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1、C h a p t e r 3/Structures of Metals and Ceramics,Why Study Structures of Metals and Ceramics?,The properties of some materials are directly related to their crystal structures.For example,pure and undeformed magnesium and beryllium,having one crystal structure,are much more brittle(i.e.,fracture at
2、 lower degrees of deformation)than are pure and undeformed metals such as gold and silver that have yet another crystal structure(see Section 8.5).,Furthermore,significant property differences exist between crystalline and noncrystalline materials having the same composition.For example,noncrystalli
3、ne ceramics and polymers normally are optically transparent;the same materials in crystalline(or semicrystalline)form tend to be opaque or,at best,translucent.,同素异型 晶系 晶格参数无定形的 晶体 密勒指数阴离子 衍射 非晶体各向异性 面心立方 八面体位置致密度 颗粒 多晶体体心立方 晶粒界 类质异象 布拉格定律 密排六方 单晶体阳离子 各向同性 四面体位置配位数 晶格 单位晶胞晶体结构,L e a r n i n g O b j e
4、 c t i v e s After studying this chapter you should be able to do the following:,1.Describe the difference in atomic/molecular structure between crystalline and noncrystalline materials.2.Draw unit cells for face-centered cubic,body-centered cubic,and hexagonal close-packed crystal structures.,3.Der
5、ive the relationships between unit cell edge length and atomic radius for face-centered cubic and body-centered cubic crystal structures.4.Compute the densities for metals having face-centered cubic and body-centered cubic crystal structures given their unit cell dimensions.,5.Sketch/describe unit c
6、ells for sodium chloride,cesium chloride,zinc blende,diamond cubic,fluorite,and perovskite crystal structures.Do likewise for the atomic structures of graphite and a silica glass6.Given the chemical formula for a ceramic compound,the ionic radii of its component ions,determine the crystal structure.
7、,7.Given three direction index integers,sketch the direction corresponding to these indices within a unit cell.8.Specify the Miller indices for a plane that has been drawn within a unit cell.,9.Describe how face-centered cubic and hexagonal close-packed crystal structures may be generated by the sta
8、cking of close-packed planes of atoms.Do the same for the sodium chloride crystal structure in terms of close-packed planes of anions.10.Distinguish between single crystals and polycrystalline materials.11.Define isotropy and anisotropy with respect to material properties.,3.1 INTRODUCTION,Chapter 2
9、 was concerned primarily with the various types of atomic bonding,which are determined by the electron structure of the individual atoms.The present discussion is devoted to the next level of the structure of materials,specifically,to some of the arrangements that may be assumed by atoms in the soli
10、d state.,Within this framework（结构）,concepts of crystallinity and noncrystallinity are introduced.For crystalline solids the notion（概念）of crystal structure is presented,specified in terms of a unit cell.,Crystal structures found in both metals and ceramics are then detailed,along with the scheme（构型）b
11、y which crystallographic（晶体学的）directions and planes are expressed.Single crystals,polycrystalline,and noncrystalline materials are considered.,CRYSTAL STRUCTURES 3.2 FUNDAMENTAL CONCEPTS,Solid materials may be classified according to the regularity with which atoms or ions are arranged with respect
12、to one another.,A crystalline material is one in which the atoms are situated in a repeating or periodic array over large atomic distances;that is,long-range order exists,such that upon solidification（固化）,the atoms will position themselves in a repetitive three-dimensional pattern（构图）,in which each
13、atom is bonded to its nearest-neighbor atoms.,All metals,many ceramic materials,and certain polymers form crystalline structures under normal solidification conditions.For those that do not crystallize,this long-range atomic order is absent;these noncrystalline or amorphous materials are discussed b
14、riefly at the end of this chapter.,Some of the properties of crystalline solids depend on the crystal structure of the material,the manner in which atoms,ions,or molecules are spatially arranged（空间排列）.There is an extremely large number of different crystal structures all having long-range atomic ord
15、er;,these vary from relatively simple structures for metals,to exceedingly complex ones,as displayed by some of the ceramic and polymeric materials.The present discussion deals with several common metallic and ceramic crystal structures.The next chapter is devoted to structures for polymers.,When de
16、scribing crystalline structures,atoms(or ions)are thought of as being solid spheres having well-defined diameters.This is termed the atomic hard sphere model in which spheres representing nearest-neighbor atoms touch one another.,An example of the hard sphere model for the atomic arrangement found i
17、n some of the common elemental metals is displayed（显示）in Figure 3.1c.In this particular case all the atoms are identical.,Sometimes the term lattice is used in the context（课文）of crystal structures;in this sense lattice means a three-dimensional array of points coinciding（相同）with atom positions(or sp
