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14967 c04 80-108 11/14/05 9:53 Page 106 po 106 + Chapter4 | Imperfections in Solids QUESTIONS AND PROBLEMS REVISED PAGES Vacancies and Self-Interstitials Element (um) 4.1 Calculate the fraction of atom sites that are vacant for copper at its melting temperature of 1084ºC (1357 K). Assume an energy for vacaney formation of 0.90 eV/atom. 42 Calculate the number of vacancies per cubie meter in gold at 900ºC. The energy for vacancy formation is 0.98 cV/atom. Furthermore, the density and atomic weight for Au arc 18.63 g/cm? (at 900ºC) and 196.9 g/mol, respective 43 Calculate the encrgy for vacancy formation in silver, given that the equilibrium number of vacancies at 800ºC (1073 K) is 3.6 x 102 mº3, The atomic weight and density (at 800ºC) for silver are, respectively, 107.9 g/mol and 9.5 glem”. Impuríties in Solids 44 Below, atomic radius, crystal structure, elec- tronegativity, and the most common valence are tabulated, for several elements; for those that are nonmetals, only atomic radii are indicated. Atomic Radius Crystal | Eleciro- Siructure negarivity —Valence Ni 0.1246 FCC. 18 +2 sites. In cach case, one site is larger than the other, and is normally occupied by impurity atoms. For FCC, this larger one is located at the center of each edge of the unit cell; it is termed an octahedral interstitial site. On the other hand, with BCC the larger site type is found at 014 positions—that is, lying on (100) faces, and situated midway between two unit cell edges on this face and one-quarter of the distance between the other two unit cell edges; it is termed a tetrahedral interstitial site. For both FCC and BCC crystal structures, com- pute the radius r of an impurity atom that will just fit into one of these sites in terms of the atomic radius R of the host atom. Specification of Composition 46 47 as c 0.071 H 0.046 49 o 0.060 Ag 0.145 19 + Al 0.1431 15 +3 410 Co 0.1253 18 +2 Cr 0.1249 16 +3 Fe 0.1241 18 +2 41 Pt 0.1387 22 +2 Zn 0.1332 : 16 +2 412 Which of these elements would you expect to form the following with nickel: (a) A substitutional solid solution having 413 complete solubility (b) A substitutional solid solution of incom- 414 plete solubility (c) An interstitial solid solution 415 45 For both FCC and BCC crystal structures, there arc two different types of interstitial 4 Derive the following equations: (a) Equation 47a (b) Equation 4.9a (e) Equation 4.10a (d) Equation 4.11b What is the composition, in atom percent, of an alloy that consists of 92.5 wt% Ag and 7.5 wt% Cu? What is the composition, in weight percent, of an alloy that consists of 5 at% Cu and 95 at% Pt? Calculate the composition, in weight percent, of an alloy that contains 105 kg of iron, 0.2 kg of carbon, and 1.0 kg of chromium. What is the composition, in atom percent, ofan alloy that contains 33 g copper and 47 g zinc? What is the composition, in atom percent, of an alloy that contains 44.5 Ib,, of silver, 83.7 Ibm OÍ gold, and 5.3 Ibm of Cu? What is the composition, in atom percent, of an alloy that consists of 5.5 wt% Pb and 94.5 wt% Sn? Convert the atom percent composition in Problem 4.11 to weight percent. Calculate the number of atoms per cubic meter in Icad. The concentration of silicon in an iron-silicon alloy is 0.25 wt%. What is Lhe concentration in Kilograms of silicon per cubic meter of alloy? EQA 
