4.12 Derive the following equations Equation 4.7a. C1=C1A1+C2A2C1A1100 4.15 What is the composition, in weight percent, of an alloy that consists of 5at%Cu and 95 at % Pt? 4.47 For an ASTM grain size of 6, approximately how many grains would there be per square inch under each of the following conditions? (a) At a magnification of 100, Hint: Directly get the number from equation 4.17. (b) Without any magnification? Hint: M=1 in equation 4.18. HW assignment (problems are from the required textbook): 4.1 The equilibrium fraction of lattice sites that are vacant in silver (Ag) at 700C is 2106. Calculate the number of vacancies (per meter cubed) at 700C. Assume a density of 10.35g/cm3 for Ag. 4.3 (a) Calculate the fraction of atom sites that are vacant for copper (Cu) at its melting temperature of 1084C(1357K). Assume an energy for vacancy formation of 0.90eV/ atom. (b) Repeat this calculation at room temperature ( 298K ). (c) What is ratio of NV/N(1357K) and NV/N(298K) ? 4.7 Which of the following systems (i.e., pair of metals) would you expect to exhibit complete solid solubility? Hint: to be completely soluble, the two elements must satisfy all the four HumeRothery rules. For the valence, the most common valences of the two elements must be the same for complete solubility. Show me your reasoning procedures. Only work on b, d and e. Atomic radius in nm for the elements: Mg:0.160;Zn:0.133;Ag:0.144;Au:0.144;Pb:0.175; Pt:0.139. (b) MgZn (d) AgAu (e) PbPt