18、here centers).,3.3 UNIT CELLS,The atomic order in crystalline solids indicates that small groups of atoms form a repetitive pattern.Thus,in describing crystal structures,it is often convenient to subdivide（细分）the structure into small repeat entities（单元）called unit cells.,Unit cells for most crystal
19、structures are parallelepipeds（平行六面体）or prisms棱柱体 having three sets of parallel faces;one is drawn within the aggregate of spheres(Figure 3.1c),which in this case happens to be a cube.,A unit cell is chosen to represent the symmetry of the crystal structure,wherein all the atom positions in the crys
20、tal may be generated by translations of the unit cell integral distances along each of its edges.,Thus,the unit cell is the basic structural unit or building block of the crystal structure and defines the crystal structure by virtue of 由于its geometry几何形状 and the atom positions within.,Convenience us
21、ually dictates that parallelepiped corners coincide with centers of the hard sphere atoms.Furthermore,more than a single unit cell may be chosen for a particular crystal structure;however,we generally use the unit cell having the highest level of geometrical symmetry.,3.4 METALLIC CRYSTAL STRUCTURES
22、,The atomic bonding in this group of materials is metallic,and thus nondirectional in nature.Consequently,there are no restrictions（限制）as to the number and position of nearest-neighbor atoms;this leads to relatively large numbers of nearest neighbors and dense atomic packings for most metallic cryst
23、al structures.,Also,for metals,using the hard sphere model for the crystal structure,each sphere represents an ion core.Table 3.1 presents the atomic radii for a number of metals.Three relatively simple crystal structures are found for most of the common metals:face-centered cubic,body-centered cubi
24、c,and hexagonal close-packed.,THE FACE-CENTERED CUBIC CRYSTAL STRUCTURE,The crystal structure found for many metals has a unit cell of cubic geometry,with atoms located at each of the corners and the centers of all the cube faces.It is aptly called the face-centered cubic(FCC)crystal structure.Some
25、of the familiar metals having this crystal structure are copper,aluminum,silver,and gold(see also Table 3.1).,Figure 3.1a shows a hard sphere model for the FCC unit cell,whereas in Figure 3.1b the atom centers are represented by small circles to provide a better perspective of atom positions.The agg
26、regate of atoms in Figure 3.1c represents a section of crystal consisting of many FCC unit cells.,These spheres or ion cores touch one another across a face diagonal;the cube edge length a and the atomic radius R are related through This result is obtained as an example problem.,For the FCC crystal
27、structure,each corner atom is shared among eight unit cells,whereas a face-centered atom belongs to only two.Therefore,one eighth of each of the eight corner atoms and one half of each of the six face atoms,or a total of four whole atoms,may be assigned to a given unit cell.,This is depicted in Figu
28、re 3.1a,where only sphere portions are represented within the confines of the cube.The cell comprises the volume of the cube,which is generated from the centers of the corner atoms as shown in the figure.,Corner and face positions are really equivalent;that is,translation of the cube corner from an
29、original corner atom to the center of a face atom will not alter the cell structure.,Two other important characteristics of a crystal structure are the coordination number and the atomic packing factor(APF).,For metals,each atom has the same number of nearest-neighbor or touching atoms,which is the
30、coordination number.For face-centered cubics,the coordination number is 12.,This may be confirmed by examination of Figure 3.1a;the front face atom has four corner nearest-neighbor atoms surrounding it,four face atoms that are in contact from behind,and four other equivalent face atoms residing in t
31、he next unit cell to the front,which is not shown.,The APF is the fraction of solid sphere volume in a unit cell,assuming the atomic hard sphere model,or（3.2）,For the FCC structure,the atomic packing factor is 0.74,which is the maximum packing possible for spheres all having the same diameter.Comput
32、ation of this APF is also included as an example problem.Metals typically have relatively large atomic packing factors to maximize the shielding遮蔽 provided by the free electron cloud.,THE BODY-CENTERED CUBIC CRYSTAL STRUCTURE,Another common metallic crystal structure also has a cubic unit cell with
33、atoms located at all eight corners and a single atom at the cube center.This is called a body-centered cubic(BCC)crystal structure.,A collection of spheres depicting描述 this crystal structure is shown in Figure 3.2c,whereas Figures 3.2a and 3.2b are diagrams of BCC unit cells with the atoms represent
