Silicon dioxide (or silica, SiO2) in the noncrystalline state is called fused silica, or

vitreous silica; again, a schematic representation of its structure is shown in Figure

3.38b. Other oxides (e.g., B2O3 and GeO2) may also form glassy structures (and

polyhedral oxide structures兵similar to those shown in Figure 3.12其); these materials, as well as SiO2, are network formers.

Si4+ O2⫺ Na+

FIGURE3.39 Schematic representation of ion positions in a sodium–silicate glass.

66Chapter 3 / Structures of Metals and Ceramics

The common inorganic glasses that are used for containers, windows, and so on are silica glasses to which have been added other oxides such as CaO and Na2O. These oxides do not form polyhedral networks. Rather, their cations are

incorporated within and modify the SiO4

4⫺ network; for this reason, these oxide

additives are termed network modifiers. For example, Figure 3.39 is a schematic representation of the structure of a sodium–silicate glass. Still other oxides, such as TiO2 and Al2O3, while not network formers, substitute for silicon and become

part of and stabilize the network; these are called intermediates. From a practical perspective, the addition of these modifiers and intermediates lowers the melting point and viscosity of a glass, and makes it easier to form at lower temperatures

兵(Section 14.7).其

S U M M A R Y

Atoms in crystalline solids are positioned in an orderly and repeated pattern that is in contrast to the random and disordered atomic distribution found in noncrystal- line or amorphous materials. Atoms may be represented as solid spheres, and, for crystalline solids, crystal structure is just the spatial arrangement of these spheres. The various crystal structures are specified in terms of parallelepiped unit cells, which are characterized by geometry and atom positions within.

Most common metals exist in at least one of three relatively simple crystal structures: face-centered cubic (FCC), body-centered cubic (BCC), and hexagonal close-packed (HCP). Two features of a crystal structure are coordination number (or number of nearest-neighbor atoms) and atomic packing factor (the fraction of solid sphere volume in the unit cell). Coordination number and atomic packing factor are the same for both FCC and HCP crystal structures.

For ceramics both crystalline and noncrystalline states are possible. The crystal structures of those materials for which the atomic bonding is predominantly ionic are determined by the charge magnitude and the radius of each kind of ion. Some of the simpler crystal structures are described in terms of unit cells; several of these were discussed (rock salt, cesium chloride, zinc blende, diamond cubic, graphite, fluorite, perovskite, and spinel structures).

Theoretical densities of metallic and crystalline ceramic materials may be com- puted from unit cell and atomic weight data.

Generation of face-centered cubic and hexagonal close-packed crystal structures is possible by the stacking of close-packed planes of atoms. For some ceramic crystal structures, cations fit into interstitial positions that exist between two adjacent close- packed planes of anions.

For the silicates, structure is more conveniently represented by means of inter- connecting SiO4

4⫺tetrahedra. Relatively complex structures may result when other

cations (e.g., Ca2⫹, Mg2⫹, Al3⫹) and anions (e.g., OH) are added. The structures of silica (SiO2), silica glass,兵and several of the simple and layered silicates其were pre-

sented.

Structures for the various forms of carbon—diamond, graphite,兵and the fuller- enes其—were also discussed.

Crystallographic planes and directions are specified in terms of an indexing scheme. The basis for the determination of each index is a coordinate axis system defined by the unit cell for the particular crystal structure. Directional indices are computed in terms of vector projections on each of the coordinate axes, whereas planar indices are determined from the reciprocals of axial intercepts. For hexagonal unit cells, a four-index scheme for both directions and planes is found to be more convenient.

References67 兵Crystallographic directional and planar equivalencies are related to atomic linear and planar densities, respectively.其The atomic packing (i.e., planar density) of spheres in a crystallographic plane depends on the indices of the plane as well as the crystal structure. For a given crystal structure, planes having identical atomic packing yet different Miller indices belong to the same family.

