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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., fra
2、cture at 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,
3、 noncrystalline 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
4、结构,L e a r n i n g O b j e 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-p
5、acked crystal structures.,3. Derive 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 di
6、mensions.,5. Sketch/describe unit cells 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 glass 6. Given the chemical formula for a ceramic compound, the ionic radii of its com
7、ponent ions, determine the crystal structure.,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-pac
8、ked crystal structures may be generated by the stacking 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 res
9、pect to material properties.,3.1 INTRODUCTION,Chapter 2 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 o
10、f the arrangements that may be assumed by atoms in the solid 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 m
11、etals and ceramics are then detailed, along with the scheme（构型） by 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
12、to the regularity with which atoms or ions are arranged with respect 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 positio
13、n themselves in a repetitive three-dimensional pattern（构图）, in which each 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 atom
14、ic order is absent; these noncrystalline or amorphous materials are discussed briefly 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 extr
15、emely large number of different crystal structures all having long-range atomic order;,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 cera
16、mic crystal structures. The next chapter is devoted to structures for polymers.,When describing 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 atom
17、s touch one another.,An example of the hard sphere model for the atomic arrangement found in 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
18、sense lattice means a three-dimensional array of points coinciding（相同） with atom positions (or sphere 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 subd
19、ivide（细分） the structure into small repeat entities（单元） called unit cells.,Unit cells for most crystal 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 ce
20、ll is chosen to represent the symmetry of the crystal structure, wherein all the atom positions in the crystal 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
21、 defines the crystal structure by virtue of 由于its geometry几何形状 and the atom positions within.,Convenience usually 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,
22、we generally use the unit cell having the highest level of geometrical symmetry.,3.4 METALLIC CRYSTAL STRUCTURES,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
23、 atoms; this leads to relatively large numbers of nearest neighbors and dense atomic packings for most metallic crystal 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.
24、 Three relatively simple crystal structures are found for most of the common metals: face-centered cubic, body-centered cubic, 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 ea
25、ch of the corners and the centers of all the cube faces. It is aptly called the face-centered cubic (FCC) crystal structure. Some 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 c
26、ell, whereas in Figure 3.1b the atom centers are represented by small circles to provide a better perspective of atom positions. The aggregate 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 diagona
27、l; 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 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 a
28、toms 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 Figure 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 c
29、enters 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 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
30、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 coordination number. For face-centered cubics, the coordination number is 12.,This may be confirmed by examination of Figure 3.1a; the front face ato
31、m 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 the 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 sphe
32、re 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. Computation of this APF is also included as an example problem. Metals typically have relatively large atomic packing factors to maximize the s
33、hielding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 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
34、 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 represented by hard sphere and reduced（缩小的）-sphere models, respectively.,Center and corner atoms touch one another along cube diagonals, and
35、unit cell length a and atomic radius R are related through Chromium, iron, tungsten, as well as several other metals listed in Table 3.1 exhibit a BCC structure.,Two atoms are associated with each BCC unit cell: the equivalent of one atom from the eight corners, each of which is shared among eight u
36、nit 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 crystal structure is 8; each center atom has as nearest neighbors its eight corner atoms. Since the coordination number
37、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 symmetry; the final common metallic crystal structure to be discussed has a unit cell that is hexagonal.,Figure 3.3a sh
38、ows 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 faces of the unit cell consist of six atoms that form regular hexagons六边形 and surround a single atom in the center.
39、 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 the adjacent two planes. The equivalent of six atoms is contained in each unit cell;,one-sixth of each of the 12 t
40、op 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 of Figure 3.3a, the c/a ratio should be 1.633; however, for some HCP metals this ratio deviates from the id
41、eal 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, and zinc; some of these are listed in Table 3.1.,3.5 DENSITY COMPUTATIONSMETALS,A knowledge of the c
42、rystal 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,Because ceramics are composed of at least two elements, and often more, their crystal structur
43、es 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 of ionic character being dependent on the electronegativities of the atoms.,Table 3.2 pr
44、esents 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 bonding is predominantly ionic, the crystal structures may be thought of as being comp
45、osed 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 charged.,Two characteristics of the component ions in crystalline ceramic materials i
46、nfluence 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 electrically neutral; that is, all the cation positive charges must be balanced by an e
47、qual 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 charge (Ca2+),and associated with each fluorine ion is a single negati
48、ve 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 metallic elements give up electrons when ionized, cations are or
49、dinarily 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 crystal 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 ca