34、ed by hard sphere and reduced（缩小的）-sphere models,respectively.,Center and corner atoms touch one another along cube diagonals,and unit cell length a and atomic radius R are related throughChromium,iron,tungsten,as well as several other metals listed in Table 3.1 exhibit a BCC structure.,Two atoms ar
35、e associated with each BCC unit cell:the equivalent of one atom from the eight corners,each of which is shared among eight unit cells,and the single center atom,which is wholly contained within its cell.In addition,corner and center atom positions are equivalent.,The coordination number for the BCC
36、crystal structure is 8;each center atom has as nearest neighbors its eight corner atoms.Since the coordination number is less for BCC than FCC,so also is the atomic packing factor for BCC lower0.68 versus 0.74.,THE HEXAGONAL CLOSE-PACKED CRYSTAL STRUCTURE,Not all metals have unit cells with cubic sy
37、mmetry;the final common metallic crystal structure to be discussed has a unit cell that is hexagonal.,Figure 3.3a shows a reduced-sphere unit cell for this structure,which is termed hexagonal close-packed(HCP);an assemblage of several HCP unit cells is presented in Figure 3.3b.,The top and bottom fa
38、ces of the unit cell consist of six atoms that form regular hexagons六边形 and surround a single atom in the center.Another plane that provides three additional atoms to the unit cell is situated between the top and bottom planes.,The atoms in this midplane have as nearest neighbors atoms in both of th
39、e adjacent two planes.The equivalent of six atoms is contained in each unit cell;,one-sixth of each of the 12 top and bottom face corner atoms,one-half of each of the 2 center face atoms,and all the 3 midplane interior atoms.,If a and c represent,respectively,the short and long unit cell dimensions
40、of Figure 3.3a,the c/a ratio should be 1.633;however,for some HCP metals this ratio deviates from the ideal value.,The coordination number and the atomic packing factor for the HCP crystal structure are the same as for FCC:12 and 0.74,respectively.The HCP metals include cadmium,magnesium,titanium,an
41、d zinc;some of these are listed in Table 3.1.,3.5 DENSITY COMPUTATIONSMETALS,A knowledge of the crystal structure of a metallic solid permits computation of its theoretical density through the relationship（3.5）公式中n单位晶胞中的原子数；A原子量；Vc单位晶胞体积；NA阿夫加德罗常数（6.0231023atom/mol）,3.6 CERAMIC CRYSTAL STRUCTURES,Be
42、cause ceramics are composed of at least two elements,and often more,their crystal structures are generally more complex than those for metals.The atomic bonding in these materials ranges from purely ionic to totally covalent;,many ceramics exhibit a combination of these two bonding types,the degree
43、of ionic character being dependent on the electronegativities of the atoms.,Table 3.2 presents the percent ionic character for several common ceramic materials;these values were determined using Equation 2.10 and the electronegativities in Figure 2.7.,For those ceramic materials for which the atomic
44、 bonding is predominantly ionic,the crystal structures may be thought of as being composed of electrically charged ions instead of atoms.,The metallic ions,or cations,are positively charged,because they have given up their valence electrons to the nonmetallic ions,or anions,which are negatively char
45、ged.,Two characteristics of the component ions in crystalline ceramic materials influence the crystal structure:the magnitude of the electrical charge on each of the component ions,and the relative sizes of the cations and anions.,With regard to the first characteristic,the crystal must be electrica
46、lly neutral;that is,all the cation positive charges must be balanced by an equal number of anion negative charges.,The chemical formula of a compound indicates the ratio of cations to anions,or the composition that achieves this charge balance.For example,in calcium fluoride,each calcium ion has a+2
47、 charge(Ca2+),and associated with each fluorine ion is a single negative charge(F-).Thus,there must be twice as many F-as Ca2+ions,which is reflected in the chemical formula CaF2.,The second criterion involves the sizes or ionic radii of the cations and anions,rC and rA,respectively.Because the meta
48、llic elements give up electrons when ionized,cations are ordinarily smaller than anions,and,consequently,the ratio rC/rA is less than unity.,Each cation prefers to have as many nearest-neighbor anions as possible.The anions also desire a maximum number of cation nearest neighbors.,Stable ceramic cry
49、stal structures form when those anions surrounding a cation are all in contact with that cation,as illustrated in Figure 3.4.The coordination number(i.e.,number of anion nearest neighbors for a cation)is related to the cationanion radius ratio.,For a specific coordination number,there is a critical(
50、临界值)or minimum rC/rA ratio for which this cationanion contact is established(Figure 3.4),which ratio may be determined from pure geometrical considerations(see Example Problem 3.4).,The coordination numbers and nearest-neighbor geometries for various rC/rA ratios are presented in Table 3.3.For rC/rA
