/Structures of Metals and

9、 CeramicsCrystal structure.For crystalline materials,the manner in which atoms or ions are arrayed in space.It is defined in terms of the unit cell geometry and the atom positions within the unit cell.A unit cell is chosen to represent the symmetry of the crystal structure,the unit cell is the basic

10、 structural unit or building block of the crystal structure对称性C h a p t e r 3/Structures of Metals and Ceramics3.4 Metallic Crystal Structuresno restrictions as to the number and position of nearest-neighbor atomsdense atomic packingsThree relatively simple crystal structuresface-centered cubic,body

11、-centered cubic,and hexagonal close-packed1.The Face-centered Cubic Crystal StructureA crystal structure found in some of the common elemental metals.Within the cubic unit cell,atoms are located at all corner and face-centered positions.面心立方晶格无限制原子密堆C h a p t e r 3/Structures of Metals and CeramicsF

12、IGURE 3.1 For the face-centered cubic crystal structure:(a)a hard sphere unit cell representation,(b)a reduced-sphere unit cell,and(c)an aggregate of many atoms.a=b=c and=90o atoms located at each of the corners and the centers of all the cube faces.the face-centered cubic(FCC)C h a p t e r 3/Struct

13、ures of Metals and Ceramics1).the cube edge length a and the atomic radius R are related through2).The number of atom in unit cell(n):原子半径晶胞 原子数3).Coordination Number(CN):The number of atomic or ionic nearest neighbors.For“FCC”crystal structure:CN=12配位数C h a p t e r 3/Structures of Metals and Cerami

14、cs4)Atomic Packing Factor(APF):The fraction of the volume of a unit cell that is occupied by hard sphere atoms or ions.紧密系数(致密度)C h a p t e r 3/Structures of Metals and Ceramics2.The Body-centered Cubic Crystal Structurebody-centered cubic(BCC)a=b=c and=90oatoms are located at corner and cell center

15、 positions.FIGURE 3.2 For the body-centered cubic crystal structure,(a)a hard sphere unit cell representation,(b)a reduced-sphere unit cell,and(c)an aggregate of many atoms.体心立方晶格C h a p t e r 3/Structures of Metals and Ceramics1)the cube edge length a and the atomic radius R are related through2)Th

16、e number of atom in unit cell(n):3)CN=84)C h a p t e r 3/Structures of Metals and Ceramics3.The Hexagonal Close-packed Crystal Structurehexagonal close-packed(HCP):The top and bottom faces of the unit cell consist of six atoms that form regular hexagons and surround a single atom in the center.Anoth

17、er plane that provides three additional atoms to the unit cell is situated between the top and bottom planes.a=bc c/a=1.633 and =90o =120oFIGURE 3.3 For the hexagonal close-packed crystal structure,(a)a reduced-sphere unit cell and(b)an aggregate of many atoms.密排六方晶格C h a p t e r 3/Structures of Met

18、als and Ceramics2).The number of atom in unit cell(n):3)CN=124)1).the cube edge length a and the atomic radius R are related throughacC h a p t e r 3/Structures of Metals and Ceramics铬镉钴C h a p t e r 3/Structures of Metals and Ceramics3.5 Density Computationsmetalsn:number of atoms associated with e

19、ach unit cellA:atomic weightVc:volume of the unit cellNA:Avogadros number(6.0231023 atoms/mol)EXAMPLE:Copper R=0.128 nm(1.28)FCC ACu=63.5 g/molThe literature value for the density of copper is 8.94 g/cm3C h a p t e r 3/Structures of Metals and Ceramics3.6 Ceramic Crystal StructuresCeramics least two

20、 elements or more,crystal structures more complex atomic bonding from purely ionic to totally covalent,sometimes,two bonding types.the degree of ionic character dependent on the electronegativities By Equation 2.10 and Figure 2.7 Table 3.2 the percent ionic characterTable 3.2 For Several Ceramic Mat

21、erials,Percent Ionic Character of the Interatomic BondsC h a p t e r 3/Structures of Metals and Ceramicscrystal structures of ceramic materials bonded in predominantly ionicCationsAnionsA positively charged metallic ion.阳离子阳离子阴离子阴离子A negatively charged nonmetallic ion.Two characteristics of influenc

22、e the crystal structurethe magnitude of the electrical charge ionsthe relative sizes of the cations and anions.the crystal must be electrically neutral.that is,all the cation positive charges must be balanced by an equal number of anion negative charges.the sizes or ionic radii of the cations and an

23、ions,rC and rA,rC rA,rC/rA1For example:CaF2C h a p t e r 3/Structures of Metals and CeramicsFIGURE 3.4 Stable and unstable anioncation coordination configurations.Open circles represent anions;colored circles denote cations.EXAMPLE:Show that the minimum cation-to-anion radius ratio for the coordinat

