Chap 09 Solns-6E - CHAPTER 9 PHASE DIAGRAMS PROBLEM...

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CHAPTER 9 PHASE DIAGRAMS PROBLEM SOLUTIONS 9.1 Three variables that determine the microstructure of an alloy are 1) the alloying elements present, 2) the concentrations of these alloying elements, and 3) the heat treatment of the alloy. 9.2 In order for a system to exist in a state of equilibrium the free energy must be a minimum for some specified combination of temperature, pressure, and composition. 9.3 Diffusion occurs during the development of microstructure in the absence of a concentration gradient because the driving force is different than for steady state diffusion as described in Section 5.3; for the development of microstructure, the driving force is a decrease in free energy. 9.4 For the condition of phase equilibrium the free energy is a minimum, the system is completely stable meaning that over time the phase characteristics are constant. For metastability, the system is not at equilibrium, and there are very slight (and often imperceptible) changes of the phase characteristics with time. 9.5 This problem asks that we cite the phase or phases present for several alloys at specified temperatures. (a) For an alloy composed of 15 wt% Sn-85 wt% Pb and at 100 ° C, from Figure 9.7, α and β phases are present, and C α = 5 wt% Sn-95 wt% Pb C β = 98 wt% Sn-2 wt% Pb (b) For an alloy composed of 25 wt% Pb-75 wt% Mg and at 425 ° C, from Figure 9.18, only the α phase is present; its composition is 25 wt% Pb-75 wt% Mg. (c) For an alloy composed of 85 wt% Ag-15 wt% Cu and at 800 ° C, from Figure 9.6, β and liquid phases are present, and C β = 92 wt% Ag-8 wt% Cu C L = 77 wt% Ag-23 wt% Cu 1
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(d) For an alloy composed of 55 wt% Zn-45 wt% Cu and at 600 ° C, from Figure 9.17, β and γ phases are present, and C β = 51 wt% Zn-49 wt% Cu C γ = 58 wt% Zn-42 wt% Cu (e) For an alloy composed of 1.25 kg Sn and 14 kg Pb and at 200 ° C, we must first determine the Sn and Pb concentrations, as C Sn = 1.25 kg 1.25 kg + 14 kg × 100 = 8.2 wt% C Pb = 14 kg 1.25 kg + 14 kg × 100 = 91.8 wt% From Figure 9.7, only the α phase is present; its composition is 8.2 wt% Sn-91.8 wt% Pb. (f) For an alloy composed of 7.6 lb m Cu and 114.4 lb m Zn and at 600 ° C, we must first determine the Cu and Zn concentrations, as C Cu = 7.6 lb m 7.6 lb m + 144.4 lb m × 100 = 5.0 wt% C Zn = 144.4 lb m 7.6 lb m + m × 100 = 95.0 wt% From Figure 9.17, only the L phase is present; its composition is 95.0 wt% Zn-5.0 wt% Cu (g) For an alloy composed of 21.7 mol Mg and 35.4 mol Pb and at 350 ° C, it is first necessary to determine the Mg and Pb concentrations, which we will do in weight percent as follows: m Pb ' = n m Pb A Pb = (35.4 mol)(207.2 g/mol) = 7335 g m Mg ' =n m Mg A Mg = (21.7 mol)(24.3 g/mol) = 527 g 2
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C Pb = 7335 g 7335 g + 527 g × 100 = 93 wt% C Mg = 100 wt% 93 wt% = 7 wt% From Figure 9.18, L and Mg 2 Pb phases are present, and C L = 94 wt% Pb 6w t%Mg C Mg 2 Pb = 81 wt% Pb 19 wt% Mg (h) For an alloy composed of 4.2 mol Cu and 1.1 mol Ag and at 900 ° C, it is first necessary to determine the Cu and Ag concentrations, which we will do in weight percent as follows: m Cu ' =n m Cu A Cu = (4.2 mol)(63.55 g/mol) = 266.9 g m Ag ' m Ag A Ag = (1.1 mol)(107.87 g/mol) = 118.7 g C Cu = 266.9 g 266.9 g + 118.7 g × 100 = 69.2 wt% C Ag = 118.7 g 266.9 g + 118.7 g × 100 = 30.8 wt% From Figure 9.6, α and liquid phases are present; and C α = 8 wt% Ag-92 w% Cu C L = 45 wt% Ag-55 wt% Cu 9.6
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Chap 09 Solns-6E - CHAPTER 9 PHASE DIAGRAMS PROBLEM...

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