Single crystals are materials in which the atomic order extends uninterrupted over the entirety of the specimen; under some circumstances, they may have flat faces and regular geometric shapes. The vast majority of crystalline solids, however, are polycrystalline, being composed of many small crystals or grains having different crystallographic orientations.

Other concepts introduced in this chapter were: crystal system (a classification scheme for crystal structures on the basis of unit cell geometry); polymorphism (or allotropy) (when a specific material can have more than one crystal structure); and anisotropy (the directionality dependence of properties).

兵X-ray diffractometry is used for crystal structure and interplanar spacing deter- minations. A beam of x-rays directed on a crystalline material may experience diffraction (constructive interference) as a result of its interaction with a series of parallel atomic planes according to Bragg’s law. Interplanar spacing is a function of the Miller indices and lattice parameter(s) as well as the crystal structure.其

I M P O R T A N T T E R M S A N D C O N C E P T S

Allotropy Amorphous Anion Anisotropy

Atomic packing factor (APF) Body-centered cubic (BCC) Bragg’s law Cation Coordination number Crystal structure Crystal system Crystalline Diffraction Face-centered cubic (FCC) Grain Grain boundary Hexagonal close-packed (HCP) Isotropic Lattice Lattice parameters Miller indices Noncrystalline Octahedral position Polycrystalline Polymorphism Single crystal Tetrahedral position Unit cell

R E F E R E N C E S

Azaroff, L. F., Elements of X-Ray Crystallography, McGraw-Hill Book Company, New York, 1968. Reprinted by TechBooks, Marietta, OH, 1990.

Barrett, C. S. and T. B. Massalski, Structure of

Metals, 3rd edition, Pergamon Press, Oxford,

1980.

Barsoum, M. W., Fundamentals of Ceramics, The McGraw-Hill Companies, Inc., New York, 1997.

Budworth, D. W., An Introduction to Ceramic Sci-

ence, Pergamon Press, Oxford, 1970.

Buerger, M. J., Elementary Crystallography, John Wiley & Sons, New York, 1956.

Charles, R. J., ‘‘The Nature of Glasses,’’ Scientific

American, Vol. 217, No. 3, September 1967,

pp. 126–136.

Chiang, Y. M., D. P. Birnie, III, and W. D. Kingery,

Physical Ceramics: Principles for Ceramic Sci- ence and Engineering, John Wiley & Sons, Inc.,

New York, 1997.

Cullity, B. D., Elements of X-Ray Diffraction, 3rd edition, Addison-Wesley Publishing Co., Reading, MA, 1998.

Curl, R. F. and R. E. Smalley, ‘‘Fullerenes,’’ Scien-

tific American, Vol. 265, No. 4, October 1991,

pp. 54–63.

Gilman, J. J., ‘‘The Nature of Ceramics,’’ Scientific

American, Vol. 217, No. 3, September 1967,

68Chapter 3 / Structures of Metals and Ceramics Hauth, W. E., ‘‘Crystal Chemistry in Ceramics,’’

American Ceramic Society Bulletin, Vol. 30,

1951: No. 1, pp. 5–7; No. 2, pp. 47–49; No. 3, pp. 76–77; No. 4, pp. 137–142; No. 5, pp. 165– 167; No. 6, pp. 203–205. A good overview of silicate structures.

Kingery, W. D., H. K. Bowen, and D. R. Uhlmann,

Introduction to Ceramics, 2nd edition, John

Wiley & Sons, New York, 1976. Chapters 1–4. Richerson, D. W., Modern Ceramic Engineering, 2nd edition, Marcel Dekker, New York, 1992.

Schwartz, L. H. and J. B. Cohen, Diffraction from

Materials, 2nd edition, Springer-Verlag, New

York, 1987.

Van Vlack, L. H., Physical Ceramics for Engineers, Addison-Wesley Publishing Company, Read- ing, MA, 1964. Chapters 1–4 and 6–8. Wyckoff, R. W. G., Crystal Structures, 2nd edition,

Interscience Publishers, 1963. Reprinted by Krieger Publishing Company, Melbourne, FL, 1986.

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