24、ion number 3 is 0.155.AP=rAAO=rA+rCAP/AO=cos=rA/(rA+rC)cos30o =C h a p t e r 3/Structures of Metals and CeramicsTable 3.3 Coordination Numbers and Geometries for Various CationAnion Radius Ratios(rC/rA)C h a p t e r 3/Structures of Metals and CeramicsTable 3.4 Ionic Radii for Several Cations and Ani

25、ons(for a Coordination Number of 6)C h a p t e r 3/Structures of Metals and Ceramics1.AX-Type Crystal StructuresA:cation X:anion.Numbers of cations=Numbers of anionsFIGURE 3.5 A unit cell for the rock salt,or sodium chloride(NaCl),crystal structure.Rock Salt(NaCl)Structure岩盐岩盐 CN=6 for both cations

26、and anions 0.411rC/rA120 oC the crystal structure is cubicC h a p t e r 3/Structures of Metals and CeramicsEXAMPLE PROBLEM 3.5On the basis of ionic radii,what crystal structure would you predict for FeO?(which from Table 3.4)value lies between 0.414 and 0.732,from Table 3.3 CN=6Predicted crystal str

27、ucture will be rock salt尖晶石C h a p t e r 3/Structures of Metals and Ceramics3.7 Density ComputationsCeramicsFor Ceramic:n the number of formula units within the unit cellAC the sum of the atomic weights of all cations in the formula unitAA the sum of the atomic weights of all anions in the formula u

28、nitVC the unit cell volumeNA Avogadros number,6.023 1023 formula units/molEXAMPLE PROBLEM 3.6compute the theoretical density for sodium chloride.n=4;AC=ANa=22.99 g/mol AA=ACl=35.45 g/molC h a p t e r 3/Structures of Metals and CeramicsVC=a3a=2rNa+2rCl-VC=a3=(2rNa+2rCl-)3rNa+=0.102 rCl-=0.181 by tabl

29、e 3.4experimental value=2.16 g/cm3C h a p t e r 3/Structures of Metals and Ceramics3.8 Silicate Ceramics 硅酸盐陶瓷硅酸盐陶瓷Silicatessilicon oxygenFIGURE 3.10 A siliconoxygen()tetrahedron.tetrahedronbasic unit:treating as a negatively charged entitySiO bonds have significant covalent characterVarious silicat

30、e structures arise from the different ways in which the units can be combined into one-,two-,and three-dimensional arrangements.basic unit:C h a p t e r 3/Structures of Metals and CeramicsSilica 硅石硅石,二氧化硅二氧化硅 SiO2silicon dioxide,or silica(SiO2).the most simple silicate materialisStructure:a three-di

31、mensional network.every corner oxygen atom in each tetrahedron is shared by adjacent tetrahedra.FIGURE 3.11 The arrangement of silicon and oxygen atoms in a unit cell of cristobalite,a polymorph of SiO2.three primary polymorphic crystalline forms:quartz,石英cristobalite,方石英Tridymite,磷石英Complicated str

32、ucture,low densitieshigh melting temperature(1710 oC)also noncrystalline or glass方石英C h a p t e r 3/Structures of Metals and Ceramicshave formulas,and so on;FIGURE 3.12 Five silicate ion structures formed from tetrahedra.cations such as Ca2+,Mg2+,and Al3+serve two roles.FirstneutralitySecondbond the

33、 tetrahedra*C h a p t e r 3/Structures of Metals and CeramicsSimple Silicates Fig.3.12(a),For example,forsterite(Mg2SiO4)ion is formed Fig.3.12(b)Akermanite(Ca2MgSi2O7)Layered Silicates：single-chain structures:Fig.3.12(e)Kaolinite clay has the formula Al2(Si2O5)(OH)4高岭石镁橄榄石镁黄长石简单硅酸盐单链结构层状硅酸盐*C h a p

34、 t e r 3/Structures of Metals and Ceramics3.9 CarbonDIAMONDFIGURE 3.16 A unit cell for the diamond cubic crystal structure.each carbon bonds to four other carbons,bonds are totally covalent.called the diamond cubic crystal structure,which is also found for other Group IVA elementse.g.,germanium,sili

35、con,and gray tin,below 13 oC锗、硅、灰锡金刚石立方C h a p t e r 3/Structures of Metals and CeramicsGRAPHITEFIGURE 3.17 The structure of graphite.more stable than diamondlayers of hexagonallywithin the layers,each carbon atom is bonded to three coplanar neighbor atoms by strong covalent bonds.The fourth bonding

36、 electron participates in a weak van der Waals type of bond between the layers.石墨C h a p t e r 3/Structures of Metals and CeramicsDiamond金刚石金刚石(Sp3)Graphite石墨石墨(Sp2+范力范力)Fullerenes 富勒烯富勒烯 C60 (Sp2)Carbon-Onion洋葱碳洋葱碳(Sp2+范力范力)Bucky-DiamondB-B-金刚石金刚石(Sp3+Sp2)Carbon-Nanotube碳纳米管碳纳米管(Sp2)Carbon Family a

