TechBooks, Marietta, OH, 1981 Buerger, M. J. Elementary Crystallography, Wiley, New York, 1956 Chiang, Y. M., D. P. Birnie, III, and W. D. Kingery. Physical Ceramics: Principles for Ceramic Sci- ence and Engineering, Wiley, New York, 1997. Cullity, B. D, and S. R. Stock, Elements of X-Ray Diffraction, 3rd edition, Prentice Hall, Upper Saddle River, NJ, 2001. Curl, R. F. and R. E. Smalley, "Fullerenes," Scien- ific American, Vol. 265, No. 4, October 1991. pp. 54-63. QUESTIONS AND PROBLEMS No. 6, pp. 203 structures Kingery, W. D., H. K. Bowen, and D. R. Uhlmann Introduction to Ceramics, 2nd edition, Wiley New York, 1976. Chapters 1-4. Richerson, D. W., The Magic of Ceramics, Americas Ceramic Society, Westerville, OH, 2000, Richerson, D. W., Modern Ceramic Engineering, 3rd edition, CRC Press, Boca Raton, FL, 2006 Additional problems and questions for this chapter may be found on both Student and Instructor Companion Sites at www.wiley.com/college/callister. Unit Cells Metallic Crystal Structures 3.1 If the atomic radius of lead is 0.175 nm, calcu- late the volume of its unit cell in cubic meters. 3.2 Show that the atomic packing factor for BCC is 0.68. Density Computations-Metals 33 Molybdenum has a BCC crystal structure, an atomic radius of 0.1363 nm, and an atomic weight of 95.94 g/mol. Compute its theoretical density and compare it with the experimental value found inside the front cover. 34 Calculate the radius of a palladium atom, given that Pd has an FCC crystal structure, a density of 12.0 g/cm³, and an atomic weight of 106.4 g/mol. 3.5 Some hypothetical metal has the simple cu- bic crystal structure shown in Figure 3.42. If its atomic weight is 74.5 g/mol and the atomic radius is 0.145 nm, compute its density. 36 Using atomic weight, crystal structure, and atomic radius data tabulated inside the front cover, compute the theoretical densities of alp minum, nickel, magnesium, and tungsten, and then compare these values with the measured densities listed in this same table. The cla ratio for magnesium is 1.624. 3.7 Below are listed the atomic weight, density and atomic radius for three hypothetical al- loys. For each determine whether its crystal structure is FCC, BCC, or simple cubic and then justify your determination. A simple cu- bic unit cell is shown in Figure 3.42. Atomic Atomic Weight Density Radius Alley (g/mol) (g/cm³) (mm) A 43.1 6.40 0.122 B 184.4 12.30 0.146 C 91.6 9.60 0.137 Figure 3.42 Hard-sphere unit cell representation of the simple cubic crystal structure.