37、t the NanoscaleCarbon Family at the Nanoscale*C h a p t e r 3/Structures of Metals and Ceramics3.10 Polymorphism And AllotropyPolymorphism:The ability of a solid material to exist in more than one form or crystal structure.Allotropy:The possibility of existence of two or more different crystal struc

38、tures for a substance(generally an elemental solid).For examples:carbongraphite is the stable polymorph at ambient conditions,whereas diamond is formed at extremely high pressures.Also,pure iron has a BCC crystal structure at room temperature,which changes to FCC iron at 912 oC.多形性，同素异构C h a p t e r

39、 3/Structures of Metals and Ceramics3.11 Crystal SystemsCrystal structrue=lattice+basislatticeLattice points surrounding of each point are identicalBasis or motif 基元基元 A group of atoms associated with a lattice point结点结点 In this section,we deal with the type of latice only.For examples:Lattice:FCC b

40、asis:NaCl晶系每个结点是等同点C h a p t e r 3/Structures of Metals and CeramicsUnit cell lattice parametersFIGURE 3.19 A unit cell with x,y,and z coordinate axes,showing axial lengths(a,b,and c)and interaxial angles(,and ).a,b,and c,and,and Crystal system:A scheme by which crystal structures are classified acc

41、ording to unit cell geometry.This geometry is specified in terms of the relationships between edge lengths and interaxial angles.There are seven different crystal systems.cubic,tetragonal,hexagonal,orthorhombic,rhombohedral,monoclinic,triclinic.立方正方六方斜方,正交菱方单斜三斜the greatest degree of symmetryLeast s

42、ymmetryC h a p t e r 3/Structures of Metals and CeramicsTable 3.6 Lattice Parameter Relationships and Figures Showing Unit Cell Geometries for the Seven Crystal SystemsC h a p t e r 3/Structures of Metals and Ceramicsmetallic crystal structures:FCC and BCC belong to the cubic crystal system.HCP fall

43、s within hexagonal.C h a p t e r 3/Structures of Metals and CeramicsThe fourteen type of Bravais lattices 十四种布拉菲晶格简单立方，面心立方体心立方简单正方，体心正方简单六方简单正交，体心正交底心正交，面心正交简单菱方简单单斜，底心单斜简单三斜*C h a p t e r 3/Structures of Metals and Ceramics3.12 Crystallographic DirectionsA crystallographic direction is defined as

44、a line between two points,or a vector.1.A vector of convenient length is positioned such that it passes through the origin of the coordinate system.Any vector may be translated throughout the crystal lattice without alteration,if parallelism is maintained.2.The length of the vector projection on eac

45、h of the three axes is determined;these are measured in terms of the unit cell dimensions a,b,and c.3.These three numbers are multiplied or divided by a common factor to reduce them to the smallest integer values.晶向做平行线求坐标化减C h a p t e r 3/Structures of Metals and Ceramics4.The three indices,not sep

46、arated by commas,are enclosed in square brackets,thus:uvw.The u,v,and w integers correspond to the reduced projections along the x,y,and z axes,respectively.FIGURE 3.20 The 100,110,and 111 directions within a unit cell.Indices exist both positive and negative,For example,the 111 directionC h a p t e

47、 r 3/Structures of Metals and CeramicsEXAMPLE PROBLEM 3.7C h a p t e r 3/Structures of Metals and CeramicsEXAMPLE PROBLEM 3.8Draw a 110 direction within a cubic unit cell.C h a p t e r 3/Structures of Metals and Ceramicsdirections family:several nonparallel directions with different indices are actu

48、ally equivalent;this means that the spacing of atoms along each direction is the same.For example:in cubic crystals,100,100,010,010,001,001 In cubic crystals:having the same indices without regard to order or sign,for example,123 and 213,are equivalent.This is not true for other crystal systems.晶向族C

49、 h a p t e r 3/Structures of Metals and CeramicsHEXAGONAL CRYSTALSfour-axis,or MillerBravais,FIGURE 3.21 Coordinate axis system for a hexagonal unit cell(MillerBravais scheme).three a1,a2,and a3 axes form a basal plane,and one Z axes perpendicular to basal plane.four indices,uvtwC h a p t e r 3/Stru

50、ctures of Metals and Ceramicsuvw uvtwn is a factor that may be required to reduce u,v,t,and w to the smallest integers.C h a p t e r 3/Structures of Metals and CeramicsFIGURE 3.22 For the hexagonal crystal system,(a)0001,1100,and 1120 directions,For example:010 1210.C h a p t e r 3/Structures of Met